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Q: How to perform a spectral density analysis in R using the multitaper package? To Burr and other experts on this topic: I tested, well rather ad-hocly the R-package multitaper, and I succeeded getting graphical outputs. I got graphs for (a) spectrum, (b) spectrum with confidence interval and a graph for the F-test.
I have a couple of questions related to the package and the output which I hope will be commented.
*
*What is the F-test testing – what is the exact null-hypothesis (I suppose the null is the "white-noise" hypothesis – a flat spectral density)?
*Why is not the critical value for the F-test integrated in the F-test plot (as a horizontal line)? The package does not produce any numerical output from the test so we have no idea how "close" to reject the null-hypothesis.
*Is the significance level in the F-test optional, for example 5 or 10%?
*When you evaluate the spectrum, how do you transform frequencies to years when you have yearly data?
*It is also possible to plot the spectrum with confidence interval. What is the big deal of showing the confidence interval without relating it to the null-hypothesis?
*You recommended plotting the spectrum from spec.mtm on a log scale. Is it possible to integrate the log-command in the code:
resSpec <- spec.mtm(willamette, k=10, nw=5.0, nFFT = "default",
centreWithSlepians = TRUE, Ftest = TRUE,
jackknife = FALSE, maxAdaptiveIterations =100,
plot = TRUE, na.action = na.fail)
and how do we do it?
A: Just noticed this question. Here's responses to some of your questions.
The F-test test is (and I quote)
an F variance-ratio test with 2 and 2K-2 degrees of freedom for the significance of the estimated line component.
In practice, the test compares the value of the background spectra with the power in a line component, resulting in the above test. High values, high(er) significance.
As far as why the critical value is not included in the plot, I assume it is largely because which critical value you choose varies from problem to problem. The package does provide numerical output from the test (it is contained in the object returned from the function call, and you can pull it out and look at it as you wish). It even returns the two (numerator, denominator) degrees of freedom so you can compute the cutoff for any significance you want, as the distribution is essentially F, and has a known CDF.
To obtain the pieces you're looking for, pull the mtm object out of resSpec and take a look at it. For example:
spect<-resSpec$mtm
attributes(spect)
dof1<-2
dof2<-2*(spect$k)-2
Fval<-spect$Ftest
I'm not sure what you're asking when you say
Is the significance level in the
F-test optional, for example 5 or 10%?
If you have data that is not sampled at $\delta t = 1s$, you can change the frequency delta by examining the spec class attached to resSpec. It is a time-series object, and can be modified in the usual way. Alternatively, if you know what you want, just create your own frequency vector and then plot(fr,resSpec$spec,etc).
The confidence interval that you can display on the spectrum is a jackknifed confidence interval. I can provide references if you'd like to read up on this a little more, but for most purposes, it doesn't provide directly applicable information for standard analysis.
As far as I know, there is no direct way to integrate the log spectrum command for the initial plot. However, I normally just turn auto-plot off and grab the resSpec$spec object and then manipulate it directly, fixing the $\delta f$ and setting the plot to plot(fr,log(resSpec$spec),etc).
Hope these answers helped.
| slim_pajama |
myiasis is the infestation of a vertebrate with dipterous larvae that feed for a certain time period on live or dead tissues of the host , substances of the host 's body , or on the food that it ingests .
myiasis can be obligatory , which occurs when larval flies develop in living tissues , or facultative , which occurs when maggots feed on decomposing matter or necrotic tissues .
obligatory myiasis is more harmful to the host , particularly mammals ( including man ) , and is found in several countries of the old and new worlds . the classification of myiasis is based on the localization within the host body ( dermal , subdermal , nasopharyngeal , internal organs , or urogenital ) or the type of host - parasite relationships ( obligatory , facultative , or pseudomyiasis ) .
the larvae that cause myiasis can be biontophagous , in which they invade tissues or natural cavities to become obligate parasites , or necrobiontophagous , in which larvae colonise pre - existing injuries and become accidental parasites .
numerous species have been reported to be responsible for myiasis in livestock and occasionally in humans .
one of these species , cochliomyia hominivorax ( coquerel ) , is well - known to be responsible for important myiasis along its wide distribution in america and in relation to the tropical climate zones .
although adult flies may be attracted to wounds or ulcers on the skin of the host , their larvae do not feed on necrotic material .
the invasion of natural orifices by larvae may result in cavitary myiasis of several types , which culminates in major tissue damage or even death of the host .
the analysis of the life cycle of the species has shown that females lay 200 - 300 eggs on wound borders , larvae eclosion occurs within 12 - 14 hr , and the larvae penetrate the tissues as they feed on them .
the risk factors that potentially cause myiasis are the exposure of ulcers and hemorrhoids , bacterial infection of wounds or natural cavities , poor personal hygiene , alcohol - related behaviors such as lack of sensitivity and sleeping outdoors , lesions resulting from itching in patients with pediculosis , and extreme lack of personal hygiene . in this work
, we provided the first demonstration of the presence of myiasis in a diabetic foot in argentina with c. hominivorax as an etiological agent .
this study also provides the first evidence of this species in tucuman province , argentina .
a male patient aged 54 years , who is now living in monteros city , tucuman province , argentina , checked into the angel c. padilla hospital in san miguel de tucuman for a consultation due to an ulcerous lesion in his right foot with a sanious bottom and fetid odour ( fig .
the clinical examination revealed that the ulcer contained fly larvae ( n=5 ) with an evolution of approximately 2 days .
the lesion had a circular shape with a diameter of approximately 4 cm ; the edge showed signs of inflammation , and the content consisted of foul - smelling necrotic tissues with a sanious bottom that corresponded to the deep aponeurosis of the wound ( fig .
the patient was diagnosed with grade ii diabetes ( under treatment with oral hypoglycemic drugs ) with a disease of over 10 years of evolution , in which the neuropathic compromise predominated with an important loss of sensibility in the area ( no pain ) , which was the reason for delayed consultation . however , the presence of peripheral pulses was determined , which indicates that the blood flow in the compromised limb was preserved .
the first surgical debridement was performed in the hospital emergency services unit . during this operation
the patient received treatment considering his basic disease ( diabetes ) with broad - spectrum antibiotics until the results of the cultures were obtained .
additionally , periodic cleaning of the wound and dressing changes were conducted every other day with gauze wetted in a physiological solution .
the wound , as well as the patient 's metabolic values , exhibited a favourable evolution .
he was discharged from the hospital after 15 days , during which time surgical debridement was performed twice .
the larval specimens were taken to the laboratory of the instituto superior de entomologia " dr .
abraham willink " , facultad de ciencias naturales e instituto miguel lillo ( universidad nacional de tucuman ) , where they were identified and later raised individually in flasks and fed beef liver ( fig .
the collected larvae belong to the species c. hominivorax with the following external morphological characters : cylindri cal , segmented , white yellow - coloured body , and tracheas with strong pigmentation that was visible until the third or fourth larval segment immediately preceding the end portion of the body . after 2 days , the larvae reached the pupal stage and were transferred to plastic cups containing vermiculite .
the humidity was controlled by spraying water , and the temperature was maintained at 27. after 12 days , the adult insects emerged .
the adults were then killed , mounted , and identified using the guidelines described by mariluis and schnack .
the adults were also identified as c. hominivorax , which is a species that had not been previously reported in tucuman province , argentina .
the morphological characters that defined the adult species were as follows : setose basal vein in the upper surface of the wing , denuded lower surface of the wing , short and reduced palps , and parafrontalia with black hairs outside the front row of setae ( fig .
the species of the genus cochliomyia present a wide geographical distribution from the central and southern united states through mexico , guatemala , honduras , nicaragua , costa rica , and the caribbean islands to argentina . in our country ,
only 2 species belonging to this genus have been reported : cochliomyia macellaria ( fabricius ) and c. hominivorax .
the latter is distributed in the provinces of buenos aires , chaco , crdoba , corrientes , formosa , jujuy , santa fe , and misiones .
the present work is the first report of the species in tucuman province , which is extremely important because c. hominivorax is potentially involved in production of myiasis in humans . c. hominivorax is an obligate parasite in homeothermic vertebrates , either domestic or wild , occasionally including humans .
it is considered that a fly has great impact on human health and on the productivity of domestic animals because it causes a decrease in their productions of meat , milk , and wool and an increase in secondary infections .
in addition , c. hominivorax is responsible for the largest number of myiasis cases in america and the most serious forms of human myiasis .
the larvae remain superficial but occasionally migrate and cause subcutaneous nodules . in general , myiasis in humans
is localized in the upper and lower extremities with a marked predominance of the latter followed in frequency by the head , thorax , abdomen , and pelvis . moreover ,
underlying pathologies have been found : varicose ulcers , infected wounds , and various dermatoses .
have cited the species incriminated in human myiasis , c. hominivorax and phaenicia sericata ( also called lucilia sericata ) ( meigen ) , to bahia blanca , buenos aires , argentina . in all patients ,
myiasis occurred after traumas , lesions , and/or infectious processes that attracted the flies . c. hominivorax was the species most common found in the cases of myiasis and was responsible for serious lesions in the abdomen , the lower limbs , and different parts of the head ( ears and eyelids ) .
p. sericata was found in lesions of the lower limbs . among other conditioning factors for the occurrence of myiasis
, the insensibility that may result from various pathologies , such as diabetes , is mentioned in this work and added to the poor personal hygiene conditions . exposed ulcers , bacterial infections of wounds or natural cavities [ 18 - 20 ] , poor personal hygiene , tasks related to livestock rearing , and behaviors associated with alcoholism , such as insensibility and sleeping outdoors , are among the risk factors that promote myiasis .
also mentioned different pathologies , such as diabetes , otitis , and alcoholism , and certain behaviors , such as lack of body hygiene , lack of personal grooming , and/or rural tasks , that favour the permanence of the wounds by causing insensibility and increasing the probability of contact with flies . in the present work ,
we agree with the hypothesis that the exposed ulcer was a conditioning factor that , in combination with the patient 's poor personal hygiene , rural tasks and insensibility associated with diabetes determined the degree of evolution of the myiasis in the patient .
we may conclude that the present investigation is an important contribution to the subject of myiasis because this case is the first evidence of c. hominivorax in a case of myiasis in a patient with a diabetic foot in argentina .
the main factor that would determine the occurrence of this myiasis would be the exposure of the ulcer to flies , foul smell of the wound , individual 's lack of personal grooming , and diabetes which was responsible for the consequent loss of sensibility in the patient 's foot . | pubmed |
study site : data collection was done during march - june 2009 as part of an ongoing ipen project on model injection centers ( mics ) at 25 partner medical colleges ( pmc ) .
the country was divided , for the purpose of the study , into five geographical zones with five pmcs in each zone .
a total of 25 districts where pmcs are located , were included for assessment of bmwm ( fig .
data collection at the districts was carried out by the site principal investigator and co - investigator of the respective pmc .
the study included different levels of health facilities ; in urban and rural areas , and from public and private sector providers ( fig .
2 ) . in every district separate lists for primary care health facilities in urban and rural areas
were prepared based on the information available with the district health department , professional associations , local bodies and the district pollution control board 's office . for rural areas ,
the lists for public sector and private sector were separate while in urban areas , only private sector facilities were included in the sampling list .
private sector lists from rural areas also incorporated clinics run by informally trained practitioners ( rmps / quacks ) .
the desired number of health facilities were then identified as per the scheme outlined in fig .
the government district hospital and the partner medical college hospital were recruited to represent secondary and tertiary care facilities , respectively . in bhubaneswar due to administrative reasons the district hospital could not be recruited and in its place , a 150 bedded private hospital run by a charitable trust was included .
non formal prescribers ( small clinics ) were 74.7 per cent in rural areas ( 71 out of 95 ) .
scheme of health facility identification for assessment for bmwm at district level . * except a secondary level private hospital in bhubaneswar other 24 were public sector district hospitals ; * * four out of 24 were private medical colleges ( jaipur , gulbarga , manipal and bhubaneswar ) .
patient care areas for observation were predetermined for each type of health facility ( table i ) .
the sites of observation were decided on the basis of group discussions and experiences of investigators in the hospitals of different settings .
the study was a cross - sectional survey with direct observation of bmwm systems at different levels of health care .
patient care areas and departments for observation during biomedical waste management assessment assessment tool : the who tools were adapted to suit the needs of the present study and two instruments were prepared .
assessment tools were common for all types of health facilities across levels , locations and sectors ( public and private ) , on the basis of who standards for bmwm12 .
separate tools were prepared for interviewing pollution control board and municipal authorities ( available on http://www.inclentrust.org/ ) .
( i ) health facility tool which comprised of ( a ) section 1 : observation checklist based on the national accreditation board standard for hospitals and healthcare providers ( nabh 2007)13 in india to assess the bmwm system and actual practices through direct observation .
the checklist included issues of system capacity , resources and processes covered under nine domains with related questions13 .
there were 31 items spread over system capacity ( 7 ) ; resources ( 8) ; and process ( 16 ) .
thus , differential weight age was given by way of variable number of items under the three major domains .
initially all items were kept with two options ( compliance yes or no ) . however , after piloting only eight items were left with two options ( no compliance and full compliance ) and 22 items had three options ( no compliance , partial compliance and full compliance ) . piloting also helped to define partial compliance .
the observations from at least three and maximum five bmw generation points were obtained in secondary and tertiary care hospitals . in primary care facilities ,
the observations were made only at one point of bmw generation ( table i ) .
( b ) section 2 : interview schedules for the medical officer , or the officer - in - charge responsible for bmw .
( ii ) interview schedule for officials from local bodies and pollution control boards ( district level only ) .
quality assurance measures : the instruments were piloted at one site in each of the five zones . before the launch of the study ,
a national protocol finalization workshop was organized to bring uniform understanding among all principal investigators .
data collection was closely monitored at central coordinating office in new delhi and central coordinating team ( cct- multidisciplinary team of investigators ; these were different from site investigators ) members visited each site to oversee data collection in at least two health facilities .
data processing : the filled questionnaires from each pmc were entered into intelligent character recognition ( icr ) sheets and scanned . before scanning ,
after scanning , the database was matched with icr sheets ; this reduced the error rates to around 1 to 2 per 1000 data points .
the forms were automatically recognized and the data were processed using abbyy forms processing software14 . after verification and validation of the data using the same software , final data was exported to ms excel 2007 spreadsheets .
a total of 19 questions in two types of interview schedules for key informants were open - ended .
responses to these questions were analyzed using qualitative methods to identify emerging themes and sub - themes .
health facility score : the questions were clustered around three major domains ( system capacity , resources and processes ) which were further categorized into nine sub - domains or items , each with 1 to 4 questions .
these nine sub - domains of bmw management included : one domain for systems capacity ; four domains each under resources and processes namely segregation of bmw ; management of sharps ; in - house transport of bmw and for storage and record keeping , respectively .
systems capacity assessed availability of guidelines , charts , designated official and provision of protection for health providers .
each question was separately assigned scores as full compliance ( 10 points ) , partial compliance ( 5 points ) and no compliance or absence of the particular component ( 0 points ) as per nabh standards , 2007 .
any health facility or individual domain could thus achieve a minimum score of 0 and a maximum score of 10 .
the median scores of domains were used to determine the overall score for health facility .
aggregate of individual health facility scores was the basis of computing median score of a particular level of health facility in the specific district / zone / overall .
as a measure of dispersion of score , along with median scores , 25 and 75 percentiles ( quartile range ) were also computed .
grading of bmwm system ( table ii ) : the decision to classify health facilities according to the status of the bmwm system ( red , yellow & green ) was arrived at the protocol finalization workshop where the site investigators participated along with principal investigators and central coordinating team ( cct ) .
cct comprised of public health specialists , hospital management professional with expertise in biomedical waste management , paediatricians , physicians , social scientists , biostatisticians and anthropologists .
the group decided cut - off median cumulative scores reflecting system capacity , resources and processes to help facility managers to take appropriate actions .
median score < 2.5 was interpreted as no credible bmwm system in place while score 2.5 to < 5.0 was interpreted as system present but that needed major improvement ; both these groups were put under red category .
median score 5.0 to 7.5 indicated system required some additional efforts and categorized as yellow while median score 7.5 indicated good system in place for bmwm ( green category ) .
median bmwm score categories for health facility & their interpretation comparison was made for health facilities ( i.e. , primary , secondary and tertiary care settings ) in urban and rural settings as well as public and private settings .
cumulative scores for health facilities of a particular level at zonal level were also estimated and compared .
multivariate analysis was done to determine the predictors of grade ( red , yellow and green ) of health facilities .
two sets of models were generated : first , in which dependent variable was health facilities graded as
yellow and above ( score 5.0 ) versus all others , and second , in which dependent variable was
independent variables for both the models were scores of individual items under system capacity , resources and processes .
health facility score : the questions were clustered around three major domains ( system capacity , resources and processes ) which were further categorized into nine sub - domains or items , each with 1 to 4 questions .
these nine sub - domains of bmw management included : one domain for systems capacity ; four domains each under resources and processes namely segregation of bmw ; management of sharps ; in - house transport of bmw and for storage and record keeping , respectively .
systems capacity assessed availability of guidelines , charts , designated official and provision of protection for health providers .
each question was separately assigned scores as full compliance ( 10 points ) , partial compliance ( 5 points ) and no compliance or absence of the particular component ( 0 points ) as per nabh standards , 2007 .
any health facility or individual domain could thus achieve a minimum score of 0 and a maximum score of 10 .
the median scores of domains were used to determine the overall score for health facility .
aggregate of individual health facility scores was the basis of computing median score of a particular level of health facility in the specific district / zone / overall .
as a measure of dispersion of score , along with median scores , 25 and 75 percentiles ( quartile range ) were also computed .
grading of bmwm system ( table ii ) : the decision to classify health facilities according to the status of the bmwm system ( red , yellow & green ) was arrived at the protocol finalization workshop where the site investigators participated along with principal investigators and central coordinating team ( cct ) .
cct comprised of public health specialists , hospital management professional with expertise in biomedical waste management , paediatricians , physicians , social scientists , biostatisticians and anthropologists .
the group decided cut - off median cumulative scores reflecting system capacity , resources and processes to help facility managers to take appropriate actions .
median score < 2.5 was interpreted as no credible bmwm system in place while score 2.5 to < 5.0 was interpreted as system present but that needed major improvement ; both these groups were put under red category .
median score 5.0 to 7.5 indicated system required some additional efforts and categorized as yellow while median score 7.5 indicated good system in place for bmwm ( green category ) .
median bmwm score categories for health facility & their interpretation comparison was made for health facilities ( i.e. , primary , secondary and tertiary care settings ) in urban and rural settings as well as public and private settings .
cumulative scores for health facilities of a particular level at zonal level were also estimated and compared .
multivariate analysis was done to determine the predictors of grade ( red , yellow and green ) of health facilities .
two sets of models were generated : first , in which dependent variable was health facilities graded as
yellow and above ( score 5.0 ) versus all others , and second , in which dependent variable was
green health facilities ( score 7.5 ) versus all others . independent variables for both the models were scores of individual items under system capacity , resources and processes .
health facility score : the questions were clustered around three major domains ( system capacity , resources and processes ) which were further categorized into nine sub - domains or items , each with 1 to 4 questions .
these nine sub - domains of bmw management included : one domain for systems capacity ; four domains each under resources and processes namely segregation of bmw ; management of sharps ; in - house transport of bmw and for storage and record keeping , respectively .
systems capacity assessed availability of guidelines , charts , designated official and provision of protection for health providers .
each question was separately assigned scores as full compliance ( 10 points ) , partial compliance ( 5 points ) and no compliance or absence of the particular component ( 0 points ) as per nabh standards , 2007 .
any health facility or individual domain could thus achieve a minimum score of 0 and a maximum score of 10 .
the median scores of domains were used to determine the overall score for health facility .
aggregate of individual health facility scores was the basis of computing median score of a particular level of health facility in the specific district / zone / overall .
as a measure of dispersion of score , along with median scores , 25 and 75 percentiles ( quartile range ) were also computed .
grading of bmwm system ( table ii ) : the decision to classify health facilities according to the status of the bmwm system ( red , yellow & green ) was arrived at the protocol finalization workshop where the site investigators participated along with principal investigators and central coordinating team ( cct ) .
cct comprised of public health specialists , hospital management professional with expertise in biomedical waste management , paediatricians , physicians , social scientists , biostatisticians and anthropologists .
the group decided cut - off median cumulative scores reflecting system capacity , resources and processes to help facility managers to take appropriate actions .
median score < 2.5 was interpreted as no credible bmwm system in place while score 2.5 to < 5.0 was interpreted as system present but that needed major improvement ; both these groups were put under red category .
median score 5.0 to 7.5 indicated system required some additional efforts and categorized as yellow while median score 7.5 indicated good system in place for bmwm ( green category ) .
median bmwm score categories for health facility & their interpretation comparison was made for health facilities ( i.e. , primary , secondary and tertiary care settings ) in urban and rural settings as well as public and private settings .
cumulative scores for health facilities of a particular level at zonal level were also estimated and compared .
multivariate analysis was done to determine the predictors of grade ( red , yellow and green ) of health facilities .
two sets of models were generated : first , in which dependent variable was health facilities graded as
yellow and above ( score 5.0 ) versus all others , and second , in which dependent variable was
green health facilities ( score 7.5 ) versus all others . independent variables for both the models were scores of individual items under system capacity , resources and processes .
data for bmw management were obtained from 24 pmc , 25 district hospitals and 400 primary care health settings . after appropriate data cleaning and validation the information from 24 pmcs , 25 district hospitals and 388 ( 194 public and 194 private ) primary care health facilities were analysed .
the number of private health facilities at secondary ( n-1 ) and tertiary level ( n-4 ) in urban areas were very few .
the biomedical waste management scenario was analyzed at two levels : type of health facility and public / private sectors ( table iii ) .
status of bmwm : distribution of median bmwm scores across level of health facilities in private and public sector the status of bmwm was alarming across the study sites ; 82 per cent ( 318/388 ) of primary care , 60 per cent ( 15/25 ) of secondary and 54.2 per cent ( 13/24 ) of tertiary care facilities were in the red category indicating need for major efforts to improve the bmwm across the country .
the median scores for secondary and tertiary care health facilities were 4.34 ( 25/75 percentile : 2.16 , 6.31 ) and 4.96 ( 25 , 75 percentile : 4.05 , 7.26 ) , respectively .
the state of bmwm at primary care health facilities [ median 1.84 ( 25 , 75 percentile : 0.76 , 4.24 ) ] indicated requirements of major inputs for the improvement ; the situation was worse in rural areas ( median score 1.58 ) compared to urban facilities ( median score 2.74 ) .
public sector providers in rural areas had better bmwm system than their counterparts in urban areas .
in contrast , there was almost complete lack of bmwm systems in the private sector in rural areas , generally reflecting on clinics of informal practitioners ( table iv ) .
status of bmwm : distribution of bmwm scores at different levels of health facilities in urban and rural settings quantity and type of bmw generated ( table v ) : bmw including plastic wastes generated in secondary and tertiary care health facilities was 3 to 10 times higher every day as compared to that in primary care facilities .
infectious waste comprised of improperly segregated bmw , and mixture of material contained in blue or red and yellow coloured bags .
the proportion of infected waste was 66.7 per cent in primary care settings , 79 per cent in secondary and 76 per cent in tertiary care settings .
type and quantity of biomedical waste generated in different levels of health facilities performance of bmwm at primary , secondary and tertiary care settings ( table vi ) : primary care settings fared poorly for most domains in comparison to secondary and tertiary care settings ( table vi ) .
there were practically no resources for segregation , in - house transport and for storage and record keeping of bmw in primary care health facilities .
it appeared that at higher levels of health settings , more resources were available and efforts were put in for establishing bmwm system resulting in better overall scores . in tertiary and secondary level facilities 82.6 per cent (
19/23 ) and 64 per cent ( 16/25 ) were having designated officials for management of bmw while in primary health facilities only 40.8 per cent ( 149/365 ) had a designated official .
only 63.3 per cent ( 216/341 ) of primary facilities were providing personal protectives for waste handling staffs as compared with 87 per cent ( 20/23 ) in secondary and 95.5 per cent ( 21/22 ) in tertiary health facilities .
similarly , waste handling staff was not trained in 56.7 per cent ( 204/360 ) of primary and 20.8 per cent ( 5/24 ) of secondary while all of such personnel in tertiary facilities had received appropriate training .
around 47.2 per cent ( 101/214 ) of primary , 81.2 per cent ( 13/16 ) of secondary and 92.9 per cent ( 13/14 ) of tertiary health facilities were using authorities other than municipalities for handling biomedical waste .
overall performances of bmwm & domain scores at different levels of health facilities multivariate analysis for predictors of higher scores : table vii gives the key items under system capacity , resources and processes that were predicting the scores of 5 and more ( i.e. , acceptable or good bmwm system ) for a health facility .
odds of a health facility entering into yellow or higher category increased significantly with every one increase in the median score of each of these variables .
although in univariate analysis these appeared important , higher scores were not independently predicted by location ( urban - rural ) or sector ( public - private ) of the health facility .
multivariate analysis for predictors of better health facilities with cumulative bmwm score above 5 ( falling in yellow & green categories ) among those health facilities which had score 5 , the possibility of being a green ( score 7.5 ) health facility for bmwm was associated with factors of system capacity ( guidelines / charts displayed at waste generation sites ) ( or 1.8 ; 95% c.i ; 1.2 , 2.8 ) , resources ( availability of personal protective equipment for waste handling staff ) ( or 1.6 ; 95% c.i ; 1.2 , 2.0 ) , and process ( disinfection of plastic waste or sharps ) ( or ; 1.4 ; 95% c.i ; 1.1 , 1.7 ) . perception of key stakeholders about bmwm at their respective health facilities : officers - in - charge of bmwm at health facilities and nodal district officers at the pollution control boards and municipalities were asked about the different aspects of bmwm in their health facilities / districts . at primary care facilities , between 34.3 to 48.9 per cent respondents
were either not concerned about the problems or denied existence of any problems in bmwm at their health facilities . at tertiary ( 16.7% ) and secondary ( 28.0% ) level hospitals , such apathy was less .
interestingly , 40 per cent ( 10/25 ) of municipal authorities and 54 per cent ( 13/24 ) of pollution control board officials also responded in a similar manner
. there was consistency across stakeholders about the need for building systems capacity ( 36 to 77.6% ) and higher resource allocations ( 32 to 55% ) if bmwm was to improve across health facilities and sectors ( table viii ) .
it was important that officers looking after bmw in pollution control boards , municipalities and tertiary care hospitals emphasized the critical role of better governance to improve the bmwm system at various levels of health care .
bmwm was alarming both at macro and micro levels across different parts of the country ; in the 25 study districts 82 per cent of primary care health facilities , 60 per cent of secondary care and 54 per cent of tertiary care health facilities were in the red category i.e. absence of a credible bmw management system in place or ones requiring major improvement .
these findings have to be attributed to lack of system capacity , gaps in resources and processes .
resources for segregation and in - house transport of bmw along with resources and processes for storage and record keeping were particularly deficient across all type of health facilities .
interview with key stakeholders in municipality as well as pollution control board in each district indicated the need for building system capacity and allocation of additional resources to improve existing bmwm systems .
a significant proportion of key stakeholders in the health facilities and district regulatory offices demonstrated apathy towards current status of bmwm in their environment .
the study provided evidence for need of major policy shifts towards improving bmwm in primary care settings both at public and private in urban and rural areas .
macro level policies and implications need to penetrate into micro level settings through better governance and improved community awareness .
the status was worst in primary care settings especially in rural areas ; 742.7 million indian people live in rural areas and are served through 147,069 sub centres , 23,673 phcs and 4535 chcs18 .
the number of private health facilities within rural primary level settings in india was unknown to the best of our knowledge , but almost all big villages have informally trained medical practitioners providing care in private settings .
many authors described the reasons for poor system in the primary health facilities as lack of sensitivity and awareness , concerning health risks of biomedical waste and economic constraints19 .
tertiary and secondary level hospitals performed better ; perhaps on account of better resources and having responded to the regulations .
radha et al20 highlighted that biomedical facilities in urban settings were marginally better as compared to that in rural areas due to greater investment and focus .
a study from gujarat ( india ) , involving 30 hospitals ( including 15 private hospitals ) showed that 74 per cent were not following segregation guidelines ; and all the private hospitals were defaulting on important steps of bmwm21 .
this indicated the need to have a comprehensive national strategy covering both urban and rural areas including public as well as private sectors .
the providers in primary level health settings had minimal capacity ( median score 1.9 ) for optimal bio - medical waste management ; one quarter of the health facilities scored zero. more than half of primary settings had no guidelines or designated person for handling bmwm ; staff was poorly trained and without adequate protective equipment . a quarter of health facilities in secondary and tertiary care settings were also in the red category .
more than 50 per cent of all health facilities had problems in resources for segregation , sharps management , in - house transport , storage and record keeping .
colour bags , a basic pre - requisite to initiate proper segregation , were not available at many health facilities .
the lack of adequate supply of resources , leading to mixing of bmw with municipal waste was reported from chandigarh and gujarat24 .
hanumantha rao et al7 reported non - compliance to bmwm guidelines by smaller hospitals but it was not clear whether the problem came up due to non availability of resources for segregation .
key stakeholders from the municipalities , pollution control boards and different health facilities also emphasized the need for capacity building including training and provision of additional resource investment for bmwm as key strategies for all round improvement .
askarin et al25 reported poor state of collection , transportation , disposal , training and personal protective equipments in iran .
a report from karachi , pakistan , highlighted issues of resource constraint leading to shortage of supplies and mixing of bmw with domestic wastes27 .
a study from senegal28 indicated the non - availability of infrastructure and lack of awareness as key contributors for poor quality of bmwm systems .
this study adapted a scoring system with traffic colour codes ( red , yellow and green ) to categorize healthcare facilities and assess the system capacity , resources and processes in bmwm .
the strategy helped to compare status of bmw across health settings in different geographical areas , public , private , urban and rural settings .
this approach also helped to assess and interpret the current bmwm state in a consistent manner .
one potential limitation in this scoring system is that on a visual analogue scale , only three points were identified .
however , each broad domain was assessed through several sub - domains or items to reduce this limitation .
though enough private facilities from primary care settings were included in the study , fewer private facilities in secondary and tertiary care settings were involved .
other bmw generating units like dental clinics / hospitals and laboratory / diagnostic facilities were not assessed and the findings do not reflect these sectors .
the processes of bmwm were poor and unacceptable across the levels of health facilities ; poorest in primary care settings as compared to secondary and tertiary care settings .
some systems existed for processes of segregation of bmw in secondary and tertiary hospitals and management of sharps in tertiary hospitals but required additional efforts to achieve optimal standards .
the study indicated deficient or lack of processes particularly in those areas where resource allocation was poor .
interviews with personnel responsible for waste management at hospitals revealed that least importance was given to the treatment of infected plastic wastes before terminal disposal which is strongly recommended by expert body like the national centre for infectious diseases and the healthcare infection control practices advisory committee ( hicpac)29 . in general , there was consistency between the scores for system capacity , resources available and process adopted from a particular type of health care facilities .
however , during in - depth interviews , the gap in knowledge and practice in relation to availability of resources and processes in place was found as was the need for organized training and structured supervision to bridge this gap . a study on tertiary care hospitals in india found that people with higher education such as consultants , residents and scientists had good knowledge of biomedical rules but was not reflected in their practices30 .
studies reported from geographically diverse , large states of india ( andhra pradesh , maharashtra and uttar pradesh ) showed that awareness among hospital staffs regarding segregation of bmw was slightly higher in urban areas compared to rural areas ; and that employee training and awareness can be a major determinant of establishing optimal bmwm31 .
the current study revealed that surveillance and monitoring of bmwm were consistently deficient and respondents from pollution control board emphasized better governance and penal provisions for effective implementation of bmwm guidelines .
these factors need close consideration while designing systems to improve compliance with the bmwm guidelines .
multivariate modelling in this study revealed several important predictors for achieving acceptable scores for the bmwm system .
significant predictors were : presence of guidelines or charts at point of waste segregation ( system capacity ) , accountability of a dedicated person , availability of appropriate containers or bags for waste segregation , availability of functional needle destroyers , personal protective equipment for waste handling staff ( resources ) , segregation of wastes at point of generation , availability of register for record maintenance and disinfection of plastic wastes or sharps at point of waste generation ( processes ) .
there are only a few studies which have correlated presence of good bmwm with different predictors .
many of the published studies acknowledge all the above components as integral part of bmwm system but their relative significance or value as a predictor for good bmwm has not been reported2532 .
recently published indian bmw rule update also emphasized the above components as an integral part of waste management system33 .
careful analysis of these specific indicators of system capacity , resources and process reveals that besides greater investment , mechanisms of accountable and responsive governance is required to get a functional bmwm system in health facilities . in conclusion , bmwm is grossly deficient at both macro and micro levels in different parts of india .
urgent interventions for improving systems capacity and greater resource commitment are required , specifically focussing on primary care health facilities both in public and private sectors .
accountable and responsive governance is likely to institute appropriate processes and establish acceptable bmwm system34 . | pubmed |
While U.S. Imposed Sanctions On Iran Take Effect Today, Oil And Gas Prices Continue Dropping
TOWSON, MD (November 5, 2018) – At $2.76, the national gas price average is at its cheapest in six months (end of April). For the second consecutive week, Maryland's average cost at the pump continues to be at the lowest levels since April.
Today's national average is six cents less than a week ago,15 cents less than a month ago but 24 cents more than a year ago. As demand continues to drop, gas prices could get even cheaper.
This price drop is happening at a time that analysts previously thought would likely see pump price increases due to the White House's re-imposition of sanctions on Iran, some of which will target the country's energy sector and impedes its ability to export oil.
However, in May, when the decision was announced (to take effect in November), the market reacted quickly with West Texas Intermediate (WTI) crude oil prices spiking as high as $77 per barrel this summer. At the same time, Iran's exports began to dip. Today, the country's exports are reported to be about one million barrels per day less than in May, while crude oil prices have stayed below $70 per barrel for two weeks.
"With the market anticipating and reacting to the pending Iran sanctions throughout the summer, motorists likely have seen the worst in terms of retail prices for the year," said Ragina Cooper Averella, Manager of Public and Government Affairs at AAA Mid-Atlantic. "If the crude oil market remains steady, gas prices are likely to continue to fall as much as ten cents in the near-term."
That being said, should any factors cause an upward shift in crude oil prices, the cheaper gas prices would likely be a temporary trend.
Mid-Atlantic and Northeast Gasoline Prices and Supplies
Motorists across the region are all seeing cheaper prices on the week. Delaware ($2.44) and Virginia ($2.52) have the cheapest gas price average in the region and land among the lowest state averages in the country.
At $2.62 per gallon, Maryland ranks sixteenth in the nation with the least expensive gasoline. The state average is six cents less than last week, 22 cents, less than last month but 16 cents per gallon more than last year on this date. Metro areas across the state continue to experience weekly declines.
For a second week, the Energy Information Administration (EIA) reports that the region saw the largest draw in gasoline stocks in the country. Similar to last week, the draw can be attributed to exports in addition to regional refinery utilization rates falling to 76 percent. Stocks drew by 3.1 million barrels for a total at 64.5 million barrels.
Oil Market Dynamics
At the close of Friday's formal trading session on the NYMEX, WTI crude oil dropped 55 cents to settle at $63.14 per barrel. Oil prices moved lower last week as total domestic crude inventories grew by 3.2 million barrels last week, according to the EIA's latest weekly petroleum status report. Stocks now sit at 426 million barrels, which is 28.9 million barrels lower than the level seen at this time last year, but the highest level since mid-June.
Steady growth, for the sixth consecutive week, in crude inventories has helped to check excessive increases in crude prices. Moreover, re-imposed sanctions on Iran's crude exports have not ignited fears in the market about constrained global supply this winter, since the U.S. will reportedly issue eight waivers that allow some of Iran's top export destinations to continue importing its oil. Oil prices could remain flat or continue falling this week due to reduced concerns about a global crude supply shortage as a result of the sanctions. | slim_pajama |
El-Molla approves Energean acquisition of Edison's concessions in Egypt - Daily News Egypt
Business El-Molla approves Energean acquisition of Edison's concessions in Egypt
El-Molla approves Energean acquisition of Edison's concessions in Egypt
Greek company competed with RWE, Neptune and Cairn, says industry source
Mohamed Adel July 7, 2019 Comments Off on El-Molla approves Energean acquisition of Edison's concessions in Egypt
The Minister of Petroleum and Mineral Resources, Tarek El-Molla, approved in principle to complete the acquisition of oil and natural gas units of the Italian energy group Edison in Egypt by Energean of Greece.
An official source in the oil sector told the Daily News Egypt that Energean of Greece competed with RWE, Neptune, and Cairn Energy for the acquisition of oil and natural gas units of the Italian energy group Edison in Egypt, Italy, Algeria, Croatia, and the North Sea off the coast of Britain, Norway, and Greece.
He added that the acquisition was made after Edison announced the offer of its concession areas of oil and natural gas for sale, and Energean's desire to expand it's gas exploration operations in the Mediterranean region.
The source explained that the Greek company is committed to the exploration and production plan agreed upon with the ministry of petroleum in Edison's concession areas in Egypt upon completion of the acquisition by the fourth quarter of 2019.
Energean has acquired gas exploration for the oil and natural gas unit of the Italian energy group Edison in Egypt, Italy, Algeria, Croatia, and the North Sea off the coast of Britain, Norway, and Greece for $750m.
Energean said that with the production of gas from the Cassiopea field off the coast of Italy by 2022, the company expects to produce $100m for Edison Italy, and the total production of Energean after the acquisition will reach more than 140,000 barrels of oil equivalent per day 2021, with the launch of the Karish and Tanin projects.
"The Edison deal puts Energean as a leading, independent, gas-focused company in the Mediterranean region primarily through a range of low-cost projects," said Mathios Rigas, CEO of Energean.
The deal will make Energean a multi-country, multi-asset company, with extensive cash flow that will significantly contribute to Energean's portfolio diversification, he added.
Topics: Edison Energean Greece Tarek El Molla the Minister of Petroleum and Mineral Resources
Mohamed Adel
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https://wwww.dailynewssegypt.com/2019/07/07/el-molla-approves-energean-acquisition-of-edisons-concessions-in-egypt/
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July 7, 2019 Breaking News | slim_pajama |
extraction of third molars is a routine procedure for acute or chronic pericoronitis , tumors or cystic lesions , periodontal problems , and dental caries .
accurate understanding of the third molar status and proper surgical technique is necessary to prevent postoperative complications . despite these efforts , immediate postoperative sequelae such as bleeding , pain , swelling , and
trismus often occur and may result in more serious postoperative complications like surgical site infection ( ssi ) , alveolar osteitis ( ao ) , hematoma , and paresthesia .
these complications are mostly transient and the incidence rates are low , but these complications can inconvenience the patients ' daily social lives and may be costly and timeconsuming with the necessary additional visits .
several risk factors associated with complications after extraction include age , gender , medication , site of extraction , smoking , previous infection , poor oral hygiene , anesthesia , and the surgeon 's experience1,2,3,4,5,6 .
previous reports suggest the use of additional interventions including local application of antimicrobials , antifibrinolytics , and anti - inflammatory medications to the extraction socket to prevent or minimize postoperative complications7,8 .
type - i collagen sponges are also known to be useful in minimizing postoperative complications due to their effect on new granulation tissue formation , blood clot stabilization , and wound protection9 .
thus , many maxillofacial surgeons have used the bullet - shape collagen sponges to obtain favorable results .
although there were several reports that collagen sponges can prevent tooth extraction complications9,10 , the number of these previous reports are limited , and more studies are indicated in a larger number of patients .
thus , we aimed to evaluate the rate of complications after using absorbable type - i collagen sponges following third molar extractions , and to discuss the effectiveness of the absorbable collagen sponge insertion in minor oral surgery .
this study followed the declaration of helsinki on medical protocol and ethics , and was approved by the regional ethical review boards of yonsei university dental hospital ( irb no . 2 - 2014 - 0009 ) and dong - a university hospital ( irb no .
this retrospective study was designed to evaluate postoperative complications after using type - i collagen sponges ( ateloplug ; bioland , cheonan , korea ) following third molar extractions .
the patients who had undergone collagen sponge insertion into the extraction socket in the department of oral and maxillofacial surgery from january to august in 2013 were included in this study , and a total 2,697 patients ' charts ( 1,163 patients from yonsei university dental hospital and 1,534 from dong - a university hospital ) were reviewed .
extraction was performed under local or general anesthesia , and the type - i collagen plugs were placed into the extraction sockets before wound closure .
surgical extractions were performed with a full - thickness mucoperiosteal flap reflection and odontomy , ostectomy using elevators , whereas the simple extractions were performed using elevators and forceps without flap elevation .
the patient 's extraction site was assessed when the patient visited the clinic for stitches removal or postoperative discomfort .
the presence and the rate of each complication related to collagen plug application , including ssi , ao , and hematoma , was surveyed .
ao was clinically diagnosed by the development of severe , throbbing pain 2 to 5 days after the extraction , and the partial or complete loss of the blood clot1,3 .
surgical complications irrelevant to collagen plug insertion , such as paresthesias , sinus perforation , and mandibular fracture were excluded from this study .
pasw statistics version 18.0 software ( ibm co. , armonk , ny , usa ) was used for statistical analysis , using the pearson chi - square test .
a total of 3,869 third molars ( 514 maxillary third molars and 3,355 mandibular third molars ) from 2,697 patients were extracted , and the extraction sockets were packed with type - i collagen plugs . of these patients , 1,458 molars from 1,163 patients were from yonsei university dental hospital and 2,411 molars from 1,534 patients were from dong - a university hospital .
surgical extraction was performed on 3,393 cases , while the remaining 476 cases were treated with simple extraction .
the overall complication rate associated with collagen plug insertion was 4.52% ( 175 teeth ) . respectively , 116 subjects ( 3.00% ) , 44 subjects ( 1.14% ) , and 15 subjects ( 0.39% ) developed ssi , ao , and hematoma . comparing the two hospitals ,
the total complication rates were similar at 4.32% ( yonsei university dental hospital ) and 4.65% ( dong - a university hospital ) ( p=0.638 ; p>0.05 ) .
however , the complication ratios showed marked differences , especially for ssi and ao ( p=0.000 ; p<0.05 ) . at yonsei university dental hospital , the incidence of ssi and ao were 1.71% and 2.06% , respectively .
in contrast , the complication rates at dong - a university hospital were 3.77% and 0.58% .
notably , the complication rates were significantly different according to the extraction method , with surgical extraction ( 5.01% ) resulting in a much higher rate than simple extraction ( 1.05% ) ( p=0.000 ; p<0.05 ) .
the extraction site was also compared , showing a complication rate of 3.50% for maxillary extractions , and 4.68% for mandibular extractions , which were not significantly different ( p=0.232 ; p>0.05).(table 1 ) when assessing the total number of complications , ssi accounted for more than half , at 66.29% .
however , a single hospital study at yonsei university dental hospital showed that ao accounted for almost half of the complications at a rate of 47.62% , while ssi accounted for more than half of the complications.(table 2 )
the purpose of this retrospective study was to evaluate the efficacy of type - i collagen sponge application after third molar extraction by assessing the rate of complications , including ssi , ao , and hematoma , to explore whether collagen sponges prevent these complications .
the total complication rate was 4.52% , of which , 3.00% were ssi , 1.14% were ao , and 0.39% were hematomas . according to previous studies , the complication rates after third molar extraction had been reported in various numbers .
reported rates of ssi vary from 0.8% to 4.2%2,3,11 and 0.9% to 4.3%1,4,12 in each study .
chiapasco et al.12 reported that mandibular extractions result in a higher rate of ssi than maxillary extractions , with rates of 1.5% and 0.2% , respectively . in the study of bui
et al.4 , the lowest rate of ssi was reported at 0.8% , and 94.3% of those patients received postoperative antibiotics .
the incidence of ssi in our study was 3.00% , which is consistent with previous studies .
the ao rates reported in previous studies were more widely spread , 0.3% to 26%3 , 1% to 3%4 , and 0.5% to 68.4%1,13 , and the ao rate has been reported up to 30% in cases of impacted mandibular third molars4 . in our study , the ao rate was relatively low , at 1.14% , which may be explained by the effects of the collagen sponge . besides , the rates of ssi and ao had variation between two hospitals with 1.71% to 3.77% and 0.58% to 2.06% .
these wide variations may have been due to different diagnostic criteria and various conditions , including the patient 's status , surgical technique , and surgeon experience .
when comparing the surgical techniques in this study , the minimally traumatic procedure may result in the lowest complications , also in case of collagen sponge insertion ( p=0.000 ; p<0.05 ) .
hematoma formation was rarely mentioned in other studies , but it could be associated with common complications , especially bleeding and hemorrhage , which ranged from 0.2% to 5.8%3 . in this study ,
bleeding was treated as a normal postoperative sequelae and not included as a postoperative complication .
after extraction , the extraction socket fills with blood clot and goes through inflammation , epithelialization , fibroplasia , and remodeling .
the gingival tissue grows into the blood clot - filled socket , thus strengthening the fibrin - covered clot to be fixed to the alveolus .
therefore , the maintenance of clots during the healing period may be one of the most important factors in preventing inflammatory complications . with this information
, various attempts have been made to stabilize the blood clot and to accelerate the healing process by way of systemic and local administration of medication .
compared to systemic medication , topical application to the extraction socket has the advantages of minimizing systemic side effects and reaching a greater concentration in a shorter amount of time .
local application of antimicrobials , antifibrinolytics , and anti - inflammatory medications has been recommended .
however , the insertion of topical substances should be performed with follow - up for undesirable local reactions7,8 .
collagen is one of the most common substances for topical application in extraction sockets because it has extensive effects on hemostasis , biocompatibility , biodegradability , and bone conductivity .
type i collagen is a fibrillar collagen , and is the main component of the extracellular matrix .
it is also a natural matrix for osteoblast migration , and has been used for both soft tissue healing and hard tissue reconstruction14 . in a previous study of collagen sponge application to the extraction socket , the collagen sponge appeared to be replaced by natural tissue and matured in the process of its resorption10 .
ateloplug is an absorbable collagen sponge extracted from pig dermis and is composed of 100% type i collagen to minimize antigenicity , and is cross - linked by heat treatment for biocompatibility .
due to its bullet - shaped matrix , it is easily placed in the extraction socket and provides excellent hemostasis by physical compression immediately after extraction .
also , it accelerates tissue regeneration and enhances natural healing by protecting the extraction site from the inflow of food and debris .
not only does the collagen sponge preserve the capacity of the blood clot , but it also prevents soft tissue collapse into the socket , which lacks the support of alveolar bone9 .
thus , type - i collagen plugs are indicated for filling extraction wounds to enhance hemostasis , facilitate granulation tissue formation , and protect the wound surface .
collagen sponges also reduce swelling and pain postoperatively . in our study , the use of collagen plugs in third molar extractions resulted in relatively low complication rates compared to previous studies on general conditions , although these differences were not significant . to manage extraction complications , the risk factors associated with complications
most complications of third molar extraction are inflammatory complications , such as ssi and ao , and they are thought to be associated with the surgeon 's level of experience15
thus , the risk factors that can not be modified by surgeons , like patient 's sex , age , and third molar impaction level , should be fully evaluated , and surgeons should take additional preventive measures into account according to the severity of the risk factors . in an effort to control complications after third molar extraction ( e.g. , perioperative antibiotics , modifications of surgical technique ) ,
to minimize complications after third molar extraction , the topical application of type - i collagen sponges in the extraction sockets could be a useful method due to its effectiveness in hemostasis , wound stabilization , and promotion of healing .
the relatively low incidence of complications in this study supports the collagen sponge 's effects .
therefore , in addition to the evaluation and control of risk factors associated with extraction , application of absorbable collagen sponges may also help prevent complications , and better results may be expected after third molar extractions . | pubmed |
March is the month that most museums in Italy change over from the winter exhibitions, which tend to end in January or February, to the Spring exhibitions that will carry on into the summer. Of the currently announced exhibits in Rome in Spring 2016, these five stand out. Go from ancient history to late 19th century Paris, to Japan for some manga and to Parma for some late Renaissance art, all without changing cities. | slim_pajama |
How to calculate the amount of aluminium that has been oxidised?
1. I have a sample of pure aluminium (100%), 1 kg, stored in "normal condition"
2. After some time the weight of sample has increased by 1%.
3. I assume that aluminium has oxidized to $\ce{Al2O3}$
I know the weight before and after, and my question is: how to calculate how much aluminium has been oxidised?
* Initially, 1 kg of $\ce{Al}$ is present.
* After some time, oxidation increases the weight by 1%, or 10 g (e.g. 10 g of oxygen has been added).
* The atomic mass of oxygen is 16.0 g/mol.
* The molar ratio of $\ce{Al}$ to $\ce{O}$, from the molecular formula $\ce{Al2O3}$, is $\mathrm{\frac{2~mol~\ce{Al}}{3~mol~\ce{O}}}$.
$$\mathrm{\frac{10~g~\ce{O}}{16.0~g~O/mol~O}=0.625~mol~O}$$
$$\mathrm{\frac{2~mol~\ce{Al}}{3~mol~O}\*0.625~mol~O=0.417~mol~\ce{Al}}$$
$$\mathrm{\frac{27.0~g~\ce{Al}}{mol~\ce{Al}}\*0.417~mol~\ce{Al}=11~g~\ce{Al}}$$
Note that even though only a single significant figure is given for each of steps 1 and 2 of the problem, I assumed that they should read "1.0 kg" and "1.0%" rather than just "1 kg" and "1%" for the purposes of illustrating the above calculation. Thereby, 0.42 mol or 11 g of aluminum was oxidized to $\ce{Al2O3}$.
| stackexchange/chemistry |
The Broken Butterfly is a 1919 American silent drama film directed by Maurice Tourneur and starring Lew Cody, Mary Alden and Pauline Starke.
Plot
While strolling through the forests of Canada, Marcene Elliot Starke, a naive young woman meets Darrell Thorne Cody, a composer looking for inspiration for a symphony. They are fascinated by each other and she abandons herself into her lovers arms. Darrell then writes a symphony and calls it Marcene after her. He then asks her to accompany her to New York City for the first time, but she refuses, fearing the anger of her Aunt Zabie Alden.
Marcene gives birth to a little girl and then her aunt rejects her. Her own fears push her to attempt suicide. Upon returning from New York, Darrell learns from Aunt Zabie that Marcene is dead. He then travels to forget his pain and meets Marcene's sister on the Riviera where she is conducting a symphony. The couple then get married. Upon returning to Canada, they discover that Marcene is still alive, but is dying, and that she has a daughter. In agreement with his wife, they hide their marriage from Marcene. She dies happy and Darrell adopts the little girl.
Cast
Lew Cody as Darrell Thorne
Mary Alden as Zabie Elliot
Pauline Starke as Marcene Elliot
Peaches Johnson *this is probably Peaches Jackson
Nina Byron
Preservation status
A print is listed in the catalog of Archives Du Film Du CNC, Bois d'Arcy.
References
Bibliography
Waldman, Harry. Maurice Tourneur: The Life and Films. McFarland, 2001.
External links
Category:1919 films
Category:1910s drama films
Category:American films
Category:American drama films
Category:Films directed by Maurice Tourneur
Category:American silent feature films
Category:English-language films
Category:American black-and-white films
Category:Film Booking Offices of America films | wikipedia |
Why are atoms not being ionized during stimulated emission?
To ionize atom at some state, as understand, it must receive the energy of that state, so for a hydrogen atom, being in the ground state it $13.6\ eV$. In the second state, the ionization energy is lower - $3.4\ eV$ and so on.
The important thing, is that the difference between the ground state and the second state is greater than half of the difference between the ground state and the infinite state, i.e., the ionization energy.
So, this means, that if a hydrogen atom will be excited from the ground state to the second with $a 10.2\ eV$ photon, and while being at the second state receive the same $10.2\ eV$ photon, it should be ionized.
---
At the same time, considering the laser system, where atoms being excited to some state, receives the same excitation photons, but instead of being ionized, they even lose their energy, moving to a lower state.
Why are atoms not ionized in that case?
**My thoughts**
I tried to search, yet have not found anything, but I assume that simply not each chemical element has a difference between the ground state and the second state (or any two other) greeter than half of the ionization energy.
The lifetime of the hydrogen $2p$ state [is $1.6$ nanoseconds](https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/12%3A_Time-Dependent_Perturbation_Theory/12.11%3A_2P-1S_Transitions_in_Hydrogen), so for the atom to be ionised it would have to absorb a second photon within this very short time. This will happen, and some ions will be formed, but the probability that the excited hydrogen atom will absorb a second photon in the $1.6$ ns it exists is very small so the number of ions formed will be very small.
It is not such a simple question. Lasers are complicated.
If an atom absorbs some energy (perhaps a photon), an electron can be promoted from a low energy state to a high energy state. If the atom sits undisturbed for a while, it can spontaneously decay. The electron returns to the low energy state and a photon of wavelength $hc/\lambda$ is emitted.
Another possibility is that a photon of wavelength $\lambda$ can pass by the excited atom and stimulate the emission of another photon. The electron drops to the low energy state. The emitted photon has wavelength $\lambda$, is in phase with the first one, and travels in the same direction. This is [stimulated emission](https://en.wikipedia.org/wiki/Stimulated_emission).
[Excited-state Absorption](https://www.rp-photonics.com/excited_state_absorption.html) can happen too. In most lasers, the photons are not so energetic that a second absorption will ionize the atom. That means a third state with the right energy must be present. In many lasers, there is no such state. When it is present, there are techniques to reduce the effect. On the other hand, some lasers take advantage of it to double the frequency of the laser light.
There is another issue related to your question.
Lasers work by stimulated emission in an [optical cavity](https://www.rp-photonics.com/laser_resonators.html). Suppose you have a population of excited atoms between two mirrors. Some of them spontaneously decay. Some of the photons happen to be in the right direction to be reflected back and forth, passing through the atoms again and again. These photons can stimulate emission of more photons. The number of photons grows, creating a producing [coherent](https://www.rp-photonics.com/coherence.html) laser beam.
This glosses over many complications. For growth:
* The cavity must be designed carefully. Light must repeat its path and interfere constructively after a round trip. Diffraction makes the beam spread. The mirrors must slightly focus the beam to counteract this. Otherwise more photons will leak out the sides than are created by stimulated emission. See [laser modes](https://www.rp-photonics.com/resonator_modes.html) and [Gaussian beams](https://www.rp-photonics.com/gaussian_beams.html).
* One of the mirrors must be perhaps 99% reflective and 1% transmissive so the beam can get out of the cavity. Not too transmissive, or more photons will escape than are created.
* Atoms decay. Atoms in the low energy state absorb photons instead of emitting a second one. For growth, a photon must encounter more excited atoms than low energy atoms.
This last point is a big one. At thermal equilibrium there will be some excited atoms, but more low energy atoms. You can add raise the temperature to get more excited atoms, but never as many as lower energy. Having more excited atoms is called a [population inversion](https://www.physics-and-radio-electronics.com/physics/laser/laser-populationinversion.html). It takes some tricks to arrange one.
Even if you start with a population inversion, you have to keep adding energy to maintain it. The first thing you might think of is making a gas discharge lamp, like an ordinary neon light. You add lots of energy and make lots of excited atoms. You can see lots of photons being given off of the correct wavelength. But this doesn't work. Even though it is not at equilibrium, it is in a steady state. The lower energy population is always larger for any system with 2 energy levels.
The simplest lasers have 3 energy levels with $E\_1 < E\_2 < E\_3$. The lifetimes of the excited states are different. $E\_3$ very quickly decays to $E\_2$. $E\_2$ lasts much longer. State $2$ winds up with all the electrons you might have expected to be in in either $2$ or $3$. This can outnumber State $1$. So the energy source pumps electrons to state $3$, but the laser transition is $E\_2 \rightarrow E\_1$.
This works, but lasers with 4 levels are more efficient.
| stackexchange/physics |
stochasticity appears to be a hallmark of many biological processes involved in signal transduction and gene regulation @xcite . over the past decade ,
there have been numerous experimental and theoretical efforts to understand the functional roles of noise in various living systems @xcite .
remarkably , the building block of different regulatory programs is often a simple two - state switch under the regulation of some noisy input signal .
for example , a gene network is composed of many interacting genes , each of which is a single switch regulated by specific transcription factors . at a synapse , switching of ligand - gated ion channels are responsible for converting the presynaptic chemical message into postsynaptic electrical signals , while the opening and closing of each channel depends on the binding of certain ligands ( such as a neurotransmitter ) . in bacterial chemotaxis ,
the cellular motion is powered by multiple flagellar motors and each motor rotates clockwise or counterclockwise depending on the level of specific response regulator ( e.g. , chey - p in _ e. coli _ ) .
irrespective of the context , the input signal , i.e. , the number of regulatory molecules , is usually stochastic due to discreteness , diffusion , random birth and death .
how does a biological switching system work in a noisy environment ? this is the central question we attempt to address in this paper .
previous studies on this topic have usually focused on the approximate , static relationship between input and output variations ( e.g. , the _ additive noise rule _ ) @xcite , while the dynamic details ( e.g. , dwell time statistics ) of the switching system have often been ignored .
our recent work suggests that there is more to comprehend even in the simplest switching system @xcite .
for example , we showed that increasing input noise does not always lead to an increase in the output variation , disagreeing with the _ additive noise rule _ as derived from the coarse - grained langevin approach .
traditional methods often use a single langevin equation to approximate the joint input - output process , and relies on the assumption that the input noise is small enough such that one can linearize input - dependent nonlinear reaction rates .
our approach to this problem is quite different as we explicitly model how the input stochastic process drives the output switch , without making any small noise assumption . in our previous paper @xcite , the input signal was generated from a discrete birth - death process and regulated the on transition of a downstream switch . by explicitly solving the joint master equation of the system
, we found that input fluctuations can effectively reduce the on rate of the switch . in this paper , this problem is revisited in a continuous noise formulation .
we propose to model the input signal as a general diffusion process , which is mean - reverting , nonnegative , and tunable in fano factor ( the ratio of variance to mean ) .
we employ the feynman - kac theorem to calculate the input - dependent dwell time distribution and examine its asymptotic behavior in different scenarios . within this new framework
, we recover several findings reported in @xcite , and also demonstrate how the noise - induced suppression depends on the relative noise level as well as the relative input - to - output timescale .
finally , we elaborate on how the diffusion process introduced in this paper can be a reasonable approximation of the discrete birth - death process .
the input of our model , denoted by @xmath0 , represents a specific chemical concentration at time @xmath1 and directly governs the transition rates of a downstream switch .
the binary on - off states of the switch in continuous time constitute the output process , @xmath2 .
a popular choice for @xmath0 is the ornstein - uhlenbeck ( ou ) process due to its analytical simplicity and mean - reverting property @xcite .
however , this process does not rule out negative values , an unphysical feature for modeling chemical concentrations .
for both mathematical convenience and biophysical constraints ( see section iv for more details ) , we model @xmath0 by a square - root diffusion process @xcite : @xmath3dt+\sigma\sqrt{x(t)}dw_t , \label{cir}\ ] ] where @xmath4 represents the rate at which @xmath0 reverts to its mean level @xmath5 , @xmath6 controls the noise intensity , and @xmath7 denotes the standard brownian motion .
this simple process is known as the cox - ingersoll - ross ( cir ) model of interest rates @xcite . the square - root noise term
not only ensures that the process never goes negative but also captures a common statistical feature underlying many biochemical processes , that is , the standard deviation of the copy number of molecules scales as the square root of the copy number , as dictated by the _ central limit theorem_. solving the fokker - planck equation for eq .
( 1 ) , we obtain the steady - state distribution of the input signal : @xmath8 which is a gamma distribution with stationary variance @xmath9 .
this is another attractive aspect of this model , since the protein abundance from gene expression experiments can often be fitted by a gamma distribution @xcite .
the parameter @xmath10 in eq .
( 2 ) can be interpreted as the _ signal - to - noise ratio _ , since @xmath11 . for @xmath12 ,
the zero point is guaranteed to be inaccessible for @xmath0 .
the other shape parameter @xmath13 sets the fano factor as we have @xmath14 . using the it calculus @xcite , one can also find the steady - state covariance : @xmath15=\sigma_x^2 e^{-\lambda|s|}$ ] .
thus @xmath0 is a stationary process with correlation time @xmath16 . [
0.42 ] represents the input signal which fluctuates around a mean level over time ; @xmath2 records the switch process which flips between the off ( @xmath17 ) and on ( @xmath18 ) states with transition rates @xmath19 and @xmath20 .
@xmath21 is the dwell time in the off state.,title="fig : " ] in reality , the output switching rates may depend on the input @xmath0 in complicated ways , depending on the detailed molecular mechanism . for analytical convenience , we assume that the on and off transition rates of the switch are @xmath19 and @xmath20 , respectively ( fig .
1 ) . as a result
, the input fluctuations should only affect the chance of the switch exiting the off state ; the on - state dwell time distribution is always exponential with rate parameter @xmath20 .
if we mute the input noise , then @xmath2 reduces to a two - state markov process with transition rates @xmath22 and @xmath20 .
however , the presence of input noise will generally make @xmath2 a non - markovian process , because the off - state time intervals may exhibit a non - exponential distribution . to illustrate this point more rigorously , we consider the following first passage time problem @xcite .
suppose the switch starts in the off state at @xmath23 with the initial input @xmath24 .
let @xmath21 be the first time of the switch turning on ( fig .
then the _ survival probability _ @xmath25 for the switch staying off up to time @xmath1 is given by @xmath26,\ ] ] where @xmath27 $ ] denotes expectation over all possible sample paths of @xmath28 for @xmath29 , conditioned on @xmath24 .
the feynman - kac formula @xcite asserts that @xmath25 must solve the following partial differential equation : @xmath30 with the initial condition @xmath31 . as we will show in the next section ,
the off - state dwell time distribution is not exactly exponential , though it is asymptotically exponential when @xmath1 is large .
a similar partial differential equation to eq .
( [ pdef ] ) has been solved in ref .
@xcite to price zero - coupon bonds under the cir interest rate model .
the closed - form solution for our problem is similar and is found to be : @xmath32^{\alpha } \exp\left[\frac{-2k_{\mathrm{on}}x}{\lambda+\widetilde{\lambda}\coth(\widetilde{\lambda}t/2)}\right ] \label{fxt}\ ] ] where @xmath33 evidently , @xmath25 remembers the initial input @xmath34 and decays with @xmath1 in a manner which is not exactly exponential . for @xmath35 , eq .
( [ fxt ] ) takes the following form , @xmath36 in deriving eq .
( [ asypf ] ) , we have used the following relationship which defines the new parameter @xmath37 as below : @xmath38 thus , asymptotically speaking , @xmath25 decays with @xmath1 in an exponential manner at the rate @xmath39 .
it can be easily verified that eq .
( [ asypf ] ) is a particular solution to eq .
( [ pdef ] ) . to gain further insight into how the input noise affects the switching dynamics
, we first study the
slow switch " limit where @xmath0 fluctuates so rapidly that @xmath40 . here
, @xmath41 is the output correlation time for the noiseless input model . in this limit
, the initial input @xmath34 in @xmath25 at the start of each off period is effectively drawn from the gamma distribution @xmath42 defined in eq .
( 2 ) ; the successive off - state intervals are almost independent with each other ( as the input loses memory quickly ) and are distributed as @xmath43 by direct integration over @xmath34 , we find that @xmath44^{\alpha } \nonumber\\ & \simeq&\left[\frac{2\beta\widetilde{\lambda}e^{-(\widetilde{\lambda}-\lambda)t/2 } } { \beta(\lambda+\widetilde{\lambda})+2k_{\mathrm{on}}}\right]^{\alpha}\simeq\exp(-\widetilde{k}_{\mathrm{on}}\mu t).\end{aligned}\ ] ] in the last step above , we have used eq .
( 8) as well as the following observation : by introducing @xmath45 which reflects the deviation of @xmath46 from @xmath4 , one can check that as long as @xmath47 ( as ensured by @xmath40 ) the following holds , regardless of the values of @xmath48 , @xmath49^{\alpha } = \left(\frac{1}{2}+\frac{1+\theta}{2\sqrt{1 + 2\theta}}\right)^{-\frac{2}{\theta}\cdot\frac{k_{\mathrm{on}}\mu}{\lambda}}\simeq1.\ ] ] our simulations show that the approximate result , @xmath50 , is excellent ( fig .
2a ) , independent of the values of @xmath48 . thus , the average waiting time for the switch to turn on is @xmath51 , longer than the corresponding average time @xmath52 for the noiseless input model .
this is similar to our previous result @xcite , and suggests that the input noise will effectively suppress the on state by increasing the average waiting time to exit the off state .
consequently , the probability , @xmath53 , to find the switch on ( @xmath18 ) is less than that in the noiseless input model : @xmath54 where @xmath55 , the _ effective _ equilibrium constant , is larger than the original @xmath56 as per eq .
[ 0.45 ] , @xmath57 , and @xmath58 ( thus @xmath59 ) .
( a ) @xmath60 versus @xmath1 for @xmath61 and @xmath62 , @xmath63 , and @xmath64 which are achieved by choosing @xmath65 , @xmath66 , and @xmath67 .
symbols represent simulation results , while lines denote @xmath68 .
( b ) @xmath69 versus @xmath70 , where different values of @xmath70 are obtained by tuning @xmath6 .
( c ) @xmath71 and @xmath72 versus @xmath73 with @xmath74 .
( d ) @xmath75 versus @xmath70 .
, title="fig : " ] therefore , in the slow switch limit ( @xmath76 ) , the output @xmath2 is approximately a two - state markov process with transition rates @xmath39 and @xmath20 .
if we further assume that the noise is modest ( i.e. , @xmath77 ) , then @xmath78 the equality above shows that @xmath48 is a characteristic parameter determined by the ratio of the input to output time scales and the relative noise strength . for @xmath79
, we have @xmath80 by eq .
( 6 ) , and the effective on rate defined in eq .
( 8) becomes , @xmath81 in @xcite , the input signal was taken to be a poisson birth - death process for which the variance is equal to the mean ( @xmath82 ) , and the time scale has been normalized by putting the death rate equal to one ( which amounts to setting @xmath83 here ) .
these two constraints reduce eq .
( 13 ) to @xmath84 , recovering the result we derived in @xcite .
the consistency indicates that our key findings are general , independent of the specific model we choose .
the continuous diffusion model here , however , is more flexible as it allows the fano factor to differ from one , that is , @xmath85 . for small @xmath48 , the stationary variance of @xmath2
can be expanded as follows : @xmath86 where @xmath87 is the output variance of the noiseless input model
( [ vardiff ] ) indicates that the input noise @xmath70 does not always contribute positively to the output variance @xmath71 .
in fact , the contribution is negligible when @xmath5 is near @xmath88 and even negative for @xmath89 ( fig .
the explanation is , as we argued before @xcite , that a two - state switch at any moment is a bernoulli random variable whose variance is always bounded by one quarter ( fig .
finally , with the effective on rate @xmath37 , the correlation time of @xmath2 becomes @xmath90 , and can likewise be expanded as follows : @xmath91 thus , @xmath92 _ weakly _ increases with the input noise in this small noise limit ( fig .
[ 0.42 ] , @xmath93 , @xmath58 , @xmath57 , and @xmath94 ( such that @xmath95 ) . ( a ) sample acf of successive off - state time intervals .
( b ) distribution of the off - state intervals , @xmath60 .
symbols are from monte - carlo simulations and solid line is the semi - analytical prediction described in the main text .
( c ) sample acf of a simulated sample path of @xmath2 in the semi - log scale .
( d ) input distributions conditioned on the output . , title="fig : " ] we now examine the fast switch " limit where the switch flips much faster than the input reverts to its mean ( @xmath96 ) . in this scenario ,
the initial input values @xmath97 for successive first - passage time intervals @xmath98 are correlated due to the slow relaxation of @xmath0 .
this memory makes the sequence @xmath98 correlated as well , as confirmed by our monte - carlo simulations ( fig .
for the same reason , the _ autocorrelation function _
( acf ) of the output @xmath2 exhibits two exponential regimes ( fig .
3c ) : over short time scales , it is dominated by the intrinsic time @xmath99 of the switch ; over long time scales , however , it decays exponentially at the input relaxation rate @xmath4 .
this demonstrates that the long - term memory in @xmath0 is inherited by the output process @xmath2 . for a fast switch ,
the distribution @xmath60 is not fully exponential ( fig .
3b ) , though it decays exponentially at the rate of @xmath39 for large @xmath1 , as predicted by the asymptotic eq .
we can still use the closed - form solution of @xmath25 in eq .
( 5 ) to fit the simulation data ( open circles ) .
specifically , we calculate @xmath100 ( blue line in fig .
3b ) , where @xmath101 is the distribution of the initial @xmath34 for each switching event ( defining the first - passage " time @xmath21 ) and can be obtained from the same monte - carlo simulations .
clearly , such a semi - analytical trial ( blue line ) provides a nice fit to the simulation results ( open circles ) .
note that @xmath102 due to memory effects in the fast switch limit . to show this
, we illustrate the input - output interdependence by plotting the input distributions conditional on the output state in fig .
in fact , we shall have @xmath103 , because : first , @xmath34 in @xmath101 denotes @xmath104 where @xmath105 is the last time of off - transition ; second , @xmath106 due to continuity and @xmath107 by definition ; third , all the on - state intervals are memoryless with the same poisson rate @xmath20 . this simple relation @xmath103
has been confirmed by our simulations ( results not shown ) .
it is also obvious from fig . 3d
that the expectation value of the input conditioned on @xmath18 is larger than that given @xmath17 .
thus the mean of @xmath0 should lie in between , i.e. , @xmath108>\mathrm{e}[x]>\mathrm{e}[x|y=0]$ ] , an interesting feature of the fast switch limit @xcite .
since @xmath25 is a decreasing function of @xmath34 and the initial input @xmath34 is likely to be larger under @xmath109 than under the measure @xmath110 , we should have @xmath111 the above inequality explains why the distribution of @xmath21 is below the single exponential @xmath112 ( dashed line ) in fig .
all the above results ( fig .
3a - d ) indicate that the output process @xmath2 is non - markovian in the fast switch limit and , again , confirm the more general applicability of our findings reported in @xcite .
in this paper , we have used the square - root diffusion ( or cir ) process to model biochemical fluctuations . here
we argue that this choice is inspired by the fundamental nature of general biochemical processes .
many biochemical signals are subject to counteracting effects : synthesis / degradation , activation / deactivation , transport in / out of a cellular compartment , etc . as a result , these signals tend to fluctuate around their equilibrium values .
a simple yet realistic model to capture these phenomena is the birth - death process , which we adopted to model biochemical noise in @xcite .
remarkably , a birth - death process can be approximated by a markov diffusion process @xcite .
the standard procedure is to employ the kramers - moyal expansion to convert the master equation into a fokker - planck equation ( if terminating after the second term ) .
this connection allows the use of a langevin equation to approximate the birth - death process .
we will explain this in a more intuitive way .
assume that the birth and death rates for the input signal @xmath0 are @xmath113 and @xmath114 .
then the stationary distribution of @xmath0 is a poisson distribution , with its mean , variance , and skewness given by @xmath115 , @xmath82 , and @xmath116 , respectively .
the corresponding langevin equation that approximates this birth - death process is @xmath117 where the stochastic term @xmath118 represents a white noise with @xmath119 and delta - correlation @xmath120 physically , the langevin approximation eq .
( [ lang ] ) holds when the copy number of molecules is large and the time scale of interest is longer than the characteristic time ( @xmath16 ) of the birth - death process .
( [ var ] ) indicates that the instantaneous variance of the noise term @xmath118 equals the sum of the birth rate @xmath113 and the death rate @xmath114 .
an intuitive interpretation is that since both the birth and death events follow independent poisson processes , the total variance of the increment @xmath121 over a short time @xmath122 must be equal to @xmath123 . as @xmath115 , we can rewrite the langevin eq .
( [ lang ] ) as the following it - type _
stochastic differential equation _ ( sde ) : @xmath3dt+\sqrt{\lambda\mu+\lambda x(t)}dw_t , \label{sde}\ ] ] which is similar to eq .
( 1 ) introduced at the beginning .
a transformation @xmath124 is convenient for exploiting our existing results , as the sde for @xmath125 is @xmath126 which is a particular cir process .
it is easy to check that the stationary variance of @xmath125 equals @xmath5 , and so does the variance of @xmath0 . in other words , we still have @xmath82 for @xmath0 under eq .
( [ sde ] ) . as a cir process ,
@xmath127 in equilibrium follows a gamma distribution , the skewness of which is found to be @xmath116 .
therefore , @xmath128 follows a shifted " gamma distribution with its mean , variance , and skewness given by @xmath5 , @xmath5 , and @xmath116 , respectively , the same to those of the poisson distribution .
this matching of moments suggests that eq .
( [ sde ] ) is indeed a nice approximation to the original birth - death process .
however , @xmath0 in eq . ( [ sde ] )
can take negative values , because @xmath128 is bounded below by @xmath129 due to its shift " in distribution .
this becomes a limitation of the langevin approximation eq .
( [ lang ] ) which could fail if the noise is large ( i.e. the number of molecules is small ) . under eq .
( [ sde ] ) for the input @xmath0 , we can still evaluate the analog of eq . (
3 ) : @xmath130 \nonumber\\ & = & \mathrm{e}^{x+\mu}\left[e^{-\int_0^tk_{\mathrm{on}}x'(s ) ds}\right]e^{k_{\mathrm{on}}\mu t } , \label{fxt2}\end{aligned}\ ] ] where @xmath131 $ ] denotes expectation over all possible sample paths of @xmath127 over @xmath132 $ ] , conditioned on @xmath133 . since @xmath127 follows the cir process eq .
( [ sde2 ] ) , the expectation @xmath131 $ ] has an expression similar to eq .
( 5 ) . in fact , the survival probability @xmath25 in eq .
( [ fxt2 ] ) equals @xmath134^{\alpha } \exp\left[\frac{-2k_{\mathrm{on}}(x+\mu)}{\lambda+\widetilde{\lambda}\coth(\widetilde{\lambda}t/2)}+k_{\mathrm{on}}\mu t\right],\ ] ] with @xmath135 and @xmath136 . at large @xmath1
, this is @xmath137 , \label{asypf2}\ ] ] where @xmath138 and @xmath139 .
thus , the dwell time distribution behaves asymptotically as @xmath140 for @xmath141 , the asymptotic rate above becomes : @xmath142 the first equality above shows that @xmath37 can be negative when @xmath143 or @xmath144 .
this arises as a curse of the possibility that @xmath0 can go negative under eq .
( [ sde ] ) . when dealing with the langevin approximation eq .
( [ lang ] ) , researchers usually assume that the input noise is small enough ( given a large copy number ) such that the random variable @xmath145 could be replaced by its mean @xmath5 in eq .
( [ var ] ) .
this results in an ou approximation : @xmath3dt+\sqrt{2\nu}dw_t , \label{ou}\ ] ] which takes a gaussian distribution in steady state with @xmath82 . compared to the shifted gamma distribution resulted from eq .
( [ sde ] ) , the gaussian model of @xmath0 has zero skewness and is unbounded below .
thus , when @xmath5 is small , the ou approximation becomes an inappropriate choice . by feynman - kac theorem , the survival probability @xmath25 under eq .
( [ ou ] ) satisfies @xmath146 which can also be exactly solved .
we omit the solution here , but later will show that @xmath147 for the ou process will lead to @xmath148 in certain regimes . [ 0.38 ] and the same variance @xmath82.,title="fig : " ] we propose an alternative fix for the langevin approximation , replacing the mean @xmath5 by its random counterpart @xmath0 in eq .
( [ var ] ) .
this yields a cir process : @xmath3dt+\sqrt{2\lambda x(t)}dw_t , \label{cir2}\ ] ] under which @xmath0 follows a gamma distribution in steady state , with @xmath82 as in all the previous diffusion approximations .
the skewness in this model is found to be @xmath149 , which is twice the skewness in the ( birth - death ) poisson distribution .
though larger than desired , it is better than none ( in the ou case ) .
4 plots a comparison of the poisson , gamma , shifted gamma , and gaussian distributions , all satisfying @xmath82 .
one can see that the shifted gamma distribution , which follows from eq .
( [ sde ] ) , gives the closest approximation to the ( birth - death ) poisson distribution , while the gamma and gaussian distributions are , roughly speaking , equally good to approximate the poisson .
nonetheless , only the gamma density from the cir model is nonnegative , like the original poisson distribution .
the diffusion approximations we have discussed so far , including eq .
( [ cir ] ) , eq .
( [ sde ] ) , eq .
( [ ou ] ) , and eq .
( [ cir2 ] ) , are all special cases of the following general it sde : @xmath3dt+\sqrt{\sigma_0 ^ 2+\sigma_1 ^ 2 x(t)}dw_t . \label{sde3}\ ] ] under eq .
( [ sde3 ] ) the survival probability @xmath25 satisfies @xmath150 again , a shortcut for solving eq .
( [ pdef3 ] ) is to introduce @xmath151 which will evolve as a cir process .
this will allow us to make use of the existing results and obtain a similar expression for @xmath25 as before . however , our main interest is the effective rate @xmath37 in the asymptotic behavior of @xmath152 , where @xmath153 is some constant .
inspired by eqs .
( [ asypf ] ) and ( [ asypf2 ] ) , we guess that when @xmath1 is sufficiently large , @xmath154 , for some constant coefficients @xmath155 and @xmath37 ( to be determined ) . plugging this expression into eq .
( [ pdef3 ] ) yields : @xmath156 which holds only when @xmath155 and @xmath37 jointly solve the following two algebraic equations : @xmath157 given @xmath158 , the solution of eq .
( 32 ) is : @xmath159 thus , by defining @xmath160 , eq .
( [ a ] ) becomes @xmath161 eliminating @xmath162 in eqs .
( 31 ) and ( 32 ) , we find that @xmath163 clearly , when @xmath164 , eq .
( [ sde3 ] ) becomes a cir process and eq .
( [ kon3 ] ) reduces to @xmath165 , recovering our result in section iii .
when @xmath166 , eq .
( [ kon3 ] ) is @xmath167 , coinciding with eq .
( [ kon1 ] ) . finally , if @xmath168 , the diffusion eq .
( [ sde3 ] ) becomes an ou process and @xmath169 by eq .
( 32 ) . in this case , @xmath170 , \label{kon4}\ ] ] where @xmath171 is the variance of the ou process
. we can define @xmath48 in the same way as in eq .
( [ theta ] ) , such that @xmath172 in eq .
( [ kon4 ] ) .
this becomes negative if @xmath173 , again a consequence of @xmath147 .
note that the ou approximation eq .
( [ ou ] ) is a particular ou process with @xmath82 .
this leads to @xmath174 in eq .
( [ kon4 ] ) .
so for small @xmath48 or @xmath175 , we have @xmath176 , consistent with our result in @xcite . in sum , the general diffusion process defined by eq .
( [ sde3 ] ) may take negative values with positive probability , unless @xmath164 which corresponds to the cir process .
negative biochemical input is unrealistic and may lead to unphysical results ( such as @xmath148 ) if the input noise is large .
for this reason , we conclude that the cir process eq . ( [ cir ] ) is more suitable for modeling biochemical noise in the continuous setup . as shown , it is analytically tractable and possesses desirable statistical features , including stationarity , mean - reversion , gamma distribution , and a tunable fano factor .
in this paper , we have extended our previous research on the role of noise in biological switching systems .
we propose that a square - root diffusion process can be a more reasonable model for biochemical fluctuations than the commonly used ou process .
we employ standard tools in stochastic processes to solve a well - defined fundamental biophysical problem .
consistent with our earlier results , we find that the input noise acts to suppress the input - dependent transitions of the switch . our analytical results in this paper indicate that this suppression increases with the input noise level as well as the input correlation time .
the statistical features uncovered in this basic problem can provide us with new insights to understand various experimental observations in gene regulation and signal transduction systems .
the current modeling framework may also be generalized to incorporate other biological features such as ultrasensitivity and feedbacks .
work along these lines is underway . | arxiv |
a healthcare system in the last decade was made possible due to the recent advances in wireless and network technologies , linked with recent advances in nanotechnologies and ubiquitous computing systems .
the term telemedicine refers to the utilization of telecommunication technology for medical diagnosis , treatment , and patient care .
the aim of telemedicine is to provide expert - based healthcare to understaffed remote sites through modern telecommunication ( wireless communications ) and information technologies .
one of the benefits of telemedicine is cost savings , because information is less expensive to transport than are people .
advances in medical technologies have led to accelerated growth of the elderly population in many countries , resulting in an increasing requirement for home health monitoring to ensure that elderly patients can lead independent lives .
many physiological signals can be measured from individuals in their living environments during daily activities and are potentially applied to observe the deviations of health status in the early phase or to alert paramedics automatically in emergency cases . especially for remote monitoring of physiological parameters , all the studies developed and currently used in this area can be categorized by several aspects : type of sensors , type of data communication , monitoring device , and signal processing / medical algorithms . so these aspects along with recent studies will be discussed in this section .
as shown in figure 1 the main telemedicine system components in recent years include biosignal sensors , processing units , data communication networks , and medical service center .
the biosignal sensors are responsible for acquiring the physiological data ( patient 's vital signs ) and transmitting it to the signal processing unit .
several studies are made focusing only on designing these sensors to be tiny in size , maintain patient mobility , and consume low operating power to reduce battery size which can last for longer durations .
a collection of wearable medical sensors could communicate using personal area network or body network , which can be even integrated into user 's clothes . at the next stage , sensor layer of every remote monitoring system
is typically connected to the processing device for signal acquisition , processing , analysis , and formatting data to be sent to the communication layer .
processing unit can be pc , mobile phone , or embedded system ( microcontroller , dsp processor , and fpga ) .
many medical algorithms were developed in recent telemedicine studies to help in patient diagnosis and early detection of cardiovascular diseases . among human vital signals ,
pulse assessment has long been a research area of interest in the physiology field , because the pulse reflects a person 's state of health .
many investigations have proposed monitoring systems that can measure various biosignals and provide qrs detection and arrhythmia classification , real - time ecg classification algorithm , and heart rate variability measurement .
also recent advances in wireless and network technologies make it possible to develop a wireless telemedicine system which offers an effective means of bringing healthcare services to patients .
telemedicine systems can be divided into two modes of operations : real - time mode , in which patient data are available at the server end immediately after acquisition , and store - and - forward mode , which involves accessing the data at a later time . in both modes , the vital signs are transmitted via computer networks , cellular networks , public telephone networks , or cable tv networks to the server . in these system models ,
an expert is expected at places where he / she can use a pc to access the server for analyzing the vital signs data , and the patient is bounded at a fixed place like home or healthcare center where a pc is equipped for transmitting these data . the use of wired network connected pcs limits the degree of freedom of both doctors and patients to move around . to improve the mobility of the doctor ,
the global system for mobile ( gsm ) communication mobile telephony network was used for connecting the server . in , hung and zhang implemented a wireless application protocol ( wap ) based telemonitoring system .
it utilized wap devices as mobile access terminals and allowed doctors to browse the monitored data on wap devices in store - and - forward mode . in such systems
the improvement on the mobility of the patient is much less , compared to the doctor . in many previous telemedicine systems ,
the sensor unit consisted of an ecg data acquisition circuit , an a / d converter , and a storage unit . to provide a very limited mobility of the patient ,
this unit was equipped with an indoor , wireless transmitter for feeding the monitored data to a network connected pc [ 18 , 21 ] .
a gsm modem was equipped with a pc for real - time transmission of ecg data from a moving ambulance vehicle in . in , rasid and woodward suggested a mobile telemonitoring system using a bluetooth enabled processor unit , which transmits the monitored data to a bluetooth mobile phone and subsequently via the gsm / gprs ( general packet radio services ) network to the server . on the other hand , engin et al . used a mobile phone to transmit the measured ecg signal in real - time mode
however , the analysis of ecg is not performed in the place where the ecg is acquired ; for example , the ecg is analyzed at the server end .
in fact , there is a loss of efficiency in the use of the gsm / gprs network because normal ecgs are also transferred , which implies a high cost .
lin et al . developed a mobile patient monitoring system that integrates pda technology and wireless local area network ( wlan ) technology to transmit a patient 's vital signs in real - time to a remote central management unit .
the system was based on a small - sized mobile ecg recording device which sends measurement data wirelessly to the mobile phone . in the mobile phone ,
the received data is analyzed and in cases of any abnormalities found among parts of the measurement data , it will be sent to a server . however , because of the limits of processing units within the mobile phone , the overall performance was hardly operated in an ideal condition .
delay in the data transmission might also disrupt the data analysis and measurement . according to the discussed components of the telemedicine system
, all systems developed can be categorized by several aspects : type of sensors , type of connection between sensors , monitoring / processing device , data communication technology , and signal processing algorithms .
table 1 summarizes a set of telemedicine studies in the last decades along with aspects which each study concern . in this paper , we propose a wireless telemedicine system which integrates sensor unit , processing unit , and communication unit in one chip bounded to patient 's body called mobile - care unit .
this will improve patient 's mobility and will not affect active daily life during monitoring .
to lower the cost of using gprs network , only abnormal readings are transmitted so the proposed system operates in two modes , store - and - forward mode and real - time mode . in store - and - forward mode the care unit records and transmits patient 's vital signs to the server through the internet . when an abnormal heartbeat that the doctor concerns is detected , the care unit transmits it to the server via gprs network in real - time
the doctor at the server side could communicate with the patient also by using sms if necessary .
the proposed system also has a friendly web - based interface for medical staff to observe immediate vital signs for remote treatment which will give more mobility for medical staff .
the hardware and software designs of the mobile - care unit are described in section 2.2 .
this section describes in detail the system design based on physiological sensor , signal processing , embedded system , and wireless communication and world wide web technologies .
the aim of this study is to design and implement a telemedicine system with intelligent data analysis based on physiological sensors , embedded system , wireless communication , and world wide web for vital signs monitoring , patient diagnosis , and home care .
it mainly comprises the following parts.mobile-care unit : it could be bound to patient 's body and could acquire real - time or periodical vital signs information without affecting their normal activities .
then an intelligent data analysis scheme is applied to identify abnormal pulses and transmits these data to the remote server by wireless communication through either internet in store - and - forward mode for normal case or cellular networks in real - time mode for abnormal case .
the transmission of patient data in real - time mode can also be operated manually .
whenever the user feels uncomfortable , he can transfer his current vital signs to the management unit for advice or a checkup . by this way
, the cost for using the gprs network is lowered because only abnormal signals are transmitted . for possible long - term store - and - forward mode
, the raw data can be stored in the extended secure digital flash memory contained in the mobile - care unit.the remote server : it stores the received vital signs in a human physiology database and displays the physiology signals to the medical personnel through application program for diagnosis .
also , it enables remote access for caregivers and physicians to obtain vital signs through web - based interface over internet to monitor these data on their pervasive devices . after examining the vital signs data
the message may contain medical advice and/or a list of control commands to the mobile - care device for resending the abnormal case 's vital signs data .
also remote server may alarm family member in abnormal case and call emergency service to transport patient to nearest medical center.pervasive devices : pervasive devices include laptop , personal digital assistant ( pda ) , and mobile phone . through these terminal devices family members or doctors can acquire abundant information about the healthcare recipients anywhere and at any time . mobile - care unit
: it could be bound to patient 's body and could acquire real - time or periodical vital signs information without affecting their normal activities . then an intelligent data analysis scheme is applied to identify abnormal pulses and transmits these data to the remote server by wireless communication through either internet in store - and - forward mode for normal case or cellular networks in real - time mode for abnormal case .
the transmission of patient data in real - time mode can also be operated manually .
whenever the user feels uncomfortable , he can transfer his current vital signs to the management unit for advice or a checkup . by this way
, the cost for using the gprs network is lowered because only abnormal signals are transmitted . for possible long - term store - and - forward mode
, the raw data can be stored in the extended secure digital flash memory contained in the mobile - care unit .
the remote server : it stores the received vital signs in a human physiology database and displays the physiology signals to the medical personnel through application program for diagnosis .
also , it enables remote access for caregivers and physicians to obtain vital signs through web - based interface over internet to monitor these data on their pervasive devices . after examining the vital signs data , the doctor can send a feedback mms message to the user .
the message may contain medical advice and/or a list of control commands to the mobile - care device for resending the abnormal case 's vital signs data .
also remote server may alarm family member in abnormal case and call emergency service to transport patient to nearest medical center .
pervasive devices : pervasive devices include laptop , personal digital assistant ( pda ) , and mobile phone . through these terminal devices family members or doctors can acquire abundant information about the healthcare recipients anywhere and at any time . this section details the system components of the proposed emergency telemedicine system for patient monitoring and diagnosis . in the proposed system
the mobile - care unit was designed to be portable and lightweight which means it is easy to carry and easy to use making patients do nothing .
these are mainly vital - sign signals acquisition module , data control and processing module ( mcu ) , and data communication module .
thus it can collect critical biosignals , including three - lead ecg , hr , blood pressure , and spo2 which are vital signs .
also , it may evaluate patient status and trends in patient 's medical condition and it may generate emergency alert if the patient 's condition is critical . moreover , it should support wireless communication and be compatible with global positioning information system to locate the patient position for emergency help .
also mobile - care unit includes local data storage which is used for raw data recording together with signals processing results .
vital - sign signals acquisition module is responsible for collecting vital signs and then sends it to processing module for adc , processing , and abnormal detection .
e - health sensor shield v2.0 is selected to work as vital - sign signals acquisition module .
this module can continuously acquire physiological signs like ecg , spo2 , body temperature , and blood pressure as shown in figure 3 .
noninvasive measurement of vital signs certainly has an advantage over its invasive counterpart due to the ease of use and lack of risks involved in such measurements .
an ecg is a bioelectric signal which records the heart 's electrical activity versus time .
the electrocardiogram is obtained by measuring electrical potential between two points of the body using specific conditioning circuit . in the proposed mobile - care unit ecg signals from the electrodes
are amplified with a gain of 300 and filtered with the cut - off frequencies of 0.5 hz in the high pass filter and 100 hz in the low pass filter .
the ecg signals are typically 1mv peak - to - peak ; an amplification of 300 is necessary to render this signal usable for heart rate detection and realizing a clean morphological reproduction .
a differential amplifier with gain of 20 avoids the noises overriding the ecg signals ; this is achieved by an instrumentation amplifier ( ina321ea ) , cmrr of 100 db , and at the end an operational amplifier ( analog ad8625 ) is used to amplify the signal with a gain of 15 .
the ecg signals are restricted in bandwidth of 0.5100 hz using second order butterworth high pass and low pass filters after the first stages of amplification .
the power line interference in the ecg signal is filtered by a 50 hz notch filter , which is user selectable to avoid loss of 50 hz component of the ecg signals .
then the ecg signal is fed to the analog input of processing unit for digitizing and analysis .
the temperature of a healthy person is about 37c ; it may slightly or temporarily increase in hot environment or in physical activity ; in extreme effort , the increase may be very high .
the reason is that a number of diseases are accompanied by characteristic changes in body temperature .
likewise , the course of certain diseases can be monitored by measuring body temperature , and the efficiency of a treatment initiated can be evaluated by the physician . an industrial cmos integrated - circuit temperature sensor shown in figure 5(a )
was chosen and connected to signal conditioning circuit shown in figure 5(b ) to calibrate and amplify the signal before feeding it to processing unit .
spo2 or pulse oximetry is the measure of oxygen saturation in the blood , which is related to the heart pulse when the blood is pumped from the heart to other parts of the human body .
when the heart pumps and relaxes , there will be a differential in absorption of light at a thin point of a human body .
oxygenated hemoglobin absorbs more infrared light waves and allows more red light waves to pass through . however , deoxygenated ( or reduced ) hemoglobin absorbs more red light waves and allows more infrared light waves to pass through .
this unique property of hemoglobin with respect to red and infrared light wave allows oxygen saturation to be detected noninvasively .
pulse oximetry is a simple yet reliable method to measure oxygen saturation that otherwise would have to be measured by invasive methods .
red ( 660 nm ) and infrared ( 940 nm ) leds were chosen and populated onto a custom - made sensor shown in figure 6 .
specifications of various physiological parameters monitored in the proposed system are listed in table 2 .
( 2 ) data control and processing module . data control and processing module is the heart of the medical care unit .
the main function of this module can be divided into two parts : in the first part the developed algorithm synchronizes , controls , and maintains the accurate operation and communication of all the other modules . in the second part the developed algorithm digitizes and processes the acquired vital - sign signals to determine if their respective values are above the preset limit or not .
if any or all of these values are above their respective critical values then triggering alarm is made .
microcontrol unit ( mcu ) with powerful processing and control capability is needed to adapt a large amount of data acquiring and processing . moreover
, this module also possesses a high degree of system integration as well as more extension interfaces .
it has input - output circuitry and peripherals built - in , allowing it to interface more or less directly with real - world devices such as sensors .
a microcontroller already contains all components which allow it to operate stand alone and it has been designed in particular for monitoring and/or control tasks . in consequence , in addition to the processor it includes ram , rom , and eeprom memory units , spi , i2c , can , adc , and uasrt interface controllers , one or more timers , an interrupt controller , and general purpose i / o pins .
figure 7 shows the architecture of the mcu . we can summarize the main functions of mcu in the proposed system as follows.it receives and digitizes the signals acquired from vital sign sensors.it controls the operation of all connected modules as shown in figure 8.it processes the received signals using different sorts of processing techniques and algorithms.it sets up a connection with the remote server and transmits to it the analysis results and raw data using communication techniques.it stores analysis results and raw data to flash memory .
it sets up a connection with the remote server and transmits to it the analysis results and raw data using communication techniques .
it is based on the following concepts.sensor and module initialization component : it is in charge of starting , initializing , and configuring the medical care unit.vital signs perception component : it acquires the values of vital signs from sensor nodes.vital signs processing component : it realizes data conversion and processing and carries out patient diagnosis by determining the health status of patient.information transmission component : data exchange between mobile - care unit and server is realized with the help of this component.information receiving component : it helps the node to receive the controlling or inquiring requests from the server.exception notification component : when the abnormal sensing information appears , it sends a message to the server immediately and sends out the alarm as soon as possible . sensor and module initialization component
: it is in charge of starting , initializing , and configuring the medical care unit .
vital signs perception component : it acquires the values of vital signs from sensor nodes .
vital signs processing component : it realizes data conversion and processing and carries out patient diagnosis by determining the health status of patient .
information transmission component : data exchange between mobile - care unit and server is realized with the help of this component .
information receiving component : it helps the node to receive the controlling or inquiring requests from the server .
exception notification component : when the abnormal sensing information appears , it sends a message to the server immediately and sends out the alarm as soon as possible .
data communication module helps the medical staff to get patient 's physiological data by connecting medical care unit to other networks such as cellular network or internet .
it is responsible for uploading the received vital signs data to the remote care server through cellular network to carry out the patients health condition monitoring and diagnosis .
this module operates in two modes : store - and - forward mode in which mobile - care device records patient 's vital signs continuously up to specified period and transmits it to the remote server and real - time mode which operates when an abnormal heartbeat is detected .
mobile - care unit transmits all vital signs to the remote server via gsm / gprs network in real - time . in the proposed system
, medical care unit can send data through internet network either by udp or tcp protocols using enc28j60 ethernet module shown in figure 10(a ) . for real - time connection in emergency cases vital signs
are transmitted through gsm / gprs networks using sim900 gsm / gprs module shown in figure 10(b ) .
the gsm / gprs module used operates at quad - band 850/900/1800/1900 mhz and is controlled via at commands . in the application of telemedicine , the medical information usually needs to be distributed among medical doctors and display , archival , and analysis devices .
therefore , the remote server unit is developed with the purpose of receiving , storing , and distributing the vital sign data from patients .
a multitier architecture allows for separation of concerns where any tier in the system can be expanded and updated with minimal or no effect on the client tiers .
the presentation tier allows the authorized user to interact with the received patient 's data through application program developed using c # language .
the interface design provides most of the general as well as functional requirements as follows.access constraints are applied all the time based on the authorized user registered in the database.it includes lists of patients and personal information about patients.it displays patients ' vital signals and sets thresholds for each measurable parameter.it alerts healthcare providers in abnormal cases.it adds new patient , new consultation , and drug prescription.it shows past medical records for all patients including diseases , past surgeries , clinical findings , past medication , allergies , and images.it provides search for all registered patients by patient 's i d or patient 's name.it shows notations ( patient experience ) while taking measurements.it sends messages including instructions for patients and drug prescription.sensor data will be automatically reloaded at predefined time intervals to keep the view updated .
access constraints are applied all the time based on the authorized user registered in the database .
it shows past medical records for all patients including diseases , past surgeries , clinical findings , past medication , allergies , and images .
it provides search for all registered patients by patient 's i d or patient 's name .
sensor data will be automatically reloaded at predefined time intervals to keep the view updated .
screen shots of the developed software are shown in figures 11 , 12 and 13 .
web tier allows different users such as physicians , doctors , and medical center to interact with the server through a web interface .
remote web user will have real - time and continuous access to patients ' vital signs through the internet .
the web user interfaces with the web components using http protocol over tcp / ip connection .
the information and content are presented to the user using an internet browser through webpage designed using microsoft visual studio 2010 .
the designed webpage provides the most general functions of developed application in the presentation tier discussed previously .
the database tier is responsible for storage , retrieval , update , and integrity of the data to and from the presentation and web tiers . the most common way to access
the database is by using drivers that allow accessing a relational database management ( rdbms ) to query or update the data records .
the driver used in the implementation of the proposed system is jdbc drivers and the database is deployed on a sql database server .
the database tier provides the ability to do the following : store , retrieve , and update patient 's record including his / her medical personnel 's contact information and other details;store and retrieve the received physiological sensor data transmitted by medical care unit;store , retrieve , and update patient 's consultations and drug prescriptions;store and retrieve patient 's notation during sessions;store , retrieve , and update registered doctors , physicians , and nurses;store , retrieve , and update the ecg data , record time , location of the r wave , and estimated ecg beat type .
store , retrieve , and update patient 's record including his / her medical personnel 's contact information and other details ; store and retrieve the received physiological sensor data transmitted by medical care unit ; store , retrieve , and update patient 's consultations and drug prescriptions ; store and retrieve patient 's notation during sessions ; store , retrieve , and update registered doctors , physicians , and nurses ; store , retrieve , and update the ecg data , record time , location of the r wave , and estimated ecg beat type .
figure 16 shows screen shot for how to search .
web tier in the remote server is designed to allow remote user to acquire abundant information about the healthcare recipients anywhere and at any time using pervasive devices such as laptop , pda , and mobile phone .
finally we can say that the proposed system can operate in the following three situations.time-based connection : all data needed by the remote caregivers or specialists should be uploaded .
the remote caregiver should determine time schedule for uploading all patient data to remote server .
the time schedule is stored in the mobile - care unit so it will upload data according to this time schedule.emergency connection : to lower the cost of using gsm / gprs network we develop algorithm which detects abnormal heartbeats .
so during sensor monitoring , if the mobile - care unit detects an abnormal condition it sends the collected data to the remote server in order to receive clinical assessment and treatment planning.(event awareness ) connection on demand : the mobile - care unit uploads the amount of data requested by the remote caregivers or specialists to monitor the health status of the patient .
time - based connection : all data needed by the remote caregivers or specialists should be uploaded .
the remote caregiver should determine time schedule for uploading all patient data to remote server .
the time schedule is stored in the mobile - care unit so it will upload data according to this time schedule .
emergency connection : to lower the cost of using gsm / gprs network we develop algorithm which detects abnormal heartbeats .
so during sensor monitoring , if the mobile - care unit detects an abnormal condition it sends the collected data to the remote server in order to receive clinical assessment and treatment planning .
( event awareness ) connection on demand : the mobile - care unit uploads the amount of data requested by the remote caregivers or specialists to monitor the health status of the patient .
this paper proposes the design and implementation of a wireless telemedicine system , in which all physiological vital signs are transmitted to remote medical server through both cellular networks in emergency case and internet in normal case for long - term monitoring . by this
, the cost of using gsm / gprs network is reduced as only abnormal cases will be transmitted through cellular network .
also the proposed system presents friendly web - based interface for medical staff to observe immediate vital signs for remote treatment .
comparing this system with other systems which are mentioned in the introduction [ 1828 ] , the proposed system integrates sensor unit , processing unit , and communication unit in one chip bound to patient 's body called mobile - care unit , so patient could do his / her daily activities during monitoring .
also the proposed system provides an ability to continuously monitor patient 's vital health conditions instead of the discrete measurements . in the future
, a lot of work could be done in the three main aspects of telemedicine systems to enhance the healthcare services .
the three main aspects are type of sensors , signal processing algorithms , and data communication technology . in the sensor layer wireless sensor network of wearable noninvasive sensor units can be designed .
fabrication of sensors can be improved to obtain small size and low power sensors to improve patient 's mobility and prolong network lifetime .
also we can increase the number of transmitted vital signs to have a complete picture of patient 's case . for more improvement in telemedicine systems
, many medical algorithms can be developed to help in patient diagnosis and early detection of cardiovascular diseases and real - time analysis of vital signs can be performed in the place where the vital signs are acquired .
the latest achievement on a smart phone market provided an opportunity to integrate smart phones in telemedicine systems .
for example , android based mobile phones patient monitoring application could be developed which allows doctors to monitor the health status of a patient using the easy to understand user interface ( ui ) .
this application also provides alerts , reminders , and emergency notifications for vital measurements to help doctors to take timely decisions in emergency situations . finally for data communication technologies , in many countries , 3 g mobile networks like the umts
are currently installed and operating , which provide bandwidth up to 2 mbps maximum ( typically hundreds of kbps ) .
this will enable the transmission of more information like continuous 12 leads of ecg when monitoring cardiac patients from a moving ambulance vehicle .
furthermore , the current introduction of new services like video telephony through wireless networks is an addition that can help with communications between a healthcare provider ( nurse , paramedics ) and an expert doctor .
the current activities in what is termed as the 4 g mobile networks promise ubiquitous access to differing radio network technologies , thus offering , beyond extended coverage , also the most effective connection mode at the point of contact , even using simultaneously more than one wireless access technologies and seamlessly moving between them . the use of locating systems such as the global positioning system ( gps ) , the geographical information systems ( gis ) , and intelligent traffic control systems also has the potential to improve healthcare services , for example , when a moving ambulance vehicle is trying to reach a patient using the fastest route or when an ambulance vehicle carrying a patient is trying to get to the base hospital . | pubmed |
Diffeomorphism group vs. $\operatorname{GL}(4,\mathbb{R})$ in General Relativity
I am quite confused with the groups $\operatorname{Diff}(M)$ and $\operatorname{GL}(4,\mathbb{R})$ in the context of general relativity. I understand that the symmetries of GR are the transformations that leave the equations invariant under under continuous smooth coordinate transformations. That is, automorphisms $f\colon M \to M$ form an infinite dimensional Lie group, the group $\operatorname{Diff}(M)$.
Now, I had the impression that the isometry group of GR is $\operatorname{GL}(4,\mathbb{R})$ and something like that is stated at the [Wiki page of general covariance.](https://en.wikipedia.org/wiki/General_covariance) In specific it says that
>
> A more modern interpretation of the physical content of the original principle of general covariance is that the Lie group $\operatorname{GL}(4,R)$ is a fundamental "external" symmetry of the world.
>
>
>
I am struggling to realise if $\operatorname{Diff}(M)$ is isomorphic to $\operatorname{GL}(4,\mathbb{R})$ and if in this context talking about diffeomorphism group of GR is the same as talking about $\operatorname{GL}(4,\mathbb{R})$ or if this is a subgroup of $\operatorname{Diff}(M)$. **What exactly is their relation?**
1. Let there be given a 4-dimensional real manifold$^1$ $M$. As OP says, the set ${\rm Diff}(M)$ is the [group](http://en.wikipedia.org/wiki/Group) of globally defined $C^{\infty}$-[diffeomorphisms](http://en.wikipedia.org/wiki/Diffeomorphism) $f:M\to M$. The set ${\rm Diff}(M)$ is an infinite-dimensional [Lie group](http://en.wikipedia.org/wiki/Lie_group). (To actually explain mathematically what the previous sentence means, one would have to define what an infinite-dimensional manifold is, which is beyond the scope of this answer.)
2. There is also the [groupoid](http://en.wikipedia.org/wiki/Groupoid) ${\rm LocDiff}(M) \supseteq {\rm Diff}(M)$ of locally defined $C^{\infty}$-diffeomorphisms $f:U\to V$ (i.e. the invertible [morphisms](http://en.wikipedia.org/wiki/Morphism) in the [category](http://en.wikipedia.org/wiki/Category_theory)). Here $U,V\subseteq M$ are open neighborhoods (i.e. objects in the category).
3. The above is part of the [active picture](http://en.wikipedia.org/wiki/Active_and_passive_transformation). Conversely, in the passive picture, there is the groupoid $LCT(M)$ of local coordinate transformations $f:U\to V$, where $U,V\subseteq\mathbb{R}^4$. Heuristically, due to the dual active & passive formulations, the two groupoids ${\rm LocDiff}(M)$ and $LCT(M)$ must be closely related at "the microscopic level". (We leave it to the reader to try to make the previous sentence precise.)
4. Next let us consider the [frame bundle](http://en.wikipedia.org/wiki/Frame_bundle) $F(TM)$ of the [tangent bundle](http://en.wikipedia.org/wiki/Tangent_bundle) $TM$. It is a [principal bundle](http://en.wikipedia.org/wiki/Principal_bundle) with structure group $GL(4,\mathbb{R})$, which is a 16-dimensional [Lie group](http://en.wikipedia.org/wiki/Lie_group).
5. Given two locally defined [sections](http://en.wikipedia.org/wiki/Section_%28fiber_bundle%29)
$$(e\_0, e\_1, e\_2, e\_3), (e^{\prime}\_0, e^{\prime}\_1, e^{\prime}\_2, e^{\prime}\_3)~\in~ \Gamma(F(TM\_{|W})), \tag{1}$$
in some neighborhood $W\subseteq M$,
then there is a locally defined $GL(4,\mathbb{R})$-valued section
$$\Lambda~\in~\Gamma(GL(4,\mathbb{R})\to W), \tag{2}$$
such than the two sections (1) are related via$^2$
$$e^{\prime}\_{b}~=~ \sum\_{a=0}^3 e\_{a} \Lambda^{a}{}\_{b}, \qquad b~\in~\{0,1,2,3\} \tag{3}. $$
6. Conversely, given only one of the sections in eq. (1), we can use an arbitrary $GL(4,\mathbb{R})$-valued section (2) to define the other frame via eq. (3).
7. Let us now return to the groupoid $LCT(M)$ and see how the structure group $GL(4,\mathbb{R})$ comes in. In details, let there be given two local coordinate charts $U,U^{\prime}\subseteq M$, with non-empty overlap $U\cap U^{\prime}\neq \emptyset$, and with local coordinates $(x^0,x^1,x^2,x^3)$ and $(x^{\prime 0},x^{\prime 1},x^{\prime 2},x^{\prime 3})$, respectively. Then we have two locally defined sections
$$\left(\frac{\partial}{\partial x^0}, \frac{\partial}{\partial x^1}, \frac{\partial}{\partial x^2},\frac{\partial}{\partial x^3}\right)~\in~ \Gamma(F(TM\_{|U})), $$
$$\left(\frac{\partial}{\partial x^{\prime 0}}, \frac{\partial}{\partial x^{\prime 0}}, \frac{\partial}{\partial x^{\prime 0}},\frac{\partial}{\partial x^{\prime 0}}\right)~\in~ \Gamma(F(TM\_{|U^{\prime}})), \tag{4}$$
in the frame bundle. The analogue of the $GL(4,\mathbb{R})$-valued section (2) is given by the (inverse) [Jacobian matrix](http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant)$^1$
$$ \Lambda^{\mu}{}\_{\nu} ~=~\frac{\partial x^{\mu}}{\partial x^{\prime \nu}},\qquad \mu,\nu~\in~\{0,1,2,3\}, \tag{5} $$
cf. the [chain rule](http://en.wikipedia.org/wiki/Chain_rule).
8. Conversely, note that *not* all $GL(4,\mathbb{R})$-valued sections (2) are of the form of a Jacobian matrix (5). Given one local coordinate system $(x^0,x^1,x^2,x^3)$ and given a $GL(4,\mathbb{R})$-valued section (2), these two inputs do *not* necessarily define another local coordinate system $(x^{\prime 0},x^{\prime 1},x^{\prime 2},x^{\prime 3})$. The $GL(4,\mathbb{R})$-valued section (2) in that case evidently needs to satisfy the following integrability condition
$$ \frac{\partial (\Lambda^{-1})^{\nu}{}\_{\mu}}{\partial x^{\lambda}}
~=~ (\mu \leftrightarrow \lambda). \tag{6}$$
9. So far we have just discussed an arbitrary $4$-manifold $M$ without any structure. For the rest of this answer let us consider [GR](http://en.wikipedia.org/wiki/General_relativity), namely we should equip $M$ with a [metric](http://en.wikipedia.org/wiki/Metric_tensor) $g\_{\mu\nu}\mathrm{d}x^{\mu}\odot \mathrm{d}x^{\nu}$ of signature $(3,1)$.
10. Similarly, we introduce a Minkowski metric $\eta\_{ab}$ in the standard copy $\mathbb{R}^4$ used in the bundle $GL(4,\mathbb{R})\to W$. We now restrict to orthonormal frames (aka. as (inverse) [tetrads/vierbeins](http://en.wikipedia.org/wiki/Cartan_formalism_%28physics%29))
$$(e\_0, e\_1, e\_2, e\_3)~\in~ \Gamma(F(TM\_{|W})), \tag{7}$$
i.e. they should satisfy the orthonormal condition
$$ e\_a\cdot e\_b~=~\eta\_{ab}. \tag{8} $$
11. Correspondingly, the structure group $GL(4,\mathbb{R})$ of the frame bundle $F(TM)$ is replaced by the proper [Lorentz group](http://en.wikipedia.org/wiki/Lorentz_group) $SO(3,1;\mathbb{R})$, which is a $6$-dimensional Lie group. In particular the sections (2) are replaced by
locally defined $SO(3,1;\mathbb{R})$-valued sections
$$\Lambda~\in~\Gamma(SO(3,1;\mathbb{R})\to W). \tag{9}$$
This restriction is needed in order to ensure the existence of finite-dimensional spinorial representations, which in turn is needed in order to describe fermionic matter in curved space. See also e.g. [this](https://physics.stackexchange.com/q/161744/2451) Phys.SE post and [this](https://mathoverflow.net/q/121620/13917) MO.SE post.
12. Consider a covariant/geometric action functional
$$S[g, \ldots; V]~=~\int\_V \! d^4~{\cal L} \tag{10}$$
over a spacetime region $V\subseteq M$, i.e. $S[g, \ldots; V]$ is independent of local coordinates, i.e. invariant under the groupoid $LCT(M)$. The action
$$S[g, \ldots; V]~=~S[f^{\ast}g, \ldots; f^{-1}(V)] \tag{11}$$
is then also invariant under pullback with locally defined diffeomorphisms $f\in{\rm LocDiff}(M)$.
13. In summary, the symmetries of GR are:
* Pullbacks by the group ${\rm Diff}(M)$ of globally defined diffeomorhisms.
* Pullbacks by the groupoid ${\rm LocDiff}(M)$ of locally defined diffeomorphisms.
* The groupoid $LCT(M)$ of local coordinate transformations, and
* The local $SO(3,1;\mathbb{R})$ Lorentz transformations (9) of the tetrads/vierbeins.
--
$^1$ In most of this answer, we shall use the language of a differential geometer where e.g. a point/spacetime-event $p\in M$ or, say, a worldline have an absolute geometric meaning. However, the reader should keep in mind that a relativist would say that two physical situations which differ by an active global diffeomorphism are physically equivalent/indistinguishable, and hence a point/spacetime-event $p\in M$ does only have an relative geometric meaning.
$^2$ Conventions: Greek indices $\mu,\nu,\lambda, \ldots,$ are so-called *curved* indices, while Roman indices $a,b,c, \ldots,$ are so-called *flat* indices.
A very good answer to the above question has already been provided [here](https://physics.stackexchange.com/a/12474/84488), where Marek summarises the differences between the symmetry group of a theory and the groups of coordinates transformations leaving the equations invariant.
In a nutshell (but it is more complex) let $f\colon U\to V$ be any coordinates transformation on charts of a manifold $U,V\subset\mathcal{M}$ (i. e. a *change of coordinates*). Under such transformation fields $\phi(x)$ are sent into $\phi'(f(x)) = S(x)\phi(x)$.
In order the equations of motion to be satisfied, one must require certain appropriate conditions on the factor $S(x)$ (in particular one can see that these could be related to the *representations* of the underlying group of transformations $f$). The set of all allowed operators $S(x)$ defines the symmetry group of the theory for the general mapping $f$ as defined above. In the case of general relativity $f$ are the diffeomorphisms and $S(x)$ span the general linear group (up to isomorphisms and cartesian products).
It is helpful to remember that the fields of general relativity are maps
\begin{equation}
M \rightarrow \Sigma \,,
\end{equation}
where $M$ is spacetime and you can think of $\Sigma$ either as the space of metrics or, better yet, as the space of frame fields at a point. In either case, the field is a four by four invertible matrix, thus an element of $\mathrm{GL}(4,\mathbb{R})$. Of course it is not just any element of this group: the metric is symmetric, and the frame field is upper trianglular. In either case, what you really have is a field valued in $\Sigma=\mathrm{GL}(4,\mathbb{R})/\mathrm{SO}(1,3)$.
Now returning to the question: $\mathrm{Diff}(M)$ acts on $M$ and $\mathrm{GL}(4,\mathbb{R})$ acts on $\Sigma$. So the $\mathrm{Diff}(M)$ symmetries are spacetime symmetries and the $\mathrm{GL}(4,\mathbb{R})$ symmetries are internal symmetries.
| stackexchange/physics |
Meydar may refer to:
Meydar-e Olya
Meydar-e Sofla | wikipedia |
Aagot Børseth 29 November 1898 19 December 1993 was a Norwegian actress.
Biography
Aagot Tangen was born in Kristiania now Oslo, Norway. She made her debut at Rogaland Teater in Stavanger during 1918 as Grete in Faddergaven by Peter Egge 1869-1959. Later she came to Chat Noir, where she noted herself as the street girl Gusti in Flammen. She came to the Nationaltheatret in 1928 and performed there for 40 years. She made her film debut in Felix 1921 and participated in numerous Norwegian films including Frestelse 1940 and Selkvinnen 1953. She was also a widely used actor on Radioteatret and on television.
She was married to Henrik Børseth 1885-1970 who was also an actor at the Nationaltheatret. She died in 1993 and was buried at Vestre gravlund in Oslo.
Filmography
Fru Inger til Østråt 1975
Eiszeit 1975 TV
Bernardas hus 1964 TV
Sønner av Norge kjøper bil 1962
Sønner av Norge 1961
Støv på hjernen 1959
Selkvinnen 1953
Frestelse 1940
Felix 1921
References
External links
Category:1898 births
Category:1993 deaths
Category:People from Oslo
Category:Norwegian stage actresses
Category:Norwegian film actresses
Category:Norwegian silent film actresses
Category:Burials at Vestre gravlund | wikipedia |
Sons of Anarchy Nomad's Reflections
**Nomad's Reflections**
**Summery: Quinn reflects on his life, and how he came to where he is today. Quinn/Emily Duncan. AU.**
**Disclaimer: I don't own anything.**
To say Quinn Thomas was a soft man would be a lie.
As he laid in the old dorm room in the SAMCRO clubhouse, his wife, Emily Duncan in his arms, and their unborn son in her belly, he couldn't help but remember how he'd become the man he was today.
He'd been a native of Nome, Alaska up until the time he was 18. When he turned 18, he'd decided to join the Navy, to prove his worth as a man. It'd been a good job. Hell, he spent 6 out of his 7 years in it as a SEAL, going on numerous black ops missions, defending his country from all enemies, foreign and domestic. But something seemed to be missing.
After he got out as a Petty Officer, 3rd Class, he started traveling up and down the west coast, on his Harley, trying to figure out what he'd do next. He'd ended up in the small town of Charming, California, and had ended up working as a bouncer there. Again, it had been a good job. But something was still missing.
Then, in his 4th month out of the Navy, he'd met the local charter of the Sons of Anarchy Motorcycle Club, or SAMCRO, as they'd called themselves. After hanging out with them for another month, they had approached him about Prospecting for them. He'd eagerly accepted, having always loved Motorcycles.
Always one for structure and organization, and with Tig as his sponsor, he had patched in a year later. At 6'10", with a body built like a wrestler, and his natural fearlessness, he quickly became an asset to the club and one of their top enforcers. Hell, Tig had even stated that if he ever died, he'd recommend Quinn to take his place as SAA. As much as he loved SAMCRO, he couldn't help but feel restless.
Then tragedy struck in 1994. His wife and unborn child had been killed in a drive-by shooting. It had broken his heart. With so many memories at SAMCRO, he did the only thing he could think of to get away. He joined the Nomads, the special forces unit of the MC.
He had quickly rose through the ranks enough to become Sgt. At Arms for them in 1996. In 2001, when the Nomad President had been killed, Quinn had become Vice President to the new Nomad President.
Finally, in 2006, when the new Nomad President had stepped down, the Nomads voted him in as their new President. With his military background, he in their minds, was the only man for the job. He had chosen Mike 'Cowboy' Ford as the man who would replace him, and Danny 'Psycho' Giving's as his Sgt. At Arms.
Then, in 2010, he began seeing a woman named Emily Duncan. After 8 months of solid dating, they ended up hitched together. Finally, in 2012, after Jackson Teller had been voted in by SAMCRO as the National President of the SOA, after Clay had finally stepped down, they were expecting a son.
He may have had a rough start, but he finally realized something. He was happy. Truly happy. And that was something, everyday, that he thanked God for.
Rubbing his calloused hands over his wife's soft hair, he whispered, "I love you."
**Author's Note: I hope you all enjoyed it. God bless and please leave a review.**
End file.
| fanfiction |
Hard Times Come Again No More sometimes, Hard Times is an American parlor song written by Stephen Foster. It was published in New York by Firth, Pond & Co. in 1854 as Foster's Melodies No. 28. Well-known and popular in its day, both in America and Europe, the song asks the fortunate to consider the plight of the less fortunate and ends with one of Foster's favorite images: a pale drooping maiden.
The first audio recording was a wax cylinder by the Edison Manufacturing Company Edison Gold Moulded 9120 in 1905. It has been recorded and performed numerous times since.
The song is Roud Folk Song Index #2659.
A satirical version about soldier's food was popular in the American Civil War, Hard Tack Come Again No More.
Lyrics
Recordings
Hard Times Come Again No More has been included in the following:
Dolly Parton opens her 1980 song Hush-A-Bye Hard Times with an a cappella verse from the song.
The North Carolina band Red Clay Ramblers featured the song on their 1981 album Hard Times.
Recorded by Irish singer Mary Black on her 1984 album Collected.
Akiko Yano sings this song on her 1989 album Welcome Back
On Syd Straw's 1989 debut album Surprise, Straw and X frontman and solo artist John Doe recorded a version of the song.
By Kate & Anna McGarrigle on the 1991 Songs of the Civil War collection.
By Emmylou Harris in her 1992 live album At the Ryman.
By Bob Dylan for his 1992 album Good as I Been to You.
As the penultimate track on the 1992 debut album from The Lost Dogs, Scenic Routes.
Harvey Reid plays his acoustic guitar on his 1994 album Chestnuts
In Series One 1995 of the Transatlantic Sessions, Hard Times Come Again No More was performed by an ensemble composed of Kate and Anna McGarrigle, Rufus Wainwright, Emmylou Harris, Mary Black, Karen Matheson and Rod Paterson.
The 1995 movie Georgia with Mare Winningham and Jennifer Jason Leigh sung by Mare Winningham and band.
The 1995 movie The Neon Bible performed by Thomas Hampson.
Nanci Griffith on her 1998 effort Other Voices Too A Trip Back to Bountiful.
Ambassadors of Harmony perform an a cappella male chorus barbershop arrangement on their 2000 album Sing Sing Sing!
The 2000 Appalachian Journey, for voice & piano with Edgar Meyer bass, James Taylor vocals Mark O'Connor violin or fiddle and Yo-Yo Ma cello.
eastmountainsouth aka Peter Bradley Adams & Kat Maslich recorded this song on their eponymous album in 2003.
Johnny Cash on the Redemption Songs disc of the 2003 Unearthed box set of out-takes and alternate versions from his American Recordings series.
Mavis Staples recorded it for the Grammy award-winning album Beautiful Dreamer 2004.
In 2005, the song was included in the soundtrack Cameron Crowe's Elizabethtown, performed by Eastmountainsouth.
The 2005 film My Brother's War by Whitney Hamilton.
Matthew Perryman Jones included it on his 2006 album Throwing Punches in the Dark.
Andru Bemis recorded it on his 2006 album Rail to Reel.
Bruce Springsteen and the E Street Band's 2009 Working on a Dream Tour and captured on their 2010-released London Calling: Live in Hyde Park concert video, in the midst of the Great Recession.
Mary J. Blige and The Roots at the 2010 Hope for Haiti Now: A Global Benefit for Earthquake Relief telethon.
In the Season 2 finale of Parenthood by the same name, the song was contributed to the soundtrack by Brett Dennen.
The 2012 Voice of Ages by The Chieftains, with Paolo Nutini.
The 2012 Eesti Kullafond collection of Estonian folk-pop group Folkmill.
An Iron & Wine performance featured in commercials promoting the 2012 Copper television series on BBC America.
Black 47, on the 2014 album Last Call.
The 2014 9/11 Memorial commemoration bagpipes adaption.
Kristin Chenoweth performed the song on her 2014 live album Coming Home.
Katy Treharne sings it on the Tearfund with 'West End has Faith' 2015 album Speechless.
Joel Plaskett's 2015 album The Park Avenue Sobriety Test.
Annie Moses Band performed the song on their 2015 album American Rhapsody.
Australian artists Paul Kelly and Charlie Owen included the song on their 2016 album Death's Dateless Night.
Civilization VI uses the song as the theme for Theodore Roosevelt of the American civilization.
Madeleine Peyroux sang it on her album Secular Hymns 2016
Jennifer Warnes, from her 1979 album Shot Through The Heart
Shully Natan sang it in Hebrew.
Mavis Staples' version opens the second episode of Ken Burns' 2019 PBS documentary miniseries, Country Music.
References
Audio
External links
Hard Times Come Again No More, Edison Male Quartette Edison Gold Moulded 9120, 1905Cylinder Preservation and Digitization Project.
Hard Times Come Again No More at the Vaughan Williams Memorial Library
Category:1854 songs
Category:American songs
Category:Songs written by Stephen Foster
Category:Bob Dylan songs
Category:Bruce Springsteen songs
Category:Emmylou Harris songs | wikipedia |
Benjamin Rowland Jones, Jr. May 29, 1906 July 24, 1980 was a Justice of the Supreme Court of Pennsylvania from 1957 to 1972 and Chief Justice from 1972 to 1977.
Biography
Benjamin R. Jones was born on May 29, 1906, in Wilkes-Barre, Pennsylvania. He studied at Wyoming Seminary, where he served as class president, before attending Princeton University, graduating in 1927, and the University of Pennsylvania Law School. While at Princeton, Jones participated in debating and managed the freshman and varsity lacrosse teams.
Following law school, Jones served in the Luzerne County, Pennsylvania, District Attorney's office before serving in the United States Navy during World War II. In January 1957, Jones joined the Supreme Court of Pennsylvania as an Associate Justice. He served as an Associate Justice until his ascension to Chief Justice in 1972. He retired from the court in 1977. He died on July 24, 1980.
Jones had two sons with his first wife, who both attended Princeton and became attorneys. His first wife died in 1953 and he remarried, to Jane Griffith, who had a son of her own. Jones served as president of the United Fund and trustee of Wyoming Seminary and his church, a Welsh church of the Presbyterian denomination.
References
Category:1906 births
Category:1980 deaths
Category:Supreme Court of Pennsylvania justices
Category:Pennsylvania lawyers
Category:Princeton University alumni
Category:University of Pennsylvania Law School alumni
Category:American military personnel of World War II
Category:20th-century American judges | wikipedia |
Banks Eager For Artificial Intelligence, But Slow To Adopt
Facebook, Google, Microsoft and Baidu spent at least $8.5 billion beefing up their AI talent. Amazon spends $228 million a year just to find people to run Alexa and related machine learning initiatives. Even small to medium businesses in every sector - from fast food chains and personal fitness centers - are reaping the business benefits of technologies like natural language processing, image recognition, and machine learning.
Source: Forbes
The Optimistic Promise of Artificial Intelligence
Andrew Ng and Tong Zhang on how Artificial Intelligence is going to be like electricity, transforming every industry
Source: WSJ
TechCrunch Disrupt SF 2017 is all in on artificial intelligence and machine learning
As fields of research, machine learning and artificial intelligence both date back to the 50s. More than half a century later, the disciplines have graduated from the theoretical to practical, real world applications. We'll have some of the top minds in both categories to discuss the latest advances and future of AI and ML on stage and Disrupt San Francisco in just over a month.
Source: TC
Fake news to grow multifold, AI to create 2.3mn jobs in 2020: Gartner
By 2022, most people in mature economies will consume more false information than true information mainly via social media platforms, market research firm Gartner predicted on Friday.
Source: The Economic Times
Google banks on artificial intelligence tools for its return to China
Google is actively promoting TensorFlow, software that makes it easier to build artificial intelligence (AI) systems, as a way to forge business ties in China.
TERRIFYING breakthrough in Chinese 'voice cloning' to bring new era of 'FAKE NEWS'
A TERRIFYING new development for Artificial Intelligence (AI) in which a Chinese algorithm can clone anyone's voice from only six seconds of audio could revolutionize 'fake news', it has been reported.
Source: express.co.uk
Gear Up Your Career With These Courses Offered By Big Tech Giants
Big tech giants like Microsoft, Google, Amazon, NIVIDIa, Baidu and Uber all have launched the popular courses for the professionals to get learn about the trending technologies like artificial intelligence, machine learning, deep learning and many more. Not only to educate them but also trying to bridge the talent gap.
Source: HOB
What Innovation And Progress Are Expected In IT Sector?
Today, tech innovations arrive faster than most of the enterprises can cope up with. All too often, before one innovation is embraced and implemented, other two appear on the horizon. To cope with these endless innovations, CIO's of the enterprises must pursue and excel the role of a business strategist first and secondly as a technologist, thereby developing an appropriate pace for the digital transformation.
The Way How Deep Learning Is Influencing Robotics?
In the course of recent years, users have doubtless seen quantum jumps within the quality of a good scope of normal innovations. Most clearly, the speech recognition functions on our cell phones work far better to something they want to. After we utilize a voice direction to decision our mates, we have a tendency to contact them currently.
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Glassdoor Reveals The 25 Best Jobs In America For 2015 – Are You Qualified?
The 25 best jobs in America for 2015 have been revealed, and most of them are in the fields of technology, healthcare, and professional services. When it comes to making money and having your career take off in new paths, Glassdoor states that these are the jobs you really want to get yourself into.
This is not just a list of random jobs and professions. On the list, the 25 best jobs are based on each job's overall Glassdoor Job Score.
According to Glassdoor, the number one overall job is that of a "Physician Assistant," which has a job score of 4.8 overall. The average base salary is $111,376 and there are more than 45,000 job openings available.
Coming in second with a job score of 4.6 is that of a "Software Engineer." Technology is advancing all the time and there is always a need to develop and enhance new software. It's obvious that good software engineers are hard to find as there are over 100,000 openings and an average base salary of $98,074.
Glassdoor doesn't want people to forget certain things when looking for a job, and one may not be what you'd think.
All of the 25 best jobs in America for 2015 have a Glassdoor score that ranges from 1.0 to 5.0, and that doesn't mean other jobs are bad. No, that just means that looking at salary and potential for advancement is highest in these.
On the top 25 list, not a single job is lower than a rating of 4.2, of which many are tied for that spot.
As the SF Gate pointed out, the highest paying job on the list is that of a "Finance Manager" which has an average base salary of $122, 865. The lowest paying on the Glassdoor list is a "Physical Therapist" with an average of $64,806 per year.
When it comes to getting a good career, you don't necessarily have to go by Glassdoor's list of the top 25 jobs in America for 2015. This just helps take some of the grunt-work out of how many openings are out there and how much they pay. Good luck! | slim_pajama |
Ranma 1. CAPITULO 1: CURSO DE ADAPTACIÓN
¿VIDA COTIDIANA?
CAPITULO 1: CURSO DE ADAPTACIÓN
Primera semana
Todo iba bien claro estaba un poco nerviosa por que como decirlo yo nunca antes había tenido amigos por la simple razón de "MI QUERIDO PADRE".
Bueno me presento me llamó Akane Tendo tengo 17 años y voy a estudiar ecología.
Mi padre se llama Soun Tendo, Mi madre Kimiko y mi hermana Nabiki
Bueno empezó el día y yo salí de mi cuarto al comedor y vi a mi madre allí preparando el desayuno y me llamo, desayune y me fui caminando a la universidad ya que quedaba cerca a unas cuantas cuadras e iba pensando "Que me espera en este nuevo ciclo".
Yo entré a la universidad muy nerviosa me senté en una esquina esperando a que me dijeran donde era el curso y me llamaron diciendo que ya me estaba esperando el licenciado, entre al curso y una chica se sentó a delante de mí y me hice mi primera amiga ella se llama Akari paso las horas y salimos a receso y como no tenia con quien salir fui con Akari nos pusimos a conversar de muchas cosas y me di cuenta que teníamos muchas cosas en común.
Acabo el receso y entramos a clases ya tenia mucha confianza en ella y cada que el profesor se descuidaba nos poníamos a conversar y allí me hice amiga de un chico llamado Gosunkugi el me molestaba haciéndome cosquillas y yo me desquitaba pegándole en el hombro, un día llegó un chico nuevo llamado Ryoga a el se le veía con una cara que no te acerques, pero como en ese rato teníamos que hacer trabajos en grupo yo muy valiente le fui a decir a la licenciada si el podía hacer con nosotras la licenciada acepto y yo le fui a decir que iba hacer grupo con nosotras, la pase muy bien por que me hacia reír mucho.
También me hice amiga de unas chicas que se llamaba Yuka y Sayuri ellas son muy buenas y se llevan bien conmigo. Acabo la primera semana.
Segunda semana
Todo fui muy bien con mis amigas Akari, Yuka, Sayuri y mi amigo Gosunkugi me la pasaba bien ya que salíamos las cuatro a comprar y en clases conversando a veces con Gosunkugi y a veces con Akari.
No hubo mayores problemas la primera semana y la segunda semana, paso tranquila con deberes risas entre compañeros y amigos.
Un día el licenciado de Química nos dejo unos ejercicios para resolver y como nadie se acordaba yo me ofrecí a ayudarles a resolverlos estaba muy nerviosa y pero di mi palabra y lo hice todos en mi curso me molestaban y Akari me estaba apoyando desde su asiento igual estaba Sinosuke.
Y el ultimo día del curso fue triste ya que baje igual a mi casa con Gosunkugi y antes de despedirnos me dijo que era el ultimo día que nos íbamos a ver ya que el no iba a matricularse, yo le dije por que el me contesto que iba irse a vivir a Kyoto y que no iba a lograr ir y venir y por eso se fue, yo me sentí triste pero le desee todo lo mejor del mundo y así fue las clases de adaptación.
Continuara…
Att: Saomin
2. CAPITULO 2: SEMANA LIBRE
CAPITULO 2: SEMANA LIBRE
En la semana libre que nos dieron no hubo mucho que hacer en mi casa ayudar a mi madre con las labores de la casa y disfrutar la última semana antes de entrar a clases durmiendo muy tarde y levantándome muy tarde.
También me fui a una fiesta de matrimonio de la hermana de mi tía Kioto pase muy bonito me invito a bailar mi primo, y paso la noche.
Fui a jugar con mis primos y así pasó volando la semana libre y preparándome para el nuevo año lectivo.
Continuara…
Att: Saomin
3. CAPITULO 3: NUEVO AÑO LECTIVO
CAPITULO 3: NUEVO AÑO LECTIVO
El primer día solo hubo formación y no fui, al segundo día me encontré con mi amiga mas cerca Akari ella me estaba esperando en la entrada de la universidad con algunos compañeros del curso y algunas amigas mías.
Pero todo no fue bueno ya que el segundo día como no sabíamos para donde ir subimos al patio central y no hubo nadie luego bajamos y fuimos al edificio donde nos dieron el curso de adaptación llegando un "poquito" atrasados, el licenciando nos dejo entrar diciendo que era la ultima vez, nosotros aceptando y nos sentamos en los asientos que habían disponibles, paso las clases y llego el receso y nos pusimos a conversar con una nueva amiga llamada Ranko y otra amiga llamada Danny.
Éramos un grupo de seis incluyéndome todas muy buena amigas, y mi amigo Ryoga, en el transcurso del tercer día me tope de casualidad con Ryoga en el semáforo mas allá de mi casa y preguntándole que como así por allí el me contesto que le habían sugerido esa nueva ruta y yo le conteste que coincidencia ya que yo vivió un poco mas allá entonces quedamos que todos los días íbamos a ir iguales a la universidad y que nos íbamos a topar en el semáforo, llegando a la universidad el se quedo a bajo a saludar a unos compañeros y yo subí al curso y allí nos hicimos amigas de un chico llamado Kuno, el es muy amable y le gusta casi las mismas cosas que a mi "las historietas".
En el cuarto día paso todo normas, con deberes, trabajos, recesos, y en fin las mismas actividades de laos otros dos días pero con la excepción de las materias claro.
Al quinto día todo común y corriente me empezaba a llevar mas con Kuno y claro Con Ryoga en algunas ocasiones yendo a la universidad conversando con Ryoga le preguntaba de cosas triviales y se me ocurrió preguntarle por mi amigo Kuno y el me respondió que es raro y que como no le conoce bien no le cae mucho y ya no le pregunte nada mas, y llegamos a la clase acabando el día y como era de esperarse la mayoría del curso hizo "san viernes" nosotras nos fuimos despidiendo una por una y la primera en quedarse fue Yuka luego fue Sayuri, y por ultimo se fueron Ranko y Danny, quedándose conmigo en la esquina del colegio de mi hermana para esperarla Akari y Kuno, Ryoga se quedo esperando a Yuka por un cuaderno.
Continuara…
Att: Saomin
4. CAPITULO 4: DESQUITE
CAPITULO 4: DESQUITE
Toda la semana fue común y corriente, sin ninguna novedad más que los deberes, las lecciones, las caminatas con Ryoga y nada más.
A y por cierto el día en que nos fuimos a comprar un libro para español nos hicimos doble viaje, ya que en un lado estaba el un libro y en otro lado el otro aparte de esto a un lado Ryoga y al orto Kuno, nos perdimos un ratito nos demoramos esperando el otro libro con hambre y todo y luego yendo a mi casa.
También me acuerdo que Ryoga se desquito conmigo ya que el no conocía la ciudad y se perdió, entonces en hora de español el me hizo poder roja por que llamo a Ranma y dijo oye ella pregunta tu nombre, el regreso a ver y dijo Ranma y entonces yo le pegue en el hombro por tonto.
Luego pasó el día y nada más pasó
Continuara…
Att: Saomin
5. CAPITULO 5: CLASES ¿AFUERA?
CAPITULO 5: CLASES ¿AFUERA?
Empezó otra semana si novedad conociendo algunos licenciados que no se habían presentado como el licenciado de investigación, hicimos algunos ejercicios en cultura física, presentando deberes y un sin numero de tareas.
Pero lo que mas me acuerdo es que por estar esperando a mis amigas que se cambiaran de ropa por que el licenciado el viernes anterior nos dijo que íbamos a entrar en el laboratorio de microbiología y que necesitábamos vestir todo de color blanco, nos quedamos afuera sin que el licenciado nos perdonara nos quedamos las cuatro horas de el afuera, estaba muy mal como iba a explicarle a mi mamá que ni primer día y me quede afuera, pero como no teníamos mas que hacer fuimos a la biblioteca a consultar el deber de investigación con mis amigas.
Luego nos sentamos afuera del laboratorio esperando a que salieran los que si habían entrado, y así pasó todo el día y me quede afuera de la clase de microbiología.
Y después la semana pasó volando otra vez. Y con la única novedad que nos fueron olvidando, por la chica nueva. Alzando la mano diciendo adiós y marchándose con la chica nueva y su madre.
Continuara…
Att: Saomin
6. CAPITULO 6: NUEVA ALUMNA
CAPITULO 6: NUEVA ALUMNA
Pasó rápido el fin de semana y tuvimos una sorpresa ese día una "nueva alumna" estaba allí conversando con mi amigo Kuno, todo el día recibió castigos por culpa de ella ya que se la pasaba conversando en todas las horas hasta en el receso.
Yo no le tome muy en cuenta ese día y pasó la mañana acabando las clases cuando algo que me extraño mucho sucedió el se había marchado con ella, a la hora de microbiología nos toca entrar y me topo en los casilleros y me dijo que si yo estaba enojada con el "que ilógico que me preguntara eso si el ya savia la respuesta pero bueno yo le conteste" tu mismo sabes por que estoy enojada, el frunció el seño y yo me fui con Akari a esperar a que abrieran el licenciado abra el laboratorio toda la mañana lo evite, hasta la salida yo por mi parte estaba con mis amigas Ukyo, Saomin, Nina, Yuka y por supuesto mi gran amiga Akari y yo, cuando Akari y yo estábamos conversando que ella le había dicho a Kuno que a ella ni le va ni le bien lo que el haga, entonces entrando al cuarto de instrumento Ukyo, Saomin y Nina diciendo como un juego que nos contaran que habían hecho el otro viernes nos dijeron que Ukyo y Ryu se había hecho novio, y allí empezó la platica de quien te gusta empezando Akari dijo que del curso nadie le gustaba ya que ella ya tenia novio que se llamaba Tofú, luego continuo Ukyo claro de ella ya sabíamos después Saomin dijo que le gustaba un chico que tenia churros, después vino Nina y dijo que ella ya tenia novio y por ultimo yo y dije que el que me gusta es el ultimo chico que llegó y se llama Ranma.
Ellas se pusieron a reír, llegando Yuka me dijeron que raro ya que parecía que Ryoga y Kuno estaba interesados por mi yo les pregunte y Akari iba a decir algo y después me dijo olvídalo, cuando mi amiga Ukyo me dijo que me iba ayudar a entrar con Ranma y la ocasión perfecta era el viernes, pasó la conversación y nos fuimos hacer los demás deberes que nos faltaba en el laboratorio.
Los otros grupos acabaron y se fueron rápido quedando solo el nuestro y mi amigo Kuno, el llego y dijo por favor quítenme el castigo, mi amiga Akari dijo que ya se vaya y luego se dirigió a mi, yo le ignore y como vi que mi compañero Sinosuke se había quedado todavía me fui a conversar con el de cosas triviales luego regrese donde estaban mis otras amigas y lo vi allí ayudando hacer lo que nosotras teníamos que hacer, salí de nuevo y me encontré con Ukyo a fuera que me dijo que no era justo hacerle sufrir yo de acuerdo le dije que hago y ella me dijo dije que le perdonas pero que amigos como antes ya no.
De acuerdo me arme de valor y le fui a decir lo que me dijo Ukyo entonces comencé deja eso ya es trabajo de nosotras puedes irte nomas y te perdono pero amigos como antes ya no, le vi tan triste pero luego me acorde como estaba con la chica nueva y le dije con mas valor anda nomas que nosotras hacemos esto.
El se fue susurrando algo que no logre escuchar, entonces sentí menos un peso encima, acabamos las labores en el laboratorio y llegue mas tarde de lo acostumbrado a mi cas y mi papá me dio una buena hablada.
Pasó ese día, y al siguiente estuvo muy raro no es que tenia celos sino que fue muy grosero de su parte portarse así ya que nosotras le habíamos rogado al licenciado de ecología que el hiciera el trabajo con nosotras claro las que fuimos a pedir por el fuimos yo y Akari, no me saludo como todos los días, se la pasó conversando con ella las clases, se fue con ella a receso y aparte de eso le acompaño a cambiarse de uniforme para cultura física, bueno no le tomamos en cuenta y creo que ese día le fue mal ya que se pasó presumiendo de que podía ganar en carreras y no lo hizo, luego salimos yo y Akari para que ella cogiera su bus y yo por supuesto esperando a que saliera mi hermana.
Al día miércoles todo pasó casi normalmente, ya que me lleve una sorpresa desagradable al verlo allí en la puerta esperando al achica nueva y para el colmo mío mi amigo Ryoga no llego como siempre para irnos iguales, yo le vi y ni en cuenta le tome, Pasó todo el día y acabo las clases saliendo conmigo mis amigas y después solo yo y Akari nos fuimos iguales y en el camino íbamos conversando que yo le diga algo a Kuno por que el estaba hablando mal de nosotras, ya que conociendo a mi amiga Akari ella le hubiera gritado, y para evitar esto me ofrecí yo para hablar con el.
En el día jueves yo la pase un poco agitada ya que nos tocaba español y la licenciada decía que si ella entraba ya nadie entraba tras de ella, acabo la hora de ella y llego la hora de química y nos toaba en el laboratorio allí pasó algo muy raro ya que oía murmullos de Kuno con Ryu, luego se me acerco Akari diciendo que por favor hable con Kuno ya que el esta hablando de nosotras entonces cogí valor y cuando iba a conversar con el, él ya se había ido con la chica nueva.
Entonces salimos del laboratorio como siempre en grupo y quedando una a una, entonces ya casi llegando a la esquina nos encontrábamos Ranko, Akari y yo hablando de Kuno para decirle que ya basta que nosotros ni en cuenta le tomamos y el anda hablando de nosotras más que todo de Akari y yo, entonces como dicen hablando del rey de roma que este se asoma y apareció como arte de magia, mis amigas lo llamaron y el no hizo caso entonces yo le llame y regreso a ver entonces le dije espera un momento Kuno tengo que hablar contigo, el paró y yo pensaba "voy para el matadero" entonces les dije que vayan mas atrás a mis amigas y le dije sabes nosotras queremos que ya no hables de nosotras mal, luego de que si el quiere hacerla entrar en el grupo de nosotras que nos pregunte.
Entonces Akari dijo que ni le tome en cuenta al hablar con Ryu, el estuvo de acuerdo y le dije adiós ya que tenia que irle a ver a mi en el colegio y entre dejándole a fuera a el.
Luego volví a salir y allí estaba el otra vez pero justo paso mi compañero llamado Belenus y me fui con el y no tome en cuenta a Kuno, entonces el se nos acerco y el dijo que ya se tenia que ir, se despidió y se fue el me pidió unos minutos entonces el me dijo que le perdone y que por que no le caía la chica nueva que se llamaba Kodachi, yo le respondí que es como un sexto sentido, así como el me pregunto yo le dije por que no se llevaba bien con Ryoga y dijo que no le caía yo le dije por que si coinciden conmigo, se despidió y se fue
AL día siguiente viernes todos los planes ya estaban hechos después de clase íbamos a ir a jugar cartas y como mi amigo Ryoga se sentía mal no pudo ir con nosotros, ya en el local se pusieron a tomar cerveza por supuesto que yo no, luego vino los desafíos y me toco besar a Ranma, claro el empezó, Luego me toco besar a Kuno me opuse pero el beso solo fue en el cuello, luego otra vez un beso con Ranma, pero esta vez me tocaba a mi, paso las horas rápido y me toco ir a ver a mi hermana en el colegia conmigo vino Akari , Kuno y Belenus, conversando de lo anteriormente acontecido llegamos a la esquinas de los buses que cogían y yo esperando a mi hermana cuando en un descuido Akari y Belenus se fueron quedando solo Kuno y yo y allí ocurrió se me declaro claro que yo le dije que no pero el me dijo no te pido una respuesta ahorita, y se fue dándome un gran abrazo.
A la tarde conversando con Ukyo que se quedo hasta el ultimo por supuesto con Ryu me dijo que habían estado platicando con Ranma de pedir una oportunidad ya que a el le había gustado Kodachi, pero como ella tenia novio entonces el había dicho que lo va a pensar.
Continuara…
Att: Saomin
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En el próximo capitulo titulado: ¿Novios?
Por favor sugerencias a mi correo , y les agradezco que lean este segundo fiction mío gracias.
7. CAPITULO 7:¿NOVIOS?
CAPITULO 7: ¿NOVIOS?
Me pase pensando todo el fin de semana en como iba hacer el lunes, con todo lo ocurrido la otra semana con todo lo que me dijo Ukyo y la prueba de ecología encima.
Pero salí de casa como todos los días cogiendo gran valor para pasará lo que pasará, además me había enterado que no iba haber clases el lunes por que había pronóstico de tormenta, o algo así.
Entonces si tuvimos clases de microbiología dividiéndonos en grupos el licenciado a mi al principio me toco con Kuno pero pasando lo del otro viernes me acobarde y decidí cambiar puestos con Sinosuke al grupo uno, pasaron todos a realizar sus labores en el laboratorio y como éramos Akari, Sayuri, Max, Hiroshi, Akira, Narami, Kertos y yo.
Como los recipientes no llegaban me puse a platicar con Belenus sobre la música y dije:
Akane: Y que tipo de música te gusta?
Belenus: A mi me gusta las baladas y a ti
Akane: A mi también y que has tenido novia
Belenus: Si pero terminamos hace varios meses y tu tienes novio
Akane: No, no he tenido novio
Belenus: Y por que?
Akane: Por que no se me han declarado "obviamente si se me declaro Kuno, pero no tenia pensado decírselo"
Belenus: HHHHAAAA! Y yo que pensaba que a usted le gustaba Ryoga
Akane: Por que dices eso?
Belenus: Por que yo les veía que pasaban mucho tiempo juntos
Akane: No, yo y Ryoga solo somos amigos. Y a ti quien te gusta del curso?
Belenus: A mi uuuumm! y a ti?
Akane: Prometes no decir a nadie quien me gusta?
Belenus: De acuerdo pero quien te gusta?
Akane: Pero luego me dices tu quien te gusta de acuerdo
Belenus: Si pero ya dime quien te gusta
Akane: Bueno me gusta Ranma
Belenus: AAAHHH!
Akane: Si me gusta Ranma y a ti?
Belenus: Bueno a mi no me gusta nadie de aquí
Akane: Pero si a de haber alguien que por lo menos te simpaticé
Belenus: No nadie
Luego me llamó Narami (por que como ella tiene clases tarde se iba a ir) entonces le dije a Belenus que me esperara para seguir conversando y cuando me di la vuelta ya se había ido.
Bueno yo regrese a mis labores con los demás cuando también se había ido Kertos, sin pedir permiso al encargado del laboratorio.
Nos quedamos hasta alrededor de las 2:45 cuando de repente sonó mi teléfono siendo mi padre al otro lado de la línea diciéndome que a que hora iba a ir a mi casa, yo le respondí que todavía no acabábamos y que me iba a quedar hasta las 3:00, se enojo tanto que dijo:
Soun: Ya subo a ver que estas asiendo
Akane: De acuerdo yo le espero en el laboratorio así que entrara nomas que aquí le espero
Y colgó, cual fue mi sorpresa al ver a unos compañeros parados en plena puerta de laboratorio llamando a Daisuke nosotros les dijimos que el ya se había ido, entonces llamaron a Akari para allá (Si se acuerdan que entre Akari y Ryu no se llevan bien) y de casualidad yo regrese a ver y también me llamaron diciendo:
Ryu: Hola queríamos hablar contigo un momento Akane
Akari: Entonces para que me llamaron a mí?
Ryu: Solo era para molestar
Mi amiga Akari salió dejándome sola con Ryu y Ranma
Akane: Si y que querías decirme?
Entre los dos se debatían para decirme algo que no se que era, yo ya me estaba cansando cuando Ryu dijo:
Ryu: Ranma quería conversar contigo un momento
Akane: Y de que será
Se me acerco Ryu y me dijo al oído: ahora dice que le gusta yo me puse de mil colores pero disimulando bien dije que?
Entonces en ese momento hablo Ranma y dijo:
Ranma: Si sales rápido nos vemos en el local del otro día
Akane: Si es que puedo "claro que iba a decir que si pero de casualidad regrese a ver a la vereda y allí estaba mi madre"
Ranma: Entonces es un si
Akane: Sabes que no puedo por que si ve para la vereda allí esta mi madre y me esta esperando "no me imagine que iba a venir a verme mi madre"
Ranma: Bueno nos vemos
Akane: Sabes mejor nos vemos mañana te parece
Ranma: Si nos vemos mañana, adiós
Ryu: Adiós
Al día siguiente llegue con Ryoga como todos los días conversando de trivialidades, claro que estaba muy nerviosa por lo que iba a pasar pero para sorpresa de todos no pasó nada por que primero no hubo las ultimas horas (claro solo no hubo cultura física) yo me ofrecí para ayudar a mis amigas con sus deberes de computación y me quede con ellas en las computadoras sabiendo que me invitaron a jugar.
Yo estaba muy emocionada, pero por más que quería irme a jugar mas me demoraba, acabe exhausta y salí corriendo al estadio seguido claro de mis amigas y de Ryoga pero no los encontré allí y llame a Ukyo a preguntar donde estaban, me contesto y me dijo que estaban más debajo de la universidad en un parque jugando.
Bajamos y los vimos jugar a todos mis compañeros, llegamos donde estaban mis amigas y "mi compañera" Kodachi viendo el partido, me puse un poco mal ya que yo baje con la intención de jugar y no me dejaban jugar pasó un tiempo y nos pusimos a jugar Yuka, Danny, Millia, "Kodachi", Hikari y yo con los demás hombres que se habían quedado. Empezó el juego y a mi me tocó contra Kodachi, Kuno, Ranma, Ryu, Hikari y Millia yo jugaba a defensiva o algo así cuando ella obtuvo la pelota, fui para quitarle y me rasguño pero yo si le saque la pelota.
Minutos después obtuvo otra vez la pelota y sin pensarlo dos veces me fui para quitarle cuando por accidente le puse el pie y se cayó yo le accedí mi mano para que se levantará pidiéndole disculpas y me tiro la mano para el otro lado, eso si me enojo claro yo no lo hice con mala intención pero así sucedió y ella me tiro la mano, claro que me olvide de todo eso ese rato pero así se porto muy mal, después le pegue a Kuno en la rodilla izquierda sin intención también, y justo acabo el partido y nos íbamos yendo todas mis compañeras para realizar otro trabajo cuando pasando junto por Kodachi le oí decir: esto no fue nada y yo mas allá le dije: eso lo veremos.
Salimos y ya en dirección del centro de cómputo me tope con un amigo del colegio Méril, el estaba cargando algo así que se sorprendió mucho al verme le salude y me fui.
Al miércoles ya se había pronosticado que si iba a ver tormenta no muy fuerte así que la universidad si iba a tener clases, salí en dirección a la universidad y me tope con Ryoga como todos los días justo antes de dar la vuelta me tope con mi primo conversando de clases, se despido y fuimos a la universidad esperando a que dijeran si había clases, la repuesta fue no ya que los profesores no habían venido.
Así que decidimos ir a la plaza comercial para realizar el proyecto de Biología, junto con Max, Yuka, Sayuri, Akari, Rashell, Sinosuke y yo nos fuimos caminando sin rumbo dimos muchas vueltas asiendo tiempo para que abrieran a eso de las 9:00 nos fuimos a un centro de computó a consultar sobre Química para la exposición después saliendo de allí cogimos un camión y nos fuimos a la plaza comercial, llegamos y nos pusimos a esperar pero se nos abrió el apetito y nos pusimos a comer pan tradicional, esperando que no abrían y ya era las 9:30 fuimos a preguntar a una persona que se encontraba allí y dijo:
Persona: La plaza comercial abre a las 10:00 de la mañana
Y en coro todos dijimos que vamos hacer aquí parados y en tremendo calor, entonces decidimos ir a un supermercado hacer el trabajo, yendo para abajo unas cuantas cuadras, llegamos y entramos a ver que había seleccionando cada uno un producto para nuestro deber, pagamos y salimos de allí quedando de acuerdo que los chicos iban a poner la pizza para el viernes y yo iba a poner mi casa y las demás chicas las sodas.
A la tarde algo me sorprendió mucho me llamo Ranma a citarme a que fuera a verlo en el parque por que quería conversar algo conmigo, claro yo salí estaba muy nerviosa y pensando en que me iba a decir llegue caminado por la otra vereda pero antes yo ya le había visto entonces me hice la que no le vi me silbó y fui para allá estaba con algunos amigos y me llevó para dentro del parque me dijo:
Ranma: Hola como estas?
Akane: Bien y tu, y allí me percate que estaba sangrando y le pregunte, Que te pasó
Ranma: Nada solo que vine peleando con unos chicos
Akane: Por que?
Ranma: Por que me estaban buscando y yo nunca me rindo
Akane: Ya lo se por tu honor
Entonces me cogió desprevenida y me beso el muy apasionadamente pero yo no sabía como hacerlo y lo peor del caso estaba muy nerviosa, entonces paro y me dijo:
Ranma: Quieres ser mi novia
Akane: Y o le dije que claro
Luego nos volvimos a besar igual que antes me abrazó y como sus amigos ya se iban me dijo haya o no haya clases mañana nos vemos me dio un ultimo beso y se fue, yo me quede congelada por una parte era lo que esperaba y por otra me cogió de sorpresa.
Llegue a donde mi hermana con una car de haber visto un fantasma mi mente todavía no procesaba la información y lo peor sería en la universidad con todos mis compañeros como iba a comportar.
En el jueves pasó algo fuera de lo normal, llegué como si nada "claro en dentro estaba muy nerviosa" así que entré a la universidad y allí estaban todos y claro también estaba "mi novio", entonces llegue a besarlo con un pico y nada más como me había dicho mi amiga Ukyo.
Luego llegó "la chica nueva" Kodachi junto con su gran amigo Kuno, yo sin hacerles caso me puse a conversar con Akari y Max de música, de la tele, de las películas y así paso mucho rato cuando Akari me dijo:
Akari: Akane ya vámonos que me prometiste ayudarme en los deberes
Akane: De acuerdo espera que me despida de Ranma y nos vamos
Claro que no sabia como iba a suceder ese milagro, me quería acercar pero como, y estando allí también Ryoga, me arme de valentía y me fui para allá peleando primero con Ryoga y luego le dije a Ranma:
Akane: Nos vemos mañana o esta tarde a las 3:00
Ranma: De acuerdo
Me dio un beso y cuando se iba a ir mi amiga Ukyo dijo vamos con nosotros hacer el trabajo de biología, yo acepte.
Me despedí de Akari y Max ya que no los podía acompañar y quedamos que los iba ayudar mañana y se fueron los dos.
Y fui cogida del brazo de Ranma se me reían Ryu y Ukyo por que decían:
Ukyo: Parecen viejitos cogidos así
Akane: Es que a mi me gusta así
Ukyo: Que no parecen novios
Akane: Es que, a mi me gusta así
Después Ranma fue a dejar su maleta en su casa y dijo que lo esperara, yo iba conversando con Ukyo y Ryu de e trabajo que íbamos hacer cuando de la casa salió Ranma ignorándome se fue para adelante con mis demás amigos y yo quedándome atrás con la pareja.
Bajamos a la plaza comercial y buscando un lugar para realizar el trabajo y como ellos nos iban a llevar lejos Ukyo y yo entramos al primer sitio que vimos claro los otros ya iban bien adelante no nos vieron pero luego entraron ellos también.
Ellos decidieron ir hacer el trabajo a otro lado, y yo me quede con la pareja y por supuesto Ranma se fue con ellos, no me enoje por que dijo que me iba a venir a ver, no paso y los fuimos a buscar yo riéndome de lo que decían los dos tortolitos las locuras que pasaban como por ejemplo
Ukyo: A te voy a contar que el otro día que bajamos yo iba siguiendo a Ryu y el a mi, ya cuando estaba bien lejos ambos nos preguntamos que a donde íbamos, entonces los dos dijimos que el uno estaba siguiendo al otro
Akane: jajajajajajaja
Ukyo: Ryu también entiende todo al revés
Akane: Por que?
Ukyo: Por que cogió mal la dirección por que Daisuke dijo vamos para arriba y el me llevo para abajo, y como no lo encontrábamos lo llamo y dijo que era para la otra dirección
Akane: jajajajajajaja, pobre Ryu ya se esta pareciendo a Ryoga
Ukyo: Si es cierto, jajajajajajaja
La pase muy bien con ellos, llegamos a donde ellos estaban, entramos y el ni caso omiso hizo que yo allá llegado, paso un buen rato y yo empecé a ayudar a mis compañeros con sus deberes, pasando el tiempo y de casualidad llegó Millia y también le ayude se marcho un poco mas tarde, y cuando yo ya me iba a ir
Ukyo: Vamos Akane a comer un helado te parece?
Akane: Ya me tengo que ir por que mi padre me esta esperando
Ukyo: Vamos Akane
Akane: No
Ukyo: Ranma dile a Akane que vaya con nosotros, si
Ranma: Vamos Akane si
Akane: De acuerdo vamos
Salimos de allí, y nos dirigimos a la heladería mas cercana, claro salimos como estábamos antes el con sus amigos y yo con la feliz pareja.
Entramos y cada uno decidió su propio helado, nos sentamos y no se que pasó pero Ranma se sentó a un extremo y yo al otro como polos iguales repeliéndose, bueno esa actitud no la iba a soportar ni siendo mi "novio" ya que si no me quería no me hubiera invitado y ya, acabaron y justo cuando nos íbamos a ir le cogí y le dije:
Akane: Ven Ranma necesitamos hablar
Ranma: De que es
Akane: Bueno tu te estas portando como un niño chiquito y a mi no me gustan esas personas, creo que nos hicimos novios muy rápido así que terminemos y quedemos como amigos, de acuerdo
El se congelo en ese rato pero luego dijo si yo le accedí mi mano y me fui con la feliz pareja dejándolo allí con los demás chicos.
A la tarde me llamó Ukyo y me dijo:
Ukyo: Que bien que terminaste con el se estaba portando mal contigo
Akane: Creo que si
Ukyo: Además, el me dijo en una ocasión que le gustaba Kodachi
Akane: En cerio
Ukyo: Si, y también me dijo que si yo terminaba algún día con Ryu, el podría tener una oportunidad conmigo
Akane: Que mal, pero que bueno que termine yo con esto antes de que creciera y me hiciera daño
Ukyo: En eso estoy de acuerdo, bueno chao y nos vemos mañana
Akane: De acuerdo y hasta mañana
Me sentí un poco mal al escuchar esas palabras, pero no sentí remordimiento "un poco" lo que si fue como un peso de encima quitándome por que sino me quería y yo si le que hubiera sufrió era yo y no el.
A la mañana siguiente, no hubo clases por el pasó de la tormenta pero yo para estar segura me fui a la universidad a ver si habían abierto, llegue y como vi la puerta cerrada me regrese cuando sonó mi celular siendo
Ukyo: Hola Akane por que te vas no me que estamos aquí
Akane: Lo siento no les vi, solo vi que la puerta estaba cerrada ya me iba para mi casa
Ukyo: Ven un rato saludas y te vas, si
Akane: De acuerdo, hay voy
Llegue y allí estaba Ukyo, Ryu, Kuno, Shampoo y Sinosuke, los salude casi a todos obviando por supuesto a Kuno que creo por no saludarle ya se daba con la pared, conversamos un rato y me despedí como salude ya que tarde me vendría a ver Akari a mi cas para conversar de lo ocurrido.
Alrededor de las 9:30 llego mí querida amiga Akari, saludo a mi madre y hermana, fuimos para mi habitación a conversar y nos sentamos
Akari: Que paso ayer
Akane: Nada solo que termine con Ranma
Akari: Y por que?
Akane: Por que se porto mal
Akari: Que sucedió?
Akane: Me evadió todo el día como que si yo no existiera para el
Akari: Que pena amiga, pero sabes que yo te lo dije pero como tú dijiste eres mi amiga y debes apoyarme, lo hice pero bueno que término sin que tú te hayas enamorado ya que hubieras sufrido
Akane: En eso tienes razón, creo que solo fue una ilusión del corazón y nada más que eso
Entonces Akari se despido ya que su madre la estaba esperando en su casa y no debía demorarse.
Continuara…
Att: Saomin
8. CAPITULO 8: NUEVA AMISTAD
CAPITULO 8: NUEVA AMISTAD
El día lunes pasó como de costumbre las primeras horas investigación el licenciado hablando de algo y yo perdida en mi mundo como siempre.
Luego la hora de ecología un poco más interesante sobre algunos trabajos y proyectos, y adelantando las clases, pasó rápido la hora y llego microbiología.
El licenciado nos enseño hacer pruebas microbiológicas para cualquier alimento, nos enseño un poco más del laboratorio y cuando estábamos en el salón de instrumento con un equipo pasó algo extraño ya que mi licenciado se acerco a mi amiga Sayuri y le preguntó si Kuno algo, no alcance a oír luego el licenciado dijo:
Licenciado: Por favor señor salga desde que ingreso le he visto que esta masticando chicle, y he esperado que lo bote pero nada, así que por favor salga
Kuno: Pero licenciado "se tragó el chicle" ya no tengo nada
Licenciado: Pero lo vi y hasta le pregunte a su compañera, además no se hubiera tragado el chicle si no lo hubiera tenido
Kuno: Pero ya no lo tengo
Licenciado: Por favor salga señor y no me haga repetir
Kuno: De acuerdo
Y salí del laboratorio sin más ni más, salimos de allí y fuimos a nuestros respectivos lugares y como el licenciado dijo vaya a dejar sus cosas salimos y cuando entre me encontré con Sayuri que decía a Akari:
Sayuri: Kuno me culpó por que el licenciado lo sacó
Akari: Que mal así no se comporta un caballero, cual pando a una dama
Sayuri: Si y yo le dije a mi no me metas en tus cosas, yo no tuve la culpa que estuvieras comiendo
Akari: Lo se y que mas te dijo
Sayuri: Solo eso y se fue
Entonces allí me daba ganas de salir y decirle que repita eso en frente mío a ver si lo dejaba hacerlo otra vez, pero cuando me di cuenta el ya se había ido.
Pasó eso y salimos más antes que todos los grupos, y como siempre fui con mis amigas a la parada del bus he íbamos conversando de:
Akari: Y que crees de Kodachi
Akane: No se pero me da mala espina
Akari: Yo pienso lo mismo tiene algo que no me cae
Akane: Yo también creo lo mismo
Akari: Y que piensas de lo ocurrido con Kuno
Akane: Que hizo mal al culparle a Sayuri de gana, si ella no hizo nada
Akari: Bueno yo pienso lo mismo
Bueno llegamos y me despedí de mi amiga, espere un momento y salió mi hermana claro nos fuimos con un amigo de ella conversando iban ellos y justo en la otra cuadro me encontré con mi amigo Belenus creo que iba pensando en algo y no me vio pero le pregunte:
Akane: Que haces por aquí
Belenus: Nada si recién salgo del laboratorio y tú
Akane: Yo ya iba para mi casa
Belenus: A por cierto el licenciado esta recogiendo el informe del otro día
Akane: Gracias
Y salí corriendo, sin percatarme que mi madre había ido en ver a mi hermana, la salude y fui corriendo a presentar mi informe cuando llegué allí estaban Ranko y Danny, llegue y les pregunte lo del informe:
Ranko: Tranquila Akane yo presente tu informe y sacaste 9
Akane: Y por que
Ranko: Es que nos faltaba unos porcentajes
Akane: Y tu Danny cuando sacaste?
Danny: Yo no presente el informe por que no lo hice
Akane: Que mal, pero bueno ya se van
Danny y Ranko: Si
Ranko: A por favor Akane préstame las copias del deber de Matemáticas
Akane: Si te espero afuera en la copiadora
Ranko: De acuerdo allí nos vemos
Yo salí y allí estaba mi madre, mi hermana y su amigo esperándome, yo le comente todo a mi madre y le presente a mis amigas.
Al día siguiente en las primeras horas pasaron rápido, cuando llegamos a microbiología todos los que no entregaron el informe "claro yo no pero mis amigos si" le dijimos al licenciado si podrían presentarle ya que como salimos más antes no le oímos, el respondió que si pero que iba a calificarle sobre 5 y nada más.
Bueno solo recogió al grupo 1 "ósea el mío" y al grupo 2, y como de casualidad no le habían presentado "mi querida amiga, y mi ex - novio" no les recogió, saliendo del edificio todavía le seguían rogando y por bueno les cogió calificándole también sobre 5, yo también presente mi informe aunque yo ya tenia la nota pero mejor percatarse y ya.
Salimos y fuimos a la hora de cultura física, corrimos y el licenciado dijo:
Licenciado: Señoritas no se fueron de paseo
Akane, Akari y Yuka: No licenciado pero si corrimos, no nos vio
Licenciado: Si las vi y por eso lo dijo, bueno quien llego primera
Akane: Yo licenciado Akane Tendo
Akari y Yuka: Y nosotras en segundo iguales
Entonces nos fuimos a sentar en las gradas, hasta que acabara con todo el curso, y nos dijo subamos en la otra cancha a que juegue futbol y básquet, claro los chicos ya habían pedido la pelota de futbol y entonces me puse a jugar y justo ella también iba a jugar Kodachi y como justo "su gran amigo" no había venido la pasó casi sola y solo casi por que Ranma tiraba baba por ella en todas las horas.
Bueno empezó el juego y me tocó escoger a mi Akari sugirió a mi amigo André que la escogiera pero ya era tarde el ya había escogido, y me tocó a mi bueno yo la escogí aunque mi amiga puso una cara de pocos amigos, jugamos yo no de tan buen animo pero allí la daba acabo el partido y ella dijo:
Kodachi: Adiós chicas
Nadie creo le presto atención, y ella se fue y por otro lado yo me fui con mis amigas, conversando de cómo ella se portaba sin mas comentarios llegamos a la estación y nos despedimos dejándome a esperar como siempre a mi hermana.
El día miércoles me tocó computación y de milagro llegué temprano ya que no había ido con Ryoga por que lo fui abandonando, acabo la clase y salí corriendo en dirección de mi aula ya que me tocaba prueba de ecología, llegue y el profeso empezó a repartir las hijas yo lo hice pensé un rato y viendo como Mousse entregaba la hoja pensaba en ir y no ir cuando vi que André también iba a entregar yo me levante y lo entregue salí y nos pusimos a conversar de la prueba cuando después de un momento mi amiga Akari bajaba con Sayuri también peleando por la prueba pasó esas horas y llegó medio ambiente, no lo tuve por que la licenciada no vino, esperamos y luego llego la licenciada de Química acabé molida con la licenciada y de cómo de costumbre fui a ver a mi hermana. A la tarde fui a un centro de computó y mi hermana a ver a su novio, salí de allí y me tope con Méril lo llame para conversar y salí diciendo
Méril: Hola como estas?
Akane: Yo bien y tu que te cuentas?
Méril: Casi lo mismo y tú has visto a alguien del colegio
Akane: No solo a algunos licenciados y tú?
Méril: Yo solo al licenciado de física que les daba a ustedes que de casualidad llego acá
Akane: Aaaaahhhhh!
Méril: Y tu por cía caso no has visto a unas compañeras tuyas
Akane: No a nadie y tú
Méril: Yo tampoco
Akane: Que mal, y por que preguntas?
Méril: Es que ella eran muy amigas mías, y desde el paseo no las volví a ver claro solo a una
Akane: Que mal pero y por que?
Méril: Es que ella me dijo que se iba a casar
Akane: En serio dijo eso, y yo ni enterada
Méril: En serio y que tal de tu vida
Akane: Allí vamos y tu que?
Méril: Yo he estado viajando, de aquí para allá con la mujer de mi padre, ya que no me pueden dejar solo por las locuras que cometí
Akane: Y que es lo que hiciste si se puede preguntar?
Méril: Solo locuras, ya que cuando estuve en Osaka me escapaba de la casa de mi padre , y como veían mal a los de acá, y te hacían consumir aunque no querías y lo peor de todo eso fue solo pro una mujer que me rompió el corazón
Akane: Y quien fue la que te rompió el corazón, si se puede preguntar claro?
Méril: Fue una compañera tuya fue Arfil, ella me ilusiono, y luego cuando ya no le servía me boto, aparte de eso me rompió el corazón por que yo de ella estaba enamorada
Akane: Que mal por ti nunca me imagine que sería así y que más pasó
Méril: Yo seguí cayendo más y más, con decirte que pelee con mi madre, mi padre y hasta con mi abuela, llegué a destruirme tanto que un día mescle de todo un poco y cuando desperté yo estaba en un hospital en la camilla de cirugía en la mitad de unas personas de blanco, me dio medio y me dijeron que había muerto por unos segundos y que luego volví,
Akane: Esa es la segunda oportunidad que te da la vida
Méril: Si yo también lo pensé y pedí perdón a mi madre, a mi padre y con mi abuela ya no me llevó
Akane: Que mal
Méril: Sin decirte que quinto y sexto curso fueron los peores
Akane: Por que?
Méril: Primero por que mi vida dio un giro extremo de 360 grados y solo por cambiar hacer lo que no era, por que yo y Sergus nos cambiamos
Akane: Y por que lo hicieron
Méril: Por que yo le pedí que me enseñara hacer como el y no lo logre, por que viendo como el se comportaba con las chicas salió de nuevo como yo era
Akane: Y como eras?
Méril: Gentil con las damas y me llevaba muy bien con ellas, en cambio él las conquistaba y andaba con una y con otra sin importarle nada hasta cuando tenia novia andaba con dos más, y ellas así lo aceptaban
Akane: Que tontas y que ciegas, como pudieron aceptar que las traten así, ese es una mala persona de andar jugando con una y con otra
Méril: Hasta te apuesto que todavía lo siguen llamando
Akane: Creo que si, bueno me tengo que ir ya que es muy tarde
Méril: De acuerdo y no te olvides de mi si
Akane: De acuerdo y cuando pueda yo te vengo a ver
Méril: Si adiós
Akane: Adiós
Y de allí salí corriendo para mi casa ya que mi hermana me estaba buscando.
Al día siguiente todas las horas pasó normal solo hubo un pequeño problema la clase de español teníamos dos lecciones, aunque no estuvo duro yo estaba nerviosa ya que no sabía bien la lección, pero justo no me tocó a mi sino a Ryoga y a Ranko yo les ayudaba desde mi puesto un poco sin que la licenciada se diera cuenta, pero la licenciada dijo siéntense que no les calificare esta sino la otra.
Se salvaron de milagro, y yo di de voluntaria otra lección, pasaron las demás horas y llegó medio ambiente vino la licenciada y nos dio unas hojas para tarea en clase de grupo de a tres todas nuestras amigas ya tenían grupo y solo faltábamos yo y Akari, y los que faltaban no eran buenas opciones eran Ranma, Belenus, Kodachi y Kuno
Yo sin pensarlo dos veces dije ven con nosotras Belenus y lo otros tres hicieron otro grupo salvándome de milagro, acabaron clases más temprano de lo usual y nos fuimos a dar una vuelta con Yamato, Belenus, Akari, Danny, Ranko y yo pasando por donde mi amigo Méril estaba pare para saludar y mis amigos se adelantaron quedándome yo y mis amigas conversamos un rato y decidimos partir y mas arriba nos encontramos con Shampoo y Hikari en una cuadra y en la otra sus respectivos novios Mousse y Daisuke era raro pero siendo pareja no lo parecían para nada, bueno subimos y se fueron despidiendo uno por uno en la parada quedándome yo con Yamato y Belenus en la parada esperando a mi hermana y comenzando a conversar dijeron:
Akane: Belenus a ti quien te gusta en el curso
Belenus: A mi no puedo decirlo por que sino se enojaría
Akane: Y por que?
Belenus: Por que si y a ti quien te gusta
Akane: A mi nadie
Belenus: Segura
Akane: Si
Belenus: Y que pasó con Ranma, por que el dijo que se te declararía
Akane: Nada solo le dije que no, por que pensaba que era una persona y no lo fue así
Belenus: Que mal yo pensaba que si usted le gustaba y el se declaraba, usted iba a aceptar
Akane: Pues no, el me dijo eso y yo le dije que no
Belenus: Que mal, pero bueno ya desechaste dos y cual será el tercero, capaz que el tercero es Ryoga y el es venció
Akane: No se
Belenus: Bueno entonces
Entonces me despedí de Yamato y Belenus, yendo para otro lado cuando desde lejos todavía los veía, y entonces ya me iba ir para mi casa y me topé con Yuka allí esperando a su padre y dijo:
Yuka: Hola Akane, que haces por aquí
Akane: Hola, yo yéndome para mi casa
Yuka: Aaaaahhhhh! Y que más
Akane: No nada
Yuka: Por cierto el otro día estábamos conversando con Kuno y yo le iba preguntando sobre ti
Akane: Sobre mí?
Yuka: Si sobre por que le gustas
Akane: Aaaaahhhhh!
Yuka: Si y me dijo que tu le gustas por los buenos sentimientos que tienes, eres sencilla y muy amable pero que a el también le gusta la chica nueva Kodachi
Akane: Que mal no se que le ve a ella
Yuka: Ni yo lo se, ya que parece escoba con patas
Akane: Si es cierto
Yuka: Pero yo si se de quien podrías confiar es de Ryoga el si te quiere y hasta que muere por ti
Akane: Que mal yo solo lo veo como un amigo y nada más
Yuka: Pero debes considerarlo ya que el si te quiere y hasta es fiel por que el me conto que su novia lo engaño ya que el lo había visto besándose con otro
Akane: Que mal pobrecito
Yuka: Y que piensas
Akane: Yo que estoy más hecho nudos ya que primero Kuno, luego Ranma, después Belenus y por último Ryoga, que mundo de locos el mío no crees
Yuka: Estoy de acuerdo contigo y que vas hacer
Akane: No se
Yuka: Creo que deberías tener novio a fuera ya que así te libras de problema y malos ratos en el curso
Akane: Yo opino lo mismo y creo que eso lo voy a hacer
Bueno nos despedimos y me fui a ver a mi hermana para ira la casa.
A la día viernes las primeras horas de microbiología salimos al laboratorio para realizar limpieza del equipo, salimos de allí a horas de biología hicimos lo de siempre y a las ultimas horas química para la exposición del tema de electromagnetismo me fue bien y salimos antes que los demás, nos fuimos despidiendo uno por uno y llegando a la parada nos topamos con Kuno el fue con nosotros, y al llegar nos pusimos a conversar de "que los hombres son los mismos" ellos decían que no y yo decía que si por que ellos no sufren y nosotros sí, pero ellos decían que era mejor cortarnos ellos y no nosotras y cuando seguía el tema su bus ya se iba se despidieron diciéndome esto no queda así y el lunes hablamos.
Llegué a mi casa y con la novedad de que mi madre me escribió en clases de natación empezando el sábado a las 7: 00 am, paso el día y llegó sábado para el entrenamiento me fue casi bien pero de que aprendo lo hago y ya
Continuara…
Espero que les haya gustado estos dos capítulos pidiendo disculpas por que, se me hizo un poco duro publicarlos ahora pero aquí tienen y que se diviertan y por cierto que tengan buena semana
Att: Saomin
9. CAPITULO 9: ¿MAGIA?
CAPITULO 9: ¿MAGIA?
En fin el día lunes pasó raro ya que de nuevo me volví a llevar con Kuno no se por que fuimos iguales a la parada a dejar a mi amiga Akari.
Y conversamos de cosas triviales claro era de esperarse que mi amiga Akari no estaba muy cómoda con la salida pero quien ni yo lo estaba y todo empezó ya que ese día a la noche soñé cosas muy extrañas como una espada y otras cosa.
El día martes la pace un poco intranquila todas las horas de clases hasta la hora de cultura física que le dije a Akari que llamara un momento a Kuno ella sin vergüenza lo llamo y de la nada apareció cuando le empecé a preguntar sobre mi sueño, el me contestaba que eso es algunas cosas raras que no entendía.
Igualmente se fue igual de nosotros a la parada de Akari, y seguíamos conversando del mismo tema que parecía tenerme muy encantada era la Magia.
Nos veíamos a la salida a veces cuando se iba a dejar a Kodachi a su casa, y paso al día miércoles las cosas parecía que se me complicaban un poco más.
En todas las horas pasaba distraídamente, por alguna razón aparente que no encontraba en mi cabeza cuando de repente me hizo aterrizar de pronto en la tierra por que se abrió la puerta de la nada.
Allí observe algo raro, y era un fantasma de color blanco.
A la tarde que salí me encontré con mi amigo Méril y me dijo:
Akane: Hola como estas pensaba que ya no te iba a ver otra vez
Méril: Yo también pensó lo mismo
Akane: Pero y que mas te cuentas
Méril: Nada de nuevo
Akane: Bueno viendo que tú eres mi amigo te preguntare algo
Méril: Que es
Akane: Pero me vas a creer loca
Méril: No, no lo hare ya dime
Akane: ¿Crees en los fantasmas?
Méril: ¿Por qué me preguntas eso?
Akane: Por que los vi en una clase que abrieron la puerta
Méril: Pues, si
Akane: ¿Por que?
Méril: Pero tu no te burlas de mí
Akane: Bueno
Méril: Mi mamá me decía que cuando era niño me la pasaba sentado en el horno de leña viendo la pared negra, y que me enojaba si me quitaban
Akane: ¿Y por que?
Méril: No lo se tal vez por que me bautizaron de muy grande
Akane: Pero eso es raro
Méril: Si y eso es poco para lo que ha pasado
Akane: ¿Cómo que?
Méril: Como cuando contaba una historia en alguna casa si contaba pasaba algo feo y si no acababa de contarla sucedían cosas raras.
Akane: ¿Porqué?
Méril: No lo se o tal vez si
Akane: ¿Cómo?
Méril: Es que algunas veces mi madre me ha dicho que parezco de otra época por las costumbres que tengo
Akane: Es extraño
Méril: ¿Qué?
Akane: A mi también me han dicho que soy rara, como que si no fuera de esta época
Méril: Wuuuuuuuuaaaahhhhhhh!
Akane: Lo mismo digo
Méril: Creo que es tarde
Akane: Si bueno nos vemos otro día
Méril: De acuerdo y no te olvides de mí
Y me fui de allí, con muchos pensamientos en la cabeza sobre todo de los fantasmas.
Continuara…
10. CAPITULO 10: MI VIDA PASADA
CAPITULO 10: MI VIDA PASADA
Ahora resulta que poseo magia y sin saberlo ya tengo una enemiga del pasado por que no se como sucedió tampoco solo se que no se nada.
Quien diría que poco a poco el destino se presentaba ante mis ojos como se me lo estaba haciendo ahora, claro que cuento con muchas personas que me apoyan, pero como será mi vida de ahora en adelante no lo se.
En la noche de ese día se me vinieron a la mente imágenes que antes no las había visto, con personas que me conocían yo lo sentía pero de que yo las conociera no, conversaciones y una en la que me encontraba en una habitación blanca, y todo allí era blanco me levante de la cama que allí se encontraba y me di cuenta que estaba amarrada a una parte de la cama cuando yo tratando de zafarme, se abrió de repente la puerta y entró un hombre que me cuando lo observe me recorrió un escalofrió horrible se me acerco y me dijo:
¿Me vas a dar lo que deseo desde hace tiempo?
De mi boca salió: No, no lo haré nunca lo conseguirás
¿Me lo dices enserio querida?
¿Claro, esperabas algo más? Lo escupí como veneno de mi boca
Cuando se acerco a mi me agarro fuerte mente el brazo acercándome a el cogió mi mano llamó a uno de sus cómplices que le trajeron una daga color blanco en el mango con una hoja filosa que brillaba en color metálico me la acerco y cuando iba a cortarme… Me desperté asustada viendo que me encontraba en mi habitación y percatándome que mi mano no estuviera sujeta a mi cama, me levante y fui a tomar un poco de aire al patio.
Pero de repente sentí que no debía salir por que algo me iba a pasar, cuando de la nada una sombra se encontraba otra mío trate de correr me cogió y cuando menos lo esperaba alguien apareció en mi auxilio pero no lo vi acabando con la sombra la persona que me había salvado también se había ido.
Y yo que pensaba que mi vida ya no podía ponerse mucho peor, me volví a costar tratando de conciliar el sueño cuando cerré los ojos ya había amanecido y me tocaba ir a la u.
Llegue con las justas a la primera hora pero me sentía tan cansada y me daba mucho sueño, tratando de mantener los ojos abrieron mis amigos y amigas me observaban preguntándose interiormente que me pasaba pero no les podía decir nada.
Hasta mi ex amigo me observaba así, yo aparentando estar bien volví a levantarme de la nada.
Pasaban las horas poco a poco como que para mí el tiempo estaba deteniéndose, pero no lo di a notar así paso para mi media semana.
Al jueves de la misma semana tenia que ir a realizar compras al mercado por que mi madre me lo había mandado, y justo pase por la casa de mi amigo Méril, asiendo tiempo me acerque a su casa y lo llame salió su madre y me dijo que ya salía.
Me dijo: Hola
Hola
¿Como estas?
¿Aquí trabajando duro y tu que tal?
Más o menos tengo sueños de lo más raros, no puedo dormir y pensando mucho en eso no me concentro en la u
Le observe la cara de susto y me dijo: ¿Por que?
No se si debía decírselo pero lo sentía muy cercano a mí y no podía mentirle así que le comente: ¿Es que tengo un sueño en común estos días?
¿Cuál?
Estoy en una habitación blanca cuando de repente se abre la puerta y un hombre que no logro ver su rostro se me acerca y me comenta que debo entregarle algo que el a esperado mucho, yo me niego y el se me acerca coge una daga y trata de….
¿De qué?
No se de que por que cuando lo va hacer me despierto, y después trato de salir de mi casa al patio cuando una sombra negra me persigue llega alguien y me defiende
¿Pero quien es?
No lo sé
Pensándolo bien, ya no le comente algo más por que lo veía a él también más preocupado que quien entonces le dije: Tranquilo todo es un sueño y no te preocupes nada me pasará; creo que eso lo tranquilizará pensé
Me despedí para ya no involucrarlo más y me fui.
Acabó mi linda semana y llegó el fin de semana, ese fin de semana dormí hasta muy entrada la mañana, me ganaba el sueño pero decidí hacer algo más que eso y empecé a ser las cosas que me faltaban por hacer.
Continuara…
Att: Saomin
11. CAPITULO 11: ENEMIGA
CAPITULO 11: ENEMIGA
Mi nueva semana había comenzado y yo ya con nuevas baterías estaba dispuesta a realizar las cosas que no había hecho por cuando me ganaba el sueño.
Cuando allí empezó mi nueva rutina con mi enemiga, no se porque pero ella tenia algo que no me cuadraba para nada, yo sabia que ella algo ocupaba y mostrándose para todos como una chica que no rompe el plato.
Cuando un día me enteré que el estaba comentado cosas de todas mis amigas justo en la hora de educación física entonces les dije Akari, Ranko, Danny, Yuka, Sayuri:
No se preocupen amigas yo le diré lo que se merece a el por meterse con mis amigas y más que todo tratando de meterle a Kodachi en nuestro grupo no
Akari me dijo: Pero anda diciendo que yo estoy en la mitad de la relación entre Ukyo y Ryu
Pero yo se que es mentira, no te preocupes yo le voy a decir
Y justo hablando del rey de roma se encontraba Kuno en la esquina dejando a Kodachi por donde vivía, entonces yo lo llame:
Entonces en ese día me sentí por primera vez como yendo al matadero siendo yo la res y le dije:
Necesitamos hablar, sobre los rumores que estas diciendo
De que será me dijo
De lo que andas diciendo de nosotras
¿De qué?
De que Akari esta enamorada del novio de Ukyo ósea de Ryu
No, yo no fui y por esta que no fui me dijo
Le creí y dijo que quería hablar conmigo
Me negué y el se marchó
Pero yo sin saberlo tenía una enemiga ya.
La semana seguía con su rutina normal de clases, ingenieros, alumnos, compañeros, amigos y sin olvidar a mis amigas.
Ocurrió algo de lo más extraño habían a Kuno le habían descolado su querida amiga y esta ultima se juntaba con Shampoo y Hikari.
Era raro viéndolo así decidimos con Akari darle una segunda oportunidad y no hubo quien se opusiera mi amigo Ryoga me dijo: Si les vuelve hacer lo mismo yo ya no me meto nos dijo por que el había sido quien nos defendió de Kuno.
El se acercaba más a nosotras pero creo que el tenia algo en mente, no sabia que pero lo traía, y por otra parte mi querida enemiga me trataba de hacer la vida imposible no lo conseguía por que en la mayoría ella perdía sola por su mano, muchas cosas trato de realizar por mal pero el mal siempre regresa por doble y para ella lo hacia así.
Yo no le tomaba en cuenta y en la mayoría de cosas íbamos de par en par ya que ella peleaba por notas no se porque pero lo hacia, yo no tenia problemas pero tenia que defenderme y así empezó nuestra batalla campal, yo por demostrar que ella no era la chica que pensaban todos y ella por su parte tratando de hacerme quedar mal sin ningún motivo además la popular era mi amiga Akari no yo.
Entonces llego el licen de Educación Física a decirnos que era nota el paseo a Arima, y además que contaba como un 50% de la calificación final del semestre, con tremenda noticia ya hacíamos planes para ir para allá la próxima semana.
Continuara…
Att: Saomin
12. CAPITULO 12: PASEO
CAPITULO 12: PASEO
El viaje ya estaba planeado para el día miércoles salida de 7:00 am, llegaríamos a la 11:00 am para realizar la pendiente expedición por Arima.
Con todos emocionados por ir incluyéndome, yo con mis amigas y amigos planeamos para hacer un pequeño picnic al regreso de la expedición.
También íbamos a llevar uno que otro aperitivo para irlo comiendo en el camino, y ya todo lo teníamos solo teníamos que esperar a que fuera miércoles, y empezando la semana no parecía transcurrirla rápido.
Las primeras horas el blablabla del ingeniero, luego ecología interesante con los temas ya que nos tocaba explicación del proyecto que debíamos realizar para nota fin de semestre.
Y las horas de microbiología, con sus temas específicos la pase mucho mejor, pensando como seria el primer viaje de la u, no importaba mucho y mi amiga Akari me dijo:
Akane ven para acá
La mire dudosa y llege a donde ella diciéndole: ¿Qué ocurre?
Te veo demasiado despistada en estos últimos días ¿que te ocurre?
Nada solo que estoy emocionada
No lo creo pero ya toma atención ¡siiiiiiiii!
De acuerdo
Acabo las horas y me fui a mi casa dejándole a mi amiga en la parada en la cual me esperaba mi hermana, la salude y nos fuimos.
Al llegar a mi casa mi madre nos recibió como siempre, al igual que un papá preocupado de todo.
Así pasa martes también vino a mi casa Akari para ir de comprar de los bocadillos que llevaríamos para el día siguiente.
Llegando el miércoles esperado yo me había levantado mas temprano para realizar mi maleta y alistarme, salí unos minutos antes para llegar temprano lo hice y me encontré con uno que otro compañero cuando a lo lejos llegaba mi mejor amiga Akari junto con otras amigas más, las salude y esperando al Licenciado y al autobús.
Diez minutos después llegó el autobús nos subimos y fui sentada con Akari, al igual que mis amigas iban en pares Danny y Ranko, en el asiento de atrás iba Yuka y Sayuri,
No importo del todo y íbamos muy felices en el viaje, cuando llegamos a un pequeño pueblo cerca de Arima, se bajaron unos compañeros a comprar sake, para "ir bien" según ellos, bueno en media hora más llegaríamos nos informo el licenciado.
Tuve una conversación con Kuno este me decía que yo tenia un lobo blanco y una pequeña hada que eran como mis guardianes que me seguían a todos lados sin importar lo que fuera hacer ellos estaban allí, además que había descubierto que en el pequeño bosque que hay en la u habitaba una espada que lo llamaba. No me importaba mucho lo que me comentaba pero era interesante hasta que mis amigas se nos unieron y ellas empezaron a preguntar cambiando de tema el empezó a contar historias de miedo y nada de lógica.
Conversábamos, íbamos escuchando música y nos también íbamos riendo de ocurrencias que todos contaban cuando el licenciado se acerco y dijo; llegamos así que dejen las cosas entro el autobús y den una expedición completa cuando regresemos iremos a comer.
Bajamos emocionados yo iba con mis amigas y Belenus conversando, cuando de la nada todos ya estaban abajo porque tenia una forma de montaña, yo me había quedado con Belenus y Kuno claro el ultimo iba con las maletas de la comida (No le hicimos caso al licenciado y bajamos la comida para hacer el picnic cerca al lago que según allí había), esa bajada era medio rocosa y sin cuidado me caí dos veces liego con la ayuda de Belenus baje sin caerme más, Kuno me quería ayudar pero con las maletas no lo deje acercársele bajamos, le agradecí a Belenus.
El lugar era muy hermoso ya que la laguna tenía el agua muy azul, me encontré con Max y para enojarle le dije:
Gracias por ayudarme a bajar
Me miro raro y me dijo: A la subida yo te ayudo
De acuerdo
Y nos fuimos para un lado de lago que allí había y nos tomamos fotos todos con todos, y como siempre me desafiaban para tirar una piedra que brincara, no lo conseguí y una persona habitante de allí nos dijo, que allí crecían unas algas de lo más verdes que si entraban al lago estas no te dejaban lavar y como si yo ni nadar podía no lo iba hacer.
Cuando a mi se me acerco Kuno y pasando me dijo: No tengas miedo no pasa nada, aunque sientas lo contrario, cuando le iba a preguntar el ya estaba en otro lugar.
Yo me preguntaba que quería decir con eso. Después armamos todo para comer pero no alcanzamos ya que no estuvimos mucho tiempo cuando el licenciado dijo les doy la nota cuando llegue otra vez al autobús, de arriba abajo no había mucha diferencia pero de abajo para arriba desanimaba a cualquiera.
Y con la promesa lo cumplido esta vez Max me ayudo a subir todo ese largo camino, hice una cuantas paradas viendo que el lago de arriba para abajo tenia una forma rara, me comentaban que esa laguna antes había sido un cráter de algún volcán que en algún pasado se extinguió.
Logramos subir con la lengua afuera la mayoría de mis compañeros hasta los que estaban con sus copitas encima subieron de rodillas, cominos arriba con mis amigas y amigos, no hubo complicación en el viaje, regresamos a la u y acabo el paseo.
Continuara…
Att: Saomin
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| fanfiction |
The Relli River is a small Himalayan river in the Indian states of Sikkim and West Bengal, flowing near Kalimpong. The source of the Relli lies in between the Alagara - Lava forest range at an elevation of known as Tiffin Dara and ends at 800 ft, confluence with the teesta . The river runs less than from central Kalimpong, separated by Deolo Hill. The main tributary are Khani River and Pala River and flows into the Teesta River about to the south of central Kalimpong.
The northerly slopes along the Relli in Upper Echhay Sherpagaon, in Sikkim, are home to a cluster of some 50 Sherpa households. The village of Relli is located on its banks downriver from Kalimpong, connected to the city by road and trails.
Tourism
Rinchingpong, a tourist area situated in the northern part of Kalimpong, overlooks the Relli. The Relli is a popular weekend destination among Kalimpong locals for attractions including local cuisine, picnicking spots, boating, and recreational fishing. A Wayside Inn managed by the West Bengal Tourism Department is located nearby.
A fair is held annually at the Relli on the Makar Sankranti holiday January 14.
Historical sites
Gompas, or monasteries, lie near the river, with an overlook at Jelep La Viewpoint.
Bhutan House, in West Bengal, also overlooks the Relli River below a deep valley.
References
Category:Rivers of Sikkim
Category:Rivers of West Bengal
Category:Rivers of India | wikipedia |
compaction can be roughly defined as the density relaxation of a loosely packed system of many grains under mechanical tapping or vibration @xcite .
both the time relaxation of the system and the steady state eventually reached in the long time limit , exhibit interesting properties , and have received a lot of attention during the last years .
the description of this phenomenon goes well beyond the scope of equilibrium statistical physics and even of usual non - equilibrium theories .
the time evolution of the system corresponds to a consecutive series of mechanically stable states in which all the particles are at rest , at least at a macroscopic level of description .
therefore , the system is not thermal , in the sense that the fluctuations of the particles around their average positions play no role in characterizing the state of the system .
in fact , in the description of the phenomenology of compaction , time is usually measured in number of taps that , of course , has nothing to do with the real motion of the particles .
edwards and collaborators @xcite formulated some years ago a theory providing a thermodynamic - like description of granular systems under certain circumstances .
the main hypothesis of the theory is that for externally perturbed powders in a steady state , all the mechanically stable ( metastable ) configurations of a granular assembly occupying the same volume have the same probability .
therefore , it is assumed that the volume plays here a role analogous to that of the energy in usual thermal systems .
the parameter conjugated to the volume , similar to the thermal temperature , was named ` compactivity ' . in principle
, the conditions under which the theory should apply are fulfilled in the compaction process .
for this reason , the predictions of the edwards theory have been compared with results obtained in experiments @xcite , numerical simulations @xcite , and simple models @xcite of compaction .
although in general a fairly good agreement is claimed , at least in the limit of weak tapping , an analysis of the situation shows that there are many fundamental aspects that can not be considered as reasonably well established .
a few of them will be addressed , although not solved with generality , here : 1 .
given that many of the experimental determinations of the compactivity are based in the measurements of density fluctuations , special care must be given to differentiate between fluctuations in the number of particles in a system of constant volume , fluctuations of volume in a system with a given number of particles , and fluctuations of density in a system whose volume and number of particle change in time .
all these fluctuations are not equivalent , in principle @xcite .
some authors have reformulated the thermodynamic theory of powders using the ( configurational ) energy as the variable characterizing the macroscopic state of the system and an _ effective _ temperature , i.e. they use a formulation much closer to ordinary statistical physics .
the equivalence or relationship between both formulations does not seem to be clear , although some ideas have been presented @xcite .
for instance , are the compactivity and the effective temperature independent variables or there is a relationship between them ?
the thermodynamic theory of powders was formulated for complete systems , and not as a local theory . in this context
, it could be thought that a column of tapped granular matter in the steady state is characterized by a unique compactivity , aside from the boundary layers , even though the system is inhomogeneous .
another possibility is to consider that the system can be divided into horizontal layers , each of them having a different compactivity ( or effective temperature ) .
in fact , this local version of the theory has been often used in describing experiments and particle simulations . which are the physical meaning and the implications of a gradient of the compactivity , or effective temperature , are also open questions .
another important aspect of compaction refers to the response to an external perturbation , e.g. a change of the vibration intensity .
it happens that many of the peculiar dynamic behaviors exhibited by granular materials under tapping are similar to those shown by conventional structural glasses .
for instance , both kind of systems present slow relaxation , annealing properties , and hysteresis effects . a necessary first step in order to understand these issues
is to study the response of the system to a small perturbation of the conditions defining its steady state ( linear response ) .
of course , the obvious external parameter to vary in the compaction experiment is the vibration intensity characterizing the tapping process , and the quantity whose response to analyze is the volume of the system . in the process
, all the system , with a constant number of particles , is considered . an additional reason to study linear response in granular systems ,
is that fluctuation - dissipation relations obtained in molecular systems in the context of linear response theory , are being used to test the thermodynamic theory of granular matter @xcite .
nevertheless , given the non thermal character of granular systems , even if the validity of the thermodynamic theory as proposed by edwards is assumed , there is no reason _ a priori _ to expect the fluctuation - dissipation relations to apply .
the aim here is to investigate the above mentioned issues by means of a very simple model for compaction @xcite .
the model dynamics is defined in such a way that it conserves the number of particles in the system , i.e. it is a closed system .
its volume changes due to the creation and destruction of empty sites or holes in the lattice over which the system is defined .
the model is consistent with the edwards thermodynamic theory , although of course it is far away of any physically feasible system . nevertheless , it is interesting to qualitatively compare its predictions with the experimental results and with the behavior obtained by means of numerical simulation ( monte carlo and molecular dynamics ) of much more sophisticated and realistic models .
the paper is organized as follows . in the next section the model to be used in the following
is formulated as a markov process , and some of its properties derived in ref .
@xcite are shortly summarized .
in particular , the steady distribution characterizing the long time limit of compaction is reminded and the edwards compactivity identified . from the steady distribution ,
explicit expressions for some average properties are easily derived .
special attention is given to the relationship between the second moment of the volume fluctuations and the average volume , since it has been used to compute the compactivity in experiments .
the detailed shape of the volume fluctuations is analyzed in sec .
[ s3 ] , where it is predicted to be gaussian in the limit of a large system , i.e. with a large enough number of particles .
this is verified by means of monte carlo simulations of the model equations .
the above model predictions are compared with experimental findings and simulation results for more realistic models in sec .
[ s4 ] . special emphasis is put on the discussion of the boundary conditions , e.g. open versus closed systems ,
the local or global character of the measurements , and the concept of effective temperature and its relationship with the compactivity . in sec .
[ s5 ] , the linear response of the model to a change in the tapping intensity is investigated .
the volume response function is computed by monte carlo simulation , and a stretched exponential decay is found in the relevant part of the relaxation . finally , in the last section , a short summary and some additional discussions are presented .
consider a one - dimensional lattice having @xmath0 particles and a variable number of sites .
the dynamics of the system is modeled trying to capture , in a very simplified way , the relevant features of compaction processes in tapped granular systems @xcite .
then , a markov process is introduced with the elementary transitions given in table [ table1 ] , where the circles represent particles and the crosses empty sites or holes , and @xmath1 and @xmath2 are arbitrary positive real parameters @xcite .
time is measured in some arbitrary units proportional to the number of taps . only those particles involved and/or conditioning each of the transitions are represented .
it is worth to point out that the equality of the rates for diffusion and hole annihilation follows from the rational of the model @xcite .
.[table1 ] elementary transitions and their transition rates for the lattice model . particles and holes
are represented by circles and crosses , respectively . [ cols="<,^,^,^",options="header " , ] the transitions in table [ table1 ] define the modeled effective dynamics connecting metastable configurations in a system being tapped .
these configurations are characterized by the property that all the holes are isolated , i.e. surrounded by two particles and , in order to enumerate them , a set of variables @xmath3 is introduced . by definition
, the variable @xmath4 takes the value @xmath5 if there is a hole to its right , separating it from particle @xmath6 . on the other hand , @xmath7 if the site to the right of particle @xmath8 is occupied by particle @xmath6 .
it is assumed that there can not be a hole either to the left of particle @xmath9 or to the right of particle @xmath0 .
note that this feature is preserved by the dynamical events allowed in the model .
moreover , the dynamics does not change the relative order of the particles in the lattice and , therefore , the identity of the particles plays no role in describing the configurations of the system .
more details , as well as a discussion of the physical motivation of the model , are given in ref .
@xcite .
introduce @xmath10 as denoting the configuration obtained from @xmath11 by modifying the value of @xmath4 , keeping the same all the other variables , i.e. , @xmath12 therefore , @xmath10 differs from @xmath11 only in the status , empty or occupied , of the site to the right of particle @xmath8 .
the probability transition rates @xmath13 from configuration @xmath11 to configuration @xmath14 defining the markov process and represented in table [ table1 ] , can be written in an analytical form as : 1
. _ diffusion _ @xmath15,\ ] ] 2 .
_ hole annihilation _
@xmath16 3 . _ hole creation _
@xmath17 this stochastic process can be proven to be irreducible .
in addition , its ( unique ) steady probability distribution @xmath18 verifies the detailed balance condition and is given by @xcite @xmath19 where @xmath20 and @xmath21 is the total number of holes of the lattice configuration @xmath11 .
finally , @xmath22 is the ` partition function ' following from the normalization condition , @xmath23 with @xmath24 being the number of metastable configurations having exactly @xmath25 holes . a standard combinatorial reasoning yields @xmath26 from eqs .
( [ 2.7 ] ) and ( [ 2.8 ] ) it follows that @xmath27 that for large @xmath28 implies @xmath29 to be more precise , the required limit leading from eq .
( [ 2.9 ] ) to eq .
( [ 2.10 ] ) is @xmath30 and @xmath31 , since if @xmath32 is of the same order as @xmath30 , the correct limiting form for the partition function is @xmath33 in the following , attention will be restricted to systems having a number of particles such that eq .
( [ 2.10 ] ) applies .
once @xmath34 is known in a analytical form , it is a simple task to compute average values characterizing the macroscopic state of the system . also , the probability distribution for the number of holes in the steady state , @xmath35 , is easily derived , @xmath36 in the second equality above , @xmath37 is the kronecker delta .
the associated moment generating function @xcite is @xmath38 thus the cumulant generating function @xcite of the variable @xmath25 is @xmath39 where use has been made of eq .
( [ 2.10 ] ) . from this expression , the steady average of the number of holes @xmath40 and its variance @xmath41
are directly computed , @xmath42_{k=0 } = \frac{n}{\gamma+1},\ ] ] @xmath43_{k=0 } = \frac{n \gamma}{(\gamma+1)^{2}}.\ ] ] from eq .
( [ 2.15 ] ) , it is seen that the steady state gets more compact as @xmath32 increases . on the other hand
, it is found that the relaxation of the system becomes slower @xcite .
this is consistent with the physical interpretation of the model , where @xmath44 is understood to play a role analogous to the tapping intensity in granular experiments @xcite .
now , in order to get a canonical distribution of the form proposed by edwards and coworkers @xcite , the ` compactivity ' @xmath45 is defined by @xmath46 so the steady distribution in eq .
( [ 2.5 ] ) can be rewritten as @xmath47 in terms of the compactivity , eqs .
( [ 2.15 ] ) and ( [ 2.16 ] ) take the form @xmath48 respectively .
combination of the above two equations gives @xmath49 showing the typical @xmath50 dependence of the relative fluctuations of an extensive quantity on the number of particles of the system .
since @xmath1 and @xmath2 can take arbitrary positive real values , it is clear from the definition of @xmath32 given below eq .
( [ 2.5 ] ) , that its range of variation is @xmath51 .
consequently , @xmath45 can take any real value , i.e. @xmath52 . more precisely , when @xmath32 is increased monotonically from @xmath53 to @xmath54 , the compactivity @xmath45 decreases from @xmath55 to @xmath56 ( for @xmath57 ) , then jumping to @xmath58 ( @xmath59 ) and decreasing again towards @xmath60 .
then , there is a parameter region , namely @xmath61 , or @xmath62 , in which negative values of the compactivity occur . with reference to the dynamics of the model ,
this happens when the transition rate for the hole creation processes is larger than that for hole annihilation processes .
equation ( [ 2.18 ] ) lead to the relation @xmath63 and considering a series of experiments with the same number of particles in which the average number of holes is changed between @xmath64 and @xmath65 , @xmath66 here @xmath67 and @xmath68 are the initial and final values of the compactivity , respectively . the generalization of this equation for three - dimensional systems in the context of the edwards theory
was first noted by nowak et al .
@xcite , and used in ref .
@xcite to obtain the compactivity as a function of the volume fraction from experimental data of a system submitted to pulses .
more will be said about this in sec .
the length @xmath69 of the system , measured in units of the distance between consecutive sites , is @xmath70 in the steady state , the average value of @xmath69 is @xmath71 it is also convenient to introduce the length per particle @xmath72 , so @xmath73 , or @xmath74 this can be transformed into a relationship between @xmath45 and @xmath75 by means of eq .
( [ 2.17 ] ) , @xmath76 it is seen that @xmath77 is a monotonically decreasing function of @xmath78 , vanishing for @xmath79 that , of course , corresponds to @xmath80 .
therefore , it is concluded that @xmath81 for @xmath82 , while @xmath83 for @xmath84 .
negative compactivities correspond to the loosest configurations and have also been obtained in other models of compaction @xcite .
the inverse of the compactivity does not vanish in the limit of the loosest possible configuration , but it tends to @xmath85 .
obviously , the existence of negative values of the compactivity does not violate any general physical principle and does not imply any instability of the steady state .
they are a consequence of the fact that the number of configurations @xmath24 is not a monotonic increasing function of the length of the system ( or @xmath25 ) , but it exhibits a maximum , going afterwards to unity for the maximum value of the number of holes , @xmath86 .
equivalently , the possibility of steady states with @xmath83 is directly related with the length @xmath69 of the system having a finite upper bound . from a formal point of view , the situation is similar to the existence of negative temperatures in systems of nuclear spins in certain paramagnetic crystals placed in an external magnetic field . from eq .
( [ 2.16 ] ) , the variance of the total length can be written as @xmath87 in order to get a more detailed information of the length fluctuations , introduce the stochastic variable @xmath88 by @xmath89 the moment generating function of @xmath88 is @xmath90_{q= k/\sigma_{n_{h}}},\end{aligned}\ ] ] where @xmath91 was defined in eq .
( [ 2.13 ] ) . then , using eqs.([2.14])-([2.16 ] ) , @xmath92 \right\ } - n \ln \frac{1+\gamma}{\gamma},\ ] ] that in the limit @xmath93 reduces to @xmath94 this proves that , for a large enough number of particles , the stochastic variable @xmath88 obeys a gaussian distribution with vanishing average value and unit variance .
formally , this is equivalent to saying that the probability density @xmath95 for the variable @xmath96 is also gaussian with average @xmath97 and standard deviation @xmath98 .
a numerical check of the gaussian character of @xmath88 for large values of @xmath28 is presented in fig .
[ fig1 ] , where monte carlo simulation results for the steady probability distribution @xmath99 are shown for several values of @xmath32 .
the number of particles used is @xmath100 .
the solid line is the gaussian distribution of zero average and unit variance .
an excellent agreement is observed , even for rather small values of @xmath99 . of the dimensionless variable @xmath88 defined in eq .
the symbols are monte carlo simulation results obtained with different values of @xmath32 , as indicated in the insert .
the solid line is the gaussian theoretical prediction .
[ fig1 ] ] in order to compare the results derived for the model in this section with some experimental findings , it is convenient to consider also the volume fraction @xmath101 defined as @xmath102 . as a consequence of @xmath103 being proportional to @xmath50 , the probability density for @xmath101 , @xmath104 is also gaussian , again in the limit of large @xmath28 , with average and variance given by @xmath105 and @xmath106^{1/2}}{n^{1/2 } \langle l \rangle^{(s)2}}\ , , \ ] ] respectively .
thus eq .
( [ 3.4 ] ) is , for large @xmath28 , equivalent to @xmath107
of course , given the simplicity of the model discussed here and its one - dimensional character , it can not be expected to quantitatively reproduce the experimental and simulation results . nevertheless , it is interesting and illuminating to qualitatively analyze those results in the light of the model predictions .
the first experimental investigation of the volume fluctuations in the steady state of a tapped granular medium seems to be the one reported in ref . @xcite .
more exactly , the property considered in that work is the density in a given region , located at a certain height of the system .
then , the volume is kept constant and the measured density changes are due to variations in the number of particles within the volume considered .
the results indicated that the probability distribution of the density fluctuations exhibited in the majority of the cases a gaussian shape , as found in the model , although some significant non - gaussian deviations were also found , particularly near the bottom of the vibrated column .
moreover , the dependence on the number of particles of the relative variance was also the same as in the model , i.e @xmath50 as shown in eq .
( [ 2.19a ] ) .
variations in the inverse of the compactivity were also measured , by using the relationship between the second moment of the volume fluctuations @xmath108 and the compactivity following from edwards theory , i.e. the generalization of eq .
( [ 2.21 ] ) . to do so
, the authors considered the specific volume @xmath109 defined as the inverse of the packing fraction .
this corresponds to the quantity @xmath96 in our model .
the reported results are @xmath110 @xmath111 where @xmath112 and @xmath113 are two dimensionless parameters .
taking into account that the available range of experimental data is rather limited and located in the proximity of the close packing limit , it can be fairly concluded that the above expressions are in qualitative agreement with the predictions of the model , namely the expressions for @xmath103 and @xmath114 , eqs .
( [ 3.11 ] ) and ( [ 3.4 ] ) respectively . nevertheless , to put this comparison in a fair proper context ,
the following two comments seem appropriated : 1 . in ref .
@xcite , the edwards theory is considered in a _
local _ form , i.e. it is assumed that the state of each subregion of the system in which measurements are carried out is described by a canonical distribution with a different value of the compactivity . although this might be a sensible idea , it is clearly an extension of the theory as originally formulated by edwards .
moreover , what is measured in the reported experiments are the fluctuations in the number of particles at constant volume .
this is different from the fluctuations in the volume at constant number of particles , although both can be associated to density fluctuations .
in fact , it can be shown that the quantity actually obtained from the second moment of the number of particles fluctuations by means of a relationship similar to eq .
( [ 2.21 ] ) is not the compactivity , but some kind of ` fugacity ' @xcite .
although both quantities are simply related and perhaps their values are very close in real granular systems , they are conceptually quite different .
another experimental study of the steady volume fluctuations in a granular medium has been carried out by schrter _
. this work might look as quite similar to the one discussed above , but they differ in important aspects , both in the methodology and in the results . in ref .
@xcite , the fluctuations of the _ total _ volume of the system were measured , although the results are expressed in terms of the volume fraction @xmath101 .
a gaussian distribution was found in all the reported cases . also , the ratio between the standard deviation and the average turned out to be proportional to the inverse of the square root of the number of particles .
both results are the same as derived above for the model considered here
. nevertheless , the variance of the volume fraction fluctuations did not show the analogous of the simple linear behavior reported in ref.@xcite that , as it has been already mentioned , is consistent with the linear behavior predicted by eq .
( [ 3.11 ] ) near the close packing limit . instead
, it presents a well defined minimum . a first
, naive explanation is provided by the fact that a wider density range is analyzed in @xcite than in @xcite .
then , it could be expected that the linear law in the latter corresponds to an approximate description of a small window of the density interval considered in the former , namely to one with the largest volume fraction values . even assuming this explanation , the origin of the minimum would remain as an open question .
the result obtained with the model , eq .
( [ 3.11 ] ) , when considered over the density range @xmath115 , also shows a non - monotonic behavior , but presenting a maximum instead of a minimum exhibited by the experimental data in ref . @xcite .
then , it seems plausible to conclude that the existence of the minimum , if confirmed , must be due to some effects that are not captured by the simple model considered here . given that it appears for high values of the density , it is tempting to speculate whether the increase of the volume fluctuations in that region , to the right of the minimum , is an indication of the presence of some ` singular ' behavior associated , for instance , with the existence of a maximum random packing , a phenomenon that is not present in the model .
the edwards compactivity @xmath45 was also determined by schrter _
et al . _ by means of the granular version of the equilibrium fluctuation - dissipation theorem . to get explicit values for @xmath45
, these authors assume that the inverse of the compactivity vanishes in the random loose packing limit .
since @xmath45 is a monotonic decreasing function of the volume fraction , this boundary condition implies that it is always positive .
as it has already been indicated , there is nothing in the granular statistical mechanics theory requiring this to be true .
if attention is restricted to the parameter region in which the model has positive compactivity , i.e. @xmath116 , the shape of the curve @xmath117 , eq .
( [ 3.11 ] ) , is similar to the one reported in fig .
4(c ) of ref . @xcite .
although the recent results presented in ref .
@xcite have not been obtained experimentally , but by means of molecular dynamics and monte carlo simulations , they deserve special attention because of their relevance and the interest of the analysis carried out . in particular , interest is focused on a parameter defined as the configurational granular temperature , instead of the compactivity , although some close relationship between both parameters is claimed to hold .
a model system of grains with normal and tangential forces is considered .
the instantaneous volume fraction is measured in the steady state and analyzed as a function of its average value . to measure them
, a region in the bulk of the system is considered .
it is important to stress that this region is defined in such a way that both its volume and its number of particles fluctuate in time .
consistently with all the results discussed above and the model predictions , gaussian fluctuations of the volume fraction are also found in the simulations .
the analysis of the results in @xcite differs , at least conceptually , of the thermodynamic theory as proposed initially by edwards @xcite . instead of considering that
the macroscopic parameter characterizing the state of the system is the volume , the energy is used like in normal molecular systems .
more precisely , the probability @xmath118 of finding the system in the blocked metastable state @xmath119 of energy @xmath120 is assumed to be given by @xcite @xmath121 where @xmath122 is referred to as the configurational granular temperature of the system .
the above expression is to be compared with edwards proposal , see also eq .
( [ 2.18 ] ) , @xmath123 @xmath124 being the volume of the system in the configuration @xmath119 .
both expressions only become equivalent if , for the relevant configurations , i.e. those with a non - vanishing probability , the energy and the volume are proportional @xcite , with a configuration - independent constant . consequently
, the configurational temperature @xmath122 and the compactivity @xmath45 also would be proportional in this case . in the paper , the authors plot ( fig .
4 ) the standard deviation @xmath125 of the volume fraction fluctuations as a function of the steady average volume fraction @xmath126 . in the plotted interval ,
a linear behavior of @xmath127 is clearly identified .
then , by using the relationship between @xmath125 and the compactivity @xmath45 , an analytical expression of the form @xcite @xmath128 is obtained . here
, the explicit form of the function @xmath129 is known , while @xmath130 is an unknown constant .
if @xmath131 , with @xmath132 a constant , eq .
( [ 4.5 ] ) yields @xmath133 in ref .
@xcite , a plot of the volume fraction as a function of the configurational temperature , obtained by means of monte carlo simulation , is also provided ( fig .
consistently , this plot covers the same density range as the one giving the fluctuations .
therefore , it is posible to check whether the linearity between @xmath134 and @xmath135 predicted by eq .
( [ 4.6 ] ) is verified .
when this is done , a systematic but quite small deviation from linearity is observed .
then , taking into account possible numerical errors as well as the fact that the measurements are carried out in such a way that both the volume considered and the number of particles inside it fluctuate , no definite conclusion can be reached on the equivalence of the canonical distribution in energy , eq .
( [ 4.3 ] ) , and volume , eq .
( [ 4.4 ] ) @xcite .
this is an important point , both from fundamental and applied perspectives and deserves further attention .
in this section , the linear response of the model to a perturbation of the parameter @xmath32 , introduced below eq .
( [ 2.5 ] ) will be studied .
this parameter measures the ratio of the transition rates of the processes associted with hole annihilation and creation , respectively .
because of the definition in eq.([2.17 ] ) , a change in @xmath32 is equivalent to modifying the compactivity @xmath45 . in the context of real experiments , it might correspond to varying the vibration intensity , defined as the ratio between the peak acceleration of the shakes and the gravity acceleration @xcite .
the typical relaxation experiment to be considered is as follows .
the system is initially prepared in a uniform density configuration corresponding to a low density state , namely with @xmath86 .
then , it is allowed to evolve with a value @xmath136 of the rate ratio , until it reaches a steady state with a probability distribution @xmath137 . at a given moment ,
taken as the time origin @xmath138 , the rate ratio is instantaneously changed to the value @xmath32 . it is assumed that @xmath139 .
then , the relaxation of the system to a new steady state @xmath140 is followed .
the probability distribution function of the system at @xmath138 is @xmath141 using eq .
( [ 2.18 ] ) , it is obtained @xmath142 the average value of a function @xmath143 of the system configuration at time @xmath144 is , by definition , @xmath145 where the probability distribution @xmath146 is obtained from @xmath147 through @xmath148 here , @xmath149 is the conditional probability that the configuration of the system is @xmath11 at time @xmath150 given it was @xmath14 at @xmath138 . by construction
, @xmath140 is stationary for the dynamics occurring for @xmath144 , i.e. with rate ratio @xmath32 , @xmath151 taking this into account and using eqs .
( [ 5.1 ] ) and ( [ 5.2 ] ) , eq .
( [ 5.3 ] ) becomes @xmath152 where @xmath153 is the steady time correlation function of @xmath143 and the volume @xmath69 defined as @xmath154 with @xmath155 @xmath156 the normalized relaxation function for the property @xmath157 , @xmath158 is @xmath159 for the special choice @xmath160 , @xmath161 this expression is an exact consequence of modelling the dynamics of the system by means of a markov process and of the canonical form of the steady probability distribution .
the monte carlo simulation results for the relaxation function to be presented in the following , have been obtained by using eq .
( [ 5.11 ] ) .
figures [ fig2 ] , [ fig3 ] , and [ fig4 ] show @xmath162 for three values of the rate ratio , namely @xmath163 , @xmath164 , and @xmath165 , respectively .
other values have also been investigated , and the results are consistent with the comments carried out below . in the figures
the quantity @xmath166 has been plotted as a function of @xmath167 .
it turns out that this is a convenient representation to identify the shape of the decay of @xmath162 .
note that in this representation , a straight line corresponds to a stretched exponential or kohlrausch - willians - watts ( kww ) function , @xmath168,\ ] ] where @xmath169 and @xmath170 are the two parameters identifying the function . in the three figures ,
two different regions are easily identified . for ` short ' times
, there is a linear region with slope @xmath171 .
i.e. an exponential decay .
afterwards , there is a region of ` intermediate ' times in which another linear behavior shows up , but now with @xmath172 .
the initial region extends over a time interval , @xmath173 , that is roughly independent of @xmath32 . in this time interval
, the response function @xmath174 decays a small amount .
moreover , this initial decay becomes smaller and smaller as the value of @xmath32 increases . on the other hand , in the second time window
in which the response function shows a kww behavior , most of the relaxation occurs . for @xmath175 , fig.([fig2 ] ) , the fit to a kww function with @xmath176 is quite good for the time interval @xmath177 , that corresponds to @xmath178 , i.e. @xmath179 . for @xmath180 , fig .
[ fig3 ] , the value of @xmath170 in the intermediate time window is @xmath181 , and the interval of the relaxation function described by it is @xmath182 . finally , for @xmath183 , fig .
[ fig4 ] , it is @xmath184 for @xmath185 . .
the latter is measured in dimensionless units proportional to the number of taps .
the dashed line is the monte carlo simulation result , while the two solid lines are linear fits as discussed in the text.[fig2 ] ] .
[ fig3 ] ] the kind of behavior of the response function has been often found in the context of structural glasses , both in experiments and in simple models , for the linear relaxation of the energy following a temperature perturbation @xcite .
then , this is another indication of a possible conceptual connection between structural glasses and dense granular systems .
moreover , the simulation results for the model clearly indicate that the value of the exponent @xmath170 characterizing most of the relaxation tends to @xmath186 as the value of @xmath32 increases . in simple models of structural glasses
, this value is associated to diffusive processes @xcite .
although an explicit analytical solution of the model has not been derived yet , it is possible to understand the diffusive origin of the exponent @xmath187 as well as to get some information about the characteristic relaxation time @xmath169 . for @xmath188 ( @xmath189 ) , a typical metastable configuration of the system consists of isolated holes separated a distance of the order of @xmath32 ( see , for instance , eq .
( [ 2.15 ] ) ) . in this situation ,
the only relevant process to decrease the volume is diffusion : holes move through the system until two of them get together and one is destroyed . in this picture , the characteristic relaxation time will have the diffusion form @xmath190 , i.e. an arrhenius type law with the molecular temperature replaced by @xmath45 . in fig .
[ fig5 ] , the monte carlo simulation results for @xmath169 , obtained by fitting the relevant intermediate time window to a kww function as discussed above , are plotted as a function of @xmath32 . note the logarithmic scale , so that the observed straight line represents a power law behavior . the best fit , given by the solid line , yields @xmath191 in good agreement with the result following from the diffusive picture . appearing in the kww expression , eq .
, as a function of the rate ratio @xmath32
. time is measured in units proportional to the number of taps .
the symbols are from the monte carlo simulation data and the solid line a linear fit of them .
a simple model for compaction in granular media has been used to investigate some static and dynamic properties of the steady sate reached by the system in the long time limit .
the simplicity of the model allows to obtain analytical expressions for some of its properties . on the other hand
, it reproduces qualitatively well many of the properties found in real granular systems . in the context of static properties , this includes the gaussian shape of the volume fluctuations , the dependence of its variance on the average volume and the number of particles , and the possibility of identifying the compactivity as defined by edwards .
moreover , the scenario obtained from the analysis of the model , provides an useful tool to interpret the experimental results and molecular dynamic simulations of more realistic models .
this is exemplified in the critical revision carried out in sec .
[ s4 ] , where the need of a clear differentiation between density fluctuations at constant volume and at constant number of particles shows up .
also , attention must be paid to distinguish between local and global applications of the thermodynamic theory .
another issue that is worth commenting is the possible existence of negative values of the compactivity and/or the effective temperature .
if the mechanical statistical description is assumed as the starting point of a thermodynamic description , there is no solid reason to deny by principle this possibility .
even more , one is tempted to conclude that it is highly probable , at least at a theoretical level .
negatives values of the compactivity will show up unavoidably if the number of metastable configurations is not a monotonic increasing function of the volume . the possible volume occupied by the tapped granular medium
is limited by the loose and random jamming packings . in both limits
, the number of possible metastable configurations can be expected to be quite reduced .
the requirement of maximum or minimum space between particles impose a rather severe restriction on the allowed arrangement of the particles .
therefore , it seems sensible to expect that the number of configurations for intermediate values of the volume be larger than at the extremes , presenting a maximum at some values .
the same qualitative reasoning applies to the effective or configurational temperature changing the volume by the energy .
the question then is why negative compactivities ( effective temperatures ) have been not identified in the experiments yet .
there are two main reasons for it .
the first one is that only differences of compactivities have been measured up to now , and it has often been arbitrarily assumed that the compactivity diverges in the random loose packing limit .
the second reason is that negative values of the compactivity , if they exist , would correspond to the lowest density theoretically accesible region , and it can be very hard to reach in practice . in any case , this is a point that definitely deserves much more study . in the last part of the paper ,
the linear relaxation of the model has been considered .
a slow relaxation , accurately represented by a kww function with exponent @xmath170 tending to @xmath186 as the parameter corresponding to the vibration intensity is decreased , has been found .
moreover , the expression of the characteristic relaxation time @xmath169 has arrhenius form ( with the consistent substitution of the compactivity by the temperature ) .
the behavior of the linear response function for the model is fully similar to what is observed in the relaxation of many structural glasses and also in models of glassy relaxation .
it must be noted that the model discussed here was built to mimic the compaction experiment and that , consistently , the relaxation of the density starting from a loose configuration exhibits the characteristic inverse logarithmic law @xcite found in experiments @xcite .
it seems interesting to experimentally investigate whether linear response in tapped granular systems is also slow and described by a kww function .
if that were the case , it would be another indication of similarity between two apparently different kind of systems , granular media and structural glasses , reinforcing the link already found in other phenomena @xcite , including the existence of hysteresis cycles @xcite and memory effects @xcite .
a. barrat , j. kurchan , v. loreto , and m. sellitto , phys .
lett . * 85 * , 5034 ( 2000 ) ; a. barrat , j. kurchan , v. loreto , and m. sellitto , phys .
e * 63 * , 051301 ( 2001 ) ; v. colizza , a. barrat , and v. loreto , phys . rev .
e * 65 * , 050301 ( 2002 ) . | arxiv |
The Lava Mountains are a mountain range in the Mojave Desert, in San Bernardino County, California. They are one of the eastern limits of the Fremont Valley.
References
Category:Mountain ranges of the Mojave Desert
Category:Mountain ranges of Southern California
Category:Mountain ranges of San Bernardino County, California | wikipedia |
Beyblade 1. Default Chapter
This time forever.
Anni: Hiya!
Kai: ANOTHER?
Anni: yes and no!
Kai: o.O?
Anni: well what I mean is that I'm ready to do a yaio.
Kai: who's the couple?
Anni: urm…you and ray!
Kai: RAY AND ME?
Anni: well if you say it like that then it does sound really bad.
Disclaimer…Anni isn't in this neither is anyone else…except beyblade characters.
Chapter 1: prologue
There he sat…away in the shadows…he loved being there…it was his thing…I only wish that I could be part of that thing…
"Hey Ray you want to practice?" I blinked coming out of my daze…
"Urm yeah Tyson I would!" I said smiling at my blue haired friend.
"3…2…. 1.LET IT RIP!" The blades swirled round the dish. Hitting off of each other…I didn't want to use too much power but I felt that I had to prove myself…to him…I could fell the phoenix's cold gaze upon me as I shifted uncomfortable.
That had ended in a draw as Tyson doesn't like to lose…I knew I had won. Driger was off the charts in Kenny's laptop. But still he said it was draws…that made the phoenix smile…well the best smile I've ever seen come off him.
He turned away. His scarf shifting in the movement of the wind. He left then…
And he still hasn't came back…
"RAY!" I heard as I reached the bottom of the airport gates. I saw Tyson leaping for me and that ended up in a really uncomfortable position.
"Ouch! Nice to see you too Tyson!" I said as I stood up with help from Max. I had noticed that I wasn't the only one who grew over the year. Tyson was now sixteen and was nearly as tall as me. (Rei's like 6ft 4) and Max now being the same age as Tyson was also as tall as me.
"WOW! Ray you've grown!" said Max as he looked up at me using his big puppy dog eyes. That was his only true cuteness. His eyes. I had only seen them upset once during the years and I didn't enjoy that week. Max was upset because Kenny had left to go to New York and never come back again…after a while he had eventually calmed down and was back to his usual self.
"So Tyson are you dating yet?" I asked. Tyson went SCARKLET!
"Well…" that was all he said before Max came up to me and whispered in my ear.
"He's going with our side." I smiled. Max and me had been close during the year we split. We had kept a better contact than Tyson and me. Tyson would phone every week and Max would phone every day. We had been talking one night when Max told me that he was gay…he accidentally spilt it out since he was a little drunk. I didn't mind I have been gay for a while and had adjusted to it. Max and me would talk about stuff like we were teenage girls. It was great…
My eyes then turned back to Tyson his face had calmed down.
"Ahh o.k. Well Tyson if you don't want to talk about it here we can talk later over the dinner!" I had remembered Mr. D saying that there was going to be a big dinner and that everyone was coming…well when I mean everyone I mean Tyson Max the Demolition Boys and me! It was a formal thing so I had came back for the full celebration. I just had a little faith that Tyson would mention Kai…I had missed him for so long…he used to come into my dreams but slowly fade away into the distance…I hated those ones…I would either be trapped in cement or sinking under water. They gave me the creeps.
"So Ray how was France?" when we had finished a year ago. I went to live with my uncle in France. I would help out there a lot and would visit Oliver on occasional meetings. Mostly at cooking classes. Him being the mentor.
"It was great! Oliver told me to say to you Tyson that you better watch out because next time you meet him. He'll be ready for anything!" I said with a slight Oliver accent and then seeing how Tyson and Max found it so amusing decided to join in with the chorus of laughter.
"Come on Ray we better get going. We'll be late for the dinner!" they said as they help collect my bags and leave the airport retreating to Tyson's house.
…………………………………………………………………………………..
Anni: FINISHED!
Kai: THAT'S IT!
Anni: Well it's only a prologue
Kai: Good point.
Anni: Yeah but I promise that the chapters will be longer!
Kai: Review pleases people. It would help us to know people appreciate yaio!
H'n'K Anni!
(Hugs and kisses)
2. chapter two
Chapter 2: Things just seem to get better.
Anni: hi!
Kai: Hi!
Anni: Thanks Desigal! The review was great!
Kai: thanks for it tough I do say…Yaoi's aren't my strong point!
Anni: Hehe well hope you enjoy!
Disclaimer…I don't own anyone from this fic. Enjoy!
Chapter 2:things just seem to get better
Tyson had moved in the past year. I swore my jaw had dropped to the ground and Max picked it back up. It was HUGE! Bigger than the dojo and bigger than the IMAX THARTRE! Well maybe I was kidding when I said the IMAX but everything else was true!
"Ray?" this house was totally cool. Inside was even as big as outside the house was all furnished up to date and there was a huge dojo where we.
"Ray!" found Tyson's grandpa.
"RAY!" what? I said as I looked at Tyson.
"Sorry what did you say?" I could tell by the look on his face that he was mad.
"YO! Homey" I turned to notice Tyson's grandpa coming towards us. I smiled and replied a small 'Hi' back.
"So what was the French like?" he usually asked these strange bizarre questions that even Max can't answer when he's sugar high.
"Well it was different from this. I enjoyed it even though I missed you all." I said making everyone 'Aww'. Max came up and enveloped me in a huge hug. I looked around to notice that Tyson or his grandpa didn't flinch or give back a remark.
"O.k. what's wrong with this picture?" I asked. Max and Tyson both looked at each other before saying.
"What?" By now Tyson' grandpa had left so we were by our self.
"Tyson?" I asked as he got up.
"Yeah Ray?" I looked about Max wasn't here.
"What's the matter?" I asked I already knew but I wanted to hear it form him.
"Urm come 'on lets go show you where you shall be sleeping."
"Cool!" I said.
"This was my ROOM!" I asked in a somewhat greedy fashion.
"Yeah it's kinda small but it'll do!" I turned to see Tyson's face beaming with delight.
"O.k. spill! What have I missed over the year."
"Well it all started when you left. The dojo was falling down, so Mr. D decided to make a new place for when everyone stays over, except it was our house just also a guest house. We agreed! I didn't want to tell you because we weren't sure what would happen but after this was built we moved in and watch the dojo fall down. It was funny but weird. I would never had thought that my house"
"Tyson"
"My house the place where I had lived"
"Tyson!"
"For years was coming down before my eyes."
"TYSON!" I shouted. It must have startled TY because he looked at me scared.
"I didn't mean that story…" I said to him. He looked puzzled.
"I don't know what you mean?" he said trying to look innocent.
"I know your…gay…" his face turned red.
"No I'm not…hehe you've been talking to Max haven't you. He's weird he thinks that I'm gay. Even though I know he's not!"
"But TY Max is gay and you know that. I know that and I also know that you two are going out."
"WHAT! DON'T BE PLAYING RAY. I'M NOT!" he said
"Well who are you dating?" I asked. He looked down at me; he stood up when I called him gay; his eyes filled with loads of emotions. He started to circle his foot on the ground.
"Maxi…" he whispered. I could hardly hear him. But with my cat senses it came out as clear as a whistle.
"But you must promise not to tell anyone!" he asked. I just laughed at him…
"Tyson…Tyson…Tyson…why do you think Maxi told me? Simple because he was drunk…. he felt the same way when he splurged it out…but he didn't worry because I helped him…I'm gay…and I think I shouldn't keep this from you any longer."
Tyson lifted his head from the spot on the floor.
"You are?" he asked me looking quite shocked.
"I've been for the past 3 years…" I drifted off.
"WHAT?" he said face turning like the tomato I had in my salad.
"Yes I didn't think much of it at the time. But I've realised that there are more gay than straight. I've been able to adjust to my feelings."
"But I thought you liked Mariah?" he asked
"NO! She's like my sister dude!" I said bringing out a total American accent so it sounded reasonable. It made us both laugh out loud.
"Yeah sure Ray. But then who do you fancy?" he asked moving towards me, putting me on the hotspot.
"Well I dunno…I haven't been able to focus on people while I was working but I did have a relationship over there. His name was Micky. He was a few months older…
…I had reached France and walked off the port to meet my Uncle. I noticed him in front of a blue haired person. His hair was ice blue and he wore tight jeans and a really baggy t-shirt. He was hot! I remember him smiling in my direction, so I smiled back getting attention off my uncle.
"Ray!" he shouted as we met in a hug.
"Hey Uncle! How's it been?" I asked he looked at me. I was still wearing the Chinese stuff as he changed the subject.
"Wow have you grown, you look so old, just like your father." It was a compliment. I was glad it wasn't something else. Anyway, as I was leaving Micky came to me.
"Hi!" his jumpy attitude had made me smile.
"Hi!" I said "what can I do for you?" I asked politely.
"Urm…well could you tell me where you are staying?" he asked. So that day we had jotted down addresses and swapped numbers. I wasn't bothered that a gave a total stranger my number, for I knew we would hook up.
Anyway when I had left the collection point we had headed straight to my uncles apartment. It was filthy a real mess. Take away boxes left around the floor and old milk cartons. I knew I had to help him, so I tided up for the first day of staying there. That's when it happened. Micky had text me while I was cleaning. I looked at it. It only said that I was to meet him that night. He wrote 'meet me beside the water at eight. Wear something cute' I replied to that text immediately saying that if I had to so did he. Well once we had finally finished the texting conversation I had decided to get dressed for my 'date' my uncle said I looked to dressed up to be going a walk, but I couldn't tell him I'm not going out a walk I'm going on a date!
I knew as soon as I left he got suspicious. It didn't bother me as much as I thought it would. I thought it would have eaten me up inside but really the butterflies were already begging their feast.
I had reached the water before our arranged time. He was already there. The moon had shown his true highlights. Body and hair. He smiled sweetly at me and began to walk over. I was too busy in thought to realise that he was already up at me face. He was taller but I was only wearing my black pumps at that time.
"HI…" He said to me I replied with a hi before he kissed me on the cheek. Saying that we were going out for dinner and he was going to show me around town. I enjoyed all of it. It was so much fun we had went to Oliver's restaurant and dinned in the upper class section. I was having so much fun and was riding his wave that I didn't know I had kissed him full force on the lips at the end of the night. He returned and it was so nice. After that we would go out and have fun…but then we broke up and I was single once more. Then the dinner thing for this came up and I knew I had to come home…
"Wow that's cool!" said Tyson.
"Yeah It was…but you can't hold onto something forever…" I said drifting off again.
"Wow! Ray stop with the page long flash backs!" I blushed as he said this.
"Sorry…" I said. Just then a knock on the door corrupted the silence.
"Come in" said Tyson. Max walked in. he looked at Tyson and smiled then looked at me confused.
"What were you two doing?" he asked. Tyson then walked away up to him and hugged him lightly kissing him on the chin.
"Something…" he said winking at me. I just laughed.
"Don't worry just setting things straight." I said max the looked more cheerful.
"Cool. So you told him about the Micky thing! Yes now I don't have to hold the secret in!" Tyson looked at Max.
"You kept a secret in? Now you're not getting anything tonight!" I laughed as I saw Max huff.
"So Ray you going out yet?" I couldn't…I didn't tell them…I didn't want to share this part of my life with them…the pain I had felt…the tears I had let flood my eyes…no…I didn't want to show them what had happened…I was covering my whole body in one big mask. Letting me smile…making everything I saw care-free…making myself seem care-free…this wasn't the true Ray Kon…The true Ray would be in a corner sitting in silence…or causing self harm…not this…never would Ray Kon fell the thrill of death playing with his mind…never…
"No!" I said Max looked at me with his puppy eyes. He had grown into them and he looked cute!
"Well we better go get changed…seeya later Ray!" they had finally left. I sat on the side of my bed…what was I doing…I had to stay strong…I must never let this weakness take over…NEVER!
"REI?" why is there a voice floating in the darkness?
"Rei?" I can hear all that there is to hear.
"Rei dude? You all right?" see all there is to see.
"BUT THIS DARKNESS WOUN'T LET ME!"
The sun blinded my eyes why was there a navy blue cloud in my sight?
"Tyson?" I said quietly. I looked around. I must have fell asleep or something…
"Sorry I must have dozed off…" I said lifting my body up.
"Well you better hurry Maxi's coming round to pick us up!" he said.
"O.k. I'll go and get changed" I said as I walked into the bathroom.
………………………………………………………………………………….
"You ready?" I remembered that voice. It was Maxi's
"Nearly…There READY!" I shouted as I unlocked the bathroom door.
Max and Tyson looked at me, Max gave me a whistle that made me blush. I now noticed that Tyson was wearing a pink polo shirt (collar up) and a pair of blue denim three-quarter lengths.
Max was wearing a pair of black baggy joggy trousers (Like the orange ones in g-rev) and a Bright blue top that matched his eyes. I took one last look in the mirror. I decided top wear my blue tunic top and a pair of black baggy pants. (Like the stuff when he's in the restaurant in the series) I had unbuttoned the top buttons so that you could see my neck.
We went outside where I was met with a big black limo. I stood there gawping for a few seconds before I realised I was being shoved in it by Tyson and Max. I guess they seem to enjoy each others company…well I better not dwell in my thoughts for too long! On with the party!
As we reached the restaurant, we were met by Mr Dickinson.
"So glad you could make it!" he said
"No prob M r. D!" Said Tyson
"Well let's hurry inside! It's far too cold to be standing out here." He said as he looked up at me. "Why Ray you've grown a lot!" I smiled
"Yes I have…Thanks for reminding me!" I said. I have grown up! I shouldn't let the small problem waist my life.
As we got in we saw a familiar team.
"Hey TALA!" Shouted Tyson. He turned and waved.
"HEY TYSON! HURRY UP THE FOOD'S GETTING EATEN BY SPENCER!"
Tala had been a changed person after the tournament they all were different after becoming the Blitzkrieg boys and fighting Tyson in the world championships. Again. Tala was more funny. He would be so open-minded and would never shut up!
I smiled as I sat next to Max and Brian. Max was talking over to Brian as I sat enjoying my dinner. There was a huge creak as the door opened. I saw Tala's jaw drop to the ground. I turned to look and see whom it was.
You…
…………………………………………………………………………………………..
Anni: WOOHOO!
Kai: Who is it?
Anni: You'll see soon enough!
Kai: Review people!
Anni: Yes please review!
3. chapter three
Chapter three: the lone wolf comes back!
Anni: hello!
Kai: Hi!
Anni: I liked the second chapter so I'm writing another!
Kai: Yay!
Anni: here it is.
Disclaimer…I don't own beyblade just the plot!
Chapter 3: the lone wolf comes back!
There was a huge creak as the door opened. I saw Tala's jaw drop to the ground. I turned to look and see whom it was.
You…
The one that left…
The one that could have been beside me…
But you weren't…
"Ahh Kai so glad you could make it!" Mr D broke the silence. I looked back to Kai. He was different. His hair was short and spiked up with bangs covering his face. He looked so much older. That had made me look up and down at him a few times.
"Yeh…sam..He-" Kai said before he fell to the ground. I was of coarse the only one who ran up to him. I lifted his body up from the ground.
"Kai?" I shouted "KAI? ARE YOU AWAKE?" again I shouted I didn't notice from far away but Kai was really small. He was about 5ft 7, and he didn't weigh a lot.
His eyes slowly fluttered open.
"Hi…who are you?" I looked at him shocked.
"He's lost it!" shouted Tyson "He thinks he's Kai!" I looked over to him.
"He IS Kai you fool! He has changed that's all!" I said as I stood up holding Kai.
"Sorry to cut the party short Mr. D but I have to go now! Seeya back at your place Tyson!" I said as I walked out of the building.
The streets where empty…no one was around. I guess because it's so late at night.
Well I walked down the streets taking Kai back to Tyson's. When I had finally reached Tyson's street it had started to rain. I tried to shield Kai, but I couldn't, I began to pick up my pace and ended up in a jogging pace. When I had finally reached Tyson's house it had stopped.
…………………………………………………………………………………………..
As I eventually reached my room I laid Kai down. I ran into the bathroom to get the first aid box.
"Hey?" spoke Kai as he began to awake. I ran into the room.
"Kai! You're awake!" I said as I fell down next to him.
"Hi…Ray why am I here? Where am I?" what does he mean by that.
"Well you passed out as soon as you entered the hall. I had to help so I took you home…well Tyson's new home…"
"What? Tyson lives here?" he spoke with his emotionless tone. I couldn't sense anything in his eyes…that's bad…
"Yes he has been for the past year." I said in a reassuring tone. I looked back into Kai's auburn eyes. He was more relaxed when he noticed that I was only here alone.
"Thanks…" he said
"Don't mention it!" I answered. AH! I nearly forgot! I ran back into the bathroom and picked up the first aid box, that I had dropped when I heard kai. I ran back into the room.
"Why do you need that?" he asked as he looked at the box.
"To help you!" I said. "But I don't know if I need it…it's more easier if you were unconscious" I blushed as I imagined Kai with his shirt off.
"I'm fine," he said as he stood up.
"Kai I don't think you should be doing that…" I said. He turned and looked at me.
"I'm fine really I just need to get home…" he said…I never thought Kai had a home?
"You actually have a home?" I asked
"Yes with my dad…"
"WHAT!" I'm sure my jaw had broke off its hinges by now.
"Well you see when my grandfather took me to Russia it was because my mother was in hospital, and my dad couldn't cope with it. Now when I got thrown out my grandfather's house he told me where to go…and I found my real dad…"
"Cool!" I said as I noticed Kai leaning against a wall, taking in deep breathes.
"Kai? Are you o.k.?" he turned to the door.
"Just need to catch my breath." I nodded as I still watched him…something wasn't right…I was so caught in my thoughts that when I came out them I ran forwards to Kai. He was on the floor!
"KAI!" I shouted he turned to look at me pain filled every part of his body. His shaking body almost made me sick.
"What?" he asked.
"You're seriously hurt!" I shouted
"No I'm not just busted rib…" he said lowering his head. I then pulled his chin up so he looked me directly in the eyes.
"Kai! You are really badly injured and I can't let you go out like that!" I said. Tears stung his eyes.
"I know…but I have to get back home…before he suspects something…" I looked down at him…
"What do you mean?" I asked in a suttle voice.
He looked at me. Since he was smaller it was more difficult to keep my head tilted like this. A tear drifted down his eyes before I got it.
"Kai? What has he done to you?" he just looked away ashamed…why was he ashamed…no he couldn't…it's his own father…why…
"Nothing…" another tear slipped out…
"Kai! I'm giving you one last time! Now what the hell did he do." Silence.
I hate waiting! It always seems forever. He slowly looked up at me before I felt something hit my chest. I fell. As I came back I noticed that Kai was hugging me and crying into my shirt.
"IT'S HORRIBLE!" He said.
"What is?" I asked.
"Him he's the reason why I came to the stupid dinner!" he said
"Kai just calm down…" I said but he didn't his sobs became hard as his breath became laboured because the sobs. I pulled his head up as he looked at me. That's when it happened. I could see in his crimson eyes what I thought could never happen. But again as I was thinking something happened? I think I did it. I DID! I slowly pressed my lips against his. He was shocked but relaxed…as we gasped for air I noticed Kai's face. He was a little shocked. But then looked up at me.
"There you're calm now…tell me what happened?" he just looked blankly.
"Well if it's what I think it is then you're not going back." He looked at me and smiled at me.
"Thanks…" he whispered. "I promise I'll tell you but not right now…I think my ribs broken…can you make it better?" I looked confused. Make it better it's bloody broken. I looked up on the bed and saw the first aid box. I pulled it down and pulled some bandages out. Kai took his top. B-E-U-T-I-F-U-L! He had the world's best body except the scars and cuts. WAIT CUTS? SCARS? Now I know this thought is true. I began to wrap his rib cage up in a bandage as he looked at me. Tears still in his eyes from the tight pain.
"Don't worry it'll make you better!" I smiled.
Kai's POV
Ouch! That hurt…I smiled at the white tiger. He was so beautiful. So together, and when he kissed me I could have swore my inner child did a victory dance. I have waited for this! Ray my crush…has told me he feels the same as me…I just need to get home soon…he'll get angry…he'll kill me… ray looked at me.
"Kai you need rest…" WHAT? ME? I DON'T. he helped me up to my feet and took me across the floor to the bed and let me go to sleep.
"I'm just going in for a shower you should get rest. I'll have to share but…" he said as he walked into the bathroom.
Slowly my eyes began to lower as the darkness took over displaying pictures of ray smiling. At me…
…………………….……………………….
Anni: FINISHED!
Kai: Yeah! I'm with Ray!
Anni: yes whom did you think you'd be with? Tyson?
Kai: don't mention that name!
Anni: o.k…ppl the reviews are great keep reviewing and find out about Kai's past and Ray's!
H'n'K
(Hugs and Kisses) Anni!
4. chapter four
Chapter four: Little Kitten don't be scared Kai's here!
Anni: Hi another chapter!
Kai: Very cough Disturbing name you got there!
Anni: Yeah! It's cool!
Kai: sweat drops Yeah whatever you say…
Anni: Thanks to everyone for the great reviews! I appreciate it so much!
Disclaimer…I don't own any one just my plot and a few milky ways…
ENJOY!
Chapter four: Little kitten don't be scared Kai's here.
Well let me take you back to about ten minutes ago…I'm Kai…I woke up here and then got kissed by the most HOTTEST, CUTEST, SEXIEST! Guy on the world Ray…but now I am asleep dreaming of Ray…
"Kai?" my eyes begin to flutter open as I see the sex god looking over me.
"Yeah?" I asked in that annoying tone…I hate that tone I wish I had ray's tone…that's a very sexy tone…WHAT THE HELL AM I THINKING? I sit up slowly remembering that I have a busted rib. He looked at me sadly.
"What?" I asked in that stupid tone!
"Good morning!" that's it?
"Oh yeah morning?" I said.
He the began to lower his eyes as he came up against me…pressing his lips against mine. I closed my eyes as I remember that taste. Ray then starts to run his lip along mine. Is this part of the plan? Well I give in anyway…I could tell that Ray was tasting things he would never taste…my feelings…I don't think anyone's saw them apart from Ray…
This felt so great. Everything about this felt so right. Wait what I he doing now? I turned to see that Ray was trying to take my top off. No! Don't my ribs!
"NO!" I screamed. He looked at me.
"What's the matter?" he said
"No!" and at that I ran out the room. Never looking back I ran. Tears staining my eyes as I ran. The door! Finally I ran for them as I looked back to see if Ray had followed me. YES! HE HADN'T! I was just about there when I heard a man at the front desk say. "Mr Hiwatri I am sorry for any inconveniences…we'll be on our look out!" SHIT! I have to go home!
……………………………………..Kai's Home……………………………………
O.k. nerves have now taken over. My shaking hand reached for the handle but it was flung open.
"Bastard!" he said as he pulled me inside…nice to see you Dad!
I was thrown on the sofa as he traced up and down the room. I knew what was going got come if I did something, so why not speak.
"What!" I said. He turned to me I could see the tension.
"YOU KNOW WHAT!" He said as he came towards me…I tried to slide back but I couldn't he had thought this one out.
"I don't! PLEASE!" I screamed. I mentally kicked my self. Stupid! I shouldn't show emotions beside him. His half brain still thinks that grandfather got rid of them completely. Since I was trying not to laugh at dada thinking about my father having a full brain and being able to love me and be nice to me…I'm now guessing this pissed him off, as I looked to notice I was on the floor. CRAP! He hurt my rib. I could taste the blood in my mouth but he forced me back up to my feet. He then punched my jaw? Why would you break your sons rib and then punch him in the jaw. It doesn't make a difference. He then lets my weak body fall to the ground I couldn't get back up so what does he do? Kick me! I now know bloods being coughed up.
General POV
The tall man walks over into the small kitchen.
"You better leave by the time I get back!" he said as he crossed through the kitchen and slammed the door. Kai took one of his hands to his lip. It was bleeding. He licked it as he tried to sit up properly.
"Ha! Always the same…" he said with a smile. "I wonder why he called the hotel and then told me to get out?" he looked around.
"Oops! I forgot Dranzer's not with me…" he looked around the room. The room was dark. It had barely any furniture, and the furniture they owned was ruined he limped into his room and sat on the small bed. There was a white envelope lying on it. He looked at it. It had a phoenix on the blood red stamp. He scowled. Slowly he began to open it. Nervous he looked at it…
_Grandson,_
_Since Boris has been put away and since you and your 'friends' had finished off our business. I have had time to reconsider your stay. If you want you can come any time, just phone before, so I can sort the room out. _
_From, Voltaire_
P.S. I expect that you will beyblade again. I expect you to blade for the Hiwatri family.
Kai growled to himself as he read it.
'Why the bloody hell does he wants me to come back?'
'I bet Boris has something to do with this.'
'I bet father has!' his thoughts where clouded by a creak on the door.
'Shit he's back! I had barely time to pack!'
"Kai?" 'Wait I know that voice'. Ray walked in.
"What?" he spat back at him.
"So this is where you live? Nice house?" he looked at him and rolled his eyes.
"Don't worry I'm not staying here…I'm going to live with my grandfather. My father kicked me out!" I laughed at the end. Imagine. I am sitting in my house that I got kicked out of.
"YOUR GRANDFATHER? ARE YOU CRAZY? COME STAY WITH TYSON!" he shook his head and smiled at him.
"No…I can't leave Dranzer there any longer…besides I think he has changed a little. Heh! It's better than staying here." Ray shook his head.
"But his…" kai glared at him
"Don't bring up my past! I don't live in the past!" he said as he got up and went to a drawer grabbing a few pieces of clothes and then stuffing them into a bag. Ray looked at Kai with concern.
"Are you sure it'll be o.k." Kai gave a weak smile.
"Nope! But he's all I've got right now." Ray walked up to Kai and looked down.
"As long as you know you will be safe, that's all that matters." Kai was unsteady.
"I'm not…I'm not sure of anything except this." He said as he tipped-toed up to Ray's height and kissed him. Ray gave back the kiss forcefully and smiled as they parted for air.
"Do you need a ride to you gramps house?" Kai smiled as Ray jingled the keys in front of his face.
"Thanks but I need to phone him first…" Ray held out his phone when Kai said this. Kai took it and dialled his number.
(Hello? Hiwatri family!)
Yes! May I speak to my grandfather?
(Why…WHY MASTER KAI!)
Yes?
(Your grandfather is at one of his meetings for Voltaire co. but I'll tell him that you are coming and make your room ready for your stay.)
Thank you!
(A/N: That was a phone conversation Kai was the one without the brackets and the butler had the brackets.)
Ray looked at Kai.
"Is it o.k?" he asked. Kai nodded and then said.
"Yeah he has a new company so I'm guessing he has changed." Ray looked like he had just been shot.
"But…K…Kai. He made you turn evil." Kai just shook his head.
"No I was under the influence of Black Dranzer…and plus Grandfather sewed BEGA for the copy right of him sighing it." Ray looked shocked again but just shrugged it off.
"O.K.!" He said as he turned for the door. "You coming?" Kai smiled
"Yeah!" he said as he ran to the door. He took one look back. 'BY HELL!' and closed the door behind him.
……………………………………….……………………
Anni: O.K. FINISHED!
Kai: THAT'S SO COOL!
Anni: yeah I would like to point something out to everyone. This takes place after g-rev. sorry I didn't mention it before.
Kai: So BEGA did get sued?
Anni: Well not in the series but in my fic yes!
Kai: HAHA! BRUN BEGA BURN!
Anni: O.K. people I'll do this I need three reviews to go onto the next chapter. I like it when I know more than three people read this chapter!
H'n'K
(Hugs and kisses!)
5. chapter five
Chapter 4: A new home…but has it changed?
Anni: THANK YOU THANK YOU THANK YOU!
Kai: why are you writing thank you?
Anni: I wrote it three times for my three fantastic reviewers!
Kai: YEAH! We can continue…
Disclaimer…. Don't own anything except the plot…enjoy!
Chapter four: a new home…but has it changed?
Kai's POV
The scenery flashed past…so fast…it was like an artist using watercolours…everything was smudged…it was so beautiful…I guess I haven't had time to look at stuff like this before. The car ride was silent…I couldn't tell what Ray was doing behind me because I had turned my head to look outside…
"So you're defiantly staying at your grandfathers?" he broke the silent. That had made me jump a little. I turned round to see his perfectly gorgeous smile…he could melt and entire village of ice with it.
"Yeah…I'm defiantly going to stay with him…" I said…I wonder if he's changed or will he want me to go after peoples bit beasts again?
"But what if he wants you to…ya'no?" no I don't
"What? Steal your bit beasts…Nah! Besides I would never take yours…" I could her him sigh "Maybe Tyson's but…" Ray looked shocked." Kidding?"
He smiled again I laughed.
"Am I not allowed to make a joke?" ray looked at me…his eyes where full of sarcasm…
"Well you are Kai! Cold hearted one!" He was ready to start laughing at me…
"Thanks…" I said.
The rest of the journey was quiet, until Ray put his 'Franz Ferdinand' c.d. he was singing along carelessly when her turned another street. I had been watching him for a while. He was just concentrating on the road but the words seemed to come out along with the tune.
"Here we are!" said ray. Damn! He stopped singing.
"Are we?" I asked looking out the window. I looked up the driveway and saw a giant mansion? YES! My old home! I missed you so much! I love you! A huge smile came upon my lips.
"Do you know this place Kai?" he asked.
"OF COARSE!" I said my voice full of glee. "This was were I grew up!"
Ray smiled at that comment.
"That's great! I guess…" I looked at him.
"What's the matter?" I asked.
"Nothing…so I'll see you later?" he said before I turned to him.
"Don't you want to come in?" I could tell that was a stupid question.
"No…I'll leave you to know your grandfather batter…here!" he said before handing me a phone?
"Why so I need this?" I asked
"So you can contact me!" Aww sweet. I quickly pecked him on the cheek and ran to the boot to get my stuff. I could hear Ray laughing. But that didn't matter! I was just so glad to be back!
As I ran up to the entranced I waved goodbye to my koi and opened the huge door…
.: Inside:.
This place hadn't changed…it still has the same welcoming smell of richness…I probably wouldn't want ray to come into my house and smell this…he might fell a tad unworthy cause of his really sexy home life…. wait did I just put Ray and sexy in the same conversation? I hope not…
"Good afternoon master Kai…" SHIT! I turned round to see a scary butler…I don't know his name? Weird? Why don't I know who he is?
"Hi urm dude I don't mean to be impolite but from now on you are called 'dude' under my watch."
The Dude nodded as he walked away.
"KAI!" I knew this person it was the person I was speaking to on the phone…he was my friend here while I grew up his real name was James…but I called him Jay…he was about 10 years older than me, so he was like a big brother.
"You Jay-Jay how's it been?" he smiled and ruffled my hair…he had brown long hair like Hiro's and wore the butler outfit but more trendier. His trousers were baggy and his shirt was too big…and he always wore his towel round his neck. That's what I liked about him…he was way too relaxed…and way to laid-back for my grandfather to get on his nerves…
"It's been boring since Gramps came back!" he was like an older brother…he had a lot more privileges than the other workers…so I guessed my grandfather trusted him…he had started here when I was five…so he was fifteen…the thing is Jay-jay was an orphan and that meant that orphans could work at the age of 15 as long as they had a room and food…so when he came it was like a new friend coming to stay forever…I never knew he was a butler till he started serving me…I guess I enjoyed having a friend…until BIOVOLT came into the picture…
"Really! Man I thought it would have been fun annoying gramps…"
"Nah he's been a little more happier and more free-spirited that his company is a huge success! It's kinda funny…he was really pleased about your arrival…" what was my grandfathers new cooperation?
"Urm…can I ask what it is gramps does?"
"What did you not have any communications to the outside world when you lived with your dad?"
"No…it was a different experience for me…" I said remembering the pain he gave me today.
"WHAT? THEE! Kai had no T.V.? THAT'S BARBARIC!" I laughed at his choice of words.
"Believe me whenever I could I would be asleep! It was hard living up to my dad…reminds me a lot of Russia…" I could see Jay's eyes trace back to that time…I remember that he came with me for a year to study the art of beyblading…but always massed about with Tala and Bryan…I wonder if they still talk to each other?
"Well gramps new cooperation is…the HFCC!"
"The what?"
"The HFCC…Hiwatri Family Computers Cooperation! We're bigger than Microsoft!"
"What do you mean we?"
"Well I'm part of the business…and soon part of this family!"
"FOR REAL!" I could finally have a big brother that would be interested in what I had to say…
"Yeah the papers are official next week!" I was so overwhelmed that I hugged him.
"Now I can finally have a big brother!"
"Yeah same!" he said. When I was finally over my little session…we placed my small bag of stuff in my room and went down stairs…
"So…you stayed in touch with Tala?" I had to ask…he's here right now if he hasn't
"No…we haven't been in touch…gramps doesn't want me to…he says that if I do I'll lose my job…I don't want to risk that." What can he be serious?
"What are you talking about Tala's not with Boris…he was in my team? Blitzkrieg boys? We were at the finals with Tyson? He won…I went in a kinda weird way and didn't see anyone…left their team…Boris came back…Tala tried to stop him…didn't succeed? We fought against his group BEGA?"
"Oh! Well I'll tell him…"
"HE KNOWS! That's why he wants me back…to beyblade or something…anyway Tala's at Tyson's staying…and you are welcome to go over with me to see Ray…"
"What? Go over…Me?"
"Yeah you're the same age as Tala right?" Here's the thing Tala looks younger for his age but really he's nearly the same age as Jay here…he's like a few months younger.
"Yeah but…Ray? Who's he?"
"Urm Ray is the only true friend…" I said "And my Koi" I also said in a murmur. We walked down the large stairs to the entrance hall where I was waited a visitor…
…………………………………………………………………………………………..
Anni: FINISHED!
Kai: Finally I thought that was never going to end
Anni: well I thought that it should end there since I was going to end up with writers block!
Kai: And we all hate that!
Anni: Yeah I do!
Disclaimer…people I would like to ask again for three or more reviews…I am very happy people enjoy this and I will try to continue it as long as possible!
R&R people! Hey I'll even give plushies to my three reviewers!
6. chapter six
Chapter six: So let's meet the Hiwatri's
Anni: WOOHOO! THREE REVEIWS!
Kai: YEAH THE NEXT CHAPTER!
Anni: And for one of my reviewers…if you read on you would have noticed that I spelt Ray like that…it was just confusing at the start to write it different.
Kai: 'cough' why is it that chapters that are like my POVs are either disturbing or just PLAIN wrong?
Anni: 'shrugs' must be something…just can't think what it is?
Chapter six: So let's meet the Hiwatri's
"Gramps?" I said. I looked at the man…he had long silver hair and still looked quite stern…but it was him.
"KAI!" He said as he opened his arms for me to hug him. I ran up to him quite fast and gave him a huge hug.
"I've missed you," I said as tears chocked half of the words.
"Now Kai calm down…lets go into the office and talk about this…" he said in a sincere tone of voice…I followed him till we got to his office he went inside and cleared a few things away first before asking me to come in…
The room was just like my bedroom HUGE! His large mahogany table sat at the end of it along with his big black chairs…I remembered when I was little…Jay and I would play hide and seek and would always get caught by gramps…he would then shout at us and then tell us to go do something else…this time was different.
"Kai we need to talk over some matters," he said as I sat down.
"Like what?" I asked. He looked more cold hearted when I asked…
"Like! What happened when you stayed with your father…like! What where you planning on doing if he continued. LIKE!" I quickly butted in…
"I get you point…" I said.
"Kai this might be hard for you to understand but…he shouldn't have done that to you at this age…" What is he foaming about?
"Urm who are we talking about exactly?" hehe my grandfather used to say that if you never ask question you'll never get the right answer…
"Your father…that man who scared out family name!" he said
"So I take it you heard what he was doing?" I asked
"No I only heard that he was drunk and abused you" O.k…who told him
"Yeah…that was one of the first nights…" I said. GOD! I hated when my dad did that to me…
"Well Kai may I ask for a statement…I want him to be put behind bars for this!" I smiled at least he cared for my free-will…
"O.k…if it gets him away from me…I'll do it!" he smiled…WOW! A smile I never thought I would see one of them from him…I always thought of seeing it in my mind when I die…he would be snickering at me and calling me worthless…hehe well I guess my hypothesis was wrong all these years.
"O.k…well when you kicked me out…Dad showed up and said that he had been looking for me for a long time…I was a mess at the time and didn't know were to turn…Boris could have came up and took me I wouldn't have minded…My mind was a mess…my goal was to beat Tyson…I didn't succeed…even though he came up to me and said I was far more powerful I couldn't believe him…I didn't want to believe him…Is this really necessary?" I asked as he nodded
"Well after the championships and BEGA I went away from all of that…I mailed Dranzer back to you when I lived with dad…he would have probably pawned it if he found it…and I couldn't risk that…So as the days went on he would ask me to do all of these different kind of chores and I would do them for him…nothing bad just do laundry and clean up…but the first night I hadn't cleaned the bathroom because I was so tired…he stumbled in drunk as I was sleeping on the chair and walked over to me…I woke up and saw him standing there…he then took me into his room…and started undressing me…I fought back but he was as strong as Boris…that was the first night…he used me…he raped me…" I said I looked up at grandfather. I couldn't see so well because the tears had fogged my vision.
"Oh dear god!" he said…"Kai what happened after that?"
"Well…he…would…sell…my…body…for…money…to…filthy…men…I was theirs for the night…they could do what ever they wanted…but during the day if dad was drunk he would just beat me up…"
I could see tears in grandfather's eyes…
"This…this won't go on…" he said I smiled…" I will see to it that he gets put behind bars…" he said. I nodded as he handed me a tissue to dry my own spilled tears. As I wiped them away he smiled at me…I wonder why he's smiling?
"Kai…Kai…Kai…" he said…WHAT?
"What?" I asked
"You look so much younger without your triangles" I must have cleared them away when I was wiping my tears.
"Thanks…" I said as I got up…
"Oh Kai I wasn't finished…" he spoke to me like I was little…
"You weren't?" I said as I was told to sit back down.
"No I did have another reason why you would be here…I wanted you to be our 'mascot' for our new company…" WHAT?
"Cool…what do I have to do?" I was afraid to ask
"Well all you have to do is go on commercials and blade using artificial help…"
"So you mean mascot the logo?" I think this could be fun…I would be a model! WOOHOO!
"Yes…but I need you to have this…" he said as he handed me something in a red box…I opened it and smiled…"Sure I'll do it as long as I don't have to lose Dranzer again…" we had an agreed arrangement and I had Dranzer back with me…I stood up and left the room.
"Kai. Is there anything else?" what?
"No not really?" he looked at me confused…
"O.k…you don't want a new car that's fine…I just got it today…but I see you too busy with you Dranzer and you new hair 'doo' to do anything…" What a new car
"I could always take that out for a test spin as well…" I said with a smile he threw the car keys at me while I was thinking about what Ray would think…
"Ouch!" I said as I rubbed my head.
"Oops sorry!" he said as he smiled at me. I had to laugh at him Jay was right he was glad to see me. I left him alone in his room to do his work.
"KAIIIIII!" Crap!
……………………………………………………………
My eyes fluttered open to see Jay looking at me…
"You o.k?" I sat up…dizziness had took over as I saw two Jay's.
"Dude there's two of you…" I said
"The butler isn't here!" said Jay
"What?" I said my dizziness was now controlled and I saw Jay staring at me.
"Never mind…what happened I just lumped on you and you fell and knocked yourself out!"
"Did I…" I now noticed the pain shooting up from my rib…"Ahh!" I hissed, as the pain grew even worse.
"You o.k?" he said should I tell him…" What did you dad do to you?" Ahh no need to tell him he already knew.
"Just broke my rib it's o.k. It'll heal…" Jay looked as though he had heard the words death…
"No that's not O.k," he said as he clenched his fists. "You're going to a hospital whether you like it or not…" No…I hate hospitals…he walked me to his car and helped me in…he told gramps everything before we left so he was coming later to check up…I had secretly texted Ray to tell him to come and told him to bring Tala and friends.
……………………………………………………………………………………….
"AHHHHHHH!" I looked around to see a young boy scream and run away from a doctor who chased after him…
"Don't worry boy you'll feel better if you take this one small injection…" he said.
The boy stopped and looked at me. Before running up to me.
"You're Kai! OUT OF G-REVOLUTION!" hehe
"Yes I am! How did you guess?" if you can't remember I got my haircut so it was now spiky.
"I could tell you from anywhere!" he said I smiled Jay just looked at me.
"Well thank you for recognising me kid!" he looked around and ran away.
"Your popular Kai-Boy!" murmured Jay beside me
"Shut up!" I said. About 2 minutes later the boy came back with a pen and paper.
"Can I have an awto-mathe?" I looked at him
"You know what you can have this!" I said as I handed him a small blade. I made it while I lived with my dad. It was different to Dranzer's it was a light blue blade with a fire symbol in the middle and round it said 'Kai's blade don't touch' He looked at me. And so did Jay.
"Wow! Really thank-que!" he said. He looked up at me
"Hewre!" he said before handing me a small nurses bracelet with his name on it…his name was Aiky…Cool name!
"Thanks kid now if you want to get better and battled everyone you gotta take the injection…trust me they aren't so bad…" I said before Aiky looked at me.
"But doctors are meanies!" I laughed and then looked at him.
"Well if you don't want to get better I guess you won't get to blade with my very own blade." He looked shocked
"You made this?" I smiled
"Yeah I did I made it for the next tournament. You are coming to watch that right?" I asked he smiled and nodded "Yippers" Hehe I laughed as the doctor came and saw him.
"Now Aiky you ready to get all better?" he asked as he looked down to see whom he was talking to.
"Ahh Mister Hiwatri nice to see you…we will be taking you to the adults room so you can be properly seen to?" I looked around to see Aiky looking at me.
"Urm do you mind if I stay in the children's section beside this little dude!"
"We'll see what we can do," he said as he walked away. I turned round to see Jay looking at me very suspicious.
"What?" he's pissing me off.
"You actually want to go in a child's room? Wow Kai! When you where younger you used to always want to be moved in the adults section."
"Yeah I guess I've changed…" I said not noticing the female nurse coming up towards us.
"Hi Mr. Hiwatri…we are ready to take you to get x-rayed" she seemed nice…I got up and walked away, following the nurse up a long narrow hallway…this was nice…it seemed quiet!
GENERAL POV
Kai was seated outside the room when another nurse came up to him and sat down asking various questions.
"So Kai what has happened?"
"I broke my ribs playing football…" she looked at me as though I was stupid.
"Right O.K. That's us finished if you go in there you'll be seen to!" she said as she walked away. Kai walked in slowly making sure this was the room.
"O.k. Mr. Hiwatri please take your shirt off and we will get you x-rayed." Kai looked around.
"Who said that?" he asked as a man appeared from another part of the x-ray room.
"Me! I'm doctor Dami! Please could you take your shirt off before you get it x-rayed?"
"No…I don't want to take it off," he said as he crossed his arms over his stomach and wimpered a little as it came in contact with his rib.
"Well if you don't take it off, we can't take a picture of it…is there anything the matter…" He stepped forward as Kai took a step back…
"Yeah there…is…I don't want to talk about it…" He said as he stopped at the wall.
"Ohh…O.k. well I won't judge you…all I want to do is take this x-ray…" the doctor said as he stopped. Kai began to take his top off slowly trying to avoid bruising the rib even more. When he had finally took the top off, the doctor looked a little scared.
"So this is what you mean…don't worry I think I know what happened…" he said as he walk away behind the silver screen.
The room went dark as a small blue light came into Kai's view. Moments after that the lights came back on and the doctor walked out.
"There all done!" he walked up to Kai as he tried to put his shirt back up. the doctor grabbed an overall and gave him it.
"It's saves you and us time…Does you grandfather know you're staying here…"
"I'm staying?" Kai asked
"Yes…you are…you probably broken rib will need to be treated…and you other wounds will need to be checked as well…" he said as Kai looked shocked.
"O.k…just don't tell Jay about the other stuff…HEY WHAT NEEDS TO BE CHECKED?" he said
"Why…STIs of coarse…" he said…" It could prevent a major downfall on you life if it isn't treated…only if you have something…" Kai placed the overall on and looked at him.
"So you know?" he asked.
"Yes I do…but I can't help I'm only a psychiatrist that does the x-rays…so if you want to talk about it your welcome to!" He said as he walked away…
Kai walked back to the hallway where he saw Ray. His heart fluttered as Ray ran towards him and gave him a hug. Kai winched at this and Ray quickly stepped back…
"What's wrong?" he asked. Kai gave a sweet smile and said
"Nothing to worry about just a busted rib…I'll be O.k…" Ray looked worried.
"Well you might not be afte" but was quickly interrupted by a naive voice.
"YOU UNFORGETFUL BASTARD!" Kai blushed from embarrassment as Doctors and security guards came rushing passed Ray and him and towards the two people.
' Things will never change between them' said Kai as he laughed.
…………………………………………………………………..Fin……………….
Anni: FINISHED THIS CHAPTER!
Kai: YEAH!
Anni: Sorry for any inconveniences I had a huge writers block and couldn't think straight for days…lol
Kai: Yeah I know her brain had a malfunction and wouldn't work properly for days…
Anni: O.k. I'm going to raise the reviews up to five…so the quicker you review the quicker this goes up! Bye for now!
7. chapter seven
Chapter seven: A really big surprise.
Kai: Anni couldn't be bothered writing this so I got help from my OTHER red haired friend!
Tala: WOOHOO! Finally I'm back!
Kai: Yes Tala…He's weird….
Tala: Weird but ORIGONAL!
Kai: yeah original…originally weird.
Disclaimer…I kinda own part of beyblade…but since I am a main character of beyblade I don't have to say anymore…enjoy!
Chapter seven: A really big surprise.
"YOU ASSHOLE!" Jay said as he held his hand up to his now bloody nose…Yes Tala had punched Jay and fought off the security.
"TALA!" I shouted.
"Oh hi Kai! Why are you in here…I heard Bastard broke your ribs." Said Tala as he spat towards Jay…Wow! So something has happened between them.
"Well…actuall…"
"Yeah I jumped on him…He's such a weakling! But yeah his ribs are broken and now he has to stay over night…am I right Kai?" He's weird
"Yeah right!" I said Ray just came out from a room behind me.
"Hey Kai is it right you're staying in a kids section?" Yes I met a kid called Aiky
"Yes…Aiky will be waiting there."
"Who's Aiky?" Asked Tala as he came forward.
"A fan…my fan…" I don't like all of you staring at me.
"O.k…Well I can't wait to meet Aiky" said Ray as he walked into the room. Aww isn't he cute!
GENERAL POV
As Kai walked in he was ushered away to his bed by the doctors but the curtain was pulled away so he could see Aiky.
"Hi Kai!" He said in a chirpy voice.
"Hi!" He said as Ray walked in.
"Wow! Ray Kon! I'm a total fan!" He said as he jumped up and down.
"Hi Aiky! How are you today!" Asked Ray as he sat down next to him.
"Wow a cool blade you got!" Said Aiky as Ray subconsciously took it out his pocket,
"Yeah Drigger is pretty cool! But your blade rules! Who made it" Ray asked again.
"Kai! He gave me it as and autograph! So now im gonna be a pro-star!" He said. Kai smiled as he turned to Tala.
"What was that all about out there?" asked Kai in a small whisper.
"He bloody well deserved it!" Said Tala.
"Why…what happened between you two?" He asked.
"Nothing just forget about it…" He said as he stood up. Kai grabbed his wrist and pulled it down.
"No! Tell me now…what happened?" Tala turned two meet two crimson orbs staring through him.
"I'll tell you tonight, when Jay isn't here." He said before walking past Aiky and throwing something on is bed.
"What was that?" Asked Aiky as he looked to see. Ray gasped at this and Kai started to laugh.
"So…what was it?" He asked after coming out of his laughing fit.
"An attack ring…" Said Ray as he turned to Kai.
"COOL!" said Aiky as Ray smiled.
"Hey Aiky do you want me to take that and get it fixed up?" Aiky's face lit up at the remark and nodded.
"Thanks!" He said as he handed Ray the light blue blade and the attack ring. Ray stood up and walked over to Kai.
"Well I have to go but I'll come and see you tonight…ok?" Ray said before waving and leaving.
KAI'S POV
I have the best of friends, and the best life!
"Wow! Kai you actually know them?" Hehe I turned to see Aiky looking at the door from where Ray and Tala had both left.
"Yeah those two are my best of friends!" I answered.
"Wow I don't have a best friend…" Aww! Poor Aiky…everyone needs to have a best friend. I know!
"Well what about me? I thought I was your best friend?" I said and pouted. Aiky smiled.
"You mean it?" He asked I smiled and nodded to him.
"Yeah…but that also means that you are part of my team now! G-Revolutions newest member Aiky!" Aiky's face lit up I was happy to see him like that. Everyone should feel special at a young age…
"Aiky?" called a nurses voice as she entered the room. "Time to go get your operation…" He smiled.
"O.k! If it helps me get better then yeah!" The nurse smiled before the other doctors came in and placed him on the moving bed. He waved at me before he left.
I wish I had a best friend at his age…
You didn't need friends
I did that would have helped me become a nicer friend…
You're pathetic!
I'm not pathetic…
You are no-wonder Boris chose you!
Boris didn't chose Voltaire did…
Oh so GRAMPS chose for him?
Yes I was the heir for black Dranzer…
He hasn't changed.
Yes he has…
Really? He could still be working with Boris!
I doubt that…
Really?
SHUT UP!
I think Boris wanted to be caught so Gramps could get him out of jail!
GO AWAY!
You know I'm right…of coarse you do…you're still the same Kai…haha
(A/n that was a conversation between new Kai and cold Kai…hope you understood it)
Who was that? That voice sounded so familiar I just don't know whose voice. I better _get_ some sleep…gramps is coming after the doctor sees me and Ray and Tala are coming before…rest must be good now…
Dream…
_A fifteen-year-old Kai was pushed against the wall as another foot came to his stomach…he fell to the ground shortly after that…_
"_Get up ya worthless LOSER!"_
_His father had been watching the new again and it said about Tyson and Kai's battle…Kai got up slowly looking up at the man._
"_Get in the room now!" He said before Kai was pushed in._
"_Your customer will be here shortly…" He said before closing the door. I didn't like this room…this was were 'it' all happened. I was so lost in my thought…it only happened once but it felt like it had happened more times…He told me that I was too beautiful for just one person…he said I had to be shared…I guess since my life was twisted anyway to agree…why did I agree._
"_Hello Kai…" came a voice…I turned to see a middle aged man like Boris. I gasped as he walked forward. I subconsciously stepped back falling onto the bed. _
"_Feisty little one aren't you?" He crawled on top of Kai. _
"_Please don't-" He said. The man grasped hold of Kai's chain so their eyes could meet. Tears held up in Kai's, as the man just wanted lust. He crushed his lips onto Kai's trying to get entry into the small boys mouth. He tied Kai hands up against the railing and began taking off his clothes. He sat there in his boxers._
"_Don't want to spoil your surprise now do I?" Asked the man, as he crushed his lip onto Kai's. The man straddled over Kai this time and began to pull at his nipples. Kai gasped at the pain, which gave the man entry into the youth's mouth. Kai was about to be sick after the taste of the man. The man started to lick Kai chest and worked down to the boxers. Kai's tears couldn't hold in anymore and streamed freely down his face. The man pulled Kai's and his own boxers off. Kai was scared…his father only did this once and that permanently scars him. The man started to suck Kai's chest again and worked down to his member. Kai gasped as he started to suck on it. _
_Kai moaned as the man started to play about with his member in his mouth. Kai didn't want this to happen, but it was. Kai was too busy in thought that he didn't know what was happening. A sharp pain ran through his whole body as he screamed out. Looking down he saw that the man had stuck one of his fingers in Kai. Another was shortly followed and another. Kai screams weren't going to save him as the blood flowed out of his body. The man smirked before Kai screamed one last time before banking out…Kai woke up to the sun blinding his eyes. He felt a warmth beside him as he looked round to see that man beside him. He gasped as he tried to get out of the bed but his arms were still stuck. The man woke again and smiled._
"_Are we going to go again?" He said_
"_NO!" Kai cried, as the man sat on top of him and plunged himself into him. Kai screamed._
"_NO! PLEASE STOP! Please…"_
_GENERAL POV_
"Please…stop!" Shouted Kai as he fought in his sleep. Ray had just come in when he saw this.
"Kai!" He said as he ran over. Kai lay lifeless no part of his body was moving, not even his chest was moving up or down. Ray placed his hand over Kai's.
"Kai…Please wake up…"
'_Ray? What is he doing in here?_
"_Kai I can't believe it!"_
"_Ray what are you talking about?"_
"_You're a slut! Nothing but a worthless slut!"_
"_What do you mean?" _
"_Ever since you told me about you with those other men it hasn't been easy…I can't stand you now!"_
"_Other men?"_
"_Don't play dumb with me…you and your gang!"_
"_But Ray-"_
"_What you didn't mean it you were pressured into doing it? Please you wanted to feel loved for once in your life! I don't care about excuses the fact that you did it with other men shows that you are worthless!" _
"_Ray…" _
Kai jumped up. Gasping for air. Ray looked at him.
KAI'S POV
'He's a traitor!'
He can't be…
'He is he called you worthless…'
He didn't mean it.
'Look at his face it's full of disgust.'
Is it?
'Yes can't you see it…he hates you!'
He doesn't
'He does he only wants you for your body…he's just like everyone else.'
He is isn't he?
'Yes! If I were you I would block him away…don't let him take your body again…'
No one will have my body like that again.
General POV
"KAI!" Ray said as he hugged him.
'He wants to feel you right now.' Kai jumped out of the bed, as Ray looked confused at him.
"What's the m-?" He said before being cut off by a teary eyed Kai.
"Get out." He said in a low growl.
"Kai what's wrong with you?" He said as he walked round the bed.
'He knows you're weak…he knows you can't stand this.'
"GET OUT!" Screamed Kai as he punched forward.
"Kai?"
"Do I have to tell you again? LEAVE OR I'LL MAKE YOU LEAVE!" At that Ray left leaving Kai alone.
…………………………………………………………………………………………
Tala: DONE!
Kai: You really hate me?
Tala: No it's just revenge for dating my sister.
Kai: Great…you make me feel so much better.
Tala: Anyway. ANNI would appreciate if she got 5 reviews…Thanks…Bye!
8. chapter eight
Chapter eight: Why?
Anni: Sorry but I'm back. Tala was annoying me so I kicked his ass!
Kai: Anni!
Anni: Kai?
Kai: Do you know what that mean Tala did to your story?
Anni: What?
Kai: just read it…
Anni reads fanfic chapter seven.
Anni: TALA I'M GONNA KICK YOUR ASS!
Kai: Thanks.
Anni: Why didn't I think of that! Man that's pretty cool!
Kai: Anni?
Anni: What well it is! He's given me a really good angle to come back with.
Disclaimers…I don't own beyblade nor do I own anime or manga or Kai…so don't steal people's ideas!
Chapter eight: Why?
"Rei? What have I done?" Kai sat in the corner of his room. Tears started to slip from under his mask…
'You told him to go away…he only wants your body.'
"You're right! I can't be fooled too easily."
'It's because you took that mask away…you shouldn't have done that!'
"I know I was in a venerable state how couldn't I?"
'Simple you shouldn't have gone to that party.'
"I'm sorry…"
'Don't apologise! Just do as I tell you too and nothing else got it?'
"Right!" said Kai as he got on his bed again. The door slowly opened and walked in a firey red haired boy.
"Tala…what do you want?" spat Kai.
"Woaw…Rei told me you were in a pissed mood but I didn't think you'd be this pissed off. What happened?"
'Don't tell him.'
"Hn…" he said
Tala looked at Kai with an unsure stare.
"So you back to the mask?" _How did he know!_
'Don't worry just don't open up.'
"Shit happens…" He said to a very angry Tala.
"Well Kai! Remember YOU! Were the one that fought this away…You can do it again."
"Why do I want to do that?" said Kai eyes still in a sleeping form.
"Because people care for you. Rei and Me care for you! Your grandfather cares for you!" he said before walking to the door.
" And before you say anything…think! You never know you might say the wrong things…huh what a surprise…" He said before walking past the doctors and nurses as they walked in with Aiky awake and lively.
"Hi Kai!" _I have to be nice to him…He's small…Young fragile_…
'Well I'm not listening so hurry up!'
"Hi Aiky are you all better?" He asked with kindness.
"Yeah I think I'm going home soon." Kai smiled.
"Great news…Well I think that's your blade in the box. Rei left it here for you!" He said pointing out a small box.
"Wow look at it…it's so cool!"
"Just remember to try your best…you'll never get anywhere in life if you don't." He smiled before nodding.
"Thanks."
"Mr Hiwatri…You have a call." Said the doctor as he handed Kai the phone.
"Hello?"
(Kai my boy! Are you all right?)
"Hi gramps…Yeah I'm fine."
(So you don't mind staying the night?)
"Actually I do…do you mind if you come pick me up?" He asked
(Why what's the matter?)
"I feel like my security around this place isn't high…I think 'he' could be here and know-body knows…"
(OH! All right I'll be there soon…) He said as he hung the phone up.
Kai looked at the doctor before handing back the phone.
"Mr Hiwatri will be coming for me soon…Just give me what I need and my nursing staff can sort it all out." The doctor nodded before leaving. Aiky stared wide-eyed at Kai before Kai turned round.
"What?" He asked in a cold voice.
"I thought you were staying the night?" Asked Aiky.
"I'm sorry…My grandfather would like it if I stayed in the house…Things have been difficult and I just need my grandfather there with me…" Aiky understood this and slowly went to sleep.
Kai stood up and began to get changed. He sat besides Aiky until his grandfather came.
"Kai?" Came a grand elderly voice. Kai smiled before standing up. His wounds had stop hurting so much thanks to the painkillers he was given.
"Yes? I'm ready to go!" He said in a loving tone. His grandfather smiled before helping Kai out to the reception. A nurse sat there with a few white bags beside her. She smiled.
"Ahh Mr. Hiwatri here are the prescription you have to take. Come in each week to get your bandage changed…Ok!" Kai nodded before the nurse started to talk to his grandfather about the amount of medicine he was to take.
Kai's POV
'Going home was a good choice'
I thought so…
'Don't trust him…'
Why not?
'He could be with Boris in this company…You'll never know.'
Unless I go to his work place.
'If you go there…IT could be a trap'
I never thought of it that way.
'You wouldn't have your niceness has left you venerable.'
It has?
'Yes…this is how you've gotten in this state!'
Oh!
"Kai time to go…" Came a voice to help Kai's blurred mind come to focus.
"Alright…lets go home." He said before walking out of the hospital…
General POV
They slowly made it towards the car when Kai felt a shot of pain climb up his entire side. He fell…Something caught him he looked to see who it was.
"You!" He screamed before shaking his head. He couldn't see past the Boris look a like.
"What's the matter Kai. Are you feisty again?"
"No! Stay away!" He screamed before his vision came back.
"Kai?" Said a voice that he knew well.
"WHAT!" He said.
"Umm…" His grandfather was taken aback "Do you want to get in the car."
Kai took time to register this in his brain before nodding. His grandfather gave a sigh of relief before entering the car. Kai still waiting outside thinking very hard.
_Why did he come up?_
'He knows you're here…He could be friends with your grandfather….
_No…He couldn't be…but to be on the safe side._
Kai opened the back door and slid in the opposite side of the car seat as far away from his grandfather as possible. The car ride home was to quiet for both of them…but neither one dared to break the silence…When they finally reached home Kai was to busy in thought to talk to anyone…He subconsciously went upstairs to his bed and fell asleep quickly.
: END OF CHAPTER:
Anni: Finished this chapter.
Kai: Hey it's a little short?
Anni: I know I had a really bad person write the chapter before it.
Kai: Ahh so it is crappy.
Anni: Not crappy it's just a little hard to come up with stuff…
Kai: Ok…so shall I kill him or should you?
Anni: Why don't we ask the reviewers…Reviewers would you like
1) Tala killed by Anni plushies.
2) Tala killed by Kai plusihe
3) Tala gets turned into a plushies and we enter him into ready teddy death on kerrang!
R&R&VOTE! PLEASE! BYE FOR NOWS!
End file.
| fanfiction |
reality always seems to fall short of conceptualization , a variety of researchers in dentistry , brought a longstanding dream to fruition by providing adhesives that could effectively bond composites to dentin as well as enamel .
however , it is difficult to achieve , as the bonding process to dentin is very different from that for enamel .
dentin is more humid and more organic than enamel , which makes bonding a difficult task , unlike enamel , which is mostly inorganic in nature . in an increasing attempt to simplify clinical procedures in adhesive dentistry ,
the most common approach was to shorten the adhesive system 's application time and reduce the number of steps .
the three - step etch - and - rinse systems have proved to be a gold standard .
self - etching systems were introduced and purported important advantages compared to the etch - and - rinse systems .
the intensity of the interaction of self - etching adhesive systems with dentin was mostly dependant on the acidity and aggressiveness of the primer used .
the total - etch technique simultaneously removes the smear layer from both the enamel and dentin surface , followed by the application of one bottle agent that combines the primer and adhesive in one solution .
the self - etch adhesives use acidic adhesive comonomers that simultaneously demineralize and infiltrate into the dentin ; adhesive stability is related to the effective coupling of the comonomers that simultaneously demineralize and infiltrate into the dentin .
self - etching systems are less sensitive to technique as compared to systems requiring separate acid conditioning and rinsing steps . despite the presence of short resin tags ,
the present day , all - in - one single bottle of self - etching adhesive systems are highly hydrophilic polymers , which are permeable to water movement and are said to be using the most promising adhesive approach .
hence , the purpose of this study is to evaluate the morphology of the resin - dentin interface of the new total- and self - etching systems and to assess the quality of the hybrid layer formed .
the present study was conducted at the department of conservative dentistry and endodontics , a.b .
forty , freshly extracted caries - free human molars were collected and stored in saline at room temperature .
protocols in cross - infection control as per occupational safety and health administration regulations in storing , surfacing , and utilization were observed .
the 40 extracted teeth stored in saline were retrieved and class v cavities ( 2 mm 1.5 mm 1.5 mm ) were prepared in selected teeth using a no .
245 tungsten carbide bur ; the length of the cutting end of the bur was approximately 3 mm .
after preparation of class v cavities in the 40 teeth , they were randomly divided into four groups of 10 specimens each . in group
i , the prepared dentinal surfaces of the teeth were etched with etchant , 35% phosphoric acid , for 30 sec , and washed .
the surface was slightly blotted with gauze to produce a visible moist dentin surface to produce moist dentin .
the resultant moist surfaces were treated with a total etching bonding agent ( xp bond , dentsply ) and cured as per manufacturer 's instructions . in group ii , the prepared dentinal surfaces of the teeth were etched with etchant , 35% phosphoric acid , for 30 sec , and washed .
the surface was slightly blotted with gauze to produce a visible moist dentin surface to produce moist dentin .
the resultant moist surfaces were treated with total etching bonding agent ( adper single bond 2 , 3 m espe ) and cured as per manufacturer 's instructions . in group iii ,
the resultant moist dentin surfaces were treated with one - step self - etching bonding agent ( adper easy one , 3 m espe ) , by applying a uniform layer , avoiding pooling , gently agitating with a microbrush for 20 sec , and allowing them to dry in a mild air stream for 10 sec .
a second layer was applied with a microbrush , avoiding any pooling , and it was allowed to dry in a mild air stream for 10 sec . the bonding agent was light cured for 20 sec . in group iv , all the prepared dentinal surfaces of the teeth were cleaned and blotted with gauze to produce visible moist dentin .
the resultant moist dentin surfaces were treated with a one - step self - etching bonding agent ( xeno v , dentsply ) by applying a uniform layer , avoiding pooling , and allowing them to dry in a mild air stream for 10 sec .
the class v preparations were then restored with hybrid composite in an incremental technique of 1 mm each , curing each layer for 40 sec .
the restored specimens were then subjected to thermocycling ( 500 cycles , 5 to 55 c , 30 sec dwell time ) .
following thermocycling , the teeth were sectioned longitudinally through the restoration in a buccolingual plane .
two sections were made per tooth , producing two specimens , which were polished with an increased grit of silicon carbide paper , under running water .
the specimens were demineralized using 6n hcl for 30 sec and deproteinized with 2.5% naocl ( sodium hypochlorite ) for 10 min , to enable examination of the interface and left to dry for 24 h. the specimens were gold sputtered and morphological evaluation of the resin - dentin interface was conducted using scanning electron microscopy under various magnifications .
group i scanning electron microscopic evaluation showed a clearly recognizable hybrid layer , which was thick , defined , and continuous . the thickness of the hybrid layer ranged between 3 - 8 m .
however , few areas showing cohesive failure were seen within the resin and the resin - composite interface . the length of the resin tags ranged between 10 - 25 m .
group i sem image of xp bond with dentin group ii a scanning electron microscopic evaluation of the specimens showed a clearly recognizable thin hybrid layer .
the hybrid was clearly defined and the thickness ranged between 3 - 6 m . however , there were areas where there was a visible region of separated layers showing adhesive failure between the dentin and resin interface .
there were few areas of separation between the composite and resin interface indicating a cohesive failure .
few voids were seen on the resin tags and they showed few lateral tags [ figure 2 ] .
group ii sem image of adper single bond 2 with dentin group iii a scanning electron microscopic evaluation of specimens showed a thin hybrid layer that was not clearly distinct and no discontinuity was noticed .
few resin tags were observed with a range of 1 - 2 m . there were no voids observed and
group iii sem image of adper easy one with dentin group iv a scanning electron microscopic evaluation showed no evidence of a hybrid layer .
the junction between the resin - dentin appeared to be tight , thin , and continuous with no adhesive or cohesive failure .
minimal formation of microtags was noticed under higher magnification with a range of 0.6 - 1.5 m . there were no evident lateral tags .
some of the dentinal tubules appeared to be obstructed by smear plugs [ figure 4 ] .
group i scanning electron microscopic evaluation showed a clearly recognizable hybrid layer , which was thick , defined , and continuous . the thickness of the hybrid layer ranged between 3 - 8 m .
however , few areas showing cohesive failure were seen within the resin and the resin - composite interface . the length of the resin tags ranged between 10 - 25 m .
group i sem image of xp bond with dentin group ii a scanning electron microscopic evaluation of the specimens showed a clearly recognizable thin hybrid layer .
the hybrid was clearly defined and the thickness ranged between 3 - 6 m . however , there were areas where there was a visible region of separated layers showing adhesive failure between the dentin and resin interface .
there were few areas of separation between the composite and resin interface indicating a cohesive failure .
few voids were seen on the resin tags and they showed few lateral tags [ figure 2 ] .
group ii sem image of adper single bond 2 with dentin group iii a scanning electron microscopic evaluation of specimens showed a thin hybrid layer that was not clearly distinct and no discontinuity was noticed .
few resin tags were observed with a range of 1 - 2 m . there were no voids observed and
group iii sem image of adper easy one with dentin group iv a scanning electron microscopic evaluation showed no evidence of a hybrid layer .
the junction between the resin - dentin appeared to be tight , thin , and continuous with no adhesive or cohesive failure .
minimal formation of microtags was noticed under higher magnification with a range of 0.6 - 1.5 m . there were no evident lateral tags .
some of the dentinal tubules appeared to be obstructed by smear plugs [ figure 4 ] .
hybridization of dental hard tissues provides a new frontier in modern adhesive dentistry because : it creates a new , advanced , multifunctional dental material that can be prepared in the subsurface of teeth .
the hybrid layer refers to the structure formed in the dental hard tissues by demineralization of the surface and sub - surface , followed by infiltration of monomers and subsequent polymerization .
dentin is the fundamental substrate of restorative dentistry , and its properties and characteristics are key determinants of nearly all restorative , preventive , and disease processes of the teeth .
dentin is a complex hydrated composite of dentinal tubules , mineralized matrix , collagen , and dentinal fluid .
dentinal tubules are not smooth , and have many lateral branches and microchannels that connect to adjacent tubules and permit fluid movement .
thus , variations in permeability arise from regional differences , tubular irregularities , mineral deposits , organic components of odontoblastic processes , collagen , and dentinal fluid . from the bonding perspective , the hydrated structure and variability of the dentin in its characteristics of permeability , cause substantial difficulties . unless the bonding agent can displace or is miscible in the fluid
, it will be difficult to achieve a stable , long - lasting bond . as bonding is created by impregnation of dentin substrate by blends of resin monomers ,
the stability of the bonded interface relies on the creation of a compact and homogenous hybrid layer . in etch and rinse strategy , bonding monomers impregnate the porous etched substrate ; and stable bonds can be achieved if the etched substrate is fully infiltrated by the monomers .
conversely , the self - etch approach uses acidic adhesive comonomers that simultaneously demineralize and infiltrate into the dentin .
adhesive stability is related to the effective coupling of the comonomers with an infiltrated substrate .
self - etching systems are generally less technique sensitive compared to systems that utilize separate acid conditioning and rinsing steps .
collapse of the air - dried , demineralized collagen is prevented as the smear layer - retained dentin is simultaneously demineralized and polymerized in situ . despite the presence of short resin tags ,
the specimen preparation in the present study involved the preparation of class v cavities for three reasons : first , because it involves three dental hard structures , that is , enamel , dentin , and cementum .
second , a class v cavity simulates a clinical situation of higher stress due to a higher c - factor , and third , due to exposure to varied fluids in the cervical region of the tooth .
radovic i , vulicevic zr , and godoy gf chose class v cavities , because samples prepared in this manner involved the difficulties in achieving the suggestive width of the adhesive layer with a higher c - factor and higher stress contraction stress .
the number of cycles used in the present study was 500 ( 5 to 55 c with 30 sec dwell time ) .
radovic i , vulicevic zr , and godoy gf also used 500 cycles , as it was based on the current iso standard . in the present study , 6n hydrochloric acid was used for demineralization and 2.5% sodium hypochlorite for deproteinization .
this ensured optimal exposure of the resin tags and hybrid layer and enabled viewing under the scanning electron microscope .
nakabayashi and pashley also stated that the study of the usual procedure for specimen preparation under sem involved preparation of polished cross - sections of the bonded interface followed by an acid challenge with 5n hydrochloric acid for 30 sec to demineralized , followed by 1% sodium hypochlorite for 10 min .
this procedure exposed the resin tags to their full length and demarcated the bottom of the hybrid layer .
the present study is in accordance with the study done by radovic , vulicevic , and garcia godoy , who also used 6n hydrochloric acid and 2.5% sodium hypochlorite for demineralization and deproteinization .
scanning electron microscopy is one of the first and most widely used tools to study the interfacial characteristics and process of bonding .
scanning electron microscopy , although very useful , induces shrinkage artifacts in the specimens during processing and in the high vacuum of the microscope , unless the specimens in the resin are perfectly infiltrated with resin .
the usual procedure involves the preparation of polished cross - sections of the bonded interface followed by an acid challenge with 6n hydrochloric acid for 30 sec to demineralize , followed by 2.5% sodium hypochlorite for 10 min .
this procedure exposes the resin tags to their full length and demarcates the bottom of the hybrid layer . in the present study
it was observed that , there was shrinkage artifacts created , which was attributed to the fact that the specimen preparation procedures in scanning electron microscopy induced artifacts .
perdigao and carvalho had investigated and found that specimens prepared for scanning electron microscopy underwent air drying , hexamethyldisilazane , or peldri ii drying .
it was concluded that specimens prepared by air drying showed shrinkage that occurred during specimen preparation and this influenced the exact dimensions of the morphology .
voids seen in the resin tags of the specimens in group i and group ii represent remnants of water , in the form of droplets , which were trapped in the adhesive before polymerization . air drying over a long time reduces the number of water droplets , but total drying is difficult to achieve . during the desiccation procedure , for gold sputtering the specimens , water droplets might have evaporated , leaving voids .
van landuyt et al , in their investigation , found that the number of water droplets was significantly reduced after strong air drying , although they did not completely disappear . in the present study
there is a highly significant difference in the thickness of the hybrid layer and the length of the resin tags formed between the total - etch adhesives ( group i and group ii ) and self - etch adhesives ( group iii and group iv ) . the total - etch adhesives use the etch - and - rinse strategy , thus removing the smear layer and subsequent infiltration of monomers and polymerization .
the primary bonding mechanism is a diffusion - based process leading to the production of a hybrid resin - dentin interdiffusion zone .
in group i , xp bond has been used , which contains t- butanol ; and in group ii , adper single bond 2 ethanol is used , which requires the wet bonding technique and thus there are lesser regions of adhesive failure seen .
this explains that although the adhesive ( xp bond and adper single bond 2 ) produces resin tags that are long , with thicker hybrid layers , adhesive failure and cohesive failure are seen due to the technique sensitivity of the bonding mechanism .
gentle postconditioning drying of the etched dentin still guarantees effective bonding for ethanol - based adhesives .
however , true chemical bonding is unlikely , because the functional monomers have a weak affinity to the hydroxyapatite - depleted collagen .
group iii and group iv , self - etch adhesives showed thin hybrid layers , with fewer microtags .
however , there is no evidence of adhesive or cohesive failures observed with self - etch adhesives .
the self - etch approach had an important advantage in that the infiltration of the resin occurred simultaneously with the self - etching process resulting in a uniform interdiffusion zone .
de munck et al , in their study concluded that the thickness of the hybrid layer was , however , much smaller than that produced by the strong self - etch adhesive or the etch - and - rinse total - etch approach .
it was proven to be minor in importance with regard to the actual bonding effectiveness .
however , the drawback of the all - in - one adhesive is its behavior as a semi - permeable membrane allowing movement of water across bonded interfaces , which may in the long term lead to potential hydrolytic degradation
. the limitations of conventional scanning electron microscopy compared to more sophisticated methods of examining tooth restoration interfaces have been recognized .
however , regardless of the method used ( sem / tem ) , no correlation between the hybrid layer width and bond strength of the adhesive systems could be determined .
within the limitations of the present study , however , the scanning electron microscopy method can provide basic information , which points to the possible specific features of the interface , which need to be examined closely . in vitro studies depend on variable parameters , such as , sample collection , surfacing , aging , thermocycling , and hurdles in specimen preparation , for scanning electron microscopy .
there being a clinical correlation with long - term studies on the effects of aging , thermal effects on the bonding process need to be examined closely .
from the present study it is concluded that : xp bond , among the total - etch bonding agents , showed good penetration of resin into the dentin by the presence of long resin tags and a thick hybrid layer .
xeno v , among the self - etch bonding agents , did not show a clear hybrid layer with few resin tags , but showed a continuous adaptation along the dentin surface .
the adaptation of self - etch adhesives to the resin- dentin interface was good without voids or separation of phases ; showing a thin , continuous hybrid layer .
it was concluded that such an adaptation of resin with dentin tissue , as in the case of self - etch adhesives , was required for better treatment outcome to reduce postoperative sensitivity . | pubmed |
How does warped spacetime affect the perceived energy of bosons within that warping? (GR & QFT)
***Disclaimer:*** I am an amateur, and an experimentalist and don't understand the equations involved.
***Intro:*** Fermions and bosons are (*we're almost definitely sure this time*) fundamental particles. Fermions have mass and make everything up so I don't trust them. Bosons are field particles like the photon. Quantum Field Theory describes their interactions. Both fermions and bosons travel through spacetime. Spacetime gets warped thanks to General Relativity, so the path that those particles take changes based on the shortest *actual* distance through warped spacetime. This appears like acceleration; the object has a new velocity, so an energy change has occurred.
You see this acceleration on fermions every time you drop your phone. It's a little more exotic to see the effect on bosons, but gravitational lensing warps light *around* massive objects. You can see a star behind another star!
***Trickier stuff:*** The equations describing Quantum Field Theory can't be solved in warped spacetime, which happens due to General Relativity. Dang. BUT, I'm curious if we couldn't just measure the impact of warping spacetime on the quantum energy of bosons. Wouldn't that basically be a brute-force transfer function between spacetime and quantum chromodynamics?
So let's say you've got two planck-length-second volumes of spacetime, $V\_1$ and $V\_2$, and a 500nm photon is traveling from one to the other. $V\_1$ is flat spacetime, but $V\_2$ is warped. The path of the photon changes based on the layline of the new volume, which appears to us (*outside* the new volume) as acceleration.
But what happens to the photon while it's *inside* that volume? Wouldn't it gain or lose energy based on the compression along its wave-axis? The reference frame for the original wavelength changed, so the 500nm photon has a different wavelength to an observer *inside* the volume. Has spacetime not only accelerated the boson, but also given it some quantum energy as well?
***Overall question:*** If the "theory of everything" is blocked by our inability to solve closed-form equations, could we try a brute force approach? Could an option for this look like: bend spacetime some known amount, fire a known wavelength boson into that volume, measure the observed wavelength differential, now you know how much energy spacetime lends bosons due to curvature. Do this enough, and wouldn't you have a transfer function between QFT and GR?
$\newcommand{\D}{\mathrm{D}}$
**[Quantum field theory in curved spacetime](https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime)** can very well be studied. The fact that we don't know many fundamental things is not due to lack of understanding, but due to the fact that real-life models, such as the Standard Model, are way too complicated to perform calculations. If we restrict to toy models, e.g. lower or higher dimensions, conformal symmetry, supersymmetry etc. we can "solve"$^{(\*)}$ QFT, either perturbatively, or numerically, or even analytically. For the rest, the distinction between fermions and bosons will not play a role, since the question is on a very abstract level, so I will refer to both as "fields" or "particles".
The keyword in your question is the word "*known*". Whenever you know how the spacetime is bent, you can write down the metric of your universe: $g$. Then you can in principle go out and calculate things at the presence of this $g$. For example you can calculate the partition function, written schematically as
$$ Z(g,\text{sources}) := \int \D[\text{fields}] \ \exp\!\Big(iS[g,\text{fields}]+\text{fields}\cdot\_g\text{sources}\Big). \tag{1}$$
From here you can ask everything that you could in flat spacetime QFT and the partition function will answer it for you. In the above formula, the fields are quantum (which is indicated by the $\D[\text{fields}]$ and the rest of the data are classical.
**Quentum gravity** is a whole different story. This is when the metric is also quantum. In this case, most of the times you can't naively write down the partition function as
$$Z(\text{sources}) = \int \D[\text{fields}]\,\D g\ \exp\!\Big(iS[g,\text{fields}]+\text{fields}\cdot\_g\text{sources}\Big),$$
except for some very special and interesting cases.
**In your question** you are concerned about QFT in curved spacetime, not quantum gravity. The setup you are proposing, translated to manageable form is that you are giving me an empty finite volume of space. Then you bend it by a known amount, i.e. you now gave me a metric $g$ of that space. Magically a particle is now in your hands. The particle has known properties (you mentioned wavelength, but let's be general). Let's call the particle with these properties $\phi$. You fire it in the curved space, and it comes having different properties; it's a $\phi'$ now. What happens in such a scenario in QFT is encoded in the [S-matrix](https://en.wikipedia.org/wiki/S-matrix), which can be inferred from the various correlation functions, which can, in turn, be derived from the partition function. Depending on the details of your question, the hands-on calculation of this can range from trivial to immensely complicated.
Regarding the last part of your question, it would not give you a "transfer function" between QFT and GR. It gives you just a GR-modified version of QFT. To have a "transfer function" you would have to calculate how the mere existence of the particle inside the curved space affects the curvature, and update the curvature before sending in another guy. This is also a well-known framework, known as [semiclassical gravity](https://en.wikipedia.org/wiki/Semiclassical_gravity).
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$^{(\*)}$ Solve is not the best word to use here. A better phrase would be "calculate the partition function at the presence of sources"
| stackexchange/physics |
Can an aluminium chip with some engravings protect people from harmful effects of electromagnetic radiation? [closed]
**Closed.** This question is [off-topic](/help/closed-questions). It is not currently accepting answers.
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We deal with **mainstream physics** here. Questions about the general correctness of unpublished personal theories are off topic, although specific questions evaluating new theories in the context of established science are usually allowed. For more information, see [Is non mainstream physics appropriate for this site?](https://physics.meta.stackexchange.com/a/4539).
Closed 2 years ago.
[Improve this question](/posts/648943/edit)
I have come to know about a product called E-Guard by a company called QNET. They say that this small device (Just an aluminium piece with laser engravings) can protect us from harmful effects of electromagnetic radiations. How genuine is this concept of a small device protecting against radiation?
Product page: <https://www.amezcua.com/E-Guard.html>
If for some reason you wanted to blockout electromagnetic ratiation from your body you would need to wear a Faraday cage (a metal mesh with holes smaller than the wavelength of the radiation you wish to block out) or alternative just a solid metal suit. A small piece of aluminium will not achieve this.
The fact you don't see scientists wearing such suits in everyday life should be an indication to whether they feel it is a necessary precaution. If you were going into a nuclear reactor or space it may be a different matter.
| stackexchange/physics |
obstetric injury is the most common cause of sphincter injury and pelvic floor failure resulting in lack of bowel control .
the pudendal nerve may be damaged during the course of prolonged vaginal delivery consequent to stretching [ 13 ] .
a third / fourth - degree tear ( involving the anal sphincter complex ) occurs in 0.52% .
eighty five per cent will have a persistent defect of the sphincter despite the immediate ( primary ) repair by the obstetrician .
conservative treatment ( diet / medical manipulation , biofeedback and pelvic floor exercises ) can be successful .
secondary repair is usually offered to patients with gross faecal incontinence [ 4 , 5 ] .
the outcome depends on the extent of the anal sphincter damage and associated neurological injury .
a 32-year - old woman was admitted electively for the management of a 2-year history of anal incontinence following a traumatic vaginal delivery of her second child .
she had undergone a manual forceful dilatation of the posterior vagina for cephalo - pelvic disproportion which resulted to a severe perineal tear .
this was repaired but she complained of severe urgency of defaecation and flatus incontinence since then .
she had awareness of the need to defaecate but was unable to retain solid stool for more than a few minutes .
reduced anal sensation for liquid stool and faecal perianal soiling followed a high residue diet .
she had severe discomfort and soiling during sexual intercourse because of the very close proximity of the anal canal to the vagina .
her faecal incontinence score was 15/20 according to the cleveland clinic scoring system [ i.e. solids ( usually ) 3 , liquids ( always ) 4 , flatus ( always ) 4 , use of pad ( never ) 0 , lifestyle alteration ( always ) 4 ] .
physical examination revealed a patulous anus immediately adjacent to the posterior for chette of the vagina indicating a poor internal sphincter function ( fig . 1 ) .
she had a lax external sphincter tone on voluntary squeezing and the anorectal angle was weakly accentuated with squeeze .
proctoscopy revealed an empty rectum and normal mucosa . a preoperative diagnosis of a fourth - degree perineal tear involving the internal anal sphincter ( ias ) and external anal sphincter ( eas ) with possible mild pudendal neuropathy was made and she consented to a perineal repair ( table 1 ) .
table 1classification of perineal tear first degreeinjury to perineal skinsecond degreeinjury to perineum involving perineal muscles but not involving the anal sphinctersthird degreeinjury to perineum involving the anal sphincter complex:3a : < 50% of ext anal sphincter thickness3b : > 50% eas thickness3c : both eas and ias involvedfourth degreeinvolves anal sphincter complex ( eas and ias ) and anorectal mucosa .
figure 1:a severe chronic fourth - degree tear secondary to birthing with grossly deficient perineum ( a thin demarcation between anus and vagina ) .
classification of perineal tear a severe chronic fourth - degree tear secondary to birthing with grossly deficient perineum ( a thin demarcation between anus and vagina ) .
following mechanical bowel preparation and i / v prophylactic antibiotics ( ceftriaxone 1 gm and metronidazole 500 mg ) given prior to induction of anaesthesia , and , with the patient in the lithotomy position a proctoscopy was carried out to irrigate the rectum .
the dissection was commenced laterally out in the ischiorectal fat to establish an appropriate plane and proceeded towards the site of sphincter injury which was in the anterior margin .
the anodermal flap was carefully mobilized from the vagina by sharp dissection in a cephalad direction to expose the entire length of the injury with the plane lying posterior to any large paravaginal veins ( fig . 2 ) .
the edges of the damaged sphincter muscle were identified and the plane between the anal mucosa and the muscle on either side was developed . as the injury extended proximally into the levator ani ( puborectalis ) muscle , an anterior levatorplasty was performed by plicating the anterior limbs of the muscle to the midline with 2 - 0 polyglactin sutures ( fig . 3 ) .
the anterior defect of the ias extended through the anal mucosa and was plicated with 2 - 0 polygalactin suture ( fig . 3 ) .
the vaginal wall was plicated with interrupted sutures of 3 - 0 polygalactin to provide added support to the rectovaginal septum . an overlapping repair of 3 cm of the mobilized edges of the external sphincter extended the length of the anal canal and was performed using five horizontal mattress sutures of 2 - 0 polygalactin ( fig .
4 ) . following irrigation and haemostasis the semi - circular skin wound which has now almost become longitudinal was closed in an inverted y fashion .
the distance between the posterior forchette and the anal canal was seen to be lengthened ( fig .
postoperatively , sitz baths were instituted and the patient was given a low - residue diet for the first 48 h. apart from constipation relieved with microlax enema , she made good recovery with no signs of wound infection nor haematoma .
postoperatively , her anal tone at rest was increased and there was reasonable increase in the maximum squeeze pressure . her incontinence score a week after repair was 2/20 , i.e. solids ( never ) 0 , liquids ( never ) 0 , flatus ( sometimes ) 2 , use of pad ( never ) 0 , lifestyle alteration ( never ) 0 .
she was discharged on the 10th postoperative day and long - term follow - up planned ( table 2 ) .
table 2ccis for the assessment of faecal incontinence neverrarelysometimesusuallyalwayssolids01234liquids01234flatus01234use of pad01234lifestyle alteration01234rarely : less than once a month ; sometimes : more than once per month or less than once a week ; usually : more than once a week but less than once a day ; always : more than once a day.ccis 0 , perfect continence ; ccis 17 , good continence ; ccis 814 , moderate incontinence ; ccis 1520 , severe incontinence ; ccis > 20 , completely incontinent .
figure 2:vagina carefully separated from the anterior rectal wall ( arrow ) ; gauze swab in the right and left ischioanal fossa , respectively .
figure 3:ias plication ( long arrow ) extending to the plicated levator ani ( short arrow ) ( forceps on the separated external sphincter , urethral catheter in situ ) .
figure 4:anterior external sphincteroplasty ( covered by isciorectal fat ; finger in anal canal ) .
figure 5:wound closed in an inverted y-shaped manner with elongation of the skin over the perineal body ( arrow - anal canal ; deeply - seated anal verge with increase length of anal canal ) .
ccis for the assessment of faecal incontinence rarely : less than once a month ; sometimes : more than once per month or less than once a week ; usually : more than once a week but less than once a day ; always : more than once a day .
ccis 0 , perfect continence ; ccis 17 , good continence ; ccis 814 , moderate incontinence ; ccis 1520 , severe incontinence ; ccis > 20 , completely incontinent .
vagina carefully separated from the anterior rectal wall ( arrow ) ; gauze swab in the right and left ischioanal fossa , respectively .
ias plication ( long arrow ) extending to the plicated levator ani ( short arrow ) ( forceps on the separated external sphincter , urethral catheter in situ ) .
wound closed in an inverted y-shaped manner with elongation of the skin over the perineal body ( arrow - anal canal ; deeply - seated anal verge with increase length of anal canal ) .
primary repair is ideal as successful primary sphincteroplasty substantially improves quality of life and reduces overall cost of treatment . following primary repair
a poor continence score at 3 months post - partum , usually with urge incontinence of faeces denotes severe anal sphincter dysfunction and is a predictive factor for persistent faecal incontinence . in a resourced area , endoanal ultrasound
will localize the injury site and size the extent of sphincter damage prior to a secondary repair [ 4 , 5 ] .
anorectal physiology is useful for patients not considered for operative repair so as to obtain baseline information and , to determine the extent of anal sphincter damage and identify pudendal neuropathy in candidates for surgery [ 4 , 5 , 7 , 8 ] .
operative management is usually offered to a patient with a score of 12 or greater , an underlying correctable abnormality and gross faecal continence [ 4 , 5 , 8 ] . these range from an overlapping eas repair for a distal sphincter defect to repair of the entire pelvic floor for neuropathic faecal incontinence [ 4 , 5 ] . where ias injury can be identified , it is advisable to repair separately .
improvement in the functional length of the sphincter corresponded to a successful outcome [ 4 , 5 , 7 , 8 ] .
patients with coexisting pudendal neuropathy or operative pudendal nerve damage will be at risk and may benefit from sacral nerve stimulation or a neosphincter procedure or even an end - stoma [ 4 , 5 , 7 ] .
it should be compared with long - term results following a structured training in recognizing and repairing sphincter injury primarily .
written informed consent was obtained from the patient for publication of this case report and any accompanying images .
a copy of the written consent is available for review by the editor of this journal.
written informed consent was obtained from the patient for publication of this case report and any accompanying images .
a copy of the written consent is available for review by the editor of this journal. | pubmed |
Ludwig Bachhofer June 30, 1894 - March 1976 was a German art historian and professor in Munich and at the University of Chicago.
Life
Bachhofer began his studies in 1916 at the University of Munich, but had to interrupt this due to the First World War. In 1918 he resumed his studies and received his doctorate in 1921 with a dissertation on the art of Japanese woodcut masters. [1]
In 1921/22 Bachhofer completed a scientific training at the Museum of Ethnology in Munich under Lucian Scherman. In 1926 he helped to establish the Department of Japanese Art of the Ethnological Museum in Munich. In 1926 he was in Munich in art history and Asian archeology and worked as a private lecturer at the University of Munich. He held lectures on Chinese, Japanese and Indian art history.
In July 1933, he was appointed associate professor, but the responsible ministry disagreed with the nomination because of the non-Aryan origin of Bachhofer's wife. Since Bachhofer refused a divorce from his wife of Jewish origin [3] and he was threatened with dismissal, the family emigrated in 1934 to the United States .
From 1935 Bachhofer worked as a professor of East Asian art history at the University of Chicago, and from 1941 as a full professor. From 1941 to 1945 he was also co-editor of the Art Bulletin. In 1965 he retired.
Research
Bachhofer's research interests included East Asian art, with a focus on the history of art in Central Asia and its connection with India, Iran and China. In Germany, he was one of the most important experts of the new discipline of Asian art history. [1] His work on the early Indian sculpture has long been considered a standard work. [1]
Works
Chinese art . Wroclaw 1923
The early Indian sculpture . 2 volumes, Munich / Florence 1929
A Short History of Chinese Art . Pantheon, New York 1946
Literature
Harrie Vanderstappen: Ludwig Bachhofer 1894-1976 . In: Hartmut Walravens: Bibliographies on the East Asian art history of Germany . 1983
References
Category:1894 births
Category:1976 deaths
Category:Art historians
Category:German art historians
Category:German emigrants to the United States | wikipedia |
fusobacterium nucleatum is a strict anaerobic microorganism commensal to the human oropharynx and gastrointestinal tract , which causes a wide spectrum of human diseases and it is an important pathogen in abscesses .
we report the case of a previously healthy 64-year - old woman with multiple abscesses due to fusobacterium nucleatum , involving liver , pleura and brain .
fusobacterium was not recovered from blood cultures nor from culture of hepatic , pleural and brain drain fluid .
the diagnosis was obtained by polymerase chain reaction amplification of bacterial deoxyribonucleic acid in brain abscess drain .
fusobacterium spp . , should be considered in patients with any organ abscess , especially in case of invasive disease with multiple secondary site involving brain .
techniques might be of special usefulness in cases that remain negative in culture to obtain the diagnosis and perform adequate treatment .
fusobacterium nucleatum , is a gram - negative anaerobic microorganism that is indigenous to the human oral cavity .
it can also be found in the gastrointestinal , urogenital and upper respiratory tract and can induce a wide spectrum of human diseases , such as adverse pregnancy outcome , pulmonary and intraabdominal infections , and it is an important pathogen in abscesses , especially in patients with comorbidities such as cancer .
a 64-year - old woman , with no significant past medical history , was admitted to intensive care unit with confusion and fever . on clinical examination ,
temperature was of 38.8 c , blood pressure at 105/73 mmhg , heart rate at 129 bpm .
blood tests showed a white blood cells ( wbc ) at 14.000/mm ( normal 4.00010.000 mm ) , an elevated c- reactive protein ( crp ) at 160.6 mg / l ( normal
< 3.0 mg / l ) , and creatinine at 126 mol / l ( normal 4990 mol / l ) .
screening for hiv , hcv and hbv as well as for syphilis was negative . a magnetic resonance imaging ( mri ) of the head ,
performed on admission showed 4 ring enhancing lesions with a surrounding edema consistent with cerebral abscesses : a 28 mm cerebellar lesion , a 15 mm frontal right image , a 17 mm parietal and a 15 mm occipital lesion .
body scan imaging revealed an 11 cm liver abscess and a right - sided pleural effusion with negative microbiological cultures from thoracentesis and liver drains which recovered a brown purulent liquid .
an intravenous ceftriaxone and oral metronidazole was started on day of admission and lead to clinical and biological improvement .
patient became afebrile five days after the beginning of antibiotic treatment and neurological symptoms have resolved .
a cerebral mri performed at 3 weeks of treatment found no major difference in the size of the brain abscesses .
a brain biopsy found a mixed inflammatory reaction with an important macrophagic infiltrate and granulomas , without any evident pathogenic microorganism .
aerobic and anaerobic cultures were performed but remained negative . polymerase chain reaction ( pcr ) product was detected with 16s ribosomal deoxyribonucleic acid ( rna ) from fusobacterium nucleatum .
ceftriaxone was changed by clindamycine and metronidazole was continued . an 18f - fludeoxyglucose positron emission tomography ( fdg - pet )
did nt show any other infection site besides the liver , pleura and the brain .
an mri of brain performed 12 weeks after the beginning of treatment showed brain abscesses decrease in size : a 28 mm cerebellar lesion decrease to 8 mm , a 15 mm frontal right image to 6.5 mm , a 17 mm parietal and a 15 mm occipital to 6.5 mm for the both .
brain , hepatic and pulmonary images performed 6 months after the initial presentation showed a stability of brain images and complete recovery of hepatic abscesses and pleural effusion .
the patient shows a good clinical recovery , especially in neuro cognitive function as well as a good biological evolution with crp at 3.7 mg / l and no fever .
fusobacterium , especially fusibacterium nucleatum and fusobacterium necrophorum , is a major cause of the well - known lemierre s syndrome , described for the first time in 1936 : a septic thrombophlebitis of the internal jugular vein that typically begins with an oropharyngeal infection but it is also one of the main protagonists of abscesses in many organs , , . in the study reporting clinical and biological features of 78 cases of fusobacterium nucleatum infections , abscess was the most common type of infection , 43 patients ( 55% ) , involving many organs but principally skin , pleura and liver .
the available bacteriological data is , however , variable on the role of fusobacterium spp . in brain abscesses .
even if anaerobes are major aetiological agents of intracranial abscess ( nearly 60% ) , the prevalence of fusobacterium spp varies from 5% to 33% according to several studies on the microbiological spectrum of brain abscesses , , , .
we present the case of woman with multiple abscesses due to fusobacterium nucleatum , which was not recovered from blood cultures nor from culture of the patient s hepatic , brain and pleural drain fluid .
the microbiological diagnosis was performed by nucleic acid amplification technique on brain abscess . in the past
the importance of anaerobic organisms in abscesses was underestimated probably because of lack of use the appropriate collection methods of anaerobic cultures and rapid transportation to the laboratory which lead to the failure to identify the bacteria .
recent studies showed an important increase in the detection of anaerobic pathogens causing abscess , .
furthermore , a review of the literature showed that diagnosis of fusobacterium nucleatum infection in most cases is based on culture ( 81.25% ) and only few cases on nucleic acid amplification technique .
the sensitivity of blood cultures is however poor , especially in association with abscesses . in our patient
, pre - culture antibiotic therapy may contribute to the negativity of culture , but the severity of initial presentation did nt permit the delay of antibiotic treatment .
the imaging exams revealed the presence of intra - uterine device which was removed but the culture of device remained negative .
concerning the underling comorbidities , the fdg - pet did nt revealed malignancies . to conclude , fusobacterium spp ,
should be considered in patients with any organ abscess , especially with peritonsillar , oropharyngeal , lung and liver abscess , but also in case of invasive disease with multiple secondary site involving brain .
indeed , pcr is not to perform routinely but pcr - mediated amplification and sequencing of 16s ribosomal rna might be of special usefulness in cases that remain negative in culture , possibly due to prior antibiotic treatment , to obtain the diagnosis and perform adequate treatment . | pubmed |
the determination of the @xmath4 and @xmath5 were recently presented @xcite and will only be briefly reviewed here .
mathematically , the @xmath4 is the sum of the antenna temperature @xmath6 in each velocity channel times the velocity with respect to the local standard of rest @xmath7 of the velocity channel over the range of emission divided by the sum of the @xmath6 in each velocity channel over the range of emission as shown in equation [ vc ] .
@xmath8 the summation extends over the range of emission .
the @xmath5 is calculated to be the region where the ta exceeds three times the standard deviation of the antenna temperature of the background noise .
the standard deviation is determined from velocity channels far away from the emission range of the source .
@xcite examined the @xmath2 and @xmath3 of the sio maser transitions without regard to the phase of the star . in this work we found that the @xmath9 was generally broader than the @xmath10 , @xmath11 to @xmath12 , respectively .
the @xmath13 are slightly more positive than the @xmath14 .
these differences indicate that the @xmath0 occurs in a dynamically different region of the circumstellar environment than the @xmath1 .
this conclusion is consistent with the observational results of @xcite .
the @xmath4 is a well suited parameter to compare our single dish observations to vlbi observations , as it is weighted to the brightest emission .
this effect is apparent in the figures b1-b3 in @xcite . @xcite
have compared sio and h@xmath15o maser emission from a 401 evolved stars .
they find that sio emission is less dependent on the optical phase than the h@xmath15o masers .
while this is a relative conclusion only , it indicates no strong phase relationship for the @xmath5 , a finding which complements our own .
@xcite concluded that @xmath0 and @xmath1 emission can form at comparable radii and in related columns of gas although their vlbi maps show few overlaps between the two transitions .
recent theoretical developments vary in predicting the radii at which the @xmath0 and @xmath1 emission occur . @xcite
have the @xmath1 emission at larger or smaller radii than the @xmath0 emission depending on the phase .
@xcite show no discernible difference in the radii at which the maser originate at any phase presented .
the phase of the star is the optical phase .
it is determined by subtracting the julian day number of the most recent stellar maximum from the julian day number of the observation and dividing by the stellar period .
the phase varies from zero to one .
the stellar maxima and periods were obtained from the aavso bulletin 74 @xcite .
stellar periods were added or subtracted from the bulletin 74 maxima as needed to determine the most recent maxima . [
tab : lpvs ] gives the stellar periods used for the sources .
@xcite investigated the dynamics of the circumstellar region in which the sio masers originate and have provided the most thoroughly developed theory for the maser spectra in lpvs from phase 0.1 to 0.4 .
they model and depict a shock traveling out from the star generating different velocities , red shifted or more positive and blue shifted or more negative , at different distances from the star . as the shock travels out the velocities change as a function of distance from the star and phase .
@xcite predicted a phase dependent @xmath9 varying from about @xmath16 to @xmath17 .
the @xmath10 varies from about @xmath18 to @xmath19 .
the difference between the @xmath3 in the two transitions is phase dependent and difficult to quantify from the information presented , but the @xmath9 always appears to be greater than the @xmath10 . in their figure 12
they show that at a phase of 0.4 only the @xmath0 emission should be present , at a phase of 0.3 the maximum @xmath5 should occur in the @xmath0 emission , several @xmath20 broader than the emission at phase of 0.1 , and the @xmath13 should undergo a redward shift with increasing phase .
no shift in the peak or @xmath4 is indicated for the @xmath1 transition .
@xcite have developed a coupled escape probability model for sio maser emission .
they present several figures indicating the @xmath5 in the @xmath0 and @xmath1 transitions . in their figure 7 , the @xmath1 emission is consistently broader than the @xmath0 emission , and the @xmath9 and @xmath10 vary by a factor of more than five over the stellar period .
the emission at their epoch 6 is several times broader than the emission at the other epochs depicted . for their epoch 11
the @xmath0 is very weak and narrow . since different distances from the star
are affected differently by the proposed shock travelling out from the star , it is reasonable to expect that masers forming at different distances from the star will exhibit different @xmath3 and slightly different @xmath2 .
the observations of the velocity parameters of the emission provide information on the locations as well as the motion of the masing material .
the 22 m mopra radio telescope is located in new south wales , australia . at mopra
each maser source is first pointed on to ascertain adequate positioning inside the beam .
the observations are then executed as 16 cycles on and 16 cycles off observation , thus lasting 64 seconds per on / off pair . for @xmath1 observations the rms noise was about 1.8 jy . for @xmath0 observations the rms noise was about 0.6 jy . the velocity resolution was @xmath21 ( @xmath0 ) and @xmath22 ( @xmath1 ) .
the mopra monitoring programme observes 121 sources since 2008 and is described in the data catalogue by @xcite .
lpvs , semi - regular variables , irregular variables , oh - ir stars , and the orion sio maser source were observed approximately monthly in @xmath0 and @xmath1 between 2008 and 2012 .
lpvs were chosen for this analysis because they present a relatively uniform collection of sources and a group of stars for which theoretical models of the sio maser emission have been developed .
for the 47 lpvs observed , the stellar velocity , the number of observations in each transition , and the number of observations of both transitions within 24 hours are given in table [ tab : lpvs ] .
the sources are listed in the aavso bulletin @xcite as lpvs with well determined maxima and periods .
non detections of the sources have not been included in the following analysis .
since observations indicate and theories predict that the @xmath0 and @xmath1 masers exist at different distances from the star a phase dependent difference in the @xmath14 and @xmath13 might exist as the proposed shock propagates outward from the star .
figure 1 shows the @xmath14 @xmath13 versus phase .
no phase dependence of the @xmath4 difference is obvious .
there are also predictions that the @xmath4 should have a redward shift in the @xmath13 versus phase @xcite .
figure [ fig2 ] shows the @xmath13 at the phase indicated minus the @xmath13 at the earliest observed phase during a stellar cycle ( normalized to the earliest observed phase ) .
at least five observations of the source during an individual phase period had to be available to include the information in this analysis .
this requirement insured that only data representing observations spread over the phase period were analyzed .
again there is no obvious systematic redward or blueward shift .
figure [ fig3 ] presents the same information for the @xmath1 . for this transition
the blueward spread is larger than the redward spread , but again no definitive trend is obvious . and @xmath13 versus phase .
457 points are included in the plot . ]
versus phase .
the @xmath4 at the earliest phase observed has been subtracted from the @xmath2 at later phases .
442 points are included in the plot . ] for the @xmath14 data .
298 points are included in the plot . ]
@xcite subtracted the stellar velocity from the `` mean velocity '' of the @xmath0 and the sio v=2 , j=1 - 0 emission from 43 late type stars .
they concluded , based on the data shown in their figure 5 , `` the mean velocity of the 28 sio v=1 and v=2 masers as a function of the optical phase shows that the redshifted emission is dominating during the phases from 0.3 to 0.8 , while the blueshifted emission appears from phase @xmath23 and is dominating during phases 0.0 - 0.2 ( or 1.0 - 1.2 ) . ''
figure [ fig4 ] shows the results of a similar analysis with our data subtracting the stellar velocity from the velocity centroid .
we have approximately 10 times as many data points as @xcite .
no phase dependent shift of the @xmath2 with respect to the stellar velocity is obvious .
@xmath24 versus phase .
the 277 @xmath13 points are indicated by circles .
the 214 @xmath14 points are indicated by squares . ]
many observers have concluded that the sio maser integrated flux density is a maximum at a stellar phase of between 0.05 and 0.2 @xcite .
@xcite stated that there was a variable contrast of the integrated flux density over the period of the stars .
the contrast was defined as the `` intensity ratio between consecutive maximum and minimum epochs . ''
the average contrast was approximately three but ranged from four to 20 for mira .
these conclusions have generally been based on observations of the brightest maser sources and all the sources were not lpvs . while the integrated flux density versus phase has been well examined , the @xmath5 has not been previously examined as a function of stellar phase .
figures [ fig5 ] and [ fig6 ] show the velocity ranges of the @xmath0 and @xmath1 transitions respectively .
the velocity range of emission does not reproduce the phase dependence of the integrated intensity .
there is no obvious maximum or minimum in the @xmath5 of either transition versus phase .
the @xmath9 generally exceeds the @xmath10 as stated in @xcite .
figure 8 in @xcite shows the full width at zero power versus optical phase for sio masers , which is a similar metric as we are employing and showing in our figure [ fig5 ] .
it is interesting to see that they do not find a strong correlation either between optical phase and peak emission from sio masers in their large sample of 401 late type stars . versus the phase .
635 points are included in the plot . ] versus the phase .
485 points are included in the plot . ]
in the future the mopra sio maser database will be used to look for periodicities in velocity parameters of individual sources .
l2 puppis , a semi - regular variable , has been examined and a 139 day periodicity in the sio @xmath4 has been found @xcite .
this periodicity likely indicates a non - radial pulsation of the star .
periodicities in the velocity parameters of the star could indicate various interesting phenomena planets , non - radial effects , or other asymmetries in the circumstellar environment .
the case of l2 puppis is similar to that of findings by a vlbi study of tx cam ( a source too far north to be in the mopra catalogue ) in which periodicity in sio emission has been observed by @xcite .
the mopra database provides the first large data set of lpv sio maser spectra ( essentially simultaneous observations in @xmath1 and @xmath0 from 2008 until 2012 ) to allow the comparison of the @xmath2 and @xmath3 versus phase with theoretical model predictions .
the velocity comparisons extracted from these observations will inform and constrain the development of future models of the circumstellar environment and maser dynamics .
the analysis of the @xmath2 and @xmath3 of 47 lpvs as a function of phase shows no shifts or variations that indicate the passage of a shock through the circumstellar material .
we would like to acknowledge the efforts of remi patriot , chad reverman , and emma molden in the data reduction that forms the basis for this paper and the support of the university of minnesota , morris , in this work .
the mopra radio telescope is part of the australia telescope national facility which is funded by the commonwealth of australia for operation as a national facility managed by csiro .
the university of new south wales digital filter bank used for the observations with the mopra telescope was provided with support from the australian research council . | arxiv |
The , alternatively misread as Ruijū myōgishō, is a Japanese dictionary from the late Heian Period. The title, sometimes abbreviated as Myōgishō, combines the ruiju classified dictionary from the Wamyō Ruijushō and the myōgi pronunciation and meaning/definition from the Tenrei Banshō Myōgi. Additional Buddhist titles, like Sanbō ruiju myōgishō 三宝類聚名義抄, use the word sanbō 三宝 Three Jewels because the text was divided into butsu 仏 Buddha, hō 法 Dharma, and sō 僧 Sangha sections.
The origins of the Ruiju myōgishō are uncertain. Bailey 1960:6 concludes it was compiled early in the twelfth century, presumably by a priest. Kaneko 1996:269 believes the received edition dates from the late 12th century, but the original version was compiled around 1081-1100 CE. There are various received texts of the Ruiju myōgishō and several indexes.
Like other early Japanese dictionaries, the Ruiju myōgishō borrowed heavily from Chinese dictionaries, in particular the ca. 543 CE Yupian and the 601 CE Qieyun. For collation of character entries, the Chinese Yupian has a system of 542 logographic radicals. The Ruiju myōgishō cuts them down into 120 radicals bu 部, even simpler than the ca. 900 CE Japanese Shinsen Jikyō system of 160.
The Ruiju myōgishō lists over 32,000 characters and compounds. The entries give both on'yomi Sino-Japanese borrowings and kun'yomi native Japanese readings for kanji, using Chinese fanqie spellings from the Qieyun, Man'yōgana, and katakana. Meanings are often illustrated by quotations from over 130 Chinese classic texts and classical Japanese literature. These quotes have two types of Kanbun Chinese writing annotations, shōten 声点 tone marks for Chinese tones and Japanese accents, and occasional kunten 訓点 reading marks for Japanese pronunciations. Many passages contain no Japanese readings at all, says Bailey 1960:6, but there are a total of approximately 10,000 Japanese readings given in the whole work. While special care is needed for its commentary nature Li et al., 2016, the Ruiju myōgishō remains a standard Japanese source of information regarding Heian era pronunciation.
Editions
There are various extant editions that still exist today. The main editions include:
The edition. It is part of the collection in the Imperial Household Agency. Compiled between 1081 and 1100. It retains signs of the original; however, it is incomplete and only contains the first half of the section. It provides detailed literary citations for entries.
The edition. It is part of the Tenri Central Library and is a national treasure of Japan. It is a mid-Kamakura period facsimile. While it is an expanded and revised edition of the original, it is the only complete edition surviving today.
The Kōzan-ji edition. Part of the Tenri Central Library collection. It is entitled , and is a revised edition. It only contains the section and part of the 巻上 section found in the Kanji-in edition.
The edition. It is part of the Tō-ji Hōbodai-in collection. Revised and incomplete.
In addition to the above, the and revised editions exist, but both are incomplete.
References
Category:12th-century books
Category:Japanese dictionaries
Category:Late Old Japanese texts | wikipedia |
How to calculate gas flow/permeation through solid metal membrane
Given the absolute pressures of air on both sides of a titanium membrane of known thickness (0.1mm) and diameter (3mm), how would one calculate the rate of gas exchange/escape through the titanium material assuming a pressure gradient? Ideal units are in cc/sec.
The Diffusion Flux of a gas through a metal membrane is theoretically given by:
$\large{J=\frac{KD(\sqrt{p\_2}-\sqrt{p\_1})}{\delta}}$
With:
$p\_1$ and $p\_2$ the pressures on the respective sides on the membrane.
$\delta$ the thickness of the metal membrane.
$K$ is a proportionality constant that connects gas concentration in the metal with pressure of the gas via:
$K^2=\frac{c^2}{p}$, where $c$ is the concentration of the gas in the metal and $p$ the pressure of the gas.
The main problem now becomes finding reliable values for $K$ and $D$. Both are likely to be very small, for example for hydrogen/iron Wikipedia lists a value of:
$D=1.66 \times 10^{-9}\:\mathrm{cm^2/s}$.
$K$ is also likely to be very small, as $c=K\sqrt{p}$ and the solubility of air in titanium metal is very small.
This means that at modest pressure differences and a membrane thickness of $\delta =1 \times 10^{-4}\:\mathrm{m}$, $J$ is likely to be negligible.
But even if the pressure was $100$ times larger on one side of the membrane than the other then J would still be only approx. $\sqrt{100}=10$ times higher.
A $0.1\:\mathrm{mm}$ thickness a titanium membrane is likely not to leak at all, at least not in 'reasonable' conditions of pressure.
| stackexchange/physics |
electrostatic interactions are of great importance in many biological and soft matter systems . for example
, electrostatics plays a key role in proteins structure @xcite , interaction of dna and proteins with charged ligands @xcite , dna packaging and condensation @xcite , conformation of polyelectrolytes in solution and their aggregation behavior @xcite and interaction between charged colloids and their collective behavior in solution @xcite .
numerous experimental and theoretical studies have been performed to understand these phenomena and to elucidate the role of electrostatic interactions .
the study of the counterions distribution and electric potential around dna @xcite , the interaction between two dnas @xcite and the same studies on similarly or oppositely charged surfaces @xcite are examples of these studies .
the difference between dielectric constant of water ( @xmath0 ) and that of organic materials ( @xmath1 ) , silica ( @xmath2 ) and air ( @xmath3 ) is an important factor in electrostatic interactions of related systems .
the role of such dielectric inhomogeneity has been investigated in systems like ionic channels @xcite , ions or colloids at the air - water interface @xcite , copolymers in electric field @xcite and polyelectrolytes adsorbed to an interface @xcite .
more efforts are needed to investigate the effects arisen from dielectric inhomogeneity on distribution of the counterions around charged objects and the interactions between them @xcite . when the electrostatic interactions in a system are much stronger than the thermal energy , mean field theories such as poisson - boltzmann formalism are not suitable for describing the behavior of the system .
in this situation , known as the strong coupling ( sc ) limit @xcite , another theory , which is derived from the virial expansion of the system partition function , can be used .
this theory has been used to study electrostatic interactions between charged objects and counterion distribution around them .
such studies have been performed for two parallel charged plates considering their surface charge density as uniform @xcite and discrete @xcite .
also , electrostatic interaction between two overally neutral plates of randomly distributed annealed or quenched charges of both signs has been studied @xcite .
corrections to the theory of ref .
@xcite are suggested to describe the system behavior in a broader range of the parameters , namely the intermediate coupling regime @xcite .
such corrections are recently formalized by expansion of the partition function around the ground state of the system in which the wigner crystal is formed by the counterions @xcite .
this approach gives a correction to the prefactor of the second term of the theory of ref .
@xcite to agree with monte carlo simulations .
the system of two uniformly charged dielectric slabs has been studied taking into consideration the effects arising from dielectric inhomogeneities @xcite .
it has been shown that in the sc limit the dielectric inhomogeneities cause accumulation of the counterions in the middle of the intersurface space between the slabs .
also , it has been shown in these studies that the dielectric inhomogeneities increase the repulsive pressure between the slabs at small inter - slab separations .
a widely used simplification in the studies of charged systems is the consideration of the charge distribution on the surfaces of charged objects as uniform . clearly , this approximation is feasible only when the ions in the solution are far from the charged surfaces and also the separation between charged surfaces are quite larger than the typical separation between charged residues on the surfaces .
when a point charge is very close to a big charged object or when two charged objects are very close to each other , discreteness of charge should be taken into account in calculation of the electrostatic interactions . in the sc limit
, it has been shown that the distribution of counterions in the vicinity of a discretely charged plate is very different from that of a uniformly charged plate . in the former case ,
counterions have a strong lateral correlation with the surface charges and counterion density on the surface is much higher relative to the case of uniformly charged surface @xcite . for the case of two
discretely charged surfaces of the same sign , most of the counterions crowd near the surfaces and the attraction between the surfaces is stronger compared to the case of uniformly charged surfaces @xcite .
the same differences have also been observed in the weak coupling limit @xcite .
the purpose of this paper is to consider the effects of both dielectric inhomogeneity and discreteness of charge on the electrostatic interaction between two similarly charged parallel dielectric slabs .
we consider the charge distribution on the surface of each slab as square shaped uniformly charged regions of side length @xmath4 whose centers are on a square lattice of spacing @xmath5 , as is shown in fig .
the case of @xmath6 corresponds to uniform charge distribution on the slabs and @xmath7 corresponds to distribution of point charges .
we use the green function method to calculate interaction energies of each counterion with its images and the surface charges , and use it to obtain the counterion density profile in the sc limit . despite previous works ( e.g. refs .
@xcite ) , all the fourier modes of the charge distribution are taken into consideration here .
this allows us to study the extreme limit of point charges on the surfaces , where the system behavior is noticeably different ( see below ) .
interaction between the slabs is calculated by two approaches : the first approach is valid for low temperatures and the point - charge distribution on the slabs in which interactions of the counterions with each other is taken into account .
the other approach is valid for room temperature and arbitrary values of @xmath4 , which is accurate in the sc limit where the effect of counterions interactions on the pressure between the slabs can be ignored .
we find that consideration of the dielectric inhomogeneity in electrostatic interactions of the system increases the tendency of the counterions to gather in the middle of the intersurface space between the two slabs .
taking into account the discreteness of charge on the slabs however , increases the counterion density in the vicinity of the slabs surfaces . resulted from these two competing effects , when the slabs are in far or close separations the counterions are mostly distributed in the vicinity of the surfaces or in the middle of intersurface space between them , respectively . in the limit of point - charge distribution of the surfaces , independent of the dielectric inhomogeneity strength , density of the counterions
is maximum in the vicinity of the slabs surfaces at all inter - slab separations .
it is found that the interaction between the slabs , at low temperatures is always attractive and its strength increases with increasing the difference between dielectric constants of the slabs and that of the environment . at room temperature , depending on the strength of charge discreteness and dielectric inhomogeneity , the system is found to have two different behaviors : the slabs stand in an equilibrium distance from each other or completely attract each other after passing a repulsive barrier in the intermediate separations .
it is also found that for a range of the system parameters there are two equilibrium separations between the slabs corresponding to two minima in the free energy of the system . in the absence of dielectric inhomogeneity , by changing the charge distribution on the surfaces from uniform to point charges , the entropic repulsion barrier between the surfaces disappears and they attract each other at all values of inter - slab separation . these results are not observed in previous works and show the importance of considering the discreteness of charge .
the effects of the dielectric inhomogeneity and the charge discreteness on the pressure between the slabs are also studied .
we consider a system of two infinite dielectric slabs of thicknesses @xmath8 and @xmath9 with dielectric constant @xmath10 .
the slabs are parallel and placed in a medium of dielectric constant @xmath11 at separation @xmath12 from each other ( fig .
[ fig1 ] ) .
we assume that the charge on the inner surface of the slabs is distributed as a square lattice of square shaped regions of side @xmath4 and charge density @xmath13 .
the centers of the square shaped regions form a square lattice of spacing @xmath5 , as shown in fig .
we define the cartesian coordinate system , in such a way that the @xmath14-axis is perpendicular to the surfaces and the origin is located in the middle of the separation area along the @xmath14 direction . by this definition ,
the position of the charged surfaces of the slabs along the @xmath14 direction is @xmath15 .
the charge density of the slabs in three dimensions can be written as @xmath16 where @xmath17 is the delta function and @xmath18 is the theta function that is zero for @xmath19 and one otherwise . keeping the value of @xmath20 fixed
, @xmath7 corresponds to the distribution of point charges on a square lattice of spacing @xmath5 on the slabs surfaces , whereas @xmath6 corresponds to the uniformly charged surfaces of the slabs .
the case of @xmath21 describes the distribution of uniformly charged domains on the slabs surfaces .
it is worth mentioning that to avoid any undesired singularities , a cut - off layer of thickness @xmath22 is supposed on each slab where the counterions can not penetrate .
we consider the system in the sc limit .
the coupling parameter is defined as @xmath23 in which @xmath24 is the bjerrum length outside the slabs , and @xmath25 is the gouy - chapman length , where @xmath26 denotes the surface charge density and is given by @xmath27 .
we note that @xmath28 is the counterions charge and @xmath13 is the surface charge density of the charged regions .
to calculate the electrostatic potential and interaction energies of the system , we use the green function method and solve the equation @xmath29 with appropriate boundary conditions , @xmath30 and @xmath31 , where @xmath32 represents the regions shown in fig .
[ fig1 ] and @xmath33 is the dielectric constant of region @xmath34 . by defining @xmath35 , the green function in the region between the slabs
is found as @xmath36 where @xmath37 ( @xmath38 ) is the larger ( smaller ) of @xmath14 and @xmath39 , and the function @xmath40 is defined as @xmath41 to find the green function in the presence of a single dielectric slab , one should substitute @xmath42 in eq .
[ green ] .
now the electrostatic energy of the system can be calculated numerically using the calculated green function and all the fourier modes of the charge distributions . in the sc limit
, distribution of the counterions can be found by calculation of the electrostatic energy of the system .
contribution of a counterion to the electrostatic energy of the system can be written as @xmath43 , where @xmath44 is the image - counterion interaction arising from the dielectric discontinuity across the interface , and @xmath45 accounts for the counterion interaction with the physical charges on the slabs . in order to find the image - counterion interaction energy of each counterion
, we assume a point charge @xmath28 at position @xmath46 located between the two slabs .
one can find the potential at position @xmath47 as @xmath48 , where the green function is introduced in eq .
( [ green ] ) . substituting this potential in @xmath49 , the total electrostatic energy of the system in the presence of one counterion can be obtained .
this energy also contains the self - energy of the point charge , which is infinite and independent of the slabs parameters .
the self - energy can be obtained at the limit of @xmath50 .
after subtracting the self - energy of the point charge , the total image - counterion electrostatic energy of a counterion between the two dielectric slabs is found as @xmath51 the electrostatic interaction energy of a counterion with the charges of the slabs , @xmath45 , can be calculated using the relation @xmath52 .
the potential of one dielectric slab containing square - shaped charged regions on its surface can be found using the green function of eq .
( [ green ] ) by substituting @xmath42 as @xmath53 where @xmath54 , @xmath55 , @xmath56 and @xmath57 .
we denote the relative displacement of the two dielectric slabs containing square - shaped charged regions in the @xmath58 and @xmath59 directions by @xmath60 and @xmath61 , respectively .
clearly , in addition to above mentioned parameters of the slabs , the interaction energy of the system depends on the values of @xmath60 and @xmath61 as well . using the green function of eq .
( [ green ] ) , the potential of the two dielectric slabs in the space between them can be written as @xmath62 the ion interaction energy with the charges on the slabs is obtained using this potential and the relation @xmath63 . in the sc limit
, @xmath64 , the counterions distribution in the system can be written as a virial expansion , and to the leading order one has @xcite @xmath65 where @xmath43 is the total electrostatic energy of each counterion discussed above and @xmath66 is a normalization prefactor that can be calculated from relation @xmath67 , which yields the total number of the counterions in the system . in the following sections , we use this relation and the calculated energy of each counterion to find the counterion distribution in the presence of one or two dielectric slabs of discrete surface charge .
as mentioned above , the electrostatic energy of a counterion of charge @xmath28 in the presence of one dielectric slab can be written as @xmath68 where the first term is the electrostatic energy of the counterion with the physical charges on the slab and the second term shows the image - counterion interaction . to write the second term in eq .
( [ e-1slab ] ) , we used eq .
( [ u - int ] ) and set the conditions of single slab , @xmath42 and @xmath69 .
the counterion interaction with the physical charges of the surface is attractive and long - ranged , whereas the image - counterion interaction is repulsive and short - ranged . for the numerical calculations and plots , we set @xmath70 and @xmath71 .
we note that the counterions can not enter a region of thickness @xmath22 on the slab
. this thickness should be in the range of the molecular size , and we consider a representative value of @xmath72 . in fig .
[ fig:1slab - energy ] , the behavior of energy , @xmath73 , is shown as a function of @xmath14 for different values of @xmath74 and @xmath4 . in this figure
, we set @xmath75 . as it can be seen , the energy has a minimum in the @xmath14 direction , corresponding to a higher counterion density . in fig .
[ fig:1slab - density ] , we present the profile of the counterion density in the @xmath14 direction for different values of @xmath74 and @xmath4 . the counterion interaction with the physical charges of the slab is attractive , whereas the image - counterion interaction is repulsive .
one can see that by decreasing @xmath4 ( approaching to the point charge limit ) , the value of @xmath14 corresponding to the maximum of the counterion density shifts toward zero .
decreasing of @xmath74 also pushes the counterions to the charged surface of the slab . at very small values of @xmath4 ,
independent of @xmath74 , the counterions completely sit on the slab surface . this behavior is summarized in fig .
[ fig:1slab - zeq ] , where @xmath76 is shown as a function of the charge discreteness parameter , @xmath77 .
@xmath76 is the position of the counterion in the @xmath14 direction , where the energy of eq .
( [ e-1slab ] ) is minimum .
it is worth saying a few words about the lateral position of the counterion close to the slab .
when the charge of the slab is discretized , the counterion prefers to be in front of the charged regions on the slab . in fig .
[ fig:1slab - e - x ] , the energy of the counterion is shown in terms of @xmath78 for @xmath79 , @xmath80 , and different values of @xmath77 . as it can be seen , the minimum of the energy corresponds to @xmath81 . at small values of @xmath77 ,
the energy has a strong dependence on @xmath78 and the depth of the energy well in fig .
[ fig:1slab - e - x ] relative to @xmath82 is quite large .
the dielectric inhomogeneity increases the depth of the energy well and the tendency of the counterions to stand in front of the charged regions of the slab .
similarly , we can calculate the electrostatic energy of a counterion of charge @xmath28 located between two dielectric slabs .
to that end , we use eq .
[ eq:2slab - phi ] , and find that the energy is minimum when the two slabs are completely in phase , meaning that @xmath83 ( see eq .
[ eq:2slab - phi ] ) .
the electrostatic energy of a counterion is found as @xmath84 where the first term comes from the electrostatic interactions between the counterion and the physical charges on the two slabs , and the second term takes into account the image - counterion interactions . in this equation , it is assumed that the two slabs are of the same thickness @xmath8 and the interaction energy is found using eq .
[ u - int ] and setting @xmath85 . by defining @xmath86 and using eq .
( [ leading ] ) , one can find the counterion density profile between the two slabs .
it is worth mentioning that it is possible to suggest several values for @xmath22 in the range of molecular size , and we consider a representative value of @xmath87 .
furthermore , in all the numerical calculations and the plots , we set @xmath70 and @xmath88 . in fig .
[ fig:2slab - density - d ] , the counterion density , @xmath89 , is plotted as a function of @xmath14 for different values of @xmath74 and @xmath90 .
interestingly , as it can be seen in this figure , when the two slabs are sufficiently far from each other ( for example when @xmath91 ) , the counterions prefer to be distributed in the vicinity of the slabs surfaces .
this behavior means that the electrostatic interaction between a counterion and physical charges on the slabs is dominant .
however , when the separation between the two slabs is small , the interaction between the counterion and the image charges dominates and the counterion moves to the middle of intersurface space between the slabs .
it is also interesting to study the effect of the discreteness of charge on the slabs . in fig .
[ fig:2slab - density - l ] the dependence of @xmath89 on the parameter of the charge discreteness , @xmath77 , is shown for @xmath92 and @xmath93 . as it can be seen , the density of the counterions in the vicinity of the slabs increases with decreasing @xmath77 .
furthermore , when the discreteness of charge on the slabs is washed out , the counterions prefer to be located in the middle of the space between the two slabs . to study the effects of discreteness of charge on the slabs and the distance between the two slabs on the preferred positions of the counterions
, we define @xmath76 as the preferred position of the counterion in the @xmath14 direction , which corresponds to the position that @xmath94 is maximum . in fig .
[ fig:2slab - zeq ] the behavior of @xmath95 is shown for @xmath80 and different values of @xmath77 .
the plots show that for sufficiently large values of @xmath90 , @xmath76 increases as @xmath77 decreases . in very small values of @xmath4 ,
the counterions distribute near the surfaces of the slabs at all separations .
in this section , we study the interaction between the two slabs in two conditions : the limit of @xmath96 and low temperatures , and the sc regime at finite temperatures . in the first approach despite the second one , interaction between the counterions is considered . in the sc regime ,
effect of the interaction between the counterions can be ignored . in this regime ,
the counterions freeze in a 2d lattice parallel to the surfaces , due to their strong interactions with each other relative to the thermal fluctuations @xcite .
the two approaches below are only applicable for divalent counterions , when counterions charge is twice the charge of each square - shaped region on the slabs ( @xmath97 ) . as one can see in figs .
[ fig:2slab - density - l ] and [ fig:2slab - zeq ] , for very small values of @xmath4 the counterions prefer to locate very close to the slabs .
therefore when the temperature is low , the entropy is negligible and half of the counterions are distributed in the vicinity of each slab . since in this limit the electrostatic interaction is dominant , the counterions follow the pattern of the slabs surface charge and make a 2d lattice to minimize the free energy ( or the dominant electrostatic energy ) . in this case
the valence of the counterions is important .
for example for mono - valent counterions , the 2d lattice of the counterions is exactly the same as the lattice of the charged regions on the slabs , whereas the lattice constant for the case of divalent counterions is @xmath98 . in this section ,
we consider divalent counterions and find the interaction between the two slabs and investigate the effect of the dielectric inhomogeneity . regarding the large energy barrier against the counterions movement out of their equilibrium positions and small width of the energy wells , when the temperature is low
, one can imagine that the counterions can not leave their equilibrium positions and their fluctuations around their equilibrium positions is negligible . in this condition , the problem is equivalent to two charged slabs , with new effective charge density , with no counterions between them . due to the location of the divalent counterions on each slab ,
the effective pattern of charges of each slab follows a periodic positive / negative scheme on a 2d lattice of spacing @xmath5 , as shown in the inset of fig .
[ fig : p - d ] .
therefore , the charge density of each slab can be written as @xmath99 where @xmath60 and @xmath61 are the relative displacement of the two slabs in the @xmath58 and @xmath59 directions . using this charge distribution and the green s function of the system , eq .
( [ green ] ) , the electric potential can be calculated . substituting this potential into the relation of energy , @xmath100 , the total energy per lattice unit
is found as @xmath101 \cos \left[\frac{(2m-1)\pi}{a}\phi_{y}\right ] \right ) , \nonumber \\ \label{eq : utot-2slab}\end{aligned}\ ] ] where @xmath102 .
@xmath60 and @xmath61 are chosen to minimize the above energy @xmath103 \cos \left[\frac{\left(2n-1\right)\pi}{a}\phi_y \right ] = -1 $ ] and the total energy per lattice unit becomes @xmath104 using the relation @xmath105 the pressure acting on each slab can be found as @xmath106 ^ 2 e^{2kd}}{\left[e^{2kd}-w(kb)\right]^2}. \label{eq : p-2slab}\end{aligned}\ ] ] we see that the pressure is always negative meaning that the interaction is attractive . in fig .
[ fig : p - d ] , the dependence of pressure , @xmath107 , on the separation between the two slabs , @xmath90 , is shown for different values of @xmath74 .
one can see that by increasing the value of @xmath74 , the attraction between the slabs becomes stronger .
at room temperature , the total free energy of the system consists of the interaction energy of the two slabs with each other and the counterions free energy .
the two slabs interaction energy can be obtained using the green function and the slabs charge distribution as @xmath108 in the sc limit , the counterions are frozen in a 2d lattice due to their strong interactions @xcite . in this regime it can be assumed that the counterions are positioned on a surface parallel to the slabs at the coordinates of @xmath109 and @xmath110 and can only move in the @xmath14 direction . with these considerations ,
the system total free energy can be written as @xmath111 where @xmath73 denotes the electrostatic energy of a counterion that is given by eq .
( [ eq:2slab - energy ] ) . the pressure acting on a slab can be obtained using the relation @xmath112 . in fig .
[ fig : p - d-2](a ) , the dependence of @xmath107 , the force per unit area , is shown as a function of distance between the two slabs , @xmath90 , for @xmath92 and different values of @xmath77 .
three interactions determine the total force on a slab : the counterions interaction with the physical charges on the slabs , image - counterion interaction and the interaction between the physical charges of the two slabs .
as one can see easily , the first force is always attractive , whereas the second and the third ones are repulsive .
when the slabs are far from each other , the first force is always dominant and the total force is attractive . in closer separations , the effects arisen from the dielectric inhomogeneity become important and the force between the slabs becomes repulsive .
hence , for larger values of @xmath4 , an equilibrium separation between the slabs exists .
this is in agreement with the result of ref .
@xcite for uniform distribution of charge on the slabs .
but for smaller values of @xmath4 , when the slabs are in close separation , the electrostatic attraction dominates again and the slabs completely attract each other after passing a repulsion barrier .
it is interesting to note that the latter behavior is completely different from the behavior of the slabs with uniform surface charge which shows the important role of the charge discreteness . the behavior of @xmath107 is shown in fig .
[ fig : p - d-2](b ) as a function of @xmath90 for @xmath113 and different values of @xmath77 .
as one can see , when @xmath4 is large and the charge distribution on the slabs is approximately uniform , the force on the slabs in close separations is repulsive which is the result of the counterions entropy @xcite .
the interaction force becomes attractive for large separations and there is an equilibrium distance for the two slabs .
furthermore , for small values of @xmath4 , the electrostatic attraction becomes stronger and overcomes the repulsion . as it can be seen in this figure , at small values of @xmath4 the two slabs
attract each other in all separations .
this is in agreement with the result of ref .
@xcite that the charge discreteness strengthens the attraction between the slabs . in figs .
[ fig : phase](a)(c ) , attraction and repulsion regions in @xmath74-@xmath90 plane are shown for the system .
one can see that by increasing the charge discreteness , the structure of the phase space changes completely . by decreasing @xmath4 , the repulsion region in small separations disappears and a repulsion region appears in the intermediate separations . at each value of @xmath4 , with increasing @xmath74 the repulsion region grows .
the interesting point in these plots is that for specific values of @xmath4 and @xmath74 , there are two equilibrium separations between the two slabs . in fig .
[ fig : freeenergy ] , the behavior of the free energy of the system is shown as a function of @xmath114 for different values of @xmath77 and @xmath115 .
as one can see , for the values of @xmath116 , the free energy has two minima showing two equilibrium separations between the two slabs .
it is interesting to note that these two minima have the same free energy for @xmath117 . for @xmath118 ,
the free energy has a global minimum when the distance of the two slabs is about @xmath119 .
when @xmath120 , the global minimum of the free energy tends to the larger distance of the two slabs , say @xmath121 .
as it can be seen in the figure , for the larger values of @xmath77 ( e.g. @xmath122 ) , the free energy has only one minimum that is located in @xmath123 .
strongly - charged biological macromolecules such as dna and filamentous actin are in the limit of strong coupling in biological conditions . for these macromolecules in solution , it is known that multivalent counterions are mostly distributed in their vicinity .
when the small ions are very close to these macromolecules or when two of them are very close to each other , the curvature of their surface can be ignored in calculation of the electrostatic interactions .
therefore , our study of the interaction between two flat dielectric slabs could be useful in enlightening the phenomenon of interaction between biological charged macromolecules in the presence of multivalent counterions .
as examples , like - charge attraction between actin filaments @xcite , the interaction between dna and charged proteins @xcite and a system of proteins confined in a polyelectrolyte brush @xcite can be considered . in
most of computer simulation studies of such systems dielectric inhomogeneity and real charge distribution on the surface of the macromolecules have not been taken into account .
this is because of intrinsic difficulty of calculation of the electrostatic interactions in the presence of dielectric inhomogeneities and massive calculations needed for modeling the real charge distribution on the macromolecules . in this subject
only simple systems like single or a couple of dielectric slabs with uniform charge distribution on their surfaces have been studied . by calculation of the green function for two dielectric slabs ( the geometry shown in fig .
[ fig1 ] ) , we calculated the electrostatic interaction between them taking into consideration both the dielectric inhomogeneity and the charge discreteness . in the strong coupling limit , it is found that the amount of dielectric constant difference between the slabs and the environment and the discreteness of charge on the slabs have opposing effects on the equilibrium distribution of the counterions between the slabs . increasing the amount of dielectric constant difference increases the tendency of the counterions toward the middle of the space between the slabs .
discreteness of charge on the slabs however , pushes the counterions to the surface of the slabs . at low temperatures ,
the interaction between the slabs is attractive , the equilibrium separation between the slabs vanishes and the strength of their attraction increases with increasing the amount of the dielectric constant difference . at room temperature
, the slabs may attract each other and come together , stay in an equilibrium separation or have two equilibrium separations with a barrier in between depending on the system parameters .
our results showed that for a system of dielectrics of a simple geometry , namely two dielectric slabs , taking into consideration the dielectric inhomogeneity and leaving the reality of discreteness of charge on the dielectrics is not a valid approach when they are close to each other . in the extreme of point charges on the dielectric slabs ,
the effect of charge discreteness completely dominates over the effect of dielectric inhomogeneity . for example , distribution of counterions in the middle of the two slabs because of the dielectric inhomogeneity ( as described in ref .
@xcite ) is the effect of the assumption of uniform charge distribution .
our results show that by taking into account the reality of charge discreteness on the slabs , all the counterions distribute in the vicinity of the slabs surfaces and the middle of the slabs correspond to the minimum of the counterions density . when the surface charge density is uniform , the pressure between the plates is repulsive at small separations and the plates stand in an equilibrium distance from each other .
this repulsion is due to the counterions entropy and the dielectric inhomogeneity .
as the charge discreteness increases , the repulsion at close separations disappears and the plates completely attract each other after passing a repulsion barrier in the intermediate separations .
also , dielectric inhomogeneity widens the repulsion region between the slabs and increases the repulsion strength . for highly discretized surface charge
, the interaction between the slabs was shown that is attractive at small inter - slab separations . in this case , the dielectric inhomogeneity may increase or decrease the attractive pressure , depending on the value of the parameters .
another point to note is the large depth of the energy wells in figs .
[ fig:1slab - energy ] and [ fig:1slab - e - x ] relative to the thermal energy , @xmath82 .
it shows that the charge discreteness and the dielectric inhomogeneity strongly affect the equilibrium distribution of the counterions and hence the interaction between the slabs .
regarding the competing effects of charge discreteness and the dielectric inhomogeneity , our results showed that considering only one of these realities and leaving out the other one may crucially bias the results of the theory . in this paper , distribution of the counterions and interaction between the slabs
are obtained from the sc theory at the leading order of the expansion .
it has been shown that this approximation is correct for discretely charged surfaces in coupling parameters larger than 20 @xcite .
many biological systems lie in this range .
however , when the separation between the two charged plates gets very large , the first order term becomes smaller than the second term and this approximation fails .
this critical distance is found for uniformly charged plates with and without dielectric inhomogeneity .
computer simulations have also been used to find the validity range of the sc theory in these systems @xcite . as a result
, computer simulations considering both the dielectric inhomogeneity and the charge discreteness effects seem essential .
the sc theory is obtained from an expansion of the system parameters in inverse powers of the coupling parameter @xmath124 .
theoretically , sc formalism is exact in the limit of @xmath125 , however computer simulations have shown that the results become accurate for values of @xmath126 @xcite . in biological conditions
, @xmath127 is equivalent to @xmath128 in our model or surface charge density @xmath129 which is of the order of the typical charge density of charged biological membranes and dna @xcite . for discretely charged surfaces ,
sc theory has been shown to be exact even in lower values of @xmath124 ( down to @xmath130 ) due to the weakened correlations between the counterions @xcite .
also , it has been shown that the presence of the dielectric inhomogeneity widens the validity range of the sc theory @xcite .
the validity range of the sc theory in the case of a single charged plate is @xmath131 in which @xmath14 is the separation between counterions and the surface and @xmath132 is the mutual separation between the counterions parallel to the surface .
this range for the system of two parallel charged surfaces is @xmath133 in which @xmath90 is the separation between the surfaces @xcite . in our model
, the lattice spacing of the regular charge distribution on the surfaces , @xmath5 , plays the role of @xmath132 of the sc theory . considering that the most of our results have been obtained using parameters in the range of @xmath134 , the validity of the sc theory is preserved .
one should note that a sharp boundary is assumed between inside and outside of the slabs in our model . in reality
, it is known that such a sharp boundary is not the case and an improvement of our model could be the consideration of a smooth profile of the dielectric constant in the slabs boundaries .
some additional points in the way of approving the theory are as follows .
the grand canonical ensemble is more proper for study of the real systems such as the system of dielectric slabs with counterions studied here but the sc theory is developed in the canonical ensemble .
developing a theory in which the number of the counterions between the slabs is not constant seems as a valuable step .
the finite distance of the fixed charges from the slab surface @xcite , random distribution of the charged domains @xcite , displacement of the charged domains by changing the system parameters in some cases @xcite and possibility of their hydration @xcite should be considered in development of the theory .
also , experimental studies on the effects of different factors on the distribution of the counterions and interaction between charged dielectrics can also be insightful .
for example , the effect of the dielectric inhomogeneity on the interaction of two charged dielectrics seems to be possible by changing the solvent @xcite and is not studied yet to the authors knowledge .
we are grateful to f. julicher , s. n. rasuli , and m. f. miri for interesting discussions and comments .
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NEWS DEEPLY
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Renewable Energy Seen as an Opportunity for the European Arctic
With geothermal energy in Iceland, hydropower in Norway and wind energy in the Faroe Islands, Europe is well on its way to decarbonizing its energy systems.
Written by Doris Friedrich Published on Nov. 21, 2016 Read time Approx. 3 minutes
A geodesic dome covers a geothermal borehole in Iceland. Flickr, CC BY 2.0/Lydur Skulason
The North could become the "green battery" for Europe through an integration into the European energy market, according to Hallstein Havåg, the director of policy and research at the environmental organization Bellona. "This could help us save the Arctic by decarbonizing our energy systems." It could also boost the economic development of Arctic countries.
Nordic countries have a great potential for renewable energy systems. The Faroe Islands, for instance, produce wind energy. Havåg also points to Norway and Iceland, which have invested in hydropower and now produce large amounts of renewable energy, exporting their surplus.
Hydropower Opportunities in Greenland
Denmark's import of this clean energy from Norway has allowed the country to derive most of its energy from renewable sources. According to Havåg, Greenland also has a great potential for hydropower due to its ample water resources.
During the Arctic Circle Assembly from October 7 to 9 in Reykjavik, Iceland, Havåg discussed renewable energies in the Arctic with Angus MacNeil, a U.K. MP and former chair of the British government's Select Committee on Energy and Climate Change; Ragnheiður Elín Árnadóttir, Iceland's minister of industry and commerce; and Bogi Bech Jensen, the president of Glasir-Tórshavn College in the Faroe Islands.
This low energy house was built to see how low energy technologies might fare in the Arctic. (Flickr, CC BY-NC-ND 2.0/destination arctic circle)
Iceland's Vision: 100 Percent Renewables
Not only is a clean energy agenda beneficial, but "it is economically necessary," said Árnadóttir.
In the 1970s at the height of the oil crisis, Iceland's politicians made the bold decision to develop geothermal energy.
Today, it has become a strong pillar of Iceland's economy and everyday life, from which the country benefits enormously. As a result, the proportion of space heating from non-renewable energy has decreased from 50 percent to about 1 percent. "And this could also be the story of the Arctic," said Árnadóttir.
Arctic as Showcase for Renewables
Árnadóttir's vision is for Iceland to become the first country to source all of its energy consumption from renewable sources. To achieve this, the focus should be on innovation, research and development of renewable energy, she said.
"Always remember that the Arctic has historically been bountiful in renewable and non-renewable energy," said Árnadóttir. "And the Arctic should be a region that other countries look to in developing renewable energy."
The Nesjavellir Geothermal Power Station in Þingvellir, Iceland. (Flickr, CC BY-NC-ND 2.0/Scott Abelman)
Creating an International Network
The North Atlantic Energy Project is investigating how isolated energy systems in the region can be connected, such as creating a renewable energy network between Norway and Greenland. The project has allowed an enormous exchange of knowledge between regions. One area of research has been on how to connect the U.K. and Iceland. Eight reports on different issues have been presented and made publicly available. In talks with the U.K. government, no decision has been made yet, but a lot of uncertainties were eliminated.
Russia Underrepresented
A comment from the audience at the Arctic Circle Assembly reminded those assembled that Russia, which makes up half of the Arctic's land mass, was underrepresented at the conference and should be included in the decision making on renewable energies.
It was also pointed out that there is a lack of interaction between the oil and gas industry and renewable energies.
A version of this story was first published by High North News and is reprinted here with permission.
decarbonization Faroe Islands geothermal energy hydropower Iceland Norway Renewable Energy wind energy
Polar Bears and People: Cataloging Conflict
HAKAI: Clashes between polar bears and people are on the rise as Arctic sea ice declines. A new digital database aims to track these encounters and could help prevent future attacks. July 17, 2017
Circumpolar Creativity: Some Takeaways from the Arctic Arts Summit
Arctic Agriculture: Norway's Ambitious Green Shift
Artist Races Against Time To Paint Mural On Melting Arctic Iceberg
Lofoten's Big Headache – We Need to Take Control
Doris Friedrich
Doris Friedrich studies human-environment relations and ethnic diversity in the Arctic and is a writer for The Arctic Institute.
The European Parliament Has Not Forgotten the Arctic
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exilarating piha Longboat competitions on saturday, feb 1st.
Hundreds of people came to Piha for the annual Longboat Competitions off South Beach. A full-on water sport for both men and women, it had its thrills and spill out there riding the 4 metre waves. Great stuff!
Some of the longboats placed ready on Piha South Beach prior to the competition.
Team work's needed to unload the longboat from the trailer.
Piha men's team standing ready at the starting line.
Piha women's team ploughing through the waves.
Race over, pulling the longboat out of the water. | slim_pajama |
Justice League Wonder Woman and Superman in Signs That You're Falling in Love
Disclaimer: All publicly recognizable characters, settings, etc. are the property of their respective owners. The original characters and plot are the property of the author. The author is in no way associated with the owners, creators, or producers of any media franchise. No copyright infringement is intended.
* * *
**Signs That You're Falling in Love**
* * *
_Wonder Woman and Superman in Love?_ By Cat Grant
Falling in love is one of the most mysterious and amazing things in the world, and it can be hard to know whether or not someone is falling or not. There's a huge difference between liking and loving or even lusting and loving someone. If you're careful and watch for the signs, you'll be able to identify someone falling in love.
If you ever wondered why Princess Jasmine shunned Aladdin for so long, it's just because women need a little more time to know they're in love.
A recent study of 1,500 men and 1,500 women showed that 20% of guys fell in love at first sight, with nearly half of them saying they were love-drunk after just one meeting.
In contrast, the fairer sex was far more calculated about the business of love. Only 10% of women have fallen in love at first sight, and most didn't determine whether it was the real thing until after six dates.
In the questionnaires, researchers found that men were checking off boxes such as "looks" as an important factor of being in love, whereas women were more deliberate across the board.
Because males are quicker to the trigger, on average, men said they had fallen in love three times in their lives, whereas women averaged out only once.
Men are also more likely to say "I love you," with women taking longer to admit the same. Why, good readers, do you believe that to be the case? And are superheroes any different?
Are Superman and Wonder Woman different from the rest of us mere mortals when it comes to falling in love? Are there signs that we, the interested public, could look for to discover whether the super powerful couple are indeed in love? Or is this a simple case of infatuation and lust, a lit candle that will burn hot and heavy for a while but has no staying power? Enquiring minds want to know.
Leave a comment, and let us know what you think. Are Superman and Wonder Woman the Power Couple for the Ages or the Power Couple of Today? Are they falling in love, one battle at a time, or have they already fallen when no one was looking?
What are the signs that two people are falling in love? I've listed a few below. From the picture of that scorching kiss between Wonder Woman and Superman, we posted a month ago, I'd wager the couple is deep into lust and have been shot with more than one arrow from Cupid.
Only time will tell.
* * *
Clark stared at the computer screen, eyes wide, mouth open in annoyed shock. Though, in truth, he should not be surprised at Cat's latest Superman and Wonder Woman installment. Ever since that damn photo was sent to her, sender unknown, she'd been milking the story for all it's worth. Which, to Clark's endless frustration, was a lot. Even after a month, people were still buzzing over the news of the Kryptonian-Amazonian pairing.
Foolishly, perhaps even naively, Clark had hoped the more sensational aspect of his and Diana's relationship would have died down. And, for many news outlets, it had. But not for CatClarkTropolis and Cat Grant, who, apparently, didn't know when to stop beating a dead horse. But, hell, even Clark had to admit that her stories and his not-so-secret relationship with Diana had garnered their little blog unprecedented attention. The visits to their site, since the picture leak, was off the charts. If it were any other story that was drawing so much traffic, Clark would be elated. Over the moon, in fact. But Clark couldn't take professional pleasure in having his personal life gossiped about.
And, crap, now, thanks to Cat's latest Wonder Woman and Superman update, people would soon be talking about whether he and Diana were in love or falling in love.
Leaning back in his bedroom chair, Clark closed his eyes. With little effort, he recalled Cat's list of signs that foretold of love. While Clark had initially scoffed at the list, upon second reflection, he now thought it to be quite accurate.
* * *
**Sign 1: You admit you are lonely.**
**Justice League #12**
Clark: "Relationships are complicated. For us even more so. I have another identity."
Diana: "The reporter?"
Clark: "My name's Clark Kent."
Diana: "Why do you have an identity like that?"
Clark: "I grew up with it. And I kept it once Superman came on the scene, to protect the people I'm close to."
Diana: "And it's worked?"
Clark: "I don't know. I still have to keep secrets from everyone. So how close I am to anyone is debatable."
Diana: "We're not like Zeus, but we're not like them either."
Clark: "We're not like anyone."
Diana: "People like us are really alone. Aren't we? Do you ever feel alone?"
Clark: "Of course, I . . . do."
* * *
**Sign 2: You flirt, laugh, and have fun together.**
**Superman #19**
Diana: "There you are stranger. I was starting to think you forgot about me. Mind if I grab a few moments with the most handsome, sexiest, most interesting man here?"
Clark: "When you put it like that, it sounds so unfair to everyone else. But sure."
Diana: "You really should show off your sense of humor more when you're Superman."
Clark: "You don't think I'm funny as Superman?"
Diana: "Is that a serious question?"
* * *
**Sign 3: You want your partner to meet your family and friends, learn who you are and where you come from.**
**Justice League #14**
Diana: "My best friend was never my friend at all. Barbara was right. I was naïve. I still am. How could I have put my trust in someone like her? How could I not see what she really was?"
Clark: "Because you were giving people the benefit of the doubt. You were looking for the good instead of the bad. Something I admire about you. Something I try to do myself."
Diana: "If I can't trust my own instincts, I can't trust anyone."
Clark: "You have an entire team of people you can trust. You can trust me."
Diana: "I don't know that much about you, Superman."
Clark: "Let's change that."
**Later in Smallville**
Clark: "I brought you here because I wanted you to meet the nice people that run this diner. And the families that come here. This is why I'm Superman."
Diana: "To protect Smallville?"
Clark: "To protect places like this. When we were stopping Darkseid from transforming this world into a firepit, or keeping David Graves from unleashing an army of parasitic spirits on the world, this is the world I'm fighting for. It's where the rocket carrying me from Krypton landed. Where the Kents found me. Where they taught me that life was about using your talents to help make the world a better place. Something you decided to do on your own."
Diana: "Can I meet your parents?"
Clark: "They passed on some time ago now. The farm's run by another family who leases the fields, but I kept the house I grew up in. Every once in a while, I need to come home to remember."
Diana: "It's beautiful, Clark."
Clark: "There is life outside the Watchtower. Outside the Justice League. And it's a good life, Diana. Don't let the evil and corruption we battle every day make that any less true. Sometimes good is what it appears to be—good."
Diana: "I thought so, but sometimes that feels too simple now."
Clark: "Sometimes it's still that simple. As simple as Smallville."
**Superman #19**
Lois to Diana: "Welcome to our humble abode."
Diana: "Hi! You must be Lois. Clark Kent told me to meet him here. My name is Diana Prince."
Jimmy: "There are the chips!"
Diana: "You must be Jimmy Olsen! Clark's told me so much about you. About all of you, as a matter of fact. It's great to finally put the faces to the names."
Diana to Clark: "All of this means so much to me. Meeting each other's friends—the ones who don't dress up to save the world. It just makes everything feel . . . so real. So . . . special."
* * *
**Sign 4: You want to spend quality time alone together.**
**Superman #20**
Clark: "So you got to meet some of my friends, I got to meet one of yours . . ."
Diana: "'Friend'" isn't really a word I would use to describe Orion. We're working together on a project."
Clark: "You don't have to explain yourself to me, Diana. Ever."
Diana: "Can we be alone for the rest of the night?"
Clark: "Ha! The rest of the evening is all yours."
* * *
**Sign 5: You support and defend your partner.**
**Justice League #13**
Clark: "Let us help you find your friend."
Diana: "I don't get involved when Lex Luthor or Metallo is causing trouble do I?"
Clark: "Not because you need it, Diana, but because we want to. _I_ want to. If this is that important to you, if it involves helping someone you care about, I want to help."
Diana: "What happened a few days ago, Superman, it just happened."
Clark: "I know. It was a kiss, not a commitment. But it was nice, Diana."
Diana: "It was."
**Justice League of America #6 (Trinity War)**
Clark: "Diana? Is that you? I can't . . . I can't hear very well suddenly."
Diana: "I'm here."
Diana to Batman: "What happened has nothing to do with Doctor Light Pandora showed up at Belle Reve when Superman and I were imprisoning Despero. And she had that box with her—Pandora's Box. . . . That box corrupted him and it looks like it's still doing something to him."
Clark: "Diana? Are you still there?"
Diana: "I'm going to help you. I promise."
**Later at Mt. Etna**
Hephaestus: "Diana? What in the hell are you—"
"Quiet, Hephaestus. I'm asking the questions here. The box, Pandora's Box . . . What does it do? . . . I have no time for pleasantries, Hephaestus. In the past we've been allies, but right now I need answers. Pandora has acted recklessly yet again, and that damn box has infected someone I—someone I care for deeply."
**Superman/Wonder Woman #2**
Diana: "Clark. I have fought warriors you would not believe. Monsters . . . Gods . . . with power to make worlds tremble. You make them all seem weak. And not because of your strength. Strength is everywhere in this world. If you have to fight Doomsday again, you will beat him because of who you are. Clark. Kal-El. Superman. And because you will not fight him alone."
**Later at Mt. Etna**
Apollo to Diana: "He's not even human! He comes from the stars. He's just some sort of thing. Not that I particularly care whom you choose to slut around with, but _mmm _standards, you know."
Clark to Apollo: "You are a god, correct? Not just some affectation?"
Apollo: "Your ignorance astounds. Yes, mortal, yes, I am a god. I am Apollo, God of the Sun and ruler of Mount Olympus."
Clark: "Good. Glad to hear that."
Apollo: "Why in the world would you say such a foolish thing?"
Clark: "Because if you speak to Diana like that again, I am going to hit you. Now, most of the time when I hit someone, I can't go all out. I have to hold back. But since you are a god . . . I can hit you as hard as I want."
* * *
Clark opened his eyes and stared back at the computer screen. Cat wanted him to write a follow-up to this recent Superman and Wonder Woman piece. No way was he going to do that. Besides the fact that Clark abhorred such fluff pieces, he had no intention of writing about his relationship with Diana, pretending on a level he was entirely uncomfortable with. But as he swiveled in his chair, eyes going to the gorgeous woman asleep in his bed, an unbidden rush of love and adoration flooded his system – a burst of filling sunlight.
Unable to help himself, Clark smiled. He may have woken early to watch the sunrise, but he would return to bed long before Diana stirred – loving the joy that came with being the first thing she saw upon waking and the beautiful smile that always greeted him.
Seeing Diana lying there, a flat sheet covering most of her nude form, a long, tempting leg unveiled, a halo of dark hair about both their pillows, Clark's body raced with lust and his mind with an idea. Swallowing the arousal that never seemed to deflate in Diana's presence, Clark turned away from the woman of his dreams and back to the computer.
A moment later, Clark began to type. Fingers flew over keys, his heart opening the gates to an easy flood of words.
When he finished the piece, thirty minutes later, Clark crawled into bed beside Diana.
Still asleep but aware of his presence on an unconscious level, Diana rolled to Clark, flinging an arm and a leg over him, blanketing Clark with her wonderfully naked and curvy body. Yup, Clark could get used to having Diana in his bed.
Holding her to him, he kissed the top of her forehead, knowing he would have to tell her about Cat's latest article on them. But that would wait. _Until after we have morning sex and I feed her breakfast. Diana's attitude is always much better when she's satiated and well fed. _
Clark stifled a laugh, knowing the truth of his thought. In some ways, Clark and Diana defied gender role stereotypes. After they made love, for example, all Diana wanted to do was fall asleep. Whereas Clark preferred to cuddle and talk. He cooked for her and she took him out to fancy, expensive restaurants. _And I lay my heart bare and she doesn't know how to do the same._
The thought had Clark tightening his hold on Diana – the Goddess of War who couldn't say three little words, though Clark had no doubt she felt them.
He could wait, though. He had waited. Writing the article had helped him process his feelings.
_But how much longer must I wait, Diana? When will you say the words I long to hear?_
* * *
_What Men Love About Love?_ By Clark Kent
Although most won't admit it, men love to be in love. In fact, many men need to be in a relationship more than women do. This is because a good relationship is settling for a man, a place where he can share feelings that he might not be able to talk about with anyone else. In our society, women are permitted to have close, bonded relationships with their girlfriends. They talk to each other openly, and turn to one another for support easily, but men don't. Believe it or not, for many guys their love relationship is the one place where they can allow themselves to be truly intimate.
But what is it about being in love that men . . . well, love? Here is my list of what men really like about relationships. I'm no expert or therapist, but I'd like to think I know a thing or two about women, men, and loving relationships.
**Reason 1: Feeling free enough to really be himself.**
When a man is in a relationship, he's a different man than when he's not. When he's out there running around with the guys, he feels part of a pack, on the hunt. Sure, it can be fun for a while. But, believe me, every one of the guys in the group is hoping to meet someone each night. And I don't just mean someone for sex. I mean someone for everything, the real thing. The real thing is someone who will take you for what and who you are. Who likes you that way and who isn't going to start finding fault, but instead, start finding all the things about you that are terrific . . . super.
When a guy is in a relationship where he is allowed to be himself, he feels more confident. He feels loveable and worthy. Just by being there, the woman he is dating or married to reminds him that she chose him out of all the others. This kind of feeling is hard to get in any other way. It helps all aspects of his life.
**Reason 2: Being inspired to be a better man**
Men love the challenge of relationships. He knows he has to work at it in order to make a love affair last. Relationships make men keep themselves up, work out, look good, stay sharp, keep his eye on the competition. After all, he doesn't want his wonder of a woman running off with some other guy. When things work out, he feels like a winner. He feels proud showing her off to his family and friends.
For many guys, relationships are a big ego boost. They keep them on the sharp edge of life, and force them to be the best they can. In _As Good As It Gets_, Jack Nicholson's character says to Helen Hunt's, "You make me want to be a better man," and it is indeed a compliment.
**Reason 3: Simply having a partner who he will see at the end of the day**
For some men, they love the rush of looking forward to spending a romantic weekend with the woman of his dreams. When they are in a relationship the woman becomes the woman of his dreams. She's beautiful. She's fabulous. The man thinks about her all week long and can't wait for them to be together on the weekend (or sometimes weeknights). It makes the whole day exciting. When things get boring or rough, he thinks of her and feel great.
It's something to look forward to. It reminds him that there's a prize for him at the end of the road. For those kinds of guys, being in a relationship fills his life with fun and joy. Seeing his girlfriend's smile or hearing her voice becomes the reward for all of his hard work. His relationship reminds him that there's more to life than the rough times, and he can enjoy himself every day.
**Reason 4: Having the chance to make your day**
What a man loves about being in a relationship is knowing that he can make someone else happy. Knowing that he's capable of doing this makes him feel good inside. It's the best feeling in the world for a guy to see his girlfriend's or wife's face light up when he walks in the door. If he know she needs him and that he can make her happy, take some of her problems away, he feels terrific, like it's all worthwhile, like he's her hero.
Men need to feel as though they're doing a good job. And they need to hear the acknowledgement of that from the woman they're with. When a man feels like he can please his girlfriend or wife, it makes him feel wonderful about himself.
**Reason 5: Enjoying the sexy returns**
Real talk now. Men love the sex. They need it, and it's important to them. When they have good sex in their loving relationship, they feel happy all week long. When they don't, it makes them edgy. A man loves to know that his woman thinks he's sexy.
Of course both partners are nourished by a relationship that includes good sex. And sex can mean different things to people in relationships. But for many men, it simply helps them feel loved, approved, admired and acknowledged. It becomes like food or sunshine that's impossible to live without.
**Reason 6: Sharing his life with someone**
What men love about being in a relationship is having someone to come home to. This may sound strange but for men, it's great knowing that at the end of the day there's someone there, waiting for him. Whether that's because they're living together, or knowing that she's someone who he can call, it's comforting. That they check in with each other, go over the day, laugh at jokes and work things out. Men need to have someone who cares about how things are going for him. This makes a huge difference in how a man does his work.
Many men are bolstered in their work and supported in their everyday lives by simply having a partner who cares what happens to them. Someone who is there for them, to help them solve problems, big or small. This kind of care provides balance and stability. But even more importantly, it reminds men in relationships that they are not alone in a competitive workplace where it sometimes seems as though people only care about themselves.
Loving couples know that a relationship is a great gift for both partners. The men who don't seem to be able to commit because they run from one relationship to another, or avoid them altogether, might simply not be able to find the right person. A man truly needs to find someone who makes him feel safe and cared for, a woman who sees the best in him and lets him know it. When she shows that she is happy with him, he will appreciate the relationship more. After all, if she loves being in love with him, what could be more rewarding?
* * *
**Justice League #23 (Trinity War)**
Superman: "Don't tell me what I need to do, Batman. I want to live a full life and that includes sharing it. And I won't let you take her away from me."
**Superman/Wonder Woman #2**
Diana: We are myths. I am the child of old stories and he is the child of new. That does not make us any less real. But it doesn't make us any less mythical either. Myths are tragedies, in almost every case. I don't want that. Not for him. Not for me. Not for us. But stories have their own lives, their own logic, and they will play out as they will. . . . For there is at least one truth, and both of us know it. It's one of the things that calls us to each other, despite everything. Because someday our battles will end. And there would be no greater tragedy . . . than facing that end alone.
**Superman/Wonder Woman #6**
Clark: "I love you."
Diana: "Of course you do."
* * *
**THE END**
End file.
| fanfiction |
INTERVIEW WITH THE VAMPIREbyAnne RiceBased on the novel byAnne RiceApril 1992Second Draft
FOR EDUCATIONALPURPOSES ONLYFADE IN:EXT. DUBOCE STREET HILL SKYLINE (SAN FRANCISCO) - NIGHTINT. BAR (SAN FRANCISCO) - NIGHTUNDER CONTINUOUS ROARING ROCK MUSIC -- we see, but do nothear:YOUNG MEN AND WOMENtalking in groups or couples, some dancing, as lightsflash. Punk hairdos, heavy makeup. Chatter.DAVID MALLOY, aged 25, well-dressed, leans close to auniformed police officer, holding a mike to the officer'slips, as the officer talks. The wire from the mike leadsto a small recorder on the bar. Malloy also wears oneearphone plug connected to this recorder, which he holdsto his left ear.CUT TO:ANOTHER PART OF BAR - BOOTHMalloy interviews two beautifully-dressed women, whoobviously flirt with him, as they answer his questions,lean forward, talk into the mike. Malloy finishes hisdrink, puts the recorder in his pocket, takes out acigarette, looks for a door.EXT. ALLEYWAY - MALLOYCigarette on lip, stumbles in darkness, amid garbage cansand debris, fumbling for lighter, then finally lighterflashes.LOUIS is REVEALED for one instant only an inch fromMalloy, his hand on Malloy's shoulder. Faces almosttouching. Malloy stumbles away in shock.Louis recedes more slowly into shadow.MALLOYI'm sorry! I didn't know... youwere there.He struggles to make out the figure but can't. Smokesnervously.LOUISI know.(CONTINUED)2.CONTINUED: MALLOYReally, I didn't mean to run intoyou.LOUISGo on. Pass by.Malloy stamps out the cigarette, holds up the hand mike.MALLOYYou don't want to tell me thestory of your life, do you?He flicks on the recorder in his pocket. Eagerly.MALLOYThat's what I do. I interviewpeople. I collect life stories.Sometimes I interview four or fivepeople a night...He backs away further. Louis is perfectly still.LOUISThe story of my life?MALLOYYes, I've been collecting livesfor years. F.M. radio. K.F.R.C.In there I just interviewed agenuine hero, a cop who...LOUIS(quietly, politely)You'd have to have a lot of tapefor my story. I've had a veryunusual life.MALLOYSo much the better. I've gotpockets full of tapes.INT. ROOM (SAN FRANCISCO)City skyline from Duboce Street hill.Louis in shadow moves to the window, as behind him Malloysets the tape recorder on the table and sits in one oftwo straight chairs. Dim light burns on chest of drawersbeyond. As they talk, Louis keeps his back to the roomand Malloy.(CONTINUED)3.CONTINUED: MALLOYThis is where you live?LOUISIt's just a room...MALLOYSo how shall we begin?(playfully, almost teasing)What do you do?LOUISI'm a vampire.MALLOYAh, and you mean this literally, Itake it.LOUISYes. I was waiting for you inthat alleyway. You or whoevercame out of that doorway. Andthen you began to speak.Malloy laughs goodnaturedly.MALLOYWell, what a lucky break for me.LOUISPerhaps lucky for both of us.Still in shadow he turns from the window and approachesthe table.LOUISI want to tell you my story. Allof it. I'd like to do that verymuch. I'm glad we've met.Malloy is uneasy as he studies the shadowy figure,fascinated but afraid.MALLOYYou were going to kill me? Drinkmy blood?LOUISYes, but you needn't worry aboutthat now. I told you in the alleyto go on. I was letting you passby. I let a lot of motals passby.(CONTINUED)4.CONTINUED: Louis stands opposite, hand on the chair.Malloy is riveted.MALLOYOh this is one I have to hear.You believe this, don't you? Thatyou're a vampire? You reallythink...LOUIS(patiently)We can't begin this way. I'mgoing to turn on the light.MALLOYBut I thought vampires didn't likelight.LOUISWe love it. I only wanted toprepare you.Louis pulls the cord of the overhead naked light bulb.LOUIS'S FACEappears inhumanly white, eyes glittering. Inhuman or notalive. The effect is subtle, beautiful and ghastly.MALLOYGood God!He struggles to suppress fear and understand.LOUISDon't be frightened. I want thisopportunity.The light appears to go out by itself and suddenly Louisis in the chair, dimly lighted by the nearby lamp and thetape recorder has been turned on. The cassette isturning.MALLOYHow did you do that!LOUISThe same way you do it. A seriesof simple gestures. Only I movedtoo fast for you to see. I'mflesh and blood. Only not human.(MORE)(CONTINUED)5.CONTINUED: LOUIS (CONT'D)I haven't been for two hundredyears.Malloy is speechless, frightened, yet enthralled.Spellbound.LOUISWhat can I do to put you at ease?Shall we begin like DavidCopperfield? I am born, I growup. Or shall we begin when I wasborn to darkness, as we call it.That's really where we shouldstart, don't you think?MALLOY(baffled)You're not lying to me, are you?LOUISNo. 1791 -- that's the year whenit happened. I was twenty-four --younger than you are now.MALLOYYes.LOUISBut times were different then. Iwas a man at that age. The masterof a large plantation just Southof New Orleans...DISSOLVE TO:EXT. LOUISIANA - DAY (1791)A disheveled Louis, hair in pigtail, in deep pocket frockcoat, rides his horse through the fields of indigo,waving here and there to the African slaves at work.He passes slave quarters and the distant colonial raisedcottage mansion of Pointe du Lac.CONTINUE V.O. as he speaks he approaches a small parishchurch and graveyard. He dismounts, approaches a rec-tangular Greek style above ground tomb. The stone islike a doorway.(CONTINUED)6.CONTINUED: LOUIS (V.O.)I had only just lost my wife inchildbirth. She and the infanthad been buried less than half ayear.Inscriptions on the high rectangular tomb show the names: DIANNE DE POINTE DU LAC 1763 - 1791INFANT JEAN MARIE 1791Louis in mix of anger and sadness pushes away the vinesalready covering the head stone and stares bitterly atthe inscription which he touches with his fingers. Takesa flask from his pocket, takes a heavy drink. He sits,exhausted, against the grave, as if close to his wife andchild. Face tender and sad.INT. DINING ROOM (POINTE DU LAC) - NIGHTTable set with candelabra, gorgeous China.Louis in soiled shirt and boots, sits at the head of thetable, staring at a plate full of steaming food.YVETTE, pretty Mulatto slave, pours his glass full ofwine.LOUIS (V.O.)I had everything a man could askfor. Yet a darkness had come thatwould not lift.YVETTEPlease, Michie, eat your supper.Please. We pray for you everyday.Louis doesn't move.Yvette takes his linen napkin from the ring and tries toput it in his lap. He takes her wrist firmly. Risesfrom table.LOUIS(patiently)I know, ma chere. I need time.EXT. RIVERFRONT STREET (NEW ORLEANS)of gunwale sidewalks and loud, crowded riverfront tavernsfull of ruffians.(CONTINUED)7.CONTINUED:Louis in ragged lace and dirty brocade coat walksdrunkenly along the sidewalk. As he enters a crowded,smoky little tavern and blunders into a card game, flat-boat men and one FANCY-DRESSED GAMBLER eye him as a mark.He lays his money down on the table. They deal him in.LOUIS (V.O.)Perhaps if I'd had time, I wouldhave come to my senses. Who cansay? I might have married again.As it was, I courted death, takingevery risk that I could.As the men play cards two tavern waitresses approach --TERESA and SUZANNE. Suzanne throws her arms aroundLouis, and exchanging glances with the Fancy-DressedGambler, puts a powder into a drink of whiskey which shepushes toward Louis, eyeing him stealthily. Teresawatches all and looks down at Louis' hand of cards.PAN OVER tavern scene -- Indians, men of color, blackAfrican freedmen, sailors and wenches.LESTAT, a hooded figure in the corner, smiles frombeneath the shadow of his hood. Gleaming blue eyes.CLOSE ON - LESTATHe approaches the table as:Louis lifts the glass of drugged whiskey. The hooded andcloaked figure of Lestat knocks it out of his hand,bumping into Suzanne and knocking Teresa roughly to oneside.Louis rises, drunk, outraged.LOUISHow dare you, monsieur.Louis pulls out a pearl-handled pistol. Teresa clingsto him. Others gasp and give way, though eager to seewhat will happen.Lestat, face half-covered by the hood but eyes gleaming,backs away through the crowd, eyes riveted on Louis,smiling. The crowd closes indifferently.Louis is slightly dazed by Lestat's eyes. Then shudders,loses interest, sits down and picks up his cards.8.EXT. NEW ORLEANS STREET - COTTAGE - NIGHTLouis and QUADROON PROSTITUTE emerge from the cottage,kissing fervently.QUADROON PROSTITUTEDon't leave me, Michie Louis.Fancy-Dressed Gambler appears from shadows.FANCY-DRESSED GAMBLERFirst you call me a cheat, thenyou try to steal my woman.The Gambler spins Louis around and goes to hit him.Louis blocks punch, knocks Gambler into the dirt.Quadroon Prostitute shouts warning to Louis as theGambler draws his pistol.LOUISGo ahead. Do it. I'm alreadydead. Finish the task, so theycan sing the Requiem.Louis shrugs.Gambler rises slowly and warily holding the gun on Louis.GAMBLERThe Oaks; tomorrow morning atsix.Louis laughs and shakes his head, no. He turns his back.CLOSE ON - LOUIS'S FACEthoughtful distant, and behind him --GAMBLERCoward!Louis staggers down the wood sidewalk. QuadroonProstitute comes after him, embracing him, and he kissesher firmly and gently pushes her away. She pleads withhim in French.LOUIS (V.O.)My invitation was open to anyone.But it was a vampire thataccepted. I had never conceivedof such a thing.Louis moves on into darkness among small colonial Frenchbuildings.(CONTINUED)9.CONTINUED: Rain falls. He looks up in it and lets it drench him.Over his shoulder, we see Lestat approach, hood stillshadowing his face.ANGLE ON LESTAT'S BLUE EYESLestat's hands clamp on Louis's shoulder and then Louisstiffens, cries out and freezes, as Lestat's teeth gointo his neck.Louis slips from Lestat's grasp, unconscious in the mudand rain.INT. ROOM (SAN FRANCISCO)Malloy and Louis facing each other.MALLOYThat's how it happened?LOUISNo. That is how vampires drinkblood. The Dark Gift oftransformation requires a gooddeal more as you'll see.Besides, this vampire wantedsomething from me. He came backfor it the following night.INT. LAVISH FRENCH-FURNISHED BEDROOM AT POINT DU LAC(NEW ORLEANS)Louis is delirious in four-poster bed, shrouded withmosquito netting. Female slave Yvette bathes his facewith a rag. She is crying. Other slave women hover inshadows. Overseer, a Quadroon male, stands weeping indoor.Yvette puts out all candles save one by the bed.LOUISMy poor Yvette. What will becomeof you -- all of you -- if I die?YVETTEYou won't die, Michie. We needyou. You won't leave us here.10.SAME SCENE - LATERLouis alone.Candlelight flickers on face of bisque virgin.Louis tosses and turns, dreaming, murmuring incoherently.Then he opens his eyes.Lestat, exquisitely dressed in French clothing, standsbeside the bed smiling. In the light of the candle, wesee that he is not human; skin too white; eyes toobright. It is more subtle than earlier electric lightshot of Louis. Lestat looks amiable, even mischievous,but impossible -- an angel or a monster.Louis rises, grabs for his pistol from the table andcocks it.LOUISWho the hell are you? What areyou doing in my house?LESTAT(looking around the lavish bedroom)And such a beautiful house. Yoursis a beautiful life.Louis takes aim and FIRES.The BULLET passes through Lestat's slightly raised hand.It leaves a bloody wound. Lestat winces, studies thewound. It begins to heal as we watch.Louis reaches for his sword, hanging over the end of thebed. He struggles to get up.LESTATYou're not afraid of anything, areyou?LOUISWhy the hell should I be? I warnyou again. Get out!LESTATAre you going to put that swordthrough me, too? Ruin my beautifulclothes?Louis rises up, jabs the rapier at Lestat who effort-lessly knocks it from his hand. It "appears" across theroom on the floor.(CONTINUED)11.CONTINUED:Louis slumps against the headboard, staring keenly atLestat. He is in a rage.LOUIS(quietly and coldly)If some voodoo priest sent youhere, say so. If you're thedevil, I'm all yours.LESTATI don't believe in voodoo priestsor the devil. Neither do you.Lestat sits on the side of the bed, facing Louis.LESTATBut I do believe in eternal life.Lestat holds up his bullet-wounded palm, and we see thevery last healing as it smooths out and is whole again.LOUIS(coldly)How was this done?LESTATI love your courage. I even loveyour grief. You're no simplesoul, are you, my friend?Louis is bewildered. Feels pain. Is becoming spellbound.Sound of SEA RISING.LESTATWhat if I told you I could giveyou back your old passion forliving, and that for those withcourage, living can be for alltime?Sound of HEARTBEAT, DRUM IN TIME WITH IT...DISSOLVE TO:DARK SEAAn 18th century ship sailing with black ragged sails.Only two figures on the top deck, Lestat at the wheel andLouis, in his soiled night shirt watching him. In thissea are the ruins of buildings, temples, churches, seendimly in the midst.(CONTINUED)12.CONTINUED:LESTAT (V.O.)Vampires, that's what we are.Creatures of darkness, only we seemore clearly in that darkness thanany mortal has ever seen!Dead men and women float in the water. Louis is amazed.Dead woman and dead infant float by. A giant dead oakfloats by. Lestat holds the wheel steady. Lestat pointsto the horizon of white clouds stacked high under themoon. The two speak together but we do not hear theirwords.EXT. PARISH GRAVEYARD (LOUISIANA) - NIGHTLouis and Lestat stand before the tall crypt of Louis'swife and baby. Sounds of WIND. Lestat leads Louis fromthe graveyard into a dreamlike swampland.DREAM SEQUENCEthickens as we see HAZY fragments suggesting possibility:A) Louis, beautifully-dressed, dancing with a woman.B)Louis and Lestat together riding horses fast throughthe night.LAUGHTER, MUSIC, HEARTBEAT INTERMINGLE.PAN OVER an audience of bejeweled and wigged spectatorsall clapping and cheering. Return to:INT. LOUIS'S BEDROOMLouis sits against the bedstead staring intently atLestat.Silence.FOCUS ON LESTATseated on the bed.Then:LESTATYou have to ask me for this. Youhave to give your full consent,do you hear?(CONTINUED)13.CONTINUED:LOUISGive it to me!LESTAT(seductive)Vampires. We slay our brothersand sisters.LOUISI want it!LESTATAnd thrive on their blood.LOUISGive it to me.Lestat bends close as if to drink Louis's blood. Louisdoes not shrink back, but stares into his eyes. Lestatdraws back, stands up, leaves through French doors, thensays:LESTATTomorrow night. I want you toprove yourself. I shall give youthe choice I never had.(looks outside)The sun's coming. Watch itcarefully. If you join metomorrow, you'll never see the sunagain.Louis sits dazed staring at the empty French windows.The sun rises over the swamplands and the plantation. Sunfills the room, striking water pitcher, glass, mirror.INT. RIVERFRONT TAVERN (NEW ORLEANS)Crowds of gamblers and revelers carry on at tables andmakeshift bar.Suzanne is slipping a poison into a man's drink and thenhelps him stagger into:EXT. ALLEYWAYThere she robs the man and lets him fall down dead in themud.14.INT. TAVERN - LOUIS AND LESTATat a corner table are watching Suzanne as she re-enters.LOUIS(fearfully, confusedly)You mean now, with this knife?He reveals the dagger inside his coat.LESTATShe's an evildoer, my friend.I've made it easy for you. Don'tyou see what she's up to? If youcan kill her, the Dark Gift isyours.Louis rises, uncertain, crazed, pushes through thecrowded tavern, approaches Suzanne and seduces her outinto the same alley.EXT. ALLEYWAYLouis stares in horror at the bloody knife in his hand asSuzanne falls back dead onto the ground.Lestat appears over his shoulder, looking coldly at thedead woman. He puts his hand on Louis's shoulder.LOUISWhat have I done?LESTAT(reassuring)It won't be this way when you'reone of us.Louis drops the dagger on the ground and moves away fast.EXT. POINTE DU LACLouis on a horse dismounts and walks towards the stepsleading up to the gallery. He is crazed with guilt.Suddenly, as he comes into light from lantern at foot ofsteps he sees --LESTATsitting collected at the head of the steps.15.LOUIS backs up as Lestat rises and descends the steps so fluidlyhe hardly appears to move. Light from lantern illuminatesLouis as:LOUISYou are the devil, aren't you?That's who you are.LESTAT(gently)I wish I were. But if I were,what would I want with you?LOUISI can't go through with this.LESTATYou're perfect for it. You'rebitter, and you're strong.LOUISBut why do you want me?LESTATBecause you're as strong as Iwas... when I was alive. Andbesides, I like you. I like yourconscience. You remind me of...myself.Louis takes out his flask and drinks. Fearlessly, drunk-enly, he turns and heads slowly for the nearby swamp.EXT. PARISH CEMETERY - GRAVES OF LOUIS'S WIFE AND BABYLouis stops in front of the crypt. Leans his foreheadagainst the stone.Lestat appears beside him, radiant, beautiful.LESTATYou really want to be with them?LOUISYes. I killed that tavern girl.I deserve to die.Lestat in quiet rage, raises his right fist and shattersinto large fragments the rectangular marble face stone,revealing two coffins on the upper and lower shelf.Insects swarm from opening.(CONTINUED)16.CONTINUED:The upper coffin slides out, cracks open, revealing half-rotted body of a woman, holding an infant, no longerrecognizable as individuals, a tangle of gruesome, rottedflesh, hair, eaten away lace, insects and worms crawlingover it.Louis gasps and bends closer taking in the full horror.LESTATIt's not your wife and child,Louis. It's death. Just thatsimple. Think and choose. Ithappens to everyone. Except us.Lestat stares at him, smiling, becoming a hazy dreamlikevision, and then hyperclear. He draws closer and closer.We hear the FLASK fall and BREAK ON paving STONES.Louis is again spellbound. Sound of HEARTBEAT.Lestate appears angelic in his radiance.LESTAT (V.O.)(patient and persuasive)We shall be this way, always.Young as we are now. I'm solonely for a companion... But youmust ask. Do you want to or no?Louis's senses are confused. He is entranced.LOUIS(tentative and then sure)Yes. Yes!Lestat embraces Louis obscuring his face. HEARTBEAT growsLOUDER. DRUMBEAT comes, OUT OF SYNC, but almost together.LOUIS'S POV The moon, the clouds, the sky, and fragments of earliervisions, blurred figures are glimpsed, with earlier dreamimages. LAUGHTER and MUSIC rise and fall under theUNSYNCHRONIZED SLOWING BEAT of the HEART and the DRUM.BACK TO SCENE Lestat lets Louis fall down beside the broken crypt.(CONTINUED)17.CONTINUED:Lestat stands over him, once again radiant. Lestat speaksgently.LESTATYou may go now.Lestat lifts his hand to his lips and blows Louis a kiss.LOUISNo! No, give it to me.Lestat lifts his own right wrist to his teeth. Fangsslash his own flesh, blood falls. Louis rises to receivethe first drops into his open mouth. Lestat gathers himup, as Louis clamps his hand on Lestat's arm and sucksfrom the wrist.HEARTBEAT AND DRUMBEAT are SYNCHRONIZED and grow STRONGERand pick up speed.Louis is released. Staggers.VAMPIRE VISIONThe world around him (and the look of the film) is trans-formed; the swamp, the CRY of the night BIRDS, the moon,the clouds, all reflect his heightened vision. He looksdown in pity on the rotted woman and infant who appear toglitter and to be beautiful rather than repulsive. Hecloses the lid of the coffin, astonished at the ease ofit. Then lifts the entire coffin and returns it to itsslot in the crypt.He turns and stares at Lestat whom he sees now with avampire's vision. Lestat's eyes are brighter. Hisbuttons are glimmering in the light.Everything is clearer, brighter, containing more facetsof light and color.LESTAT(lighthearted)Stop staring at my buttons.Didn't I tell you it was going tobe fun? But we've work to do.Lestat leads him into the swamp. Tiny CREATURES move orSING everywhere; leaves move as if growing before Louis'seyes. The water makes myriad OVERLAPPING sounds, and hecan see deep into it, to the creatures swimming in thedepths.(CONTINUED)18.CONTINUED:Louis stops, hand going around his waist as he feels acramp of pain.LESTATYour body's dying, pay noattention. It will take twentyminutes at most.Louis is horrified, but the beauty of moon flowers andbanana trees continues to distract him. The sky isviolet, flooded with luminosity. Again he feels pain.LESTATCome, you're going to feed now.LOUISI want a woman.Lestat laughs and the laughter echoes like bells inLouis's ears.LESTATThat doesn't matter anymore,Louis. You'll see. Come...LOUIS'S DAZZLED POV - SWAMP Small high ground. Camp of runaway slaves. Several sharea bottle of rum around the fire. Male slave rises, agorgeous hunk of flesh in the firelight, simply beautiful(Razor Rudduck) and goes into swamp to relieve hisbladder.LESTAT (O.S.)They're all beautiful now. Men,women, the old, the young... simplybecause they are alive.BACK TO SCENELouis sees.The slave comes nearer.Louis pushes past Lestat. Lestat is surprised but amusedand proud, and folds his arms to watch. Louis sees thetiny crucifix on a chain around the slave's neck. Stops.Lestat snatches the crucifix off the man and throws itaway, urging Louis towards him.19.SLAVE'S POV Two gleaming white beings stand before him with devil'seyes.BACK TO SCENEAs the slave tries to bolt, Louis embraces him easilythen his teeth into the powerful neck. They are newfangs, he has to really bite into the victim, but he isravenous to do it. Holds tight to the man as he drinks.LOUIS'S POV Trance as he drinks the blood. ECHO of Lestat's LAUGHTERas the swoon thickens. Distant firelight gets brighterand brighter.INT. POINTE DU LAC - NIGHT Main floor parlor and dining room with floorlength windowsto porches on all sides. Building for all its high ceil-ings is crude. Furnishing is lavish Parisian Louis XVI.Lestat plays the harpsichord rapidly and exuberantly...an improvisation on Bach as Louis -- skin whiter, eyesbrighter -- wanders from room to room, dazzled by thecandles, the light on the furniture, the petit pointtapestry of the chairs, the draperies. Before a mirrorhe stops amazed to see his reflection. In the distance,over the MUSIC, Lestat laughs.LESTATYes, that's you, my handsomefriend. And you'll look that wayuntil the stars fall from heaven!Louis draws closer to the mirror, and sees his small, nowfully-developed fangs. He runs his tongue over them.LESTATThose will make it easier nexttime to neatly puncture the flesh.We are well mannered immortals,always remember.WILD MUSIC.YVETTEthe mulatto slave, stands still in alarm on the porchgazing at Louis as he stares into the mirror.(CONTINUED)20.CONTINUED:Slowly Louis turns to her and is stupefied by her naturalbeauty.The MUSIC gets LOUDER and more FRENZIED.Louis moves out past the dazzled Yvette, along the --EXT. GALLERY AND STAIRS TO GROUND He moves out onto the grass and looks up at the stars.He begins to turn around. And suddenly he raises hishands to his lips and he roars. It's a long, horrified,grief-stricken roar. It DROWNS OUT the MUSIC.INT. BASEMENT OF POINTE DU LAC A brick walled storage room. Two coffins stand on thefloor. Lestat, holding a lantern, closes and bolts thedoor. Then turns to see --LOUIS a full-fledged vampire of high gloss -- sitting on a benchstaring at the coffin. Louis is stunned.Lestat is apprehensive and protective of Louis. Heapproaches the nearest of the coffins and opens it. It isfitted with satin inside. Louis stares at it in shock.Then looks away sharply, staring at the lantern.LESTATYou must get into it. The sun canburn you to ashes.LOUISBut is it magical or merely ashelter?LESTATIt's the best shelter that you canhave.Louis rises, approaches the coffin, hands trembling as hepeers into it.LESTATDon't be afraid. In moments you'llsleep as soundly as ever you sleptwhen you were living. You'll dream.And when you wake I'll be waitingfor you, and so will all the world.(CONTINUED)21.CONTINUED:Louis looks for assurance at Lestat's beaming face. Wecan see the fear behind Lestat's smile. The uncertainty.LOUISYou told me something. Earlier.You said that you didn't have achoice. Was that true?Lestat smiles bitterly and nods.He points to the coffin.CLOSE ON HIS HAND pointing into the coffin.LESTAT (O.S.)Some night I'll tell you thatstory, if you like. We have a lotof time now to talk to each other.Louis gracefully crawls into the coffin, fearful yet fas-cinated, and is suddenly lying on his back as the lidcomes down with a bang. Total darkness. Sounds of hisbreathing, of his gasp. Of a whispered prayer:LOUIS (O.S.)Dear God.EXT. NEW ORLEANS A big lavish drinking place with a raised stage.Italian actors in buffoonish costumes act crude commediadell'arte on the stage.Plantation owners in soiled brocade, lace, crooked wigs,some pretentious, some drunk, some merely young and happy,watch the show as tavern wenches move about.CLOSE ON TERESAentering. Looking about.TERESA'S POVLouis and Lestat at a small table watch the comedy.Lestat laughs uproariously at the antics of the actors,who trip or hit each other Punch and Judy style. Louisis quietly amused and amazed as much by the wine in hisuntouched glass, or the light on his boot. But he toowatches the stage.22.BACK TO SCENETeresa comes, offers the men two more drinks, even thoughtheir wine is untouched. Sits in Lestat's lap.Lestat winks at Louis who is enthralled.Teresa lifts the fresh glass to Lestat's lips as he flirtswith her.TERESACome on, mon cher. The best inthe colony. Once you taste this,you never go to any other tavernagain.LESTATYou think so, cherie? But what ifthat's not what I want to drink.Lestat sinks his teeth into her neck as he looks playfullybeyond her at Louis who is amazed and amused in spite ofhimself.ANTICS ON STAGE Laughter rocks the tavern.Lestat slips the dying, dazed Teresa onto Louis's lap.Louis studies her but does not drink. Gently he puts herin the chair beside him, and folds her hands on the table.She appears drunk. He wants to laugh but is ashamed. Noone notices. Lestat lays gold coins on the table, andtouches Louis's knee.LESTATLet's get out of here!Delighting in their own mischievousness, they rush out.EXT. STREETLouis is suddenly distracted by the moon moving beyondthe clouds. Distant MUSIC from a ball room. The breeze.LESTATCome, let me show you a lovely game.EXT. BALLROOMQuadroon house of ill fame. Beautiful dark-skinnedquadroons, octaroons, mulattresses are dancing with whitemen as a mulatto or quadroon orchestra plays.(CONTINUED)23.CONTINUED:Men and women dance minuet. But even more men and womenmerely cluster everywhere, talking and laughing andflirting. Drinking wine.Lestat spies a pretty dark girl, neglected.LOUIS(in a whisper)Have you ever been caught?LESTATOf course not. It's so simple.You almost feel sorry for them.Now watch me. This is called theLittle Drink. You take itwhenever you wish.Music rises and becomes faster as Lestat embraces darkgirl, startling her with sudden kiss on the neck, hiseyes closing for one minute, and then leaving her dazedbefore she even knows she's been bitten.Lestat embraces a red-haired yellow-skinned girl, turningher in a wild embrace, and giving her the same "littlebite." Then goes to an elderly quadroon, a chaperone, andflirting with her, takes "the little drink" from her.Lestat backs up next to Louis. Lestat is dazed. Thereis a faint sheen of blood on his lips.LESTATOh, it takes skill, and restraint!But it's worth it. It's fun.Louis is suddenly drawn to a victim.Toinette, a beautiful girl with cold eyes, who has beenstaring at him all this while. Very pale, very calcula-ting, and very luscious.Louis is dazed with hunger. Moves towards her, embracesher and leads her into --ALCOVElighted by candles.Louis kisses her lips and then sinks his teeth in herthroat. The swoon takes him into the realm of light andmusic only.Suddenly Lestat pulls him away.(CONTINUED)24.CONTINUED:Toinette lies against a chair, dead.LESTATYou need a little practice.Louis stares at the body.LESTATBut never mind. She was amerciless little schemer. Thetown is thick with them.Lestat leads Louis out into the night.LOUISBut how do you know? All I tastedwas... innocence.LESTATFrom her thoughts. Couldn't youread her thoughts?Louis shakes his head.LESTATYou can't hear anything they'rethinking?LOUISNo. I hear no thoughts fromanyone.Lestat considers, then shrugs. He throws his arm overLouis's shoulder and they walk together.LESTATThe Dark Gift is different foreach of us. But one thing istrue of everyone. We become morepowerful as we go along. You'lllearn to pick the evil ones.LOUISYes, I see things in the faces ofmen and women...LESTATOh, I'm not the right hand of God,mind you. Nor the local constableor judge. It's just thatevildoers are easier. And theytaste better.25.EXT. GIANT OAK TREE BESIDE COLONIAL MANSIONLestat leads Louis with preternatural ease up high intothe tree, then onto the gallery of the mansion. Theypeer through glass doors into huge library.LOUISYou hoped I'd be better all this,didn't you?Lestat interested in the library inside.LESTATI didn't know, to tell the truth.And you're doing very well.Lestat easily pries open the door and enters. A man dozesby the fire in a chair. Lestat moves all around himsoundlessly, and smiles as he takes books: TristramShady, Robinson Crusoe, Moll Flanders. He tosses avolume of Byron to Louis, who catches it easily, wary ofthe sleeping man, who never stirs. They leave, the manstill dozes.INT. POINTE DU LAC - LOUIS'S PARLORLestat sits paging through his new books.LESTATWonderful new novels from England.Remember, you can move easilyaround them without making a soundthat they can hear. Look, henever even read any of thesebooks, he never cut the pages.Louis follows Lestat out onto the gallery of Pointe DuLac. They look out over the river.LOUISBut what are the rules? What isit we can not do? What are we,really?Lestat looks at the river:LESTATWhat in the world makes you thinkthere are any rules for anyone,Louis? We're vampires, I've toldyou. You must find your own wayon the Devil's Road, as I did.26.EXT. STREET Louis and Lestat argue as they hurry past riverfronttaverns and lighted colonial houses.LOUISBut surely you must know somethingabout the meaning of it all, youmust know where we come from, whywe...Lestat in rage comes to a halt.LESTATWhy? Why should I know thesethings? Look.He points into the tavern.LESTATDoes anybody in there know theanswers? Go to the priest. Askhim!LOUISBut the vampire who made you.What happened. What did he tellyou? There must be some purpose.LESTAT(laughs in spite of himself)Purpose? Louis, what purpose wasthere to your life last week, orlast month, or last year?Lestat rushes along, impatient, hating this discussion.LOUISI cursed God that he took my wifeand my child from me. But Inever doubted...Loses conviction. Louis questions himself silently.LESTATShall I make up stories for you?LOUISNo. But you must have learntsomething from the one who madeyou.LESTATI learnt less than you've learntfrom me. I wasn't given achoice, remember?(CONTINUED)27.CONTINUED:He comes to a halt before a little theatre. Sounds ofLAUGHTER, CATCALLS, CLAPPING from inside. Postersannounce a Shakespearean play by English actors.Lestat caught by the SOUND moves inside.INT. SMALL WOODEN BUILDINGSmoky footlamps reveal crude Macbeth and Lady Macbetharguing with each other. Crowd talks, eats, drinks,yells for more action. Actors ignore them.CLOSE ON LESTATWith Louis beside him.LOUISHow did it happen? Where?EXT. WOODEN BUILDINGLestat angrily shoves Louis back out into the night.Louis is vulnerable.LESTATListen, my beloved fledgling.I'll say this once and once only.I've no secrets to tell you. I'venever laid eyes on God or theDevil. And pity the Devil if Iever do. You have received fromme all I have to give!Louis is wounded, but quiet. Lestat goes on morepatiently.LESTATThe one who made me was mad.That's what often happens to theold ones. He'd lasted a few morehundred years than most of them.And he wanted an heir before heburnt himself on his own pyre. Heleft me there to witness it.Newborn. There was no one thereto guide me as I've guided you.Louis tries to accept this, bowing to Lestat's anger.Lestat walks on and Louis follows.Lestat talks as we see:28.ENGLISH STAGEMacbeth and Lady Macbeth engaged in conversation.LESTAT (V.O.)You want to know how it happened?I was an actor. Oh, nothing sovery great. Just the boulevardsin Paris, but if you'd come fromthe provinces as I had, theyseemed splendid enough.INT. BOULEVARD THEATRE (PARIS)Lestat as a human (far less lustrous) plays Lelio in theCommedia. He bows and introduces himself to the audience.We can not make out his words, only that he is making themlaugh. He pretends to be choking on the smoke from thefootlamps. Then goes back into character. More laughter.LESTAT (V.O.)You might say he picked me for myyellow hair. Or perhaps becausein my country youth, I'd been agood hunter. And we must be goodhunters, we vampires. We must likethe hunt, or we can't survive.CLOSE ON LESTATTransfixed on the stage.HIS POV - MAGNUSAn old male vampire heavily cloaked, with a face almostlike a skull, peering from the audience at Lestat.LOUIS (V.O.)So it's passed on, one to another,century after century. And heleft you no secrets except thatfire can destroy you. And so canthe sun.LESTAT (V.O.)Jewels, that's what he gave me,and a coffin such as you'll neversee in this damned wilderness.And a tower, yes, and clothes.He left me such fine clothes. Weare the secret, Louis. Maybe thisis all a secret. Maybe Godhimself has forgotten we're allhere.29.INT. POINT DU LAC - DINING ROOM - ANOTHER NIGHTLouis XVI chairs, table, sideboard. Crystal glassesgleam on sideboard.Louis sits at the table watching Lestat as Lestat paces.LOUISWhat if we are wounded, a stakedriven through the heart, a bullet...Lestat is vaguely amused.LESTATWe heal. You saw this for yourselfthe night you aimed your pistol atme. It may take time but we heal.Only the destruction of our bodiesbrings us to the finish. Crosses,garlic, all that rubbish has nopower over us, naturally. We cannot turn to mist and pass throughkeyholes. We are not magicalcreatures, really, merely luckylittle devils, so to speak.LOUISPreternatural.LESTAT(kindly)Good word. Come with me. It'sbeen weeks since we've huntedtogether. Let's go...LOUISHow long can I go without feeding?One night? Two?LESTAT(impatient but kind)You'll have to find that out foryourself. Never let yourselfbecome so weak that you can'tfeed. That's an endless livingdeath in itself.Louis ponders.LESTATAre you trying to tell me youdon't like it? Are you trying tosay that every time the bloodtouches your tongue you don'tfeel that pleasure.(CONTINUED)30.CONTINUED:LOUISYou know I do. But I didn't seethings clearly before. I didn'tsee them for what they are.LESTATAnd now you know what life is andyou have eternity to enjoy it.LOUISI have eternity to destroy it.LESTATLouis, there's nothing beyond yourreach now. Stop grieving foryourself. And for your victims!Louis does not respond.LESTATLook, you need a littlerefreshment. Here, let me showyou another little trick. Yourtrouble is you don't experimentenough on your own.He picks up one of the crystal glasses, holds it to thelight of the candelabra and then sets it before Louis.He turns, one eyebrow raised, listening, and then hedarts too fast for us to see through the French door,curtains closing behind him.Louis gasps as Lestat appears before the table, holding along-tailed gray rat. The rat appears paralyzed, asLestat tears open its throat with his own teeth, and letsthe rat's blood gush into the crystal glass. Lestatbegins a low, helpless laugh. Absently he lays the ratto the side on the lace tablecloth.Louis is impressed in spite of himself. Smiles, shakeshis head. Lestat hands the glass to Louis. Louis drinksthe blood, and stares at it in surprise.LESTATI know. It gets cold so fast.LOUISWe can live from this, the bloodof animals?Lestat shrugs.(CONTINUED)31.CONTINUED:LESTATI wouldn't call it living. I'dcall it surviving. And you mayhave to do, now and then. You'dbetter know the trick if ever youfind yourself for a month on aship at sea, unless you mean toslay all the passengers and thecrew.Louis downs all the blood in the glass. His eyes aresuddenly bloodshot. He wipes his mouth.He stares at the body of the rat.Rat is soft and beautiful to behold. Very delicate littlehands and feet; lovely eyes.LESTATIt doesn't disgust you, does it?Lestat strokes the belly of the dead rat, studying it,smiling.LESTATThere's nothing in the world nowthat doesn't hold some...LOUIS... fascination.LESTATYes. And I'm restless. I don'twant to spend another eveninghere. There's an opera in NewOrleans tonight. A real trueFrench opera.LOUISBut we can live on animals. Wecan live without taking humanlife.LESTATYes, I suppose we can. But howlong do you think you can resistmortals? Give it a try.LOUISI can't take blood from mortalswithout killing. You know that.(CONTINUED)32.CONTINUED:LESTAT(imploring)But don't you see, it's the deathyou want, as surely as the blood.It's the life that flows with itwhen you drink.LOUISMy God. I know. I do see. Iknow. I know.LESTAT(patient but frightened)I won't stay here engaging in thissophomoric prattle. You have allof them out waiting for you. Takethe evildoers if you must. Mondieu, are there not hundreds inthis miserable little place? Andwhat a paradise they make for us,Louis, with their dancing anddrinking till dawn?LOUISWasn't it that way in Paris? Whydid you come here?Lestat laughs beguilingly as he rises.LESTATIn Paris, a vampire has to beclever for many reasons. Here,all one needs is a pair of fangs.He becomes frustrated at Louis, snatches his cloak and tri-corne hat from the chair and turns to go. Louis saysnothing.Lestat, stubborn and conflicted, leaves.Sound of LESTAT'S SINGING an Aria in Italian as he leaves.Then sound of the HORSE RIDING AWAY.Yvette, the slave woman enters.YVETTEMichi Louis? You don't want anysupper?Louis stares at the glass with its thin residue of blood.He laughs soundlessly.(CONTINUED)33.CONTINUED:LOUISNo, ma cher. I need nothing now.Is all well at Pointe du Lactonight?Yvette draws closer. Light reveals her beauty.YVETTEWe worry about you, master. Whendo you ride the fields? How longis it since you've been to theslave quarters? Have you seen thenew baby born to Charlotte? Whydo you let the overseer whip somany so often? Always before youlooked after us.Louis listens, but in spite of himself he is gettinghungry. Yvette looks more and more succulent. Throatlong and slender. Skin gorgeous.LOUIS(dazed monotone)Leave me alone now, Yvette. Goout.YVETTEI will not go unless you listen tome. Send away this new friend ofyours. This Monsieur de Lioncourt.The slaves are frightened of him.They are frightened of you.LOUIS' POVShe approaches the table, skin gleaming, but her voice isno longer audible, only her beating heart. As she placesher hands on the table to lean forward, she sees the deadrat lying on the tablecloth.BACK TO SCENELouis' hunger crests.Yvette, staring at the rat and then at Louis, starts toscream. He upsets the wine glass as he rises and clampshis hand over her mouth.The GLASS rolls to the floor and BREAKS.In horror, he realizes he has accidentally broken herneck. He stares at her dead eyes, and he isgriefstricken.(CONTINUED)34.CONTINUED:For one moment he is tempted to drink her blood, thenhorrified by the incestuous and monstrous idea. Hecradles her as he would a precious friend, overcome withgrief.LOUISYvette, my poor faithful Yvette.EXT. SWAMP - NIGHTLouis watches the body of Yvette sink deep into the muck.He is utterly dejected. He hears SOUNDS, turns, seesslaves at a distance spying on him.He walks back to:EXT. SLAVE QUARTERSA row of brightly lighted little pitched roof bungalows.Not turning his head he walks past the slaves in thedarkness of the porches as all greet him softly with aBonsoir, Michie. He makes no answer. He stands lookingat:MANSION OF POINTE DU LACThe rich house with all candelabra and chandelierslighted, all windows open. He stands rapt by the vision.Behind him slaves gather, uneasy, whispering.Suddenly galvanized, Louis rushes up the stairs, snatchesup the candelabra and sets fire to the drapes. He goesfrom window to window doing it.SLAVES' POV - MASTERsetting fire to the house.BACK TO SCENEThey rush up the stairs, with shouts of "Stop him, he'smad."INT. BEDROOM Louis stands surrounded by flames, ready to be consumed.The night is full of SHOUTS and SCREAMS and the planta-tion BELL CLANGING. GLASS BREAKS. Louis turns to see --(CONTINUED)35.CONTINUED:Lestat stepping through the broken window. Louis squintsas he looks beyond at the paling sky.LESTATYou fool, what have you done?LOUISIt's almost sunrise. You promisedme that the sun or the fire couldkill me! Now leave me, saveyourself.Lestat pulls Louis' left arm around his shoulder, as ifhefting a drunken companion. Carrying Louis, he rushesout on the porch and leaps over the railing to the ground.He climbs on his horse, lifting Louis before him. Louiscovers his eyes as the barest light of morning fills thesky. He slumps forward over the horse's neck.Slaves rush towards them, but Lestat drives them backeffortlessly with several swipes of his riding crop andrides out the road and out the gates. The sky is violetwith the coming dawn.EXT. LARGE GRAVEYARD With many large crypts. Louis, now unable to uncover hisface, is being carried over Lestat's shoulder.LOUIS'S POVPassing crypts, light coming in orange flashes. Sound ofRUSTED HINGES. Then darkness.INT. CRYPT Louis is flung down on the floor of a large crypt.Lestat fits the iron door back into place and secures it.The gleaming burning light is gone.LOUISWhere are we?LESTATWhere do you think, Louis? We'rein a nice filthy cemetery. Doesthis make you happy? Is thisfitting and proper enough?Louis laughs softly.(CONTINUED)36.CONTINUED:LOUISWe belong in hell.LESTATAnd what if there is no hell, orthey don't want us there? Everthink about that?Lestat lies down in the shadows beside him.LESTAT(defeated)Never mind, don't answer.Sometimes this is close enoughto hell as it is.INT. INN (NEW ORLEANS)Lavish little supper chamber with coffered bed, fancyFrench furniture. Open window to rooftops of colonialcity.Louis is in fresh clothes and sits calmly in a chair.Lestat before the mirror fusses with his lace collar.LOUISWhy did you bother to save me?You can make another. Someonebetter than me.LESTATYou're too strong. That's yourtrouble. You feel too deeply.You see too much.LOUISYou spoke of old ones, you saidin time they went mad. Is thatwhat will happen to you and tome?LESTATSome do, some don't. There arelegends of those who've livedfor a millennia. Why can't welive for eternity. We have thechance!Lestat pauses, perplexed, plunged into thought.(CONTINUED)37.CONTINUED:LOUISI'm leaving you. I'vedisappointed you, Lestat. Andthere's no reason for me toremain. You have no need of me.You never did.Lestat looks sad.LESTAT(compassionately)And where are you going? Youthink you'll find others in theNew World? Or will you attemptthe voyage to Europe? Supposethe ship sinks, Louis, and youand your coffin are plunged tothe bottom of the sea. You won'tdie, you know. You'll lie there,struggling forever. And you'llhave forever to realize all yourquestions were in vain.Louis rises and moves to the door.LOUISI'm sorry I've failed you. Itold you I wanted it, and I waswrong. I'm going. Where, how --I don't know the answers. I'lllive from the blood of animals, Iswear it. I shall never takeanother human life again. AndI'll search... for what I can'tsay...Lestat shakes his head, trying to suppress his dismissalof this. He is losing Louis and afraid.LOUISThere's nothing more you canteach me, you've said so yourself.LESTATAnd you think there are others whocan teach you things? That you'llfind them? You don't understandabout the others. They're lonepredators, jealous of theirterritory. They'll see youcoming. You'll be a mark.LOUISAll of us lost... lone wolves.(CONTINUED)38.CONTINUED:LESTATNow that is the truth. And allwe have is the companionship wecan give each other. That's allanyone has, Louis. Go out, walkthe city streets, peer throughthe windows at the couples intheir beds.Lestat takes Louis by the shoulders and tries to get himto listen. He hovers like an angel whispering in Louis'ear.LESTATIt's part of our nature tomeditate, to seek, to see through... to understand.Louis tries to remain resolute. Does not reply.LESTATWe are creatures of the earth, myfriend. And yes, like a thousandother species we kill so we maylive. This world is a savagegarden. We're no different fromother beasts of prey.Louis looks at Lestat. Sincerely:LOUISAdieu, Lestat. I'm sorry.LESTATIn the old world, they called itthe dark gift, Louis. And Igave it to you.LOUISI know. Forgive me. It was allan error, a tragic error from thestart.EXT. STREET (NEW ORLEANS) - NIGHTDeserted narrow muddy streets of small, pitched roofbungalow cottages. Louis walks alone, seeing things in adaze.He sees a white X marked on an empty house.A MAN with a lantern lifts it as he passes.(CONTINUED)39.CONTINUED:MANDon't go that way, monsieur. It'sthe plague, monsieur. Go back theway you come.Louis smiles at those words, repeating them softly.LOUIS... the way I came.He walks on. More houses marked with X's. MOANS andCRYING come from the houses. Sometimes only the soundof someone GASPING for BREATH.A black cat darts past Louis. Crazed with hunger, hestares at it, watches it speed away. He trembles. Hewalks on.A CHILD'S CRYING becomes LOUDER and LOUDER. Gradually,we realize it's a child of perhaps six, crying inexhaustion and fear. It is coming from a dark house.Louis pauses before the house. The child is sobbing.CLAUDIA (CHILD) (O.S)'Mama, please, wake up. Mama,I'm frightened, please...LOUIS' POVCLAUDIA, in a ragged little gown tugs at the dead body ofher mother, crying softly and wearily.CLOSE ON the dead mother. Her eyes are being eaten awayby ants.BACK TO SCENELouis gasps in horror.Claudia turns. She is a radiant doll or angel as shestretches out her hands to Louis.CLAUDIAMonsieur, please, help us. Wehave to get to the ship. Mypapa's waiting for us. Please,monsieur, help me. Wake Mamma,please.Louis stares past her at the dead mother.(CONTINUED)40.CONTINUED:Instinctively, he gathers the child to him, protectively,looking back at the spectacle of the mother's faceswarming with ants.Claudia chokes and sobs against his shoulder.He turns her face upward looking at her, stricken withpity, and then the hunger glazes his eyes. Her cryingbecomes louder yet ever more distant, and we see onlyher beauty, her cheek, her throat.Louis closes his eyes, hand touching her throat, andslowly he bends to kiss it, and then we see his fangs forone instant as he eases them into the flesh.The CRYING DIES away as Louis goes into the swoon.Gradually another sound replaces it.LESTAT'S LAUGHTER, GROWING LOUDER AND LOUDER and moredistinct.Suddenly, Louis breaks away, caught redhanded, the childin his arms. He sees Lestat laughing in the doorway,pointing at him, slapping his knee, and laughing again.LESTATAh, my philosopher, my martyr.'Never take a human life again.'Well, really, you must admit it'sterribly funny. Or is it merelytouching? I'm not sure.Louis stares down at the unconscious Claudia in horror,then lets her slip gently into a chair. Shamefully hewipes at his mouth, sees the streak of blood on the backof his hand, and the tiny wounds on her throat.Lestat rushes past him. He snatches up the dead motherfrom the bed, and begins to dance with her in greatcircles, humming and talking. Her head falls back.Black water flows from her mouth.LESTATWell, let's make a party of itshall we? The child's still alive,Louis. Look at her, you've leftsome life in her, and some bloodtoo.Louis flees into the street.Lestat runs behind him.(CONTINUED)41.CONTINUED:Men with cart of corpses pass by, peering into eachhouse.LESTATCome back, Louis. Come back. It'sonly your vampire nature.Louis runs. Lestat follows taunting him.LESTATLouis, do you want me to go backfor her?Louis scales a wall and runs from rooftop to rooftop,Lestat following him easily, dancing alongside of him.LESTATOh, come on, it's not so veryshameful! She'd have died of theplague if you hadn't taken her.Oh, Merciful Death, how you dolove your precious guilt.Louis turns on Lestat and attacks him with all hisstrength. They fight, Louis again and again assaultingbravely, Lestat easily blocking the blows.Finally Lestat's hand rises.BLACKNESS.INT. INNWindow open to the setting sun. Night comes over thecity.A maid enters, puts a lighted candle on the table.Full darkness outside.CUT TO:LESTAT AND LOUIS seated by the candle. Lestat is talking.LESTATWhat can I tell you? How can Imake you understand?LOUISTalk to me. Where did you comefrom? How did it happen with you?DISSOLVE TO:42.EXT. LESTAT'S CASTLE IN AUVERGNE (FRANCE 18TH CENTURY)Snow storm.LESTAT (V.O.)We were country lords. Proud,penniless, the old order who neverwent to Paris to wait hand and footupon the king. If I didn't hunt, westarved in our ancestral castle.INT. GREAT HALL Three tradesmen from the village stand with platters ofhot food before --Lestat, a crudely dressed Robin Hood style lord, dappledwith snow, walks in with two slain wild rabbits over hisshoulder. Stops, sees the laden table, and acknowledgesthe tradesmen with a bow.LESTAT (V.O.)(bitterly)Unless the villagers fed us,bringing their gifts of roast pigand wine, as if they were tributesand not charity to keep us alive.CLOSE ON GABRIELLE at nearby hearth in much mended and faded finery. Pale,obviously ill.Lestat approaches her, lays down the game, and thenkisses her on the mouth.Lestat and GABRIELLE gesture for the tradesmen to placethe food on the table, and we see --LESTAT'S FATHER blind, dignified, seated at the table, making a grandoisegesture of acceptance as the villagers back away. Twobrothers also watch stiffly and uncomfortably, giving thevillagers nods of thanks.Lestat leaves with the villagers, talking together,escorting them to the doors. They talk.LESTAT (V.O.)And when a pack of wolves beganterrifying the villagers, it wasI who had to hunt and kill them.I was the only one left who couldsit a horse, the only Lord whocould hunt our ancestral lands.43.CLOSE ON BLIND FATHERgroping for cup of wine. Two brothers begin to dine aswell.EXT. SNOW-COVERED VALLEY Lestat, in crude garments, with crude weapons -- flail,old broad sword, musket in its belt, flintlock rifle --rides his mare through the deep snow. Behind him plodtwo giant mastiffs with spiked collars.LESTAT(singing)Come out, brother wolf. I'mwaiting. I'm waiting for you all.Whistles as he rides on, enjoying wind and blue sky.Two wolves appear, rushing from the dark woods towardshim.Lestat is galvanized, takes aim with FLINTLOCK RIFLE andbrings one down as the other charges and kills one dog.Lestat has no time to reload. He aims the MUSKET, woundsthe wolf, but the dog is dead. Then to his horror --Three more wolves suddenly come running from far ahead.LESTAT (V.O.)It was an ambush. They are suchclever animals. And I should haveknown. I'd hunted them before.Lestat fights at the wolves with his sword, killing athird, as the other one attacks and kills his other dog.The wounded wolf and the last of the five come back,charging him, striking his horse, and wounding thehorse's hind quarters so that it falls.Lestat slips out of the saddle. He grabs the flail fromhis belt. He strikes the wounded wolf and kills it. Thelast wolf, very canny, merely watches him.Lestat looks at the nearby forest. It's too far. Thebranches are too high. Nevertheless he backs towardsit, staring down the wolf who begins to pace.Lestat turns and starts to run. The wolf chases.Lestat pivots and rams the sword right through the wolf'sthroat. In exhaustion he collapses, arm over the warmbody of the wolf, staring back at...(CONTINUED)44.CONTINUED:His HORSE emitting terrible WHINNIES as it tries to standup but cannot.LESTAT (V.O.)How did I slain the entire pack?Another man might have lost hislife then. It seemed the greatestvictory, but afterwards it cameto mean so much more.Lestat reloads his MUSKET and executes his horse.Bitter. Heartbroken.INT. GREAT HALL with table and fire.Lestat and Gabrielle greet THREE VILLAGERS. Villagerspresent Lestat with beautiful red velvet cloak lined withwolf fur.VILLAGER #1From the wolves, my lord, thoseyou slew with your own hand.LESTATThank you, Antoine, thank you all.Lestat turns, sees four villagers filling the table withmeat and drink.As villagers leave, Lestat slumps into a huge medievalstyle chair by the fire.Gabrielle comes to him. He rises, but she bids him tostay seated and she sits on the broad arm of the chair.He is alarmed at her pale appearance. He goes to kissher. She pushes him away.GABRIELLEListen to me, my youngest and mydearest. Listen well. I knowwhy you don't leave here...LESTAT(resigned)I'd never leave you, Mother.Don't talk of such a thing.She takes gold from her pockets. Lestat is shocked atthe sight of so many real gold coins.(CONTINUED)45.CONTINUED:GABRIELLEThis is all I have left of myfamily's money. You're to takeit, do you hear me? You're to goto Paris and make your fortune.Lestat tries to protest.GABRIELLE(forcefully)Lestat, I'm dying. I can't livethrough another winter. Now youmust do this for me. Go to Parisso that I know you are happy andaway from here as my eyes close.Again, Lestat tries to protest. Gabrielle looks almostcruel.GABRIELLEGive me this gift, my son. Formy sake, leave tonight.LESTAT (V.O.)I could hardly bear to leave her.But I couldn't deny her either.That she knew.Gabrielle kisses him, slightly intimate for mother andsone, but very full of love.RETURN TO INNLestat talking to Louis who is rapt.LESTATIt was the boulevard theatres Iwent to. I loved them. No decentlord would have ever acted upon astage but what did that matter tome? Thanks to my mother I wasfree.INT. RENAUD'S THEATRE Lestat in the red cloak with its wolf lining, cavortsbefore the audience as the younger lover in the play. Hewinks as he chases the beautiful heroine. A buffoonishold man with a fake nose suddenly blusters between them,grabbing the heroine, who takes one look at him and fleesinto Lestat's arms.Roars of laughter from the audience.46.CLOSE ON LESTAT'S FACEas he sees in the audience, third row:MAGNUSA skull-like visage with dark, gleaming eyes, watchinghim from beneath a dark hood of black velvet.LESTATin a trance senses danger.SOUNDS OF AUDIENCE GROW FAINT.CLOSE ON MAGNUSMAGNUS (V.O.)Wolf killer.SOUNDS OF THEATRE GROW FAINTER. Magnus smiles.LESTATbreaks into a sweat.LOUIS (V.O.)He could read minds as you could.LESTAT (V.O.)Oh, yes!INT. ATTIC ROOM (PARIS) - NIGHTLestat and two actresses and actors sleep on pallets onthe floor. Snow falls outside. Lestat wakes, shivering,hearing.MAGNUS (V.O.)Wolf killer.The WINDOW SHATTERS. Lestat is dragged by a hoodedfigure out of the bed, out of the window and up into theswirling snow. He fights like mad, even biting at thewhite hand that holds him. We hear Magnus's LAUGHTER.The HOWLING STORM.47.INT. TOWER ROOM - FUNERAL PYRELestat newly made a vampire with blood on his lipswatches in terror as Magnus, leaping about like a spidermonkey, sets fire to the pyre and then ascends.LOUIS (V.O.)He told you nothing.LESTAT (V.O.)Only where I might find my coffin,and how I must find it. And thathe'd left me the tower and all hiswealth.LOUIS (V.O.)He thought you were strong.Lestat wanders through the dungeon of the tower. Comesto a cell where he sees something which horrifies him.LESTAT (V.O.)And I was strong. I'd fought himthrough every step of it. Thatmust have been why he had let melive. Because there had beenothers, lots of others whom he hadchosen and then allowed to die.Lestat grabs the bars of the cell, staring at what'sinside.CLOSE ON GREAT HEAP OF BODIES OF YOUNG BLOND-HAIRED MENSome long dead, some recently dead. All resemble Lestat.All have his height, coloring, even similar garments. Andthe most recent corpse, swarming with flies, has blue eyes!Lestat backs up, doubled over with nausea and vomits astream of blood onto the stones. Stunned, he stares atthe blood and instinctively, arches his back and reachesdown and laps it back up with his tongue.Realizing what he is doing, he rises, slamming back intothe bars, against the corpses and then he lets out a roar.It is like the roar we have already heard from Louis inthe swamp. It echoes throughout the dungeon and the tower.EXT. BOULEVARDS (PARIS) Lestat, a vampire, beautifully dressed in brocade and lace,walks through the crowds of jugglers, vendors, ladies ofthe street, city strollers and stops at Renaud's Theatre.He watches from a distance, as the crowds go in.(CONTINUED)48.CONTINUED:LESTAT (V.O.)Of course I learned how to huntinstinctively. That was nothing.But as for the rest, I was asconfused as you ever were. Ididn't dare return to my mortalcompanions. To Gabrielle, mymother. I sent vague lettersdescribing my turn of fortune,and all the money she couldpossibly desire. I thought I'dnever lay eyes upon her again.Lestat turns away from the theatre and goes through thecrowd.LESTAT (V.O.)All around me, I could hear thethoughts of mortals. I alwayshave been able to hear them. It'slike a chorus of whispers. And inthe midst of that chorus, I wasalone. Until one night, I heardthe voice of a different soul, amonster like myself.EXT. PLACE DE GREVELestat stops, listening, wary. A shadowy shape rushesaway from the facade of Notre Dame.LESTAT (V.O.)Soon, I heard them often. Theywere following me. I could feeltheir hatred, and when I glimpsedthem, I saw ragged, filthy littlegoblins. Why, they reeked of thedirt of the grave!EXT. DOORS OF NOTRE DAME (PARIS)Lestat rushes toward them as a little band of raggedvampires in rags hurries silently after him. He seesthem up on the roofs. He rushes into the:CHURCHHe peers back out at them with curiosity and contempt.Three little vampires hang out in the shadows trying tokeep an eye on him.(CONTINUED)49.CONTINUED:A man passes before the cathedral with a lantern and thethree vampires run cowering from the light.LESTAT (V.O.)It was very easy to elude them.All I had to do was seek shelterof a church. They were afraid togo into them! They ran fromcrosses. They ran from the light.RETURN TO:INN (NEW ORLEANS)Louis listens rapt, as Lestat talks, walking back andforth.LESTATI soon realized they lived in thecemetery of Les Innocents. It'slong gone, that place. But inthose days it was in the heart ofParis.EXT. LES INNOCENTS CEMETERYGigantic place full of many crypts. Three vampires dartthrough the darkness and disappear through a crypt door.LESTAT (V.O.)They inhabited the catacombsbeneath the cemetery. And theybelieved the cross could hurtthem, that holy water would burnthem, they believed it, do youunderstand?LOUIS (V.O.)Yes, I can understand it.RETURN TO:INN (NEW ORLEANS)Lestat talking to Louis.LESTATAll that superstition. And I, theorphan was breaking all theirrules, because I didn't know therewere any rules at all.RETURN TO:50.INT. BALLROOM TUIELIERES (PARIS)Lestat in dim light dances with a mortal woman.LESTAT (V.O.)What was it they later accused meof? Ah, yes, walking in theplaces of light. I didn't servethe devil properly as they saw it.I tempted the fiend to drag medown into hell for my sins. Andof course, there was anotherthing. I'd made a companion soonafter. And broken more of theirrules when I'd done that.EXT. ILE ST. LOUISLestat on horseback rides over bridge behind Notre Dameand stops before a mansion, anxious, looking up at alighted window.LOUIS (V.O.)A companion! Where is this beingnow?RETURN TO:INNLestat smiling sadly at Louis. Louis studies him, curiousyet patient.LESTATIf only I knew.RETURN TO:ILE ST. LOUISLestat dismounts, enters:INT. MANSIONHe rushes past attendants up stairs.LESTAT (V.O.)As I told you, my mother wasdying when I left her Thatjourney to Paris was the hardestthing I'd ever done.(MORE)(CONTINUED)51.CONTINUED:LESTAT (CONT'D)Yet with the wealth I showeredupon her -- the wealth Magnus hadgiven me -- she accomplished theone thing I never expected. Shemade the journey to Paris to seeher son for the last time.Lestat stops before a bedroom door.A NURSE emerges gesturing for him to be quiet.NURSEMadame is very ill. Yet she isdressed and waiting to see you.All day we've waited for you! Doyou think death waits on everyspoilt young lord?Lestat is anguished. Slowly he goes into the room. Hestands in the shadows. In the light of a candle, we see:Gabrielle, his mother, pale and very sick obviously, yetbeautifully dressed and seated in a gilded armchair bythe big heavily-draped bed. She is almost too weak torise.GABRIELLELestat, oh, my darling... Comeinto the light where I can seeyou.Lestat remains in the shadows.LESTATPut out the candle, Mother. I wasa pauper when last you saw me. Imight dazzle you now.GABRIELLESo were we all, my darling, beforeyour good fortune. It is you Icame to see. Not your fineclothes.LESTATPut out the candle, Mother.She pinches out the candle. Only light comes throughhigh window.GABRIELLEPlease, come to me. Let me takeyou in my arms.(CONTINUED)52.CONTINUED:Lestat draws nearer, trancelike.LESTAT (V.O.)How could I tell her? How couldI explain I wasn't her sonanymore, that this is what I'dbecome? You know what you seewith your vampire eyes. Imaginethe sight of her to me with mynew vision. She was dying. Shecould not have lived anotherweek, perhaps not another night.And her thoughts, I could hearthem. She was afraid of dying!That's why she'd come to me.She'd thought it would be easierwith me there!Lestat in anguish draws nearer. Gabrielle struggles toher feet, eyes full of tears and reaches out. As shetouches him, she realizes he's not human anymore. Shefalls back, losing her balance, grabbing for the bedpost.Lestat stares at her sadly.LESTAT (V.O.)Countless mortals I'd deceived inthe ballrooms and the theatres,in the boulevards and the cafes.But I could not deceive her. Sheknew the moment that she touchedmy skin. What could I do butexplain to her silently, makingher see it in images, that Ihadn't chosen it, that it hadbeen done to me, against my will.CASCADE OF IMAGES A)MagnusB)The TowersC)JewelsD)Lestat drinking blood from a mortal in an alleyway.BACK TO SCENEGabrielle moves trancelike toward Lestat. Though hislips don't move, we hear his whisper.(CONTINUED)53.CONTINUED:LESTATI hide nothing from you, not myignorance, not my fear, not thesimple terror that if I try Imight fail. I do not even knowthat it is mine to give more thanonce, or what is the price ofgiving it, but I will risk thisfor you, and we will discover ittogether.GABRIELLETake me. Bring me with you! Doit!Gabrielle opens her arms just as she is about to fallfrom weakness. Lestat enfolds her in his arms, lovingly,sinks his teeth into her throat and enters a swoon. Theyembrace tightly. As she weakens he wakes her and slash-ing his own throat with his fingernail puts her lips toit and she begins to suck his blood. Again, he closeshis lips on her wound. They make a cycle, each drawingblood from the other. Sound of HEARTBEAT. Sound ofDRUM.Gabrielle steps back, wiping the blood from her lips,transformed.EXT. ROOFTOPS Gabrielle and Lestat hurry over the roofs together. Theydrop down on the top of a passing coach, laughing, hold-ing tight to each other.EXT. HOTEL PARTICULEIR (PARIS) - NIGHT Gabrielle is dressed as a man now, standing over a corpsefrom which she took the clothes. She ties her hair in along pigtail with the dead man's ribbon and taking Lestatby the arm they walk off together.GABRIELLENow, don't look so heartbroken.There's no reason for me to wearskirts any longer.Lestat reaches for her long hair.LESTATJust... don't cut your hair,Mother. Do that for me, don'tcut your hair.(CONTINUED)54.CONTINUED:GABRIELLEGabrielle now, Lestat. Let go ofthat word, Mother. Let it go withthe mortal coil. And if the hairmeans so much to you, very well.Gabrielle kisses him. They walk off together, arm inarm.BACK TO:INN (NEW ORLEANS) - LESTATHe smiles sadly at the amazed Louis.LESTATYes, my mother. I am such adevil. If you were I, would youhave let her die?LOUISI don't know. But she was thestrong companion you needed, thatmuch is plain.LESTATYou think so? But how thisangered the ragged coven beneathLes Innocents! I had broken therule of all rules. Being abastard was one thing. Makinganother of one's own mother, why,you'd think I'd trampled on theSacred Host itself.INT. LES INNOCENTSThe ragged coven of twelve vampires surround Lestat andGabrielle. Gabrielle is in her male garb with her hairin a braid. The vampires hold torches with which theytaunt the pair. Gabrielle clings to Lestat but she is asgrimly angry as he is.ARMAND, a boy with an angel's face and auburn curlinghair appears. He points a denouncing finger at Lestat.LESTATWhat devil do you serve? Where ishe? Who says that you cannot gointo the cathedral of Notre Dame,if you want to? That you must livehere in filth among the old bones!(CONTINUED)55.CONTINUED:ARMAND(gently, sadly)Blasphemer. We are the devil'schildren.LESTATYou're a pack of fools.Suddenly he remembers something. He drags a jeweledrosary out of his pockets. The vampires gasp and backaway.GABRIELLELook, he took it from one of hisvictims. He's stolen a hundred.The cross has no power.She snatches the rosary from Lestat and dangles the crossin the light of the torches.GABRIELLEThese are but superstitions. Youare as deluded as mortals. Moredeluded. Who in the Paris aboveyou believes in God as youbelieve?CLOSE ON ARMAND'S STRICKEN FACEas the argument continues. Armand is being mentally andspiritually destroyed.LESTAT (V.O.)Don't you see? I was the firstone among them to discover thatthese old curses didn't matter.A bunch of monks and nuns, that'swhat they were, Satan'smendicants. And it was allnonsense.LOUIS (V.O.)But had they all believed it?Every one?LESTAT (V.O.)No. Their leader, Armand. TheBotticelli angel with the darkred hair. Oh, how deceptive wasthat innocent face! He had beentaught it.(MORE)(CONTINUED)56.CONTINUED:LESTAT (V.O.) (CONT'D)And he had believed in it, whichwas far worse than believing it.That's why he had always orderedthe destruction of any hereticor rogue outside the coven.Armand steps forward, obviously issuing judgment.Gabrielle draws close to Lestat as the torches ring them.Lestat in desperation looks at ELENI, a ragged, half-naked vampire woman who comes at him with a torch.LESTATAnd you, ma cherie, what has thedevil done for you of late, thatyou should serve him sodevotedly? Ah, but you'd look sopretty if only you'd let me fityou in a proper dress.Eleni is startled, lowers the torch. Others cry"Burn them."Lestat turns to a tall boy of twenty or so -- Laurent.LESTATAnd you? How many years have youendured the smell of death inyour nostrils? Wouldn't you liketo walk with me for an hour alongthe boulevard? Perhaps sit fora while among mortals in a warmcafe?Lestat turns this way and that. The vampires are losingtheir nerve. They turn to Armand.LESTATWhy, some of you are cold! Weneed never be cold. Why have youno hearth here?Armand does nothing. He appears brokenhearted, sad. Aswe CLOSE ON him, he turns his back slowly on the proceed-ings. Eleni throws aside the torch.ELENIYou can take me into thecathedral?(CONTINUED)57.CONTINUED:LESTATYes, once you're bathed andpropertly attired. I could takeyou to Versailles.Whispers, murmurs from the confused vampires.GABRIELLECome with us, all of you. We'llshow you. The lights of the nighthave no power. By day, we mustsleep in the dark of course, butonce the sun sets, we are free tohunt and do as we please.The vampires degenerate into loud quarreling.Suddenly Lestat seizes the torch from Laurent andGabrielle snatches up the torch that Eleni has let dropto the dirt floor.Lestat and Gabrielle flee, brandishing the torches. Theyrush up --INT. WINDING STAIRSstrewn with skulls and bones, with bodies in niches alongthe walls, until they reach --CEMETERY - HUGE CRYPTout of which they run, throwing aside the torches, jumpingto the top of the wall, and dashing away.RETURN TO:INT. INN (NEW ORLEANS) - LESTATHe looks dejected.LESTATThey soon scattered. The covenwas destroyed. Armand, the devilwith the angel's face, hedestroyed most of them becausethey could not survive withouthim, and he could no longer lead.58.INT. LIBRARY (PARIS) - CLOSE ON ARMANDdressed now as a French gentleman, standing in a lavishlibrary in Paris. He is addressing Lestat who stands bythe fireplace, equally well-dressed.ARMAND(gently)You were our ruin. You drove usout of Eden with your burningsword.LESTATYou were in purgatory. What doyou want of me! All I did wastell you the truth!ARMANDAnd what was that? That there isno truth to be known? Our beliefswere our strength, our survival.They were our citadel againsttime.LESTATLies? Lies can't be the strengthof anyone. We are monsters. Soare mortals. If we cannot facethe truth we are lost.ARMANDStop speaking of the truth asthough it were something. It isnothing.LESTATOh no, you're wrong. The truth isin the flesh, in the beauty we see,in the blood we drink. It's inthe mystery of the rainfall, andthe clouded sky, the flight of alone bird over the sea.He pauses, entranced for a moment with the beauty ofArmand himself. He reaches out, touches Armand's cheek.LESTATHow many centuries lie behind thisradiant face?He pulls Armand to the window and points down into thecrowded Paris street. A mob is surging by.(CONTINUED)59.CONTINUED:LESTATDo you hear them, they'rescreaming for the death of KingLouis and his Queen, MarieAntoinette.ARMANDWhat do I care what they want?LESTATThe old order has fallen for them.It's fallen for you as well. Makea new order as they must make it.ARMANDAh, but you know so little,fledgling. With your jewels, andyour velvet, and your shiningsword. You think it will be easyto see everything you lovedisintegrate and crumble away?LESTATThe blood, the warmth, the love...that is what will keep meimmortal.ARMANDGabrielle. Your companion. Shegives you what you require. Thatis why you say all these things.But will she remain with youalways? You cannot read herthoughts, can you? Though youcan read mine?Lestat looks afraid.ARMANDBut you could before you took herin that lovely bedroom on the IleSt. Louis, is that not so? Youcould know her soul as I knowyours now.Lestat refuses to answer Armand, but we hear:LESTAT (V.O.)He was right. Gabrielle's mindhad been closed to me from themoment my blood had filled herveins. As closed as your mind isto me now.(CONTINUED)60.CONTINUED:ARMANDIt's always so with master andfledgling. You can hear otherchildren of darkness, you cancommune with mortals. But wemaster and fledgling are divided.We must speak to and reach outfor each other. And with no vowsto bind her, she will tire of you,your mother. She tires of youalready. She has never neededanyone, your mother. She isharder than you!LESTATStop!ARMANDOh, you'll make others. You'llseek for better, more genialcompanions. But it will alwaysbe the same. They'll turn on you.They'll leave you. They may evenhate you for making them. Ourservice to Satan has held ustogether. You have nothing, andyou will go into the fire somenight as the old ones have alwaysdone.LESTATNever.ECHO. Never. Never...Armand looks sadly after Lestat and then sadly at all thebooks on the shelves. He stands back and with the powerof his mind makes the books suddenly fall in heaps allover. They cascade to the floor from all the surroundingwalls.Lestat is afraid of this show of telepathic power, butangry that he is afraid.Armand smiles sadly.ARMANDPatience. All these little skillscome... if you last long enough!LESTATGet out of here. Get away from me.With your dark prophecies andmaledictions.(MORE)(CONTINUED)61.CONTINUED:LESTAT (CONT'D)To keep those fools in slavery asyou did. It was unspeakable.Armand gives one last wan smile. A vision of beauty. Heseems to vanish. Lestat searches the empty spaceanxiously.Gabrielle becomes visible, in fancy male dress, hairbraided down her back. She is merely watching. She andLestat exchange glances.LESTATHe's right, isn't he? You dreamof being free of me already.You've had no need of me sinceour enemies were destroyed.Grabrielle opens her arms to him.GABRIELLE(kissing his cheek)To love and to need -- these aredifferent things. And what doesit matter if some night we decideto part for a little while?Backs up, smiling, with deliberate reassurance:GABRIELLEIt's too soon now to speak of it,anyway. Let's go out into thecrowd.They walk down the corridor together:GABRIELLELet me tell of my most recentdiscovery. Last night I abandonedthe coffin. I slept in the earthitself.LESTATBut how?GABRIELLEI dug deep beneath the ground,and when the sun set I rose as aswimmer rising to the surface ofthe sea.Lestat is fascinated.(CONTINUED)62.CONTINUED:LESTATSo the coffin has no magic power.It is pure darkness which werequire.GABRIELLEWe should leave Paris. I'm tiredof it already. Tired of all thesemortals. I long for exotic placeswhich I have never seen.They go out into Paris streets.DISSOLVE TO:INT. INN (NEW ORLEANS)Lestat sits at the table staring away from Louis.Silence. Then...LESTATI could have told you Armand'slies. That we were the childrenof darkness, that we travel theDevil's Road. That Satan is ourmaster. I could have used apinch of stolen incense when Imade you. And Latin mumbo jumbo.Instead I made up a little testfor you, that you kill that tavernmaid. And then I told you... whatI've seen for myself.Lestat looks searchingly at Louis.LOUIS(compassionately)But Gabrielle. Where is she?Surely she didn't leave you. Notin hatred and coldness as Armand.Louis shakes his head, disapproving.DISSOLVE TO:EXT. SNOW-COVERED MOUNTAIN SIDE - FORESTLestat and Gabrielle dressed in fur garments walk, armin arm. Then they stop and part and Gabrielle moves onalone...(CONTINUED)63.CONTINUED:LESTAT (V.O.)Where is she, tonight? I can notimagine. What continent, whatnation, what wilderness does sheroam? She was always the lone one.That was the argument. We neverhated each other. We love eachother even now. It's only thatshe sought the wilderness -- theforests and the mountains. And Icould scarcely bear it. I needthe cities, the lights, themortals around me, the thingswhich men and women have built.INT. INN (NEW ORLEANS)LOUISAnd a companion... at least one ofour kind.Lestat nods, admitting it defiantly.LESTATYes -- not to be the only oneamong all the others, not toknow... love.LOUISAnd when she left you, you came tothe New World.Lestat reflects; decides not to answer directly.LESTAT(impishly)Well, I couldn't stay in Paris.Armand's power was incalculable.And there were too many othersleft in Paris. I loathe them,really. And you would too.LOUISWhat do they do now?LESTATWhat we do. Wander the savagegarden in pairs or littlefamilies. Same thing mortals do,really. The world's enough todrive mortals mad if they thinkabout it. You ought to know.(CONTINUED)64.CONTINUED:Louis smiles.LOUISYes, on that I agree with you.LESTATAnd... besides...(smiles)They said it couldn't be done,that no vampire had ever crossedthe great sea. And so I did! Assoon as I could book passage formyself a great ebony coffin!Lestat laughs. Louis smiles sadly.LOUISHow could I pass up a challengesuch as that?LESTATExactly. That's when I learnedto live off rats. And drunkensailors. Never forget the littledrink. It tortures me, but thenI like being teased... well, for alittle while.LOUISAnd the ship did not sink, ofcourse.Lestat shrugs.LESTATWhat if it had? I can swim betterthan a shark. Would you like toswim the river some night, thetwo of us together? I've done it.I'll race you to the far bank.Louis shakes his head, no.LOUISYou made one error in judgement,however.LESTATOh? What was that.LOUISWhen you found yourself aloneagain -- the only one -- you werea little more desperate thanbefore.(CONTINUED)65.CONTINUED:LESTATI picked you carefully anddeliberately, Louis. And I'vealways found it boring... to bealone.LOUIS(nodding)Yes, that I understand as well.LESTATHave patience with yourweaknesses. All our powersincrease with age. When the oldones give you their blood, whichthey can when they choose, theygive you greater strength.LOUISHave you drunk the blood of oldones? Have you...? Did you?Did Armand...Lestat interrupts.LESTATDon't let's talk of Armand. Itgives me a mortal headache tothink of Armand. Besides,reading minds -- it's not such ablessing as you might think. Idon't like knowing when othervampires despise me, or whenmortals find me ugly or don'teven notice me at all!LOUISAs if that ever happens to you!Lestat preens at the compliment, and shrugs. Suddenly hestands up.LESTATCome, not only do I hear themortals about me, I breathe theirscent. I hunger for them. We'llhunt together. I won't let youhate me so soon. I won't letArmand be proved right, do youhear me?(CONTINUED)66.CONTINUED:LOUISI want him to be wrong. For yoursake. But I can't bear this,Lestat. And you know it now.Choose another, and let me go.Lestat smiles seductively.LESTATBut Louis, you haven't tried!EXT. DARK STREETwith lights and NOISE of the CITY in the b.g.Lestat and Louis walk arm in arm. Partygoers pass them.A coach rushes by.LESTAT(tenderly)Pain is terrible for you. Youfeel it like no other creaturebecause you are a vampire. Youdon't want it to go on.LOUISNo...LESTATDo what it is your nature to do.And you will feel as you felt withher in your arms, your littlechild.LOUISWed to her, and weightless as ifin a dance.LESTATThat and more.Lestat looks about, gets his bearing, is seized by anidea. He takes Louis's hand.He leads Louis as if searching for some specific place.LESTATEvil is a point of view. Armandknew it. You know it. Gabrielle,my beloved mother never forgot it.(MORE)(CONTINUED)67.CONTINUED:LESTAT (CONT'D)And what we have before us are therich feasts that conscience cannever appreciate and mortals cannever know without regret!Louis almost winces in pain at the accuracy of it. Lestatquickens the pace as they come to --LIGHTED BUILDINGSLestat speaks while searching each with his gaze.LESTATGod kills, and so shall we. Forno creatures under God are as weare, none so like him asourselves...LOUISYes, merciless and greedy and cruel.That I do believe.Louis looks at the stars. He is soothed by the breeze.LESTATAh, but we have even more incommon with our creator. Come, Iam like a mother tonight. I wanta child.Louis is baffled. He follows as Lestat enters --LONG COLONIAL HOSPICE OR SHELTERwith rows of wooden beds. Children moan and cry beneaththe covers. One nurse and one doctor attend, each withcandle in hand.Lestat peers into the shadows.LESTATShe's there, your wounded one!LOUISWhat are you saying? What is thisplace? These are foundlings,starving children...Intrigued and seduced, he watches as Lestat moves fastdown the ward, and points to Claudia, pale and uncon-scious on the bed.(CONTINUED)68.CONTINUED:Louis recognizes her.The doctor approaches Lestat. The doctor wraps thesleeping child up in her little white blanket, as Lestattakes money from his pockets and flings it on the bed.Many gold coins.LOUIS(whispers)Lestat, what are you doing?Lestat is murmuring politely to the doctor, who is bowing.Lestat turns and hurries silently past Louis, with Claudiaasleep on his shoulder. Louis hurries after him into thenight.LOUISLestat!EXT. DARK STREETWe see only dim figures and the white blanket as if itwere flying through the dark like magic.INT. INN - SUPPER ROOMBedroom as before. Candle on the table.Lestat lays Claudia gently on the coverlet of the bed.Louis draws near, looking down at her, stricken by herbeauty and her fragility.LESTAT(gently)You haven't fed yet at all tonight.And last night you took so little.LOUISNo. Don't demand this of me.Don't make me do this. It's toolike your old Paris coven. Norituals between us.But he cannot take his eyes off Claudia who tosses inhalf sleep.LESTATSee how plump and sweet she is,still. Even death can't take herfreshness. The will to live inher was so strong. Death mightmake a sculpture of her tiny lipsand rounded hands, but he cannotmake her fade!69.CLOSE ON LOUISbecoming desperate with hunger and anguish.Lestat whispers in his ear, compassionately.LESTATYou remember, how you wanted her,the taste of her...LOUISI didn't want to kill her.But he is overcome with the memory of the ecstasy.HIS POV - CLOSE ON CLAUDIAClaudia is lifted towards him, slipped into his arms.LOUIS (O.S.)Poor cherie, no chance...LESTAT (O.S.)No chance at all.BACK TO SCENE Louis closes his eyes as he caresses her, holding hercheek against his own and kissing her forehead, verypaternal. And then he opens his eyes and looks at herneck, and sees the traces of the wound of last night andhe becomes a ravenous vampire, and slowly, gently sinkshis teeth once more, careful not to hurt her.LESTAT(whisper)Just a little tear. It's just alittle throat.Louis moans as he sinks into the swoon. HEARTBEAT.DRUMS. The ECHO of Claudia's crying from the nightbefore. His hand cradles her head tenderly. He is likea father kissing a child.LOUISSo strong.LESTAT(whispers)Is she?The HEARTBEAT and DRUM are getting SLOWER and SLOWER.(CONTINUED)70.CONTINUED:Suddenly Louis opens his eyes in shock as Lestat snatchesthe child from him.LOUISFor the love of God, let mefinish!Lestat shakes her, talks to her, staring at her enthralled.LESTATClaudia, Claudia, listen to me.That's your name, isn't it,cherie. Claudia! You're ill, myprecious, and I'm going to giveyou what you need to get well.LOUISLestat! This is sorcery.Louis lunges at him, but Lestat brushes him aside effort-lessly, so that he falls to the floor, from which he risesat once.LOUISStop this, now.Lestat bites his own wrist and presses the bleeding woundto the child's mouth. He winces in pain.Louis is fascinated. Dazzled.LESTATThat's it, dear. More. You mustdrink it to get well.Claudia sucks on the wound, reviving, making little noiseslike a person waking from sleep.Louis rises to his feet as Claudia clutches Lestat's arm,sucking the blood fiercely, and Lestat moans.LESTATStop, that's enough. No more.He pulls her loose, as she growls, and she stares at himwith big clear astonished eyes.CLAUDIAI want more.LOUISWhat have you done!(CONTINUED)71.CONTINUED:Lestat puts her down on the bed and sits beside her,holding his wrist, obviously in pain.CLAUDIAMore.LESTATYes, cherie, of course you wantmore. And I'll show you how toget it. Louis, the bell rope.Pull it.(to Claudia)You drink from mortals, my beauty,but from me? Never again.LOUIS(whispers)Burn in hell!Impatient, and still suffering, Lestat reaches for thebell rope himself.LESTATOh, come now, the child's hungry.CLOSE ON CLAUDIAbeing transformed. Becoming white yet robust, bright-eyed yet crazed. She shakes her dusty curls and the dustfalls from them. They are shining in the candlelight.BACK TO SCENELouis cannot stop looking at her. He does not notice --As the MAID enters.MAIDAh, quelle belle enfant!The Maid comes near to the bed, kneels in front of Claudia.Lestat lays his hand on the Maid's throat and Claudiawatches keenly.LESTATGently, cherie. They are soinnocent. They must not be madeto suffer.Claudia lunges for the throbbing vein in the neck, veryserious, gnawing, growling slightly, then locking on theflowing blood.The Maid is transfixed.72.CLOSE ON LOUISAs we see his anguish, we hear Lestat's voice.LESTAT (O.S.)That's enough, cherie. Stop beforethe heart stops. It's best inthe beginning, lest the death takeyou down with it. Ah, yes, that'sit. My child. My beloved child.LESTAT AND CLAUDIAsit on the Louis XVI settee. Claudia is a vision, a dollmade out of pearl. Animated, voice crisp.CLAUDIAWhere is Mamma?ANOTHER ANGLEThe words ECHO in Louis's head as he puts his hands tohis ears.LESTATMamma's gone to heaven, cherie,same as that sweet lady there.They all go to heaven. And youdid very well, cherie. Not adrop spilt. Very good! You'regoing to be our child now.Lestat and Louis exchange glances. Claudia looks at eachof them.LESTATThis is Louis, and I'm Lestat.Lestat takes out his comb and begins to comb her hair.At once, it curls resiliently. He smiles with delightand kisses her cheek.LESTATYour mamma's left you with us.She wants you to be happy. Sheknows we can make you happy.LOUIS(whisper)You are the Devil! You are theinstrument of Satan.(CONTINUED)73.CONTINUED:LESTAT(shhh)Do you want to frighten our littledaughter? What's the matter withyou?CLAUDIAI'm not your daughter.LESTATYes you are, dearest. You are mydaughter and Louis's daughter.Louis kneels before her as the Maid did. He is struckwith compassion and fascination. It is done and she isirresistible. He cannot help but reach for her, and holdher gently as if she were a doll that might break.Claudia smiles at him.CLAUDIALou... eee...Louis is conflicted. He cannot leave her. He touchesher cheek, her hair. Same as his. Vampire skin and hair.He draws in his breath, shocked at her beauty, and thenhe clasps her head again, tenderly kisses her forehead.His body relaxes as he embraces her, takes her to himselfas a father might a daughter, his eyes closed.LOUIS(whispers to Lestat)You devil, you monster.Lestat is sort of amazed. He stares at Claudia as thoughfascinated by what's happened, and then:LESTATYes, Claudia dearest, you areour little daughter. Now whomshould you sleep with? Darknessand safety are so important.Perhaps you should sleep withLouis. After all, when I'm tiredI'm not always... so kind.DISSOLVE TO:ROOM (SAN FRANCISCO) - PRESENT Malloy looking at Louis.(CONTINUED)74.CONTINUED:MALLOYHe did it to make you stay withhim! He made a vampire of a child!LOUISPerhaps. The answer to why isn'tso simple. Lestat was always theman of action. And that nighthe'd bared his soul to me. He'dshowed me his own weakness, hisown failure.MALLOYThat Gabrielle had left him. ThatArmand had been right.LOUISMaybe he didn't know himself whyhe'd done it.EXT. NEW SPANISH TOWNHOUSE (RUE ROYALE, NEW ORLEANS)Two husky movers bring furniture through the back court-yard, past the fountain and the banana trees, and up theback stairs and into --INT. FLATStriped wallpaper gives way to flowers in the bedrooms.And though huge four posters fill three of these rooms,we also see large chests, as big as coffins, standingagainst the walls. Everywhere there are candles, andpretty Louis XVI furniture.There are oil lamps about.As we MOVE INTO:DIMLY LIGHTED PARLORwe see Claudia resplendent in white lace standing on apetit point chair, as a DRESSMAKER hems her garment withpins.LOUIS (V.O.)Life was very different withMademoiselle Claudia, as you canimagine. And he loved her. Oh,he loved her as much as I lovedher and that was more than wordscan express.(CONTINUED)75.CONTINUED:Lestat stands in the French window, open to the porch,watching as Louis sits at the desk, his hand idly on anopen book.DRESSMAKERMonsieur, I need more light. Ishall go blind if you do not bringme a lamp, or let me fit this childduring the day.Claudia laughs, languidly, beautifully. Laughter seemsto echo off every surface. Lestat smiles at Claudiaand winks.INT. ST. LOUIS HOTEL (NEW ORLEANS) - LOBBY - EARLY EVENINGSlave auction going on under the rotunda. Spectatorseverywhere.Lestat and Claudia (mentally six years old) sit at smalltable in the open bar.Lestat points to a man passing.LESTATAll yours to choose from. Alwayspick carefully. Always pick oneyou want to hold in your arms.One you want to know for aprecious moment.Claudia nods.CLAUDIAThat one!She points to a well-dressed WOMAN WITH a BABY in herarms who has just come down the stairs. A black slavewoman follows.Lestat is obviously a little distressed. But he doesn'twant to question her.He follows Claudia as she slips after the Woman outinto...EXT. DARK STREETWOMAN WITH BABYHush, my little one. The cathedralis only steps away. Here, take her,Annette. I won't be long.(CONTINUED)76.CONTINUED:The Woman gives the baby to the slave woman who rocks itin her arms as the Woman enters the cathedral.INT. ST. LOUIS CATHEDRALThe Woman approaches the shrine of the Virgin and kneelsand quickly makes the sign of the cross. She looks upstartled to see...CLAUDIAradiant, still as a statue, beside the altar.ANOTHER ANGLEThe Woman is entranced as Claudia draws nearer. Othersmove quietly about the church.WOMANWhat is it, little one? Are youlost? Come here to me, darling.Claudia winds her arms around the Woman's neck, looksdeep into her eyes. Then awkwardly, quickly, lessgracefully than Lestat or Louis, she sinks her teeth.The Woman freezes.WOMAN'S DAZED POVas she is dying: Lestat beside the altar watching,amazed at Claudia's determination and fearlessness. Yeta little put off.EXT. CROWDED STREET CAFE (JACKSON SQUARE)Lestat and Claudia talk together.LESTATI like the evil ones, I told you.I like the taste. I like the rumin their blood. It gets me tipsy.Claudia laughs scornfully.CLAUDIAAnd I like the innocent and theyoung. Come now, I dare you.Take that little orphan there,wandering outside. Look at him.(CONTINUED)77.CONTINUED:FOCUS ON ragged boy selling matches in the street.LESTATYou're a little fiend, you knowit?CLAUDIAAnd you love it.LESTATI want a sodden drunk tonight.Come, I'll show you. We'll findsomeone who's had at least a fifthof the best wine.They leave together.CLAUDIAYou really can taste it.LESTATCherie, I'll have to carry youhome.INT. FLAT (FURNISHINGS - 1815)Louis and Claudia sit together on the French couch asLouis reads to Claudia from Moll Flanders. He stops,tired and sits back.CLAUDIAHere, Louis, let me read to youfor a while.LOUISBut I've never taught you...CLAUDIAWell, I don't think it's so veryhard. Not after watching you.Claudia begins to read the page, haltingly, then fasterand more fluidly and finally as eloquently as Louis.Louis is amazed. We hear:Lestat's laughter.Lestat appears with a handbill. He drops it over thebook. He gives a little belch.LESTATHere, my precious, read this.(CONTINUED)78.CONTINUED:CLAUDIA(reading)'The Saint Charles Theatre herebyinvites all young actors of thecity of New Orleans to auditionfor the leading role inShakespeare's tragedy... 'Oh, not Macbeth again, Lestat.We've seen it a hundred times.And you've been hunting among thesots again, haven't you?Louis laughs softly to himself.LESTATAh, but not with Lestat deLioncourt in the leading role,you haven't seen it!CLAUDIAYou? As Macbeth? How marvelous!Jumps off the couch and runs to him. Lestat picks herup.LESTATI intend to try for it fair andsquare.LOUISIt's too risky and you know it.To be that close with mortalsnight after night.Lestat dances around the room holding Claudia as if shewere a woman dancing partner.LESTATI have it all figured out, Louis.I'll go to the audition with myface painted. I shall always havemy face painted. They can lookas closely as they like!INT. ST. CHARLES THEATRE - LOUIS'S AND CLAUDIA'S POValone in back row watching:Crowd of actors on the stage. Dickensian theatricaldirector motioning for quiet.(CONTINUED)79.CONTINUED:Lestat dressed as Macbeth with face painted heavilyholds the script and begins to read.LESTAT(with great but subdued feeling)' ... Out, out brief candle.Life's but a walking shadow, apoor player that struts and fretshis hour upon the stage, and thenis heard no more...(hesitates, struggles to continue)... It is a tale told by an idiot,full of sound and fury, signifyingnothing.'BACK TO SCENEClaudia makes a silent delighted gesture of clapping herhands, and in her excitement kisses Louis who watchessmiling as --Other actors applaud, nod in agreement. Stage managergoes into raptures of approval, jumping to the stage totake Lestat's hand.Lestat stands transfixed staring at the dark emptytheatre.The mortals all around him.BACK TO LOUIS'S POVwho realizes Lestat is suffering.Lestat stares into emptiness.INT. FLAT - SEVERAL EVENINGS LATERLestat enters the parlor with Claudia rushing behind him.Louis looks up from the evening paper.CLAUDIAWhat do you mean you won't be inthe play? Why? Why did you backout? Tell me.Lestat sits at the harpsichord and starts fussing throughthe music.(CONTINUED)80.CONTINUED:LESTATI told you, I decided not to doit.CLAUDIABut it wouldn't have been suchfun! They'd have never guessed.LESTATThat's just it. It didn't seemfair, really. It's their realm,their time... the mortal actors.Lestat and Louis exchange glances.CLAUDIAFair! To mortals! I've neverheard such nonsense. Lestat,what is the matter with you?Lestat deeply distressed begins to play a slow melancholytune.Louis rises and sweeps Claudia up in his arms.CLAUDIAWhat's wrong with both of you?LOUISGreat actors have their moods.Maybe he'll try again sometime.He carries Claudia down the hall. Glancing back he seesLestat sitting with his hands over his face.Louis carries Claudia down the stairs, and through thecourtyard and out the gate.LOUISCome, let's walk together, wehaven't done it in a long time.CLAUDIAYes, I'm hungry for your lessons.Teach me to see with my vampireeyes, as you always do.EXT. ROYALE STREETLIGHT RAIN. Aureoles around the crude oil lamps. Richlycolored walls, mud street, gleaming carriage passes.Claudia leans close to Louis's ear.(CONTINUED)81.CONTINUED:CLAUDIALet me see you kill tonight.You've never let me see you kill.Lestat lets me see it all thetime.Louis is unperturbed.LOUISThat's because he's so much betterat it than I am.They turn on a side street. Flowers pour over gardenwall. Louis grabs a handful of loose blossoms andsprinkles them over Claudia's hair.LOUISLet me sing a song to you, or tellyou a story. I'm better at thatsort of thing.She smiles.CLAUDIANot Macbeth!LOUISNo, not Macbeth!CLAUDIAAnd no silly child's story either.They laugh and whisper together as they walk AWAY FROMUS.EXT. RUE ROYALE (1830'S - 1830'S) - NIGHT(CHANGES INDICATING PASSAGE OF TIME)Mud has given way to flagstone. Lamps are bigger andmore stately. Passing carriages are now big andlumbering. Streets are crowded with people in the dressof the 1830's.EXT. SHIPS AT PORT/CROWDED MARKETS (NEW ORLEANS) - EVENINGTheaters emptying out.(CONTINUED)82.CONTINUED:LOUIS (V.O.)Oh, it was a very different life.Every burden seemed somehowlighter. And the new century wassimply wondrous. What had oncebeen a small godforsaken Frenchcolony was growing into a greatport.Claudia walks with Louis and Lestat on either side ofher. All are dressed in 1830's fashions. The hair ofLouis and Lestat is trimmed according to the newerfashion. Bushy, but no longer pigtails.They enter --CROWDED OPERA HOUSE - LOBBYLouis picks up Claudia, who allows herself to ride in hisarms.INT. OPERA BOX - LESTAT, LOUIS AND CLAUDIAwatch the performance, applauding enthusiastically.LOUIS (V.O.)Time can pass fast for mortalswhen they're happy. With us, itwas the same.INT. CLAUDIA'S ROOM (1840 Styles) CANARIES SING in a cage.Claudia is writing at a secretaire. She is writing inher diary with a quill pen. She reads aloud as shewrites. Her cadence is now entirely mature.CLAUDIASeptemmber 21st, one hour aftersunset. The sky is still violet,the way Louis loves it, and asalways Lestat was gone when werose...Lestat appears in the doorway. He has a big box in hisarms.CLAUDIAAnother doll? I have ten yourealize.(CONTINUED)83.CONTINUED:FOCUS ON early 19th Century French dolls -- wood, glass,wax, bisque -- all around the bedroom, on chairs, on thebed.LESTATWell, I thought you could useanother.He hands her the box. She opens it. It's a fine ParisianJumeau Doll. She likes it and strokes its face.CLAUDIAWhy always on this night?LESTATWhat night? What do you mean?What are you writing there?Claudia shuts the diary, playfully making an indignantface. Lestat pretends to sulk.CLAUDIAYou always give me the doll on thesame night of the year.LESTATI didn't realize.CLAUDIAIs this my birthday?He examines the other dolls.LESTATSome of these are so old andtattered. You should throw theold ones away.CLAUDIA(patiently)I have. Or there would be twiceas many.LESTATAnd you're the fairest, by far.Lestat drops to his knees, kisses her hand. They doteon each other. Then Lestat leaves whistling to himself,as she watches, vaguely distressed.INT. PARLOR - 3 A.M.by the mantel clock.(CONTINUED)84.CONTINUED:Claudia enters, dressed as a vagabond boy. The clothesare even soiled. Her long hair mussed.Louis rises from his chair.Claudia goes to the secretaire and removes a bigscissors.LOUISWhat's happened to you?CLAUDIANothing's happened to me. There'sno need for me to be dressed likea doll, is there? I'm impatientwith all this childish fuss. Asa boy I can go about scarcelynoticed.She goes into the hall, and stands before the mirror andbegins cutting off her hair.LOUISNo, please don't do it! Claudia,don't!She turns around, an angelic little boy with soft curlsaround her face. Her hair is all over the floor.CLAUDIANow, Louis, don't give me a longlecture. It's almost dawn. I amready for sleep.She disappears into the bedroom. Glimpse of coffinagainst the wall as she shuts the door.Louis stares at the long blonde hair all over theOriental carpet. He kneels down and gathers up a handfulof it. As he brushes the cut ends across his left hand,they leave thin trails of blood.Lestat enters noisily letting the door bang. Come to ahalt.LOUISHistory's repeating itself? Whyshould a girl child be a girlchild, when a boy has such freedom?LESTATShe cut off her hair!(CONTINUED)85.CONTINUED:LOUISYes.He stands up, holding the tresses.LESTATDid you tell her? Did you explainto her?LOUISNo.LESTATLouis, you should have.INT. PARLOR - FLATBeyond the French windows, the sun sinks over the roofs.Darkness falls. A lamp is lighted. Louis stands at thewindow looking out into the night.A HORRID SCREAM pierces the silence. MORE SCREAMS whichbecome roars.INT. CLAUDIA'S BEDROOMShe stands before the dressing table, all her long hairgrown back hanging down around her. She holds it withboth hands screaming and screaming and screaming.Lestat grabs her by the shoulders.LESTATStop it. It's only... our nature.Now stop!He's very frightened. She falls silent staring at him.CLAUDIAAnd if I cut it off again!LESTATIt will grow back again!Claudia backs away from him, her hand raised to herlips.CLAUDIAMy God! Day after day it wouldgrow back, until my cut tressesfilled this room the way the dollsfill it.(CONTINUED)86.CONTINUED:She screams again.Louis brushes past the panic stricken Lestat, scoopsher up in his arms and takes her into the --PARLOR and out --ONTO PORCHThey look down into the Rue Royale. An old woman with apushcart passes. She is selling flowers. A man pausesto buy a bouquet with a coin.Louis holds Claudia, and wipes her soiled face with hishandkerchief.LOUIS(tenderly)We're immortal. You've alwaysknown that. We don't age ordecay. And that means we don'tchange either.Claudia nods. She's in shock.LOUISYou see the old woman? That willnever happen to you.She nods in acceptance. Gently he puts her down.She stands in the doorway looking at Lestat in the parlorwho gazes at her fearfully, then back to Louis who triesto be calm.CLAUDIAAnd it means something else, too,doesn't it? I shall never nevergrow up!With outstretched hands, she looks down at her own smallform.Lestat is stunned. Then hurries away in panic.Louis tries to calm her with firmness.LOUISClaudia, stop this...Claudia rushes after Lestat...87.SERIES OF SHOTS - CONTINUOUS ACTIONdown the hall, down the exterior stairs, through thecourtyard and the carriageway.CLAUDIAYes, go out, run from me, run frommy questions. You want me to bethe doll forever, don't you?That's what you think I am.Lestat in a fury turns. He drops on his knees, angrygritting his teeth, but his anger leaves him as he looksat her. He is suddenly overcome with conflictingemotions.In a broken voice he quotes Webster.LESTAT'Cover her faceMine eyes dazzleShe died young.'CLAUDIAAnd what is that, Father? Morelines from a play? Do you nevertire of them?She slaps him with the full force of her right hand,stepping back to see tiny pink imprint of her hand on hiswhite face. Then it vanishes. He is completely unaffec-ted by the blow otherwise. He merely looks at her. Andthen slowly:He stands up, on the edge of tears, looking down at her,towering over her.CLAUDIA'S POVStaring up at his great height. He pivots, departs.EXT. WALLED CEMETERY AND CHURCH - ANOTHER NIGHTon outskirts of French quarter. Claudia dressed as a boywith hair tied back. Louis with her.Claudia stares at corpses piled up to be buried in massgraves.CLAUDIAYellow fever...(CONTINUED)88.CONTINUED:LOUISYes, every year it's the same.And you know. Please come homenow. Come back. It's almostmorning.CLAUDIAI see the light coming as well asyou do. I don't want to sleep inthat coffin. I want to sleep ina grave.Lestat appears.LESTATClaudia, please, for Louis' sake,come home. You can torment me allyou like. But please don't besuch a nuisance to Louis.Claudia walks past them towards the church. Forces lockon the side door and goes in.INT. CHURCHCandlelight and sanctuary light illuminate altar and pews.Lestat and Louis follow.CLAUDIAYou slept in a grave once. Louistold me. Remember, Louis? Thenight he saved you from the fire.LESTAT(ironically)And it was so thrilling! Whydon't we all move to a graveyardpost haste.She ignores him. She walks past the altar rail andstares at the memorial stones in the floor beneath whichpriests are buried. Reads the names carved.CLAUDIAFather Michael, of yellow fever...LESTATClaudia, we can not remain hereanother minute.CLAUDIAThen go.(CONTINUED)89.CONTINUED:She falls on her knees, rips up the stone, revealing adeep and wide crypt.LESTATFor the love of hell!LOUISClaudia, we can't leave you here.Lestat reaches for her. She backs away, glaring at him.Louis tries but she slips out of his arms.She peers down into the crypt. There is plenty of room.The old coffin is rotten and fallen to splinters. Shelies down in it. Lestat and Louis join her. Lestatmoves the stone back into place above.LESTATI loathe places like this! Damnit!Claudia lies there still peering into the eye sockets ofa skull, her hand on it. She says bitterly.CLAUDIAThen leave me, Father. Nobodysaid you had to be properlyburied.LESTATYou brat!Claudia suddenly turns over and in panic snugglingagainst Louis, who holds her patiently, his eyes closed.BLACKNESS.We hear SINGING. A whole CHORUS SINGING a Latin hymn:CHORUS (O.S.)O Salutaris HostiaQuae caeli pandis ostium.A seam of light falls on --LESTAT'S SLEEPING FACEHe opens his eyes.INT. CHURCH ALTAR CRYPT - NEXT NIGHTHe sits up staring wildly --(CONTINUED)90.CONTINUED:CHORUS (O.S.)Bella premunt hostilia,Da robur, fear Auxilium...He stares at the sleeping Claudia and Louis. He tries towake them but it is too early. They lie as if dead.FROM ABOVE, come sounds of the PRIEST INTONING a litanyto the blessed sacrament to which the CONGREGATIONRESPONDS.PRIEST (O.S.)Blessed be God --CONGREGATION (O.S.)Blessed be God --PRIEST (O.S.)Blessed be thy most holy name.LESTAT(comically enraged)Oh, you little monster! I couldbreak your pretty neck!Louis opens his eyes slowly, like a corpse coming backto life.LOUISWhere are we? What's happening?LESTATThe six o'clock novena andbenediction. The church is filledwith people. The Priest isstanding right over our heads.Louis laughs in spite of himself. Lestat, trying not tolaugh, and still angry, clamps a hand over his mouth.INSERTverses of Litany. (Take from Roman Missal.)CLAUDIAopens her eyes. She sits up. She hears the LITANYcoming to a close.Congregation sings.(CONTINUED)91.CONTINUED:CONGREGATION (O.S.)Tantum ergo SacramentumVeneremur cerniu...She's frightened. She looks around at Louis and Lestat.And she tries to stand up but the roof of the crypt won'tallow it. Louis and Lestat sit there, Louis still laugh-ing and Lestat trying to control his temper.LESTATYou see what you've done? Thisservice will go on for two hours!It's the first time I've been madeto go to church since I was twelve.LOUISShhh. You want them to hear us?LESTATAnd what would they do if theydid?Claudia is panicking.SOUND suggestion of dim memory of early church services.She stares at the skull, at the bones, the splinteredcoffin. Claustrophobia. She tries to stand up. Louispulls her down.CLAUDIAI can't stay in here. I have toget out of here!LESTATIt was good enough for you lastnight!LOUISClaudia, we have no choice but towait!CLAUDIAI know it. The blessed sacramentis on the altar!LESTATSo what!Louis can see this is irrational, phobic. He tries toembrace her. She tries to push up the stone and againhe stops her.(CONTINUED)92.CONTINUED:The HYMN CONTINUES ABOVE.CLAUDIAI can't stay in here, I tell you!Louis is confused.LESTATAll right, then we shall go outof here. But we are going to doit as proper vampires, do youhear? We will do it in style!He picks up handfuls of grave dirt and smears it allover the bewildered Louis and the petrified Claudia.LESTATYou have money? Get it out ofyour pockets.Louis and Claudia both find several gold coins. Theynod. Claudia is shaking violently.LESTATNow when I lift the stone, makethe most horrible faces you canmuster ! And show your fangs andhowl!Claudia rises heaving the stone back.CLAUDIA, LOUIS AND LESTATleap up into the lighted Sanctuary of the crowded church.PRIESTdrops the Monstrance with the blessed sacrament and fallsdown. The altar boy screams.Lestat bares his fangs and gives a great roar, and so doesClaudia who runs for the front door which is open to thenight. She drops the coins. Louis flings them into thepanicstricken congregation as he follows. Lestat howlingand growling, pitches the coins everywhere.People scream, fall back, scurry to pick up the gold.PRIESTThe devil and his cohorts throwmoney! Catch them!93.EXT. CEMETERY - SWAMP BEYOND - NIGHTClaudia, Louis and Lestat rush into the darkness, up ontop of the cemetery walls, easily outdistancing the fewfaithful Catholics following, and soon they are deep intothe swamp.Lestat slumps down beside a huge cypress, laughing help-lessly. Louis is beside him, also laughing, hand on hisshoulder. Claudia stands there. She can't repress asmile, and then she too laughs, quietly.CLAUDIAWell, they'll be talking aboutthat till the twentieth century!Lestat and Louis respond with more laughter.CLAUDIAThe devil throws money! Indeed.Lestat climbs to his feet, brushing the dirt off hisclothes.LESTATLook what you've done to me! Ihate dirt!LOUISWell, there was no one there whowould ever recognize us, you canbe sure of that!LESTATNot like this! I never lookedlike this in my entire endlesslife!(eloquent)Yuk!Claudia laughs more freely. Lestat tries to be angry buthe is only pretending. He lets her laugh. They alllaugh.INT. FLAT - LESTATin style of 1840s, comes into Claudia's room. She isdressed neatly in boy's clothes, and is throwing herbobbed hair onto the coal fire in the grate.LESTATI loathe that smell.(CONTINUED)94.CONTINUED:CLAUDIASo do I. That's why I do itbefore I leave, so that I canwalk away from it.LESTATWell, don't walk out so fasttonight. I have a surprise foryou.CLAUDIAWhat in God's name could that be?LESTATCome. The workmen have been verybusy in the last few days. Youmight have noticed if you werehome anymore with us.Lestat leads her into the parlor. Louis is waiting. AsLestat nods, he turns up the wall switch of the newcrystal gaslight chandelier, filling the room with light.Lestat hurries to turn up the sconces and soon the wholeflat is full of light.Claudia smiles. She loves it, the vision of light every-where. So does Louis. Claudia is softened utterly.LESTATNo expense spared, my child. TheQuadroon ball room is no betterlighted, or the suites in theSaint Louis hotel.CLAUDIAI do believe you.Louis watches as Lestat turns away. Claudia watchesLestat lovingly, forgivingly, as if she can't resist him.CLAUDIA(sincerely)It's beautiful, Father. You're aPrometheus. You've brought thefire from heaven.LESTATYes, that's true, my dear. Inmore ways than one.Lestat breaks off, realizing this might be taken thewrong way. But Claudia is smiling.(CONTINUED)95.CONTINUED:LOUISAnd we've a pair of new servants.Lestat's found a mother anddaughter, excellent maids.LESTATYes, I'm tired of all this dust,and strange charwomen coming andgoing.LOUISThey think us most peculiar, ofcourse, but they will clean byday, and take their wages from thehall table, and be out of the waybefore we rise.Claudia laughs at the irony of it.She sits at the piano, looking around at all the gaslight, even the gas sconce that lights her music, and shebegins to play a somber piece by Beethoven, become evermore morose and involved.Lestat and Louis exchange glances, amazed at her absorb-tion and her skill. She doesn't notice. She continuesto look dreamily at the light.CUT TO:INT. FLAT - PARLOR - ANOTHER NIGHTPaintings have changed, and some furniture.Louis watches Lestat go through a pile of books on thetable:LESTATMy, but she reads dreary things.Boetheus. Plato. And MarcusAurelius. What's the matter withDickens or Thackery or WilkieCollins!LOUISYes, and she reads her booksfaster than I can.Louis and Lestat realize that Claudia has appeared in thedoor:(CONTINUED)96.CONTINUED:Claudia is dressed gorgeously in a violet dress withribbons and silk flowers. Her hair is long and shining.She holds a big bouquet of chrysanthemums.Lestat is alarmed. Claudia steps menacingly into theroom.CLAUDIAWhich of you made me what I am?They are stunned.CLAUDIA(to Lestat)Did you do it! Was it you? Orwas it Louis!She points to --Louis. Then turns back to Lestat approaching him.CLAUDIAOne of you had to do it. Youdidn't find me on All Hallow'sEve. You were the one, weren'tyou! Answer me.She hurls the chrysanthemums at Lestat's feet.CLAUDIAMonstrous parents! To give meimmortality in this helplessguise, this hopeless shape.Lestat is angry.LESTATI was a sorcerer's apprenticeonly! I didn't know what wouldhappen!CLAUDIAThen it was you, wasn't it? Youwere the one!Louis steps forward.LOUISClaudia, it was no simple thing,I swear it.Lestat rushes out as he has done before. The door bangsbehind him.(CONTINUED)97.CONTINUED:CLAUDIADid you do it? Did you? It wasLestat. I know it was. You wouldnever have done such a thing.Louis says patiently.LOUISI want you to come with me. Andlisten.EXT. OLD PART OF CITY - OLD PITCHED ROOF OF FRENCH HOUSES - MUD STREETLouis talks with Claudia as they walk slowly, finallycoming to a halt beneath a dim gaslamp.ECHO of Claudia's CRYING of years before.LOUISIt was the old days, there, thereis the house, or perhaps it's thatone. I can't tell. The plaguewas raging in the city. I heardyou crying. You were there in aroom with your mother, and she'dbeen dead for days. You didn'tknow it. You clung to her. Youbegged me to help you. I cameinto the room. I felt pity foryou. Pity... but something else.CLAUDIAYou fed on me! I was your victim!LOUISYes! I did it! But you had aheart like no other heart I'dever felt. It wouldn't stop.Then Lestat came. He found meout. He laughed at me, Louis thesentimental one, with a holyinnocent in his arms. I ran fromhim, from you.CLAUDIAYou meant to kill me! You leftme for dead.LOUISYes. The next night, he foundyou in the hospital where they'dtaken you.(MORE)(CONTINUED)98.CONTINUED:LOUIS (CONT'D)I never knew what he meant to dobut teach me my nature. 'Finishit,' he said.Claudia backs away. He grabs her wrist.LOUISOh, I know I've lost you. Youlook at me now as you look atmortals, from some cold self-sufficiency I can't understand.But the hunger, that we allunderstand! I felt it for youthen, a vile unsupportable hunger,a hunger for your hammering heart.For this cheek, this hair.Claudia lets him touch her.LOUISYou were pink and soft as mortalchildren are, sweet with the biteof salt and dust.Claudia's face softens only a little.LOUISI held you again. I took you.And when I thought your heartwould drag me down with it andI didn't care, he parted us. Hecut his wrist. He gave you theblood to drink. And drink youdid. And you became one of usthat night. And drank bloodfrom your first victim. And youhave drunk the blood of mortalsevery night ever since.He waits. Claudia looks at him, unreadable.LOUISIt was I who took your life. Hegave it back to you.CLAUDIA(holding out her hands)And here it is, and I hate youboth!99.INT. PARLOR OF FLAT - SUNRISEStillness reigns over all.Quadroon maid and teenaged daughter arrive. Both wear redtignons or scarves, and gold earrings. The maid picks upall the withered chrysanthemums, clucking over the mess.The teenaged daughter begins to sweep. Return to:MALLOY AND LOUIS (SAN FRANCISCO) - PRESENTOrder of opened tapes on the table indicates the tape hasbeen changed, if anyone cares.MALLOYDid you lose her? Did she leaveyou?LOUISHow could she? Little boy.Little girl. She was a childno bigger than that. Whatwould her life have been? Andsomething in her was kin to me,kin to Lestat. We had eachother. We had endured for halfa century in harmony. We couldnot bear to be alone.INT. FLAT (1860)Claudia at her dresser, dressed as a little girl,brushes her long hair. Louis stands behind her. Thendrops down beside her, takes the brush and brushesher hair for her.She watches him through the mirror.CLAUDIALocked together in hatred, that'swhat we are.LOUISNo. You feel that now. But it'slove that binds us. Love is theonly thing that allows us to goon.CLAUDIA(softening)You think so?LOUISI know so.(CONTINUED)100.CONTINUED:Claudia turns and touches his face and kisses him. Shecannot help herself. They embrace.We hear...Lestat's voice SINGING a Verdi aria as he comes in.Lestat enters. Looks about.LESTATWell, I see the maids are doingtheir usual fine job.LOUISI raised their wages as yousuggested. They're happy. Thisevening, I saw them as they wereleaving. I told them how verymuch we appreciated their work.LESTATYes, Jeannette the daughter hasgrown so pretty.CLOSE ON CLAUDIA'S STILL FACELESTATAnd do pay them more. That's onething I've noticed about even themost superstitious mortals. Paythem enough and they question nota single thing.Louis smiles.LOUISI think you're right. They'rehappy. And so are we.Lestat snaps his fingers and points to Claudia.LESTATUptown, in the Rue Camp, a hauntedhouse! Ghost appeared three timesthis very week. Want to go seeit.Inspite of herself, Claudia smiles, sadly, wisely. Sherises and goes to his waiting arms. She is womanly,cool, but pleasant.(CONTINUED)101.CONTINUED:CLAUDIABut we aren't going to merelywatch, are we? Maybe we should... you know... make a littlesupernatural mischief ourselves,don't you think? Louis, want tocome?LOUISI wouldn't dream of spoiling yourevening.INT. FLAT - PARLOR - EARLY EVENINGLestat is reading a newspaper -- Mercurie De France --which he then throws into the fire.Claudia enters, dressed in velvet, with muff and bonnet,to go out. Bad mood.CLAUDIAAnother newspaper from Paris?Lestat turns round, stares at her. Tension.CLAUDIAWhy don't you ever save them?LESTATHave you been searching my room?CLAUDIAWouldn't do any good, would it?She approaches the grate, confirms the paper is nowashes.CLAUDIAYou have no keepsakes, do you?Only a wardrobe worthy of Czar ofRussia or the King of France.LESTATStay out of my room!She looks up at him coldly.Lestat is confused.LESTATYou look very beautiful tonight.I love you in red.(CONTINUED)102.CONTINUED:CLAUDIAI know. There are many vampiresin Paris, aren't there. Many ofus in the old world.LESTATYou'd despise them. We're theonly vampires on this earth whomatter! And New Orleans is ours.We've never had to share it withanyone.He tries to laugh.CLAUDIAPerhaps it's time I saw Paris.LESTATPerhaps so. Though frankly, I'dprefer New York or maybe London...CLAUDIAYou'd let us go to Paris, me andLouis?LESTATOh, I see, so that's how it is.I won't stop you, but you'd be afool if you didn't take me withyou.CLAUDIAWhy?LESTATLouis can't protect you as wellas I can. And our kind can beyour worst enemy.CLAUDIAAre there others like me there?Little ones.Lestat is overcome with emotion. He shakes his head.He whispers.LESTATClaudia, you would have died if Ihadn't done it. I didn'tunderstand what I was doing. Itwas an impulse.(CONTINUED)103.CONTINUED:CLAUDIAI know. Poor darling. Poordarling, Lestat, the thoughtlessone. And you'd protect me fromall the big bad vampires in Paris,wouldn't you?LESTATYes, I would. You think theydon't war with one another, thatthey don't try to destroy oneanother? Remember the fire, mychild, and the light of the sun.And there are other ways as well.They won't share the City of Lightwith a vagabond.CLAUDIAYou're serious, aren't you?You're telling me the truth.LESTATDarling, I've never lied to you.I've teased you, taunted you,shouted at you, kissed you, evenstruck you. But I've never lied.She watches Lestat leave.CLOSE ON HER FACEInscrutable.INT. FLAT - SUNSET (ANOTHER NIGHT)through parlor windows.CLAUDIA'S ROOMHer coffin lid is raised.Claudia sleeps inside against satin lining like a deadbody.CLOCK TICKING.Then her eyes snap open.Lestat is looking down at her. From nearby Louiswatches.(CONTINUED)104.CONTINUED:Still sluggish and weak, she sits up slowly with no helpfrom her own hands. Her eyes clear.Lestat smiles thinly.LESTATWe thought we'd wait for you,tonight.Claudia now fully awake smiles coldly.CLAUDIAAll right. We hunt, then,together?As he turns to go, unseen by him, her face becomes cold,masklike with hatred.Louis sees it.EXT. JACKSON SQUARE - ANOTHER NIGHTStanding against the new iron fence before the Cathedral,holding the bars and peering through it. Louis in tophat and gloves and opera cape looks down at her.CLAUDIAIf he made the journey we can makeit. We feed off the rats ofcourse. We take the little drinkfrom the elder passengers. Wecan do it if he did it.LOUISBut why must we go without him?It's time we all went traveling... together.CLAUDIAHe can't come with us.LOUISWhy not? I think he's ready fora journey.CLAUDIAYou misunderstand me, beloved. Hewon't be here when we leave.LOUISWhat do you mean?(CONTINUED)105.CONTINUED:CLAUDIAHe'll be in hell when we leavehere. I intend to kill him.LOUISClaudia, you can't do this!Claudia turns and walks away impatiently. Louis follows.CLAUDIAWhy can't I? You don't think hecan die? We can all die! Thereare lots of ways. He's told me.LOUISHe's part of us! He's... he'sLestat! You can't simply turn onhim.CLAUDIAOh, yes, I can. I want to killhim, and I'll tell you a secret,Louis, if you come down so I canwhisper it in your ear.Louis kneels.CLAUDIAI want to kill him! I'll enjoyit. Killing mortals can't behalf as much fun.Louis draws back.LOUISNo. You can't mean it. I won'tlet you do it.CLAUDIAShhh, don't you want to be freeof him! I hate him. The mortalsI kill. I care nothing forthem. But him I hate.LOUISImpossible. You can't succeed atit. You don't know his strength!He do can things neither of uscan do.CLAUDIAYes, and do you think thatstrength will pass into me when Ikill him?(CONTINUED)106.CONTINUED:LOUISI won't allow this to happen.CLAUDIAWhy don't you admit that you hatehim as much as I do?LOUISBecause I do not hate him. Hatemyself? Yes, often.CLAUDIAHe made you too, didn't he? Hedid it to you as he did it to me.Why don't you hate him?Louis shakes his head.LOUISIt's not as easy as that, my dear.and I will not let you harm him.Maybe we should go away for awhile, travel on our own, see ifwe can manage.CLAUDIAOh, we'll manage. Don't seek toknow the week or the night, orthe hour. And don't seek to comebetween us, I warn you. Or --LOUISOr what? You'll destroy me too?Claudia is shaken.CLAUDIANo. I would never harm you. Butif you do seek to interfere...LOUISYes?CLAUDIAYou'll never see me again.She leaves so fast she seems to vanish.INT. FLAT - ANOTHER NIGHTLestat marches through the place, seeing mess everywhere,a theatre program on the carpet, a newspaper lying on thesettee. The window is open and the rain is coming in.(CONTINUED)107.CONTINUED:LESTATMon Dieu, where is Jeanette?Where's Marie? They haven't beenhere for days!LOUISMaybe we've frightened them someway. I'd better call at theirhouse when I go out.LESTATJeanette would have come to meherself if she were troubled.She's never suspected a thing.Lestat stops. He lifts his chin. He catches a scent.LOUISWhat is it?LESTATDamn her into hell. She's donethis!LOUISWhat? What are you talking about?Lestat, wait.Lestat goes DOWN the hall, OUT on the porch, DOWN theback stairs, ACROSS the courtyard, and INTO old deserted...BRICK KITCHENAs he rips open the wooden doors, a huge swarm ofgnats rises and nearly suffocates him. He waves themaway in disgust.Louis looks over his shoulder.They both see Jeanette and her daughter, Marie, freshlydead in each other's arms, yet already devoured by heatand insects.Lestat bangs the shutters closed.LESTATHow dare she! Our own servants!Mortals under my protection, andto kill here, in our lair, andleave the remains!(CONTINUED)108.CONTINUED:LOUISI'll talk to her. I'll reasonwith her. She's full ofresentments. Now, come, help meget rid of these two. I can'tbear to be near them.Lestat shudders. Opens kitchen doors again.LESTATDamn her. Only the mad ones aretoo lazy to clear away theremains! She knows this isforbidden.He opens the old, unused iron-doored brick oven, andturns and stares at the two bodies, disgusted that hemust touch them. He reaches down and touches Jeanette'sdark hair.CUT TO:Sound of a MATCH.FLARE OF FLAMESBodies burning amid kindling and paper.CLOSE ON LESTAT'S FACEin firelight.LOUISThere'll be more trouble from her.And we must ride it out. She'llcome round to herself again.LESTATI'm mortally tired of her!LOUISLestat, she broods. She makesthreats. It's idle talk --LESTATThreats? What do you mean,threats?Lestat is furious. Louis is stymied. Sees the dilemma.LOUISIt will run its course. We mustbe patient.(CONTINUED)109.CONTINUED:Lestat looks hard at Louis, then turns his back walksoff.Louis realizes full dilemma, says nothing.Lestat turns back, deeply aggrieved.LESTATDoes she despise me so much?LOUISShe's so small, so powerless.What can she do to either of us?She is a woman, and the pain runsdeep.CLOSE ON OPEN OVENand bodies burning.LESTAT(whispers)No, not a woman. That she neverwas. And that's the horror.LOUISShe harms herself more than --LESTATLet her try to harm me and I'llput her out of harm's way fastenough!Leaves.CLOSE ON LOUIS'S FACErealizing he's caught between the two of them.INT. PARLOR - LESTAT - ANOTHER NIGHTin formal dress comes in, sees all the doors are shut.Listens, catches scents. Angrily he walks into theparlor.Louis is playing solitaire at a small game table.(CONTINUED)110.CONTINUED:LESTATShe's back. What a surprise. Ithought she'd run away with thegypsies. And she's got twomortals with her.LOUISSeems so. I don't like it either.LESTATHow dare she bring them here!LOUISPatience, mon ami. She wants anindependence that she can neverhave. Let it go... for my sakeand your sake.Lestat is too disgruntled.Sounds of Claudia CLOSING DOOR at the end of the passageand coming down the hall. She is a vision in lovelywhite lace, pink ribbons, long hair.CLAUDIABonsoir, mon pere!She beams at Lestat who sits down at the piano with hisback to the keys.LESTATAh, the prodigal daughter! I'dgiven you up nights ago, afteryou left those two murdered inthe kitchen. Where have you been.CLAUDIAOh, little people can hide inlittle places. And how considerateof you to burn those bodies. Ashesto ashes. My thanks.He gets angry, but she gestures for patience. Sheapproaches him, smiling, radiant, seductive. She putsher little hands on his shoulders.CLAUDIA'Bless me, Father for I havesinned.' I'm sorry. Truly. I'vea gift for you. To make up forthe whole thing.(CONTINUED)111.CONTINUED:LESTATGift? What do you mean, gift?What are those mortals doing underour roof?CLAUDIAThey are my gift for you, darling.LESTATI don't need such a gift.Claudia grabs his right hand in both of hers and tugshim to his feet and after her down the hall.Louis follows, alarmed, suspicious.CLAUDIAOh, come see! They're the mostbeautiful tavern girls I've everbeheld.LESTATTavern girls. You know myweaknesses...CLAUDIAYour favorite kind. Faces likeangels and hearts of coal. They'vesent many a sailor to his death,those two...Lestat stops in the doorway of a back parlor, seldomused dusty. Two gorgeous women -- a blonde and abrunette -- lie tumbled on the couch, heavily painted,full breasts, gorgeous, very flashy and tacky and fastasleep.Lestat laughs.LESTATAh, yes, from Lafitte's. Doesthe world never stop giving usthese luscious little ladies of thestreets! Oh, you're right, theyare my favorite meal, surely.CLAUDIAKilled a man this very evening.For a single gold coin.Lestat hardly hears her. He walks toward the women.He's getting hungry. On the table are bottles andglasses.(CONTINUED)112.CONTINUED:Behind him, Louis is very wary. Can't quite figure allthis out.LOUISHow did you get them to comehere?CLAUDIAIt wasn't difficult. I'm anadorable little girl when I wantto be. I led them to believe Iwas alone in this great big flatfull of such fine furniture andsilver!LESTATYou are a genius, Claudia.He kneels down before the two irresistible women,tumbled against each other.CLOSE ON LESTATsavoring them. He runs a finger over the lips of thebrunette.CLAUDIAWell, it was you who gave me theidea, actually. Burning theremains of the maid and herdaughter. I thought why notbring the meal home now and then,and use the old oven again.LESTAT(uneasy but dazed with hunger)Where we can really savor it.LOUISDon't take this victim here,Lestat. Claudia, I want noneof this!LESTATDon't fuss, Louis. I'll burnthe remains myself.She draws near to Lestat who is bending over the brunette.(CONTINUED)113.CONTINUED:CLAUDIAGo to it, let me watch you.Lestat lifts the brunette, who groans and he sinks histeeth into the flesh above her breast and drinks, givingoff long savoring moans as he does so. They look likelovers.Claudia watches.Louis turns angrily to return to the parlor, then hears:LESTATHmmm, absinthe...CLAUDIAYou've always liked the taste ofit, Father.Louis comes back. Lestat continues to drink. Thenglaze-eyed, he pulls himself up and reaches for theBlonde. He takes her ravenously, like someone kissingfarewell before a war.He moans again, and she slips out of his arms and backon the couch onto the body of the other one. He staresforward...LESTATAbsinthe!Almost paralyzed, he stares wildly as he slips to asitting position on the floor. With effort he focuseson Claudia who comes toward him on tiptoe, and then bendsover him.CLAUDIAThat's right, Father, and laudanum,so much of it, they would not havelived another hour had you not come!LESTATLouis! Louis... she's... poisonedme! Louis, put me in my coffin...Claudia slips a huge knife out from under the pillowsbeneath the whores. She drives it right through hisheart.CLAUDIAI'll put you in your coffin,Father. I'll put you thereforever!(CONTINUED)114.CONTINUED:Louis rushes to stop her, as Claudia stabs Lestat overand over in an orgy of wounds, blood pouring out of him.Louis reaches her just as she has slashed Lestat'sthroat, and he grabs for the knife, lifting it, and herwith it because she will not let go of it.LESTATMy God, Louis... it's too manywounds! Too fast!Claudia kicks at Louis heaving him backwards over thetable, BOTTLES CRASHING as he falls. As he climbs tohis feet, she pounces upon Lestat and sinks her fangsinto his neck and sucks his blood ravenously.Louis rushes to Lestat just as Claudia draws away,repelled and stunned by what is happening to Lestat:Lestat is shriveling, as if he'd been a bag of blood.His skin is shriveling against his bones like parchment,his eyes are slipping back into his skull-like face. Anoise escapes his lips. His lush, beautiful hair remainsunchanged. But his clothes are virtually being emptiedof the body.It is now no more than the bones, wrapped in paper andthe pupils of the eyes suddenly roll up into the paperedskull.Claudia stares at the shriveled skeleton in its skin wrap-ping, which looks totally dead. She is fascinated.Louis kneels beside the ghastly spectacle.He reaches for Lestat's shoulders. But it's just bones,held together with cloth, or so it seems, and Louis dropsthe skeleton in fear and horror. It lies in the puddle ofblood. The eyeballs, blank, now look yellow. All theskin looks yellow.Claudia pulls herself out of her thrall.Tenderly, she approaches Louis, patting his shoulder ina reassuring way.CLAUDIAGo now, go on. It's my doing andI shall finish it.LOUISNo!(CONTINUED)115.CONTINUED:CLAUDIAHe's dead, Louis! Spare yourselfthe sight of the flames.Louis begins to gather up the dried limbs though theyflop free like sticks.LOUISNot in that filthy oven, not withthose charred bones. Not likethat, no.INT. LESTAT'S BEDROOMThe shriveled skeleton lies on the lace coverlet. Louisstares at it. It looks deader than ever.EXT. OLD CEMETERY NEAR POINTE DUE LAC - NIGHTA carriage stands on the distant road with its lampsburning.Louis, carrying the white wrapped body of Lestat wandersamong the old tombs.LESTAT (V.O.)I loathe places like this, damnit!CLAUDIA (V.O.)Then leave, Father. Nobody saidyou had to be properly buried.Louis, in grief and confusion, leaves the cemetery.Goes into:EXT. SWAMP A still pool under the moon.ECHO of Lestat's LAUGHTER.LESTAT (V.O.)Didn't I tell you it was goingto be fun?CRIES of BIRDS merge with Lestat's LAUGHTER. RAPIDHARPSICHORD MUSIC.(CONTINUED)116.CONTINUED:LESTAT (V.O.)I'm so lonely... I want acompanion.Gently Louis lowers the body to the surface of the pooland then lets it sink.LOUISWho can forgive me, Lestat? Whocan give me absolution?He gives up in despair.FOCUS ON YELLOW HAIRbillowing from the sheet beneath the water.EXT. CEMETERY - TWILIGHTThe next NIGHT FADES TO NIGHT:EXT. COURTYARD Claudia stands in the open brick kitchen watching theburning of Lestat's belongings in the furnace. Shethrows a top hat into it, a pair of gloves. Her faceis grave, sad.She turns as Louis returns.CLAUDIAAt last! I've been sick withworry.As she tries to go to him, he moves past her up thestairs and into the...INT. FLATClaudia comes behind him, distressed and perplexed.CLAUDIADon't you see, we're free now? Wecan go. What's wrong with you?Louis, look at me. Louis, hedeserved to die.Louis turns around in the doorway of his room:(CONTINUED)117.CONTINUED:LOUISThen so do we! Every night of ourlives. We should die, both of us,now. He was my brother! Mymaker! He gave me eternal life.CLAUDIAI told you I meant to do it.LOUISYes, you did! And I didn't darewarn him because I didn't believeyou could do it! And I wasafraid that if I did warn him,that if he believed me, he'ddestroy you!CLAUDIA(hurt)Please, Louis... He wronged usboth when he made us. He keptus under his dominance always...LOUISLeave me alone. I can't look atyou. I'll care for you becauseyou can't care for yourself. ButI don't want you near me. Getaway.Claudia's eyes are glazing over with faint bloody tears.She turns away.Louis walks into his room, stares blindly around him.Then he's distracted by:Claudia's CRYING. A terrible heartbroken crying, likethe crying he heard the first night he ever saw her,utterly defenseless, but it's ECHOING like a vampire'scrying.He can't quite believe his ears. He moves into the hall-way and then into her room. She lies against a heap ofpillows on the bed, truly sobbing. He draws near,touches her shoulder and when she looks up at him, hereyes and face are stained with blood tears. The bloodruns down her cheeks. Her lips tremble. She sobsuncontrollably, lips trembling.(CONTINUED)118.CONTINUED:CLAUDIALouis, I did it for us. So wecould be free. I did it becauseof what he did to us. I triedto forgive him. I couldn't doit. Louis, if I lose you... Ihave nothing. I would undo itto please you. I would, I swearit...He shushes her gently, gathering her into his arms andsits on the bed covering her hair and her blood-stainedface with kisses. She cries softly, allowing herself tobe comforted.LOUISVery well, my darling. Very well,my love...Claudia crying softly against his blood-stained shirt.CLAUDIAWe'll leave here, Louis. We'll goto Paris. We'll forget he everexisted. We'll find others.We'll see the world. Who knowswhat the old ones know? What theycan do.LOUISAll right, my darling. All right,my love.INT. FLAT - TWO NIGHTS LATERMovers take out two trunks. The parlor furniture is alldraped with white sheets.Louis and Claudia both have on cloaks and gloves. Theyare ready to go. Louis takes one look around. He standswith the poker looking down at the small coal fire. Thenhears...The BIRDS. CANARIES SINGING in Claudia's room.LOUISAh, the birds. I forgot thebirds. There's nothing to do nowbut let them go.(CONTINUED)119.CONTINUED:Claudia, weary, melancholy sits down on the sofa as heputs down the poker and goes down the hall. He stops,staring at the back door.Sound of FOOTSTEPS SHUFFLING in the courtyard. ThenHEAVILY TREADING on the stairs.Louis is frozen. Claudia rises and comes toward him,takes his hand.LOUISIt can't be.CLAUDIABut it is!She turns in panic to the front of the flat. STEPSCONTINUE UP the STAIRS. ON the PORCH. The DOOR CRASHESopen.Lestat in filthy swamp-soaked rags nearly falls into thehall. He is robust again, but his entire body is coveredwith creases where the flesh had wrinkled and shriveled.He is scored all over with these scars. His eyes arebloodshot. He can hardly steady himself.Louis tries to stop him, but Lestat contemptuously andclumsily throws Louis to one side.CLOSEUP OF LESTAT'Sscarred face, seemingly without reason.LESTATClaudia!BACK TO SCENEClaudia rushes into the parlor, but he's after her. Shesnatches up the poker from the fireplace and batters himwith it fiercely, knocking him backward. He staggers.Louis comes in and throws his arms around Lestat'sshoudlers. Lestat hurls him back and off balance againand then kicks him a powerful kick in the gut. Claudiascreams.Lestat snatches the poker from Claudia and reaches forher. She shoves him with all her might and he fallsback against the gas sconce, SHATTERING the GLASS. Thefire burns his face. He cries out.(CONTINUED)120.CONTINUED:Claudia regains the poker and whips the burning coals outof the grate at Lestat's feet. They land on the carpetand near the draped furniture and begin to smolder.Sheet over chair begins to burn. Lestat stares down atthe smoking coals trying to get his bearings. Claudiaslams him with the poker again in the GAS flame, and thistime the SCONCE SHATTERS and the flame EXPLODES up thewall.Louis struggles to his feet. The wallpaper is burning.Lestat's hair catches. She turns, sees the burning sheeton the chair and hurls it at Lestat. Her dress catches.She screams.The room is exploding into flame.Lestat is on his knees, choking, hands up over his face,in the smoke. Louis grabs up Claudia smothering theflames of her skirt with his hands. The whole parlor isafire.Louis carries her out, down the back stairs, throughcarriage way and through the gathering crowd of mortalsand away down the...STREETFinally, he stops and sees that she is not badly burnt,only terrified. She clings to him. He looks back at theglare of the distant burning house.He puts Claudia down in a doorway.LOUISStay here, until I come back.CLAUDIANo, Louis, don't leave me. Theship is about to sail.Louis runs back toward the townhouse. It is surroundedby mortals. Fire roars out of the parlor window. Louiswalks closer, cleaving to the wall, trying not to rousenotice. He looks up. The parlor is an inferno.Claudia catches up with him. Desperate.CLAUDIAThe tide's going out! The ship'sgoing without us.(CONTINUED)121.CONTINUED:LOUISNot yet.Picking her up, Louis hurries away.EXT. DECK OF SHIPLouis stands at the railing in the morning mist as theship moves down river. He sees...CITY OF NEW ORLEANSwith its flickering lights.LOUIS (V.O.)Until the very dawn I stood onthat deck, watching, fearful hewould come again, out of the veryriver like some monster to destroyus both. And all the while Ithought Lestat, we deserve yourvengeance. I deserve it. Yougave me the Dark Gift. And I havedelivered you into the hands ofdeath for a second time.Return to:MALLOY AND LOUIS (PRESENT)LOUISWe had the voyage to ponder it,how he had survived. Claudiaswore we had a fatal error when wehad failed to burn his remains.EXT. DECK OF SHIP - CLAUDIA AND LOUIS at the rail. Stars over the sea.CLAUDIAPray he died in the fire! Didyou see him? Did you see thescares all over him? Hecouldn't have gotten away.(CONTINUED)122.CONTINUED:LOUISOh, yes, he could have. Hecouldn't come after us, no, hewas too weak for that. But hecould have gotten away.CLAUDIAYou sound as if you wanted himto escape. When will you admityour own hatred for him?She cleaves to Louis. In spite of himself, he strokesher soft little face.RETURN TO PRESENTMALLOYWas she right? Did he die in thefire?LOUIS(smiling sadly)How could we know? You canimagine how powerful he was torise from the swamp as he had...MALLOYHe was conscious all the while,waiting to get his hands onsomething living, something withblood in it...LOUISExactly. It isn't very hard toenvision. There must have beenblood filled creatures all aroundhim in those waters. And he wasLestat after all. Maybe he fed onthe smallest at first, and then thegreat alligators of the wildernessuntil he was healed enough to takesome hapless human on the road.CLOSE ON MALLOY'S FACEAs:LOUIS (O.S.)You know as much about us now,perhaps, as I do. We can sufferterrible blows, blows that wouldkill a mortal, but if we are notburnt to ashes, we heal. We comeback.123.EXT. 19TH CENTURY STEAMSHIP moving at sea under night skies.LOUIS (V.O.)I think I did pray that he escapedthe townhouse. And yet I fearedfor Claudia at the very thought.Meanwhile, each night brought uscloser to Europe, closer to Paris,closer to a world of which we hadonly dreamed.EXT. BOULEVARD FACADE OF GRAND HOTEL AND PARIS OPERACrowds and gaslight everywhere. Carriages, horses.OPERA coming from the opera house.LOUIS (V.O.)Ah, Paris. How many mortals haveuttered that name with reverence.Is there any other place thatevokes such love? But understandwhat Paris meant to us... we twohad lived a century in NewOrleans. Paris was a universe,whole and entire unto herself!EXT. 18TH CENTURY PALACES ALONG THE SEINE - NIGHTThe high walls of the Louvre, dark figures walking inpairs through the shadowy tulieries.EXT. STREET - SHOP WINDOWClaudia, in furtrimmed muff and bonnet, peers through theglass at the dolls. They resemble her markedly, these,with blonde hair and blue eyes. She peers deep into theshop to see:MADELINE, a young woman bent over a workbench painting adoll's face, oblivious to being watched. Claudia smilesat her lovingly. Then looks with a troubled expressionat the dolls.INT. OPERA STAIRCASELouis and Claudia hurrying hand and hand with crowd ofmortals as we hear the sound of the ORCHESTRA TUNINGbeyond. Both are excited and happy.124.INT. NOTRE DAMEClaudia and Louis standing in the deep shadows of NotreDame, looking up at the branching arches. Louis is over-come with the beauty. He is excited. Claudia isfascinated.INT. GALLERY Louis and Claudia walk among paintings of 1870 with otherspectators. Louis studies them intently. He studiesthe mortal ladies passing, studies their big fashionablehats.INT. CAFEClaudia watches the waitress flirt with Louis as sheteases him about not liking his wine. She smiles toherself thoughtfully.LOUIS (V.O.)We were alive again. We were inlove, and so euphoric were we thatI yielded completely when Claudiamoved us into the Grand Hotel, thevery largest in Europe on theBoulevard des Capuchines.INT. SUMPTUOUS SUITEfull of late 19th century furniture, lots of Empirestyle, Regency, gilt, the usual velvet and brocade.CLOSE ON HUGE, BLACK, EBONY CHEST against a wall, solemn among all the light and glitter.CLAUDIAat the open French windows listens to sounds of the CROWDoutside. Busy night.Louis approaches, drops on one knee and presents her witha little string of pearls. He puts them on her, gazingat her slightly uneasily and then he kisses her on bothcheeks.She forces a smile.(CONTINUED)125.CONTINUED:CLAUDIAWhere are the others, Louis? Ican hear them. I can sense theirpresence. But they hide.LOUISLet's not be so eager to findthem, my fairy princess. Lestatwarned me often enough about them.They may not be willing to sharetheir territory, even with twosuch human creatures as you and I.CLAUDIABut they're like us! They arewhat we are!LOUISAre we so alike, Claudia?Claudia smiles at him, kisses him.CLAUDIAAlike enough, don't you think?LOUIS(thoughtfully)Yes.She looks out at the crowds below. Then:CLAUDIAMaybe they know things.She looks at her hands, her own reflection in the openFrench door beside her.CLAUDIAOld magic, secrets. Charms. Whoknows?LOUISCharms for what, my dear?Claudia looks down at her little hands, at her arms, thenmuses.LOUISLestat would have told us ifthey had some precious secret.You know what they'll be like.City cousins and we, theridiculous rustics.(CONTINUED)126.CONTINUED:Louis admires her. She watches carriages stop below.Porters rush to gather luggage. Ring of LADY'S LAUGHTER.CLAUDIASometimes it's almost worse here.The loneliness, the separateness.Louis controls his inner thoughts. He says only.LOUISSometimes, but not always. Anddefinitely not tonight.He takes her hand. She gives in. As they open the doorto the hall to leave, sound of ORCHESTRA SWELLS fromlobby below.INT. HOTEL SUITE - ANOTHER NIGHTLouis wakes up from a nap, rumpled on the lavish bed,picks up his book -- David Copperfield -- and tries tofind his place. He is wearing distinct clothing -- agreen frock coat and striped waistcoat, cream-coloredpants. Claudia enters, shuts the door.She has a large parcel. She strips off bonnet and glovesand then tears loose the ribbon from the box.She lifts a huge doll from the box, a duplicate ofherself.LOUISWherever did you find that?CLAUDIAYou thought I hated dolls now,didn't you?LOUISYes, I did. But that one looksexactly like you.Claudia flings the doll gently in the chair. She stripsoff her own cape. Her hair is loose. Her manner andexpression are entirely womanly.CLAUDIAIt should. It was made for me, bythe doll maker, Madeleine. I askedher to make it. All her dollsresemble me.Claudia tosses her hair, scowls at the doll and picks itup and begins fussing with it. Suddenly something snapsin her expression.127.CLOSE ON HER FACEas she looks down at the doll. She blinks as we hear theGLASS BREAK. She flings the doll onto the empty hearthwhere its broken head is utterly shattered.Louis studies her sadly, but not with complete sympathy.He looks at the broken doll. He holds his tongue.Claudia runs her fingers back through her own hair in awoman-like gesture, her face ironic and grim. Louisdeliberately looks away.CLAUDIAWhy do you look away, why don'tyou look at me?Louis puts down the book on the table, rises, brushes offhis coat and straightens his coat. He lifts a dark greenwool cape from over the arm of a chair and puts it overhis shoulders.LOUISYour tone is unkind with meagain, tonight. It seems yourhabit of late. Maybe I should gowalking and leave you to yourmeditations for a while.Claudia approaches, face molded in a sophisticated expres-sion of ironic dissatisfaction.CLAUDIA'S POV - LOOKING UP AT LOUISCLAUDIA (O.S.)Ah, but tell me something fromthat lofty height, before you go.BACK TO SCENELouis nods, he sits down on the bed beside her and hebends to take her hand and kiss it.CLAUDIAWhat was it like... making love?Louis is stunned. He blushes. He rises and goes to thedoor. He reaches for the knob.CLAUDIAYou don't remember? Or you neverknew.She stares at him coldly, mocking him. He turns around,leans against the door. He answers candidly.(CONTINUED)128.CONTINUED:LOUISIt was something hurried. Seldomsavored. Quickly lost. I thinkthat it was... the pale shadow ofkilling.They look at each other.CLAUDIA(in pain)Ahhh. Like hurting you as I donow... that is also the paleshadow of killing.LOUISYes, madame. I am inclined tobelieve that is correct. Bonsoir.He goes out and closes the door.EXT. WINDING STREET (LATIN QUARTER)LOUIS (V.O.)I knew her dissatisfaction wasgrowing. Her resentments wereincreasing night after night.Though she'd claimed to hateLestat, now she missed him, andher anger was turning slowly onme.Louis walks briskly, inspecting the old buildings abouthim, enchanted with them, yet worried about Claudia.Suddenly he stops. Listens. He takes a step. He hearsa STEP behind him. He takes two steps. He hears TWOSTEPS. He takes three, four, five and the STEPS MIMIChis. He senses danger.He stares ahead at the light of a lone gaslamp at the topof the hill and then a figure materializes there underthe gaslight, or appears to do so.SANTIAGO, a tall vampire stares down at him. And gradu-ally we realize as does Louis that this vampire hasassumed the same attitude and posture as Louis and thathis clothes are identical to Louis's and his black hair iscombed in the same way.Louis gives a little involuntary shake of the head.Santiago mimics. Louis takes a step forward. Santiagomimics. Louis utters a syllable and so does Santiago.Louis falls silent and folds his arms. So does Santiago.The timing is preternatural.(CONTINUED)129.CONTINUED:LOUIS AND SANTIAGO(simultaneously)Clever.LOUISYou mean me harm?SANTIAGO(a beat behind)You mean me harm?Louis calculates.LOUISTrickster. Buffoon!Santiago echoes the first word but not the second. Louishas broken his composure. He turns his back on Santiagoonly to come face to face with Santiago right in front ofhim.Again Louis turns his back to find Santiago facing him.Louis turns, glowers, refusing to look at him.LOUISI've been searching for you. I'vecome to find you and this is whatI find?Slowly he looks up. Santiago draws close, breaking themirror tricks and suddenly pushes Louis who is slammedback against the wall. Santiago smiles.Louis is furious. He quickly regains his balance and hedeals Santiago a great blow, catching him just as hetries to dodge. Santiago staggers, is amazed and asSantiago rushes at him, Louis deals him a strong blowagain.LOUIS'S POVas he struggles to see where Santiago has fallen. Hehears sounds of a SCUFFLE. BLOWS. Silence.Then Louis seesArmand, standing alone with his back to the light.Armand's hair is trimmed short nineteenth-century style,like Louis's and he is dressed for the period in a blackfrock coat, and high-collared white silk shirt. He lookslike an angel.130.BACK TO SCENELOUISArmand!Armand looks momentarily confused, then regains his calm,tranquil expression.ARMANDLouis, is it not? Louis de Pointedu Lac.He cocks his head, scanning Louis's mind.Louis becomes faintly suspicious.Armand takes an engraved invitation out of his pocket andthrusts it at Louis.Louis reads aloud as we see:THEATRE DES VAMPIRES By Special Invitation Friday, 9 p.m.ARMANDBring the petit beauty with you.No one will harm you. I won'tallow it. But you must explaintomorrow how you know my name.Armand vanishes.Louis listens to the silence.EXT. BOULEVARD DES CAPUCHINES - THEATRE DES VAMPIRES- NIGHTLouis formally dressed, with Claudia in rich attire, inhis arms, approaches the theatre as others buy ticketsand go in.LOUISRemember what I've told you.They'll have different strengthsand weaknesses. Some will readyour thoughts if you allow it.Be on guard.They draw close to:HUGE POSTERSannouncing the Theatre Des Vampires showing cliched imagesof vampires in cloaks overcoming damsels.131.ANOTHER ANGLECLAUDIABut this can't be real. This isnonsense.LOUISI think it's nonsense, all right.But something tells me it's goingto be the strangest nonsense we'veever seen.Warily, they show their invitation to the mortal tickettaker at the door. He glances away indifferently.INT. THEATRE BOX POV - STAGE BELOWClaudia and Louis look about at crowd as lights go down.CLAUDIAMortals, mortals everywhere. Andlots of drops to drink.LOUISThey are here. I know they are.Listen for something that doesn'tmake a sound.Stage; curtain rises.A vampire disguised as an old woman comes out on thestage, limping to COMIC MUSIC, basket on her arm, as thegrim reaper, a vampire, holding a skull mask on a stickbefore his face, follows her.Suddenly she sees him. MUSIC is poignant. She kneels,prays to him silently to take her. She lays her headagainst her folded hands in weariness.The grim reaper comes for a closer look, then backs off.Laughter. The old woman rises and chases the grim reaper.Laughter as they run round and round on the stage.The grim reaper hides behind a painted tree. The oldwoman gives up, goes away. Grim reaper now lowers themask and yawns. Revealing that he is Santiago. Bored,he lifts the mask again, appears to fall asleep with itover his face, against the painted tree.LOUIS(whisper)It's a vampire. It's the oneI saw in the Rue St. Jacques.(CONTINUED)132.CONTINUED:Santiago affects a bored air as if about to go to sleep,when a spotlight uncovers --A MORTAL WOMAN suddenly forced out upon the stage.CLAUDIAShe's no vampire.LOUISNo. And she's frightened. Shedoesn't know where she is.The audience laughs uneasily, then stops as the MortalWoman comes into the footlights. She is too beautiful,too confused. Silence falls.The grim reaper throws up his hand in adoration. Thenhe tears away the skull mask and his white face grimacesat the audience, looking as frightening suddenly in itspreternatural gleam as the mask.The Mortal Woman sees him and is more frightened. Tearsstand in her eyes.Vampire men and women, clothed in black emerge from theshadows, each holding a skull mask before his or her faceas they make a great horseshoe behind the Mortal Womanwhich she does not see.Suddenly, the Mortal Woman sees them and is morefrightened.CLOSE ON VAMPIRE MEN AND WOMENas in concert, they cast down before them the skull masks,the sticks stack like crossbones, the skulls gleaming atthe audience. It is a preternatural trick of skill.The vampires are seven -- five women and two men in addi-tion to the grim reaper. All beautiful gleaming white,aged 20 or 30 in mortal appearance.LOUIS(whisper)They use no paint. And theaudience thinks it is paint!CLAUDIACLAUDIAOh, Lestat would have loved this!(CONTINUED)133.CONTINUED:LOUISI'm not so sure you're right. Idon't love it!MORTAL WOMANI don't want to die!She looks around in panic. Santiago swoons, arms overhis breasts as if he is hopelessly in love.SANTIAGOWe are death!The Mortal Woman steps to the footlights.MORTAL WOMANSomeone help me. Please... Whathave I done?LOUISThis is no performance!CLAUDIAAnd you and I are the only onesin the audience who know.SANTIAGOWe all die. Death is the onething you share with all thosehere.Santiago gestures to the audience.FOCUS ON AUDIENCERapt faces.ON STAGEMORTAL WOMANBut I'm young...SANTIAGODeath is no respecter of age. Youcould harbor an illness in youryoung body. Outside a man mightwait to kill you simply for youryellow hair. Need I tell youwhat fate has in store for you.MORTAL WOMANI would take my chance. Let mego! Please...(CONTINUED)134.CONTINUED:SANTIAGOAnd if you take that chance andlive, what is your fate. Thehumpbacked toothless visage ofold age?SANTIAGOapproaches her, and tears the drawstring out of her pea-sant blouse. It opens completely, and starts to slip.She tries to catch it, but he gently takes her wrists andlifts them down. The blouse falls revealing her youngbreasts.LOUIS AND CLAUDIALOUISThis is monstrous!CLAUDIA(dazed with hunger)Yes, and very beautiful.ON STAGESANTIAGOJust as surely as this flesh ispink now, it will turn gray andwrinkle with age.MORTAL WOMANLet me live, please. I don'tcare.SANTIAGOThen why should you care if youdie now?She shakes her head, confused. He catches her wristsbehind her back.AUDIENCE is awestruck by her beauty, her suffering.SANTIAGOdraws near her cheek.(CONTINUED)135.CONTINUED:SANTIAGOAnd suppose death had a heart tolove and he did release you? Towhom would he turn his passion?Would you pick a person from thecrowd there? A person to sufferas you suffer now?AUDIENCEA YOUNG GIRL cries out from the third row.YOUNG GIRLOh, yes, take me, MonsieurVampire! I adore you.Audience roars with laughter.ON STAGESANTIAGO(aside to the girl)You wait your turn.Laughter.The Mortal Woman shakes her head in panic.SANTIAGOWell, have you a sister, a mother,a daughter you would send in yourplace?CLOSE ON CLAUDIAEven she is repelled by the cruelty of it. Shakes herhead.MORTAL WOMANshakes her head no. She is helpless.ON STAGESANTIAGOUnconscious death waits for youeverywhere. But we are consciousdeath. Do you know what it meansto be loved by death, to becomeour bride!136.MORTAL WOMANlooks up on the verge of hysteria or fainting. But thenher eyes mist over. She is being entranced.FROM HER POVwe realize she is looking past Santiago at Armand who hasjust stepped out of the wings. Armand has entranced her.He passes Santiago. Santiago stiffens, but yields thestage.ARMANDNo pain.MORTAL WOMAN (O.S.)(entranced)No pain?ARMANDtakes her by the naked shoulders.ARMANDYour beauty is a gift to us.Armand gestures to the others who slowly, gracefully closein.ARMANDWho deserves such a gift?He pulls the drawstring from her skirt and it fallsrevealing her nakedness. But she is spellbound.MORTAL WOMANNo pain...Armand embraces her, drinks, her naked body stark againsthis black clothes, then he passes her to the othervampires one by one.CLOSE ON LOUISwho battles desire and hunger with anger. Pushes histongue against his fangs, and frowns.LOUISI've seen enough of this.CLAUDIA(cajoling)Be still!137.ON STAGEThe naked Mortal Woman lies dead on the floor of thepainted forest. The vampires seem to vanish one by one.The AUDIENCE LOUDLY APPLAUDS the tricks.ANOTHER ANGLEAPPLAUSE, CHATTER. But the audience is uneasy and eagerto escape. They hurry to the exits, whispering anxiously,with forced smiles.CLAUDIAPatience, Louis. Patience.Houselights go up as Louis sees Santiago standing in thedoor of the box gesturing for them to come.INT. FOOT OF STAIRWAY opening into aHUGE UNDERGROUND BALLROOMWalls are painted with copies of famous Brueghels, Goyas,depictions of death. Fine wooden coffins lie in nichesset into the walls up and down both sides of the longroom. Some are very old, some lustrous, some rusted.Candles burn in sconces.Armand stands in the center of the ballroom, handsclasped behind his back, as Claudia and Louis come downthe stairs and into the room.Vampire men and women seem to appear all around Louis andClaudia deliberately startling them. Hands dart out totouch Claudia as if she were a doll. Shrieks of preter-natural laughter. She cleaves to Louis. He is silentlyenraged. He looks to Armand.Armand gestures for the vampires to back off.All obey but ESTELLE.ESTELLESuch a darling. Whoever made you,my dear?She menaces Claudia, her breasts enormous, her fangsbared.(CONTINUED)138.CONTINUED:Armand glares at her. Suddenly she is forced off herfeet and back against the wall by something invisible.She slams into the plaster and glowers at Armand.ESTELLEThat was crude of you!She vanishes.Blur. Armand reappears with a lighted candle in his hand.He gestures for Louis to follow him. Claudia remainsbehind, watching warily.Armand and Louis walk along the walls, the candle flaringon the ghastly murals: The Triumph Of Death; The Fall OfThe Angels; Bosch's Hell.Armand's face gleams like that of an angel above thecandle. Louis is horrified by the paintings as he was bythe performance.LOUISMonstrous.ARMAND(lips not moving yet echoing Claudia's earlier words)Yes, and very beautiful.LOUISYour lips, they didn't move.ARMANDI'll speak in audible words if itmakes you happy. I can do iteither way.Louis looks at him, drawn to him, yet wary.Armand snaps his fingers.A mortal boy of fifteen comes forward. Armand gesturesto Louis. And the boy offers himself. Louis is utterlyconfused. Can't resist. Sees marks on the boy's throat.Drinks his blood.Other vampires appear all around Louis who suddenlysenses it and draws back, releasing the boy, ashamed.CLOSE ON CLAUDIAfar away, watching contemptuously and warily.139.LOUISis disoriented, trying to regain his equilibrium.BOYsmiles as he withdraws, spellbound and weak.LOUISglares at the others.ANOTHER ANGLEArmand beckons for Claudia and Louis to follow as hereveals a door in the wall by opening it and leading themdown stairs into a passage and into a stone room withmedieval chairs, table, an old coffin, a blazing fire.Books on one wall.MEDIEVAL PAINTING OF SATANhangs over the fire.ON SCENEA door is open to the rainy night outside and anotherstairway to the street above. Armand closes it. Louisfalls into the chair, hands to his temples.Armand turns to Claudia. Claudia's eyes mist. Without achange of expression, she sits limp in a chair, her eyesmoving listelessly over the books.CLOSE ON BOOKS Withcraft, demonology, lives of the Saints, GrandGrimoire.BACK TO SCENE She refuses to lose consciousness.Armand sits in the chair opposite Louis as Louis looks up.ARMANDDisappointing, isn't it? To comeso far, and find so little! Jadedlords and ladies of darknessamusing themselves like the OldRoyal Court.140.CONTINUED:LOUISYet, you are their leader! Youlet them do all this. This play,this horror...ARMANDYou sound like your maker. Itwas Lestat de Lioncourt, wasn'tit, who made you both? Hecomdemned me once in the sameway. All I do is give the otherswhat they need of me.LOUISAnd this theatre sustains them,and gives them contentment.ARMANDSo they let me believe. Orperhaps I must believe it.LOUISYou can read my thoughts, can'tyou?ARMANDNow and then. You don't know yourown strength. The child knowshers. Her purpose she can'tconceal, but her deeper thoughtsare closed to all who wouldpillage them.LOUISShe's no child. You know thatwhether you can read her mind ornot. And what purpose do youspeak of?ARMANDShe has the charm of a child. Andthe wisest of us can be lulled byappearances. And we needinteresting and new companions.LOUISDo we?ARMANDYou know we do. Time is ourenemy! What would we do withoutthe fledglings to guide us intothe new era as all we love slowlyrots and fades away?(CONTINUED)141.CONTINUED:Louis tears his eyes off Armand and looks up at thepicture of Satan.ARMANDWhy do you stare at that? It's apicture, nothing more.He rises suddenly, composure broken, grabs the pictureoff the wall and throws it into the fire.LOUISIt has no meaning.ARMANDYou know it does not. It's asymbol.LOUISBut the old ones, the very oldones...Armand takes his hand.ARMANDI know nothing of God or the Devil.I have never seen a vision, norheard a divine voice, nor learnta secret that would damn or save mysoul. And I am the eldest. Forall I know I am the oldest livingvampire in the world.Louis is thunderstruck. He stares at the angelic facewhich is very sad.CLOSE ON ARMAND.Louis falls back into the chair.Armand waits patiently. Then:ARMANDThis doesn't surprise you. Youknew you would find no answershere.LOUISOh, but I hoped and I dreamed.That Lestat was wrong, that therewas some framework, some place forus. Children of Satan... thatsomeone somewhere knew why we wereallowed to exist.(CONTINUED)142.CONTINUED:ARMANDChildren of Satan? Didn't Lestattell you of those old customs.LOUISYes.ARMANDAnd if there is a Satan, who madehim, pray, whom do think?LOUISWhy, God made Satan. Who else?ARMANDThen we're all Children of God,aren't we? And that is whatmortals believe. How can weimprove upon that?Louis is struck by the simplicity of it.LOUISThen we are damned in hell, allof us. We are evil...ARMANDBut what is evil?LOUISNow it's you who are deceivingyourself. You know what it is.You saw it on that stage tonight.Evil is cruelty. Evil is murder.Evil is the taking of a singlehuman life!Armand is deeply moved by Louis' sincerity.ARMANDI fear for you!LOUISAnd not for yourself?(OPTIONAL. SCENES OF VENICE WITH VOICE OVER)ARMANDNo. I was born to Darknesscenturies ago, in Venice by aMaster who brought me to him inlove. He told me no tales of godsor demons. It was the others whotold those lies.(MORE)(CONTINUED)143.CONTINUED:ARMAND (CONT'D)Those who came to destroy himbecause he was an outlaw and ablasphemer. Those who took meaway and taught me the Ways OfSatan, and the Rules Of TheChildren Of Darkness, the oldcatechism of the damned.CLOSE ON Louis's face.ARMANDAnd I took their vows, and saidtheir litanies, and sang theirhymns and danced at their sabbats.Until Lestat came. Your maker.The innocent one, the perfectspirit of the last century,believing in nothing but thegoodness of his own nature. Andhe was right.Louis doesn't answer. Then:LOUISLestat knew we were evil. He justdidn't care.ARMANDKnew? You say knew? You meanLestat is...Claudia appears suddenly at Louis's shoulder, inter-rupting. She is fighting a spell, as if it is a drug.Trying to see and move with clarity.CLAUDIACome, beloved. It's time we wereon our way. I'm hungry and thestreets wait.She stares hard at Armand and he stares back at her.She looks away warily, as if his eyes have a power.ARMANDYou can leave by this door. Theothers won't hurt you. I won'tlet them. This I swear.(CONTINUED)144.CONTINUED:Armand looks meaningfully at Claudia who eyes himsuspiciously.ARMANDI have no magic potions for you,little one. No charms.Claudia is shocked by his words.ARMANDYou will be as you are and as youwere made... a child forever.Claudia is enraged and humiliated, glaring at him andthen at Louis.CLAUDIAI made no requests of you!LOUISWhat are you saying to each other?ARMANDGo. Your finely appointed roomsawait you. You can always come tothis door if you wish to find me.I'll be here.INT. HOTEL SUITE (PARIS) - BEFORE DAWNClaudia paces in a rage. Hair wild, dress undone,looking entirely like a little woman, voice resonantlike a woman. All childish innocence long lost.CLAUDIAI detest them, I can't stand thesight of them! They disgust me!Stupid, bourgeois Parisians.Fools! They all dress in black,did you see it? It's a damnedorganization, a private club!Louis stares into the fire, dejected.CLAUDIAGod in heaven, what I wouldn'tgive to speak with Lestat forfive minutes! And there are nolittle ones among them. I am theonly one! The only one! Andtheir leader mocks me!(CONTINUED)145.CONTINUED:Louis takes her in his arms, tries to still her withkisses.CLAUDIAWhat a fool I was to kill Lestat.And I'm in danger.LOUISWhat danger?CLAUDIAI can feel it emanating from allof them! They want to know whatbecame of our maker. They'resuspicious. They have their rules.Their idiotic rules!LOUISThey don't know what happened toLestat. They search our souls butthey don't have the answers. Notyet. And we are in danger, mycherie. We. Not you.CLAUDIANo, it is I who am in danger. Andas much from that ghastly Armandas from the rest.LOUISThat's not true.CLAUDIAHe wants you, Louis. He wantsyou for a companion. He bideshis time in this place. 'How weneed new companions.' Do youremember what he said? And hetaunts me with my foolish dreams!LOUISWhat dreams, Claudia?CLAUDIADid you think you were the onlyfool, beloved? I dreamed of somewizardry that would make me...He kisses her, smooths back her hair.LOUISYou are perfect to me as you are.You always were. You are mybeloved.(CONTINUED)146.CONTINUED:She leans on him, closes her eyes, confides:CLAUDIADo you know what Armand's soulsaid to me -- 'Why not end thepain now, child? The sun can beyour deliverance.'LOUISNo.CLAUDIAOh, yes. He can't make me growinto a womanly shape but he canshow me how to die.EXT. FOOT OF STEPS (PARIS) - NEXT NIGHT (RAIN)by Armand's door.Louis knocks. Armand opens.ARMANDYou've come early. I'm gratefulto you. I was waiting for you,of course.LOUISListen to me.He follows Armand into the room.LOUISClaudia, she is dear to me, my...daughter.ARMANDYour lover.LOUISNo, my beloved, my child.ARMANDIf you say so. You are soinnocent.LOUISI'm not innocent. But I'm afraid.She feels she's in danger from theothers.ARMANDShe is.(CONTINUED)147.CONTINUED:LOUISBut why? Why would they hurther. What right have they to doanything to either of us!ARMANDThey are the coven. They havetheir laws. It's forbidden tomake one as young as she is, oneso helpless, one that cannotsurvive on its own.LOUISIt wasn't her blunder!ARMANDShe's too small to make a vampireof a male or female old enough toprotect her. She can't... makeanother at all. Do you know whatshe hoped to find here?LOUISYes. She should have known sucha thing wasn't possible. But youhave to protect her.Armand nods.ARMANDI know.Louis sinks into the chair, looking up at Armand.LOUISThere was so much I wanted tosay to you, so much I wanted toask, to learn from you.ARMANDAnd I'm here to teach. I needyou, young one, just as you needme. I'm the teacher Lestatwouldn't be. And you're thepupil he didn't want.He draws close to Louis, a picture of boyish innocence.ARMANDHow many vampires have the staminafor immortality? Do you knowhow quickly they perish of theirown will.(CONTINUED)148.CONTINUED:LOUISYes, because I almost did it onceto myself.ARMANDNo, you'd never give up on life.I know you wouldn't. If the worldwere reduced to one empty celland one fragile candle, you'd stayin that cell studying that candle.You see too clearly. You see toomuch.LOUISThat's what Lestat said to me.And I failed him! I wronged him.Oh God.ARMAND(smiling)How he must have loved you. Ilove you.LOUISBut why?ARMANDI need you more than he ever did.To make my link with this century,to carry me into its art and itsphilosophy, and all the things Idespair of understanding on my own.LOUISOh, but you'd be making a terriblemistake. I'm at odds witheverything and always have been.I wasted life when I had it. Iwaste my gifts now. I have neverbelonged anywhere with anyone atanytime.Armand laughs softly.ARMANDYou are so nearly perfect. Louis,don't you realize everyone in thisNineteenth Century feels as youdo? You are the very spirit ofthese times! Your melancholy isthe melancholy of the century.Louis is speechless, and in love.(CONTINUED)149.CONTINUED:ARMANDThere's so much I can show you. Iwant to go back to Italy, back toVenice, to the palace where I wasmade. I can teach you thingsabout your powers you haven'tbegun to learn. But listen. Youmust... you must get the childaway from here. They won'ttolerate her. They'll destroyher.LOUISI can't leave her. Oh, I want tocome with you. Talking to you,it's...ARMANDLike feasting? Like the deep richtaste of blood?LOUISYes.ARMANDCome, I'll hold them off. They'reall cynical little cowards whenwe get right down to it. Thetrash of the era, just as you areits essence. I'll keep them atbay, but you must think of someway to get her safely out of hereand on her own.EXT. STREETS (MONTMARTRE)Louis walks up the hill past lighted cottages.LOUIS (V.O.)Of course I couldn't leave her,get her safely away! What didsuch words mean to me. But Iwanted to leave her! For thefirst time, I admitted it. I hadwanted to leave us since thenight she's tried to kill Lestat.I loved her, yes, beyond reason,but since that night, we had beena torment to each other now and Icould deny it no longer.Louis stops. Peers into --150.PAINTER'S STUDIOThe mortal painter is fast at work on a huge canvas,vaguely impressionistic, very early Monet. He stopsin his work as he sees Louis in the doorway.The painter wipes his hands on his smock, beckons forLouis to enter. The room is brightly lighted, full ofglorious pictures. A fire blazes in the little stove.Louis is hungry. He lets the painter, enrapt, put himin the chair.The painter begins Louis's portrait.CLOSE ON Louis who becomes ever more hungry staring atthe painter who works furiously sketching Louis's face.The painter stops, disturbed.LOUIS(dazed monotone)Save yourself. Beware.The painter drops the brush, backs away in fear.Louis takes him. The painter fights, but Louis sinkshis teeth and drinks.LOUISDie. Die... Give it up...He releases the painter, still alive but comatose, ontothe floor.Louis stares at the canvas, the sketch is a portrait ofinnocence, a young man, wholly compassionate and gentle.LOUISI'm mortal now, like you, mybrother, with your blood.He touches his face.Louis touches his own face.LOUISWarm and wanting to be warmer, togo on existing, and thriving onyour blood!The painter's eyes close.(CONTINUED)151.CONTINUED:Louis lifts the painting and starts to leave with it,when the painter opens his eyes, and rises up, grabbingthe painting from Louis.They wrestle with it, Louis winning, but casting asidethe painting and drawing the painter up to him andgashing his throat in rage for the final drink.INT. HOTEL SUITE - NIGHTLouis enters. He is carrying the painting sketch,which he props on the mantel. Suddenly he catches ascent. Small lift of his chin. He looks into themirror. He sees in the glass.MADELINE, the Doll Maker, resplendent in green taffeta,sitting like a Madonna with Claudia on her lap.Claudia's arms are around her neck. The contrast betweenmortal woman and immortal child is plain.Louis turns around.LOUISWhy did you bring her here? Whatdoes this mean?Claudia slips from Madeline's lap. She approaches,looking womanly and cruel.CLAUDIADon't you know?LOUISNo.CLAUDIAEven now you dream of leaving me,of wandering the world with yournew teacher. Well, you will makeher one of us before you leave me!You will do that for all you'vedone to me!Louis recoils.CLAUDIADo you know how I despise you?Your evil is that you cannot beevil! You will not! You didn'tstop Lestat when he made me! Youdidn't stop me when I destroyedhim. Well, you will do evil nowand for me!(MORE)(CONTINUED)152.CONTINUED:CLAUDIA (CONT'D)You will make her strong andimmortal so she can care for me,so I can leave this place!Madeline is stricken with love for Claudia. Claudiapaces, a woman in a doll's body, enraged.Louis is not surprised so much as defeated. Bravelyhe listens.CLAUDIASnatching me from mortal handslike two grim monsters in anightmare fairy tale! You idle,blind parents! Fathers!She spits blood at his feet.CLAUDIAAnd you weep. You haven't tearsenough for what you did to me.Six more mortal years, seven,I would have had that shape.She points to Madeline.CLAUDIANow, you give her to me! You dothis so I can go on with her! Iwill not live with this hatredany longer. I will not live withthis rage!CLOSE ON Louis accepting, and identifying with her com-pletely without defense.CLAUDIAOooh!! I love you still, that'sthe core of it.She pivots. Bending at the waist as if struck by a blow.CLAUDIALestat I never loved, but youalways. The hate I feel is equalto the love. Louis, do you knowhow much hate that is?LOUISYes, I know.(CONTINUED)153.CONTINUED:Claudia begins to tremble and cry blood tears. Madelinecomes to her side.MADELINEOh, my precious one, don't cry.Don't.They embrace each other. Louis watches.Pause.He goes to Madeline and he draws her near to him. Hecradles Madeline's chin in his hand.LOUISYou must do as I tell you. Lookat the gaslight. Don't take youreyes off it. I'm going to drainyou to the brink of death butyou must stay alive, do you hearme?MADELINEYes!Louis bends and starts to drink her blood.EXT. HOTEL SUITE - BALCONYLouis emerges from the room and puts his hands on therailing. The wind blows the curtains. Behind him wesee...Madeline dancing in mad circles with Claudia. Theirmingled laughter becomes louder and louder. Louis staresdown into the Boulevard. At the corner of...CAFE DE LA PAIXhe sees...Armand. Solitary. Watching him from the street.HOTEL SUITE - NEXT NIGHTLuggage being carted out by bellhops. Madeline is tracingthe flowers in the carpet with her foot like a personon LSD, giggling, and dancing around the flowers.(CONTINUED)154.CONTINUED:Louis pays the last bellhop. He leaves. Claudia, dressedand ready for the journey, shuts the door. She comesback and she looks at Louis.CLAUDIAForgive me.LOUISThere's nothing to forgive.CLAUDIAI showed you my pain, Father.LOUISThat you did, child, and Ideserved to see it. All of it,and your anger as well.Claudia reaches up for him with both arms. He lifts her,embraces her.LOUISMy darling, my love...Claudia kisses him on the mouth. She draws back, bitesinto her tongue, and when the blood flows, she kisses himfull on the mouth again. He closes his eyes, receivingthe kiss, and then he pulls away holding her.CLOSE ON MADELINElooking up, startled.Lights dim all around her.LOUISis fully alert. He looks around.OTHER VAMPIRESin their black clothes are all around them. Pressingcloser and closer.ESTELLETime for justice, little one.SANTIAGO(to Louis)Yes, you blundering fool!As Louis starts to fight, we hear Madeline scream.155.INT. FACADE OF THEATRE which is closed. Carriages stop before the doors. Wesee the whole crowd in black, with Louis, Claudia, andMadeline, emerge from the carriages. The prisoners areshoved inside.INT. BALLROOMLouis, Madeline and Claudia are forced inside, and thevampires make a circle around them.LOUISWhere is Armand? I demand thatyou wait for him.SANTIAGOYou can make no demands here,rogue! Bastard!Louis rushes at him and is knocked back. Madeline andClaudia cling to each other. Claudia appears fatalistic.Madeline sobs in fear.Louis gasps.HIS POVLestat, dressed beautifully but horribly scarred now fromthe fire more than from the early stabbing, is shovedforward, teetering and reaching for Santiago's shoulderto steady himself. He is clearly confused.LESTATLouis... Where is Armand? Armandpromised me...BACK TO SCENEHe stares, disoriented, at the others. Claudia looks athim, but he does not seem to recognize her or anyone, butLouis. Claudia is fearless and resigned.SANTIAGOYou rose up against your maker.You tried to destroy one of ourown kind! You rose against thecoven master!LOUISBut he's alive. We didn't destroythem. Lestat, I beg you if everthere was a particle of lovebetween us...(CONTINUED)156.CONTINUED:Lestat tries to follow the words, but can't.LESTATWhere is Armand? He promised mehis healing blood. I need it. Ineed the blood of the old ones.(recognizes Louis again)Louis?(smiles)It's you.Vampires scream over and over, Justice, Justice, Justice...Santiago points at Claudia. Lestat appears to see herfor the first time.SANTIAGODenounce the rebels. Name themand pass sentence.LOUISWhere is Armand? This creaturedoesn't know what he's saying.You have no right to condemn us.Lestat, look at me. Tell them tolet the other two go. I am theone who hurt you. Tell them.Lestat tries to follow, but can only express a fainthappiness at the sight of Louis. He tries to gather histhoughts.A BANGING, DRAGGING NOISE distracts Louis.ESTELLEEnough. The outcast has confessed.The child is an abomination. Thewoman is a weak and stupidfledgling. The sentence on allis death.Louis goes wild, fighting, but they overpower him,dragging him to a big iron coffin which they havedragged to the spot. They force him down into it.They lock a chain over his chest, and hold him.Santiago bends over the coffin.SANTIAGOFor you, the slow way. Perhaps itwill take centuries. Perhaps itwill never really come at all.(MORE)(CONTINUED)157.CONTINUED:SANTIAGO (CONT'D)Deep in the old dungeon, no onewill ever hear your screams asyou thirst, as you wither. Timewill have you all to itself.Louis struggles. The lid slams.INT. COFFINLouis struggles, breaks the chain, and beats his fistsagainst the lid of the coffin. All in vain. He triesto turn over, he can't. It's too tight. He goes wild,beating at the lid. Then stops.TREAD OF FEET on stairway, and going down a long passage.Seems endless. Louis feels all around him for some weak-ness in the coffin, can find none.Sounds of BRICKS and MORTAR. Louis stares. One morestruggle. Then he loses consciousness.BLACKNESS.INT. COFFINDim light. Louis sleeps. Sounds of BRICKS being BROKEN,thrown aside. Then of LOCKS BREAKING.Louis opens his eyes. He is at once alert.The lid opens. He sees.ARMANDabove him, reaching down to lift his hand. A torch burnson the wall behind Armand.CUT TO:LOUISStanding beside Armand, in vast long catacomb. Very farat the end, we see the broken wall. Louis runs to it.CUT TO:LOUIS AND ARMANDstepping through the broken brick wall.(CONTINUED)158.CONTINUED:LOUISWhere is she? What's happened?Where is Claudia?ARMANDCome, we must go, that way throughmy cell.Points to his cell at the end of the passage, foot ofthe steps. We can hear the RAIN through the open door.LOUISNo, not without Claudia andMadeleine. Where are they?ARMANDI can't save them.LOUISThat's not true. You don'tbelieve I'd go without them doyou. Good, God! They have themhere, somewhere, you must help mefind them.He goes up the stone stairs and enters the ballroom.Estelle stands far off, looking at him coolly. She liftsthe stage skull mask and laughs softly behind it. A malevampire slumps in a chair staring fully at Louis.Silence. Indifference.Others hover in the same manner. A door is open to thefalling rain.Louis sees Lestat sitting in a far corner. He rushes toLestat who looks up, confused. He's holding something,crumpled, made of cloth.LESTATLouis, we should go home now. Weshould go back where we belong.LOUISClaudia! Claudia!Louis turns round and round in rage. Passive still faces.The open DOOR BANGS suddenly in gust of breeze and openson the RAIN once more.Louis glares at it, at Lestat. Lestat's hands releasethe cloth. We see it is a small torn bloodstaineddress. Claudia's dress.(CONTINUED)159.CONTINUED:Louis sees it. He snatches it up and stares at it. TheDOOR BANGS AGAIN. Estelle laughs. RAIN GUSTS into theballroom.Louis goes to the door. Armand approaches, tries to pullhim away, but Louis shrugs him off, advancing on thedoorway. He draws nearer and nearer and stares out --INT. BRICK AIRWELLOn the stones lie Claudia and Madeline, burnt to greasyashes, in each other's arms, exactly like the maid andher daughter in the brick kitchen in New Orleans. Sameattitude, as if they died embracing each other.Only Claudia's blonde hair and Madeline's red hair remainunburnt.Louis look at the walls of this airwell, he looks up manystories to the sky.Santiago shoves Louis suddenly into the ashes. Louisroars in horror, then attacks Santiago, overpowering him,ashes scattered into the RAINY WIND. Claudia's goldenlocks fly up into the wind, they swirl around the twowarring figures.Santiago tries to escape, dragging Louis back with himinto --BALLROOMwhere the others close in.Armand pulls Louis free of them. Louis fights.BLACKNESS.EXT. DOOR OF NOTRE DAME (PARIS)Louis is slumped against the stone wall. Armand standsbeside him like a guardian angel.ARMANDI couldn't prevent it.LOUISI don't believe you. I do nothave to read your soul to knowthat you lie.(CONTINUED)160.CONTINUED:ARMANDLouis, they can not be broughtback. That is impossible. Theirremains are destroyed.LOUISYou let them do it.Louis climbs to his feet.LOUISYou held sway over them. Theyfeared you. You wanted it tohappen.ARMANDI swear I did not.LOUISI understand you only too well.You let them do it, as I let herrip Lestat's heart to pieces!You let it happen as I let himmake her! Well, I am your passivefool no more. Your melancholyspirit of this century! I knowwhat I must do. And I warn you,do not seek your cell in theTheatre des Vampires again. Donot go near it.EXT. STREETS (PARIS) - ALMOST DAWNWet and deserted. Theatre Des Vampires is quiet.CLOSEUP ON CLOCKCHIMING five a.m.CLOSE ON LOUIS looking at the paling sky. He is in the alleyway, out-side of Armand's cell. He has a huge keg with him. Hefinds the door unlocked. He enters.INT. CELLempty. The hearth is cold. The old coffin is gone.Louis silently closes the door to the passage, and barsit with the immense bar. He looks about. Looks at thebar. It's enough to block this exit. He rushes backout.161.INT. THEATRELouis hurls kerosene all over the stage curtain, thepadded seats, the carpet. He leaves a long trail ofkerosene behind him like a wick. He rushes to the wingsand down the stairs, dribbling the kerosene behind him.He sees the candlelight of the ballroom below. Then thecandle goes out. He listens, creeping quietly into theballroom, leaking the kerosene from the cask. He splashesover the coffins that gleam in the dimness.Then he strikes a match and heaves it at the kerosene.Everything bursts into flames. The trail of keroseneROARS INTO FIRE through the ballroom over the coffinsand up the stairs. We hear EXPLOSION of FIRE above.LOUISshudders all over, fighting the morning weakness. Hetakes a small scythe from his belt and stands like theGrim Reaper.Estelle rises from her burning coffin, screams and triesto run through the fire, but Louis slashes at her with thescythe, and she goes down screaming, her dress in flames.ESTELLEStop him. It's morning. Thesunlight. Stop him.Others rise, choking in the smoke. SCREAMS come fromeverywhere. They are burning.Louis backs to the stairs to the dungeon. He can seedown there a thin pale light under Armand's bolted door.Morning coming.Santiago suddenly appears behind. He turns. Santiagorushes him in a blur. Louis lifts the scythe, too fast tosee what he himself is doing. Santiago's head streamingblood flies through the air. The body drops, flappingits arms.SCREAMS come from everywhere.Another vampire rushes burning towards Louis. He decapi-tates the burning vampire.The light from below is nearly blinding him.LOUIScovers his eyes with his arm and descends, rushing pastthe door of Armand's cell with its burning gleam oflight. He runs down the long passage to the brokenbrick wall. He enters the --162.DUNGEONHe stops once to catch his breath in the cool dark,listening to --SCREAMS ABOVE. ROAR of FIRE.PASSAGEWAYbefore and behind are empty.He rushes back the long dark passage and finds the ironcoffin in which they locked him. He digs the scythe intothe ceiling, over and over, causing RUBBLE to FALL in agreat heap before the coffin, and then he climbs inside.INT. COFFIN - CLOSE ON LOUISHis eyes closing. Oblivion.STAIRWAY - LOUIS - FOLLOWING NIGHTMoves slowly up the sooty stone stairs, hearing the SOUNDSof the CITY above. He emerges in the --BURNT-OUT BALLROOMunder the naked sky. Above, on the --EXT. SIDEWALKS there are hastily constructed wooden barriers, a fragmentof a wall, heaps of rubble, but the theatre is gone.He climbs up over the heaps of rubble. A high wallremains, a piece of burnt roof and rafters.Carriages and pedestrians go by, ignoring him.INT. CROWDED CAFE across from the theatre. Louis sits at a table, paperfolded in front of him. We see headline: FIRE DESTROYS BOULEVARD THEATRELOUIS (V.O.)The mortal world did not guesswhat had taken place. Few bodieshad been found in the ruins.(MORE)(CONTINUED)163.CONTINUED:LOUIS (V.O.) (CONT'D)In other words, the younger oneshad left their bones; the olderones had been obliterated. Nomention of an eyewitness or asurvivor. How could there havebeen?INT. LOUVRE - NIGHTS LATERIt is already a museum by this time, and Louis fancilydressed and composed, walks alone through the rooms,looking at the painting by moonlight that comes throughthe windows and the skylights. He pauses before aGericault. The Wreck of the Medusa.Armand appears standing beside the painting.Louis sighs.LOUISYou didn't even warn them, didyou?ARMANDNo.LOUISWhy not?ARMANDI didn't want to.LOUISYou were their leader. Theytrusted you.ARMANDNo. That was never true. Thetheatre was mine. But I wasnever the leader, not since thetime when Lestat destroyed theold ways.Louis stops.LOUISAnd Lestat? Was he there whenthe theatre burned?ARMANDDid you want him to be there?(CONTINUED)164.CONTINUED:Louis walks on.LOUISI don't know. That's the truthof it. I don't know.ARMANDYou are much changed, and yet youare the same.Armand looks at him affectionately.LOUISWhat a pair we are. We deserveeach other, don't we?ARMANDWhat does it matter, innocent one.We are a pair! That is what counts.Armand and Louis walk slowly through the Louvre together.LOUIS (V.O.)That is the end of my storyreally. I never changed afterthat. I left Paris shortly afterand Armand followed me. For yearswe wandered the world. Greece,Egypt, all the ancient lands.But Claudia's death is truly theend of my tale.RETURN TO:EXT. DIVISADERO STREET - PRESENTTRAFFIC ROARING along Divisadero Street below the window.LOUIS (V.O.)We were in Venice when Armandwent his own way. I feared forhim going off on his own, but notenough to utter a single word tostop him. From time to time, Iglimpsed others... old ones.Sometimes they fled. Sometimesthey were indifferent.EXT. OLD DELHI (INDIA) - PRESENT TIME Crowds swarming in the early evening. Autos push againstthe endless stream of motley pedestrians.(CONTINUED)165.CONTINUED:LOUIS (V.O.)Then only a few years ago, Icaught a glimpse of anothervampire, and I knew at once ithad to be Gabrielle!CLOSE ON Louis in gentleman's white tropical suit staringthrough the crowd.Distant figure of Gabrielle, her hair tied back, dressedin khaki men's clothes, white-faced, oblivious, like awalking statue. Unnoticed yet horrifying in her trance-like movement.LOUIS (V.O.)I didn't dare call out to her.What could I have said to her? Itwas like seeing a goddess!He watches as she suddenly vanishes. He hurries throughthe crowd trying to catch another sight of her, but hecan't. She seems to have disappeared. He's alone in themortal crowd.LOUIS (V.O.)Every memory of Lestat I'd everburied in my soul came back to me.Oh, I'd never really forgottenhim, but now he crowded everythingfrom my mind. He became myobsession.EXT. STREET (SAN FRANCISCO) - MALLOY'S FACE (PRESENT)MALLOYLestat is still alive. He didescape the fire.LOUISThat's what I had to find out.I'd been back to Paris innumerabletimes. I would have known had hebeen there. Now I wanted toreturn to New Orleans. FinallyI could think of nothing else.The idle dream that if he existedstill, he might be there. And Iwanted to see my home again. Mycity. Where we had been so happyall those years. It was areason... for existing.166.EXT. GARDEN DISTRICT - NIGHTLouis in Twentieth Century suit walks past the many GreekRevival Mansions.LOUISMaybe I sensed something in thosedark streets. I saw and heardsounds. And then on PrytaniaStreet, only blocks from theLafayette Cemetery, I caught thescent of death and it wasn'tcoming from the graves.PAN OVER white-walled Lafayette Cemetery, surroundingmansions.LOUIS (V.O.)The scent grew stronger as Iwalked on uptown. Old death. Ascent too faint for mortals todetect.Louis sees rats darting along the street. One, then two,then two more together. They rush into a great overgrowngarden surrounding a ruined mansion. No lights.LOUIS (V.O.)Someone was luring them.A cat darts along the top of the wall and into thegarden.LOUIS (V.O.)The smell of death grew stronger.Louis stops at rusted gate. He forces it open andenters --EXT. VERITABLE JUNGLEof overgrown rose and oak tree and wisteria. He sees afaint glimmer of light coming from a distant glasslesswindow of a huge two-story Greek Revival house.He approaches, and then he sees --HIS POVOld shriveled corpse of a man, long dead and dried up,snagged in the thorny rose vines.167.BACK TO SCENEHe looks around. Walks on. Sees another corpse, almostnothing but bones sinking into the wet earth, the rootsof the oak overgrowing it.He looks up at the distant light.He passes a third corpse, caught in wisteria and rosevine, only bones and clothes.LOUIS (V.O.)They were like the doomed princescaught in the thorny vines ofSleeping Beauty's castle. I knewwhat it meant. A vampire hadlured them here, but had been tooweak to get rid of them.Louis sees dead rats lying near the steps.LOUIS (V.O.)No vampire can linger near theremains of his victims. It speltdespair -- the behavior of a dyinganimal that pollutes its own nest.Perhaps it meant madness.Louis treads carefully on the rotted steps. He movesalong the porch. More dead rats. He sees through thefloor-length windows into rooms lined with stacked books.Virtually walled with them. Water seeps down over thebooks. It gleams as it drips from the ceiling. Thefloors of the splendid rooms are bare, except for arotted French chair by a dead fireplace. A single mirrorreflecting the moon.Dead rats.He moves along the porch to the parlor windows. Thecandle flickers inside. He sees --HIS POVLestat lying on the floor. He is gaunt to near starva-tion. All his scars are gone, but he is almost a skeletonand his eyes are enormous in their sockets. His clothesare rags. Blond hair beautiful as always.One tiny candle stands beside him. He reads:The Black Mask Magazine. 1929.(CONTINUED)168.CONTINUED:He reads aloud the second installment of DashielHammett's, The Maltese Falcon, laughing now and then, withdelight. He affects a tough American voice, lapsing intoFrench accent for narrative.Without turning his head he speaks.LESTATCome into my parlor, Louis, saidthe spider to the fly.He goes on reading, as Sam Spade bullies Joe Cairo.INSIDE Louis studies him. Lestat ignores Louis.LOUISI prayed you were alive!LESTATDid you? To whom did you pray?Lestat continues reading. He is Sam Spade.Louis approaches and takes the magazine tentatively fromLestat's hand. Lestat allows this.LOUIS1929. Do you know what year thisis?LESTATWhy don't you bring something newto read then? A long time agothe magazines stopped coming. Ihad no more bank drafts, no moreink to write. No more stamps.Lestat appears almost too weak to lift his head. But heis very composed. Mentation perfect.LESTATYou are beautiful, Louis. Youalways were. The strong one.Armand's no longer with you, ishe? That's better for you, thoughyou may not know it now.LOUISWhere is the coffin?(CONTINUED)169.CONTINUED:LESTATWhat does it matter? There aremany dark places in my house andbeneath it.LOUISLestat, this place is a ruin.This is no longer safe. Mortalswill come here.Lestat laughs softly.LESTATThat would be lovely. I haven'ttasted mortal blood in so long.Could you get me a mortal, Louis?Lestat struggles to sit up. He is straightbacked, smi-ling, a horror of starved limbs.LESTATYou know, some nasty little thiefor killer, like in the old days.Some bittersweet trash from theriverfront. I can still hear theriver. I can smell it. Can you?Don't bother. I don't reallywant a human. If I did, I'd getone for myself.LOUISHow long have you been here?Lestat falls into thought, then suddenly excited:LESTATLouis, last time I went out I sawthe most marvelous thing.LOUIS(compassionately)What was it?LESTATA motion picture, Louis. Peoplemoving on a giant screen. Oh, itwas magic. And there wasdialogue, written on cards inbetween the moving pictures. Itwas a whole story. Orphans InThe Storm. Lillian Gish. It wasbeautiful. Surely you've seenit. You look so fit, so well.(CONTINUED)170.CONTINUED:Lestat's face darkens.LOUISWhat is it?LESTATThey showed the daytime sky! Iwas frightened. I left thetheatre. I ran all the way backhere. Do they still make thesemotion pictures? I know all aboutradios, I can hear them, I lovethem, and some sort of... I don'tknow what it is...LOUISLestat, they make motion picturesin color. The actors speak. Thedaytime sky in a film can't hurtus. The rising sun in a film isjust an illusion.Loud noise from the street of TRUCK RATTLING BY.Lestat shivers, covers his ears. He's terrified. Hecrosses his legs Indian-style and bends over.LOUISLestat, it's only a truck passing.Lestat takes his hands away from his ears.OTHER SOUNDS of the night. DISTANT TRAFFIC. A SIREN.Lestat winces at the siren, but it DIES AWAY.LESTATI know what these sounds are,Louis. I saw the automobiles whenI went out last. I saw themchugging and racing through thestreet. Here... look!He holds up the Black Mask magazine. Points to an adver-tisement of a young man riding a motorcycle. Year 1929.LESTATMotorcycles, they pass sometimes.Lestat shivers.LESTATAnd there are aeroplanes... in thesky.(CONTINUED)171.CONTINUED:A silence falls. Lestat's mind appears to wonder. Helooks about and then looks up at Louis in happy surprise.LESTATYou are here, I thought I wasdreaming! See the rats? In theold days in France, they calledus country lords harecatchers --we starved if we didn't kill thesmall game. And now I'm the ratcatcher!(laughs)The Pied Piper. And the rats,they are marvelously reliable.They never learn not to come whenI call.Lestat laughs softly.Louis smiles bitterly.They look at each other.LESTATI didn't go to Paris for vengeance,Louis.Louis says nothing.LESTATI came for the blood of the oldones. For Armand's help. I washealing, but it was so painful andso gradual, and I was still, well,you know... young.Louis says nothing.LESTATI did tell them she'd tried tokill me. You can't blame me forthat, can you?LOUISNo. I can't blame you for it.LESTATBut it was Armand who directed thewhole trial and execution as ifit were the final play for hislittle stage.(CONTINUED)172.CONTINUED:LOUISI suppose I've always known thatwas so. And yet I stayed withhim.LESTATLoneliness. You needn't tell me.You should develop a taste forrats again. You tried once,didn't you? Sometimes I talk tothem before I kill them. I neverdid that with innocent mortals.Did I? I was never cruel tomortals, was I?Louis shakes his head.LOUISYou must come out of here.Please. Come with me.Lestat shakes his head.Sudden sound of DIESEL TRAIN from the riverfront. PIER-CING WHISTLES. Again, Lestat cowers, covering his ears.He trembles violently. He shrinks up, knees under hischin. The SOUND DIES AWAY.A pause.LESTATThere are machines out there, thatcool the houses. In summer theyroar like wild beasts. But thewarmth is lovely then. I don'tmind it. Only I wish the treeshadn't grown so thick. I can nolonger see the stars.Louis drops down beside him. Urgent.LOUISLestat, let me get you out ofhere. Let me show you the worldthe way it is now. It's full ofmarvels. Of all of us, you shouldsee it, you above all should --Lestat smiles.LESTATShould what? Respect it? Havethe stamina for eternity? Apassion for beauty that helps meendure the passage of time?(CONTINUED)173.CONTINUED:Lestat laughs bitterly.He gathers up the Black Mask magazine. He begins to readagain out loud -- Sam Spade and Joe Cairo. Tough guyaccent.Louis stares at him. He speaks his name, but can't gethis attention.He grabs Lestat and shakes him.LESTATBack off, my friend! I may not beas weak as you think.He sits up again very straight, in full command.LOUISThat's the point! You've healed.You're whole again. But you mustfeed.LESTATGo away, Louis.LOUISYou'll be destroyed if you stayhere. You'll be discovered. Thisplace... it could...LESTATBurn? Like Pointe du Lac. Likeour townhouse? Like the Theatredes Vampyres? Oh, and thank youfor that last conflagration. Ithought they deserved it.Despicable liars. They neverhelped me. They never gave metheir healing blood. And to thinkArmand's blood was so powerfulwith age. Do you know what hereally did?EXT. TOP OF TOWER (PARIS) (1870)Armand forcing the wounded, scarred Lestat to thebattlements.LESTAT (V.O.)He took me back to the Magnus'stower, the very place where ithad all started. He lured methere with his promises.174.ANOTHER ANGLEArmand strikes Lestat and sends him over the battlement.He falls and falls until he is smashed on the stones.Blood flows from his fallen body but his blue eyes arewide open. He is alive.RETURN TO SCENE - NEW ORLEANS MANSION (PRESENT)Lestat sitting on the floor.LESTATHe had his reasons. I'd destroyedthe old coven. My broken boneshealed. Everything healed. Weare immortal, more or less.He reaches for the Black Mask magazine. Louis lets himtake it.LESTATSome night, something will rousemy curiosity. Give me a reasonto rise and become the vampireLestat again. But not you, Louis.You remind me of too many things.He lies back down and opens the magazine.LESTATYou knew she meant to destroy me.LOUISYes, I did.LESTATYou left me in the burningtownhouse.LOUISYes, I did.LESTATAnd when you burnt the Theatre,for all you knew I was there.LOUISHate me for it. Come back to dobattle, to quarrel. Take yourvengeance!Lestat laughs softly, shaking his head.LOUISMy blood isn't as powerful asArmand's, but it can revive you.(CONTINUED)175.CONTINUED:LESTATNo, thank you, my dark brother.I remember that taste only toowell.LOUISLestat, don't you want to makeme suffer for what I've done toyou?Lestat merely smiles at him, seeing through the taunt.LESTATLouis, I think you are sufferingbeautiflly, just as you havealways suffered. Why should Ilift a finger? It isn'tnecessary.Louis smiles ironically and nods in agreement.LESTATGo away now, mon ami. Go backto your modern world of marvels.Let me have my peace and quiet.And if you do come back, bringsomething new to read. Andcandles. Bring me candles. Youknow how I love the light.EXT./INT. RUINED MANSION - NEXT NIGHTLouis comes up the steps and into the parlor. He has asmall parcel. Lestat reads as before. He does not lookup. Louis tears open the parcel, and removes a smallWatchman portable TV with earphones. He kneels by Lestatand he turns it ON.We see the tiny screen glimmer with a ROCK VIDEO, Madonnadancing wildly.Lestat sits up, clasps it, amazed.LOUISThis is to blot out all the soundsthat hurt you. Here.He drops extra batteries on the floor and they gleam inthe light. He puts the earphones over Lestat's head.Turns up the volume.Lestat smiles in delight. He begins to laugh, and thensway with the music which he can hear and which we cannot.(CONTINUED)176.CONTINUED:He holds the little Watchman like a treasure, singing inperfect pitch the words of MADONNA'S song.LESTAT'Like a Virgin, kissed for thevery first time.'INT. MANSION - HALLWAY - ANOTHER NIGHTLouis stands in the doorway, arms folded. He watches --Lestat, a skeleton in rags, dancing as he wears theearphones and holds the Watchman.We hear a very THIN SOUND from the earphones: ROLLINGSTONES. "I Can't Get No Satisfaction." Lestat danceswith eerie grace in perfect time.MUSIC GROWS LOUDER.As Louis watches, Lestat becomes the performer, singing,dancing to the music, a spectacle among the ruins, as hedoes the modern Michael Jackson-style move to perfection.Louis tries to clear his vision, to shake the illusionor suggestions of Lestat as rock star.LOUIS (V.O.)I don't remember how many times Icame back. Three? Four. Itdoesn't matter. He would not lookat me or speak to me. And finallyone night he wasn't there.EXT. MANSION From a distance behind its jungle of vine and trees.LOUIS (V.O.)But I could hear the music, comingfrom somewhere, perhaps beneaththe foundations. I went away. Inever saw him again.EXT. MANSIONWe DRAW AWAY FROM the mansion, THROUGH the Garden Districtstreets, PAST huge Magnolia trees, PAST iron fences.Oaks hung with moss.(CONTINUED)177.CONTINUED:LOUIS (V.O.)That's my story. You have it all.I go on, night after night. Ifeed on those who cross my path.But there is no passion in me anylonger. I am reverent. A spiritwith preternatural flesh. Itended when I saw Claudia burnt toashes in that airwell. My dreamsdied with Claudia. My faith.RETURN TO SCENE (SAN FRANCISCO) - PRESENTMalloy staring at Louis.MALLOYNo! It can't end like that.LOUISBut it did. It's finished. Thereis no more to tell.MALLOYBut it's not over. Your passionfor all of it, your vision -- It'sstill inside you. It comes out inevery syllable you speak. You'reimmortal! Truly immortal --LOUISI tell you it's over! As Lestatonce said to me, I have given youwhat I have to give!MALLOYLouis, listen to me. Lestat maystill be there.LOUISIt makes no difference now. It'sfinished.Louis looks at the cassettes on the table.LOUISDo with this story what you will!Learn from it what you can. Giveit to others. I'm glad I've toldit. Maybe for the first time Iunderstand it myself.Malloy rises.(CONTINUED)178.CONTINUED:MALLOYOne more chance, Louis! Take me!Make me one of you! Do it.Louis is slowly horrified and then outraged and angry.LOUIS(barely able to contain his rage)This is what you want? After allI've told you! You ask me forthis!MALLOYYes. I can be your link with thiscentury! I'm the one to take youboth into these times. Louis,give it to me. You don'tunderstand your own story. Youdon't understand the intensitythat you yourself described!You've forgotten what mortal lifeis!LOUISDear God. I've failed again,haven't I?Louis rises, overturning the table, scattering the tapes.He disappears.Malloy sits there trembling. Quickly he gathers up thetapes, and the recorder. He puts away the mike. He ismuttering to himself almost feverishly. He stands upand turns to go and --Louis is right before him, inches away, a figure ofmenace, as in the alleyway at the start.Malloy falls back in terror.Louis reaches out, drags Malloy to him. Malloy drops thetapes and the little machine.LOUISYou want to go a little deeper?One final lesson to make you see!Malloy panics and tries to get away, but Louis gashes hisblood, sucking the blood fiercely and then throwing thegroaning Malloy on the floor.(CONTINUED)179.CONTINUED:Malloy, badly weakened, hand to his heart, gets up. Louisadvances on him in menace.Malloy staggers out of the room. He makes for thestairs. Louis grabs him again, drinks again, as Malloytries to push him away. Louis drags him from the stairsto the second staircase which leads to the roof. Hethrows him down. Malloy is weak, his throat torn.LOUISYou like it? You like being foodfor the immortals! You likedying? Is it beautiful? Is itintense?MALLOY'S POVHis heart is racing. In a haze, he flees up the stairs,as Louis comes relentlessly after him, barely seeming totake steps, he moves so fast and so gracefully.BACK TO SCENEMalloy pushes open door to the roof.EXT. ROOF (SAN FRANCISCO) - NIGHTTIMElight of San Francisco all around him. He staggers tothe right and to the left. No escape.He turns.Louis smack dab against him again.Malloy screams.Louis sinks his teeth again.MALLOY'S POVof view as he loses consciousness. Haze. Confusion.He sees --Blurred image of Louis standing over him looking down athim.His eyes close.180.EXT. ROOFTOP - MORNINGFROM ABOVE we see the body of Malloy like garbage on theroof.As we DRAW IN, we see Malloy looks dead, eyes half open.Sun strikes him. Wind blows torn newspapers across theroof and out into the sky. A cat approaches, licks atMalloy's neck, then goes away.CLOSE ON MALLOYHalf-mast eyes look dead.Then suddenly the eyes open. He sits up. He staresaround him. He is pale and feverish and trembling. Likea drunken man, he makes his way --INT. STAIRS - BACK TO ROOMThere in the sunlight is the tape recorder and all thecassettes, just as he left them.He falls on his knees gathering them up.CUT TO:INT. MALLOY'S CARHe hunches over the wheel. Looks impossibly sick andweak. He holds the RECORDER, rewinds the tape. Thenhears:LOUIS (V.O.)(on tape)And then on Prytania Street, onlyblocks from the Lafayette Cemetery,I caught the scent of death andit wasn't coming from the graves.Relief. Excitement. Malloy turns ON the IGNITION. HeROARS out of the parking place while with his right hand,he STOPS the RECORDER, puts in another tape, hits therewind button.EXT. FREEWAYFROM ABOVE we see Malloy's car on the freeway.We see it on the open road:(CONTINUED)181.CONTINUED:LOUIS (V.O.)(on tape)1791. That's when it happened...I was twenty-four -- younger thanyou are now.PAN TO sky;ROCK MUSIC RISES. ROLLING STONES. "I Can't Get NoSatisfaction." GROWING LOUDER and LOUDER and BLENDINGwith the motion picture THEME.EXT. CAR - NIGHTis a tiny speck on the dark desert highway.We DRAW UP again and FROM --EXT. DESERT SKYDISSOLVE TO:EXT. LOUISIANA SKYOaks with moss, magnolias... CRY of BIRDS...ROLLING STONES and THEME CREST.FADE OUT. THE END | screenplays |
Festival line-up update – 28 Apr 2010
By CMU Editorial | Published on Wednesday 28 April 2010
LARMER TREE, Larmer Tree Gardens, Dorset, 14-18 Jul: Frank Turner and Babylon Circus have been confirmed to play at Larmer Tree this summer, completing the line up that includes the likes of Newton Faulkner, Martha Wainwright, Tunny and James Yuill. www.larmertreefestival.co.uk
LATITUDE, Henham Park Estate, Suffolk, 16-18 Jul: Frightened Rabbit, Villagers and These New Puritans have all been added to the Latitude line-up, along with Angus & Julia Stone, Lissie, School Of Seven Bells, Rox and John Grant. www.latitudefestival.co.uk
T IN THE PARK, Balado, Scotland, 9-11 Jul: D12, Detroit Social Club, Yeasayer and Corinne Bailey Rae head up the latest acts to play at T in the Park. Other acts added to the bill include 3OH!3, Bombay Bicycle Club, Kids In Glass Houses, Yeasayer and Unicorn Kid. www.tinthepark.com
READ MORE ABOUT: Larmer Tree Festival | Latitude | T In The Park | slim_pajama |
Ranma, X-overs 1. Chapter 1
**Dark Magician Girl 1/2**
**Chapter 1 Old Surprises**
"Japanese"
[Chinese]
_Thought_
I do not own Yu-Gi-Oh or Ranma ½.
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"Master I have failed you. I'm so sorry." The crying girl was flying through the air at an incredibly fast speed. Her master had failed and he had been sealed into stone in the form of his guardian spirit by that murderous bandit king. Her current dilemma was caused by the humanoid snake like monster that said bandit employed. She had finally achieved the pinnacle of any Egyptian wizard and called forth her guardian to protect her master's stone from the bandit, but she was swatted aside and then punted through the air by the beast. She flew through the air for a long time until she started to rapidly descend. She could see pools below her in a valley. Her guardian spirit tried to fuse with her just as they hit the water...
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5000 years later...
"What the hell is that?" A teen with black hair and a pig tail stared at the giant panda that had come out of the pool where his father had fallen in.
A portly man in a green military uniform approached and held out a sign while explaining. "Oh, customer unlucky. Fall in spring drowned panda, tragic tale of panda drowned 1300 year ago. Now whoever fall in spring take form of panda."
"That's insane!" The teen didn't notice the panda as he was paying attention to the guide. This cost him as the panda caught the teen in the gut and tossed him back into a spring.
"Oh no customer fall in spring of... Hmm, don't know if that spring cursed with form yet. Hope not blank spring, no had death here in past 400 years. No wish that on young customer."
The spring frothed for a moment before something breached the surface. A figure sat in the spring wearing strange blue and pink body armor with a blue, funnel-like hat and a pentagram pendant. The figure sat there stunned for a moment before looking down at its reflection. Blue eyes, long blonde hair, rosy cheeks, and ample breasts were the first things noticed by the figure.
She let out a high pitched squeal of anger. "Pops, ya better run cuz I'm going to roast ya if you don't!"
Suffice to say, the panda ran as an angry teenage girl flew after him. She didn't even realize that she was flying.
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The guide shuddered as he dragged the panda into his house. He didn't know exactly what the young customer had become but it had to be a powerful witch or sorceress. She flew around and somehow pulled a large gnarled wand out of nowhere and started firing off shots of some kind of magic at her father. He did not want to be on her bad side.
The new girl then walked into the hut. "Alright, now explain why ya stopped me from skinnin him."
The guide nodded his head and immediately removed a kettle of boiling water off of the stove. "Water change form yes. Well, hot water change back."
The man poured the hot water over the panda and it changed back into Genma's human form. "Ow, that's hot. Why'd ya beat yer old man like that Ranma? See, we can change back."
The guide shook his head. "No Mr. customer, curse permanent. Cold water take form panda, hot water return to original form. Would young customer like hot water?"
Ranma snatched the hot water out of the guide's hands and poured it over herself. Nothing changed. She turned on the guide and he held up his hands. "No hurt. I no know why this happen. No know what spring was either. It not spring drowned girl. Maybe Amazon elders know. We go see yes.?"
Ranma looked at the guide and narrowed her eyes. "Alright, let's go. I wanna change back and if they know then we're gonna find out."
XxxxxxxxxxxxxxxxxxxxxxxxX
Shampoo smirked as her opponent fell off the log. She had finally won. Her win not only guaranteed her the feast and title of village champion, but also earned her right to have her guardian spirit unlocked by the elders. She would... _Why is there a girl and a panda eating the prize?_
XxxxxxxxxxxxxxxxxxxxxxxX
Ranma groaned as they trekked through the forest. She had finally willed away the body armor that she had been wearing somehow and was now wearing her old clothes. Three days with no food and little water. How far was this village? She then spotted smoke close by. A large blur ran past her and towards the smoke. It was her father. "Hey, wait up! I smell food and I know you're gonna eat it all! If ya do, I'll really kill ya."
Ranma ran after the panda and found him eating at a table loaded with food. She ignored all of the people staring and dug into the food. It was so good after three days of nothing. Her feast was shattered literally as a bonborri fell on the table. [Who are you to eat my food outsider?]
Ranma looked up to see a purple-haired girl staring angrily at her. "What? I was starving and there was food here?"
The purple-haired girl snarled at her. "That Shampoo food. Prize for fighting contest. No belong to outsider!"
Ranma looked between Shampoo and the food. "So, if I win in a duel, I get the food?"
Shampoo smiled viciously. She would beat the outsider to a pulp for her insolence. That would teach this girl to talk back to her better. "Yes. Fight on log. First fall off lose. Let duel!"
Ranma shrugged and flipped onto the log as did Shampoo. The air seemed to darken some but neither Ranma or Shampoo paid attention to it. Ranma didn't take a stance as Shampoo took out her bonborri. Shampoo lunged at Ranma but missed as Ranma slid around the attack. Shampoo charged again and tried to hit the girl in rapid succession with the bonborri, but Ranma just seemed to float around all of the attacks. Ranma then swung around and tripped Shampoo so she fell off the log and fall face first into the dirt.
Shampoo whirled around on Ranma with an angry scowl on her face. Ranma backed up but the girl lunged at her and kissed her.
The guide's eyes widened and he grabbed Ranma. "Sir, need be running. That Amazon kiss of death. Now she hunt you end of earth to kill you."
Ranma's and Genma's eyes widened as Shampoo and an angry mob of Amazons started to come towards them with sharp swords. The panda held up a sign. 'Boy! It's time to run.'
Genma and Ranma ran for their lives as angry Amazons chased after them.
XxxxxxxxxxxxxxxX
A shriveled, elderly woman hopping on a cane approached the scene of the disturbance and shook her head at the mess. [Impetuous youth.] She then noticed the guide nearby. [What has gone on here Po Ta?]
The guide shifted a little and sweated. He was responsible for bringing the outsiders here. [I brought some Jusenkyou cursed men here for help. One in particular honored elder Kuh Lon.]
Cologne (Kuh Lon) raised an eyebrow. [One in particular. What was special about one of them?]
The guide rubbed the back of his neck. [The young man fell into a spring with an unknown curse. When he came out, he was a girl and was wearing strange blue and pink armor. She then flew in the air while attacking her father who was cursed to turn into a panda. She also summoned a gnarled staff and started firing off some kind of powerful magic at her father. When I calmed her down, the armor and the staff disappeared. I took them back to my hut to get hot water but hot water did not work on the young customer so he remain a she. That's why I brought them here.]
Cologne nodded her head. It wasn't impossible for a curse to lock, just improbable for it to lock from the get go. The power the girl held was also of interest. [Go on.]
The guide looked nervous. [We were tired and hungry when we got here because we had nothing to eat for three days. The customers saw the food and nothing else. They ran over and started eating. The panda ate the most though.]
Cologne sighed. She knew where this was going. [Shan Pu challenged the young one to a duel on the log. The customer stated that the stake for the duel was the food. They fought and Shan Pu lost. Shan Pu gave her the Kiss of Death and the customers fled.]
Cologne groaned. It wasn't illegal for an Amazon to give the Kiss of Death in this case. It was just not favorably looked upon when there was a stated stake for a normal duel. It was then that something pulled on the navel of the elder. _Kuh Lon, I sense wisps of a shadow duel and a guardian spirit not known to me._
Cologne's heart nearly stopped at those words. Her guardian spirit's words sank into her like a steel trap. _A shadow duel and a guardian spirit? Can you divine whose they are?_
The spirit hissed for a moment before speaking. _I believe it is the one she fought on the log. The stated goal for the duel was the food on the table. The stranger won the duel and the right to all the food. The stranger was denied the rest of her prize as Shan Pu and the others attacked. By the rights of the shadow duel, Shan Pu's soul now belongs to that girl since she denied the girl her prize. Worse yet your young heir has declared to kill her new master. When her sword plunges into her new master, she will be the one to die instead._
Cologne's grip dug into her staff. How could her heir be so stupid? She knew that she had given the girl some spiritual training and that she should have recognized the beginning of a shadow duel. The only thing she could think of was that the girl had been too prideful and forgotten her surroundings. Cologne turned to the guide. [Tell me everything about the outsiders Po Ta. I need to get to them before Shan Pu does.]
XxxxxxxxxxxxxxxxxxxxxxxxX
A girl with blonde hair was floating in a lotus position beside a giant hulking panda. "So why are we here again?"
The panda held up a sign. 'My old training partner lives here.' Flip. 'Our school was split into two parts.' Flip. 'It would do you good to see the other half.'
Ranma raised an eyebrow. "And why didn't we do this before now? I mean ten years learning one half of a school. Do I gotta go another ten years to learn this one too? And why aren't we looking for a cure? I mean ain't that more important. I ain't gotta remind ya of what happened last month do I. What was that anyways?"
Genma-panda shuddered and then harrumphed for a moment before pulling out a sign. 'No, Soun's style should be easier.' Flip. 'We can always go on short training missions to look for cures.' Flip. 'Nothing happened last month.' Flip. 'Remember you're a man!'
Ranma got red in the face. Nothing happened. NOTHING HAPPENED! "Nothing happened! So the whole emotional roller coaster and that pain and... anyways that won't nothing old man! If ya don't tell me what it was, then I'm gonna beat it out of you cuz I know you know something!"
The panda ducked as a foot flew through the space its head had been. A fist then connected with his stomach and he hit a fence hard. "Serves ya right old man! I'm going back to China."
Ranma turned and stomped off, but didn't notice that the panda had gotten back up and grabbed a sign post. The panda swung the sign post down over Ranma's head. Ranma hit the ground unconscious and the panda scooped her up. It then turned and growled at the onlookers before running off.
XxxxxxxxxxxxxxxxxxX
"Kasumi, Nabiki, Akane come here! I have great news!" Soun Tendo was waving a postcard in his hand as he entered the room. Nabiki was the first to arrive down the stairs.
"What's got you so excited daddy?" It had been a long time since she had seen her father this excited. It was probably something she wasn't going to like.
Soun turned to Nabiki smiling. "Get Akane and Kasumi. You all need to hear this." He then marched to the dining room. Nabiki rolled her eyes. Kasumi would be there in a moment anyways thanks to his shouting and Akane would be in the dojo.
Nabiki walked off to the dojo to get Akane only to find her headed back to the house wiping away her sweat with a towel. "Hey Akane, daddy wants us in the dining room. He's got an announcement to make."
"Okay, I wonder what it is?" Nabiki shook her head as she and Akane walked into the dining room. They sat down next to Kasumi and faced their father.
Soun held up a postcard with the picture of a panda on it. "Good news. My friend Genma and his son are coming here today. They just got done training in China and have come back to Japan."
"And what's so important about that daddy?" Nabiki knew the other shoe was going to drop. Her father really didn't have any friends that she knew of that ever got him this excited.
His smile widened as he set the postcard on the table. "I trained with him in my youth. We each practiced Anything Goes. In order to join the branches of our schools, we made a pact that our children would marry."
Everything was silent for a moment and then all hell broke loose.
"What? How could you engage us to some pervert?"
"Oh my! I hope he's older."
"Daddy how could you do this?" Internally Nabiki was scheming. _I hope they're rich. They did go to China. Maybe I should wear a yukata just in case._
Nabiki slipped out of the room as the arguments became more heated between Akane and her father.
XxxxxxxxxxxxxxxxxxxX
The doorbell range and Soun rushed to the door with Nabiki tagging behind him. She was now sporting a light blue yukata and was hoping that, whoever the guy was, he was handsome. Soun flung the door open only to gawk as a giant panda pushed its way into the house with a person kicking and screaming in its arms. "Let me go pop. You're scaring them spit-less!"
The giant panda set the person down in front of Soun who looked at the person. "Ranma?"
The person looked nervous. "Uh yeah."
Soun rushed forward and hugged the person. "Oh happy day. The schools will be joined! I..."
He got a strange look on his face as he ran his hands down Ranma. He pushed Ranma away. "You're a... You're a..."
Nabiki answered him as she walked up and squeezed one of Ranma's breasts. "This is a girl daddy. Couldn't you get this right?"
Ranma sighed as Nabiki continued to squeeze. "Would ya stop that. It feels awful weird."
Akane had approached at this point and was mollified as it was a girl instead of a guy. "Nabiki stop that. Can't you see that she wants you to stop. Hi I'm Akane."
Ranma looked over at the new girl as Nabiki stopped rubbing her breast. "Uh, yeah. Thanks."
"Do you practice Anything Goes? Do you want to spar in the dojo?" Ranma smiled at Akane's words. That was just what she needed.
"Sure, I need to work off some of the anger at my old man. Let's go."
The two of them left the room with a somewhat perturbed Nabiki, Soun, and a panda bear that was headed towards the kitchen where Kasumi was fixing dinner.
XxxxxxxxxxxxxxxxX
Akane stretched out while looking at the girl across from her. The girl was supposed to be Asian but she had long blond hair and blue eyes. Two things that were in no way Japanese characteristics. She shrugged at that though. Her mother or father could have been American or European so who was she to judge. "You ready, I'll go easy on you."
Ranma shrugged. Akane didn't seem to really move with grace so she really didn't expect much. It would be interesting to see how good she really was. Akane moved in with a punch at Ranma's chest only for her to seamlessly glide around it. Akane was left over-extended and almost fell on her face. Akane spun around and tried again with a leg sweep only for Ranma to lazily jump over it.
Akane started to get flustered and tried some harder hits only for the same thing to happen. She was getting aggravated. "Hold still would you."
Akane charged forward as fast as she could only to have Ranma leap frog over her and send her to the floor. Akane sighed and stood up. "Alright, you got me. I'm just glad your a girl."
Ranma seemed to frown at that response and was about to retort but Kasumi called to them. "Dinner will be ready soon."
They both walked out at that declaration and into the house. Akane walked up the steps and Ranma walked into the dining room. A long-haired brunette walked in and greeted Ranma. "Hi, I'm Kasumi. You must be Ranma-chan. Why don't you take a bath before dinner? The furo is ready. It's over in the hallway to your left."
Ranma sniffed herself and shrugged as she walked off towards the bath. While she didn't know much about these people, Ranma had to admit that a hot bath and good food would be nice.
XxxxxxxxxxxxxxxxxxxxX
Nabiki sat in her room contemplating their new guest. She was an oddity and a problem. How could her father just accept that the girl was this Ranma person and why did the panda drag her father away right after they arrived?
The bad part was that her father would probably insist on them staying in their house for free which really ticked her off. She tapped her hand on her desk until a letter fell out of her stack and into her lap. She looked it over and smiled as she realized what she could do. She had no real interest in the offer, but she was sure she could convince the new 'guest' to accept it. It would be a good public event full of the kind of people she was sure would buy some 'Ranma' merchandise, once she got the photos. She could even get her contact in that city to house them.
Nabiki laid the letter down and rummaged through her stack of papers until she pulled out a clear card with something etched into it. She put it on top of the letter and headed downstairs. The top of the letter said in bold letters: "Domino City Duel Monsters Championship..."
XxxxxxxxxxxxxxxxxxxxX
If you like a story and want me to continue with it, let me know in the comments. If you want to use my idea, just PM me.
2. Chapter 2
**Ranma: Change of Pace**
I do not own Ranma ½.
XxxxxxxxxxxxxxxxxxxxX
"You know Saotome. You owe me a favor." Ranma groaned from his perch in the tree as Nabiki showed up to collect on her usual fees and favors. He didn't see how she tricked him all the time. He was a little incensed this time though considering the failed wedding. He had a damn good idea who helped that happen. Not to mention the spring of drowned man water...
Ranma jumped down from his perch and looked at Nabiki. "Take it from what you owe me for the wedding fiasco."
Nabiki narrowed her eyes on him. "Oh, I wasn't aware that I did anything."
Ranma let out a weary sigh. "Thought ya'd say something like: 'It was to save you from getting married so you owe me one.' or somethin along those lines. Hearin that from you is about as much as admission of guilt if I ever heard it."
Nabiki was bristling now. "Fine, then pay up the tab you owe me."
Ranma waved his hand at her as he walked out the gate. "I'll pay the damages to the dojo to Kasumi. How bout that? I think you need to pay for em too. Hope you got enough from selling that information about the wedding not to mention how mad Kasumi is about you reckin your mother's shrine. Think I heard her mumbling somethin about talkin to you soon after we started pickin people out of the rubble the other day."
Nabiki stared at the martial artist as he wandered out of the gate.
XxxxxxxxxX
Ranma sighed as he walked down the street towards a small park. The one good thing about the failed wedding was that everyone there had agreed to give him wide berth after he yelled at them the other day. Sure it wouldn't last but a couple of days reprieve was good enough for him. He was walking by a bench when he saw an old lady having trouble steadying herself so she could sit down on the bench. He immediately moved over to help the old lady sit down.
The old woman started to thank Ranma when a kid ran by and hit Ranma with a blast from a super soaker and the change took place. The old woman's eyes opened wide when she saw the boy change into a girl with bright red hair. Ranma frowned as she looked down at her soaked shirt and sighed as she knew taking it off at the moment to wring it out would freak the poor old lady out more than she was at the moment. She took this as a sign to leave but was stopped when the woman grabbed her arm. "Please dear, sit down. I don't bite."
Ranma raised her eye at the old woman and sat down next to her. "Kay, whatcha want?"
The old woman bopped Ranma's head. "It's 'Okay. What do you want?' Talk like a proper young lady!"
Ranma rubbed the back of her head. "Seesh, didn't haveta hit me. And I ain't a young lady."
The old woman bopped Ranma on the back of the head again. "Right now you're a young lady so act like it. I am curious though as to why you are a young lady?"
Ranma scratched the back of her head. "Eh, it's a long story."
"I have all the time in the world dear. My ears are yours."
XxxxxxxxxxX
Back at the Tendo home...
Nabiki was fuming as she walked back in the house. "The nerve of that arrogant bastard. Who is he to question me. I'm going to..."
"...going to what?"
Nabiki slowly turned her head to see Kasumi with a a frown on her face. Normally Nabiki wouldn't even react to someone frowning at her but Kasumi was another case. She had never seen Kasumi frown like that and she was now frozen like a deer caught in the headlights of a car. "Nabiki, sit at the table."
Nabiki obediently sat at the table. "Uh sis."
Kasumi sat in seiza across from Nabiki. "Yes."
Nabiki really couldn't think of anything to say. The cold stare she was getting from her sister was starting to freak her out.
"Do you know why I'm mad Nabiki?" Nabiki slowly shook her head to answer even though her brain told her not to move a muscle.
Kasumi sighed letting her frown drop to a serious expression. "I can make a new shrine for mother. I recovered what I needed from the old one. No, the dojo that mother and father built was utterly destroyed. Sure we can still use some of the timbers but it was special because it's the one thing that both mother and father poured their souls into. When mom died soon after it was finished, she told us to treasure the memories that we would make in it."
Nabiki relaxed some. She saw a way out of this dilemma. Place the blame. "Well, Saotome and the rest of them wrecked the place going after that cask and the rest of them fighting only added to the destruction. I'm sure..."
Nabiki stopped when a hand slammed down on the table. She watched Kasumi stand up and leave the room. Kasumi returned with a cask in hand and put it down beside her as she sat down again. She started drumming her fingers on the top of the cask. "Nabiki did you know that the curses mix."
Nabiki lost her already jumbled track of thought as Kasumi moved onto a tangent. "Uh, what?"
Kasumi continued to drum her fingers on the cask. "The curses. The ones from Jusenkyo. I looked it up just after Ranma's adventure in China. You know, after the little spats that have been occurring recently turned into more than just fun between martial artists. Ranma was rather distraught after what happened in China and I can't blame him for that.
I told father this, but he ignored my concerns and bought a cask from Jusenkyo. I had the bright idea of hiding the cask and convincing father that it was a good idea just to leave it be before the wedding. At the very least, I knew there would be a fight if anyone saw the cask and I hate to say it, but our father has broken many promises.
I made sure after hiding it to keep father distracted before the wedding to make sure he wouldn't get the bright idea of trying to find it again. Somehow, he ended up with it at the dojo just as the ceremony would have started. Now how do you think it got there? I had made sure that father was distracted and didn't come back to the house."
Nabiki started to sweat as she knew the game was getting harder. "I'm sure he could have just wandered off for a second and found it under the cupboard."
Kasumi stopped drumming the barrel. "Now how would you know that it was under the cupboard? Father certainly didn't know."
_SHIT!_ I screwed up. "Look Kasumi I..."
Kasumi raised her hand up. "Enough, just enough of the excuses. You knew damn well what would happen. It was bad enough that you purposefully invited all of them here. You just had to incite them further, but then I suppose that it's for the best."
Nabiki was confused for a second time. "Uh, what?"
Kasumi's frown returned. "Did you know that P-chan was Ryoga?"
Nabiki thought it over for a second before responding. "Not until recently. It finally clicked in my head after the numerous times that P-chan and Ranma fought that it was him. Why?"
Kasumi's frown became deeper. "I caught him changing after the wedding. I confronted Ranma about it and he explained the situation. I gave him a stern lecture on it. Since he promised on his honor not to reveal Ryoga's secret before Ryoga started taking advantage of it with us, I forgave him. I found that father and Genma on the other hand had known about this for quite some time. They thought jealousy would push Ranma into the marriage. They are both on a journey with grandfather Happosai so they can repent."
Nabiki gulped. There was definitely more.
"Since Akane slept with him and had him nestled in her bosom, even unknowingly, Ryoga's little trick as P-chan has sullied our name. Before father left, I had him and Genma make a written agreement to have Akane wed Ryoga. When I see him next, I will ensure that Ryoga honors the agreement or atones for his dishonor."
Nabiki nodded her head slowly. "So, Ranma and Akane are no longer engaged?"
Kasumi nodded her head and the frown seemed to lighten some. "I suppose it is for the best. Akane could never keep her temper in check around Ranma. The problem is that one of us needs to take over the engagement. I'm working on Tofu to see if he'll finally get over his craziness so that only leaves you."
Nabiki's eyes widened and she waved her hands in front of her. "No, no, no. You know how well that worked out last time. I also don't want to deal with the rivals."
Kasumi began drumming the cask again and Nabiki's eyes finally drifted down to look at it. "Uh, sis. What's with the cask?"
Nabiki began to squirm as she saw a familiar smile grace Kasumi's face. It was one that she wore often herself. "I'm glad you asked Nabiki. You can call it karma if you want to. It turns out that I thought someone might find the cask under the cupboard so at the last minute I exchanged it with a fake and put the real one in the dirty clothes pile. No one ever checks there. Guess what's in the cask Nabiki."
Nabiki paled and started backing away from the table. "No way. No freaking way. I am not going to be turned into some damn freak because you think it's punishment for what happened to the dojo and there is no way that I'm marrying Ranma."
Nabiki bolted out of her seat and ran for the front door. She opened it as quickly as she could only to be splashed in the face by something. It didn't take long to figure out what as her or now his blouse top split from the pressure and he let out a shriek. "Dammit Kasumi. What the hell?"
Kasumi calmly walked to the front door. "I put some clothes that are more suited to your new form on your bed. Oh and this time the water heater really is broken so it will be awhile before you can change back. I'm going out for groceries so I should be back later this evening. You really should go change."
Nabiki would have hit his sister if the excruciating pain of wearing panties as a male didn't hold him back.
XxxxxxxxX
In the park...
"...And that's my life." Ranma finished her explanation as the sun was starting to dip in the sky.
The old woman shook her head. "Dearie, dearie. You could fix many things in your life if you just took the reigns away from your father."
Ranma shrugged. "Been trying to fix what he's done and stop him from doing more, but it just gets worse. All the girls wouldn't stop coming after me even if I ditch pops now."
The old woman rubbed her chin and looked the girl over. "Why not stay a girl then? They would have no claim on you then would they not."
Ranma looked a little angry at that statement. "Hey, I ain't no girl. Ain't no way I'm going to stay a girl."
The woman raise an eyebrow. "And what's wrong with being a girl? I've been a girl for a good ninety years. Trust me, there's nothing wrong with being a woman."
Ranma shouted at the woman. "Cuz women are weak. I was raised to be a man. I can't give up on that now."
The woman whacked her cane on the back of Ranma's head. "Weak am I? Is that Cologne woman weak? She taught you much of what you know and beat you several times. Are the girls pining over you weak? No. Every time you made fun of that Akane girl, you admit that she beat you soundly. What of any of that sounds weak to you?"
Ranma stared at the woman. "Uh.."
The old woman shook her head. "Fine then. Tell me. Where do you see yourself down the road say in ten years?"
Ranma thought for a minute before responding. "Well, I'll be teaching classes in the dojo, teach my kids the art, and um, I guess that's it."
The old woman shook her head. "Wrong. I can already tell you aren't college material kid. Maybe you could get a Phys ed degree at a community college but that's it. Dojos don't always have good business nowadays so you'll need more income. You need to marry someone that can actually support the family financially dear because you don't have the ability to do so."
Ranma looked a little shaken but shot back. "Is that a challenge? Cuz if it's a challenge then Ranma Saotome don't lose!"
Ranma started to get up but the old woman bonked her on the head again. "Sit down this instant!" Ranma sat down rubbing her head. "Look here Ranma! I never said anything about a challenge. Besides, you have lost challenges."
Ranma turned around the lady with an angry look. "I have not!"
The old woman mocked surprise. "The first Phoenix pill incidents, moxibustion technique, Taro, Gambling King, that Nabiki girl repeatedly... I could go on. They did beat you at some point."
Ranma was starting to get furious. "I beat all of those people. You have no right..."
The old woman glared at Ranma. "You lost some battles but won the war, no. The incident with the Phoenix people should have woken you up dear. Someone actually died and you killed someone else even if they did come back to life. You have lost but learned from it and come out better for it, but only in the short term. If you want to sort out the long term, then you need to see your flaws.
It's obvious that everything tying you up is related to those engagements. Every single girl you described is lost in some delusion and I don't think a single one of those relationships would end well. Why not take the path no one would expect you to take?"
Ranma eyed the woman suspiciously. "So, what's that got to do with staying a girl?"
The woman sighed. "A lot. If you stay a girl, then those other girls would lose interest or take actions that would throw a negative light on their engagements to you. End of story. As for the future... You would be running an in-house dojo, am I correct?"
Ranma nodded and the woman continued. "Would it really be that hard to run a household and a dojo as a woman?"
Ranma shrugged. "I still don't get it. I could still do it as a guy?"
The old woman nodded her head slowly. "True. You also have the ability to change back and forth. No, what I'm saying is that you need an out and that's it. Why don't we pick this up tomorrow? Same time and place."
Ranma looked warily at the old woman and nodded slowly. The old woman hopped up and smiled at Ranma. "Good. My name is Omamori Hito."
XxxxxxxxxX
Nabiki was swearing under his breath. The water heater really was broken and for some reason he couldn't turn the stove on. He was going to beat the living daylights out of Kasumi if he could bring himself to do it. He then heard someone entering the house. "Dammit Kasumi, I told you..."
Nabiki blinked as she looked down at Ranma-chan. Ranma looked up at him with a confused look. "Uh, do I know you?"
Nabiki rubbed his temple. "Yes. It's... Nabiki."
Ranma's eyes bugged out as she looked over Nabiki. "Uh."
"Sit down at the table Saotome and I'll..." Nabiki sucked in a breath. "..tell you for free."
Ranma's eyes really shot open as she moved to sit down. "Are you really Nabiki?"
Nabiki sat down across from her and rolled her eyes. "Yes. Kasumi was kind of mad so she used some of the Spring of drowned man water on me. And before you ask, she dumped the rest of it out. Apparently, she was keeping it away from everyone because she knew the curses mixed. You'd be part man and woman at the same time."
Ranma shivered. "No cure?"
Nabiki threw her hands up. "Nope. At least none that are safe or keep you in your birth form."
They were silent for a second before Nabiki spoke again. "And they, uh, moved the engagement over to me again."
Ranma's eyes widened. "No way. Not again. Ya ain't tricking me again."
Nabiki shook her head. "It's not the game we were playing before. Kasumi found out who P-chan really is. Guess who's engaged to Akane now."
Ranma scrunched up her nose. "No idea."
Nabiki slapped her face. "Are you really that dense? It's Ryoga. Something about honor being smeared and such. Kasumi's going to put him to marrying her or put him to the knife."
Ranma blanched. "Better him than me."
Nabiki shrugged. "Guess he does kind of deserve it."
Both let silence reign for a few minutes.
"Soooo, the water heater's broken and Kasumi cut off the stove so I can't turn it back on. No hot water."
Nabiki watched Ranma groan and then shake her head. "Guess we deserve it. Kasumi was really mad about the dojo and shrine being destroyed."
Nabiki frowned. Usually Ranma became flustered by a statement like that. Now Ranma was dropping in and out of the conversation with an almost contemplative look on her face. "We can go to the bathhouse later I suppose."
Ranma waved his hand in front of his face. "That always ends in disaster. It'd be better to just get the heater repaired and let Kasumi cool off. I think staying this way for awhile is her punishment."
Nabiki's eyebrows rose at that statement. _Ranma's not fighting to change back._ "Uh you don't want to change back Saotome?"
Ranma got a look on her face like she was constipated. "What would happen, and I'm only sayin if, I was permanently stuck as a girl?"
That statement really caught Nabiki off guard. "You aren't stuck again are you?"
Ranma waved her hands in front of her. "No, no. I was just curious. I talked to some old lady about my life and she said I could probably solve most of my problems by staying a girl."
Nabiki sat in thought for a little while. "I guess it would to some extent. Most of the engagements wouldn't hold up and there wouldn't be a real stain on honor because Genma technically would no longer have a son. I doubt the Kuno's would let up but they're going to have to start facing the music some time soon. Some of their more recent activities have started to bring undo attention to themselves from the authorities. A little push of information to the right people would stop them. I know the Amazons wouldn't stop on their own, but the actions they've taken here and the reason they're here would be frowned upon by the government. I'm kind of surprised that no one from foreign affairs or the immigration bureau hasn't stopped by to question them."
Ranma nodded her head. "Right. I kinda thought some of that might happen, but what do you think it would mean for my future maybe. I mean if I stayed a guy or a girl. Whatcha think of either of those paths."
Nabiki's eyes shot open as she stared at Ranma. _Hmmm, may need to find that old woman. She actually __got the great Saotome thinking._ "Not much either way. You'll never get into college with your grades. Well, maybe community college or a trade school if you work hard now. You won't be able to get a good job with any of those degrees. If you teach at the dojo, you'll have to work a second job or your wife will have to get a really high paying job but it's not easy for a woman to get a good position and nearly impossible for a married woman. Frankly, I see you being broke. It's why I didn't take the engagement to begin with. I don't want to be tied down to a husband because it would kill any kind of advancements I want for work."
Ranma nodded her head. "And as a woman?"
Nabiki kept his eyes on Ranma for any reactions as she spoke. "Same deal except you might be able to keep the dojo afloat and not be financially strapped if you had a husband working a good job, but I can't really see you marrying a guy and getting pregnant."
Ranma shook her head and stood up. "Uh, thanks Nabiki. I'm, uh, gonna go nap for a bit."
Nabiki watched Ranma climb up the stairs in thought.
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When Kasumi got home from shopping, she saw a contemplative Nabiki sitting at the table. "So, has reflecting on what you've done helped any?"
"Hey sis, what do you think would happen if Ranma took my last name in the marriage?"
Kasumi put down her groceries and looked over Nabiki as she sat down. "I don't know. Would Ranma even consider that?"
Nabiki frowned a little before speaking. "Uh, he or rather she came home asking me what I thought would happen if she stayed a girl permanently after I told her about the switch in engagements. It was kind of strange. She seemed to already guess at what I had to say and even asked of what I thought would happen to her in the long run. What was really strange was that when I suggested that she could have a husband, she didn't baulk at it. She just stood up in thought and left the table."
Kasumi shook her head. "I don't think Ranma would really go for that."
Nabiki waved his hand. "I'm sure that you're right, but let's just say for a minute that Ranma got stuck as a girl and I got stuck as a guy."
Kasumi nodded her head and Nabiki continued. "We wouldn't owe a dowry so Genma would have to leave the house because I certainly am not going to let him stay here. All of the honor agreements on Ranma would be null and void because he would no longer be a guy and would take on the Tendo name.
I wouldn't have to worry about the discrimination against women in the workplace anymore. I also wouldn't have to worry about housework because Ranma would take care of it. You know that I suck at it and Ranma's actually pretty good at the sewing, cooking, and cleaning stuff. Hell, Ranma would be staying home anyways if he or she taught the dojo. If dad's worried about the inheritance tax, then we'd just make the estate the dowry for your wedding."
Kasumi openly frowned at this speech. "Nabiki, I don't think you're thinking about Ranma. Maybe I should have thought more before giving you that curse. It seems you haven't learned your lesson yet."
Nabiki shook her head and hands. "Woah, stop right there. Ranma was the one that brought this up. Not me. It's just that I've had some time to think it through. Everything would work out if we got stuck in our cursed forms."
Kasumi's frown deepened. "What about children? I know father would want some but you wouldn't be able to have them if you stay male."
Nabiki shrugged her shoulders. "I never wanted to get pregnant to begin with. If Ranma's serious about this, then she might be willing to..."
Kasumi put her hand up to stop Nabiki. "I'm going to call up Akane's friend Yuka and tell her that it would be a good idea to keep Akane over for a sleepover. We will discuss this between the three of us tonight."
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3. Chapter 3: Goblin Law HP
**Goblin Law**
**Chapter 1**
Disclaimer: I do not own Harry Potter.
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Griphook was angry, no he was livid. He had recently become head of his small clan and received a promotion that came along with such an honor. He was proud of this until he found out that he had been foisted as the head of the wizard and goblin affairs office. He had prided himself on his ability to keep agreements, make deals, and manage money as a young teller and vault keeper, but the letter in front of him nearly had him crawling up the wall. The ministry had sent the Goblins a few letters. As most of the senior goblins didn't think much of the ministry, these letters ended up being passed to him to deal with as part of his new position. The problem was that the letters requested the seizure of sealed documents and accounts. These documents were deeds, wills, and accounts that were to be locked and only opened in contingency with certain key factors. They were entrusted to the goblins under their sworn oath and watchful eye and these blasted wizards were demanding that they hand them over by breaking their laws and the ancient rites!
He had overlooked a number of... questionable activities over the past few years to keep from causing bad blood with the wizards. While not illegal or completely against goblin laws, the wizards had been moving funds around in ways that displeased him. The outright demand that he hand over accounts and documents in this matter went against the the very nature of goblin laws and honor!
He was about to grab his axe off the wall when who should walk in the door unescorted but the one person who many of these actions affected either directly or indirectly. Griphook lowered his hand and watched as the boy walked up to Slash at the teller. He then had an epiphany, a wonderfully awful, pernicious epiphany. Oh, this could work out well for both himself and the boy and if nothing else it would be a slap in the face of many wizards. It was perfect.
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Harry was glum. His godfather had to escape once more and Remus had to leave his teaching post. He walked into Gringotts thinking about this and didn't pay attention until he reached a teller. "Hello, Mr. Potter. How will you be managing your funds this day?"
Harry blinked and looked up at the goblin. "I was going to ask about money transfers and setting up an account so someone can access under an assumed name if they are approved."
Harry had thought about this and if he was right then maybe he could help his godfather out. The goblin looked over the boy. "That's a more private matter than what we do at the teller stand boy. There are some fees..."
A hand fell on the goblin's shoulder. Both the goblin and Harry looked over to see Griphook smiling. "Ah, Mr. Potter. I would be willing to talk of such matters with you. In fact, I have several matters to discuss with you. Matters that would be … mutually beneficial. Slasher, I'll be taking over Mr. Potter's instruction."
The goblin at the teller grunted and waved his hand. Harry followed Griphook to his office. He had never been in a goblin office before and it was rather intimidating with the axe and several heads of magical creatures adorning the walls. "Uh, Griphook sir..."
Griphook smiled as he pulled a number of sealed documents out of a file folder and put them on the desk in front of him. He also pulled the letters he had received from the ministry. He put on his reading glasses and sat down. "Mr. Potter, you should know that we goblins pride ourselves on keeping secrets amongst ourselves, warding off thieves, and managing accounts. You have seen this, have you not Mr. Potter?"
Harry nodded and Griphook continued. "Good. Now what do you make of what the ministry has said here.
I quote:
'_Dear Goblins,_
_Immediately release the accounts, wills, and documents pertaining to one Sirius Black, Scion of House Black. He is a fugitive and we cannot allow him funds or means beyond what he may scrounge up. To this end, we expect said documents and accounts by week's end._
_Sincerely,_
_Minister Fudge'_
End quote."
Harry was angry. How could they do that to Sirius. He was innocent! Griphook seemed to guess Harry's line of thought. "We do not care if he is guilty or not Mr. Potter. It is the letter of the law that matters. In this case though, the letter of the law is in Mr. Black's favor. He never went to trial and is thus only a fugitive in lieu of trial. We do not hand over accounts on that alone as the law makes no mention of this. In fact, only accounts belonging to those _sentenced_ to life or death may be handed over to the ministry or another governing body and only if there is no direct living relative of age. If no one claims the account of those sentenced to life or death, then it is liquidated and the Goblin Nation takes control.
I find this seizure request to be a violation of these long-standing writs. There are also a number of accounts belonging to quite a few death eaters serving life sentences at Azkaban that are currently open. Why might you ask? Because the ministry is holding them for the next heir to come of age and claim them under a loophole law written for orphaned children. While I must confess that I applaud the ability to use loopholes, the use of this law in this case is non-applicable as all of these heirs are currently cared for by a parent or standing guardian or in a few cases no direct heir exists. It would be understandable if said persons had sealed wills or accounts as goblin law recognizes sealed wills and accounts as contingents for the continuation of accounts held by persons regardless of current mental state, incarceration, or death. This is not however the case with said incarcerated individuals with the exception of one Sirius Black."
Harry was seething now. How could they do this? It was outrageous! Griphook shook his head and pulled out another letter.
"This one came in not long after the first:
_'Goblins,_
_Immediately release the wills, and documents of Lily and James Potter to the holding of the ministry. Also, immediately release the accounts, wills, and documents of any and all deceased or on hold accounts that have yet to be liquidated to the tender mercies of the ministry for review. To this end, we expect said documents by week's end._
_Sincerely,_
_Lucious Malfoy'_
End quote."
If Harry was angry before, he was livid now. He had so much anger bottled up that he didn't know what to do with it. Griphook shook his head. "I know boy. It boils my blood too. Not only is there no precedent for what the ministry is asking for, they dare to demand that we hand over documents and accounts that are sealed and only to be opened by those meant to open them. Added to this is that a non-Ministry employee is making this request for the Ministry. It defies the proper chain of command. I seek to remedy this."
Some of the fire went out of Harry. "Huh?"
Griphook walked around to Harry's chair. He put a hand over the boy's shoulder. "How would you like to fix all of this?"
Harry blinked. "Follow me boy."
Harry sat for a moment and then noticed that Griphook had opened a hidden door. He quickly followed and the door slammed shut behind them.
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They were in a tunnel system that Harry had never seen before. "Harry, I will make you a deal. There is a way to get back at those conniving ministry wizards, but you must understand that you will never be viewed in a welcome way by the whole of the wizarding world ever again."
Harry gulped. Did he have to do something evil like Voldemort would do? A pit formed in his stomach as they came to a room with several circles in it. The circles had three goblin heads carved into the points of a triangle circumscribed by the array. "It's not something to turn you evil boy. No, this is a ritual to make you goblin kin. It is a rare honor that no wizard has taken in the last 700 years. It will not turn you into a goblin and will not mess with your current lines of ancestry. It simply tests you and places your rank within our society. I'm afraid that I cannot tell you the benefits of this ritual. The only thing that I can say is that this will solve many of your problems and many of ours as well."
Harry looked over the ritual array and pondered if it was another of Voldemort's traps. He let out a sigh and threw caution to the wind. "How does it go?"
Griphook's grin grew very wide. He pulled out a ritual kriss with green and gold lines. He pricked his finger and let some blood drop onto the inner circle. The runes glowed a light silver color. "Prick your finger and let a drop of blood fall on each goblin head. The ritual will complete itself."
Harry followed the directions and pricked his finger. He walked around the circle and let a drop of blood fall on each goblin head. The glow turned gold and a flash of light blinded Harry. He then let out a scream as his scar lit up. The screaming continued but in a different pitch and not emanating from Harry's mouth. Something came howling out of the scar and promptly shattered. Griphook's eyes narrowed at the thing that had come out of Harry's scar and if his guess was right then he needed to talk to the elders and look at their library.
The light show ended and Harry lay on the ground. He turned Harry over and raised an eyebrow at what he saw. There was a crown tattoo over the lightning scar now and two tattoos around Harry's wrists with black and white triangles that looked similar to bracelets. Griphook flipped Harry over and uncovered his back and his eyes opened wide. There on Harry's back was the tattooed face of a rather nasty goblin with two very long razor sharp tusks. A huge grin appeared on Griphook's face. "Even better than I could ever imagine. A fine goblin you shall make child."
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Harry groaned as he woke up. He felt like a bus had hit him. He nearly jumped back at the smiling visage of Griphook. "Good, you're awake. Welcome to the family Harry. You are now a rare contridiction: a wizard and a goblin. In truth, you are no different than the human you were beforehand, but there are now many things you may know that no other wizard, alive or dead, has any right to know. I'd like to take care of business first though so explanations will have to wait for another day.
Harry James Potter Grishnash, you of age thirteen are now of the majority in the eyes of the Goblin Nation and are hereafter responsible for the trusts, documents, agreements, and accounts implaced on thee. I have taken a blood sample to be tested for lineage and the results were given to me while you slept.
You Harry James Potter Grishnash are an heir of all four founder's lines and are hereby awarded all held accounts of known death eaters, deceased parties, and other miscellaneous deeds..."
Griphook paused after saying miscellaneous deeds. A gleam came to his eye and he chuckled at just what all said deeds were. He continued reading, "As the ministry has declared one Sirius Black a fugitive in lieu of trial, you are given temporary powers of attorney as his officially listed heir and therefore must maintain his accounts, agreements, and deeds until he is sentenced or proven innocent.
Official reading of the will of James and Lily Potter will occur at weeks end. May your coffers overflow with gold."
Harry blinked and then spoke. "And may yours always overflow with gold?"
Griphook slapped Harry on the back. "Ah yes, young blood. I will have to teach you many things, but I must truly thank you boy. You have saved us more trouble than you can imagine. Let's gather your things and settle you into your apartment."
Harry blinked again. "Apartment?"
Griphook's grin grew. "Yes, the one in your new family compound. I can't have a new relative of mine living in some muggle or wizard dump now can I."
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Petunia Durseley stayed out of the creatures way. She wasn't sure what it was but it looked evil. She should have expected Harry to start cavorting around with such devils. She dared not even acknowledge it's presence in her home.
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Griphook looked into the cupboard that the boy had lived in and shook his head. Did muggles really make their children live in such things. Not even the poorest goblin would shack up in this chamber. He noted Harry gathering some ragged looking clothes out of the corner of his eye and shook his head. "Leave everything except for your trunk with all of your magical items and books. Maybe take whatever is truly precious to you, the rest of what is in this house is junk. We'll have to have you fitted for clothes and get you some appropriate items."
Harry shrugged as he dropped the clothes and went to find his trunk. The goblin turned to the woman who was trying to ignore his presence. "And Miss Durseley. Since Harry will no longer be in your care, the stipend from the orphans fund will no longer be deposited into your account."
Petunia whirled around. "WHAT?"
Griphook smiled at the angry human. "I manage the account and I personally know where this orphan is going and it's not your care. I do hope this won't be a problem."
He turned his back to her seething form as he watched Harry lug a chest down the stairs. When Harry reached the bottom, Griphook raised an eyebrow. "Why don't you shrink it?"
Harry scratched the back of his head. "I can't use magic here and I don't have a special trunk."
The goblin scratched his chin at that. The boy was no longer underage so he could use his magic anywhere, but Griphook wanted to keep that a secret for as long as possible. He had already sent a letter to the ministry stating that it would take at least until the end of summer to sort through everything that was asked for, which was true. He just sent it as a blanket response for all of the demands and said that resolutions to all requests would be found by mid-Fall. By the time the ministry figured out what was going on, it would be far too late. He had plans for this boy. Ones that would show up those stuck up wizards and ones that pertained to the potential importance this boy now represented for goblin-kind.
His other thoughts centered on the boy's lack in the department of finer things. Goblins didn't really care particularly for all of the trinkets that the wizards and muggles gathered, but owning quality goods was a must. From what he could see, less than 1% of the funds from the Orphan's Fund were being used on the boy. While this was not a violation of wizarding law, it was a violation of goblin law which stated that funds given for a specific purpose from trusts specifically geared towards said purpose were to have at least 60% of those funds devoted to said purpose. He smiled as he remembered this law. Oh, this young boy would be helpful on many fronts. Why this case alone would easily win in Wizemgamot and, with the right lawyers, the precedent set from this would also help to curb further abuse of such funds. It made the goblin feel giddy.
Griphook looked back at his charge. "Worry not boy. I shall show you the finer side of living. Come on. Let us leave this bungalow."
The goblin grabbed Harry and the trunk as he activated a portkey, leaving a seething Petunia behind.
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"And here we are." Harry shook his head to slow the motion sickness again. When he came back into focus, he saw that they were in a rather spacious apartment made mostly from smoothed blue granite. It was lit by glowing yellow and blue stones in the ceiling. There was little to nothing there except for them at the moment.
"Leave your chest here boy. I've contracted some decent goblins and fairies to take over the work in here. It'll look much different when we get back. I want to show you our family compound and some of your new relatives." Harry followed the goblin out the front door and into an illuminated mammoth cavern. They were standing on top of moderately-sized, 3 story, cascade of blue granite apartments that were surrounded by a high fence. He could also see similar structures with some having pink, white, green, or multi-color patterns to the stones.
Harry would have an interesting time exploring this new world.
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4. Chapter 4: Parent Guardian
**Parent Guardian**
**Chapter 1: New Mother**
Disclaimer: I do not own Ranma ½ or the Tenchi Muyo/Universe/GxP series.
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Ranma Saotome, heir of Anything Goes Martial Arts, was searching for some poor animal that would be dinner. Not having food for two days was nothing new for him, but adding hunger to his current female form was greatly eating away at his patience. So far, she had found nothing and it seemed that they would go hungry for another night. She cursed her father for taking them to Jusenkyo. She was turning to go back to camp when she heard a noise. She walked around a small mound where she found a woman lying on the ground she rushed up to her and checked her over. The woman was bleeding profusely from a crack in her skull and her vitals were dropping.
The woman slowly turned her face to look at Ranma. Hope seemed to well up in her eyes. She pushed a bundle that she had been cradling in her arms towards Ranma. "Take her. Promise me that you will raise her."
Ranma blinked. she didn't know what was in the bundle and it was strange to find a native speaker of Japanese in the wilds of China. "Look lady. I'll get my pop an' the guide. Maybe we can get you some help."
The woman tried to shake her head and held the bundle out further. "Take my child as yours. Raise her. I will not let her die. I am not long for this world."
Ranma looked the woman over again. She was growing quite pale and her arms were trembling. She reluctantly grabbed the bundle and opened it and saw a little baby inside. She looked back at the woman to ask her something else but the woman had fallen silent. Ranma felt for her pulse but felt nothing. She closed the woman's eyes and set the child down. "I promise to take care of her. Guess I'd better get digging. I need ta give your mom a proper funeral."
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A sullen and dirty Ranma walked back into camp with a bundle under her arm. #Boy, what took you so long?# flip # The guide just came back# flip #and said that he found that Amazon village not too far from here.# flip # You're lucky you got back before we left.# flip #And why are you in that weak girly form?#
Ranma frowned as she encountered her father. Since Jusenkyo, she was starting to figure out how much of an ass her father could be. "Says the giant walking rug. So we gonna get going or what old man? I hope they got hot water and food in that village cuz we'll be needing it."
The guide walked over at that point with his pack on. "Yes, Amazon village mile that way. We go now yes?"
Ranma looked at the bundle she was carrying and sighed. She didn't know how to take care of a child so it was probably a good thing that the village wasn't too far ahead. At least the kid had only cooed softly as Ranma stroked the baby's chin under the blanket. She had to hide it from her father for as long as possible.
Genma Saotome, in his panda form, shoved Ranma and the guide out of the way as he raced to a table full of food. Ranma missed this as she curled around the baby protectively and rolled with the panda's blow. When she stood up, she could here shouts of anger. "Oh no, customer shouldn't eat food. Is Amazon prize!"
She looked around and spotted her father greedily eating from a table full of food. She was almost tempted into joining her father until she noted all of the spears surrounding him. A girl with purple hair was shouting something at the panda while pointing a pair of giant bonborri at him. The girl then looked over at her and the guide and marched over to them. She started shouting again and the guide tried to translate. "She say you pet panda eat her prize. She want fight you."
Now Ranma would never normally turn down a fight, but she was currently holding a baby. Whether it was some maternal instinct or just some common sense leaking through the chauvinistic brain of the martial artist, she didn't trust leaving the child alone to fight at the moment. "Uh, I can't fight right now. Look just tell her that I got..."
Ranma didn't finish the sentence as the girl took a swipe at her only to meet air. "Hey, whatcha do that for?"
Ranma had sprung back ten feet as the bonborri landed where she had been. "Shampoo speak Japanese. She know what outsider say. Shameful not to fight. Coward."
The words stung and if she didn't have the child, Ranma would have pounded the girl into the ground for that insult even if she was a girl; however, Ranma was holding a baby and she wasn't about to let this psycho harm her. Shampoo continued her assault and Ranma kept dodging until she lost her grip on the cloth the child was wrapped in. Time slowed for the martial artist as she saw a bonborri coming down towards the bundle. Ranma used all of her skill to roll around the other bonborri as she dived in to rescue the child.
The poor baby finally decided it had had enough and began to wail. Shampoo did not hear this in her rage and didn't stop her swing as the outsider had foolishly dove to retrieve what she had been carrying which was in the path of her swing. The bonborri never connected. Shampoo couldn't fathom why her bonborri had stopped cold as the outsider was huddled over the bundle of cloth she had been carrying and had not done anything to stop the blow.
"ENOUGH!" Shampoo's eyes widened as she knew that voice. She saw her great-grandmother holding her staff against the bonborri, stopping it. Her face was red with anger that she had never seen there before.
The diminutive elder creased her brow and shook her head. "LISTEN child. Don't you hear it. Do you even know what you almost did?"
Shampoo frowned and listened as her great-grandmother had told her to do. It didn't take long for her to figure out what the elder meant and she paled. "Is..is baby no?"
The elder nodded sagely. "Thankfully I stopped you child. You know the penalties for killing a baby and worse yet, killing a mother protecting her child. That is why she did not want to fight. She had her baby with her Shampoo. Have you learned nothing in our village? No matter, we owe her safe passage in our lands and a few favors thanks to your rash actions unless you'd like for her to take this case for judgment by the elders."
Shampoo paled and shook her head. "No, we treat her good."
The elder nodded and turned to Ranma who was getting up. The elderly woman could see the grace of the red-head's movements and the strength hidden within the tiny frame. She shook her head and smiled. Maybe it was a good thing that her great-granddaughter had not had to fight this outsider as she was certain the outsider would have won. What puzzled and worried the elder though was the exceptionally heavy yang ki in the tiny girl and the fact that she showed no signs of childbirth from what she could sense. Talking with the child would clear up some things.
"Child I must apologize for my great-granddaughter. She acted rashly. It is a sin in this village to attack one with a child. We shall therefore treat you to dinner in our hut. Come with us." Ranma blinked a couple of times before shrugging and following the elder and the purple-haired girl.
She didn't even notice her father being hit back and forth between Amazon's with pointy sticks. #Ranma stop wandering off and help your father!#
"Uh, so who are ya?" The elder shook her head at the red-head's speech.
"Kuh Lon but you would probably pronounce it Cologne. And who are you child?"
Ranma smiled. "Ranma Saotome, heir of Anything Goes Martial Arts."
Cologne had to hold back a chuckle when she heard that. Oh what would old Happi have done if he found out the heir to his school was a girl. She really liked this girl now. Any woman who could take over as the heir to Happi's school was a either the ultimate pervert or possibly one of the strongest woman she'd likely ever meet. Since this girl seemed to have no overly perverse reactions to the rather voluptuous women and strapping young men in the village, then she was probably the latter. Cologne smiled as the males brought in the post-competition feast as the one by the log had been destroyed.
Ranma had to admit that the spread was good. Chicken, ramen, pork buns, some sort of soup, fresh fruits, and bread were all served in a large buffet. She would have dived into it if the elder didn't stop her by hitting her hands with her cane.
When they had finished the meal, the baby started wailing. Ranma tried cooing and making funny faces but the baby wouldn't stop crying. "She's hungry."
Ranma blinked and looked back at the elder. "Huh?"
Cologne nodded her head sagely. "You've never had a child have you?" Ranma nodded. "How did you happen upon this child then? She seems to respond to you and you seem to sooth her."
Ranma explained how she found the woman and how she made Ranma promise to take care of her child. Cologne nodded sagely and left the room. When she had returned, she had a small vile in her hand. "The problem with a child this young is that she cannot eat the food we do. Even ground up. I have a potion here that will help you with that. If you drink it, then you will be able to feed your child properly."
Ranma looked at the vial warily and then back at Cologne. "Uh, can't you take the kid and feed her or something."
Cologne frowned and bopped Ranma on the head. "Ranma, this child is attached to you and besides that you swore to look after her. Will you go back on your promise?"
Ranma shook her head. "No. A true martial artist never goes back on his word."
Ranma took the potion out of Cologne's hand and drank it in one go. It was kind of refreshing. Ranma waited a few moments but she didn't really note a difference until her chest felt tight and the front of her shirt was straining. She unbuttoned her shirt to find that her breasts had grown larger and some kind of liquid was oozing out from the tips. "What the heck is this?"
The elder noted the panic in Ranma's eyes. She was surprised that the child didn't know how to feed a child, but to not understand her own body. Oh well, it could wait til the child was fed. It's wails were growing even louder and higher in pitch. She deftly removed the cloth from the child to reveal something that shocked her. The child had a tail and ears like that of a squirrel. It was a Musk child, but Ranma had said the mother was Japanese. More and more questions were coming to the elder but they would have to wait.
Cologne pushed the child into Ranma's arms. "What are ya doin ya old..."
Ranma didn't finish as the baby found it's target and latched on. Ranma's eyes widened and then glazed over as the child began to feed. "Great-grandmother, that Musk baby, is not? They need to go. We no want trouble."
Cologne nodded her head. "We still owe her a debt, but you are right. They cannot stay in the village. I doubt the Musk are after this child though. The Musk would have been on her long before she reached the village and would have taken both her and the child for breeding stock if they had been looking for this child and her mother. No, I can tell the baby is of one of the lower caste clans in the Musk and that it is female. No, they only value the male children enough to look for them should they go missing."
Shampoo moved around Ranma to look at the baby feed. "OOH, is too too cute though. Shampoo want to have baby. It look like Ranma really enjoy this yes."
Cologne shook her head. "Why are you insisting on speaking Japanese when you sound like a twit? Ranma isn't with us at the moment so talk in Chinese."
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Ranma awoke slowly with light hitting her eyes. It was strange. No water, no kick out of bed, maybe this was a dream. She yawned, looked down, and blinked. She was dressed in clothes similar to those that Shampoo girl was wearing the other day. "I see you are finally awake child. I have many questions but I believe you will have to deal with another feeding before that. Your baby is quite hungry."
Ranma's eyes flew open as she remembered the nightmare from the other night. She crossed her fingers and shook her head. "Uh uh, ain't no way I'm doing that again! What the hell was that..."
She didn't finish as she found something latched onto her. She looked down to see the baby from the night before latched onto her chest and suckling away. She started to grab for the child to remove it, but a cane wrapped her hands. "Whatcha do that for ya old ghoul!"
Cologne laughed and shook her head. "Let the child feed. You don't seem to be in shock and it isn't harming you. Your child needs the food you provide for her."
Ranma blinked. "She's sucking the food outta me?"
Cologne raised an eyebrow and sat down on a pillow. "Yes Ranma, babies get food from their mother which is produced in the breasts. They are there for more than a show for males you know. Hasn't your mother ever explained the facts of life to you?"
Ranma shook her head. "Uh well, I don't really remember mom. Pops said she's dead so I guess I'll never know. What are the facts of life anyways? They some kind of martial arts philosophy or something?"
Cologne's expression was stern after that comment. "So, your foolish father has taught you nothing of your body then? I wondered why you had no supporting undergarments."
Ranma looked curiously at Cologne. "No, pops taught me a lot 'bout the body: how to build up ki, weak points in the body, pressure points, and a lot of other stuff in the Art."
Cologne shook her head. This is just what she'd expect from a student of Happi's school. Keep a woman ignorant and you could do whatever you want with them. She shuddered at the thought of this child possibly being raised by one of Happi's students to be his 'plaything'. She would rectify that immediately. "Ranma, I'm going to tell you the facts of life and a woman's roll in them. Now a woman..."
XxxxxxxxxxxxxxxxxxxxxxxX
A rather pale Ranma was following Cologne as she pogoed towards a sty where the Amazon's kept their pigs. "Ah, here is your pet panda. I'm afraid we had to cage it and put a watch on it as it was rather unruly."
Ranma slowly turned her head to see a beaten up panda laying in a cage on a mud floor. It stirred at the sight of Ranma and pulled out a sign. #Boy, get me outta here now!# flip #Those crazy women are gonna kill me!#
Ranma frowned and let her anger rise to the surface. "This is your fault old man! Who was the one who insisted on coming to this village; who was the one who insisted on going to Jusenkyo; and who was the one who decided teach me the Neko-ken? Huh, old man! I should just let them take that prize ya ate outta your hide!"
A few things clicked in Cologne's mind at that moment. "Oh dear."
She turned to one of the guards while Ranma kept yelling at her father and spoke in Chinese. [Get me two pales of hot water.]
Cologne then pogoed next to Ranma and whacked her on the head. "Ow, why'd ya do that old ghoul?"
Cologne shook her head. "Berating the fool will get you nowhere child. If half of what I heard is true, then we have some more things to discuss. Although, I admit that it should have been obvious to me."
The Amazon guard that had left returned with two steaming pales of water. Cologne tossed the first over the panda. He immediately turned into a fat, balding man. "Yeow, not that hot woman!"
Cologne whacked the fat man over the head. "Be glad I do not skin you alive fool! You stole our food, you took your child to Jusenkyo, and you taught your child the Neko-Ken. The only thing keeping me from killing you is that your child would most likely not agree with that."
Genma paled and turned to Ranma. "Boy get me outta here! We need to leave. And why the hell are you in that weak, girly form! Change back."
Genma reached for the other pale of hot water through the wooden bars and threw the hot water into Ranma's face. Genma and Ranma blinked as Ranma didn't change. Cologne sighed. "Come Ranma, I need to tell you some things..."
XxxxxxxxxxxxxxxxxxxxxxX
Two months later...
A red-haired girl was walking down a quiet street in a small town. She wore a red Chinese shirt and black kung fu pants and had a sleeping baby strapped to her front in a leather carrier. The few people who were around stared as she passed, not because she was a beauty but rather because of the large panda following her. "I guess having a place to stay for awhile will be good for Hitomi."
The panda held up a sign. #Yes# flip #I'm sure Noboyuki will let us stay at his house for awhile.# flip #He was fairly well off due to his building design firm.# flip #I'm sure he'd be delighted to see us.#
Ranma's eyes narrowed. They rarely, if ever, stayed in one spot for too long. Her father hightailing it back to Japan just to go to this friend's house had to mean something. Given that her father said he was well off, that most likely meant they'd be mooching off of him. There had to be something else though. "Yeah, well what was with the rush? Ya never rushed anywhere unless it's ta feed your belly. And since when did you care about Hitomi?"
The panda quickly flipped through some signs and pulled out one that he thought would work. #Don't talk back to your old man boy!# flip #I'm certain old Noboyuki will let us stay.#
Ranma narrowed her eyes. "Yeah, whatever old man. If this is some guy you owe something to and he tries to hurt Hitomi, then what I did to you after that crap you pulled in Shanghai with Hitomi is gonna seem like heaven compared ta the hell I'll put ya through."
The panda shuddered at that thought. The boy had become more willful after the Amazons had talked to him for a couple of days. He was just lucky the boy still had enough honor in him to follow him. And Shanghai... He shuddered again. Now the worthless boy was a weak, worthless girl and looked to be staying that way if what the Amazons had told them was true. He should have been taking the boy to Soun to marry him off to one of the Tendo's daughters, but no he had to become a girl. He was thankful he had this backup engagement for if he had a daughter. He had to get the boy married off before his wife found out what had happened. If she found out before he could marry the boy off, then he'd try the grandchild card and see if she bought it. He'd have to make sure that Ranma's new fiance understood the importance of taking care of him in his 'old age'.
#This way boy.# The panda looked around. When he was pondering, the boy had ran off.
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Ranma had noted that Genma was distracted for a moment and decided to use that time to make a split for it. She'd go to this Noboyuki's house and meet them, but she wanted to know the lay of the land in case she needed to make a quick exit with Hitomi.
The town wasn't too big and appeared to have mostly residents surrounding a central market street. She could see a Yamada's grocery and convenience store, a small bookstore, and … an ice cream shop! She ran over to the ice cream shop and opened the door. The only person there at the time was a boy manning the counter. She smiled as she knew exactly what to do. She carefully set Hitomi down on a table close to the counter and within her field of vision. She sashayed up to the counter and caught the attention of the boy at the counter. "Hey there handsome, got some chocolate ice cream."
The boys jaw almost dropped at the beauty in front of him. She was short but had a beautiful face and a rather prominent rack that she was pushing out towards him. He gulped. "Y-e-yess."
Ranma smiled and pouted her lips. "Maybe you could give me two scoops. Can ya do that big boy?"
"Uh-uh, s-s-su-sure. How about a sundae?" He was sweating and trying not to stare as she leaned over the counter.
"But I don't have enough money for that..." Ranma pouted and smiled internally as she saw that this was the clincher.
"Uh, on the house." Ranma nodded and the boy quickly got to work. He handed an abnormally large banana split with chocolate and vanilla ice cream to Ranma.
"Thanks." Ranma laughed inside. _Sucker._ Sure the curse had been bad at first and the first month stuck this way was as close to hell as she wanted to get but it did come with perks. If she was lucky, she could find some way to unlock herself. She had learned the hard way that Hitomi came first. She'd never let some fake cure or some bullshit story her father cooked up separate them again.
Ranma dug into the ice cream with her usual gusto and finished it in under a minute. She was considering going back for another bowl when Hitomi woke up and let her know it was feeding time. "All right Hitomi. Hold on, I gotta get the towel."
Ranma reached into her hidden weapons space and pulled out a towel to cover herself as she fed Hitomi. She had to thank Mousse for showing her how to do that sometime.
The bell of the shop rang and two figures walked in. "Mihoshi, we need to go on patrol. We can get it after we finish."
Ranma looked over to see a woman with green hair berating a tanned blonde. The blonde seemed to ignore the green-haired woman as she bounced over to the counter. The boy at the counter could be seen with his head bouncing up and down in time with the blonde. "Three sundaes please."
The boy at the counter seemed to get a goofy grin on his face and drool some. "Uh, sure. How about four for the price of two? You can take the extra one to the lady with the red hair."
Ranma cursed the boy for putting their attention on her. She wasn't sure what it was but she was getting some odd vibes from the two women that had entered the shop. She smirked though when she saw the disappointed look on the teenager's face when he saw her feeding her child under a blanket. The blonde bounced over to her table with two ice cream sundaes while followed by the grumbling green-haired woman carrying the other two. The blonde got up in Ranma's face as she sat down. "Hey, I've never seen you around here. Oooh, is that a baby? Can I see?"
Ranma was about to smack the blonde away when the green-haired woman grabbed her by the ear and pulled her back. "Mihoshi! She's feeding the baby right now. I think you should let her be." She then turned to Ranma. "I'm sorry about that miss. My partner doesn't really think sometimes. I'm Kiyone Makibi by the way and the ditz here is Mihoshi Kuramitsu."
The blonde waved like a crazy person to Ranma. Ranma shook her head. There was nothing wrong... well nothing dangerous about these two yet so maybe that feeling she was having was just telling her that the blonde was crazy or something. "Yeah, I'm Ranma Saotome and this is my daughter, Hitomi."
Kiyone's eyes widened a bit when Ranma brought her daughter out from under the blanket. This didn't go unnoticed by Ranma. "Oooh, she's so cute."
Mihoshi tickled under Hitomi's chin before Ranma could stop her. The baby giggled as she did so. "Huh, guess she likes you."
Kiyone frowned as she watched the byplay between her partner, Ranma, and the baby. It was obvious that the child wasn't human which meant that the child and her mother probably shouldn't be on Earth. "Excuse me, but are you from 'out of town'? I'll need to see some identification."
Ranma narrowed her eyes. She unfortunately didn't have any identification thanks to her father, but what worried her more was the way the woman looked at her child. "No, you can thank my father for that. He also dragged me here for some reason."
Kiyone put a hand on Ranma's shoulder and was going to suggest that they move to a different location so she could question the girl when Ranma threw off her hand and stood up. "I think I should be goin'."
Ranma backed out the door as she put Hitomi in her carrier and strapped it on. She quickly set off down the street with the intention of getting out of town. She started heading for the hilly forested area to the east as it would provide the most cover and a route of escape. She rounded another corner only to face Kiyone and a gasping Mihoshi. "Ki-yoneeeeeeeeeee! Why did we have to run?"
Ranma backed away from the duo. While she didn't see anything to indicate that these two were master martial artists, they had to have had some training to figure out where she was going and outpace her there. She'd have to turn it up a notch. "Listen we need to talk to you privately if possible. You may not be in trouble, but we'd like to find out how you got here."
Ranma sized the woman up. She could probably beat her but it might hurt Hitomi. She'd still be better off outrunning them. "And why should I trust you?"
The green-haired woman looked around the empty street before pulling out some kind of flashy badge with the letters GP on it. "We're officers with the Galaxy Police ma'am. We simply want to find out why you're on a restricted world. Official visits are supposed to be documented and planned with resident officers beforehand."
Ranma looked at Kiyone like she had a screw loose. "Huh? Never heard of no Galaxy Police before. And what are you talking about restricted world? That some kind of zoo or something?"
Kiyone had a puzzle in front of her. This girl had a child that obviously wasn't fully human, but claimed to know nothing of the GP. She pulled out a scanner that Washu had made for her and hit a few buttons. She noted that the girl tensed some as the scan started. The results only added more questions. The child was human which was odd as the scan showed that the non-human appendages were real. The scan also showed that the baby was not her child but the girl showed signs of a recent pregnancy. The girl also showed up as human but the ambient energy radiating from her was anything but human. The scan was telling her that the girl's energy was equivalent to a young Juraian tree.
Kiyone looked up from the scan to see the girl crouching down some. "Uh, look, Ranma. Could we just talk somewhere less public?"
Kiyone patted herself on the back mentally as Ranma seemed to relax until Mihoshi ruined the moment. The blonde had been toying around with her cube again as she wanted to get some of her stuffed animals out of her subspace storage to show the baby when her gun fell out and went off. Kiyone could only watch in horror as the beam seemed to make a bee-line for the baby only to see Ranma disappear and reappear on top of a roof before bounding off towards the east by jumping to the next building.
Kiyone turned back to her partner and was going to chew her out only to find the blonde crying and apologizing. She sighed and patted her on the back. "Come on. We've got to catch her and find out what's going on here."
Ranma sighed as she realized that she had given the duo the slip. The problem was that she now didn't know where she was. She jumped to the top branch of a tree and looked around. She was outside of town and the only thing she could see was a temple on top of the mountain nearest her and a house surrounded by fields not far from it. She could head off into the woods and disappear, but she didn't know what to do after that. Her father would come looking for her eventually and drag her back. She also had to worry about Hitomi. She weighed her options and headed for the temple.
Genma let out a contented sigh as he had found some hot water at a ramen shop. He was also happy that the owner didn't call the police when he barged in as a panda. He was about to swipe some buns off of a patron's plate as he passed by when he heard someone call his name. "Genma, is that you?"
He turned around and smiled as he saw the very man he had come here for. Noboyuki stood in the door of the ramen shop and walked over to him. "It is you, you old dog? How is Nodoka doing?"
Genma laughed nervously and motioned for his friend to take a seat as he sat down. "Good. Actually, I came hear for a reason. You remember our pact awhile back, the one we made when you, Achika, Nodoka, and I met at the Three Dragons bar."
Noboyuki nodded as he grabbed a menu. "Yeah, actually I do. We signed a contract stating that if you had a daughter, then she'd marry our son." He paused in his perusing of the menu and lowered it as a shit eating grin came across his face. "You're here with her now aren't you. Is she a looker? Where is she?"
Genma smiled as he knew he had his friend's support. "Oh she's a looker alright." He pulled out a photo and handed it to Noboyuki. "Lost her in town a little bit ago but she should be around here somewhere."
Noboyuki almost drooled looking at the picture. She put Ayeka and Ryoko to shame with her looks. He looked closer though as he noted something. "Old friend does she have a baby?"
Genma blinked and looked at the photo. He cursed to himself as he had handed the only one he had with the baby in the picture to his friend. He needed to think fast. "She adopted the child in China. She apparently found some woman dying in the woods and promised the woman to take care of the child as her own as it was the mother's dying wish."
Noboyuki teared up at the sob story. This girl was a perfect choice for Tenchi. She was beautiful and best of all caring and sweet unlike two alien women. "Tell you what old friend. Ramen and buns on me. Heck I'll throw in two beers."
Genma wanted to cry and hug the man. He was so easy to manipulate.
XxxxxxxxxxxxxxxxxxxxxxxxxxxxX
Ranma dug some wax out of her ear as she entered the shrine grounds and looked it over before flicking it off. She was going to look for the priest to ask for some room for the night when Hitomi started squirming and bawling. The smell also gave away the problem. "Aww dang it Hitomi! You had ta reach your limit right now didn't ya. Guess I gotta clean ya up."
Ranma reached into subspace and pulled out what Cologne had lovingly called her 'Motherly Load'. This translated to an old leather bag that she had given Ranma with various powders, towels, and cloth diapers for her baby. She found a flat stone and laid out the cleaning blanket. She gently put Hitomi down on top of it and removed the soiled garments. She placed the diaper into a special pouch of the bag that was supposed to ward off odors and proceeded to wipe off any extra mess before applying the drying and cleansing powders Cologne had shown her to use. Hitomi giggled as the powders were applied and squirmed around as Ranma tried to pin a new diaper on her. When she was finished, she reloaded the bag and slipped it into her subspace pocket.
She picked up Hitomi before sighing and turning towards the temple. "C'mon out old man. I know you're there."
An elderly priest fully opened the back door to the temple while chuckling. "You have sharp senses miss. I'm the priest of this shrine, Katsuhito Masaki."
Ranma looked the man over. "Uh yeah, I'm Ranma Saotome. Pleasure ta meet you I guess."
The amusement never left the old man's eyes as he walked over to Ranma. "I'm sure. I must say though. Aren't you a little young to have a child."
Ranma didn't take up a guarded stance but she did tighten her muscles a bit. The man was skilled to have barely registered on her senses before. "Well, I kinda adopted her. Her mother died in my arms asking me ta take care of her child so I couldn't refuse that could I?"
The old priest nodded sagely. "A noble goal for one so young. Did her mother have the same ears and tail as she does?"
Ranma automatically tensed at that. The last priest that asked a question like that had tried to 'exorcise' the both of them with purifying arrows. She didn't want a repeat of that. The old man seemed to catch on though and waved his hand. "I mean you and your child no harm. I am just curious."
Ranma loosened up and eyed the man over. "No, but Elder Cologne told me that the Musk tend to have them. She said something about Hitomi's mother just being in the wrong place at the wrong time."
Ranma felt something waver in the elderly man before he spoke. "And these 'Musk', how do they get their women exactly?"
"Uh, they either catch any woman they come across or turn animals into women. That's what Cologne told me. She said I was lucky I didn't get caught by one of their patrols or I woulda been poppin' out their kids right now. They live adjacent to the Amazons and the Phoenix people in China." Katsuhito noticed her shudder at the mention of 'poppin' out their kids'. He had a sinking feeling as he knew what that meant.
He seemed to contemplate what she said for a minute before before nodding. "And what of the Amazons and the Phoenix people?"
"The Amazons are female warriors. They kinda took me in for a little while after we sorted out the problem with pop stealing their prize feast. They got a ton of cool secret techniques although they only showed me a couple cuz I'm an ally or something. Don't know much about the Phoenix people. Cologne said they got wings coming out of their backs and can fly. They got talons for hands and feet and they don't like humans much cuz they usually kill humans on sight. Said they evolved from birds or something."
The elderly priest studied the enigma before him. The girl was obviously human but the child and possibly the Musk and Phoenix people she was talking about were not. This also brought up the question of how these non-humans came to be on this planet and why no one knew about them. The other issue was the power radiating off the girl. It was not Juraian but she was no push over. "Hmm. While I would like to claim this shrine to be the most hospitable in Japan, it is no place for a young mother and her child to hang around as they talk to an old man. Why don't we go to my grandson's house down the hill to talk and have something to eat?"
Katsuhito had Ranma hooked the second he said 'eat'.
"Old friend, we've been around most of the town looking for your daughter. Are you sure she didn't run away?"
Genma nodded his head. The problem was that nobody seemed to have noticed where she went. He was proud that she could hide her presence but annoyed that they were having trouble finding her. He was sure the boy wouldn't shirk his duties, even as a weak girl... though he had become willful after the Amazons and the Shanghai incident. He was going to suggest a different tactic until he literally ran into someone.
The blonde blur had come around the corner and managed to entangle herself in his limbs. He looked up to see some blonde foreigner trying to extract herself from him. "Dammit woman, get off of me!"
The blonde teared up and he could feel his annoyance building until he heard his friend's voice. "Mihoshi, you need to stop running into people. I'm sorry sir, my partner doesn't know any better."
The other woman stuck out her hand and helped him to his feet. He was about to say something, but Noboyuki beat him to it. "Mihoshi, Kiyone. It's great seeing you like this! Can you help us? We're looking for Genma's daughter. Hey Genma, show them her picture. These two are police officers and I'm sure they can help."
Before Kiyone could protest, Genma eyed the two warily before reaching into his gi and pulling out the picture he had shown Noboyuki. Kiyone's eyes widened before she looked back at the two men. "Uh, why are you looking for her?"
Noboyuki smiled. "She's Tenchi's fiance."
5. Chapter 5: Tenchi cross
Chapter 1
Ranma cracked his neck as he tracked up the hill to the shrine in the brochure. Sure some wonky wish granting tree seemed far-fetched but he wasn't about to pass up this opportunity even if it was a hoax. Beside the flier promoting the tree, he had a scrap of paper with a boy holding up a kendo trophy. _If the tree doesn't pan out, then maybe I can learn their martial arts style or something. Hope its not just kendo stuff though._
He tucked the posters into his pack as he approached the crest of the hill and blinked before looking at the valley before him. It was filled with plowed fields, a house, and a pond with a huge tree in the middle. He could also make out a shrine on the next hill. He had to admit it was quite beautiful and, thanks to him giving the slip to the fruitcakes back in Nerima, he had it all to himself.
He walked up to the house first and knocked the door. "Yo, anybody here?"
He was greeted by dead silence and shrugged his shoulders. He then went around to the stone steps and hopped up a flight of stairs at a time until he reached the top. Again, there was no one there to greet him. "Huh? Maybe they're on vacation or somethin'. Well, I guess I could hang around the place and camp out until they get back. Ain't like I came all this way for nothin'."
Ranma hopped back down the steps and walked towards the tree surrounded by the pond. It had a knot and ofuda tied around it and it resembled the tree from the poster. Might as well make his wish. He hopped on top of the stones to get to it but one was wet. He slipped off and fell in the pool. A soggy, well-endowed red-haired girl pulled her self up and started wringing out her shirt while cursing. She pulled up to the small island the tree was on and stood before it. "Hmm. Uh, I wish I wasn't a girl no more. Well that didn't work. Figures the damn poster wasn't right. Ya really do look like one 'a those magic type trees though. Don't suppose ya could get me outta the engagements or just do somethin that could help me out could ya."
Ranma was about to turn and leave when she thought she felt something... probing her ki? She turned and just stared as the tree seemed to dance with lots of little ki lights. She felt like it was saying something like 'Who, who, who?' She felt kind of strange answering but _eh what the heck, why not?_ "Ranma Saotome, heir of the Anything Goes School of Martial Arts."
The lights lessened but the feelings became more pronounced. 'Welcome, welcome. Come, come.' Ranma shrugged her shoulders and went back to the tree. "Uh, so, ya gonna help me?"
The tree seemed to pause for a moment before glowing again and scanning Ranma's ki once more. 'Yes, yes. Take, take.' Ranma was about to ask what that meant when something hit her in the head. "Hey, what the heck was that for?!"
'Take, take.' Ranma frowned and looked for what hit her. It was a necklace with a caged pendant at the end. She held it up to eye level and saw a purple seed the size of a pea floating in the cage. 'Help, help. Wear, wear.'
Ranma looked sceptically at it. How was a seed supposed to help out. _Not like it would hurt nothin anyways. _Ranma put the necklace on and felt something ripple along her ki. Then nothing. She shrugged her shoulders and walked towards the shore while shaking her head. Like a seed would change her life.
Ranma then heard screaming and looked around for the threat only to get beaned in the head by a bicycle before blacking out.
XxxxxxxxxxxxxxxxxxxxxX
Ranma felt herself being dragged and groaned to herself when she remembered a bike hitting her in the head. _Shit, how did Shampoo find me already? I lost her in Sapporo damn it. Time to break and get out of here._ Ranma's eyes flew open and she tried to twist out of whoever was holding her only for the person to trip and end up in a tangled mess with the person. She could feel something squeezing her breasts. Wait, someone was squeezing her breasts!
She shot straight up which threw off the person on top of her. She turned on the person to find.. a kid prostrating himself before her. "I'm sorry, I'm sorry. Please don't hurt me!"
Ranma let out a huff. It was only some wimpy little 14-15 year old guy that was maybe a step up from Gosunkugi on the athletics department. He had short black hair and was maybe only as tall as her girl form. She rolled her eyes at his antics thinking back to how Mr. Tendo and pops would prostrate themselves before the 'Dreaded Master'. "Yo kid, get up. You're making a fool of yourself. Just tell me why ya were draggin me off."
The kid bowed again. "I'm sorry! I sort of went out of control and my bike hit you while I was trying to get here. Uh, have you seen Tenchi? I wanted to talk to him."
Ranma raised an eyebrow. Tenchi was the name of the guy that won that kendo tournament. "Nope. Don't live here either so I don't know when he'll be back. Name's Ranma by the way."
The boys eyes widened and he hit himself in the head. "Oh, I knew I should have called or asked Airi. Stupid, stupid."
Ranma raised an eyebrow as he hit himself in the head. Eh, what was one more nutcase in her life. "Yeah, so you know Tenchi. I came here to see the shrine and ask about martial arts. Ya wouldn't happen to know anythin about their style would ya?"
The boy seemed to collect himself and face Ranma before the boy had one of those epiphany moments. "Oh right, I didn't introduce myself. I'm Seina Yamada. Pleased to meet you Ranma."
Ranma watched him stick out a hand and sighed. She shook it and tried to remind him of her question. "Uh, shrine, martial arts, whaddya know about that stuff?"
The answer never came as three people suddenly became visible. They were all wearing what Ranma remembered as something called 'pirate costumes'. She had only seen them on Halloween when some errant trick 'or' treat martial artist came by and was soundly beaten just by uttering the word 'Boo' to him. It was pretty pathetic. She did however note that one of the men looked like that tiger Musk warrior except a little hairier. "Seina Yamada, this is the end! You have no one to support you. We've put out a communications block and several of our hide'n'go seek ships are distracting your crew. You're at our mercy. Mwahahahah!"
Ranma looked at the guy with an eyepatch and shook her head. Really? This was just pathetic. None of them had any ki to speak of and they honestly thought they could attack them and win. Ranma looked over and saw Seina shaking in fear. _Great, I guess I gotta uphold the code, but these guys ain't worth it._ "Why don't you leave now before I have to hurt'cha? I mean, what's the point of beating up on a defenseless kid like this?"
The three men in the pirate costumes looked at her like she was crazy. The one with the eye patch pulled out a light-saber and said, "Forget the bitch and get Seina."
That cry seemed to break the others out of their stupor as they charged Seina only to be sent sailing as a foot impacted each of their faces. "Ya know, ya shoulda listened. Why don't ya get going?"
Ranma cracked her neck and looked down at the unconscious men. "That was a waste. Didn't even break a sweat. Ya okay kid."
Seina just nodded. "Right. Look, I'm going to another temple to the south of here to check out their training routine. I'll be back here in one or two days so could ya tell the priest and his grandson that I'll be back sometime soon. Need ta talk to him about training and that talking tree they've got in the pond. See ya."
Seina watched as the girl bounded away. "That was strange. Maybe she's another of Tenchi's girlfriends."
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Ranma grumbled as she set up her camp stove to heat some water. It had been two days of nonstop rain on her way to the Daito temple only to find that it had been turned into a tourist trap. The only 'martial artist' there was a balding fat man that was a little too grabby and was below even Akane's level. She sighed as she took the whistling kettle off the stove. It was very hot but at this point she didn't care. She needed to be male again after two straight days of being female. She emptied the water over her head and screamed. _Okay, dumb idea, but I'm a man again._
Ranma got up to grab some noodles to use the rest of the hot water on when he felt a weight on his chest. He looked down. "Crap! Not again."
Ranma sighed as she pulled out a packet of noodles and set it into the leftover hot water. She sat there grumbling to herself. "Damn curse. What was it this time? Wasn't that Daito temple for sure. Nothin on the way there. Pirate guys did nothing. THE TREE."
Ranma's eyes widened as she grabbed the necklace and tried to pull it off only to find that she couldn't do it. "Nuts. Well, I was gonna go talk to the priest anyways."
XxxxxxxxxxxxxxxxxxxxxxxxxX
Katsuhito was sweeping off the back keep of the shrine when he heard the bushes rustle. He stopped sweeping in time to see a red-haired girl exit the forest in front of him. "You know, most people use the stairs dear."
Ranma lifted her head and looked a little sheepish. "Uh, I kinda lost my way. Is this the Masaki shrine?"
Katsuhito smiled. It wasn't every day that a beautiful young girl visited his shrine, except for Tenchi's 'girlfriends'. He had to chuckle at that. His grandson would figure it out eventually. "Yes. What brings you here Miss...?"
"Ranma, Ranma Saotome. Uh, did that Seina kid tell you I was coming?"
Katsuhito thought for a moment. He remembered Seina visiting a couple of days ago. He also remembered him going on about some girl beating up three space pirates and then bounding off into the woods. He needed to word this right. "Hmm, he said something about a girl beating up some thugs that were after him."
Ranma nodded. "Yeah, that was me. Don't know about thugs though. They went down with a single kick. Pretty pathetic."
The older priest raised an eyebrow at that. They were fairly weak pirates but they still had body enhancements. A normal earthling would have had more trouble taking such opponents down. "Really? I would not expect such a young lady to be so strong."
Tic marks formed on Ranma's brow as she ground out. "Yeah, but I'm a trained martial artist."
Katsuhito looked thoughtful at that statement. The girl must have been truly skilled to beat anyone with body enhancements. It was time to see what she was here for and find out more about her. "So Miss Saotome, what brings you to my shrine?"
Ranma snapped her fingers and looked the priest in the eye. "Ya gotta help me fix this problem your dang wishing tree caused. Maybe you can talk to it better than I can. It just kept spoutin out single phrases and stuff."
Katsuhito's eyebrow's shot into his hairline. Funaho had... talked to the girl. "Um, what did it say?"
Ranma huffed as she tried to remember. "It kept saying welcome, help, take, and wear." Ranma pulled out a chain with a little purple seed on the end and continued, "It then gave me this thing. Whatever it is. It won't come offa me at all. Can ya take this necklace off?"
The old priest's eyes widened more at what the girl was holding up. It was a Juraian seed. He didn't know why Funaho had given it to this girl but it certainly complicated things. "You can't take it off?"
Ranma nodded her head. "So can you get it off?"
Katsuhito looked down at the seed and sighed. There was one possible reason why she couldn't remove it. He needed to test it. "I'll try."
He reached down to grab it but the girl's hand shot out and twisted his hand away forcefully. He had to admit she had a good grip. "I see."
Ranma looked at her own hand and frowned. She had unconsciously protected the damn thing. This didn't bode well. "Uh, sorry?"
Katsuhito pulled his hand back after she released it and shook his head. "No apology needed. I feared as much. I'm afraid that seed will stay with you for the rest of your life."
Ranma's eyes widened. "What?!"
The priest shook his head. Another house guest. He then chuckled to himself. _A rather fine house guest._ "Follow me. We need to go to the house to discuss this."
Ranma grumbled as she followed the priest around the shrine and down the steps.
XxxxxxxxxxxxxxxxxxxxxxxX
This is not a fic where Ranma gets stuck as a girl if I continue this. I'm not really sure when or if I'll get to any of these ideas, but que sera, sera.
6. Chapter 6: Senshi Vacation
**Senshi Vacation**
I do not own Sailor Moon or Ranma ½. This is just a parody made from sweat, tears, and slight amount of inebriation. I'm not really sure where I was going with this, but it's another one of my non sequiturs. It's a 'sort of' fuku fic so don't complain when you finish this.
** X**
Pluto had been scouring the time stream looking for any problems in the next two weeks. Her princess had been very clear about the importance of this mission. The time senshi half dreaded and half desired the upcoming mission but she had to be sure that nothing would go wrong. After a number of calculations and double checking, she let out a sigh of relief and proceeded to lock down the gate and teleport back to earth. She left just in time to miss a small divergence in the timeline.
** X**
Usagi was pacing the floor in Rei's shrine while Rei watched her with a tick in her eye.
"Usagi would you please stop pacing. Your going to wear a hole in my floor."
Usagi stopped for a second. "I know but I wish she would hurry up. Everyone else is packed and ready to go. She needs to hurry up. We've been planning this for a long time and I'm starting to regret that we invited everyone for it."
A new voice joined the conversation, "Oh really princess! You were the one whining the most about everyone going on this trip. Don't worry though. I thoroughly checked the time gates and didn't see anything for the next two weeks."
Usagi's eyes lit up at this statement. "Two weeks of fun and sun, whoo-hoo! I just know we'll have fun in Hawaii."
The three girls left the shrine and headed down the path to meet their friends. The next step was to hit the airport and forget their troubles in Juuban.
** X**
"Master, we have confirmation that they have left."
A dark figure stood up in front of the pudgy boy with a lot of pimples. "Good, good. Proceed with the plans. Tell Cairn to lock Nerima down with a time loop and isolate Japan with the last of the temporal shielding crystals. We won't be able to make any other time and space adjustments beyond those given our limited supplies. I also want the rest of the troops to speed up the recovery of the stones, especially the pure one. Having another crystal like the Ginzuisho just floating in the wind is unsettling to me."
** X**
In Nerima...
Ranma had been really pressed after his failed wedding attempt. Shampoo kept pouring love potions into his food, Mousse pressed on even harder, Akane started cooking more, etc. He just couldn't take it anymore but he didn't know what to do. He was currently walking on a fence in the Harajuku area when he noticed something shiny on the ground. Curiosity got the better of him and he hopped down to get a better look.
Of course he somehow missed the puddle of water on the ground. After splashing down in the puddle, she let out an unhappy grunt. "Damn water!"
She then shrugged her shoulders and bent over to see what had been glinting in the sun. It was some kind of large crystal. It was clear, as big as her fist, and shone with an almost inner light. Normally Ranma wouldn't bother with something like this, but a thought came to her. _I wonder if Akane would like this stone. Maybe she'll forgive me for whatever it is I've been doing wrong._
Ranma bent over and picked up the stone. It felt warm in her hand, almost like a living animal. She didn't notice that it started to take on a light blue cast as she stuck it in her pocket.
**XxxxxxxxxX**
A toad-like man with green eyes and slicked back hair bowed before a large figure cast in shadow. "Master, I have sealed Nerima with the time-loop barrier. An old gnome-like creature almost got out but for some reason turned back and went after some clothes on a clothesline. Other than that, the operation went off without a hitch."
The dark figure smiled beneath a black hood. "Good, good Cairn. Now nothing can stop us from our goal. I'm most pleased with your work. Go, rest in the lounge. There are cookies and tea there for you. My voodoo apprentice is there as well. Talk over strategies with him while I consult the book for more insight into preparing our inevitable defense against the Senshi once they have realized what we have done."
Cairn bowed once more. "Master is most gracious."
Once the minion was gone the Master looked around and pulled a book out from under his seat, the title read: 'Being a Villain for Dummies: How to Make Sure You're Evil Plots Don't go to Pot.'
**XxxxxxxxX**
Ranma was whistling as she walked back to Nerima. Maybe a simple gift was enough to sort out all of the mess back home. _I hope Akane likes this, although I'm not sure what..._ "Owww!"
Ranma's head smacked against some type of invisible force field. Ranma rubbed her nose and proceeded to flick the space in front of her. It was like a ripple on a lake formed in front of her. "The hell."
Ranma tried punching the space in front of her only to have her blow deflected along the invisible barrier. "Huh? Doesn't feel like ki. Somebody playing around with magic again?"
Ranma sat in thought for a minute before snapping her fingers. "Got it!"
Ranma stood before the barrier and closed her eyes. When she opened them, she hit the barrier with hundreds of strikes yelling out, "Kachu Tenshin Amaguriken!"
Ranma was rewarded by a warping of the space in front of her. The barrier seemed to bend but it did not break. "Well, I'm out of ideas. Maybe the old ghoul will take care of this or she might have caused it. Eh, might as well scam some ice cream while I wait for them to fix this cuz I ain't gonna waste my time on it anymore."
Ranma jumped up to a building and headed for the Juuban district.
**XxxxxxxxxX**
Setsuna was relaxing on the plane with the rest of the scouts. They were just about to land in Hawaii when Setsuna felt a massive jolt of pain in her head. She would have screamed out if the pain weren't so mind numbing. Haruka and Michiru who were sitting beside her started to worry as their friend clutched her skull and seemed to scream out silently before suddenly relaxing and drooling into her lap.
Somehow all of the girls managed to weasel their way through customs and security with their 'sick' friend. When they found a place out of view, Ami summoned her computer and started to scan Setsuna. "She's alright. She's just in shock and should be coming out of it any second now."
As if on cue, Setsuna sat up rubbing her head. "Damn, that's the worst %#$*^ headache I've ever had."
Setsuna looked around to see her concerned friends and colleagues. "We've gotta go back to Japan. I would never have caught it if someone hadn't tried to fight against it. I just wish that they didn't fight so hard. Space-time barriers are sensitive and breaking them the wrong way can be disastrous."
"Aw, do we..." A hand cut off Usagi.
"Yes, we do. I only got a glimpse of what was going on in Japan thanks to whoever attacked the barrier, but I was able to glean enough to tell that some dark entity has erected a space-time barrier over Japan. I just hope whoever is fighting against them is on our side."
Rei nodded her head. "You don't know."
Setsuna glared at her. "I only got a glimpse. Warped space and time kind of gives me a massive migraine, thank you very much. All I know is that the girl that did it had blazing red hair."
**XxxxxxxxX**
"Master, Master!" The hooded man made a mad dash for his seat tucking the book he had been reading under it.
"What is it Cairn? I'm busy." The toad-like man entered the room sweating profusely.
"Someone has greatly disturbed the Nerima barrier sir."
The hooded figure raised an eyebrow. "That... should not be possible unless you left one of the residents out."
Cairn thought for a moment and shook his head. "No, we made sure that no one walked out of the place before erecting the barrier."
The Master rubbed his chin. "Who's the closest to the one that disturbed the barrier?"
Cairn seemed to think for a second. "Duly I believe."
The Master nodded his head. "Send him. Give him permission to go all out."
Cairn's eyes widened. "But isn't it too early to start with the..."
The Master waved his hand. "No. If there is a threat that has yet to be neutralized, then it should be taken care of with extreme prejudice. Now send him his orders. Dismissed."
Cairn bowed and left. The Master let out a sigh and pulled the book out again. "Hmm, guess the book is right. 'Always be prepared for a new hero to pop up.' and 'If there is threat that has yet to be neutralized, then it should be taken care of with extreme prejudice.' are definitely good pointers. I've got to get the guy who writes these things on my staff."
**XxxxxxxxX**
Ranma was purring as she downed the last of her chocolate parfait. Who knew they had ice cream this good in Juuban? _I should come here more often._
"Smoking isn't allowed here sir. Could you please step outside?" Ranma turned her head to see some weird guy dressed up as a cowboy enter the ice cream parlor.
"Sorry, ma'am. I'll put it out." Everyone was surprised when he took it out of his mouth and punched her in the gut with the hand holding it or so they thought. Instead, there was a red-head holding the hand back and smothering the cigar between their hands.
"What do you think you're doing?" Ranma was pissed. What was with this guy?
The man seemed to chuckle deeply before pulling back. He pulled some contraption off his back that attached to his arm. It kind of looked like a wing with a bunch of slots in it. "Name's Duly little girl. Time to die."
Ranma jumped out the door just in time to miss a barrage of something hitting where she had just been. When she looked back she gawked, there was cute little pink bunny with a hammer in its hand standing in front of the guy. "Hoppy-hop. Use your hammer of doom on her."
Ranma cursed under her breath. 'Why's it always the cute ones with angry hammers?' "That all ya got. Some fluffy bunny with a hammer."
Ranma flew around the hammer and slammed her fist into the creature only to have it pop out of existence. She saw some numbers in front of the Duly guy change but didn't really think anything of it. "Darnit lost some life points, but when Hoppy-hop is destroyed, I can summon Kung fu Hop."
Ranma watched as the guy put down a card on the wing and a bunny with a rising sun headband popped up. "Seriously, ya gonna tickle me to death or somethin."
"Hey, mommy isn't that a duel..."
"Hush child! We don't want to get sued."
Duly was steaming at these interruptions. "Hell with it. I'm not going to explain my grand strategy even if it was good. Kung fu kick Hop."
The bunny jumped in the air and hit Ranma in the gut. She actually felt that one. She got up and got ready to attack only to be ensnared by glowing chains. "Pervert's snare!"
Ranma blinked for a second and wondered why he wasn't attacking. She then looked down to see that the glowing ropes binding her were pushing out her breasts and pressing her in strange ways. She then remembered the name of the move. "Dammit! I'm going ta pound ya now."
Duly drooled a little before responding. "I think the boss'd like you just as you are now. No need to ruff you up more."
Ranma started to see red. She tried to grab around for something to untie or cut the rope when she felt the rock in her pocket. She grabbed it firmly and brought it out to cut the rope. Duly was surprised as his energy rope winked out of existence. He then noticed the stone and narrowed his eyes. "Hand over the rock sweetheart and I won't haveta hurt ya."
Ranma put the stone up to her chin and then nodded. "No."
Duly sighed. He then placed a green card on the field. "I sacrifice Kung fu Hop and two other monsters from my hand to summon Orochi the Great."
Ranma stared upwards as a giant monster appeared with eight snarling dragon heads. "Well, shit!"
**XxxxxxxxX**
Pluto and the sailors were on a boat back to Japan. They had found out that they could not simply teleport there. Thus, Setsuna had procured a craft and they had set out to sea. They shortened their trip by teleporting the craft about 200 miles off of the Japanese coast which had tired out the Inners. They were currently resting in the hold of the ship when Setsuna clutched her head again.
Haruka bent over and patted her back. "Is it happening again?"
Setsuna shook her head. "Not quite, I think the girl is fighting one of their minions or something. Michiru, bring out your mirror. We're close enough so it should work now. Try divining for the red-headed pig-tail girl."
Michiru nodded and brought out the Deep Aqua Mirror. She scryed for a second before a picture started to appear. The scouts gathered around and looked into the shifting images. Usagi gasped as did the rest of the inners. They saw the girl standing in front of a giant eight headed dragon. Setsuna's eyes bugged out as she saw the image. "How in the hell did someone break the seal on the Orochi?"
Ami turned around to Setsuna. "What was the Orochi? I know about it from myth but it sounds like you knew it better."
Setsuna nodded her head. "It liked to eat young virgins and drink wine. It was sealed before my time but the pictures of it are the same as that one. It was one of the experiences my predecessor had."
Usagi cried as a head lunged for the girl. "Oh no, she's going to die!"
**XxxxxxxxxxxxxxX**
Ranma jumped away as a head tried to eat her. _Shit, same ol' Orochi. Damn thing still goes for women and booze, but I'm stronger now. I'll kick it's ass._
Ranma's thoughts were stalled as she noticed some of the heads turn towards the crowd of people that were nearby. She then saw a head narrow down on a small girl that couldn't protect herself. "Shit!"
Ranma raced ahead of the head and grabbed the little girl while rolling away. "Get out of here that thing'll eat ya."
Unfortunately for Ranma, this caused a panic as people scattered everywhere. She continuously fended off heads as she tried to figure out some way to attack the creature. She finally suffered a harsh blow to her side as a head struck her, but at least the people had left the vicinity. Ranma got on one knee and looked up to the wide open jaws of a mouth that was about to snap shut on her. "Well, crap!"
**XxxxxxxxxX**
After Ranma's initial save, the scouts started to cheer the red-haired girl on. They were surprised at how easily she moved and weaved around the monster. The girl kept moving around saving people from being eaten or crushed. The cheering stopped when the red-head was broad-sided by a head and barely got up on one knee before another head moved down to devour her.
They all whispered hoarsely. "No!"
**XxxxxxxxxX**
It was at that time that Ranma let her arm slide down to her waist where it made contact with the now glowing stone in her pocket. _Dammit, I don't want to die. I can't die here!_
Ranma was then surrounded by a brilliant blue glow as the head started to surround her. The mouth snapped shut over her for a second before the blue glow seemed to show through the head. The head started to smolder and then exploded outwards to reveal a stunning sight. Ranma stood there in a crystal blue cheongsam blinking while holding the glowing stone in her hand. She wasn't sure what was going on but she wasn't dead so that was good. The stone almost screamed at her to put it in front of her and release some kind of energy that was sizzling around it.
Ranma held the stone out in front of her chest with both hands and focused whatever energy it was using towards the Orochi. "I don't know what the hell's goin on but I can say this: Suck on it ya bastard!"
**XxxxxxxxX**
The scouts eyes nearly bulged out when the head exploded to reveal the red-haired girl standing there in crystal blue Chinese dress. Their eyes then fixed on the stone she was holding which seemed to hum with power. The girl then held it out in front of her and they actually heard her shout. "I don't know what the hell's goin on but I can say this: Suck on it ya bastard!"
The scouts watched as the Orochi disintegrated into nothingness. The stone then seemed to sink into her body as the girl slumped to her knees.
She raised one hand up into the air while yelling out. "Ranma Saotome doesn't lose!"
As she said this, she slumped to the ground unconscious. They then noticed the man that had been controlling the creature approach the girl and start picking her up.
Usagi's eyes widened. "No! We can't let them get her now. Not after she saved all those people."
Setsuna concentrated for a second and nodded her head. "Alright, we have a 1 minute window to transport into that area. Everyone form up for the transport."
There was a flash of lights as they all transformed and then another round as they transported out of the ship.
**XxxxxxxxX**
Duly hefted Ranma up but was having trouble getting her in a good position to carry. "Damn, this bitch really needs to lay off the ice cream."
A bright flash of light off to the right caught Duly's eyes. He chuckled to himself as he saw who it was. "So, did you enjoy your trip scouts? I imagine Hawaii is nice this year."
Sailor Moon pointed her rod at him while striking a pose. "Hawaii would have been great if we could have stayed. In the name of ruining a vacation and the Moon, I will punish you."
Duly shrugged and patted the girl that he held. "Whatever, I don't really care what you do. I've already got the main prize here. You'll just be a bonus."
Duly let Ranma fall to the ground as he pulled out a card and put it down on the machine on his arm. A large octopus monster appeared. "Go Scary Tentacle!"
Sailor Uranus stared at the creature before yelling out, "Oh hell no, he did not just summon a damn tentacle monster!"
Sailor Venus nodded her head. "I know, it's like one of those novels they sell at the back of the manga stores!"
All heads whipped around to look at Sailor Venus. "What?"
Sailor Moon turned around to deliver another speech when a blue blur raced towards the monster and exploded on impact. All heads turned to see Ranma wobbling along lobbing blue energy blasts at the creature. "No, no, no. No more tentacle monsters! I swear Akane! Make another one and I'll freaking level the kitchen. Damn things are as bad as cats!"
After Ranma finished leaving a smear where the creature had once been, she once again fell forward but into the arms of Sailor Moon this time. "I got her. Let's get that big meanie now."
Duly was blinking rapidly as a gaggle of magical girls with evil smirks on their faces started to surround him. He slapped a card down and yelled out in a panicked voice. "Coward's retreat!"
He quickly vanished in a beam of light, leaving behind some fuming magical girls. Sailor Mars was the first to speak up. "If I see him, I'm going to roast him slowly over the sacred fire."
After a round of 'here, here's,' they went over to look at the downed red-head. Sailor Uranus and Neptune whistled when they got a better look at her. They said in unison."Now that is a perfect 10."
Sailor Pluto rolled her eyes before speaking. "Let's get to the shrine. We'll need Mars to do a fire reading as these guys seem to have a way to block my time sensing abilities. I'm also worried that they knew our identities. It's the only way they would know that we were going on vacation."
**XxxxxxxxxxX**
Duly bowed before his Master. "I am sorry sir. They were too powerful and the red-haired girl had the stone."
The Master tapped his fingers together and glared at Duly. "Red-haired girl? Did she give her name?"
Duly nodded. "Ranma Saotome."
The Master seemed to tense but then a malicious grin spread across his face. "Did the crystal enter her body?"
Duly again nodded and the Master waved his hand to dismiss him. "Go Duly. Know that while you lost you have not completely failed me as you have brought back important information regarding our enemy. However, do not screw up next time or else."
Duly bowed before leaving. The Master started to chuckle as he brought out his copy of 'Being a Villain for Dummies.' He turned to a page that had an itemized list called the 'Objectives for World Domination or Stuff Like That' and crossed out the name Ranma Saotome. He then looked over a large dark crystal that was in his other hand. He seemed to have trouble holding its weight with his scrawny arms, but he didn't let it go. "Well, it's not quite how I imagined it working out but then again, I can kill two birds with one stone so to speak. Hmm, well, Ranma's girl side is pretty hot and after reading all of those books about Jusenkyo and the other tomes I know it's real. Oh yes, no voodoo doll could have ever netted me as many as I'll have. I just need to gather the other fragments and activate them. Then..."
The Master's nose bled as his thoughts wandered.
**XxxxxxxxxxxxxX**
This is just a silly little jaunt. If you want to adopt any of my short starters, let me know before you do and I'll most likely give you my blessings.
7. Chapter 7: Ninja no Subaku
**Ninja no Subaku**
I do not own Naruto or Desert Punk so please don't sue.
**XxxxxxxxX**
"Dammit! Where the hell am I?" Kasuna started rubbing her bum from the sharp fall as she tried to stop the spinning in her head. She just had to be stupid enough to let Kaizuka try out that experimental transporter on her. "Man this sucks!"
Once the spinning stopped, Kasuna looked around at her surrounding. "What the crap? The hell is this place?"
She was surrounded by forest though she didn't know that. Plants were rare and almost never seen in the Kanto desert so she had no idea what was surrounding her but as her old teacher always said, "Adapt or die!"
Kasuna hauled herself up and took in her surroundings. She didn't know where she was; she could hear creatures rustling around her; and she didn't know where the nearest village was. "Well, nucking futs!"
She turned on her enemy locator device and the damn thing had more creatures on scope than she really wanted to deal with. As she noted that several of the larger creatures, were starting to move into positions around her, she did the only thing she could do. She picked a direction and ran.
**XxxxxxxxX**
Kasuna was panting at the steps of what looked like a temple about five hours after she arrived. She had managed to blow up two huge snakes, gun down a giant toad, and skewer the rat-like creature she was dragging behind her. She didn't see any reason for wasting the meat and she was hungry after beating the crap out of the forest animals. She searched around for a place to set up camp and then she saw it. "A water fountain! Holy shit, I musta found a freakin oasis! I'm gonna be rich!"
She quickly set up camp next to the fountain and started cooking the rat. "Oh man, this is the life!"
**XxxxxxxxxX**
Outside the forest, a watcher from one the internal tower of the Hidden Leaf spotted smoke coming from the forest.
**XxxxxxxxxX**
Sarutobi, the Third Hokage, was sitting at his desk while stroking his beard. Young Naruto had just started the final year at the Academy and it wouldn't be long before he knew if the youth would turn out to be a capable ninja. He was brought out of his musing as an Anbu reported to him.
The monkey-masked man bowed his head. "Someone is in the forbidden forest. No one was seen entering so it is strange that there is a solitary fire going on the inside."
Sarutobi narrowed his eyes. "Hmmm, call Anko and tell her to find the source. Bring the person to me and we'll decide where to go from there. Have two Anbu follow and report back to me should something go wrong. Tell her to use her own discretion but no reckless behavior."
**XxxxxxxxX**
Anko grumbled as she headed out to the station in the center of the Forbidden Forest. She wanted to know what kind of idiot would be camping in such a place. It was either a trap or some really stupid person with a death wish. She drew closer to the compound and quirked an eyebrow when she saw a small, pink-haired girl sleeping beside a fizzled out fire and some animal bones. She was about to move down to capture the kid when she saw a panther moving around to get the kid. She tossed around the idea of helping the child out but decided against it. She sat down on a tree limb instead and pulled out some dango while waiting for the show to start.
The panther circled around and moved towards an advantageous position. Anko was on the edge of her seat when the panther... suddenly sprung a trap and got trussed up in a large casing of mesh wires. She saw the girl stir and look up at the cat. The girl giggled. "Oh well, guess you'll be breakfast."
The little girl seemed to be going back to bed when she stiffened. She then noticed the girl scramble to put her clothes on and what seemed to be a bowl over her head. The girl then looked straight at her and pointed something at her. "Who's there? Show yourself!"
Anko's eyebrow's raised and she jumped down from the tree. The child jumped up a hair on her threat-O-meter. She walked up slowly while making sure she was ready for a fight. As she got within the fire's dim light, the girl stiffened and seemed ready to fight. She then heard something that made her veins throb in anger. "Hold it right there sluts-McBoob! I'd recognize those ta-tas anywhere Junko!"
Anko clinched her fist while saying. "I ain't a slut little girl and I ain't Junko! My name is Anko."
Kasuna looked up at the woman's face and let out a sigh. "Oh good, I swore the next time I saw that big-boobed bitch that I'd blow her ginormous ta-tas away."
Anko slowly counted to three and then said screw it. "What the hell are you doing in the Forbidden forest kid!"
Kasuna turned her head to one side. "Uh, so if I'm in this Forbidden forest. Where would that be exactly?"
Anko looked at the kid like she was crazy. "It's in the middle of the Hidden Leaf territory. How could you not know where you are?"
Kasuna scratched the back of her head. "Uh, there was this crazy old coot who was experimenting with transporting things and he kinda transported me here. You should see some of the stuff that guy does. I mean those soldiers that he controls like puppets. The shit he did when he transformed Striker's arm. Heck, he blew up half of western badlands."
Anko's eyes narrowed as she took in what the girl had said. _Sounds like my old master is up to something again. I better get this girl to interrogation. It's kinda sad really. They're going to put her through the same shitty ass interrogation that they gave me. Hopefully the old man sees fit to help her out. At least she doesn't have a curse mark from what I could see. Time to get one last bit of info before __lights out. _"So uh, where did you come from?"
Kasuna smiled under her helmet. "The western oasis in the Kanto desert."
Anko looked at her funny. "Doesn't ring a bell, but it was in the desert right."
Kasuna nodded and the woman in front of her disappeared. Kasuna suddenly felt tired. "Well shit!"
**XxxxxxX**
Kasuna woke up with a bucket of water to the face. She looked around blearly noting that she was bound to a chair. _Well shit! I'm going to get that walking milk bar when I get out of this. Never trust a woman with boobs bigger than her brain._ She then saw a scarred man in front of her as her eyes came into focus.
The man was sitting on a backwards chair tapping his fingers on the top of it. "Name, rank, and village."
"Huh?"
The man looked at her coldly. "Name, rank, and village."
Kasuna looked around herself as far as she could and grasped the situation. _Greaaat! Another torture session, hope this doesn't last a freaking week. _"Kasuna, mercenary, western oasis village # 28."
Ibuki raised an eyebrow and continued. "So, you're not a ninja?"
Kasuna gave him a funny look. "No. I'm just a mercenary."
The man stood up and made some motion she didn't understand. He turned back to her. "And what were you doing here? "
Kasuna sighed. "There's this crazy old coot named Kaizuka who was experimenting with transporting things and he kinda transported me here. Though I still don't really know where here is."
The man seemed to nod. "Okay. Say I don't believe you?"
Kasuna frowned. She knew what was coming next. She had already said too much but everyone knew she was with Kaizuka and the underground mercenaries at this point so what did he really want from her. She put on a saccharinely sweet smile and said, "Bite me!"
The man seemed to fluster up a bit before removing his bandana to reveal a really messed up head. "I'd start telling me everything you know girl or else you'll end up like me."
Kasuna looked over the screw holes in the man's head and whistled. "Now that's a piece of work. Surprised you made it through that kind of torture."
"Then let's see how well you answer my questions." She gulped as the large man left the room.
**XxxxxxxxX**
Anko wandered in to Sarutobi's office while picking her teeth. The old man looked up at her entering the room. "So, where is our guest?"
Anko sighed. "I found a small girl in the forest. She's currently with Ibiki."
Sarutobi stood up and glared at Anko. "I asked for the person to be brought here. What warranted taking her to Ibiki? Explain on the way we're heading down to the interrogation room now."
Anko frowned as she followed the old man. "She was going into some rant about experiments and some of them sounded like what my old master did. I figured it warranted interrogation to make sure she wasn't following his orders or just some puppet under his power."
She heard the old man mutter several curses as they walked briskly down the corridor.
**XxxxxxxxxxxX**
As Anko and Sarutobi got closer to the interrogation room, they could here screams. They both ran to the door and were shocked to see what was going on inside. The young girl was furiously fighting against her restraints and a Yamanaka was sitting back on the floor looking up at the girl.
They watched as the girl thrashed around while she screamed out. "I'll fucking kill you master! How could you? How could you kill them? How could you side with the enemy?"
Kasuna then fainted in the seat after her exertion. Sarutobi frowned after hearing that outburst and turned to the Yamanaka on the floor. "Alright, I don't care who ordered this at this point even though I specifically asked for the girl to be brought to me first. Tell me what that was about."
The yellow-haired Yamanaka lifted himself off the floor and bowed to the Hokage. "Sir. The girl... as strange as it may seem is definitely not from this world. It seems that she was part of a botched experiment that someone was performing on summoning sir. The technology of her world is completely different from our own."
Sarutobi nodded. He knew of other worlds. The bijuu and some of the summons they used were not from this world so, while rare, this was not completely unexpected. "And the outburst?"
"I was digging through her memories. I happened across a rather potent one. She was surrounded on all sides by the enemy and found her former master, one Demon of the Desert, as the commander of the invading force. She had guessed at his betrayal and had set up a trap hastily before confronting him. Her trap worked and crippled his forces, allowing her and her comrades to escape but her former master also survived. She swore from that day that she would not be weak and hunt him down for betraying her village and murdering fellow comrades.
The strange thing is that she was apparently aware of my genjutsu as I performed it. She said something about seeing my spirit leaving my body before I entered her mind. From some of the memories that I recovered in her mind, I ran across a battle from her early tutelage under her master. She had witnessed what was apparently an invisible type of attack from what I can only classify as a bijuu from their world. She then witnessed the actual manifestation of the attacks from her master and the bijuu which surprisingly ended with her master killing the bijuu. I believe she carries a kekkai genkai that allows her to see chakra manifestations with the possibility of seeing through henges. It may be possible for her to reject genjutsus as well as she cut me off from her side."
"Wow, no wonder the kid sensed me up in the tree." Anko whistled. Only the Hyuugas had better eyes in that regard.
Sarutobi frowned. He would have rather given the child a warmer welcome and found out about this in more subtle ways but what was done was done. "Is the child a threat?"
The Yamanaka shook his head. "I don't know. You'll have to make that call. I believe that she wouldn't do anything as long as we don't harm her further."
Sarutobi nodded his head. "Very well. Anko, you disobeyed me but thought you were doing the right thing. Here is what I propose: you will take her to the hospital and monitor her until she recovers. Once she has rested, I want you to bring her to me."
"Hey, why do I have to babysit the brat?"
Sarutobi chuckled before pulling out his pipe and lighting it. "Because it was your screw up."
**XxxxxxxxX**
Kasuna slowly woke up from her torture induced nap to find herself staring at a sterile white ceiling. "Hn? Hospital. Hope it's not another sick torture game."
She heard a chuckle from her side and turned her head to where her eyes met a familiar pair of breasts. "Oh, it's tits-McGee! Here to lord your mammary mountains over me."
A knuckle lightly wrapped her on the head. "If the Hokage didn't want to see you, I would have caved your head in by now you little brat. And my name is Anko, not tits-McGee."
Kasuna shrugged as she sat up. She stretched out her sore muscles. She didn't look at Anko as she asked her next question. "So, ya happy with whatcha got out of me? Didn't know someone could actually get inside my head like that."
Anko frowned. This kid could still be dangerous. It took someone with real talent to force a Yamanaka out of their mind. "Get up. I'm taking you to see the leader of this village. He actually wasn't happy that I dragged you to interrogation first and actually stopped your little inquisition from continuing so be sure to thank the old man when you meet him."
Kasuna jumped off the table and headed to the door. She decided to take one more jab. "So, ya coming or are your boobs slowing you down?"
**XxxxxxxxxX**
A rather irate Anko stepped into Sarutobi's office with a little pink-haired girl. The old man scratched his beard as he watched the child. She was a little short but the steel in her eyes as she looked at him told him that she had more experience than someone her age should have. He had noted that upon entering the room the girl had done a quick sweep of the room before staring directly at him.
Anko pushed the girl forward before muttering something under her breath. She looked up at Sarutobi. "She's all yours." She then disappeared in a cloud of smoke.
The old man's eyes moved back to the girl and she did the same. He pointed to a chair and she took the seat. "I'll have to apologize for Anko. She tends to get riled up easily."
Kasuna giggled at his comment. "I know. I was having some fun with old fun bags. Name's Kasuna by the way. Also known as the Demon of the Desert."
Sarutobi made a mental note that the girl had taken up the mantle of her former master. "And I am Sarutobi, the Third Hokage or leader of this village. I suppose I should explain some things. It would seem that you are no longer in your world. I believe you would call it crossing dimensions or some such."
He let that sink in and watched as the girl sat in thought. "Well, I guess that could have happened considering what Kaizuka did. So, what's that mean?"
Sarutobi steepled his fingers. "We have no way of sending you back home. From what I was told, you are a mercenary." He watched as she nodded. "In this world, most mercenaries don't last very long or they are just low level thieves. Instead, ninja do most of the jobs that you would have done as a mercenary on your world."
Kasuna nodded as his words sank in. "And what are you offering?"
Sarutobi smiled as he leaned back in his chair. "Good. You are sharp. I'm offering you a chance to be a ninja of our village. You will have to train and I think I've got someone in mind for it. You'll also have to go to a ninja school."
Kasuna sat back in thought. _Don't know if he's telling the truth, but I don't know where I am and this doesn't look like any place remotely near Kanto. OK. Rule 1 of the desert: Do whatever it takes to survive. Rule 2: Milk 'em for all they got. Rule 3: It's a suckers bet that someone will just do something for you out of the kindness of their heart. Rule 4: Always get it in writing._ "Where is the contract for this?"
Sarutobi raised an eyebrow. "No contracts yet. Food, clothing, housing, and some spending money will be provided as long as you attend school and take training seriously. Contracts only come into play when you take on actual paying missions once you complete your training."
Kasuna looked the man over. "Kay old man. I'll take it."
**XxxxxxxxxxxxxxxX**
"Today, we have a new student joining our class. She'll be behind in her studies so I suggest that you help her out. She could be your teammate in the future and it wouldn't do for you to have a teammate that cannot perform. Come in Kasuna." A pink-haired girl walked into the room and stood beside the young man with black hair.
"Hey everybody, I'm Kasuna no Subaku." Kasuna looked around at the bored to generally laid back atmosphere of the classroom. She then noted another pinkette who was waving at her.
"Go to your seat Kasuna and we'll start the lesson." Kasuna sat down and looked over what they were teaching. It confused her. What the heck is Chakra?
**XxxxxxxxxxxxxxxX**
"Chakra is the physical and mental energy that flow through your body brat. I'm going to show you the elementary lessons for this so you better keep up." Kasuna giggled as an irate Anko tried to show her how to perform a simple chakra movement exercise.
After she had gone back to the old man to tell him that she didn't understand what was going on at the school, he had ordered Anko to be her personal tutor. This was fun for Kasuna and a living hell for Anko. Kasuna soon found that she could feel something flowing through her so she guessed it was chakra. "Got it! You'd think they'd do this in that academy."
Anko rolled her eyes. "Most of the idiots in that Academy couldn't teach a horse to piss straight."
Kasuna giggled at the comment. She had to admit that this woman was different than that money grubbing bitch Junko. "You get to pay for my dango after this is done brat." Or not.
**XxxxxxxxxxxxxxxxX**
Kasuna was smiling to herself. She had just come back from the R&D department of the village. They had managed to come up with an improved design to her desert gear and wench based off of Chakra batteries, sealing, and explosives. She no longer needed to buy batteries. All she had to do was pump chakra into the system and it would work. Kasuna couldn't wait to test this stuff out once she got it back from R&D. They were a little hesitant in producing some of the ammo for her use but the Hokage had approved it and asked for more work to be done in finding new ways to use these 'firearms' that Kasuna had brought with her.
**XxxxxxxxxxxxxxxxX**
"Damn brat, what kind of poison is this! No taste, no smell, and I can't even see it. I gotta say, good work." Anko had been stunned for a couple of seconds from just a whiff of the stuff which told her that it was some damn good paralysis gas, especially since she was a poison mistress.
"Oh yeah, it's the 'Uber badass paralysis spray' that my.. er old Master invented. We used to use it when we needed to capture someone for questioning." Anko could see that her old master was still a sore spot for the girl. It was something she could relate to.
"So kid, you mentioned questioning. What kind of questioning have you done?"
Kasuna thought for a moment. "Well, we usually had to do questioning on the fly so a lot of it was improvised but my former master liked to do uh, nude torture most of the time. Humiliation and degradation were his strong suits and I don't even think I could match what he could do. I decided to learn more varied approaches cuz I didn't quite feel comfortable with his methods. I've also gone through torture and interrogation before so I've got an idea of methods to use from that to."
Anko seemed to think for a second before nodding her head. "If you promise not to kill him, I'd like you to meet someone kid. Let's get going."
**XxxxxxxxxxxxxxxxxxX**
Kasuna was standing in the interrogation department once more, but was able to look around the place. It was exactly what she expected, dank, dark, and smelly. She noticed the man who had interrogated her before approach and look down at her. "Anko tells me that I should give you a test. If you don't remember, I'm Umino Ibiki, the head interrogator. If you'd follow me."
Kasuna followed the man to one of the interrogation rooms with a man who was strapped to the table with only his boxers on. Ibiki read off of a chart. "Zazu Ikari from Hidden Rock. Rank Chuunin. Caught trying to sneak into the restricted section of the Hokage Tower. We want to know what his mission was and anything else he can give us. I want to see what you can do. No killing or releasing the prisoner."
Kasuna raised an eyebrow at what he was asking. _So this is the test huh? I guess I better do a good job._ "Okey dokey smokey."
Ibiki shook his head as the girl entered the room where the prisoner lay. He saw her skip up to where he was restrained through the one-way mirror. He then noticed Anko sitting down beside him. "50 ryo says she has him squealing in 5 minutes."
Ibiki raised an eyebrow. Maybe this would be interesting. "Deal."
**Xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxX**
Kasuna skipped over to the man lying half naked and restrained to the chair. The man finally noticed the little girl and smiled to himself. Some kid had wandered into the interrogation department. He knew Konoha was soft. Now all he had to do was trick the kid into letting him out of the chair and he'd get the hell out of Dodge. "Hey kid. Let me out of here and I'll give you some candy."
Kasuna looked disgusted for a second before frowning at the man. "That's just sick you pervert. I've heard about older men offering candy to kids and it never ends well. You know I was going to do this by the book, but as my old master used to say 'there's no reason to make things difficult; dirty, cheap and easy is always the best'. I hope your prepared ya bastard."
Kasuna looked around for something to get this started when she saw a toothpick, a lighter and some cigarettes on the table. She smiled viciously as she picked up the items and walked back to the man. She smiled sweetly as she picked out the toothpick and grabbed the man's hair. "I would suggest that you don't move too much. It'll hurt worse if you do."
**Xxxxxxxxxxxxxxxxxxxxxxxxxxxx xX**
5 minutes later...
Anko was slapping Kasuna's back and laughing. "I can't believe it 3 minutes in and he broke. That's gotta be a new record. Well, a new record for a non-Uchiha anyways. Where'd you learn all of that anyways; it's more than just a little experience."
Kasuna put her hand into her pocket and pulled out a book. Anko looked at the title and smiled. " '1001 Ways to Absolutely Get Someone to Squeal' written by Kanta."
"Keep it. I've already memorised the entire thing. Besides, I've got another one anyways. My former master made over a hundred copies of his book in the hopes of selling it, but no one wanted to buy a copy." Anko nodded as she tucked the book into her jacket.
"Up for some dango kid? I got 50 ryo to burn and you to thank for it." Kasuna smiled and nodded her head. Maybe life in a ninja village wouldn't be to bad.
**XxxxxxxxxxxxxxxxxxxxxxxX**
This is an old story and one that could be interesting if continued.
8. Chapter 8: Jackpot
**Jackpot**
I do not own Ranma ½ or Tenchi Muyo.
**XxxxxxxxxxX**
**Chapter 1: In for the long haul**
A short red-haired girl was walking down the street which was not odd. What was odd was the large panda that was walking beside her. The girl seemed to be depressed about something while the panda kept pushing her forward. "What are we doing here pop?
The panda pulled out a sign. 'I made a marriage proposal to one of my old drinking buddies and his wife from around here to marry our kids before you were born.' Flip. 'Honor demands that you fulfill the engagement.'
Ranma turned a hard glare to her father. She hefted up her chest towards him. "How do you propose to do that when I'm like this?"
Genma sighed. _I should be marrying the boy to one of Tendo's daughters, but his current condition won't allow that. He, well she's only good for marrying off to their son now. What a waste! Years of effort down the tubes. No woman can carry on the Anything Goes Martial arts legacy. I just need to get her to marry their son. He may be a bit older but at least that will play into my plan. Plus, I'm sure that after she's married to someone and can give Nodoka those grandchildren she's so intent on then she'll forget about that blasted contract. Better prepare in case she decides to bolt._
'Well, you were born a boy and they only had a son so I never brought up the engagement again.' Flip. 'However, things have changed with you having that body now.' Flip 'It's family honor boy or should I say girl.' Flip. 'You can't back out of this.'
Ranma turned red with anger. "A guy! You want me to marry a guy! That's it I'm out of here."
A small crowd had gathered now and was gawking at the site of a panda in the middle of town. They watched as Ranma turned her back to the panda and started walking away. The panda then bent over and pulled a road sign out of the ground and beat Ranma over the head viciously knocking her out. The crowd started backing away and several cries for help were heard. Genma blinked several times as two armed officers approached with their weapons pointed at him. Another person approached with a hunting rifle. Genma really didn't want to use that here, but he didn't have a choice. People watched as the panda took an odd stance and simply vanished before their eyes.
**XxxxxxxxxxX**
Katsuhito was enjoying his tea in the living room. It was nice to have the house to himself for once. Washu was in her lab. Tenchi and the others were off on some less dangerous adventure on one of the vacation planets. It was something about Ayeka trying to outdo Ryoko in a swimsuit contest. It would be funny when they came back and Mihoshi or Sasami won instead.
He was quietly laughing to himself when his tea cup cracked. He stopped laughing and examined the chip in the tea cup. _It shouldn't have broken that easily. Hmm, bad luck._ He was broken out of any other thoughts as the phone rang. He move over to the phone and picked it up.
"Oh, hello Mr. Tanaka! What can I do for you?"
The man on the other end seemed stressed as he spoke. "It was a demon. It beat up this girl with fiery red hair on the street and took her. It then just vanished with her into thin air before we could fire on it."
Katsuhito's eyebrows raised at this statement. _What could it be? It could be a demon but it could also be an alien. I know some slave traders come here once in awhile for the 'easy-pickings' but to do it in front of a crowd in broad daylight..._ "What did this demon look like?"
"Well, I know this sounds strange but... It was a giant panda bear. It was bigger than any I've ever seen and it could communicate using signs. I would swear that I was hallucinating if other people didn't see it as well."
Katsuhito mouthed, 'Panda bear.' "Uhm, I'll look into it."
"Thank you."
Katsuhito put down the phone and walked over to Washu's lab to knock on the door when it opened. "Already on it Katsuhito. I was tracking some weird energy signatures that were headed toward the town and they just vanished a short time ago. I'm guessing that that's what you're here about."
Katsuhito nodded. "Yes, according to the local police, a young girl with red hair was beaten and captured by what they thought was a demon. He said that it looked like a giant panda bear."
Washu raised her eyebrow. "Well, even that's odd for me. I think it would make an interesting guinea pig but there's a problem. I lost them."
Katsuhito looked critically at her. "Lost them?"
Washu nodded her head in contemplation. "That's what was odd. They just vanished into the background layers of reality. It's like they completely melted into the landscape. No cloaking, inter-dim travel, teleport, or even self-destruction could do that. There's always some signature to follow but in this case they completely vanished. It's baffling."
A sinking feeling hit Katsuhito in the gut. _Maybe it is good that Tenchi and the others aren't here. This sounds like an extremely dangerous foe._
**XxxxxxxxxxX**
Genma was starting to wonder if he should have given that sedative to Ranma. He was getting winded carrying Ranma like this, especially with all of his fur. Why did his old friend have to relocate his house so far into the mountains? It was then that Genma crested the hill and came into view of the compound. A beautiful two story house sat next to a private lake. There were fields of some strange crop, a workshop, a grand tree, and a shrine that seemed to connect to the house from on top of a peak. His mind slowly came back into focus as dollar signs filled his eyes.
Genma smiled inwardly. _Heh, it's a good thing that this engagement is a written agreement instead of a spoken pledge like the Tendo agreement. Those copies I made will work well too. If the boy marries into this family, then I'll be set for life._
He reached a wooden gate and stepped through it while ignoring the painted posts. He raced towards the house releasing the thief's cloak.
**XxxxxxxxxxX**
Washu and Katsuhito were disturbed from their contemplations as several proximity alarms started going off. Washu pulled up her monitor and frowned at what it showed. "It's already at the front door. Damn, how did it get by all of my defenses?"
Katsuhito was worried now. An enemy that could breach Washu's defenses undetected would not be easy to defeat, especially if it had a hostage that it could use as a shield. He pulled out Tenchi-ken, thankful that Tenchi had left it with him. Both Washu and Katsuhito were surprised when they heard the doorbell ring.
Katsuhito cautiously approached the door. It was strange for a malevolent being to be courteous. He slowly opened the door to find a panda bear towering over him with a girl halfway slung over his shoulder. Instead of engaging it, Katsuhito backed up in surprise as the bear pushed his way inside. The panda proceeded to dump the girl in a boneless heap on the floor before pulling out a sign.
'Is this the Masaki residence?'
Katsuhito just stared at the bear for a second. He then registered Washu sneaking in from the side grabbing the girl and moving her out of harms way. "Yes it is."
The bear seemed pleased for some reason. 'Get me some hot water so' Flip ' I can explain.' Flip. 'I know it seems weird but I'm actually human.'
Katsuhito nodded. "Washu could you.."
Washu appeared before them with a steaming cup of water. "Will this do?"
She barely said those words as the panda grabbed the cup and poured it over himself.
**XxxxxxxxxxX**
Three people were now sitting at a table in the Masaki living room. An old man, a seemingly young girl, and an middle-aged man in a dirty white gi. The man in the white gi pushed up his glasses and started the conversation. "I'm guessing that you want to know what happened to me and what's going on."
Katushito nodded. "That is quite an understatement."
Genma nodded and continued. "I've trained Ranma, my uh daughter, to be the best martial artist in the world for the past ten years on the road. Unfortunately, we ran afoul of some cursed springs. I fell into one and am now cursed to become a panda when hit with cold water and back into a man with hot water."
Katsuhito nodded once again but set to thinking. _A curse, huh. I guess Washu's found a new guinea pig. I can see her eyes gleaming right now. Why is he here though? _"Why are you here?"
Genma smirked in a way that made Katsuhito feel that he needed a good bath to wash the filth off. He then pulled a parchment out of his pack and handed it to Katsuhito. "It's an agreement between me, Noboyuki, and Achika. I'm here with my daughter to fulfill this agreement."
Katsuhito started to read the document and froze midway. He then speedily ran through the rest and confirmed the signatures. He was frowning when he dropped the parchment on the table. He spoke to himself for a second but still loud enough for the others to hear. "What have you done Achika and Noboyuki? How could you be so stupid?" He then turned to Genma. "I cannot deny this agreement; however, Tenchi and Noboyuki are not available at the moment. I'll get Noboyuki when he gets off work but Tenchi is on vacation and may not be back for another day or two."
Genma smiled inwardly. _Hah, gives me time to prepare the boy._ "That will be fine Masaki-san. Where is Ranma by the way?"
Suddenly, a beeping alarm drew Washu's attention away from the conversation. She tugged on Katsuhito's sleeve and nodded towards her lab. Katsuhito nodded back to her. " Washu took her to her room to rest for the moment. We'll get her down here when she wakes up. Why don't you relax in the living room? We have cable."
Genma nodded and headed for the couch while Washu and Katsuhito slipped away.
**XxxxxxxxxxX**
Once inside Washu's lab, she quickly threw up in a bucket. Katsuhito became a little worried at this behavior. "Are you alright Washu?"
She held up a hand and wiped off her mouth. "Not really but thanks for asking. Do you plan to have Tenchi honor that arranged marriage?"
He raised his eyebrow at this statement. "I have to. Achika signed it. You know that any marriage contract signed by the parents of a noble Juraian must be honored. Why, is something wrong?"
Washu sighed before answering. "Yeah, something foul is definitely going on here. Actually, it's probably a good thing that she's going to marry Tenchi or I wouldn't expect her to live for much longer."
That statement really got Katsuhito's attention. "And why is that?"
Washu just shook her head in frustration. "I can't prove it right now but I'd guess that Genma is really abusive. I just got the analysis from the recovery chamber that I put Ranma in. She had numerous old and new breaks in her bones, scar tissue littering her body, bruised organs, and strange, almost pinpoint brain damage in certain developmental areas of her brain. The current crisis though is the amount of barbiturates in her system. She has double the dose that would be used to put down a horse in her system. I was surprised that she was only in an induced sleep when I brought her down here. I'm frankly surprised that she's still alive. She's lucky that I can fix this. Normally, she'd simply die in a hospital and even if she survived she'd need to take barbiturates just to stay alive afterward because the withdrawal effects would kill her. All in all, she's lucky to be alive."
Katsuhito now had a grim look on his face. "I'll kill that bastard for doing all of that to his child."
Washu grabbed onto his hand to stop him. "Aw-aw. Don't go losing it now. We still don't know enough. We don't know that he was the one who did all of that and I'm still worried about how I couldn't detect him earlier. Something just isn't right about that. If he can do all of that... We need to observe him for now. I won't let him harm anyone else, but we should keep a close eye on him. Besides, I've already added him to the top of my guinea pig list."
Katsuhito shuddered but got over it. _Couldn't happen to a nicer man!_ "I can already guess that he was the cause of some of this. He seems like the type to me. I'll do as you say but I swear that if he causes too much trouble. I will take care of him. By the way how did you help the girl anyways?"
Washu cackled for a bit. "Yeah, you can take care of him. Just leave me some samples. As for the girl, I put a couple of Masu in her. Before you start to berate me on that, there are often many beings that fuse with at least one or two Masu during there life with the only side effect being a slightly longer life span. There's no way one or two Masu could cause any harm."
Katsuhito bit back his retort and sighed. "Fine. Let's go see our other guest."
Washu would later eat those words.
**XxxxxxxxxxX**
Katsuhito blushed as he saw the girl in the healing tank. "I think you forgot to mention that she did not have any clothes on Washu."
Washu raised an eyebrow and smiled. "Oh, you only think I forgot."
Katsuhito shook his head. "A little modesty goes a long way Washu. Although, I must say that Tenchi is going to marry quite a catch."
Washu nodded her head. "That's skin deep. Look a little deeper."
Katsuhito looked at Washu and then back at the girl. She looked normal but... "By Tsunami! It's not Juraian but... She has a huge amount of life energy. This is remarkable!"
"I know. I think she'd give Ayeka a run for her money in a fight. It will be interesting to see how much she progresses once she receives her own tree."
Katsuhito froze at those words and hung his head. "We have to contact my parents about this don't we?"
Washu frowned a little. "Misaki's going to be coming here again isn't she?"
Katsuhito shook his head. "Let's get her to Ayeka's bed before she wakes up."
**XxxxxxxxxxX**
Ranma groggily woke up on something soft. She shook the cobwebs out of her head and looked around the room. A lot of the furniture looked like logs or some kind of strange, wavy wood. The clothes and jewelry laying around screamed out that it was a girl's room. "Great, I guess we already made it here. I wonder what lies pops is spewing out to butter them up."
When she stood up, something seemed odd. Her chest didn't sag down into her shirt and something was pressing... "I've got a bra on. When did that happen?"
"I figured that it would give you better support than nothing at all. You should really take care of yourself you know. I bet you no longer feel a strain on your back."
Ranma turned to see a red-haired girl at the door. She looked young but in a way she seemed older. _Oh man, it does take the weight off my back._ "I suppose. So uh, where is here?"
"You're in the Masaki household."
Ranma bit back a curse. _Damn panda, I bet he's already talked them into going through with the marriage. _"I don't want to marry anybody."
Washu quirked an eyebrow. "And why is that?"
Ranma was about to scream out that she was really a guy but held it in. She had been a female for a little over three months now.
**Flashback...**
"Pop why are we going to this training ground again?"
"It's one of the mystic training grounds. Jusenkyo! It's supposed to be extremely dangerous." He and his father walked out of the pass to see bamboo poles sticking out of the ground.
Genma jumped up to one followed by Ranma. A man came out of a nearby hut and started yelling. It was too late as both had started into combat. Genma was the first to fall and nearly gave Ranma a heart attack when a giant panda came out.
"What is that?"
"Oh, he fall in spring of drowned panda. Whoever fall in take body of panda."
Ranma would have gotten down at this point but he was in shock and his father hit him into a pool. A very irate girl popped out and looked down at her chest.
**XxxxxxxxxxX**
Ranma was fuming as the guide boiled some water. He then took it and poured it over Ranma and a bruised panda. "See hot water turn you back."
Ranma nodded. _At least I can change back._
It was then that Genma did something stupid. He grabbed a glass of water off the table and threw it on Ranma. "And cold water causes us to change. Hah, now you really are a weak girl Ranma."
Ranma's cool completely gave way at that insult. He had enough. Genma saw the murderous gaze of his son and for some reason it reminded him of his wife. Before another word was said, Genma was flying out the door running for the mountains with Ranma hot on his trail.
The guide raced out of his hut trying to stop the customers. "Ah, wait! No go that way! That Musk territory."
**XxxxxxxxxxX**
Ranma had been chasing his father for two days now. He was currently in his female form after it rained and was hoping his father was slowed down by wet fur.
He then noticed his father and about twenty guards trying to wrestle him down. Ranma ran toward his father, ready to join in the melee beating him down, when a chop to the neck sent him into unconsciousness.
**XxxxxxxxxxX**
When Ranma woke up, he was facing some kind of weird man with pink hair and his father was beside him. They were being restrained by two men. "Hey what's going on here!"
The pink haired man sneered at him. "You filthy scum. Your father ate and defiled half of our food stores before we stopped him. Normally we would kill you for this offense, but I've learned that you both have Jusenkyo curses so now I will give you a punishment worse than death. I will seal you in your cursed forms!"
The pink-haired man held up a bucket with a ladle full of water. He splashed Ranma with the water and she turned into a girl. Her mind caught up to what he had said and she promptly passed out. At this point, Genma's self-preservation instinct kicked in and he threw off his captor with a mighty roar and proceeded to grab Ranma. He then disappeared from sight.
The pink-haired man cackled after him. "You may have eluded me you fat bastard but there is no way to restore your son."
**XxxxxxxxxxX**
A month later...
A pale Ranma was coming out of the restroom as Genma shook his head. "You are no longer my son."
**End Flashback...**
Ranma shuddered at that thought. She mumbled but Washu could hear it. "Damn pops. Almost disowning me just because I have a monthly visitor. Like to see how he handles it."
Washu frowned at that statement. _So he thinks women are worthless huh? Boy is he in for a surprise when the rest of them show up. Should be interesting._ "I'm sorry. I didn't catch that."
Ranma refocused and stared at Washu. "Because I don't want to get married right now. Who are you?"
Washu nodded her head. _That's a honest answer. Plus, being drugged and brought here against her will probably has something to do with it. It's too bad that everyone's hands are tied in this case. Since Achika is dead and the signature is legitimate, they don't have a choice._ "Sorry, my name is Washu Hakubi, but I prefer to be called Washu-chan or little Washu. So what's your name?"
Ranma sighed and relaxed some. "My name is Ranma Saotome, heir of the Saotome Anything Goes School of Martial Arts, well was."
Washu let the ending comment slide for the moment and continued. "So, would you like to be friends?"
Ranma watched as Washu extended her hand. She weighed her options. She didn't really have many friends and she never really saw the few friends she had. Ranma shook Washu's hand. "I'd like to be friends."
Washu inwardly chuckled. _Encounters of the Fifth Kind eat your heart out._ "So, want something to eat?"
Ranma's eyes glazed over, her stomach growled out and she started drooling. Washu raised an eyebrow. "I guess you are hungry."
**XxxxxxxxxxX**
**Twenty minutes later...**.
Washu was typing away on her computer and analyzing the anomaly. Katsuhito took a step back when a bone nearly hit him in the eye and looked a little green. "Amazing, simply amazing. I've never seen this type of mass to energy conversion before. It's like they're those Saiyajins from Dragonball Z. I've got to see that show more often. Maybe they can do their attacks too. This is awesome."
A very green Katsuhito turned to Washu. "I don't know about that. It's also just as sickening. How can they eat like that? Mother and father would not approve of this?"
Washu just waved her hand and barely missed some spittle that came flying her way. "Don't worry! Lots of cultures have different eating habits. It's also interesting that they're fighting over their food."
Katsuhito shook his head. "This will not do."
**XxxxxxxxxxX**
Noboyuki walked in the front door tired from a long day at the office. He had been spending time with his father-in-law and Washu since Tenchi went on vacation. He was sure his new wife wouldn't mind tending their apartment for another day alone. He patted the large brown bad in his hand with a smile.
He barely set his foot in the door when Katsuhito dragged him into the kitchen. "Would you mind explaining this?"
Noboyuki had a piece of paper shoved in his face. He then started reading.
_'I Saotome Genma, Masaki Noboyuki, and Masaki Achika do declare that should we have children of the opposite gender then they will marry when one has reached the age of 19 and the other is at least old enough for permission to marry. Dowry is dependent on what the party giving it has available._
_We do hereby swear on our family's honor._
_Saotome Genma_
_Masaki Noboyuki_
_Masaki Achika_
Noboyuki scratched the back of his head. "Oh yeah, I haven't heard from Genma in the past sixteen years. The last I heard his wife was pregnant. If I remember correctly, we were having a drinking contest with Soun and Genma's master. He was always a hoot."
Katsuhito rolled his eyes. He remembered that old coot all too well. _Wait, I remember, that old man had a similar bio-energy as the girl and her father. Interesting._ "Do you know what you have done? Tenchi has to marry Genma's daughter now!"
Noboyuki's eyes lit up. "If you have the contract and you're talking about his daughter then..." Noboyuki stuck his head into the living room to see a fat man with a dirty white gi. "Genma, old buddy! Are you in luck! I just got some really good plum sake. Let's drink to the union of our families!"
Katsuhito could only slap a hand over his face as the two men began to guzzle liquor. He would get no more answers for the moment.
**XxxxxxxxxxX**
The lights were out and Ranma and Genma were getting ready to sleep in the den. When the other residents left, Genma pulled Ranma to the side and slurred, "Don't wuin dis!"
Ranma looked angrily at her father while holding her nose. "Oh, and why shouldn't I?"
Genma pulled out a piece of paper and shoved it in her face. "Honor demands vat you marry Tenchi."
Ranma looked over the document. "You're kidding right!"
Genma held up his hand and handed Ranma another document he had been hiding. "Dook at dis one."
Ranma looked over the document and then paled. "You're shitting me right. Wait, didn't you tell me she was dead."
Genma shook his head and sobered up a bit. "She's not dead. I simply thought that if you knew she was alive you would go crying back to her and left our little journey prematurely. And yes, she would certainly make both you and me commit seppuku if you don't fulfill it. The only way for the both of us to stay alive is if she doesn't find out about us until you're far along enough with a child that she'll be mollified about having grandchildren that she can spoil. Heh, spoil them or kill them, she's such a pathetic woman."
Genma was surprised at the force with which Ranma shook him. "I can't believe you. First the training trip and now I find out that my mom is some psychopath out to kill me! What's wrong with you? What's wrong with her?"
Genma saw the same fiery red-head that had cowed him into her bed in the girl standing before him now so he did the only thing he could. He pulled out a glass of cold water and transformed into a panda. 'Don't hurt me.' flip 'Pandas are endangered.'
This did not mollify Ranma as she continued to beat down Genma.
**XxxxxxxxxxX**
Katsuhito shook his head and turned toward Washu. "The girls won't like it when they find out, but there is no way I'm going to try and call it off now. Not that it would matter. I'll send mother a message tonight so they'll arrive around the same time or a little before Tenchi. Misaki and Funaho should keep them from tearing the poor girl apart."
Washu was pinching her nose. "That man has to be the biggest idiot in the universe. Though I've got to give the girl credit. I didn't think it would be possible to tie those short panda legs into a pretzel."
**XxxxxxxxxxX**
Katsuhito and Washu were woken up by the sound of someone crashing through glass and a yell of "Dammit pops! You broke their door!"
"It looked clear to me. How was I supposed to know it was glass?"
Katsuhito popped some aspirin into his mouth and sighed. "I hope mother gets here soon. What am I saying?"
#Crash# "Pop! You broke a section of their dock!"
Several thuds were then heard followed by a splash. Heavy but wet footsteps were heard entering the house. "Sorry bout the mess. I guess I've got to start cleaning and rebuilding."
Katsuhito popped some more aspirin and started to pray that his mothers showed up soon.
**XxxxxxxxxxX**
Washu was pouring herself some orange juice for breakfast. She was thinking over how to tell these earthlings that they weren't from earth. It had to come sooner or later. She just needed to... She was broken out of her thoughts as a wet panda pushed her to the side and started raiding the fridge.
The panda held up a sign. 'Elder men first. Little girls should know their place.'
_Oh, what the hell._ Washu whipped out her keyboard and hit a special key. Genma then shrank and became a cross between a panda and a kappa. Ranma walked in the kitchen just in time to see it happen. She was amazed at this and disgusted at the same time as he now looked like a hairy toad or salamander. "Uh, Washu-chan? What was that?"
Washu laughed maniacally. "Why its only my hyper-dimensional genetic realignment device! Am I a genius or what?"
Ranma actually looked intrigued. "Uh, can that hyper whatever change someone's form?"
Washu cocked her eyebrow. "Well, only for about ten minutes then they change back. It's hard to actually..."
Washu was interrupted as the panda suddenly exploded in size and sent off some arcs of electricity. "Whoa, it's never done that before! Why did he change back so fast?"
Ranma wanted to know too. If she could find a way to change back into a guy...
She was interrupted as Washu began to comment again. She was reading off of her... _ultra thin board of light?_ "Wow! You have two locked forms of dimensional space." Both of them looked at her funny. "I can't change his form because he has two locked forms. The Jusenkyo curse limits you to only those two forms. I could lock him in one form or the other but if I did that then I might lose the other form. Interesting..."
Washu didn't notice as Ranma paled at her statement.
**XxxxxxxxxxX**
The doorbell rang. Katsuhito popped some more aspirin and turned some beads over in his hand. He rarely liked dealing with his mothers but it would be a blessing this time. He took in a breath and opened the door. As soon as he did, Misaki tackled him to the ground.
"Oh Yosho, it's been too long. Why don't you call us more often? How is our favorite son?"
Funaho stood over him with a tilt of her head. "Yes son. How have you been? What trouble are you in now? You tell us it's an emergency, hint at our great-grandson getting married, and told us to leave your father on the ship for awhile? Now what, pray tell, is going on?"
Katsuhito motioned towards a couch. From there, they could see a spaced out red-haired girl, Washu ranting, and... a bear? Funaho pointed to the kitchen only to be stopped by Katsuhito. "That's what we're here to talk about."
Katsuhito pulled out a piece of paper and handed it over to Funaho and Misaki. Funaho's brow furrowed and Misaki started clapping. Funaho turned to her son. "Is this for real?"
Katsuhito nodded. "I'm afraid so. She's about 3 years younger than Tenchi, but her father has given his consent for them to marry and Tenchi just reached the agreed upon age."
Misaki started jumping up and down. "Yeah, Tenchi finally has a bride."
Katsuhito sighed. "Yes, I suppose so."
Funaho sat back in her seat. "Is it the spaced out girl in the kitchen?"
Katsuhito nodded his head. "Yes, her name is Ranma Saotome. She claims that she doesn't want this, but I think it's starting to sink in that her father simply won't break off the contract."
Funaho looked askance at Katsuhito. "She doesn't want to marry Tenchi? Surely she's seen what a good looking and good-natured boy he is. Why wouldn't she be interested?"
Katsuhito sighed again. "They haven't met yet."
Silence reigned for a second. Funaho slowly drawled out. "Haven't met yet?"
Katsuhito just kept on sighing. "She and her father just showed up yesterday. When I confronted Noboyuki about it he suddenly had to drink with his best friend to celebrate. He's still recovering from the hangover upstairs."
Funaho stood up. "Well, let's meet the girl then. By the way, why is there a panda in the kitchen stuffing its mouth with food?"
**XxxxxxxxxxX**
Katsuhito moved the red-haired girl to a couch in the living room while trying to keep Misaki from crushing her to death. Genma continued to consume from the refrigerator while Washu kept analyzing him. Katsuhito wasn't sure what would be better: letting the panda continue to raid their food supplies or have the sleazy man meet his mothers. He left the panda in the kitchen.
After a moment of silence, Funaho spoke to the girl. "Hello, I am Funaho Masaki Jurai. It may seem odd but I'm Tenchi's grandmother. I hear that you are betrothed to my grandson."
Ranma continued to stare blankly forward. Funaho snapped her fingers in front of the girl's face. "Hey wake up! The building is on fire. There's a meteor headed towards the house. Dammit respond to me!"
Misaki then commented. "Oh the panda looks like it's going to eat all of the food."
Misaki's comment seemed to bring Ranma back as she sat straight up and yelled, "Like hell!"
Ranma picked up a glass on the table and beaned the panda in the back of the head knocking it out. She then heard some clapping behind her and saw two women behind her. One looked like a normal Japanese woman with long black hair and the other had blue hair. They both had strange clothing on. She turned her attention to the Japanese woman as she motioned to the girl to sit down.
Funaho reintroduced herself. "Let's try this again. I'm Funaho Masaki Jurai, Tenchi's great-grandmother."
Misaki joined in as well."And I'm Misaki Jurai. I'm also his great-grandma, but I prefer Misaki or Misaki-oneechan if you don't mind."
Ranma looked between the two women and noted their age. _How are these two great-grandmothers?_ She then replied intelligently, "Huh?"
Funaho turned an eye to Katsuhito. "You haven't told her anything yet have you? Yosho my boy, you are a fool."
Katsuhito shook his head. "I had to make sure the contract was authentic first and then call you. Not to mention that the secrets..."
Funaho finished his statement for him. "...are part of the family that she is now bound to join. Seriously son, what were you thinking?"
Katsuhito scratched the back of his head. "Well, you see, I was afraid of how Ryoko and Ayeka might react so I figured..."
Funaho once again finished his statement for him. "...that we would intervene and save this poor girl from getting slaughtered while keeping the others under control. Well, we will save the girl from them, but you're going to have to explain it to them. You know that the royal court will not accept her even with the contract unless she can find a tree. Don't worry too much Yosho. We'll take good care of her. I think a solid month will give us enough time."
Ranma had been trying to follow the conversation but only picked up pieces of what they were discussing. "Uh? Who's Yosho? And what do trees have to do with royalty?"
Funaho looked over at Ranma. "Good questions my dear. And to start it off... Yosho! Lower your disguise field."
Katsuhito sighed and held his hand to his neck. The old man vanished to be replaced by a vibrant young man. "This is my true form Ranma."
Ranma looked at him and shrugged her shoulders. "Okay, so you're a ninja and not really some old man. What's the point?"
Misaki placed a finger to her lip. "Yosho is a ninja?"
Funaho shook her head. "No. My son is not a ninja. He really is Tenchi's grandfather. Considering that he's more than 700 years old, you would think that he would have had more than one heir."
Katsuhito sweated a little at that comment and coughed. "Well, how should we do this then?"
Funaho sighed. "I'll give her the pertinent details. We are not from Earth but a planet called Jurai. Misaki and myself are the current empresses of Jurai. Earth is a protectorate of our empire and has yet to develop enough to join our ranks. You are currently betrothed to my great-grandson who is the next in line to the throne. Therefore, you will be Tenchi's first wife and empress of Jurai."
Ranma's eyes widened at that proclamation. "I'm going to be empress? Like hel..."
Ranma was cut off as a panda paw covered her mouth. It then held out a sign. 'Don't mind Ranma.' flip 'She would love to be empress.' flip 'Besides, honor demands it.'
He then let go of Ranma while she darkly muttered to herself. Misaki clapped her hands and pointed at the panda. "It's so cute."
Funaho raised an eyebrow. "Yosho, I repeat. Why is there a panda in this house?"
Katsuhito pulled out the bottle of aspirin again and took a few pills. "He is her father."
Funaho began to laugh. She continued to laugh and almost rolled on the floor until she saw the serious look in her son's eye and sat back up. "Bullshit."
Washu appeared behind the panda and poured hot water over it. "It needn't be that hot little girl!"
Misaki frowned when she saw this. "He was cuter the other way."
Funaho just turned back to Katsuhito. "Explanation now!"
Katsuhito hunched back in his chair. "From what the man told us, he visited some cursed springs and became cursed. Whenever cold water hits him, he becomes a panda and with hot water becomes a man. Uh, mother why not take Ranma with you now. I'm sure that..."
Funaho turned to the man in the dirty gi. She found that the daughter had a naïve, arrogant, and annoyed disposition from talking to her and watching her body language. Her father, however, gave her the feeling of one of those underhanded spaceship salesmen. The type that would sell you a ship with potentially lethal pressurization problems and simply not care. "So Mr..."
"Genma Saotome." She could now smell the gi which smelled of wet fur.
Funaho held back from scrunching up her nose and focused on the man in front of her. "So, Mr. Saotome. I'm sure you already know who we are and what we were discussing so I'd like to ask some questions. What do you do for a living? Does your daughter actually want to go through with this?"
Genma puffed out his chest. "I'm a master of the Saotome branch of Anything Goes Martial Arts. I help the weak as it is the duty of a martial artist. It doesn't really matter what she thinks because she is honor bound to marry Tenchi."
Ranma had finished pulling the fur out of her mouth at this point and turned a heated glare at her father. "Like hell I wanna marry somebody. And what do you mean help the weak? You stole from every person you met on the road. I was only able to pay half of them back for what your fat hide..."
"Look! Some pork buns!" Ranma looked around to where her father was pointing. She was about to respond that there was nothing there, but she didn't get the chance as a knife hand was brought down on the back of her neck. Genma scooped her up before she fell and turned toward the others. "Oh, she doesn't know what she's talking about. She likes to spin a lot of stories so just ignore her. I'll just take her out back and talk to her."
Genma turned to leave when a hand tightly grasped his shoulder. What he didn't expect was the blue-haired woman. Her smile actually seemed kind of scary. "Oh, I think that we'll be taking her from here. Isn't that right Funaho?"
Funaho nodded her head. "Yes. I would so like to get to know our new daughter-in-law. I'm sure she'll have many stories of you."
Genma was starting to break into a cold sweat. The stares from these women were kind of predatory and it scared the shit out of him. "Uh, here you go!"
Genma tossed his daughter at Misaki and disappeared. Misaki picked the girl up and walked over to Funaho. Both of them frowned while turning to Katsuhito. Funaho spoke to him. "I expect you to keep that mongrel of a man on a leash. We do not need more scandals in this family. Keep us informed of any new developments. Goodbye son."
As his mothers vanished with Ranma, Katsuhito released a breath that he didn't know he was holding. "Oh boy!"
**XxxxxxxxxxX**
Ranma woke up on a soft bed. What she didn't expect was to wake up wearing something similar to what those other women were wearing. Where theirs had been green or purple, hers was a light red color. She sprung out of bed and looked herself over. "What is it? Dress up Ranma day."
Ranma then noticed someone else in the room with her. It was young woman with a similar style of outfit, but the design was simpler and brown in color. The woman bowed slightly to her."Ah, Lady Ranma! Empress Funaho told me to bring you to her and Empress Misaki's chamber after you awoke."
Ranma was about to blow a gasket at being called a 'lady.' The entire day was starting to turn into one major migraine. "Uh, could ya just call me Ranma? Lady just doesn't suit me."
The servant bowed to her. "Yes. I would like it if you would call me Erica as well. It's not often that I run into nobles that are informal with their servants so I think I'll enjoy working with you. Just remember that I'll have to call you Lady Ranma when in public. I guess it's not everyday that one gets swept off their feet to find that they are about to become a princess."
"A prin.. princess?" Ranma was really starting to become confused with everything that was going on.
"Of course, you are betrothed to Prince Tenchi-sama so that would make you a princess. All that is left is for you to go through the tree selection ceremony. I hope you get a wonderful tree."
"Huh? Tree?"
Erica nodded to Ranma. "Yes, I think that Funaho wished to discuss that with you. It's not my place to tell you. Now come along Ranma."
Ranma looked down at her garb. "Can't I get some pants first?"
**XxxxxxxxxxX**
Ranma looked around the spacious room in awe as Erica closed the door as she left the room. The entire room was arched over by roots and there was an open back wall showing forest with a waterfall. She then saw two figures at a table sitting there sipping on tea. Funaho motioned for Ranma to sit down in a chair at the table.
Funaho turned to Ranma and began to speak. "I must apologize for that short and somewhat less than informative talk that we had at the Masaki household. If anything I think I said too much there. I did a little digging into you and your father's past. I found many confusing records and was hoping you could clear them up for me.
First, I found many confusing police reports of a man claiming to be Ranma causing many vandalisms, theft, injury, etc; however, this man was described as a fat, balding man. Was that your father?"
Ranma nodded her head. "Damn Oyaji, blaming things on me."
Funaho nodded her head. "As I suspected. Now the second part is more confusing. I found records stating that you were male until about three or four months ago. Now I know that you are that man's daughter. Genetic tests prove it so the contract that he wrote up with our granddaughter and grandson-in-law is valid. Are you his unrecorded love child or are you really Ranma or is it something else? It would be hard to believe that he faked you being a boy. Believe me, I saw everything when we dressed you after taking those filthy clothes off."
Ranma was halfway between being angry and scared. _Damn it, they were the ones that dressed me up. Now the problem is they want to know what happened. How the hell do I tell them I'm really a boy? What the hell?_ "Uh, I'm actually male or I was."
Funaho took another sip of her tea while Misaki scanned over the girl. Misaki then leaned back in her chair. "No way are you a boy! Trust me, I know."
Funaho turned her tea cup. "It wouldn't have to do with those cursed springs would it."
Ranma sighed. _Finally, I can tell someone the truth. _"Yes."
Funaho nodded. "Do you change back with hot water?"
Ranma hung her head at that statement. "No, it's permanent. Someone sealed the curse on me to punish my father for stealing their food. I've been a girl for three months now."
Funaho nodded her head sagely. "And how have you been taking it?"
Ranma sighed once again. "Not too well. Pops keeps telling me that I'm a weak little girl. When I bled down there, well, he almost disowned me. He never told me what that meant and just kept saying that I could never be his heir."
Funaho put her cup down on the table with a little bit of force. "You're a complete woman then. That means the marriage contract is still on at least. So, has anyone given you the talk yet?"
Ranma looked confused at her for a moment. "What's the talk?"
Funaho and Misaki both looked at each other and sighed. "Come stand over beside me Misaki dear. I guess we need to start from scratch with her. It's time for biology 101 Ranma."
**XxxxxxxxxxX**
Erica led a very pale Ranma back to her room.
**XxxxxxxxxxX**
Funaho sat back down in her seat pinching her nose. "Well that could have gone better!"
Misaki put her cup down on the table and placed a hand over one of Funaho's hands. "Don't worry Funaho. We've already set aside a whole month to work with her. I'm sure things will work out."
Funaho shook her head. "That's not the problem. I'm sure we can prepare her for at least some of what she'll have to deal with, but I'm more worried about the long term. I can see that she's given up some hope of returning to her male form but will that be enough. She has to be willing to bear children and actually have a relationship with Tenchi. The real problem is that Achika isn't alive. Bless the poor child. If she were, then we could just have her break the contract and pay the fee for breaking the contract with that fat father of hers. Now the only one that can break the agreement is that fat fool. After hearing that we were empresses, I doubt he'll break it off and even then the price he and especially his daughter would have to pay would not be worth it. The sad thing is that the one being hurt by this the most is his own daughter."
A beeping caught their attention as a message pulled up on a light screen. It had little dancing crabs attached to it. Funaho pressed the open button. "Aw, the medical report from Washu. She said that she had needed a little extra time to extrapolate her medical history from her scans and memory dive."
Misaki clapped her hands. "Ooh, let's see what she's like."
Funaho sighed and shook her head. "You know this would be considered a breach of privacy, but my preliminary investigation demands a more thorough look at the girl."
Funaho pushed the open button for the attachments and sat back as a list of incidents and statistics displayed on the screen along with several video files. Both Funaho and Misaki started pouring through the data on separate screens. Funaho wasn't surprised when Misaki jumped up from her seat and started puking over the balcony. The enraged face that came back into view also was not surprising but it was very disturbing.
Misaki didn't even register Funaho as she started for the door. "We're turning the ship around! I'm going to kill that man!"
Funaho was out of her seat in a flash and had her arms securely around Misaki. "Calm down! We can't turn around now. Besides, she won't be near him while she's with us."
Misaki kept struggling against Funaho's hold. "Dammit let go! I'm going to make a panda skin rug for our room!"
Funaho strengthened her grip. "If we do that, then other people are liable to catch wind of this. It would do more to hurt the girl than help her. Washu also left a note saying that she would turn him into her newest guinea pig. I can assure you that that will be enough punishment until we return with her a month from now. We'll also have some time to think out a truly fitting punishment for him during that time. It's not like he's going anywhere."
Misaki's struggle ceased as she calmed down in Funaho's embrace. "Alright, but we better think up something fitting."
Funaho released her hold on Misaki and sat back down. "So, what set you off like that?"
Misaki turned a little green before responding. "Read text C1-5 but whatever you do don't play the video file that goes with it unless you want to be scarred for life. I made the mistake of playing the video file first."
Funaho nodded her head and then turned toward the screen selecting the file. As she read through the file, her face turned pale. "This really happened."
Misaki nodded her head. "It explains why files from later in her life reported that strange behavior and fear of cats. After watching that video of her or rather him in the pit, would you mind telling the palace guards to remove all felines from the palace."
Funaho nodded her head. "It would be best I suppose. We can't have the poor girl freaking out at the palace."
Misaki shook her head. "That's not why I asked. What I mean is that I'll probably start blowing them up with energy blasts and I wouldn't want to ruin the palace. Evil little vermin."
Funaho started to sweat. _That must have been one hell of a video._
**XxxxxxxxxxX**
Ranma once again woke up on a soft bed and sighed to herself. _This is getting to be annoying._ She sat up to see Erica sitting in a chair next to the bed. "I see you're taking this rather badly Ranma."
Ranma lifted herself up from the bed and shook her head. "Yeah, things have been rather confusing."
Erica nodded her head and walked toward the door opening it. "Funaho-sama told me to bring you to the dining room when you awoke. They should be starting dinner soon."
Ranma once again walked down the corridors of the ship, admiring the wide halls and strange plant life that could be seen around the ship. Erica continued to lead her until they reached a large, open room with a wooden table at the center. She saw Funaho, Misaki, and a man with long hair and a long beard sitting at the table. Erica announced her arrival. "I present to you Lady Ranma Saotome."
Funaho nodded to the servant. "You may leave now."
Erica bowed and left the room as Ranma made her way to an open seat. She wasn't sure of what was going on as no food had been served yet and the three people at the table were looking at her intently.
The man sitting directly across from her coughed slightly and started to speak. "I am Azusa Masaki Jurai, Ruler of the Juraian empire. I take it that you're Tenchi's fiance. I hope you understand the importance and prestige of the position that you will take up as future empress of the Juraian empire. I expect many great things from you."
Funaho laughed and grinned slightly and looked over at her husband. "Don't worry dear. Both Misaki and I will take care of that."
Azusa frowned at that declaration. "I'm sure you will. I'm guessing you're going to impart you're infinite wisdom on her."
Funaho's grin grew. "Of course. She'll need to learn about space, our history, and many types of politics. I'm sure you know the type to which I refer dear. I'm sure you won't mind her learning directly from us dear unless you'd like to be sleeping on the couch for the next century."
Azusa started to sweat until he saw the food arrive. "Aw, why don't we partake in the feast dears."
Funaho and Misaki chuckled at his expense as food was laid out on the table. Azusa was about to start in on the feast when a large portion of the food started disappearing. He looked up to see something that in his millenniums of rule he had never seen and never wished to see again. The little red-haired girl was literally inhaling food in front of him. He then looked over to his wives to see... expectant, if a little annoyed expressions on there faces.
"Oh dear, Washu's words doesn't do it justice." Misaki was actually frowning a little.
"This is a habit we will have to break." Funaho just shook her head at the red-head's actions.
**XxxxxxxxxxX**
After dinner was complete, Funaho and Misaki pulled Ranma into their chamber. They sat her down on the edge of their bed as each one took a position beside her. This made Ranma squirm as she had nowhere to go as these women stared intently at her.
"Now why did you eat so fast dear." Funaho had a good idea of why that might be but she had decided to post-pone reading more about Ranma's life for a later date after reading the description of the Neko-ken.
Ranma shrugged her shoulders. "It's always been that way with pops. If I wanted to eat, then I had to fight for my food and eat it quickly or pops would steal it from me. He said it was speed training. I really didn't get fast enough to beat him until I was about twelve. I'd go days without food because I either couldn't beat him or he had spent all of our money on sake when we needed food."
Misaki's hmmphed as she turned her gaze back to Funaho. "I told you we should have turned around. That panda skin rug is sounding better every minute."
Funaho faced Misaki and sighed as she spoke. "How about a compromise? We go back and see how Washu is punishing him. If you don't think it's enough, then we'll initiate the plan I came up with for him a little early. Agreed."
Misaki nodded her head. "Agreed."
Funaho turned back to Ranma. "We'll get you over that dear. No one will steal your food here. Now, let's start talking about your tree ceremony. It's probably going to be the first thing that we do when we get to Jurai."
Ranma quirked an eyebrow at that. "Yeah, everybody keeps talkin about that but I still don't know what that is."
Funaho nodded and folded her hands in front of her. "What I say now and every step of the process is highly classified so you can tell no one of this except those of the noble houses. Do you understand?"
Ranma nodded her head and Funaho continued. "The tree ceremony is where one finds a tree to bond to for life. This bond allows one to tap into the power of Jurai, specifically that of Tsunami. This link also occurs to a lesser extent for those that do not have a bond but only for the citizens of Jurai. In your case, you already have a ki supply that is far greater than most humans so I can only imagine how the bond will affect you."
Ranma raised her hands up and waved them in front of her. "Uh-uh. I don't want any other weird thing happening to me."
Funaho cracked a smile but it soon turned to a slight frown. "It won't hurt you dear. I went through it myself so I should know. It's a wonderful feeling. The tree is sentient and it is like a warm mother, child, or some other form of partner as you might imagine. Unfortunately, you don't have a choice like most do because of the marriage contract. You see only noble Juraians can marry into the royal family as the first and second wives of the emperor. Since you weren't born into a noble family, the only other way to reach noble status is to have your own tree."
"So I'm going to have some plant bonded to me? It isn't going to change me is it?" Ranma really didn't like where this was going. If changing genders hadn't been enough.
Misaki leaned a little against Ranma and started stroking her hair. "Don't be scared; it won't change you. It's a wonderful experience where you share a link with another living thing. It will always be present in your mind but it does not change you. Rather the tree selects you and you the tree based on similar personalities. The tree grows and is influenced by you rather than it influencing you as much."
Ranma seemed to relax some with that statement, but she was still on edge as the two women hung to her sides. "I guess it's okay then. Uh, what else did you want to talk about?"
Huge grins spread across both Funaho's and Misaki's faces as they turned around to face Ranma. "Oh, how about a grand introduction to what it means to be a woman."
**XxxxxxxxxxX**
Katsuhito was broken out of his peaceful tea sipping as the front door opened and he heard a number of people enter.
"Hah, told you I'd beat you!"
"That isn't fair you monster woman! You cut holes in our bathing suits before the competition!"
"Oh quit your whining miss prissy pants. You're just a sore loser!"
"You're one to talk. You only got second place!"
"Better than third."
"Look at how my first place medal shines!"
He saw the fuming figures of Ayeka and Ryoko enter with heated glares at Mihoshi. "Shut up!"
"Now girls, try to calm down some." Katsuhito turned his eyes to his grandson. _Well, the choose has already been made for you boy. I'll hold off telling them for a little while to give mother some time with Ranma until she has the protection of her own tree._
He then heard another voice call him from the kitchen. "I'll start on supper grandpa!"
He smiled at Sasami's happy demeanor. He turned his attention back to Tenchi as he started to approach him. "Hey grandpa, where's Washu?"
Katsuhito snickered. After Washu had recovered and had some time to view some of Ranma's memories, she had simply brushed Katsuhito aside, grabbed the panda bear by the ear, and dragged it to her lab, slamming the door. He didn't know what set that off, but he could only imagine. "Oh she found a new guinea pig while all of you were out. I think she muttered something about a month long experiment with pandas, weasels, and circus clowns. She also said not to disturb her."
Everyone fell silent at that comment until Tenchi spoke up. "Uh, should we be worried about the person that..."
Katsuhito shook his head. "No, her new guinea pig is just getting his just desserts."
The normal muss and fuss of the house started up again.
Katsuhito sighed in relief. He had just avoided a major disaster or so he thought.
**XxxxxxxxxxX**
Soun Tendo was humming joyously as he walked up the mountain road outside Okoyama. He was trailed by his three daughters. Akane was in her yellow dress, Nabiki was wearing dark pants and a brown shirt, and Kasumi was wearing her usual blue dress and white apron.
"Daddy, why did we come all the way to Okoyama to climb a hill for a picnic. It doesn't make sense. For that matter, why did we walk instead of paying for the bus. I mean we spent a hell of a lot of money for the train just to get here." Nabiki was seriously starting to wonder what her father's real motives were.
Soun chuckled. "Oh, my old friend has a house in these mountains. Although, I wish I had known that he moved the house to the shrine. It is quite a walk."
They arrived at the edge of a bend in the road and were able to take in a spectacular sight. They saw a two story house below them that was sitting next to a sparkling lake. There were fields of carrots, a giant tree, a shrine, and a wonderful forest.
Nabiki whistled out loud. "Didn't know that your friend was loaded daddy."
"Oh my, it is such a beautiful home!" Kasumi was holding a hand to her mouth and smiling.
"It is rather nice looking. So what are we here for dad?" Akane scanned the place noticing the open fields around the house.
Soun sweated a little as he led his daughters down the steps to the house. "The thing is... I made a promise to my friend Genma Saotome to marry you to his son but I haven't heard from him in ten years so I gave up hope on that idea, but there was another marriage contract. Two years after Nabiki was born, I made a marriage contract with my friend Noboyuki and his wife Achika to marry our children. He told me that he already had a contract with Saotome to marry his son to any daughter he had, so we agreed that we would break off our agreement if it conflicted with Saotome's agreement with him. Since Genma had a son and no other children it then falls to you three girls. Tenchi is currently 19 and you girls are the right age so..."
Soun was cut off as Akane started blazing with fury. "Like hell I will. I'm not marrying some dumb boy. I'm going home."
Soun started to tear up. "My baby is abandoning me."
Akane stormed back up the steps as quick as she could. Nabiki rolled her eyes while Kasumi seemed torn between trying to get her father to stop crying or following Akane to make sure she was okay. Nabiki walked over to Kasumi and handed her some yen. "Take miss hot-head home. She'd only blow up at these people and we are guests here. Somehow I don't see you going through with this either."
Kasumi started to walk up the steps but turned back to Nabiki with a slightly worried look on her face. "Don't worry sis. Everything will be fine. Just move along now. Come on daddy let's go."
Nabiki waved goodbye to Kasumi and started to lead her weepy father along. _Heh, works to my advantage. This guy must be loaded. I've hit the jackpot here. If he's ugly or strange, I'll just pass the buck to Akane. No sweat._
**XxxxxxxxxxX**
Katsuhito had finished his dinner a half hour ago and was peacefully reading the newspaper until he felt a terrible omen when the doorbell rang. He then felt a shiver when Noboyuki yelled out 'I'll get it.' He reached for his aspirin when he heard Noboyuki say, "Well if it isn't my drinking buddy Soun and is this your daughter? Come on in. Why don't we go to the living room."
Katsuhito looked over at his son-in-law as he led a long-haired, moustachioed man in a brown gi with his daughter. She had brown hair in a pageboy cut and was wearing earth-tone pants and white shirt. His foreboding feeling of doom only increased as the man pulled out a parchment and laid it on the table. Before a word came out of the man's mouth, Katsuhito grabbed the paper off of the table and scanned over it quickly. He then slapped his hand over his forehead before suddenly grabbing the girl and dragging her into the hall.
The girl tried to break his grip and yelled at him. "Hey, what's the big idea buddy."
Her father also ran after them but just barely missed them as Katsuhito disappeared into the doorway under the stairs.
**XxxxxxxxxxX**
Washu was having a fun time. Sure it wasn't really an experiment, but it was fun. "Hah, weasels win again. It's time for a clown penalty again Mr. Panda."
In the arena below her, a panda was running away from clowns with half full water balloons. One of the clowns almost got to him before an alarm went off which disturbed Washu's focus. "Dammit! Who is it?"
Katsuhito wiped some sweat off of his forehead. This may have been more dangerous than protecting the girl from the others. "We need to contact my mothers. We have another one."
"Hey, mind explaining what's going on and another thing... Is that a panda... How can someone shove a fish that large up there?" Nabiki's fury was sidetracked by the sight of a panda fighting and losing to rodeo clowns with fish sausage, tuna, and half-filled water balloons?
"Another?" Katsuhito held up the contract so that Washu could see it. "Oh well, daughter of mine won't be happy and neither will Ayeka, but those are the brakes. They can always jockey for third and fourth."
Katushito nodded. "Can you contact them and have them send a transport?"
Washu looked over her light panel screen. "I can do you one better. They came back. Initiating live com link."
A large screen appeared before them. Misaki showed up on the screen and shouted, "Where is that rat bastard Genma Saotome?"
Washu cleaned her ear out after that scream. "Oh, I have him dancing prettily. Here's some feed."
The woman on the large screen seemed to look over at something and giggle. "Ok, that will do. Just don't kill him. I want to have some fun too."
Washu nodded her head in satisfaction. "Wouldn't have it any other way. Oh, by the way, it seems that Tenchi has his second wife lined up. It appears little Achika was quite busy in her youth. I'm sending her to you now. I'll leave the explanations to you."
Nabiki had started to regain her wits after seeing all of these impossible sights and responded to Washu's comments. "Hey! What do you mean by sending me to them? I demand..."
Nabiki disappeared in a beam of light.
Katsuhito sighed and sat down beside Washu. "Got some popcorn."
Washu handed him a bag. "This kettle corn stuff is pretty good. Now that the previews are over let the play begin."
**XxxxxxxxxxX**
"...to know what's going on." Nabiki finished her sentence in a totally alien room. The previous space had been nothing but blackness as far as the eye can see while this room was highly decorated with a view of a waterfall and a ceiling made of roots?
"Where the hell am I now?" (Remind you of someone.)
"Don't worry dear. Come sit down and we'll explain." Nabiki turned around to see two regal women and a nervous teenager. The woman on the left had long-flowing black hair and wore some type of flowing pinkish-purple dress and the woman on the right had blue hair and a greenish-blue dress of the same style. The teenager sitting next to the woman with the black hair had red hair, blue eyes, and a red dress of a similar make. The girl didn't seem to be too comfortable at the moment.
Nabiki eyed them as she sat down next to the woman with blue hair. "Mind telling me what's going on. I remember being in a house in Okoyama and suddenly I'm whisked away to some lab and now this place. I want some answers or there will be hell to pay!"
Funaho chuckled and Misaki patted the irate girl on the head. Funaho turned to face the new teenager. "Now, now dear. I believe introductions are in order. I'm Funaho Masaki Jurai, First Empress of Jurai. And this," she pointed over to Misaki, "is Misaki Jurai, second Empress of Jurai and my co-wife. And the little redhead over there is Lady Ranma Saotome, first fiance of Prince Tenchi and soon to be First Princess of Jurai."
Nabiki looked dumbly at them. _These people are nuts. I've got to get out of here._ "Aw, I'm Nabiki Tendo. Wait, Saotome. As in daddy's other friend, the one who had a contract first. So, I'm guessing that makes you Tenchi's fiance."
Ranma nodded her head. She didn't want to admit it, but from what she could tell, it was a foregone conclusion. Nabiki nodded her head as well. "I guess that means I'm not needed. Uh, can you show me to the exit?"
Nabiki started to stand up but the blue-haired woman put her hand on Nabiki's shoulder. "Oh no dear. Both of you need to be here."
Funaho smirked as she sat back in her chair. "Think about what I said earlier for a second. You seem like a smart girl."
Nabiki looked over at Funaho and began to reason out what had happened. _Okay Nabiki, time to think this out. First, daddy said something about the Saotomes and our clan having marriage contracts with the Masakis. We get to the Masaki household only to have that old man drag me off the minute he sees the contract. We end up in a dark lab with a panda and other stuff before I magically end up here. I then meet the two empresses here and Saotome's daughter. Empress Funaho tells me that Ranma is Prince Tenchi's first fiance and … Wait two empresses, but that would mean... _"Hey, having two wives is illegal in Japan. What's going on here?"
A cheshire grin spread across Funaho's face. "Yes, it is, but then we aren't in Japan anymore."
Nabiki cocked her head to the side. "Okay, I'll bite. Where are we then?"
Funaho's grin spread even wider. "We are in outer space dear. Currently on route to the planet of Jurai."
Nabiki started chuckling and then laughing out loud. She then faced Funaho wiping away some tears. "Oh, you had me going there for a second. This must be some prank. This has to be the most elaborate set up ev..."
Nabiki's rave halted there as she noted the deadly serious expression on Funaho's face. "I am not joking dear. Does it look like I'm joking?"
A sinking feeling started to come over Nabiki as she realized that the woman in front of her was not joking. "So, everything you said is real? What am I really doing here?"
Misaki rubbed her hand through Nabiki's hair which annoyed her to no end. "It means that you're fiance number two for Tenchi-kun. Isn't that wonderful? You're going to be the second princess of Jurai!"
Nabiki numbly nodded her head. This was very surreal for her and she had no control of the situation. It was all very alien to her. "So why two wives?"
Funaho nodded her head and smiled. "That's a very good question. We were just about to discuss that with Ranma here. The Juraian empire is vast beyond imagination. Even though it is ruled by a monarch, it is in actuality run more so by his wives and the nobles, servants, and military under their direction. Think of us as the heads of the executive staff. While the monarch technically runs the empire, it is his two wives that direct military, domestic, diplomatic, and commercial affairs throughout the empire. This is also a reason why we want to start teaching you two starting now. Many events are being rushed and there is less time than we can hope for to prepare the two of you for your future duties."
Nabiki sat back and thought for a second on what she had just learned. _Hmm, queen of an empire? Empress Nabiki has a nice ring to it._ She then eyed the red-headed girl who still looked a little out of place. _She's pretty easy on the eyes as well. I'll have to question her when we're alone but I'd have to guess she's pretty shaken up by this. I mean who would believe in an alien empire really existing. Now, if what these women are telling me is true, then I'm about to become one of the most powerful women in the universe. Boo-yah!_ "I think this will work out just fine. So where do we begin?"
**XxxxxxxxxxX**
Back at the Masaki household...
Katsuhito was leaving Washu's lab after her rendition of several King novels using Genma. He never knew that a panda could move like that.
He was blown off his feet as a giant demon head hovered above him. "What have you done with my daughter?"
Katsuhito was about to pull out the Tenchi-ken but he reevaluated the situation. The head was attached to a very familiar body. He then noticed a tall girl with long brown hair approach it with a pin. She stuck the pen into the head and it immediately deflated into the familiar face of Noboyuki's friend as he fell onto the floor. The girl then turned and slightly frowned at him. He didn't know why but he was certain that the slight frown was far worse than the demon head had been. "While father can get excited easily, I'm afraid I would also like to know what happened to my sister."
Katsuhito picked himself up and bowed slightly to the girl as she pulled her father to his feet. "I will explain in due time. Please follow me to the living room."
She followed as he rounded the bend in the hall and froze as soon as he entered the living room. Everyone was gathered there. He wished that he still had a bottle of aspirin or some really strong alcohol.
He turned his head as the complaints started rolling in. Ryoko was the first. "Hey old man! What gives? All of my sake is gone. Even the emergency stashes that I hid."
Ayeka was next. "All of my jewelry is missing and while loathe to admit, Ryoko had nothing to do with it. What is going on?"
Sasami piped up after her sister. "All of the food in the refrigerator is gone. I stocked it with enough food for a month thanks to Washu's stasis field and subspace fold."
Mihoshi followed with her usual whine. "Someone ate all of my snacks."
Tenchi was last. "Someone broke the dock and several of mother's heirlooms are missing."
The last comment really started to tick Katsuhito off. He would have to force that idiot Genma to give back those heirlooms and the other things that he stole. "Sit down everyone. I will explain."
Once everyone was seated, he took note of a dark blue-haired girl who was sitting next to Noboyuki's friend. _Must be another daughter._ "I bet you all are wondering what has caused all of this turmoil."
Nods were seen across the room. Katsuhito then continued. "It is all due to one man who is currently suffering at Washu's hands. She's given up slightly on the guinea pig aspect for the moment and decided entertainment value would be the best use for the man."
He could see the shivers run through the residents of the household. "Yes, I know it seems a little cruel at the moment, but there are other extenuating circumstances. The man's name is Genma Saotome and he..."
Katsuhito didn't finish as Soun butted into the conversation. "Genma? Genma is here?"
Katsuhito nodded and Soun began to dance again bringing out fans. "Oh happy days! Now the schools can be joined. Where are Genma and his son?"
Katsuhito responded a little heatedly. "That filth Genma is currently with Washu receiving his just desserts and as far as I know he doesn't have a son. His daughter, however, is currently with my mothers."
Soun stopped dancing around and turned back to the man. "What do you mean by daughter? I thought he had a son. I need to speak with my old friend."
Ayeka also noted something wrong with that statement. "Our mothers! What do you mean she's with our mothers?"
Katsuhito sighed. It was time to start revealing the truth. "First of all, it would be ill advised to disturb Washu and her new play toy. Secondly, he has tried to rob this house clean. Thirdly, I have never seen such stunted growth and clear signs of abuse as the ones that I saw on his daughter. I would not be surprised if his son died due to his negligence and abuse."
Soun was now teetering on being furious. "Genma would never do that. He was training his son to take over their branch of the Anything Goes school."
Katsuhito shook his head. "Regardless, he arrived without a son and a very put out daughter. He might even end up on charges considering that there are several standing warrants for his arrest."
Soun stood in shock for a second before sighing. "I guess he let the master's lessons get to him. What of my daughter?"
Katsuhito started to sweat as he knew the next words out of his mouth would start a rather nasty chain reaction. "She is also with my mothers."
Ayeka's interest skyrocketed with that statement. "Why are both of those girls with our mothers?"
_Time to let the cat out of the bag_, Katsuhito thought. "Well, Funaho and Misaki wanted to get to know their future daughter-in-laws. They're going to be gone for the next month."
Silence reigned for a moment before both Ayeka and Ryoko exploded. "WHAT?"
Katsuhito knew he was in for it now. "Now, now girls calm down. It just so happens that my dear Achika signed two marriage contracts. One was with the Saotomes and one was with the Tendos. You know that official marriage contracts must be carried out."
Ayeka spat as she angrily yelled. "They can be annulled!"
Ryoko snarled. "Then get them annulled!"
Katsuhito waved his hands in front of him. "Calm down and think about it. The only one who can officially annul them was Achika and she has passed on."
Ayeka fell back into her seat. "Dammit that's right, but what about having the other party pull out?"
Katsuhito shook his head. "You know that that cannot be done. They don't have the resources to pay the penalties and the annulment would only occur once all of those are paid off."
Ayeka slammed her hand into her palm. "I could pay off the penalties."
Ryoko nodded her head. "I can scrounge up some money as well."
Katsuhito shook his head once again. "I'm afraid Misaki has grown rather attached to them both and Funaho approves of them so far. They have personally taken them under their wing. I would suggest not going after them."
Both Ayeka and Ryoko flinched at that statement. Funaho and Misaki could be really scary.
Ryoko purred to herself. "Well, it doesn't mean that me and Tenchi can't get married right now and put an end to those silly contracts. It would be the Masaki family's fault then but I'm sure it would be covered up."
"He's my Tenchi!" Ayeka grasped onto that new idea as she firmly grasped Tenchi and held him to her chest.
"No, he's mine." Ryoko nearly smothered Tenchi with her boobs. His nose began to bleed as his head acted like a volleyball between their chests.
What no one expected was a battle cry of "PERVERT!" as a hammer slammed down on Tenchi's head, driving him through the floor.
All eyes slowly turned to the blue-haired girl who now had a hammer in her hand. "Hah, take that you dirty pervert!"
The remaining residents of the house slowly backed out of the room as Ayeka and Ryoko started crackling with energy. "WHAT are you doing to my Tenchi you bitch!"
Akane blinked at the threat directed towards her in stereo. She was just taking care of a pervert. There was no need for them to ruffle their feathers. "He was rubbing himself in your breasts! He's a pervert!"
Ryoko cocked her head to the side. "Huh?"
Ayeka also wavered at that statement. "We were the ones who grabbed onto him."
Akane let out another burst of rage. "All men are dirty perverts!"
Ryoko smiled and teleported behind Akane. She then rapped her arms around Akane and rubbed her chest. "Oh, so you play that field then?"
The words had barely left Ryoko's mouth when a mallet impacted her head. Ayeka chuckled as the short girl hit Ryoko with the mallet. "Now that she deserved!"
Her chuckle died when Akane kept beating Ryoko's head into the floor. Sure Ryoko would be fine, but the bloodshot eyes and splinters digging into Akane's skin from splintering the mallet were cause for alarm. Several residents rushed the girl and subdued her as Ayeka called out. "Someone get Washu!"
**XxxxxxxxxxX**
Nabiki was putting on her nightie for bed time. While she liked having the servants, she was still a little uncomfortable with the idea of them dressing and undressing her. She carefully turned her eye to catch Ranma fingering her nightie as she faced away from Nabiki. The girl had barely spoken as the two empresses went into detail about the Juraian empire's history, some recent political events, and something called a tree ceremony. She had to admit that that part had her a little on edge. Apparently, she was expected to share her life force with some kind of weird tree. She had thought about refusing, but the knowledge that she would help rule an empire helped her to bite it back. The trees were also supposed to 'not alter ones personality,' but she was hard pressed to believe that.
Nabiki stood up after she finished adjusting her nightie and walked over to Ranma. Ranma was obviously lost in thought as she ran her fingers over the string of the top because she was startled when Nabiki placed her hand on her shoulder. "No need to be jumpy. I'm already on edge."
Ranma put her hand to the back of her head and bowed slightly. "I'm sorry."
Nabiki waved her hand. "Don't worry about it. It sounds like we're in the same boat, which is why I think it would be a good idea to get to know each other. And would you stop fingering that nightie and put the blasted thing on already."
Ranma sighed as she slipped the garment on. She was acting like she had just been defeated. "Whaddya want to know?"
Nabiki shrugged. "Anything I suppose."
Ranma thought for a minute and shrugged her shoulders. The girl really should know. "I was originally a guy, but I got a curse, thanks to my pop, that has made me permanently female. I've only been a girl for the past three months."
Silence reigned for a moment followed by a whistle by Nabiki. _Wow, I was not expecting that. Ok, given the situation, this isn't so far fetched. I'm betting that this whole deal is even more awkward for her. It would explain the brooding silence._ "O-K, the really heavy shit first huh. So what was it like being a guy?"
Ranma shrugged her shoulders. "You're stronger, you've got something down there, and you can inherit the martial arts school that you've only worked your whole life to master. I lost everything three months ago."
Nabiki was a little heated after hearing that but she'd give diplomacy a try. "Oh, and why'd you lose everything when you became a girl huh?"
Ranma sagged a little in her seat. "Pops says women are weak. He always has. He used to taunt me all the time about how I was weak like a woman. I guess he got his wish. When I had my first period, I was scared out of my mind because I thought I was dying. Pop wouldn't tell me what was happening and tried to disown me after it happened. The funny thing is that I received this curse when he dragged me off to some cursed springs because he thought it would be good training and then the curse was made permanent by some people that my father stole from. What was really funny was that I was trying to help those people stop my father."
Nabiki cooled off at those words. _Yeesh, and I thought daddy was bad._ "Look at it this way Ranma. We've now gained a position where we'll be the most powerful people in the universe. Kick your pop to the curb cuz we've got it made sister."
Ranma looked a little thoughtful at that comment. "But he's still my pop. I haven't abandoned him yet."
Nabiki's eye twitched a little when she heard that comment. _Really now. Let's find out a little more shall we._ "Oh, what has he done to earn your respect?"
Ranma put her finger to her mouth in thought. "He's taught me our family's school of martial arts."
Nabiki nodded her head. "What else?"
Ranma started to look a little uncertain as she replied. "Uh, can't think of anything else."
Nabiki pushed onto her next question. "And what has he done that has hurt you or been dishonorable?"
Ranma didn't have to think long as she started to list off his misdeeds. "Well, he stole, drank, let me starve once in awhile, and constantly called me a weak little girl for the past ten years that we lived on the road together. There were times when he made these agreements with men about something saying that he would give me to them in exchange for food, money, or booze, but he'd always steal me back when they got drunk and would scam another person. He defiled several temples and dojos. The damn Neko-ken training. He also didn't tell me about this arrangement until we arrived in Okoyama and knocked me out so I wouldn't run away."
Nabiki started rubbing her nose hard at those statements. "Ranma, your father is a moron."
Ranma shrugged. "Can't argue with you there."
Nabiki giggled at the laissez-faire attitude of the girl, especially considering the little bit of her past she had learned about. She was brought out of her revelry when Ranma asked her a question. "So what are your parents like?"
Nabiki pulled up a seat next to Ranma. "Well, my mother died when I was young. I had some memories of her but not a lot. The problem was that my father completely stopped teaching martial arts and fell into a booze soaked depression. At the age of 8, I was hustling kids and blackmailing people just to get enough money to pay our bills, food, and clothing for my father, my two sisters, and myself. The sad thing is that I'm still supporting the household. It's been 9 years and my father still sulks around the house."
Ranma nodded her head. "Yeah, guess that's been tough. What was your martial arts school?"
Nabiki shrugged her shoulders. "Anything Goes Martial Arts."
Ranma shot up from her chair. "WHAT? That should be our family art, the Saotome Anything Goes Martial Arts School."
Nabiki let that sink in for a second and then started to laugh out loud as she remembered what had happened when she arrived. She also started rolling on the floor. Ranma looked rather cross at her. "Hey what's going on? What's so funny?"
Nabiki started to wipe some tears from her eyes and sit up. "Only the biggest joke in the galaxy! Apparently, my dad and yours studied under the same master and made branch schools. They wanted to rejoin there sections by marrying their children together. Even had a contract! Don't you get it, we're marrying each other and that Tenchi guy. We're fulfilling both contradictory contracts at the same time."
Ranma chuckled a little nervously at that comment. "Ah yeah, I suppose."
Nabiki sat back down in her chair. "Whew, that was a good laugh. Got any other good jokes."
Ranma shrugged. "Not ones that ain't dirty as hell."
Nabiki laughed. "The raunchier the better. Let's get something to eat before we start though. Maybe some ice cream."
Ranma's eyes lit up at hearing the girl say that. _Maybe this girl ain't so bad. Still don't wanna marry that guy, but being with her ain't too bad._
**XxxxxxxxxxX**
Funaho stepped away from the monitor to fix herself some tea. "They are getting along quite amicably. I guess Yosho's idea was a good one. These young girls already seem to have some talents that will suit them well in their positions. I actually appreciate what Achika did for us by netting us these girls."
Misaki looked over at Funaho with a spoon hanging out of her mouth and chocolate ice cream dribbling down her cheek. "What's wrong with my little cutesy utsey Ayeka and little Ryoko."
Funaho took a deep inhale of breath and then spoke her mind. "Don't take this the wrong way but Ayeka can be an airhead and is quick to anger. She doesn't know how to budget at all and she's far too rigid in rules and regulations of the court. She really doesn't suit the positions of first or second wife because she would either screw up or end up being a political puppet. Ryoko... It was hard enough to pardon Ryoko. Sure, she did help to save Jurai and has been rather helpful lately, but many people are still wary of her given her background. She has an equally bad temper as Ayeka. Don't even get me started on Mihoshi. I may put my foot down on that one. That child is nothing but a walking disaster and our empire would crumble if she were ever to be made empress."
Misaki licked her spoon and eyed it speculatively. "Putting cuteness aside for the moment. These girls still have a ways to go. Even though Washu did some work with Ranma, she still has a number of mental scars and I imagine Nabiki has some as well. We still have our work cut out for us."
Funaho nodded her head. "I agree. Maybe some sleepovers are in order for these girls. It would give us more time to bond with them."
Misaki clapped her hands happily. "Yeah, sleepovers."
**XxxxxxxxxxX**
Washu was typing away on her computer while a blue-haired girl was strapped down to one of her tables unconscious. "Hmmm."
"What are you doing to my baby!" Soun's demon head disappeared as Washu stuck a needle in his arm.
She shook her head as she continued to type away on her computer. "Hmmm. That makes the third time I've had to use a sedative on him. Ryoko, put him in a stasis field until I'm done."
"Ummm, I have been trying to ask, but what are you doing to my sister again?" Washu turned to face the innocent looking girl.
"Well, Kasumi dear. I'm trying to find the root cause of this aggression. So far I've found one major trigger, but some of this other stuff has definitely led up to this. Has your father always molly-coddled her like this?"
Kasumi put a finger to her lip. "Ever since I can remember. It got worse after mother died. He always had a soft spot for Akane. He barely let's me go outside anymore for fear that something should happen to me. He does get a bit emotional."
Washu raised her eyebrow. "Right."
Washu finally finished going through the personal data she had accumulated on the girls and their father. _Good grief. Soun Tendo is an idiot. He stopped working after his wife died, let his children fend for themselves, and coddled this one girl so much that she has a horrible neurotic complex. Akane has absolutely no idea of how to carry herself in the real world and that lunatic going after her has only added to her problems. Kasumi... well, I'm going to have to have Ryoko or myself show her the ropes on getting out of her shell. And Nabiki. She turned into some kind of hustler to earn the bread for the family. I guess some families can screw up worse than I have. What I don't understand is who this MASTER is. They completely shut down when I try to access memories of him but he seems to have pushed the two men over the edge._
Washu turned back to Kasumi. "I'll give it to you straight. I'm going to set up some time with a psychologist for Akane. She will attend the appointments if she doesn't want to end up in jail. Blowing up the way she did at my daughter was justified in some way, but she will end up killing someone one day with a temper like that. I'll be hanging onto your father for awhile as he, Genma, and I need to have some discussions. Both you and Akane are welcome to stay here as we work on certain issues."
Kasumi nodded her head nervously. "I suppose. Akane has been a tad bit out of line on some occasions. Will father be alright?"
Washu smiled as she took Kasumi by the hand and started leading her out of her lab. "Don't worry, he'll even get better accommodations than his friend. Now I'd like you meet my daughter..."
**XxxxxxxxxxX**
"Again!" Nabiki was starting to hate those two. This was her first time handling a sword but those two simply wouldn't let her quit. Her instructor seemed a little nervous as he was instructed to pick up the pace.
"I thought you were from a martial arts family. Pick up the pace!" Nabiki turned a icy glare to Funaho. _Oh is she going to get it later!_
Funaho chuckled at that look. The girl was about on par for a normal Earthling physically. Mentally though she seemed to be a powerhouse. Even though Nabiki was losing horribly in her first practice spar against the Juraian sword instructor, Funaho could see Nabiki leading the instructor into areas of the field that were more suited to her smaller body. She was surprised to see a few clumsy and powerless swings get to the instructor.
As Nabiki started propping herself up by her sword, Funaho decided to end the test spar. After all, she only wanted to see what the girls abilities were, not kill them. "Take a break Nabiki! Ranma you're up."
Ranma nodded and jumped down to the field below them. Nabiki dragged herself to the sideline and held up the wooden sword for Ranma to take. Ranma shook her head and smirked at Nabiki. "Don't need it. Why dontcha take a break."
Nabiki nodded her head, walked to a nearby bench, and collapsed on it. Ranma walked out to the middle of the field cracking her neck on the way. The instructor looked her over and noticed the lack of a weapon. He frowned a bit until Ranma spoke. "Alright gramps! Let's get this going. I've already seen you're moves so this shouldn't be more than a warm up."
The instructor looked her over and quirked an eyebrow. "Where is your weapon child? How do you expect to fight without one?"
Ranma only smirked as she dug her hands into her practice pants. She had been lucky enough to convince those old women to at least let her wear some slacks to practice. "Heh, weapons are a crutch! As soon as your weapon is gone, you'll be defenseless if ya haven't practiced without one."
The instructor's eye twitched at that. "Oh, I suppose that may be the case for Earth, but weapons of Jurai are not so easily taken."
Ranma snorted and spat into her left. "Ha, I'd like ta see that gramps."
"I'm only 42 young lady." He was starting to get mad at the girl.
"Yer still older than me. That and yer slow to boot. I mean we've been sittin here talkin fer about five minutes and ya ain't done nothin. Ya going to use that wooden stick as a cane. If ya are, it might be a good idea ta put it on the ground, don't ya think so Grandpa. Or maybe you're compensating for some..."
Ranma ducked to the side as the man thrust his wooden sword at her. He then repositioned himself before using an upward thrust in a half moon arc only to have her disappear on him. "Where are you?"
He heard a giggle and then looked up to the end of his sword. She was standing there on the end of his sword, smirking at him. "Could you go faster gramps? I'm still waiting for you to start."
He tossed her and his sword away only to have her somersault off of it and land neatly in front of him. He then pulled out a laser sword and charged at with eyes glazed over in rage. "I'll f***ing kill you! You stinking bitch!"
Funaho was about to jump in to stop the man when an arm gently held her back. "Let's see what she can do Funaho. They'll both have to deal with assassins sooner or later. If she can't even stop that instructor, then there's no way they would even survive a night at the palace."
Funaho sighed. "I suppose Misaki. Is that why we're taking a week to get back to the capital?"
Misaki only pointed out to the field. Both watched as Ranma dodged each blow.
The instructor was starting to tire and he was getting nowhere. _Dammit! This bitch is fast. I need something to slow her down._ He looked around the field until he spotted Nabiki.
In a last ditch effort, the instructor kicked up a cloud of dirt with his sword to hide his presence. He then made a bee line for Nabiki. Both Funaho and Misaki jumped down to the field, but were too far away to do anything and they knew it. Nabiki's eyes widened. She had been surprised when the instructor had pulled out a light saber, but now she was scared out of her mind as the tip of that sword was about to be driven into her... She closed her eyes and expected a sharp pain but nothing happened.
Nabiki slowly opened her eyes to see Ranma standing in front of her. She then saw the blood that was trickling down her body and starting to pool on the floor. As the implications of what was going on hit her, she shakily called out to Ranma. "R..Ranma?! Ranma are you okay?!"
Ranma turned her head to the side and smiled. "Never better. I'm just gonna take care of this guy and then maybe we can have some ice cream."
What Nabiki didn't see was the tip of the sword embedded in Ranma's left shoulder. She had her bloody left hand wrapped around the laser sword. A light blue aura surrounded her left hand as she crushed the sword in her grip. When the sword simply vanished into the ether, Ranma's left hand fell limp to her side.
The instructor's mind was reeling as the implications of what she had just done sank in. He didn't have much time to think as a nasty right hook connected with his head, sending him to a blissful unconsciousness.
The next thing Ranma knew. Misaki had her in a fireman's carry while trying to apply pressure to the wound. Medics were rushing in and Funaho was binding the instructor.
**XxxxxxxxxxX**
Misaki was sitting outside of the medical wing with furrows forming in her brow until Funaho appeared. She turned her head to her co-wife. "Was it an assassination or something else?"
Funaho sighed and sat down next to Misaki. "It wasn't an assassination attempt, I think. He just completely lost it, but that still does not make what he did acceptable. He's going to be scrubbing toilets at the men's prison facility for those mud people for the next 200 years."
Misaki smirked at that. "You always seem to come up with appropriate punishments."
Funaho nodded her head. "So what did you think of their performance today?"
Misaki put her finger to her lip. "Not bad but we had better get them a tree the minute we land. I think they'll both have the skills they need to survive after we give them some personal attention this week, but they lack power."
Funaho chuckled. "I don't know. Ranma did shatter a light sword with only one hand. Even I can't do that."
Misaki sat back in her seat and pondered it for a second. "I see your point. She will be a formidable force physically, but her intelligence is pretty low."
Funaho looked thoughtfully at the hospital room door. "I think Nabiki will fill that gap. Together they will be quite formidable."
**XxxxxxxxxxX**
In the hospital room another conversation was starting...
"Huh? Wazza going on?" Ranma woke up groggily as she tried to adjust her eyes to the bright light. She then noted her state of dress. She frowned at the paper gown and the sling she was wearing. "The hell? A hospital. I'm so out of here."
Before she got up, she felt a hand rest on her right hand. "You shouldn't move around yet. You don't want to reopen the wound do you?"
Ranma turned her head to see Nabiki beside her. Her eyes seemed a little red but she otherwise seemed okay. "I guess I'll sit here for a bit then. Anything else?"
Nabiki nodded. "The empresses said something about taking us on as personal students and expanding our training."
"So, I won right."
Nabiki just couldn't keep her cool around this girl as she started to heat up. "Yeah, you knocked him out good. Only, YOU ALMOST DIED! WHAT THE HELL WERE YOU THINKING?"
Ranma flinched back a little at her words, but she set herself back up straight. "Well, it looked like he was going to kill you and I wasn't in a good position to just pull him back. I was actually trying to catch the damn thing using the sword capture technique that pop taught me but it kind of slipped through my grip and got me in the shoulder. Thankfully the sword breaker technique worked better than expected."
Nabiki looked a little cowed. "Thanks for saving me, but why did you do it?"
Ranma smirked at her. "It's a martial artist's duty to protect the weak and you were tired and couldn't move out of the way. And maybe... well... you're my friend."
The words sank into Nabiki and she bent over to hug the red-head who flinched a little at her contact. "I owe you one. It's good to know how much you care."
Ranma beamed at her new friend. Her stomach then grumbled. "Uh, I'm a bit hungry."
Nabiki smirked. "I got one of the servants to go get some chocolate ice cream awhile ago. He should be back in a minute."
Ranma's eyes sparkled at that comment. She would have put Nabiki in a bear hug if it weren't for her arm sling.
**XxxxxxxxxxX**
Several men sat in a dark room looking at a screen as a wiry man appeared. "The rumors are true sir. The two fiances hale from Earth. I sent them an unstable instructor to get a gauge for how vulnerable they are. He knows nothing of us and was rather useful. Reports state that he severely injured one of the girls and almost killed the other. It should be rather easy to either kill or use them."
One of the men waved his arm. "Heh, why should we deal with Earth scum. I say assassinate them and put some of our puppets up as brides."
Another shook his head. "Easier said than done. Funaho, Misaki, and definitely that damnable Seto would figure it out. Remember what happened to that GP army unit that was in cahoots with Shanks. No, either make them have an 'accident' or use them while they are ignorant. A straight assassination attempt would only lead back to us."
"Even doing that would not be foolproof, too many complications would arise from the more complex plans."
"Then what would you suggest?"
"Poison?"
Groaning could be heard across the darkened room. "And how well has that worked in the past? They will be heavily guarded before the tree ceremony so any attempt before is fruitless."
"What about after? What if we move the unstable wormhole from sector eight to ship training ground 1?"
"That could work."
"They would need to be completely isolated from their guard detail."
"That can be arranged."
"Good."
**XxxxxxxxxxX**
_This is one of my earlier works. I've cleaned it up some and put it out as a possible teaser._
9. Chapter 9: Ranma GXP Universe
**Ranma GXP Universe**
**I do not own Ranma ½ or Tenchi Muyo GXP.**
**Chapter 1: Beginnings**
**XxxxxxxxxxX**
A woman with with long green hair and tan skin had a girl's head in her lap stroking her hair. The older woman looked with care down at the young red-haired girl. She had already wiped the blood off her face and found that she only had minor scratches, bruising, and a lump on her head. "How is she Mira?"
The green haired woman, Mira, turned to a woman that definitely wasn't human. She had a slight muzzle, reddish-brown fur, and dog ears. She was a Wau. The green haired woman shook her head. "I can't be sure but I hope it's only a light concussion. It looks like she gave them a bit of a fight, but considering she was picked up on that primitive world they stopped at to finish their repairs, she probably didn't have the means to truly fend them off. I'm not sure if it's really a good thing she survived though. I'm afraid of what they'll do to us."
The Wau lowered her eyes and sat back against the wall. They were interrupted by a snort of the fourth woman in their cell. She had Red skin and brilliant green eyes. "Yeah, you two sulk all you want. I'm going to kill the first damn 'Master' I get sold to. I'm not going to service some damn punk that buys me."
Mira frowned. "How? They've injected all of us with nanites that not only disable our enhancements but our physical strength as well. I'm sure if we disobey too many times they'll just shove some obedience chips in our skulls. I'd rather not live that kind of nightmare."
The red-skinned woman crossed her arms under her breasts and stuck out her forked tongue at the woman. Mira just shook her head and continued to run her hand through the red head's hair. She smiled when the girl started to mumble as she moved into what she thought was more of a sleeping state than the unconscious state she had arrived in.
That smile died a painful death though when a guard approached their cell. He had a rather nasty smirk on his face. "Well, well. How's our crew of 'We'll never give up.' You all folded rather quickly after we took your ship. It was rather funny how your captain begged for your lives until he found out what we really wanted. I still remember the shock on his face when the captain blew his brains out. That was a good laugh."
The red-skinned woman snorted at him. "What do you want? You just here to rub salt in our wounds you bastard."
The man's grin widened. "No. I'm just checking up on our newest acquisition. The captain told me to notify him as soon as she's awake. When we found her knocked out in the area where we landed for repairs, the captain claimed her for his personal use. I hope she'll last longer than the captain's last toy."
Mira's grip tightened on the red-haired girl and the other two in the cell scowled at the man. The man chuckled as he left with his back to them. "You know. I'm not sure if the captain made the right choice. I think the red-skinned girl would last longer than that beat up red-head. Might have to make a couple of suggestions to the captain. Oh, and just so you know. We don't use obedience chips so don't worry about becoming some mindless bimbos. Our clients like their women feisty."
If anything, the guards comments only made them feel more uneasy.
**XxxxxxxxxxX**
The red-haired girl started to stir after awhile and stretched out while reaching up to rub her head, except her hand landed on something soft. As she became more coherent, she could tell that her head was also laying on something soft. She then opened her eyes and they nearly bulged out when she saw she was grabbing a woman's breast and her head was in her lap. The girl then bolted out of the lap and crouched in a corner of the cell with her arms up over her head. "I'm sorry! I didn't know you were there or I... I didn't mean to a... I'm sorry!"
Three occupants of the cell looked at her with raised eyebrows. The green-haired woman spoke first with a chuckle in her voice. "Don't worry child. I'm not mad. It's obvious that you were just getting up. No harm done."
The red-haired girl let down her arms and eyed the three in the cell suspiciously. "Uh, ok. I'm Ranma Saotome heir of the Anything Goes School of Martial Arts. Uh, where am I? It kinda looks like a jail cell but with no bars."
The red-skinned girl answered her. "Well, you got the jail cell part right, partially at least. You're currently a guest of the slavers that are holding us in this cell until they can sell us to someone. However, you got lucky and the captain decided you're going to be his little..."
The green-haired woman interrupted. "Shut up Deira! Don't try scaring her right now."
Deira rolled her eyes and replied in a fake sweet voice. "Ooh, let's just sugar coat it then Mira! She's going to lollipop land with you, her, and fido over there. You're going to have a wonderful time picking strawberries and picking out cutesy outfits. Yeah, let's just do that!"
The Wau woman growled at Deira. "I've got a name you know! It's Czeska! Not Fido dammit! I'm tired of you calling me that!"
Deira rolled her eyes and shook her head. Their attention was drawn back to Ranma when she let out a disgusted sound. "Lollipop land! Cute outfits, blah! No thanks!"
Deira started laughing and then started rolling on the floor with tears coming out of her eyes as she cried out, "She took that seriously! Ha. Ho. I... I... Oh, man. Such a good... laugh."
Mira was about to say something when two guards came around to their cell. Both of them quirked an eyebrow at Deira's display. The guard that had previously been there shrugged as he let the force field down. He then grabbed Ranma by the arm. "Hey leggo. Whatcha doing?"
Mira stood up and walked towards the guard. "Please. Don't take her. Take me. She's too young for this!"
The guard snorted as he backhanded the woman, sending her across the cell. "Dumb bitch. You'll get your turn."
"You bastard!" The guard then felt something hit his face. He looked over at Ranma with a nasty smirk on his face. He spoke in a mocking tone, "Ow, that hurt."
Ranma looked at her hand and frowned. She didn't have any power behind the hit. _What the hell?_ Her answer came from the guard. "We've limited your physical power sweet cheeks. Nice try though."
He then crossed a line when he grabbed one of her breasts. Ranma started pumping out a battle aura in anger, but this had the secondary effect of burning out the nanites in her system. Ranma noticed this as her feeling of strength increased with her aura. As it peeked and came into the visible spectrum, the women and guards gasped just before Ranma's fist plowed into the face of the guard holding her. Ranma's smirk broadened when she saw that the guard slumped down on the opposite wall unconscious. "How was that one ya bastard?"
It was then that alarms started blaring as the other guard had reinstated the force field and hit the alarm, but he wasn't fast enough to stop the red-head that had made it out before the force field closed and knocked him unconscious. The stunned women in the cell really didn't understand how the girl got her strength back or if this was just a toned down version of her power but they didn't care. She could get them out. Deira ran up to the force field. "Hey, kid! Get us out of here!"
Ranma turned back to her and said, "Huh? Can't ya just walk out of there?"
Deira slapped her hand over her face. Of course, the kid was from a primitive world. "Press the green button on the side of the cell!"
Ranma shrugged her shoulders and pressed the button and was promptly joined by the three women. Mira turned to Czeska. "Get the other two out of that cell!" She pointed to a cell across the room with a purple-haired woman and a girl that had green skin and a tail. "Deira, grab their weapons and take point at the door. I'll see if there are some controls in this room to find out where we are and maybe sabotage some systems to give us time.
Ranma scratched her head as everyone seemed to be ignoring her now. She then felt a dozen men with killing intent approaching the only door to the room. Ranma smiled as she cracked her neck. Her memory was still a little fuzzy, but she did remember an unfinished fight with Mousse and Ryoga so she was itching for another round. Ranma made her way to the door with a purposeful stride.
Everyone else turned their heads to the door when it opened and a dozen men in armor filed into the room with their weapons drawn. They all then noticed that Ranma was walking calmly towards them. "Stop! If you surrender now, we'll only shackle you. Otherwise all of you will be slightly damaged or dead."
Ranma smiled as she neared the man that had said that. "Yeah, you and what army?"
All of the people in the room looked at the red head like she was crazy. "I've got a dozen men here. You're not going anywhere weak bitch."
And that was when all hell broke loose. Ranma disappeared in a blur of motion and two men slid down the wall. The remaining men fired at her afterimage only to have two more meet the same fate. The men started to spread out and try to fire their lasers from a variety of angles to keep her moving and out of range only to find that she could throw bright blue energy blasts at them. The only one left conscious at the end of Ranma's assault was the commander.
Ranma bent over with a cruel smile on her face. "Who's the weak bitch now?"
Ranma chopped the back of the man's neck sending him into La-La land and left the room through the only door. All of the women in the room simply stared at where she had left them. Mira broke out of her stupor first and started giving commands. "Everyone get a weapon from those men and move down the corridor. I've got the schematics for the ship's layout. If we can make it to the bridge, then we should be able to take over the ship. Try to guide Ranma to where we need her. I think our pirate friends managed to pick up a Juraian noble without doing a proper check. Sucks to be them."
**XxxxxxxxxxX**
Ranma was having a blast, literally. Enemies kept coming out of the woodwork and she couldn't be happier. For some reason, Ranma had something tickling the back of her mind that told her that she should be pissed and depressed, but she was having so much fun letting that pent up anger out that she didn't bother to explore why she should be so pissed or depressed. She was brought out of her revelries as the green-haired woman from before caught up to her. "Ranma, we need to go the other way! The command deck is over here."
Ranma looked at where Mira was going and saw even more enemies that way. She shrugged her shoulders and followed.
**XxxxxxxxxxX**
All of the women made it to a large cylindrical room when all the doors around them slammed shut. They looked around until a screen popped up to show a bald man with gray skin and piercing red eyes. "I see that you have incapacitated most of my crew. Let me congratulate you by ejecting my male captives into space."
The screen changed and they watched in horror as the male prisoners were jettisoned into space. Many clutched their throats and flailed before suddenly stopping. "You only have to blame yourselves. I couldn't take the risk of them revolting as well. It's too bad I made sure to reinforce most of my ship to prevent leaks and depressurization otherwise I would have simply done the same to you. No matter though. You all will instead be my entertainment."
It was then that they all noticed a large door on the far end of the room open. It was then that several members of the group grew pale. Mira was the first to state what it was. "Shit he's got a Siphore!"
What stood before them could only be described as a horrible assemblage of mutated animal parts. It looked like a giant meatball with tentacles, claws and mouths that looked like those of lamprey. Ranma eyed the creature and gave a shrug before cupping her hands in front of her. _Eh, 'Kane's made scarier things in the kitchen._ "Mouko Takabishi!"
Mira had tried to stop Ranma before she let loose her energy but was too late. She watched the ball scream towards the enemy only to be absorbed. "Ranma don't use any more energy blasts on that thing. It sucks out energy and can't be beaten with physical strikes either. It just absorbs the shocks of blows. I'm going to try to open the doors. Just keep it at bay!"
Ranma frowned. Her two best weapons and they were useless against this thing. She noted that the creature was slow but it was big enough to take up most of the room. She was brought out of her thoughts when she heard a scream. She saw that the creature had grabbed the green, lizard-like girl by the tail and was swinging her around wildly. Ranma tried to grab the girl but a claw raked across her back. She started to hear other screams as she tried to get back up. She then remembered what had happened to her the night before.
**Flashback...**
Ranma was walking through the woods looking at a note. '_Help! I am being held captive by a horrible man. Please help!'_
Ranma rolled his eyes at the message. He knew it was a trap, but he was bored and since the wedding fiasco and Saffron, he really hadn't had anything to do. He then saw two figures land in front of him. It was Mousse and Ryoga. "What's happening?"
"You're end," stated Mousse.
"See you in hell Saotome." Ranma raised and eyebrow. They seriously thought this was the end of him after all the times he beat them. He just shrugged his shoulders. He needed the exercise.
Mousse let out a barrage of chains and Ryoga used the Breaking Point on the ground in front of him. Ranma just jumped back only to have someone else join the fray as he saw a wolf skin before jumping to the side. "Sup Lime, where's Mint?"
Ranma got his answer as Mint tried to bum rush him from the side only to have Ranma side-step him. Ranma tisked before turning to look up at a tree. "Hey Herb. Knew you'd come along with these knuckle-heads."
Ranma didn't like the smirk on his face and barely dodged to the side as a firecracker landed at his feet. Things had gotten serious now that Happosai had joined the fray. It was then that Ranma was splashed with water from behind. She looked behind her to see a smiling Taro holding a ladle and pale. It was then that Ranma remembered what those were. Her anger started building up. "You locked me! You bastards f*^%# ! locked me!"
Ranma was so distracted while she was bearing down on Taro that she didn't notice a pipe coming towards her head.
Ranma then remembered falling a long ways and then splashing. Hitting stones... Hard to breath... Can never change back...
**Flashback end...**
**XxxxxxxxxxX**
Two of the girls had been captured by the creature and it was having fun siphoning off their life energy. It was then that everyone there felt a foreboding of dread and depression. Time seemed to stop as they slowly turned to see Ranma get back up. Her head hung down and a blackish green icor seemed to surround her. "Shi-Shi-Hokudan Perfect Edition!"
Upon uttering those words, the dark aura formed into a giant, eerie green ball and blasted forth. It ripped through the Siphore, leaving a gory mess, and continued to rip through the blast doors behind it. This time the women sprang into action as Deira shook the cobwebs out of her head after unraveling the tentacle that had held her and the unconscious lizard-like girl. Mira had rushed over to Ranma who was still hunched over. She noticed Ranma wrap her arms around herself and shiver.
"Hold me," was the last thing Ranma said before collapsing into Mira's arms.
**XxxxxxxxxxX**
The group made it to the bridge to find it abandoned. A screen popped up and revealed the same man as before. He clapped his hands and had a smug look on his face. "Bravo. I commend you. I had to escape on my backup craft but the show was rather entertaining. That red head does not disappoint me. In fact, she would be perfect for my collection if I can find a way to train her properly. Take care of her for me won't you and I may even consider adding some of you should you prove interesting. Oh, by the way. I smashed all of the systems except for life support before leaving. Ta."
The screen went dark. Mira moved over to the control panel and frowned. "He's telling the truth. Deira, Czeska go find some escape pods and remove the emergency transponders. Bring them here and I'll try to repair communications. Restrain any of the crew that are left and if you have no other choice then kill them."
Mira then turned to the purple-haired girl. She had a light tan and green GP uniform. "Amanda, go through the components here and find ones that work. I'll be working on the programming and repairs as needed."
Mira then turned to the lizard-like girl who was starting to sit up. She had on a pink Academy uniform. "Cadet Angela, now that you are conscious I want you to watch over Ranma. That last attack drained her."
They all set off to work.
**XxxxxxxxxxX**
The group of women had barricaded themselves in the command cockpit. While none of the slaver crew had yet to move, they were not taking chances. Once they had what they needed, they sealed the corridor and set up some secondary barricades. The conscious members of the group were drinking hot tea courtesy of a functioning replicator on the deck.
Mira looked over at the unconscious mystery of a girl that was supposedly from a backwater planet. She displayed many of the powers of a Juraian except for the last attack. She frowned as she noted the girl curling back into a fetal position. Ranma kept rolling around in a fitful sleep and many emotions seemed to play across her face. Mira was starting to think that last attack was in some way psionic in nature as it had made them all feel like they wanted to die right then. What puzzled her though was that Siphore's absorbed all ambient energies. The only way to hurt or control the damn things was to use metal cages and slice it with metal tools. This girl had used some sort of energy that it couldn't absorb or an energy that would cause the creature to explode.
They all felt relief when a voice came over the crude communicator they had built. "This is the GP! You have been designated as a slaver vessel. Stand down and prepare for boarding."
**XxxxxxxxxxX**
Angela sat on a chair beside Ranma as she lay peacefully on a bed in the infirmary of a GP cruiser. She had been there for two days watching over Ranma. She had heard from the others how Ranma had saved her life and was grateful for how much Ranma had done for them. She wiped a stray piece of hair out of Ranma's eyes and bowed her head before her savior.
Mira chose that moment to enter the room. "Hello, Angela. Still no change."
Angela looked up with a sad smile. "She's not weeping anymore and she seems to be sleeping peacefully now. I think she'll wake up soon."
Mira smiled at the girl. She had fallen into hero worship now and Mira was hoping that when Ranma woke up that she wouldn't disappoint. "We've collected the bodies and given them a proper burial now. We've also processed the remaining crew. It appears our ship was targeted because we were the only ones using shipping route 503 on that day, no witnesses. They also claim that they would rather die than divulge who their captain was but I'm sure we'll find out soon."
Angela looked up at Mira with a little worry in her eyes. "You told me that he wanted to come back for us, well for Ranma. Do you think he's going to come after us?"
Mira held back her emotions. She didn't want to scare the girl, but the man, while insane, appeared to be sincere about his threat. "Don't worry about that right now. We're in a heavily armed cruiser instead of a transport. We should be fine."
They were broken out of their conversation as they heard a groan from Ranma. They both smiled as they saw her yawn and sit up. She looked right at them and then down at herself. She frowned as she saw she was wearing a hospital gown. "Uh, ya got my old clothes?"
Mira shook her head. "I'm afraid they were too torn. All we have are standard issue GP uniforms and casual wear on board."
Ranma sighed. She'd just have to hope it wasn't some girlie getup. "I guess it'll hafta do. So where am I anyways? And why ain't there any windows?"
Mira slowly breathed in and then sighed. "Your currently in outer space. You were picked up by some slavers when they made a pit stop on your world."
Ranma blinked. Aliens? Seriously? _Oh well, bound to happen with my kind of luck._ "Uh, then can you take me home?"
The woman started wringing her hands and looked pitifully at the girl. "No."
Ranma mouthed out what she said. "N-o."
Mira nodded. "Well, not no in the sense that you can never go back. It's just that you'll have to be debriefed and put up by someone. You can't live on your planet anymore but you can visit. The reason is that when you burned out the nanites, you actually fused some of them into your physical structure and they can't be removed. Effectively, you are what we term as a 'contaminated being.' It means that you contain technology in your body that is too advanced for your civilization."
Ranma turned her head to the side. "Huh?"
Mira frowned but decided to dumb it down. "You have alien technology that can't be removed and thus you cannot live on your planet because it would be harmful to others on your planet."
That caused Ranma's eyes to widen. _I can't go home. I can't see mom or dad. I can't kick Herb's a... _Ranma's eyes widened. _I can't change back. Shit! I almost forgot. _Ranma's fists then balled up and she started breathing hard. She didn't turn to the women in the room, she wanted them out for now. Her words came out tersely. "Leave me alone."
Mira looked at the girl with pity before grabbing Angela and pointing towards the door. They both left the room as Ranma fell into her stormy thoughts.
**XxxxxxxxxxX**
Mira walked down the hall towards communications. She was deep in thought as to what she should do about Ranma. DNA tests had concluded that she was a human from Earth. She couldn't fathom what the girl was going through as she had told her that she couldn't go home, well at least live there anymore. The anger and sadness the girl portrayed after she had told her had her worried and she had had a guard posted to make sure she wasn't hurt and to make sure she didn't hurt herself. She broke out of her musings as she opened the door to a secure communications room on the ship and locked the door behind her. She had received a notice to make this call to none other than Seto after she had delivered the report.
She dialed in the number and waited. The screen came to life and she was greeted by the visage of a neutral faced Seto. "Good day First Detective Mira. I would first like to commend you and your crew for your actions and console you for your losses. Your quick actions and judgment show good character."
Mira nodded. "Thank you but our escape really didn't have anything to do with our crew. It was Ranma. The girl from my report that helped us out. If it wasn't for her, we would be in a slaver's market by now."
Seto frowned a little at Mira's comments. "Maybe, but you were able to keep a level head during the whole affair and that is commendable. I am curious though as to how a Earth human displayed those powers you reported as are a number of other noble Juraians now that the report has undoubtedly spread around thanks to gossiping at GP headquarters. That girl is going to need some rather high level security in the near future."
Mira pursed her lips before speaking. "And our mysterious kidnapper?"
Seto's eyes became stony at the mention of the man. "A yes, Dugal."
Mira blinked. They never got a name for him. Seto merely waved her hand as she saw the look on Mira's face. "I already knew of him dear. He's been a thorn in my side for many years. One that I hope to pluck out rather forcibly which brings me to my next topic. I'm reassigning all of you to the Academy for protection. That goes doubly for Angela and Ranma. I'm actually sending another human from Earth there now as he was picked up by accident for an enrollment to the Academy. He has also exhibited some unique abilities but none that would draw the kind of attention that Ranma's abilities do. Your little debacle has set a precedent so I'm going to use it."
Mira slowly nodded her head until she realized something. _When did Ranma sign up for the Academy?_ "Wait, when did Ranma sign up for the Academy?"
A genuine smile crossed Seto's face as she held up her fan. "Well, I picked up temporary guardianship of Ranma after the report and signed her up. If she wishes, then I'll adopt her as my daughter. It will be some time before she can go back to her planet and she needs someone to look out for her. I wish to talk to all of you aboard my ship and iron out all the details so I will be picking you up a day from now after the cruiser you're on enters Kupri Belt. Good day Officer."
Mira saluted as the communication ended.
**XxxxxxxxxxX**
Mira looked back at the others as they looked around in wonder or unease. She laughed a little to herself as she saw the nervous look on Amanda's face. No doubt she had heard the stories of the Devil Princess and as a common citizen of Jurai she had some fear instilled in her. She had to admit that she had been nervous when she first boarded this ship as well but she now knew that the Devil Princess was only devil to those that she was displeased with. Deira and Czeska were looking around in wonderment as they passed through a wide open plain in the middle of the spaceship. Angela was playing with her tail nervously, but was also looking around in wonder. The one that had her worried though was Ranma as she was simply following them with a dead look in her eyes.
They made their way to a small villa made by roots to see a woman with sea green hair and red eyes waiting at a table for them. "Come and sit down. There is much to discuss."
All of them sat down and faced the woman in front of them. A servant walked in and set some tea in front of them. Mira was the first to pick it up and take a sip. "Thank you Lady Seto. I must admit I do not know this blend."
The eyes of her crew mates widened slightly at the familiarity that Mira had shown to Seto. Seto chuckled. "Good I hope. It's a type of Oolong tea that I picked up on Earth during my last visit. Although I see our resident Earthling hasn't decided to partake in it yet."
All eyes turned to the sullen figure of Ranma. She had her hand around the tea cup but her eyes were still expressionless. Seto frowned as she saw Ranma's state. She looked over at Mira and nodded to her. "Mira, Ranma follow me. Would the rest of you stay here?"
Everyone watched as Mira, Seto, and Ranma walked out of the room. They then tried the tea. Deira, Czeska, and Angela spit it out upon trying it while Amanda took another sip.
**XxxxxxxxxxX**
Seto closed the door behind them as the others sat down in some open chairs. Seto turned her attention to Mira. "Why didn't you report her condition?"
Mira sighed heavily. "She just woke up before I went to call you. I didn't think her depression would last this long."
Seto shook her head. "Dear, she just got told that she would have to leave her home world for a long time. How do you think she would feel?" Seto turned to Ranma. "I know you are aware of what's going on dear so please tell me what is troubling you."
Ranma slowly turned her expressionless eyes on Seto and said in a dead voice, "I can never change back."
Seto blinked. She hadn't expected that. She thought she would say 'Why can't I go home?' "What do you mean?"
"I can never be a man again."
Seto blinked and blinked again. _A man? What did that mean? Did they change him into a her through some experiment?_
Almost sensing her question, Ranma replied. "A curse. It changed me into a girl with cold water and hot water back into a man. I was beaten and the curse was locked. Only revenge awaits."
Seto narrowed her eyes. She then walked over to the red head and whacked her on the back of her head. "Get over it."
Ranma seemed to come out of the trance at once and whined out, "What didja do that for lady?"
Seto laughed out loud. "I've seen my share of emotional repression techniques dear and have dealt with them. The only thing I can tell you is this. Get over it and move on! I will not have my daughter live in self denial!"
It was Ranma's turn to blink. _Daughter?_ "I ain't your daughter."
Seto smirked as she sat down next to Ranma. "Well, you need a guardian out in space and you won't be able to return to earth for one to possibly two years before you learn everything you need to know. I am thinking of adopting you because without someone backing you, you will end up living in a slum and most likely will never be able to go back home at all."
Ranma digested this for a moment. "But what about my folks back home?"
Seto shrugged her shoulders. "You'll still be Ranma, their daughter..." She noticed Ranma wince at that statement. "... on Earth's records, but outside Earth you will legally be my daughter."
Ranma rolled it around in her head. "So I accept being your daughter and I get to go home in one or two years and if I don't I'll never get back home?"
Seto smirked. "Is it really that bad?"
Ranma sported a similar smirk. "I guess not, but why one to two years?"
Seto leaned back in her chair; she knew she had won. "You need to go to the Academy of course, even if you don't become a police officer. You still need to learn about space so the school will help with that. It will take you that long to truly become integrated into space life and pass the GP Academy. You must also come to terms with the fact that, while you can visit your friends and family, you cannot live with them anymore unless they swear to secrecy about what you now know. Is that acceptable?"
Ranma's smirk widened. _A year or two to train so I can beat the snot outta those bastards. Yeah, it'll work. Just don't like having to go back to school._ "It's a deal."
Seto smiled as she shook Ranma's hand.
**XxxxxxxxxxX**
Three figures were talking calmly amongst themselves as they headed back to the open air room. They could hear an argument going on as they entered. "... horrible! I mean what the hell is this shit! It's like drinking grass!"
Another voice chimed in. "It most likely isn't something palatable for your species. All you had to do was ask for a different drink. What will Lady Seto think of you making such a mess by throwing your cup at the wall? I mean she could have us executed by just claiming that we were disturbing the peace on HER ship. We have no lineage protecting us."
A hand settled on Amanda's shoulder as she finished the statement. "An agreeable sentiment my dear. I do so hate messes on my ship."
Amanda nearly jumped out of her skin at the touch and voice. Seto laughed heartily as she, Ranma, and Mira sat back down. "I am kidding my dear. I've flayed nobles for less, but I understand what's going on so I have no qualms. One of my maidens will clean it up later."
Seto unfolded her fan as she sat down. "Now that I have helped to alleviate some of Ranma's fears. I have some announcements to make. You all are in quite a predicament. Very few have escaped the clutches of your former captor alive so I commend you; however, even fewer people have escaped from him and survived his secondary attempts. Yes, he will come after all of you. He sees this as a game, a very dangerous game mind you."
Angela began to cry. "I don't want to die!"
Seto closed her eyes and slowly opened them again as she looked over Angela. "Do not fret dear. I will do my best to help you and the others though there are others things in play that may make it hard for even me. All of you are going to be assigned to the GP Academy. The officers will become staff and Ranma and Angela will become students. Ranma and Angela will room together along with someone who is an heir to one of Jurai's better martial arts schools. Even Dugal isn't stupid enough to make a direct attack on the Academy, since it's located near GP HQ. The most likely time he will strike will be when the practical exams and training periods begin. I'm currently running through some ideas for what we will do then. Officers will receive orders from Mikami as to what they will teach. I hope this is agreeable."
Deira stood up and slammed her hands on the table. "Agreeable! I'm not teaching some snot nosed brats!"
Seto leveled a deadly glare at the woman. "I could just put you on a ship then. I am not technically your supervisor even though I control most of the interests of the GP, but a word of warning. You have a snowball's chance in hell against Dugal."
Deira sat back down grumbling. "Fine, I'll teach some damn brats."
Seto sat back and waved her fan in front of her. "Good. I'd hate to hear about something bad happening to you. Now since we will work together, I wish to hear about your lives, special abilities or techniques, and any other interesting things. Why don't you start us off Mira as most everyone knows about me?"
Mira nodded her head. "I'm First Officer, First Class Detective Mira Kuro of the lower house of Misaki Kai. I am from a lower noble family of Jurai. I have no special abilities but I was in the top tenth percentile of my graduating class. I've been on about 50 missions so far and have only failed on two occasions."
Amanda stood up and looked around before speaking. "I'm Second Class Mechanic Amanda Tuo, a common citizen of Jurai from the fourth planetary space station of the Jurai system. I have no special abilities but I am working towards First Class mechanic. I've never really been outside the system and GP HQ until now."
Deira stood up next. "Second Class Gunner Deira Slove. I'm a Dragoth from the Antilles System. We're known for our superior strength, heat resistance and overall charm though I'm not sure why people don't understand that. Not much to say about my life except no one gets in my way for long."
Czeska rolled her eyes and spoke from her spot. "Yes, charming, I'm sure. Anyways, I'm Second Class Detention Officer Czeska Birath. I'm a Wau from the Therra system. We're known for our sense of smell, loyalty, and enhanced strength and speed. I enjoy a good long soak in hotsprings and want to settle down on my families ranch after I've finished my five year contract with the GP."
Angela twiddled her thumbs together as all eyes fell towards her. "Uh, Cadet Angela Spiels. I'm from the Antilles system as well. I'm from the Basilisk tribe. We're known for stealth and speed. I like to collect shiny rocks and hang out with my friends at the passing merchant market ships when they come through the system. I'm planning on becoming a medical officer."
It was then Ranma's turn as they turned towards her. She looked at them and shrugged. "I'm Ranma Saotome, the heir of the Anything Goes School of Martial Arts. I'm from Earth. Uh, special techniques... Where to start? Let's see, there's Mouko Takabishi a ki attack, Hiryu Shoten Ha another ki attack that makes a tornado, the Amaguriken which is a fast punching technique, the Umi Sen Kan techniques which make me invisible, the Yama Sen Kan techniques that cut through anything, haven't quite got the Breaking Point down yet, Hidden Weapons space, ki detection, uh know I'm forgetting some."
They all looked at her like she was crazy except for Seto who had a calculating look and Mira who had a pensive look. Respective thought processes were interrupted by Deira. "Bullshit. Some of that stuff sounds made up."
Ranma frowned and stood up. "Then how about I show you."
Ranma took a funny stance and disappeared. All of them looked around wildly for the girl only for her to tap Deira on the shoulder as she appeared out of thin air. "Ta-da."
The startled Deira jerked to the side. "The hell!"
Mira saw this display and then nodded her head. "Well, she did show us the Mouko Takabishi before when we battled the Siphore and some of the slavers. Actually, I want to know what the Shi-Shi-Hokudan was. It was.. unpleasant."
Ranma shrugged her shoulders as she sat back down at her place. "Ki attacks are based on emotion. The Mouko Takabishi's based on confidence and it's my creation so nobody else know how to do it. The Shi-Shi-Hokudan was something I learned from a friend and it's based on despair. It's a more powerful technique but it has a drawback. It puts the user in an cycle of despair if used too much and it messes with your psyche. I only use it as a desperation move."
Mira nodded her head. Her statement explained a lot. "You know an attack like that would probably kill a telepath or empath. You need to be careful with it."
Ranma frowned as she thought about it. "Don't really wanna kill anyone if I can help it, though I've learned the hard way that sometimes there's no other option."
Seto moved over and hugged Ranma. "I am sorry to hear that you have lost your innocence at such a young age but at least you are able to admit it."
Ranma squirmed a little in the hug before responding. "I guess."
Seto let go and clapped her hands. "Well, now that business is over. I think a small meal will do."
**XxxxxxxxxxX**
Ranma stood in front of a red door while trying to pull her pink dress further down. It was embarrassing enough to be wearing a mandatory skirt but it had to be pink to boot. Ranma rang the buzzer on the side of the door. It quickly opened to reveal Angela who tackle hugged Ranma. "Oh, Ranma-oneechan! I was wondering when you'd get here. You've gotta see what Seto gave us. We've got an NB reasoning unit, Juraian subspace closets, a private subspace holo-room, and she even got Platinum club credit cards for both of us!"
Ranma cleaned the wax out of her ears after the squeal and pushed the excited girl off of her. While the girl wasn't a fiance, it was still creepy the way the girl clung to her. "Ah, that's uh, great. So this our room?"
The room was a standard GP dorm with three open bunk beds, a bathroom and a common room with a table a half floor below the beds. What was uncommon were the four wooden cylinders and the round ball with a pink hair bow on top. Ranma watched as the now detached Angela retrieved the ball and brought it up to Ranma. "Wow, look at this NB! We're so lucky. This is like one of the most awesome accessories. You can program these guys to do almost anything."
Ranma rolled her eyes while looking at the ball. What the hell was a ball going to do? Angela's giddy explanations were cut short as the doorbell range. Angela jumped over Ranma and answered the door. She would have tackled this person too if a wooden sword hadn't appeared beside the green-girl's neck. Ranma heard a cold voice from the door. "Who are you to attack me?"
The haughty tone made Ranma groan. She didn't need another Kuno. She moved beside Angela and moved the bokken away with one finger. She then looked at the owner. She was a slightly taller brunette who was wearing something that was a cross between a kimono and what Seto had been wearing. "Are you the ones that Lady Seto has adopted?"
Ranma scratched the back of her head. "Something like that."
Ranma cocked an eyebrow at the girl as she had pointedly turned her gaze to her. "The council of noble houses is in an uproar that someone with your abilities is not bonded to a tree. Half are in shock that a human like you would have such power and the other half is salivating over the thought of marrying you off to one of their sons. Considering the station you will be taking, however, that will soon be remedied."
Ranma blanched. "I don't need more fiances."
The girl raised an eyebrow. "That is not what I meant Lady Ranma. You will most likely go through the tree ceremony at some point in the near future."
Angela interrupted them. "Uh, maybe we should introduce ourselves. I'm Angela Sp.. I mean Angela Kamiki."
The brunette inclined her head. "Sakura Kanemitsu of the Kanemitsu Ryu."
Ranma puffed out her chest. "Ranma Saotome of the Saotome Anything Goes School of Martial Arts."
Sakura shook her head. "That was your former name Lady Ranma." Ranma's eye twitched at the word Lady being used before her name again. "You are now Lady Ranma Kamiki. Do remember that for now."
Sakura stepped into the room and shook her head. "Is this it? It hardly seems accommodating."
Ranma grumbled under her breath as the door closed. "Why do I gotta be stuck with a Kuno?"
**XxxxxxxxxxX**
Ranma looked around at all of the assembled recruits. _Why was pink the standard for female cadets? And why were most of the boys wearing paper bags over their heads?_ Ranma then noticed the man at the front of the room reading some gibberish poem. Now that guy really reminded her of Kuno. "... and so class representative Seina Yamada, from Earth, will make the freshman speech!"
Ranma watched a short, black-haired boy make his way to the podium woodenly. She then felt a shift in aura and a danger sense go blaring as he picked up the microphone. She pushed her roommates to the ground and yelled "Cover your ears!" just before Seina spoke and the speakers exploded.
**XxxxxxxxxxX**
Ranma was laughing at Sakura. She hadn't heeded Ranma's warning and had to have her eardrums reset. "Shut up! How did you know that was going to happen?"
Ranma shook her head. "How could I not? His aura started flaring when he picked up the mike so it was obvious something was going to happen."
Sakura stopped rubbing her ears and turned to Ranma with a quirk in her eyebrows. "What do you mean by his aura flared. I saw nothing."
Ranma grinned toothily while shaking her head. "I thought you were a master of your school or something and you can't see auras. It's the state of one's life force and when it flares like that kid's did then it usually means an attack or something powerful. Come to think of it, he didn't seem to be in control of it. You know that's kind of like Ryoga and his..." Ranma's giddy expression left her and her eyes drooped. Her hand clenched and unclenched as she started to breath hard until she pushed it down and took on a neutral expression. "Yeah, just like those bastards back home."
Angela looked at her friend worriedly and did the only thing she knew would cheer someone up. She hugged Ranma. This did two things: one, Ranma broke out of her impending soul of ice; and two, Ranma became nervous. "Ah, thanks I guess Angela. Look, can we just get back ta the room?"
Sakura had slowed down while she watched a bouncy Angela and a nervous Ranma walk in front of her. The being known as Ranma Kamiki was starting to interest her. _Maybe Lady Seto stumbled onto something with these Earthlings. Lord Tenchi certainly turned out to be a surprise._
**XxxxxxxxxxX**
"Hey sis, they've given us the week off except for physical training and that doesn't start until tomorrow for the girls. You know what that means!" Ranma let out a non-commital grunt as she rolled herself around her bed. She was used to waking up early, but to a cold splash of water, not a happy-go-lucky girl.
"Huh... Wah, don't know what your talkin bout." Ranma was roughly pushed out of bed.
"OOOOh! Come on, shopping! Lady.. I mean mom didn't give us more than our single uniforms and two pairs of formal wear. We need a better wardrobe. I'm sure Sakura would agree." The other girl who had been rudely awakened by the activities narrowed her eyes at the hyper active lizard girl.
"Shut up and order our breakfast if you want to get out so bad. It isn't like curfew is upon us and we need to be out and in beforehand." Sakura rolled over and put on her slippers while stretching out.
Ranma trudged her way down to the table where the food had just appeared. It was strange to her how much the paltry meals seemed to fill her up even though the meals on the road and at the Tendo's didn't. It was a mystery for another time. The bad thing about the food though was that it was nowhere close to Kasumi's standards; hell, he had made better tasting stuff on the road. Ranma looked up and groaned as Angela flung her uniform at her after she finished eating.
"Why do we need to shop? These clothes are supposed to clean themselves." Angela pouted at Ranma's whine.
"You sound like my old boyfriend sis. I mean honestly. You need to live a little." Angela pulled out her purse and started on her makeup.
Something finally clicked in Ranma's mind after the last statement. _Wait, sis, mother._ "Wait, why are you calling me sis and Seto mom?"
Angela's brow furrowed. "You didn't listen to me when we were in transit to customs did you? I told you that Seto adopted me with you. It's part of the culture of my tribe. I think I've heard it called a life debt before by some of the mammalian races. Anyways, if someone from my tribe has their life saved by someone else, then that person becomes a member of their lifesavers family either as siblings or spouses so I asked Seto to adopt me with you to satisfy our traditions. Thus, I am now your sister."
Ranma shivered a little. This was one of the few times she was thankful to be a girl. It meant no new fiance this time around. "Ah great. So, how long are we going to be shopping?"
**XxxxxxxxxxX**
Ranma never thought someone else would actually tire her out. She was kind of surprised that Sakura could still stand with the way she was breathing and supporting herself on a post. "C'mon guys! We still have the shoe stores and some video stores to find. We can go out for some food afterward."
Ranma prayed that the excitable girl would stop only at one shoe store. The load wasn't considerable thanks to the fact that Ranma had learned Hidden Weapons space. In fact, Sakura and Angela had been overjoyed when Ranma had shown her that she could do that, especially when the young Basilisk woman had bought two mascara cases and a basket full of clothes and knick-knacks. Ranma was really glad that she had learned this technique not because she couldn't carry what they bought but because she would be embarrassed showing what they had bought. The fact that Angela had forced her to buy five sets of bras and panties didn't help.
Ranma was overjoyed when she found out that there were three shoe stores adjoining a video gallery. It meant that she could drop down and rest beside the now barely conscious Sakura. The drool and blank eyes just meant that the girl was tired. Ranma pushed them both up onto a bench and fell asleep.
Ranma didn't know how long it had been but she was awoken by an irate Angela. "Hurry up, there's this place some of the teacher's talked about that has a good spread. It's near Washu's pore and we aren't too far away come on."
Ranma grabbed Sakura and pulled her along.
**XxxxxxxxxxX**
Ranma had to admit that the little place Angela had picked out was nice. It was a small, quiet restaurant that had a good view of an unusual bay. The only other people in the restaurant were the cook and three people in a booth behind them. She could tell that two of them were female GP officers and the one with short black hair facing away from her was probably a student. The blonde woman pointed to the chef and told the black-haired kid, "Remember to call her Granny and yell it cuz she can't hear that well!"
Ranma then noted the woman with long brown hair try to stop him but it was too late. Ranma once again felt something like a small flare in ki and decided to cover her ears again. She could slightly hear the boy yell "Granny!" and then watched as the chef produced a demon-head technique as she started yelling at him to not call her 'Granny.'
"Lady Airi! What are you doing working in a restaurant!" Ranma glanced over to Sakura who had stood up and walked over to the counter.
Ranma watched as the green-haired woman shook her head while cleaning her hands. She walked around the counter and put a hand around Sakura's shoulder. "Sakura! It's been so long since I've seen you. I'm frankly surprised. I didn't think my stuck up little god-daughter would show up here unless your father was dragging you in."
Ranma and Angela sniggered as Sakura's face flushed red. "I am not stuck up. It's just that there are exacting social standards."
Airi rolled her eyes. "Sure, I'm sure Kanemitsu was the roll model for _those_ exacting standards. Hmmmm?"
Sakura flinched back. "Father is unique."
The black-haired boy decided to join the conversation. "Wait, wasn't Kanemitsu working for Seto?"
Airi turned her attention back to the boy. "Oh, that's right! I suppose I should make introductions. This is Seina Yamada. He's a new recruit from Earth. Seina, this is Sakura Kanemitsu. Daughter of Kanemitsu."
Ranma had hopped out of her seat at that point got up in Seina's face. "You're from Earth!"
The boy tensed for a moment before nodding. Ranma grabbed him by the collar. "Where are you from? How did you get here?!"
Ranma's tirade was broken as two angry women flanked her. The brunette clamped her hand on her shoulder. "What are you doing to Seina?"
The blonde also tightened her grip on the opposite shoulder. "Yeah, what's the big idea?"
Ranma didn't particularly acknowledge them as she stared down Seina. "Because I'm from Earth."
**XxxxxxxxxxX**
Airi had managed to diffuse the situation and moved everyone to the patio while she served them. "I remember Seto mentioning you would be joining us. Ranma correct?"
The red head nodded and Airi continued. "I must say that I'm impressed by the reports I received on your apprehension of the slaver vessel that picked you up. The GP and Royal family are in quite an uproar over some of the things you did."
The blonde woman slammed her hands on the table. She pointed at Ranma with a shaking finger. "She was the one that apprehended that slavers' vessel single-handedly! You expect me to believe that this little girl actually took out a crew of over 300 slavers in full plate armor and class B weaponry with her bare fists. And there's no way she beat a damn Siphore with an energy attack!"
Airi developed an angry tic above her eyebrow as she swatted the back of the woman's head. "Stop spewing out classified information Amane. Besides, it was in a report written by First Class Detective Mira and confirmed by the forensics crew."
Amane sat back down while looking at Ranma. "And my promotion was denied why? It's obvious Earthlings have some strange and useful powers. It's a waste to deny that potential."
Airi smacked the woman in the back of the head. "And a felony to interfere with their developing world unless there are mitigating circumstances or family involved. You're lucky that you're not in jail. I wouldn't use Ranma's example for a good case. She was kidnapped unwillingly from her planet. Seina's involvement in the pirate capture was the only reason why you aren't being court martialed."
Seina waved his hand slightly to grab the attention of the others. "Ranma said she was from Earth, right? Why didn't you erase her memories? She could've gone back home."
Airi frowned. "She's tainted."
She saw Ranma anger slightly but continued quickly to dispel the apparent slight she had unconsciously made. "The slaver's used a type of control nanite to overwrite GP enhancements and limit normal abilities as well. Ranma found a way to burn out the control nanites but they fused into her physiology so that they can't be fully removed. She has the same classification as an enhanced human in the case of primitive world regulations so she can't just be sent home with a few missing memories. If nothing else, I doubt the royal family would just let her alone after her performance."
Ranma's anger diminished but was replaced by apprehension as the brunette woman slung her arms around her in a hug. Ranma felt very uncomfortable and was about to push her way out when the woman slackened her hold and said, "I'm so sorry Ranma. That must have been quite an ordeal. I can't imagine what it would be like in a situation like that."
Amane nudged the brunette with a mischievous look on her face and her hand over her mouth. "Oh Kiriko, you swing that way then."
Kiriko flared with an angry red glow. "AMANE!"
Ranma shrugged as she inched away from the woman and diffused the short feud by speaking. "Eh, it was nothin. Well, except for the Siphore thing. I've fought demons, Phoenix gods, martial artists, half-dragons, and a lot of other things but the only thing I've fought worse than that thing was some of the creations 'Kane made."
Everyone blinked at that and Airi raised a skeptical eyebrow. "So this Kane has made something worse than a Siphore? And what do you mean you've fought demons and gods before?"
Ranma looked at Airi and dryly spoke while counting on her fingers. "1. Akane's made things in tha kitchen that either eat through any substance or come alive with tentacles, slime, and other things that violate every order of the natural world. 2. Most of the demons I've fought were pretty wimpy so I ain't really gettin' inta them. 3. I've fought the Musk. That's where the half dragon came from. They're a race that's half-animal, half-human. 4. I've fought in more esoteric martial arts styles than most people even know about. 5. I killed the Phoenix god Saffron of the phoenix people. They look kinda human 'cept they aren't and they have wings and talons like birds do. I didn't like that I had ta kill him but it was the only way I could save Akane's life."
This really got Airi's attention. "Wait, I've never heard of these Musk or Phoenix people. And you killed a god?"
Ranma shrugged. "Most people have never seen 'em. The Musk and the Phoenix live in a remote part of the world and rarely interact with most people. As for Saffron being a god, I think he was only a demi-god. He could regenerate from any wound no matter how grave, could fly, and shot fire out of his hands that could burn anything. I remember that we leveled most of a mountain range fighting one another. I had to destroy his entire body to defeat him and then I had to bring Akane back to life. Thankfully, he was reborn outta his ashes as an egg or I'da never forgiven myself for it."
Amane was the one to butt in this time. "Wait, you leveled a mountain range as collateral damage, killed a demi-god, and brought someone back to life?"
Ranma nodded her head and then shook it. "I helped level the mountain range and killed Saffron but 'Kane was a slightly different story. See Saffron turned her into a desiccated doll and I had to get water from the dragon tap to restore her back to normal. The problem was that during the fight she technically died to save me from one of his fiery blasts. I still went for the tap after I killed Saffron in a fit of rage and restored her back to normal but she was lifeless in my hands. I kissed her and she came back to life. I think that's it."
Angela wrapped her arms around Ranma and swung around her. "Wow! That's just like a fairy tale, except I'm not sure who the prince was."
Airi had a different take on the story. _Well, well, this is interesting. Seto will definitely want to know this. If half of what this girl claims is true, then I believe we've found a diamond in the ruff so to speak. And from the way she described it, it sounds like she'd do quite well in any polygamous marriage that Seto set up for her. I better not tell Seto about that though. _"Yes quite interesting. Now if you wait a minute, I'll make some dessert."
Airi turned back to the kitchen and the rest of them turned back to the meal that Airi had brought in before they started talking. Sakura scowled at the way Ranma ate but kept her displeasure to herself. They were halfway through their meal when a glove landed on Seina's hand. "Huh?"
"I, Seiryou Tennon, challenge you to a duel Seina Yamada!" They all looked over at a pink-haired man in a GP instructor's uniform with various sea life attached to him.
"Seiryou? Duel?" It was a bit muffled thanks to the fork in his mouth."
The man laughed and ran his hand through his long hair. "Hah, are you so scared that you can't answer properly! My Amane is not for your filthy earth scum hands!" Seiryou then noticed Ranma and hearts formed in his eyes. "And who is this?! A wonderful pig-tailed goddess. Come to me Amane, pig-tailed goddess."
He didn't finish his step towards the table as red and blonde blurs shot forward. The red blur hit his gut and the blonde one hit his face. "No more KUNOS!" "Die Seiryou!"
Airi shifted his trajectory from the hits and he was redirected from his flight path into the kitchen to the off-world packaging deposit where he was immediately wrapped up. "Where should I send him?"
Amane smiled wickedly. "To the farthest regions of he universe!"
Airi snapped her fingers and the man was gone. Amane put her hand on Ranma's shoulder and smiled. "I think we'll be good friends."
**XxxxxxxxxxX**
This was one of my first tries at fanfiction.
10. Chapter 10: New Cadet
**New Cadet**
**I do not own Ranma ½ or Tenchi Muyo GXP. This one definitely has bashing in it.**
**Chapter 1: Kaboom**
**XxxxxxxxxxX**
Raj and Kenneth Barl were eating ramen in their observatory above earth. It was a boring outer rim post that should have little to no action and that's why the both of them had signed up for it. They just sat down to eat when something unexpected happened.
"Aaaaaaaaaaaaaaaaaaaah! Splat!" Raj's and Kenneth's ramen fell on the floor. Both of them groaned. Sure the floor was clean enough to eat off of …. but still. It was also improbable to hear anything but themselves in space but it happened. Ken opened up a screen showing the outside security footage and before Raj could ask, Ken had manned the transporter and beamed something inside. Raj was stunned at seeing the red-headed girl in tattered clothes laying unconscious in the transporter.
"Hey Ken! Where did she come from?"
Ken turned back to Raj. "As soon as she wakes up, I'm going to ask her out."
Raj planted his muzzle in his hand. "Not that,what is she doing here?"
Ken worked the computer for a second. "From the sensor's log, it appears that she launched herself off the planet and hit us. I don't think she meant to do that though. The log shows high-bio energy signature from when she left the surface and gets the same reading from her. The pattern's not exact but it points to Juraian type energy. I can't get a good match on DNA, but there are a number of strands that would indicate some type of Juraian ancestry."
Raj pulled up his own screen and looked through a list of names. "Not on the list for visitors or known inhabitants. I guess we need to fill an actual report." Ken turned on his 'why me face.' Raj just sighed. "Fine. I'll fill out the report while you make a decent dinner for all three of us. And put that girl on your bed with a life pack attached. I can hear her breathing, but I still bet she got some damage from exposure to open space." _She should be dead._ "If she's still unconscious after we finish the initial scans, we'll do some deep medical scans and call for help. Now get to it."
Ken hummed happily as he set to work while Raj groaned and pulled up several incidence forms.
**XxxxxxxxxxX**
Ken and Raj had just finished supper. The girl was still unconscious and they were starting to get worried. They put her on their medical bed and turned on the medical diagnostic program. It seemed pretty advanced to them considering how backwater this planet was but the dancing crab was just ridiculous. They could only gawk at the results.
"Whoa, Raj. You seeing this man."
Raj nodded. "She's packing enough energy to support a C-class transport cruiser and the energy seems to be rising. Her healing is unbelievable. The radiation damage has already healed, frostbitten and burned tissue is already replaced, and the lungs are nearly back at full capacity." _The old scar tissue and knit bones are a little worrisome though. If a being like her can take open space even for a few minutes and live, then whatever gave her those scars all over her body must have been a real beast._ _It's like she's been constantly fighting in a war for years._ "There's nothing to suggest why she's still asleep though. We need to call this in. An injured Juraian noble all the way out here is a bit much."
Ken scratched his chin. "You know we could be handsomely rewarded for rescuing a Juraian princess."
"Yeah, you're right. We'll be living the good life from now on." Raj envisioned booze, women, and money all around him.
Both of the boys started imagining cozy beaches with a lot of hot babes...
**XxxxxxxxxxX**
Lady Seto was lying down on her bench when an alarm blared and an incoming message was received. She sighed, hoping that it wasn't another attack by the good luck fleet. She had just sent Seina out to confront them.
"Lady Seto, we have intercepted a message from earth. There is a report of an injured Juraian from the space observatory over earth. She appears to be stable but unconscious." Minaho looked over at the lounging green-haired woman.
Seto sat up and quirked an eyebrow. "Is it someone I know?"
Minaho shook her head. "I can't say for certain. Medical scans were sent with the report. The funny thing is that the person has a number of genetic markers that match with the Kamiki branch of the family. Something like a great great well.. grandniece. It doesn't look like anyone from the Masaki line." _The scans also show numerous scars and callous tissue from years of fighting. Hmm, better examine her myself before letting her go to the bath with Seto._
Seto's eyebrows raised even further. One of her close relatives had either survived the pirate raid that had decimated the Kamiki house or had children as a slave. She thought that she had lost all of her close family from the Kamiki branch when that attack had occurred. "Send a message to Washu and the GP that I will handle this matter personally. Jump to Earth commander Minaho. I would like to see if I have a grandniece."
Minaho actually looked happy for once. _If she has a someone else to.. fawn over, it'll give us a break. Yes!_
"Get to work Minaho!"
"Yes ma'am!"
**XxxxxxxxxxX**
Ranma awoke with a splitting headache. She remembered the shocked look on that pompous half-dragon's face when she finally copied his flight ability and then proceeded to blow him away but something went wrong and the energy mixed and exploded, violently. She shook the cobwebs out of her head. _Alright, time to get the kettle. _She then noticed her surroundings. She was wearing a well-fitting shirt and skirt. She was also lying down on a funny medical bed. She sat up and faced a young boy and a .. humanoid dog?
"If ya'll don't mind, I gotta go do something. I don't want to know why I'm dressed like this but could ya get my old clothes."
Raj looked at Ken. He shrugged. "Had to throw them out. They were torn to shreds."
Ranma's head sunk down. "Then could you at least get me some guy clothes. I don't like skirts."
Raj scratched his head. "We..."
Ken clapped his hand over Raj's mouth and shook his head. "...don't really have anything else, but help should be coming soon so you could ask them."
Ranma stared at the strange dog-like creature. _Hmm, must be a really hairy Musk._ "Don't suppose you'll let me leave now would you."
Raj just turned his head to the side. "Huh? We're on a space station. There is nowhere to go."
"What?!" Ranma ran out of the room and to the window. She could see the earth below and stars all around. "Dammit! I got blown into outer space."
"Yeah, about that. When you launched from the surface, you sort of destroyed a mountain." Raj and Kenneth had followed the red-head out into the living room. Raj nodded in contemplation."It's good there were no casualties."
Ranma sat in thought for a second. _Wait, mountain destroyed! The kettle!_ She got down on her knees. "Dammit, the kettle is gone. I can't get the cure."
Raj and Ken blinked again. Ken coughed slightly. "What cure?"
Ranma eyed the duo. "Eh, it's to take care of a curse."
Ken smiled at this. _Time to spring my trap with a good hook-line. _"Hey babe I'll cure your curse with my sweet lips."
Raj slapped his hand over his face as Ken went into his dating speech.
**XxxxxxxxxxX**
The Mikagami set orbit near the earth observatory and Seto beamed into the living room area with Minaho and one of her handmaidens in tow. She was treated to a red-headed girl with a red-headed boy in a headlock turning him purple while the Wau tried to stop her. She chuckled lightly at the display. They stopped and looked up at her. "Oh, don't stop! This is quite entertaining."
The Wau fell into a salute while the red-headed male fell to the floor unconscious and the red-headed girl simply stared at the woman. Seto then noted that the girl's eyes widened and she took a combat stance. The girl's aura became visible and she seemed ready for anything. Seto quirked an eyebrow at this. "Don't worry child. I am not your enemy though I am curious as to who you are."
Ranma didn't relax from her stance, but the battle aura receded. "Hah, I'm not goin' to fall for it lady. Every time someone as powerful as you shows up, it turns into a fight for my life or an attempt to marry me. I ain't gonna trust ya just yet."
Seto raised an eyebrow. "So you've had to fight to survive? How did you know I was powerful by the way?"
Ranma looked at the woman like she was insane. "You're kidding right? I mean you at least have 2 or 3 times the amount of ki that Cologne or Happosai have and you can't sense ki. You don't really carry yourself like you know much more than a family style though so I guess ya just built it up without any knowledge of how much. Ya look younger than they do though."
Seto smirked with her lip curled up. "Quite the compliment. I believe we haven't introduced each other yet. I'm your great aunt, Seto Kamiki Jurai and this is Minaho Masaki Jurai."
Ranma scratched the back of her head. "Aw, yeah. I'm Ranma Saotome... wait did you say great aunt?"
Seto nodded. "These young boys did some testing while you were unconscious. It would seem that you are a relative of mine."
Ranma sat in thought for a bit before responding. "Pop never mentioned any relatives. Although, he did tell me that my mother was dead. Are you on my mom or dad's side of the family?'
Seto shook her head. "I don't know, but I should be able to tell if I see him. Why don't we go visit your home?"
"But Seto, you can't just..."
Seto waved her hand. "This is an exception remember. She is a member of my family. She and her immediate family should know."
"But we have yet to confirm..."
Seto pulled Minaho to the side. "I feel the power flowing through her. She has yet to obtain her tree or the waters of life but both Mikagami and I feel it in her. In many ways, it's very similar to that of our dear Tenchi."
Seto turned back to Ranma. "Now come along Ranma, I need you to tell me where you live."
Ranma nodded her head and Seto walked along with Minaho and the attendant following as they beamed out of the asteroid observatory.
"Uh, Ken."
"Yeah, Raj."
"Let's eat some Ramen."
**XxxxxxxxxxX**
A bright flash in an alley revealed the forms of Seto, Minaho, and Ranma. Ranma was staring around in amazement. "How do ya keep doing that Auntie?"
Seto beamed at that response. _Already calling me Auntie_. "Ah, it's a secret you'll be learning about soon enough. Now which way is your home."
Ranma pointed to the right. Seto noted that the red-headed girl was now on high alert, as if they would soon be under attack. She didn't have to wait long as she and Minaho were pushed to the side by Ranma as the wall next to them exploded outwards. The shards missed Seto and Minaho but collided with Ranma.
"Ranma, prepare to die!"
Ranma flipped through the air and faced the black-haired, bandana wearing boy. "Huh, whatcha pissed at now P-chan? Did ya at least get the kettle out before the mountain fell?"
"Hah, that was destroyed with the mountain! Now hold still while I kill you!" Ryoga raised his umbrella, but it stopped moving. He looked to the end of it only to find that Seto was holding.
He blushed looking at the beautiful woman. "Uh, mind letting go? I kinda gotta kill this guy."
Seto's red eyes bored into the young boy. "I just got reacquainted with my long lost niece and I'm not about to let you hurt her. You've got one shot. Let go and cease what you are doing!"
Ryoga tried to look away from the gaze, but it continued to bore into him. He dropped his umbrella and faced the woman. "Yeah, well Ranma's an honor-less bastard. He's a coward for always running from fighting me."
Seto ignored the pronoun and moved on. She had an even sterner look on her face. "Honor-less? You're the one that performed a sneak attack on her! And it doesn't look like she's running from a fight to me. Don't you dare insult my grandniece! You're insulting her and the royal family when you do that!"
"Look, Ranma's just... Wait, did you say royal family?" Seto nodded and Ryoga continued. "Uh, what's the relationship again?"
Seto sighed. "I'm Ranma's great aunt and I'm also the grandmother of the empress." _Of Jurai._ "So show a little respect!"
Ryoga was floored. Ranma was the empress's cousin?! "Bullshit! There's no way..."
Ryoga petered out as Seto bored into his face with a deadly gaze. "Do you really want to challenge me on that? Now Ranma, let's get moving."
Ranma broke out of her daze and nodded dumbly before continuing to lead them to the Tendo's. _I'm a member of the royal family, but pop couldn't be part of it so it's gotta be mom. Ya woulda thought pops would have already drained the country dry if he knew that._
Minaho just shook her head. This was going to be a long trip. Ryoga followed silently behind them.
**XxxxxxxxxxX**
Kasumi answered the door to find Ranma with Ryoga and two strange women. One was an older sea green-haired woman and the other was a black-haired younger woman about her age. "Come in please. If you wait at the table, I'll have tea and cookies out in just a minute."
Seto smiled. She liked this one. Her calm peaceful manner was charming. "Why thank you dear. At least some people around here have manners."
Kasumi blushed at the praise as she led them to the dining table. No sooner had they entered the room than they saw two men playing shogi. When the bald one looked up from the game, Ranma groaned loudly. _Damn it! I forgot that I can't change back til I find the stupid kettle. Why didn't I go back to the mountain to find that first? Now the old man's gonna chew me out._
When Genma saw his son, he was disappointed to see that he was still a girl. "Ranma my boy, why are you still a girl? How can you stand being such a weak and cowardly girl!"
Genma didn't know what hit him as Minaho had moved around the table and clocked the oaf sending him into the wall. She then said in her most innocent voice, "Oops. I guess I don't know my own strength." _Please no more interruptions. Seto's got that 'There is going to be hell to pay' twitch in her eye._
Ranma sweat-dropped at the show of force. "Uh, that's my pop."
Seto shrugged her shoulders. "He deserved that I suppose. Well, let's get down to business."
Soun took this moment to approach. The women seemed too old to be fiances but one could never be sure. "Umm, if I may be so bold, what is your business here?"
Seto smiled slightly. "Oh, I just want to know all about my grandniece here. I just found out that she's a long lost relative."
Soun looked at her confusedly. "Who?"
"Why Ranma of course? I just found out after she was rescued when that mountain blew up."
Genma was back on his feet again. "How can you be so pathetic boy? You had to be rescued by some weak and worthless women. Why I could..."
He didn't say another word as a fan was stuck to his throat. "I suggest you don't say another word."
Genma unknowingly tapped into past experiences. "Yes, No-chan."
This caused Seto to quirk an eyebrow. "Oh, and who is this No-chan."
Genma sweated even more as he could feel the fan being pressed against his throat. "Uh, nobody important."
Seto removed her fan and became silent for a moment. She then calmly spoke in a commanding tone. "Sit!"
Genma was sitting at the table in a flash. Seto turned to Ranma and Minaho. "Why don't you sit as well? I'd love to hear about your life Ranma."
Ranma nodded and sat down. Soun, Ryoga, and Minaho followed suit. Ranma started to talk. "Well, I guess the first thing that I should say is that I'm really a guy."
Seto raised an eyebrow at this. "I wondered why your father had called you son. My question is how are you a boy when you have those impressive assets?"
Ranma blushed a little before continuing. "Ah, it's a curse. Cold water I'm a girl, warm water I'm a boy."
Seto's eyebrows really raised at that. "That is quite interesting. I'd like to see it if possible."
Ranma hung her head at those words. Before she could answer, Ryoga did it for her. "Hah! She's stuck as a girl because she couldn't get the magic kettle to remove the lock on her curse."
The room exploded into a tirade from the two fathers.
"Ranma how could you fail!" Genma jumped up and grabbed Ranma by the collar.
"The schools will never be joined!" Soun weaped as Genma struck a pose.
"Wait, I know! You can marry Soun. He's a Tendo." Soun turned to Genma and clasped his hands.
"Are you sure Saotome?" Genma nodded fervently.
"Of course, the school's must be joined!" Both of the men hugged and separated.
"If you say so Saotome." Both of them turned back to Ranma.
They were interrupted by a very irate Ranma. "No way! I'm not marrying Soun. Ain't no way, ain't no how!"
"You don't have a choice! We made a pact to join the schools. You will marry a Tendo!" Genma said in a huff.
Seto broke into the conversation with a playful smile on her face. "I didn't know men were such good matchmakers. Do you have any proof of this vow?"
Genma blustered for a second forgetting the ferocity of the woman before him. "Listen here woman! This was a sacred vow we made before our children were born. Honor is on the line here. Now butt out of where you do not belong you weak woman!"
Seto's smile turned into a cold frown. Minaho inched away from the table and pushed Kasumi back into the kitchen just as she was bringing out snacks. Little lightning bolts started flickering around Seto. "Get out of my sight vermin."
Genma started dancing around as lightning bolts fell down around him. He suddenly took a funny stance and disappeared. Seto raised an eyebrow. "I see that he's good at running away."
Ranma snorted. "Typical pop."
Seto chuckled to herself. "Yes, men tend to run at the first sign of trouble. Don't you think so Ranma-chan?"
Ranma shrugged her shoulders. "I suppose so- hey! What's that supposed to mean?"
Seto shrugged. "It means what I said. Why are you getting so worked up dear?"
Ranma spat out. "Cuz I'm a guy!"
Seto moved over quickly and cupped Ranma with one hand. "I don't think so and I certainly haven't seen any proof yet."
Ranma had turned pale at the contact. "Look I really am a guy!"
Seto sat back and removed her hand. "If and I say if you were a man, then you can no longer change back into a man according to yourself and the others here. If that's the case, it would be best to start accepting that sooner or later."
Seto turned to face a blushing Soun. "So what is this marriage contract about Mr. Tendo?"
Soun coughed slightly before replying. "Well, Ranma here is supposed to marry one of my daughters so that our martial arts schools can be joined."
Seto flashed a knowing smile. "Oh, is that all. I think I can arrange that."
Minaho stepped out of the kitchen and started crossing herself. Seto had that same look when she started pressing Seina together with Amane, Kiriko, Ryoko, and Neju. "Um, Seto-sama, we must be going. Seina should be reporting his battle with the good luck fleet soon."
Seto sighed. "Is it already that time? Then I'm afraid we must be going."
Seto stood up and faced Ranma. "Come along dear. It seems that your father has abandoned you so I'll be acting as your guardian for awhile."
Ranma stood up and followed. She was still uncertain of the woman, but if staying meant marrying Soun, then she figured a getaway would be good.
"Wait, what about the schools?" Soun wouldn't let them go without an answer.
Seto shrugged her shoulders. "I'll be back in one month. Whichever daughter or daughters want to marry her, have them decide by that time. I would definitely support Kasumi if she decided to do so."
Kasumi blushed a little. "Um, I'll think on it."
Seto nodded and walked out the front door followed by Ranma and Minaho. When they reached the far side of the gate, all three vanished.
**XxxxxxxxxxX**
All three figures reappeared on the deck of the Mikagami. Minaho walked over to the command deck while Seto motioned for Ranma to sit with her on her bench. When Ranma was seated, she almost jumped out of her skin when a light screen popped into existence in front of her.
Seto turned her attention to the screen. Seina could be seen on the screen rubbing the back of his head with flushed cheeks. "Uh, hi Seto. We uh completed the mission and destroyed the good luck fleet."
Ranma moved her hand back and forth through the screen with a perplexed look on her face. She jumped back when a blond woman and a black-haired woman popped onto the screen. "Hey! Why'd you cut off our vacation time for this? According to our logs, you're currently at Earth. Why couldn't you do this?"
Seto laughed heartily. "Well, I had to pick up a relative of mine and settle some issues. Why don't you greet them Ranma?"
Ranma sat back and scratched her head. "Uh, hey! I'm Ranma Saotome. Uh, how does this thing work?"
The brown-haired girl took up the screen while looking worried. "You didn't pick up another Earthling, did you Seto?"
Seto laughed and smiled. "Don't worry Kiriko. She is from Earth, but it so happens that she's a recently discovered relative of mine. She managed to manifest her powers and ended up blowing up a mountain on Earth. The resulting blast sent her flying into outer space. So far she's managed to entertain me. Maybe I should introduce her to Seina."
Kiriko's eyes flashed for a second. "No!"
Seto waved her hand at the girl. "Calm down. It was only a suggestion. Besides, she already has another engagement."
Kiriko visibly relaxed but frowned. "And what are you planning on doing with her? How do you expect her to acclimate to space life? How do you plan to keep her safe?"
Seto tapped her finger on her lips and then turned back with a vicious grin on her face. "I know! I'm going to get her her very own tree. It'll also help when I announce her lineage to the public. I imagine that she'll have very interesting life. The GP academy wouldn't be a bad idea either."
Kiriko almost looked gobsmacked. "A tree now! Are you crazy Seto? And putting her in the academy would be just as bad."
Seto carefully schooled her face as her expression fell into more of a pout. "Well... I could always just take her under my wing and make her my protege."
Numerous frantic voices shouted out in unison. "No! The tree and academy are fine."
Seto nodded her head. "Good. Now, I'm going to reward Seina and the rest of you. I've reserved a private villa at vacation planet V2X9. Go, have some fun!"
Seto ended the communication at that point. She chuckled and then started laughing out loud before she felt a tugging on her sleeve. She looked over at Ranma who had one eyebrow raised. "Uh, don't mean to bother ya or nothin but what're ya'll talking about."
Seto patted her hand next to where she sat and watched as the teen sat down nervously. She noted that when she lightly put an arm around Ranma that she tensed up and made a mental note to look into it later. "I was discussing your future Ranma. Since you are a member of my family and apparently my charge now that your father has abandoned you, I must see to your care. The problem now is that knowledge of your heritage cannot be hidden. The information was sent through GP headquarters which means everyone in the galaxy knows by now that you are my niece. Many powerful people will want to kill you or manipulate you for what may seem little or no reason. I am going to do everything in my power to make sure that this does not happen. I will get you a tree, I will teach you personally, I will have you guarded, and I will make sure you get an education. You're the only child left from my side of the family other than my children and grandchildren. I will treat you as my own daughter."
Seto noted that anguish, hope, and sadness all pass started playing across Ranma's face as she spoke. Ranma's face became stony as she stared into Seto's eyes. Seto saw the girl roll her tongue across her lips and teeth before she spoke. "Do you mean it?"
Seto blinked. It was a very straight forward question but she felt there was a deeper meaning to it. She gently rubbed her hand through Ranma's hair and watched as the girl flinched like she would be struck because of the contact. _I see. _"Yes I do dear. I won't press you to do the things I ask of you but you must understand that things can never be the same as what they were. You will have to adapt to your new life. When you feel like it, I would like to hear more about yourself. I'll explain some more later. You look tired right now and I imagine you would like to sleep."
Ranma nodded her head and stood up. She turned back to Seto while rubbing the back of her head. "Thank you."
Seto nodded and motioned for one of her handmaidens to lead Ranma to her bedroom.
**XxxxxxxxxxX**
As Seto rolled some ideas through her head, she flipped open a communication relay. A girl with greenish-blue hair appeared on the screen. "Noike, I'm currently in earth space right now. I'm planning to visit tomorrow with a surprise. Toodles."
She watched the confused look appear on Noike's face before turning the display off. She chuckled to herself before turning in for the night.
**XxxxxxxxxxX**
Seto sat at her breakfast table gracefully eating ….. "SLLLLLLLLLPPP!" Gracefully eating... "Pafff da egff." Gracefully eating... "Buuuuuuuuuuuup!" Gracefully eating... "SLLLLLupppp!"
Lady Seto's eyebrow twitched as her new niece/daughter continued to inhale her food. Once the girl let out a contented sigh, Seto finished her meal and faced the reclining girl while favoring her with a frown. "Why did you eat like that dear?"
"Huh?"
Seto rolled her eyes. She knew this was probably going to be hard. After all, it had been a thousand years since she had last had a teenage child. "Why did you inhale your food? It's bad manners dear."
Ranma rubbed the back of her head sheepishly. "Uh, well. You see. Pops kind of stole my food all the time. Said it was trainin. Had ta inhale my food or he'd eat it offa my plate."
Seto sighed. She'd just have to take this slowly and find out her quirks one at a time. It couldn't be that bad, could it? "I'll be teaching you proper grammar and etiquette later. For now, how would you like to meet some relatives. One of my adopted daughters, great grandchildren, and great-great grandchildren are actually living on earth right now and since we're in the neighborhood, I thought we might go visit them."
Ranma had never actually met any relatives other than Genma and now Seto so she nodded her head in approval vigorously. Seto smiled. "Good but first, your attire needs to be changed. It is quite dirty and not appropriate for a formal meeting. I'll have the maids bring you the proper attire."
Somehow that statement sent a cold chill down her spine.
**XxxxxxxxxxX**
Noike, Sasami, and Ayeka were all standing near the end of the dock waiting for Seto to appear. She had been rather elusive and they were starting to worry about what her plans were. A light shown for a second and two figures appeared on the dock. One was Seto and the other was a red-headed girl wearing a simple red Juraian dress similar to the purple one that Ayeka wore. She also seemed to be embarrassed. "C'mon Auntie. I can't wear this thing. It's too girly."
Seto smiled and waved her hand. "Come now Ranma-chan. You do need to wear appropriate attire now. You will have to learn to be more womanly eventually."
Ranma paled at that comment and was about to speak when she heard someone cough. She turned to see three women on the dock. The one with short teal hair spoke first. "Lady... Er, mother. Is she the surprise you were talking about?"
Seto's smile broadened but not in her usual menacing way. "Why yes actually. I would like all of you to meet my great-great grandniece Ranma. She's a long lost relative from one of my siblings that must have survived the pirate raid all those years ago. Low and behold, she showed up on earth when her powers manifested. I just wanted to introduce her to family."
The teal haired woman smiled and bowed slightly to Ranma. "It's a pleasure to meet you Ranma. I welcome my new member of the family. I am Noike Kamiki Jurai, Seto's adopted daughter."
The purple-haired girl made a similar bow. "And I am Ayeka Masaki Jurai, Seto's granddaughter." She then gestured toward the smaller blue-haired girl. "And this is my sister, Sasami Masaki Jurai."
Ranma bowed to them and introduced herself in the usual manner that she did. She scratched the base of her ponytail when she came back up. "Hi, I'm Ranma Saotome, heir of the Anything Goes School of Martial Arts."
Seto's eyes lit up a little as something she had observed before clicked in her mind. "Yes, you are the heir to your father's family art. Aren't you? Would you also like to learn the Juraian sword arts and martial arts styles? They all belong to our family and have thousands of techniques."
Seto wasn't prepared for the industrial strength glomp from the girl. She saw Ranma's eyes glitter with the excitement of a child about to get their favorite present. "Really, you got some techniques that you're going to teach me."
Seto peeled Ranma off and patted her on the head. "Yes dear, among other things that I'm going to teach you."
Noike and Ayeka looked at each other for a moment and confirmed their fears. Seto was getting ready to make her apprentice. Ayeka motioned toward the house. "Seto-sama, Ranma-san, why don't we go in and have some tea and cookies. Sasami just finished making them."
That was all that Ayeka needed to say as Ranma was now pulling Seto along toward the house. All three raised an eyebrow at how much leeway Seto was giving this new child.
**XxxxxxxxxxX**
When Seto and Ranma entered the house, they were greeted by an elderly man and a boy with black hair and a pigtail. Ranma raised her eyebrow. Maybe she really was related to these people. She could tell that the boy had a strong ki signature and the look was pretty damn similar to his own. She was brought out of her thoughts as the smiling older man greeted them. "Why hello Seto! It's a pleasure to see you. And who is the young lady with you?"
Seto smiled back while she motioned for Ranma to sit next to her at the table. She then introduced the other two who sat down beside them at the table. "This is Yosho Masaki, my grandson." She then motioned toward the black-haired boy. "And this is Tenchi Masaki, my great-great grandson." She then patted Ranma on the shoulder. "And this is my long lost great-great grandniece Ranma. It seems that one of my brothers or sisters made it out of the pirate raid alive and had children. Low and behold, I found her after she blew up a mountain here on earth."
Ranma waved sheepishly at the other two as they both raised their eyebrows while looking at her. Yosho was the first to speak. "Hnnn, I suppose that's the energy flux Washu detected not too long ago. Mt. Horai correct."
Ranma nodded and blushed. "Uh, I didn't mean to do it. Well, I was kind of fighting a dragon and..."
"A dragon!" Everyone looked at where Tenchi had stood up with wide eyes.
Seto merely waived her hand. "You're surprised by that Mister 'I tear apart the universe every time I have a power meltdown.' Is it that hard to believe? I'm sure there's some race out there that resembles them."
Ranma nodded her head and put her fist in her hand. "That's it. I forgot, he's part of the Musk race. They're humans from China that've been mixin themselves with animals for the last couple thousand years. Well, he's the prince, the half-dragon guy. Man was Herb pissed over nothin."
Seto sighed, the girl's grammar was atrocious. "Yes, well, I came here to introduce her. I'm sure she'll be coming by to visit quite a bit since she's from earth so I thought this would be a good place for her to stay when she does. I'm afraid her father flat out abandoned her when I showed up."
Yosho frowned. "What did you do grandmother?"
Seto chuckled and flapped her fan. "Oh nothing. He was being rude so I simply had a talk with him and he ran off like the ghosts of hell were after him."
Yosho was about to comment again but was interrupted as Ranma started laughing out, "Ha, that was so funny! It never gets old seeing that damn panda run with his tail between his legs. He deserved that. 'Noo, Noo-chan."
Ranma's mocking tone of her father's words brought something else to mind. "That reminds me. Yosho, I want you to do a search for this girl's mother. I heard her father call her No-chan."
Ranma stopped laughing as she sat up with a stony expression on her face. "Pop said she was dead."
Seto gave Ranma a dubious look as she sighed. "And do you truly believe that. Your father gives me the impression of a slippery snake. I want to see if she is alive or not."
Yosho coughed and looked at both women. "I will see what we can do. I'm sure Washu can find her. What is your father's name so that we can start searching?"
Ranma responded. "Genma Saotome."
Ranma then felt a spike of heated energy coming from the old man. Ranma rolled out of her sitting position and into a fighting stance. The old man slowly looked up a her with flustered red cheeks. He then bit off his words. "Where. Is. That. Filth?"
Ranma didn't move an inch, but responded in a chuckling tone. "Last I saw him was the Tendo Dojo in Nerima, Japan. He's been drinking and moochin off the Tendo's for awhile now. So what's the fat ass done now cuz if he sold me to you at some point and stole me back then I don't swing that way if ya know what I mean. Or did he steal somethin from ya? If it wasn't sold off to a pawn shop, then he's probably already defiled it."
Yosho only seemed to get more angry before he was broken out of his thoughts as a commanding voice took over. "STOP! SIT DOWN YOSHO! BOTH OF YOU BE QUIET!"
Both were now seated and quiet. Seto turned to Yosho first. "What did that man do?"
Yosho schooled in his features and let out a long breath before speaking. "He stole Achika's jewelry. Including her wedding ring. He also stole some of the scrolls with a few of the basic stances of our sword art written on them. He then had the gall to defile Achika's death marker while drunk. To top it all off he scrawled No & Gen with a heart around it onto the sacred tree. You know which one Seto."
Ranma held back a whistle. Her old man really pulled all the stops here. She was brought out of her musing by the serious tone in Seto's voice. "I see." She didn't want to voice that at least two of the things that Genma had done were punishable by death with Ranma sitting there.
Seto then turned to Ranma and said in an icy tone, "Care to enlighten me about your father 'selling' you off?"
Ranma sweated a little as all eyes were on her again. "Uh, well. He kinda engaged me to a bunch of people for food, money, or booze. Couple times he'd abandon me with someone that wanted me and then he'd come back at night and take me back. Did most of that during the ten year trainin trip he took me on. Can't believe he traded me for only a fish, some rice and a pickle one time though."
Seto narrowed her eyes further. "And what happened during this training trip?"
Ranma looked at all of the eyes looking at her in rapt attention. _Oh the hell with it._ "Started when I was five I think. Pop left home with me and we spent the next ten years on the road trainin so I could carry on the Anything Goes Martial Arts School. He trained me in things like the Ca-Ca... those furry things. I had speed drills like swatting at hornets while being tied to a tree, outrunning wolves with weights and steaks tied to me, running behind a train he tied me to, and stealin my food to make me fast with my hands or go hungry. He got the bright idea that he could make me fly by throwing me off of cliffs. He had me steal things for stealth training until I figured out that stealing was bad. Jusenkyo. He at least managed to teach me tha art though."
Seto was clinching the table with her hand so hard that it cracked some. Her left cheek was twitching as well. "Yosho. Do not kill that man. Simply bring him to me. Ranma, do tell me the full story when we're back on the ship with every gory detail."
Yosho nodded. He really couldn't think of a worse punishment than to send that man to his grandmother for her brand of punishment.
It was then that Ryo-Ohki showed up. "Meow."
**XxxxxxxxxxX**
Three people watched as a red blur ran around the house like a madman. "AUUUUUUUUGHH! Get it away!"
All that time the little cabbit happily chased her as it meowed thinking this was a game. Everyone was wondering what was going on until the red blur met a corner and went into a fetal position. Seto was the first to speak. "Ranma what..."
She was interrupted by a deep guttural meow that didn't come from Ryo-Ohki. They all stared at Ranma as she came up on all fours. All the human intelligence had drained from her eyes and she had taken on a more feral disposition. The scene was interrupted as a head floated through the wall right in front of Ranma. "The hell's with this racket."
Everyone pointed to the corner and Ryoko slowly turned her head. She didn't know what it was but she had the sudden urge to get away. She managed to phase back through the wall in time to miss five ki claws moving through the space she had once occupied. Said ki claws extended far enough to slice apart a chair on the opposite side of the room into five pieces.
Nobody moved as the catlike girl sniffed the air and padded around. She then turned to Seto and looked at her puzzlingly. Ranma moved around Seto sniffing her and then decided to rub her head on Seto's thighs. Seto slowly reached down and petted Ranma. Ranma responded by rubbing her mouth along Seto's hand and started purring. Seto sat down and Ranma moved into her lap. Her purring increased as Seto continued to stroke her head and scratched her behind the ears. Ranma laid down and purred as she drifted off to sleep in Seto's lap.
Yosho and Tenchi had been watching the girl the whole time. The ki claws alarmed them as they could mean something else. They were stunned when Seto managed to get the girl into her lap. Once they felt Ranma was no longer a threat, they sat down and looked up at Seto to see her crying. Seto, the Demon Princess of Jurai, was openly weeping before them. This was something that no one had witnessed beforehand unless it was from the woman laughing herself to tears.
They were about to comment when Seto beat them to the punch. The voice was soft but loud enough to hear. "My poor Ranma-chan, what has your father done to you? "
Seto sat up wiping her tears away. She turned to a side door. "Come in. Haven't you been there long enough?"
Five people fell out the door in a dog-pile. Sasami, Noike, Ayeka, Ryoko, and Mihoshi were all sitting there. They quickly moved over to the table and sat around Seto. Mihoshi started scratching Ranma's head. "She's so cute."
Seto smiled. She always loved how Mihoshi always seemed to bring the best out of people even if she was a walking disaster. "I know dear."
Ayeka coughed slightly bringing attention to her. "What happened when she started acting so weird I only uh, heard some of what was said?"
Seto laughed while shaking her head. "Really dear, try being less transparent sometimes. I don't know much more than you. She's just a little enigma that I picked up earlier today. An enigma I plan to adopt as my daughter."
Yosho nodded his head. "I suppose that would be a good idea, but what of her mother?"
Seto frowned while stroking Ranma's hair. "Her mother doesn't deserve this child right now if she's still alive. If she let that oaf take her and do Tsunami knows what to her, then she will have to earn the title of mother back."
**XxxxxxxxxxX**
**Chapter 2: Broaden Your Horizons**
When Akane and Nabiki had returned home from school, they found their father crying and Kasumi humming happily in the kitchen. What surprised them though was Ryoga sitting with what looked like a contemplative face sipping tea next to their father. Nabiki raised an eyebrow as she never expected the most dense of all the martial artists to be thinking long and hard about something in their dining room. "Yen for your thoughts Ryoga?"
Ryoga broke out of his contemplation to look at the Tendo girl. He seemed to be measuring her or something. "Call my debts even and I'll tell you."
Now that shocked Nabiki. Ryoga had very little debt owed to her, only 2000 yen, but she did have blackmail material on him that was worth much more. "And this information is worth 2000 yen?"
Ryoga nodded. Nabiki smirked. She was curious now. "Deal."
Nabiki sat down across from Ryoga and started sipping on tea that Kasumi had just brought in. "Well, I attacked Ranma as usual, but found him, er well, her with another woman. Not a fiance because she was too old. I found out that Ranma didn't get the tea kettle of liberation and it was destroyed so he's stuck as a girl permanently now."
Nabiki spit out her tea. Her cash cow had lost. She only had a few people bet that Ranma would get permanently stuck as a girl but now she had some markers to pay. She was going to lose money. She was about to storm off but Ryoga continued. "... The funny thing though is that the older woman grabbed my umbrella and held me back from beating Ranma. She actually held me back with her strength alone. And then something weird happened. I called Ranma an honorless cur and she lit into me. She went on about how I ambushed hi.. her and that she was Ranma's great aunt. What's even weirder was she said that she was the emperor's grandmother and Ranma was the emperor's cousin or something."
Nabiki's temper did a 180 as she turned back to Ryoga. A malicious smile was on her face. "Go on."
Ryoga nodded and took another sip of tea. "Well, I followed them back here to the Tendo's. When we got here, Genma and Mr Tendo got after Ranma about being stuck as a girl. Genma suggested switching the engagement to your father to satisfy the agreement, but the old lady said something about men and matchmakers. Genma got mad and got in her face. That's when the old lady became really scary and Genma ran off. She then talked to Mr Tendo about coming back in one month to determine who would marry Ranma and said something about Ranma being her charge now or something like that. She then left with Ranma and some servant woman that I didn't notice before."
Nabiki's smile was now nearly to her ears. Ranma was freaking royalty and the servant was an obvious tip that the woman was loaded as well. Maybe Ranma wasn't such a bad choice after all. She needed to play her cards right. "Anything else."
Ryoga looked thoughtful for a moment. "I think she said her name was Seto Kamiki something or other. I didn't catch her last name but those were her first and maiden name."
Nabiki handed Ryoga a thousand yen note. Ryoga looked at Nabiki like she had grown a second head. "Don't spend it all at one place."
**XxxxxxxxxxX**
Seto watched her new daughter as she slept on the bed next to her. She gently stroked the red-head's hair. She thought about what Washu had told her and frowned.
**Flashback...**
Washu had put a probe on the sleeping girl's head. Seto watched the googly eyes flash and chuckled to herself at how silly the contraption looked. She then heard a ding and watched as hundreds of screens popped into existence around them.
Washu whistled next to her as her wide eyes flitted across the screens. "What a mess! This is as bad if not worse than Seina's data. Her personality is fractured and her physical health is atrocious. The only thing holding this girl together is her life energy. In fact, I've never seen this level of control in life energy in any creature."
Seto frowned at that assessment and watched as Washu flipped through several screens. "Hmm, those claws weren't light hawk wings but they could still manipulate matter. They have a very short range and a lot less power than light hawk wings, but much more control and finesse than the wings do. Whatever gave her this ability though left some deep mental scarring. It'll take time to figure out how to heal that."
Seto thought for a moment about what Ranma was talking about and the appearance, no the sound that Ryo-Ohki had made. "Cats. I remember Ranma started talking about a training technique but quickly stopped talking about it. It had something to do with cats though."
Washu nodded her head and kept typing and pulling up screens. "Yes. I think your right. The smaller scars are consistent with cat claw marks and the shear number of them... What worries me though is how old these marks are. She would have only been five or six when she got these. The number of cuts though, considering blood loss and infection that would have occurred from this many, is worrisome though. She should have died from something like this. It's a miracle she isn't dead, but eventually these scars, along with the others, are going to start affecting her movements and quality of life before she turns 50. I'll make a custom nutrient and protein supplement that should fix the physical malnourishment and scarring. I'm afraid I'm going to have to leave the mental healing to you Seto. I'll give you my full findings later."
Seto nodded as she stood up with Ranma in her arms. "I'm afraid I'll be leaving you prematurely. Washu please send the supplement to my ship."
**End of Flashback**
**XxxxxxxxxxX**
A large gathering sat around the Tendo's table that night: three Chinese Amazons, a chef, three sisters, and two half drunk men. Nabiki was sitting at the head of the table and clapped her hands to get all their attention. She had made a killing for this session on their usual topic Ranma. "Alright, I'm sure you all are wondering why I charged so much for the meeting tonight."
Everyone there nodded. Ukyou slapped her hand on the table. "It better be good. 20,000 yen isn't easy to come by you know."
Nabiki sported a feral grin and cracked her neck. "Ranma's stuck as a girl. Permanently this time. No way to change back."
There was a clamor as the fathers, Akane, and Ukyou started yelling as one. They were interrupted by Cologne beating her stick on the table. "I know that already. I was hoping to see if a cure could be found or see if the kettle turned up soon. You are wasting my time."
Nabiki's smile widened. "Oh, that isn't all. Apparently, Ranma was saved by someone that turned out to be his great aunt when he blew up the mountain. She also stopped an attack by Ryoga with one arm."
This brought the silence she had been craving. The stupefied looks from all people present, including the old matriarch. She then continued. "Lo and behold, this woman also turns out to not only be Ranma's great aunt but the grandmother of the emperor."
Genma burst out of his seat gripping the table. "What!? Nodoka's related to the emperor!"
Nabiki smiled as another tidbit of information fell into place. "Oh, who's Nodoka?"
Genma began to sweat and looked around before diving through the door and running off to parts unknown. Nabiki shook her head. "That. Is going on his tab." She turned around to face everyone else. "Now onto the fun part. The woman took Ranma and said she would be back in a month to settle the fiance mess. She doesn't believe that Ranma is a boy and without a way to change him back we don't really have much clout in the coming debate unless other measures are taken."
Cologne was the first to catch onto this line of thought. "My great granddaughter will not use Jusenkyo to become male. Although, I don't suppose the Kisses will be appreciated at this point. I may want him in the tribe but I'm not stupid enough to force a foreign dignitary's relation to join my tribe. The only thing I might consider now is Mousse marrying her to link her family to our tribe."
Mousse looked at her like she was crazy, well looked at flower pot. "I'm not marrying Saotome."
Shampoo also expressed her feelings. "No, Airen no marry duck boy. We just use water, make Ranma half-man again."
Cologne wrapped her cane over both their heads. "No and no. The water will no longer work on son-in-law and Ranma has beaten Mousse in combat multiple times. Since she is fully female now, she technically owns him. Males defeated in combat by an outsider woman are the property of that woman unless they are married, and as Mousse is a bachelor, he belongs to her. The Kiss of Death is null due to the clause about foreign dignitaries. We don't need the Japanese government meddling in our affairs. She can either keep Mousse as her servant or marry him now. I'd prefer it if she marries him to strengthen our relations."
Nabiki clicked her tongue and thought for a second. She was going to use the old bat to get her some Nannichuan water, but since she still had some plans, she would have to find another route. _Oh well. _"Well, we all have a month to start making our cases. I think this woman is a no nonsense type so don't try pulling your usual tricks and traps people. You all are going to have to win by your own merits."
**XxxxxxxxxxX**
Ranma woke up with with something soft in her face. She blinked a couple of times and tried pushing herself up. She suddenly stopped when her hands hit the squishy things in front of her face. Ranma slowly looked up to see the smiling face of Seto. In the blink of an eye, Ranma was in the corner of the room hunkering down with her hands over her head. Seto frowned as she got off the bed and approached Ranma. She then heard a mantra. "I'm sorry, I'm sorry, I'm sorry, I'm sorry."
She lightly put her hand on Ranma's shoulder only to have the girl flinch at her touch. "Ranma, what's wrong? Why are you cowering like this?"
Ranma stopped shivering and slowly turned to look up at Seto. "You aren't going to hit me for touching you there?"
Seto shook her head and chuckled. "No dear, you simply woke up in that position. Nothing to be ashamed of. Why would I hit you?"
Ranma stood up and they both calmly walked towards the bed. "Now tell me dear. Why would you expect to be hit?"
Ranma frowned and sighed. "Akane Tendo. She's one of my fiance's and she hits me any time that she thinks I do something perverted. She even hits me when I just talk to a girl. An' the others glomp me or sneak into my bed at night and make it look even worse."
Seto let this sink in. Lover's spats were quite common and something like Ranma described was all rather common among the more jealous in a love triangle. She chuckled thinking of Seina. "She's jealous then."
Ranma nodded her head. "I know, but she never gives me a break."
Seto hugged the girl lightly and was rewarded as Ranma didn't flinch back this time. "I told them that I would resolve this fiance situation so would you like to tell me more about it so I can help you with it."
Ranma smiled. Seto really did care. "Okay, the oldest was with the Tendo's. I'm supposed to marry one of the daughters to continue our martial arts school. Akane got picked. I like her but she just gets too jealous. Nabiki, Kane's sister, is a... well she likes to handle money. She's pretty but she can be hard to handle. Kasumi's the eldest and the sweetest one there, but she's almost like a mother to me. Ukyou's a good friend, but she's just that. Shampoo... don't wanna go there, er, well she just wants to drag me to this village in the middle of nowhere and make me her slave. Kodachi, she's just a murderous nut that would either kill me or keep me in a drugged up coma."
Seto whistled at the list. "You're father I presume?"
Ranma nodded her head and frowned. "There were a lot more but I managed to get rid of those. It's just those girls left."
Seto sat in contemplation for a second. "Ukyou and the Tendo girls sound nice enough. Why not them?"
Ranma shrugged her shoulders. "I know picking one of them would be the best option but I pick one and the others would lose honor an' attack the one I chose."
A smile crept onto Seto's face. "Chose, you don't need to chose dear."
Ranma looked at Seto like she had grown a second head. "Huh?"
Seto waved her fan in front of her face. "Why Ranma I must tell you a bit more about our culture for you to understand..."
**XxxxxxxxxxX**
Nabiki was flipping through some interesting bios that her network had gathered. Apparently, Ranma's mother was known quite well among the older matrons of the Nerima beauty parlor. She was a kenjutsu specialist, flower arranger, and a respected woman that held onto the older beliefs. She was also a certifiable nut. Outside of the older social circles she was shunned by the younger generation as her ideas of manliness and how young women should behave was not only expressed in her words but actions. She had repeatedly tried to help some young men find a wife and their mistresses or had dragged several girls into a kimono shop for a fitting.
What interested her the most was how this Seto Kamiki woman fit in. She had found through records that the Kamiki name showed up around the 1100's as a young man named Jiro Kamiki set up a small fiefdom and led a respectable sect. What was strange though was the fact that Jiro had no children and disappeared from record until another Kamiki showed up on record in the 1820's. He also called himself Jiro Kamiki. This Jiro Kamiki somehow reestablished the noble house of Kamiki. What caught her eye was that this Jiro married a woman who was a relative of one of the earlier emperors in the 1840's. They had a child named Hiro Kamiki in the 1850's. Hiro went on to become a respectable merchant but had no children until 1930 when he had a daughter named Sakura Kamiki. Sakura Kamiki then married a man from another well to do house, one Gendo Hime, in 1960 and they had female child named Nodoka Hime the following year. Nodoka Hime married one Genma Saotome, not from a noble house, in 1978 and had a child one year later.
The problem came with Seto Kamiki. She showed up on record around 1810 but was not listed with the other Kamiki as a relative. Her name was listed without association previous to that point and her listed children and grandchildren went under the family name Masaki, but the Masaki family that was listed under her was established from the 1280's. What was even more strange was that there were no recorded deaths for both Kamiki families until Sakura Kamiki who died in a car crash in 1972. The Masaki family had listed deaths, but, with the exception of an Achika Masaki, all of the Masaki deaths had a repeated pattern. All of them were a single male dying at the approximate average lifespan for the current generation. What was stranger was that upon the event of these deaths, a male heir of around 20 years old would appear to take over the Masaki estate even though this person did not exist on record beforehand. She could understand this happening sometimes as old records tended to get lost over time but after the fifth generation following this pattern she became suspicious.
After more digging, she found out that there had only ever been the one Seto Kamiki. She appeared in record in 1810, but not again until 1982 when she was cited for loitering around a storefront. _The hell. Either these people are hiding their names or... Cologne's supposed to be 300 years old but she looks it. This Kamiki woman was supposed to look like she was in her early thirties. No it has to be even though it seems impossible. The Masaki men are the key. The way the post changes hands screams that it's the same person taking over again and again, but that would mean that he's nearly 700 years old! And Jiro Kamiki... If the same theory holds true, then he would have been over 700 years old as well. What's even more interesting is that they always spring up as a lower noble house with no evidence as to how they did it. Wait! There was one reference._ Nabiki dug around the reports. She then found a report of some legend centering around the Masaki estate's shrine.
Nabiki read the report softly to herself. "...And so Yosho Masaki plunged the glowing Tenchi-ken (Heaven and Earth Sword) into the foul demon that burned the lands and the sword stuck fast. Yosho then took the body of the demon and sealed it in a cave using his sword as the key to its imprisonment. Yosho then spoke to the people: 'Hear me now. I shall now make a shrine here and keep faithful watch over the demon so that it may no longer burn the lands. My faithful watch shall never end.'" Nabiki paused for a second as something started creeping into her mind. Seto claims to be the grandmother of the current emperor. These people were older than dirt or something else was going on. Yosho used a sword called Heaven and Earth to subdue a demon that no one else could and then sealed it. He then proclaimed that he would forever watch over the damned thing. She then noticed the last person in the Masaki line and that both this Katsuhito/Yosho(?) person and Tenchi were both alive and on record.
Nabiki's thoughts suddenly started to become more coherent and she started to sweat as she realized the implications of what this all meant. She rushed over to the phone on the nightstand. She dialed as fast as she could. Beep, beep. "Yes, it's me Nabiki. I'll pay his price; just have that Touma guy send the water over in heavily sealed barrels. Absolutely water-tight mind you... Also, I want you to send me some of the more obscure translations of some legends. The ones I specifically want are the ones on the Orochi and Kusanagi, Masaki and the sealing sword of Heaven and Earth, and any of the more obscure stories about Amaterasu and her siblings."
**XxxxxxxxxxX**
Ranma was looking around at the huge trees surrounding her as she walked down a wooden walkway with Seto and two of her handmaidens. She had never seen such a beautiful landscape. It was more grand than the forest on Seto's ship and that was saying something. She was broken out of her musings as a large man with a giant beard stretching across his face approached them. Seto waved to him and he bowed curtly. Seto then turned to Ranma as she smiled. "I'd like you to meet my husband Utsutsumi. He is the guardian of the trees. Unfortunately, he is not allowed to leave his post unless it is for important state affairs so he doesn't get out much."
Ranma bowed to her great great uncle. She wore a cocky smile as she came back up. "Uh, I'm Ranma, yer uh, grandniece."
He sported a similar smile. "It is good to see some fire in you young one. You will need it for the selection ceremony. The approval for your ceremony just came in."
Seto flashed her fan out and hid her smile. "I'm glad they did as I would have been most disappointed if my dear grandniece had been turned down."
Utsutsumi kept from cringing at her response as he knew what a disappointed Seto could do. "Follow me and we shall get you ready for your ceremony."
**XxxxxxxxxxX**
"Curly we need some heavy tranquilizers stat."
A flying plate almost hit the silver-haired attendant. "I'm not going back out there! She'll kill me."
"How can she throw like that?"
"It's just a ceremonial dress princess." Another plate crashed against the wall as the green-haired attendant dodged some forks that impaled themselves above her head. "It's not that bad is it."
Ranma screamed. "I ain't wearin no wedding kimono."
Seto was sitting back laughing. "Isn't she just a lively child."
**XxxxxxxxxxX**
After Seto stopped laughing and stepped in, Ranma settled down. "Now Ranma dear. It's not a wedding kimono and is required for the ceremony. You are not going to have a wedding... today. It's either this or round the clock surveillance and guards with little ability to go outside on your own."
Ranma froze for a second. _Don't want to be cooped up and coddled like some kind of princess. Well, this should be over quickly though._ "Alright Aunty."
"Good, now behave for the attendants. Besides, you don't want to upset your Uncle Utsutsumi, would you? You'll get a surprise at the end of this if you behave."
"I'll behave Aunty." Seto smiled as Ranma calmed down. Having the child around her and all the interesting situations she got into excited her. She also knew that while Ranma didn't notice it, she was changing ever so slightly. Some of the rough edges were starting to smooth and what was once a boy in girl guise was slowly becoming a tomboyish girl.
"Good, I'll meet you after the ceremony." Seto left the room with a smirk on her face. _Never a dull moment with this one._
**XxxxxxxxxxX**
Ranma walked into the the door of the tree vault with two guards trailing her leaving Seto behind. She was wearing a white Juraian kimono with a large white hood.
When she was inside, she was greeted by Utsutsumi. "Why hello Ranma. It's a pleasure to meet you again. Why don't we get started? It can be quite daunting looking for a tree."
Ranma nodded her head. She left the antechamber with him and stared at the huge complex housing the trees. She could feel tremendous amounts of ki flowing out of all of these trees. They're ki was caressing hers and vice versa. It felt quite peaceful to her.
"Hey, Utsus... I mean Uncle. How do I select a tree?"
Utsutsumi nodded his head sagely. "Well, we find a tree that is willing to bond with you and you with it. Its a mutual relation..."
Utsutsumi was cut off by a rustling noise that suddenly grew to deafening proportions. Both he and Ranma looked up just as a slew of roots fell down around them. The roots seemed to batting at each other with sturdier roots winning out.
Utsutsumi gasped. "By the name of Tsunami! What is going on?"
"Uh, Uncle, is this bad cuz..." Ranma was cut off as a large pair of roots ensnared her from behind and pulled her into the morass of roots. Utsutsumi gasped in shock and tried to follow only to be blocked by the wall of roots. Then, just as suddenly as they started, the roots receded back to their trees.
Utsutsumi turned back to his stunned guards. "Find Lady Ranma now."
The guards spread out searching the many trees until one called out and motioned to the other. Utsutsumi was happy to find Ranma unharmed but was in shock to find what tree had selected her. It was the Hime. The one stubborn tree that had absolutely refused all candidates with the exception of its first owner which had been the only female empress that had been the state head of Jurai rather than her male spouses. This tree was heavily sought after because it was one of the pillars of the House of Jurai and anyone selected by it was not only immediately initiated into the house but would also be put in as a candidate for succession of Jurai.
Ranma stood dizzily up and said, "Anybody catch the number of that bus."
**XxxxxxxxxxX**
In a dark meeting room...
"What do you mean Hime chose her?" A large man in the shadows yelled at a guard from the tree room.
"It is just as I said. The trees seemed to go crazy trying to grab her and then Hime beat them all back to get her. There is no record of this ever happening before."
"Hmmm... This actually could work to our advantage in several ways. Lady Seto may have done herself in by adopting that earth whelp. Good, now go." The guard bowed to the darkened man as he left.
**XxxxxxxxxxX**
Ranma exited the tree vault with torn clothes and messy hair. It looked like she had been in a fight, but she didn't look too worse for wear. She then noticed Seto who was giggling at the gate. "What happened Ranma-chan? Did you fall into a bush or something?"
Ranma crossed her arms and pouted which in turn caused Seto's smile to widen more. "Was the trees fault, damn fightin over me and all!"
Seto raised an eyebrow and turned to her husband who coughed. "Yes. Actually they did fight over her. Literally. I've never seen the trees send out roots to actually claim a candidate. What was even more shocking was that Hime chose her and won out over the other trees."
Seto's eyes really widened at that statement. The last time she had been through the tree vault Hime was still a seed floating over a patch of grass. Granted that seed was well over 1,000,000 years old and she had visited the inside of the vault 300 years ago, but that meant that Hime had finally taken root and was still a relatively young/older than dirt sapling. "Well, I'm sure this will circulate many different circles. This is the best and worst thing that could have happened."
Ranma looked at Seto with apprehension. The way she stated that sent a shiver up Ranma's spine as if the to warn her of the impending doom, but of course Ranma had to open her mouth. "Whatcha mean?"
Seto turned back to Ranma as she considered a simple way of stating everything that might happen. "You are now a direct candidate for empress which means that you are now the most sought after bachelorette in the universe, the biggest target on every assassin's hit list, and one of the most influential noblewomen, other than myself, that exist in the universe. Now let's get you started on the basics of tree care."
**XxxxxxxxxxX**
Nabiki had a smile plastered across her face as she finished hiding the last of the barrels she got from a man named Touma. He had even been kind enough to give her a demonstration with a passing rat so she knew the product was good. Once those were securely hidden in a place that not even Akane would look for 'ingredients,' she turned to another barrel that she had managed to get through other means. She took the stopper out and carefully poured the contents into a thermos which she immediately sealed.
She whistled on her way out the door. She had an appointment to keep and some information to gather.
**XxxxxxxxxxX**
This is anther old one that I've cleaned up. It took a little longer due to its length.
End file.
| fanfiction |
If the universe is flat, does that imply that the Big Bang produced an infinite amount of energy?
Too much density and the universe is closed, analogous to a sphere in four dimensions: you travel in a straight line and you end up where you started. Too little and you have a saddle: not sure about the destination if you travel in a straight line. Just the right amount and the topology is flat. The flat topology is infinite: you travel in a straight line forever.
If the topology is flat (and at this point all evidence indicates that it is to within 0.4%), then multiplying the critical density by an infinite amount of cubic meters gives you an infinite energy/stress.$$\rho\_{CRIT}\space kg\space m^{-3}\times \infty\space m^3=\infty\space kg$$
Is that a reasonable interpretation?
What you calculated above ($\infty$, for a flat space universe) is just the *proper mass-energy* of matter. It doesn't take into account the - negative - energy of the gravitational "field" itself, which cannot be localised in General Relativity. The "total energy" of the universe could be 0, but there's no way we could give a physical sense to it, since the whole universe energy cannot be measured from "inside".
You have to be careful with the interpretation of energy when you don't know what sort of gravitational potential well might be involved. For example, you might find some amount $m c^2$ of rest-energy of matter when calculated in an inertial frame near but outside the horizon of a black hole, but in order to use this energy at some other location, you would first have to pull the matter up against gravity, expending energy $E$ in order to do so. After spending that $E$ you acquire just $m c^2$ at your location, so overall you have gained $(m c^2-E)$ and this will be small compared to $m c^2$ if the matter started out near a horizon. This is the sense in which gravitational binding energy is negative. When applied to the whole universe, this consideration makes a calculation of the type you are proposing questionable, because it is hard to say what physical meaning it has.
A better analogy is, perhaps, with the concept of escape velocity. A flat universe is one where the motion of matter everywhere is just enough to keep escaping from its own mutual gravity.
Finally, the topology of a mathematical space is not in one-to-one correspondence with the curvature, and in particular, if a space is flat it does not necessarily follow that it is infinite. There are a number of different topologies that are mathematically possible for a flat space, and some of them are bounded (i.e. not infinite). So this may apply to the physical universe too. We don't know.
If it was completely flat, you wouldn't talk about volume. The universe isn't completely flat, it does have a volume (like a pancake, it's called 'flat', but it definitely has a volume). For a truly flat object, your formula would need a surface density and surface area, and you would get a finite answer.
| stackexchange/physics |
our thesis in this paper is that mathematics ( including logic ) can be used to attack the problem of finding a realistic interpretation of ( standard dirac - von - neumann ) quantum mechanics ( qm ) .
mathematics itself contains a very basic duality that can be associated with two meta - physical types of reality : 1 . the common - sense notion of objectively definite reality assumed in classical physics , and 2 . the notion of objectively indefinite reality suggested by quantum physics .
the problem of interpreting quantum mechanics _ is _ essentially the problem of making sense out of the notion of objective indefiniteness .
the approach taken here is to follow the lead of the mathematics of partitions , first for sets ( where things are relatively `` clear and distinct '' ) and then for complex vector spaces where the mathematics of full qm resides .
there has long been the notion of subjective or epistemic indefiniteness ( `` cloud of ignorance '' ) that is slowly cleared up with more discrimination and distinctions ( as in the game of twenty questions ) .
but the vision of reality that seems appropriate for quantum mechanics is _ objective or ontological indefiniteness_. the notion of objective indefiniteness in qm has been most emphasized by abner shimony ( @xcite , @xcite , @xcite ) . _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ from these two basic ideas alone indefiniteness and the superposition principle
it should be clear already that quantum mechanics conflicts sharply with common sense .
if the quantum state of a system is a complete description of the system , then a quantity that has an indefinite value in that quantum state is objectively indefinite ; its value is not merely unknown by the scientist who seeks to describe the system .
@xcite the fact that in any pure quantum state there are physical quantities that are not assigned sharp values will then mean that there is _ objective indefiniteness _ of these quantities .
shim : worldview _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the view that a description of a superposition quantum state is a _
complete _ description means that the indefiniteness of a superposition state is in some sense objective or ontological and not just subjective or epistemic .
in addition to shimony s `` objective indefiniteness '' ( the phrase also used by gregg jaeger @xcite and used here ) , other philosophers of physics have suggested related ideas such as : * peter mittelstaedt s `` incompletely determined '' quantum states with `` objective indeterminateness '' @xcite , * paul busch and gregg jaeger s `` unsharp quantum reality '' @xcite , * paul feyerabend s `` inherent indefiniteness '' @xcite , * allen stairs `` value indefiniteness '' and `` disjunctive facts '' @xcite , * e. j. lowe s `` vague identity '' and `` indeterminacy '' that is `` ontic '' @xcite , * steven french and decio krause s `` ontic vagueness '' @xcite , * paul teller s `` relational holism '' @xcite , and so forth .
indeed , the idea that a quantum state is in some sense blurred or like a cloud is now rather commonplace even in the popular literature .
thus the idea of objective indefiniteness ( described in various ways ) is hardly new . our goal is to give the mathematical backstory to indefiniteness by showing how the mathematical framework of qm can be built up or developed starting with the ( new ) mathematical logic appropriate for indefiniteness that is duality - related to the usual boolean logic associated with classical definiteness .
how can indefiniteness be depicted mathematically ?
the basic idea is simple ; start with what is taken as full definiteness and then factor or quotient out the surplus definiteness using an equivalence relation or partition . starting with some universe set @xmath2 of fully distinct and definite elements , a partition @xmath3 ( i.e. , a set of disjoint blocks @xmath4 that sum to @xmath2 ) collects together in a block ( or cell ) @xmath4 the distinct elements @xmath5
whose distinctness is to be ignored or factored out , but the blocks are still distinct from each other .
each block represents the elements that are the same in some respect ( since each block is an equivalence class in the associated equivalence relation on @xmath2 ) , so the block is indefinite between the elements within it .
but different blocks are still distinct from each other in that aspect .
consider the calculation of the binomial coefficient @xmath6 .
the idea is to count the number of @xmath7-ary subsets of an @xmath8-ary set ( @xmath9 ) where the different orderings of the otherwise same @xmath7-ary subset are surplus that need to be factored out .
the method of calculation is to first count the number of possible orderings of the whole @xmath8-ary subset which is @xmath10 .
then we want to quotient out the cases that are distinct only because of different orderings . for any given ordering of the @xmath8 elements ,
there are @xmath11 ways to permute the first @xmath7 elements in the given ordering leaving the last @xmath12 elements the same .
thus we take the first quotient by identifying any two of the @xmath13 different orderings if they differ only in a permutation of those first @xmath7 elements . since there are @xmath11 such permutations , there are now @xmath14 equivalence classes or blocks in the resulting partition of the @xmath13 orderings .
but these equivalence classes still count as distinct the different orderings of the last @xmath12 elements so we further identify blocks which just have a permutation of the last @xmath12 elements to make larger blocks .
then the result is @xmath6 blocks in the partition which is the number of @xmath7-element subsets ( which equals the number of @xmath12-element subsets ) out of an @xmath8-ary set disregarding the ordering of the elements . in this example , the set of fully determinate alternatives are the @xmath13 orderings of the @xmath8-element set .
then to consider the subsets of determinate or definite cardinality @xmath7 ( and thus the complementary subsets of definite cardinality @xmath12 ) , we must quotient out the number of possible orderings @xmath11 and @xmath15 to render the ordering of the elements in the subsets indefinite or indeterminate . to be concrete , consider a set @xmath16 of @xmath17 elements so the universe @xmath2 for fully distinct orderings has @xmath18 elements @xmath19 .
how many @xmath20-element subsets are there ?
the first quotient groups together or identifies the orderings which only permute the first @xmath21 elements so two of the blocks in that partition are @xmath22 and @xmath23 , and there are @xmath24 such blocks .
each block has the same final @xmath25 elements in the ordering so we further identify the blocks that differ only in a permutation of those last @xmath12 elements .
one of the blocks in that final partition is @xmath26 and there are @xmath27 such blocks with four elements in each block .
each block is distinct from the other blocks in the first @xmath7 elements and in the last @xmath12 elements of the orderings in the block so the block count is just the number of subsets of @xmath7 elements ( which equals the number of subsets of @xmath12 elements as well ) where each block is indefinite as to the ordering of elements within the first @xmath7 elements and within the last @xmath12 elements .
hermann weyl makes the same point using an example slightly more complicated than the binomial coefficient .
he starts with a set or `` aggregate @xmath28 ... of elements each of which is in a definite state '' @xcite and then considers a partition or equivalence relation whose @xmath29 blocks or classes @xmath30 can be thought of as boxes into which the @xmath31 elements of @xmath28 may be placed ( some boxes might be empty ) .
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ a definite _ individual state _ of the aggregate @xmath28 is then given if it is known , for each of the @xmath31 marks @xmath32 [ de : which distinguish the @xmath31 elements of @xmath28 ] , to which of the @xmath29 classes [ or boxes ] the element marked @xmath32 belongs .
thus there are @xmath34 possible _ individual states _ of @xmath28 .
if , however , no artificial differences between elements are introduced by their labels @xmath32 and merely the intrinsic differences of state are made use of , then the aggregate is completely characterized by assigning to each class @xmath35 ( @xmath36 ) the number @xmath37 of elements of @xmath28 that belong to @xmath35 .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ those occupation numbers @xmath37 would then characterize `` the _ visible _ or _ effective state _ of the system @xmath28 . ''
@xcite thus weyl points out that the mathematical treatment of indefiniteness starts with the definiteness given here by the markings @xmath32 on the @xmath31 elements distributed between the @xmath29 boxes @xmath35 , and then one erases the markings @xmath32 so the blocks or boxes in the partition have only an occupation number @xmath37 with no distinctions between the @xmath37 elements in each box @xmath35 . when this scheme for representing indefiniteness is applied in quantum mechanics , then it is an objective indefiniteness in that no further differentiation between the elements of a box @xmath35 is possible . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ since photons come into being and disappear , are emitted and absorbed , they are individuals without identity .
no specification beyond what was previously called the effective state of the aggregate is therefore possible .
hence the state of a photon gas is known when for each possible state @xmath38 of a photon the number @xmath39 of photons in that state is given ( bose - einstein statistics of radiation ) . @xcite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ thus within qm , the treatment of the indefiniteness due to the indistinguishability of quantum particles of the same type is to artificially treat them as distinct and then collect together or superpose the permutations of the particles ( in a totally symmetric or totally antisymmetric manner ) that factors out their supposed distinctness ( see any qm text such as @xcite ) .
our point in this section is the general mathematical theme that indefiniteness is described by taking a partition or quotient of a set of definite entities .
a partition is a mixture of indefiniteness and definiteness .
each block is indefinite between the elements within it , but the blocks of the partition are distinct from one another .
the common - sense classical view of reality is that it is completely definite or determined and fully propertied all the way down .
every entity or thing definitely has a property @xmath40 or definitely has the property @xmath41 .
peter mittelstaedt quotes immanuel kant s treatment of the idea of complete determinateness : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ every thing as regards its possibility is likewise subject to the principle of complete determination according to which if all possible predicates are taken together with the contradictory opposites , then one of each pair of contradictory opposites must belong to it .
( kant quoted in : @xcite ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ given a universe set @xmath2 , a predicate @xmath40 is represented by the subset @xmath42 of elements that have the property , and the complement subset @xmath43 represents the elements that have the property @xmath41 .
the two mathematical concepts of subsets and partitions are thus associated with two aforementioned metaphysical types of reality : 1 .
the common - sense notion of objectively definite reality assumed in classical physics , and 2 . the notion of objectively indefinite reality suggested by quantum mechanics .
subsets and quotient sets ( or partitions ) are mathematically _ dual _ concepts in the reverse - the - arrows sense of category - theoretic duality , e.g. , a subset is the direct image of a set monomorphism while a set partition is the inverse image of an epimorphism .
this duality is familiar in abstract algebra in the interplay of subobjects ( e.g. , subgroups , subrings , etc . ) and quotient objects .
william lawvere calls the general category - theoretic notion of a subobject a _
part _ , and then he notes : `` the dual notion ( obtained by reversing the arrows ) of ` part ' is the notion of partition.''@xcite the logic appropriate for the usual notion of fully definite reality described by subsets is the ordinary boolean logic of subsets @xcite ( usually mis - specified as the special case of `` propositional '' logic ) .
we have seen that the other vision of objectively indefinite reality suggested by qm is mathematically described by the equivalent concepts of quotient sets , partitions , or equivalence relations .
the boolean logic of subsets has an equally fundamental logic of the dual quotient sets , equivalence relations , or partitions ( @xcite and @xcite ) .
the two logics of the dual concepts are associated with the two visions of reality .
boole developed not only the logic of subsets , he defined a normalized counting measure on subsets of a finite universe set to yield the notion of _ logical _ finite probability theory . by making the same mathematical moves in the logic of partitions , i.e. , by defining a normalized counting measure on the partitions on a finite universe set ( where partitions are represented as the complement of the associated equivalence relations ) ,
one obtains a notion of _ logical _ _ entropy _
( @xcite and @xcite ) that adds to the interpretation of qm mathematics .
since our topic is to better understand objective indefiniteness , and thus to better understand the reality described by qm , we will be following the math of partitional concepts .
the development of the mathematical concepts from the logical level up to qm is based on the natural bridge between set concepts and vector - space concepts using the notion of a basis set .
we will transport partitional concepts across that bridge in both directions .
we will see that the mathematics and logic of set partitions can be lifted or transported to complex ( inner product ) vector spaces where it yields essentially the mathematical machinery of qm ( of course , not the specifically physical postulates such as the hamiltonian or the debroglie relationships ) .
this shows that the mathematical framework of qm is a type of _ logical _ system developed using complex vector spaces .
the vector space concepts of full qm can also be transported back to set - like vector spaces over @xmath1 to yield a pedagogical model of `` quantum mechanics over sets '' or qm / sets @xcite .
the probability calculus of qm / sets is a non - commutative version of the usual laplace - boole logical finite probability theory .
the traffic in both directions supports the idea of interpreting qm in terms of objective indefiniteness as illuminated by the logic and mathematics of partitions @xcite .
in subset logic , each element of the universe set @xmath2 either definitely has or does not have a given property @xmath40 ( represented as a subset of the universe ) .
moreover an element has properties all the way down so that two numerically distinct entities must differ by some property as in leibniz s principle of the identity of indiscernibles.@xcite change takes place by the definite properties changing . for a hound to go from point @xmath44 to point @xmath45
, there must be some trajectory of definite ground locations from @xmath44 to @xmath45 . in the logic of partitions ,
a partition @xmath3 is made up of disjoint blocks @xmath4 whose union is the universe set @xmath2 ( the blocks are also thought of as the equivalence classes in the associated equivalence relation ) .
the blocks in a partition have been distinguished from each other , but the elements within each block have not been distinguished from each other by that partition , i.e. , they are identified by the associated equivalence relation . hence each block can be viewed as the set - theoretic version of a superposition of the distinct elements in the block .
when more distinctions are made ( the set - version of a measurement ) , the blocks get smaller and the partitions ( set - version of mixed states ) become more refined until the discrete partition @xmath46 is reached where each block is a singleton ( the set - version of a non - degenerate measurement yielding a completely decoherent mixed state ) .
change takes place by some attributes becoming more definite and other ( incompatible ) attributes becoming less definite . for a hawk , as opposed to a hound , to go from point @xmath44 to point @xmath45 , it would go from a definite perch at @xmath44 into a flight of indefinite ground locations , and then would have a definite perch again at @xmath45 .
fig1-qtrajectory.eps + figure 1 : how a hound and a hawk go from @xmath44 to @xmath45 the imagery of having a sharp focus versus being out - of - focus could also be used if one is clear that it is the reality itself that is in - focus or out - of - focus , not just the image through , say , a microscope .
a classical trajectory is like a moving picture of sharp or definite in - focus realities , whereas the quantum trajectory starts with a sharply focused reality , goes out of focus , and then returns to an in - focus reality ( by a measurement ) . in the objective indefiniteness interpretation
, a subset @xmath42 of a universe set @xmath2 should be thought of as a single indefinite element @xmath28 that is only _ represented _ as a subset of fully definite elements @xmath47just as a single superposition vector is represented as a weighted vector sum of certain basis of eigen ( `` eigen '' should be translated as `` definite '' here ) vectors .
abner shimony ( @xcite and @xcite ) , in his description of a superposition state as being objectively indefinite , sometimes used heisenberg s @xcite language of `` potentiality '' and `` actuality '' to describe the relationship of the eigenvectors that are superposed to give an objectively indefinite superposition .
this terminology could be adapted to the case of the sets .
the singletons @xmath48 are `` potential '' in the objectively indefinite superposition@xmath28 , and , with further distinctions , the indefinite element @xmath28 might `` actualize '' to @xmath49 for one of the `` potential '' @xmath48 . starting with @xmath28 , the other @xmath50 ( i.e. , @xmath51 )
are not `` potentialities '' that could be `` actualized '' with further distinctions .
this terminology is , however , somewhat misleading since the indefinite element @xmath28 is perfectly actual(in the objectively indefinite interpretation ) ; it is only the multiple eigen - elements @xmath48 that are `` potential '' until `` actualized '' by some further distinctions .
a non - degenerate measurement is not a process of a potential entity becoming an actual entity , it is a process of an actual indefinite element becomes an actual definite element .
since a distinction - creating measurement goes from actual indefinite to actual definite , the potential - to - actual language of heisenberg should only be used with proper care if at all .
note that there are two conceptually distinct connotations for the mathematical subset @xmath42 . in the classical interpretation , it is a set of fully definite elements of @xmath52 . in the quantum interpretation of a subset @xmath28 , it is a single indefinite element that with further distinctions could become one of the singleton definite - elements or eigen - elements @xmath48 .
consider a three - element universe @xmath53 and a partition @xmath54 .
the block @xmath55 is objectively indefinite between @xmath56 and @xmath57 so those singletons are its `` potentialities '' in the sense that a distinction could result in either @xmath58 or @xmath57 being `` actualized . ''
however @xmath59 is not a `` potentiality '' when one is starting with the indefinite element @xmath60 .
note that this objective indefiniteness of @xmath60 is _ not _ well - described as saying that indefinite pre - distinction element is `` simultaneously both @xmath61 and @xmath62 '' ( like the common misdescription of the undetected particle `` going through both slits '' in the double - slit experiment ) ; instead it is indefinite between @xmath61 and @xmath62 .
that is , a superposition of two sharp eigen - alternatives should _ not _ be thought of like a double - exposure photograph which has two fully definite images ( e.g. , simultaneously a picture of say @xmath61 and @xmath62 ) . instead of a double - exposure photograph , the superposition should be thought of as representing a blurred or incomplete reality that with further distinctions could sharpen to either of the sharp realities .
but there must be some way to indicate which sharp realities could be obtained by making further distinctions ( measurements ) , and that is why the blurred or cloud - like indefinite reality is represented by mathematically superposing the sharp potentialities .
this point might be illustrated using some guy fawkes masks .
fig2-guymasks.eps figure 2 : objectively indefinite pure state _ represented _ as superposition of distinct eigen - alternatives instead of a double - exposure photograph , a superposition representation might be thought of as `` a photograph of clouds or patches of fog . ''
( schrdinger quoted in : @xcite ) schrdinger distinguishes a `` photograph of clouds '' from a blurry photograph presumably because the latter might imply that it was only the photograph that was blurry while the underlying objective reality was sharp .
the `` photograph of clouds '' imagery for a superposition connotes a clear and complete photograph of an objectively `` cloudy '' or indefinite reality .
regardless of the ( imperfect ) imagery , one needs some way to indicate what are the definite eigen - elements that could be `` actualized '' from a single indefinite element @xmath28 , and _ that _ is the role in the set case of conceptualizing a subset @xmath28 as a collecting together or `` superposing '' certain `` potential '' eigen - states , i.e. , the singletons @xmath48 . the two dual subset and partition logics are modeled by the two lattices ( or , with more operations , algebras ) of subsets and of partitions . the conceptual duality between the lattice of subsets ( the lattice part of the boolean algebra of subsets of @xmath2 ) and the lattice of partitions
could be described ( again following heisenberg ) using the rather meta - physical notions of _ _ substance__[multiblock footnote omitted ] and _ form _ ( as in in - form - ation)which might be compared to the terms `` matter '' or `` objects '' on one hand and `` structure '' on the other hand in some modern metaphysical discussions . for each lattice
where @xmath53 , start at the bottom and move towards the top .
fig3-twolattices.eps + figure 3 : conceptual duality between the subset and partition logics at the bottom of the boolean lattice is the empty set @xmath63 which represents no substance . as one moves up the lattice , new elements of substance always with fully definite properties are created until finally one reaches the top , the universe @xmath2 . thus new substance is created in moving up the lattice but each element is fully formed and distinguished in terms of its properties . at the bottom of the partition lattice is the indiscrete partition or `` blob '' @xmath64 ( where the universe set @xmath2 makes one block ) which represents all the substance but with no distinctions to in - form the substance . as one moves up the lattice , no new substance is created but distinctions objectively in - form the indistinct elements as they become more and more distinct , until one finally reaches the top , the discrete partition @xmath65 , where all the eigen - elements of @xmath2 have been fully distinguished from each other . it was previously noted that a partition combines indefiniteness ( within blocks ) and definiteness ( between blocks ) . at the top of the partition lattice ,
the discrete partition @xmath46 is the result making all the distinctions to eliminate the indefiniteness .
thus one ends up at the `` same '' place ( macro - universe of distinguished elements ) either way , but by two totally different but dual ways . and the discrete partition @xmath66 as the `` same '' we are neglecting the distinction between @xmath67 and @xmath68 for @xmath5 . ] the progress from bottom to top of the two lattices
could also be described as two creation stories . *
_ subset creation story _ : in the beginning was the void , and then elements are created , fully propertied and distinguished from one another , until finally reaching all the elements of the universe set @xmath2 . * _ partition creation story _ : in the beginning was the blob , which is an undifferentiated substance , and then there is a `` big bang '' where elements ( its ) are created by the substance being objectively in - formed ( objectified information ) by the making of distinctions ( e.g. , breaking symmetries ) until the result is finally the singletons which designate the elements of the universe @xmath2 .
these two creation stories might also be illustrated as follows .
fig4-twocreations.eps figure 4 : two creation stories one might think of the universe @xmath2 ( in the middle of the above picture ) as the macroscopic world of definite entities that we ordinarily experience .
common sense and classical physics assumes , as it were , the subset creation story on the left .
but _ a priori ,
_ it could just as well have been the dual story , the partition creation story pictured on the right , that leads to the _ same _ macro - picture @xmath2 .
since partitions are the mathematical expression of indefiniteness , our strategy is to first show where set partitions come from and then to `` lift '' or `` transport '' the partitional machinery to vector spaces using the notion of a basis set of a vector space .
the result is essentially the mathematical machinery of quantum mechanics all of which shows how quantum mechanics can be interpreted using the objective indefiniteness conception of reality that is associated at the logical level with partition logic .
take the universe set as some specific set of people , say , in a room .
people have numerical attributes like weight , height , or age as well as non - numerical attributes with other values such place of birth , family name , and country of citizenship .
abstractly an _
attribute on a universe set _ @xmath2 is a function @xmath69 from @xmath2 to some set of values @xmath70 ( usually the reals @xmath71 ) . in subset logic ,
an element @xmath5 either has a _ property _ represented by a subset @xmath42 or not ; in partition logic , an attribute @xmath72 assigns a value @xmath73 to each @xmath74 .
the two concepts of a property and an attribute overlap for binary attributes where the attribute might be represented by the characteristic function @xmath75 of a subset @xmath42 .
is given by a binary attribute @xmath75 _ plus _ the designation of an element @xmath76 so that @xmath77 as in lawvere s well - known subobject - classifier diagram @xcite . ] each attribute @xmath69 on a universe @xmath2 determines the _ inverse - image partition _ @xmath78 .
attributes are one way to define a partition on a set @xmath2 .
since this method of defining a partition starts with a numerical attribute @xmath73 already assigned to each @xmath5 , it may be called the _ top - down _ method . another more `` bottom - up '' way to define a partition on @xmath2 is to map the elements @xmath5 to `` similar '' ( i.e. , same block ) elements @xmath79 by some set of transformations @xmath80 .
this defines a binary relation : @xmath81 if there exists a @xmath82 such that @xmath83 in order to define a partition , the binary relation @xmath81 has to be an equivalence relation so the blocks of the partition are the equivalence classes .
the three requirements for an equivalence relation are reflexivity , symmetry , and transitivity .
* for the relation to be reflexive , i.e. , @xmath84 for all @xmath5 , it is sufficient for the set of transformations @xmath85 to contain the identity transformation @xmath86 .
* for the relation to be symmetric , i.e. , @xmath81 implies @xmath87 , it is sufficient for each @xmath82 to have an inverse @xmath88 where @xmath89 .
* for the relation to be transitive , i.e. , @xmath81 and @xmath90 imply @xmath91 , it is sufficient for each @xmath92 that @xmath93 is also in @xmath85 .
these three conditions , the existence of the identity , the existence of an inverse , and closure under composition , define a _ transformation group _ @xmath80 , i.e. , a _ group action _ on a set @xmath2 .
equivalently , a _ set representation _ of a group @xmath85 is given by a group homomorphism @xmath94 , where @xmath95 is the symmetric group of permutations @xmath96 of the set @xmath2 ( and where the transformation group @xmath97 is the image of the map ) .
an _ abstract group _ satisfies these three conditions where the composition is also required to be associative in the sense that for any @xmath98 , @xmath99 . for a transformation group , the composition is automatically associative .
this connection between groups and equivalence relations or partitions is well - known , e.g. , @xcite , and is probably as old as the notion of a group .
instead of elements @xmath100 being collected in the same block by have the same attribute value @xmath101 , the group transformations take any element @xmath67 to a `` similar '' or `` symmetric '' element @xmath102 .
a subset @xmath42 is _ invariant under
_ @xmath85 if for any @xmath82 , @xmath103 .
a minimal invariant subset is an _ orbit _ , and the partition defined by the transformation group @xmath85 is the _ set partition of orbits_. that is the _ bottom - up _ method of defining a set partition since we do nt begin with some attribute - value already assigned to the elements of @xmath2 . what is the significance of the blocks in the partition of minimal invariant subsets
often the treatment of symmetry groups focuses on what is invariant or conserved , e.g. , the perspective of noether s theorem @xcite .
there is _ another _ perspective with which to view the representations of symmetry groups . to represent an indefinite reality
, there is first some notion of the fully definite eigen - alternatives that are then collected together or superposed to represent something indefinite between those alternatives . _ what determines the set of definite eigen - alternatives
? given a set of symmetries on a set , in what different ways can there be distinct subsets that still satisfy the constraints of the symmetry operations ? the minimal invariant subsets or orbits of a set representation of a symmetry group provide the answer to that question about the variety of `` atomic '' eigen - forms consistent with the symmetries .
this question and the answer become more significant when we move beyond structure - less sets to linear vector spaces .
the minimal invariant subsets , the orbits , then become the minimal invariant subspaces , the irreducible subspaces , which are the carriers of the irreducible representations or irreps in vector space representations of groups . the notion of distinguishability ( in principle , making a distinction )
has long been recognized as fundamental in qm .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ if you could , in principle , distinguish the alternative final states ( even though you do not bother to do so ) , the total , final probability is obtained by calculating the probability for each state ( not the amplitude ) and then adding them together . if you can not distinguish the final states even in principle , then the probability amplitudes must be summed before taking the absolute square to find the actual probability . @xcite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ in the foregoing , we have frequently referred to the making of _ distinctions _ as the set version of a measurement .
on @xmath2 is an ordered pair @xmath104 of elements of @xmath2 in different blocks of the partition .
the set of distinctions , @xmath105 , of a partition @xmath106 is called a _ partition relation _ ( or _ apartness relation _ in computer science ) and is just the complement of the associated equivalence relation .
the notion of a distinction of a partition is the partition logic analogue of an element of a subset in subset logic .
for instance , given two partitions @xmath107 and @xmath108 on a universe set and two subsets @xmath28 and @xmath109 of a universe set , the partition join @xmath110 combines the _ distinctions _ of the partitions , i.e. , @xmath111 , just as the subset join or union @xmath112 combines the _ elements _ of the subsets ( see @xcite or @xcite for further developments ) . ]
what is the mathematical operation for making the distinctions ( as in a measurement ) ?
it is the _
join operation _ from partition logic .
but before two set partitions can be joined to form a more refined partition with more distinctions , they must be _ compatible _ in the sense of being defined on the same universe set .
if two set partitions @xmath113 and @xmath108 are compatible , i.e. , are partitions of the same universe @xmath2 , then their _ join _ @xmath110 is the set partition whose blocks are the non - empty intersections @xmath114 .
since two set attributes @xmath115 and @xmath116 define two inverse image partitions @xmath117 and @xmath118 on their domains , we need to extend the concept of compatible partitions to the attributes that define the partitions .
that is , two attributes @xmath115 and @xmath116 are _ compatible _ if they have the same domain @xmath119 .
given two compatible set attributes @xmath115 and @xmath120 , the join of their eigenspace partitions has as blocks the non - empty intersections @xmath121 .
each block in the join of the eigenspace partitions could be characterized by the ordered pair of eigenvalues@xmath122 .
an eigenvector of both @xmath72 , @xmath123 , and of @xmath124 , @xmath125 , would be a simultaneous eigenvector : @xmath126 .
a set of compatible set attributes is said to be _ complete _ if the join of their partitions is discrete , i.e. , the blocks have cardinality @xmath127 .
complete set of compatible attributes _ or csca characterizes the singletons @xmath128 by the ordered @xmath31-tuple @xmath129 of attribute values .
all this machinery of set partitions can be lifted or transported to vector spaces to give the mathematical machinery of qm .
there is a natural part - of - the - folklore bridge or ladder connecting set concepts to vector - space concepts .
the basic idea is that a vector @xmath130 , represented in terms of a set @xmath131 of basis vectors , is a @xmath132__-valued set _
_ where each element @xmath133 in the basis set takes a value @xmath134 in the base field @xmath132 . given a set concept , the _ basis principle
_ is that one can generate the corresponding vector - space concept by applying the set concept to a basis set and seeing what it generates . starting with the set concept of cardinality ,
one arrives at the corresponding vector - space concept by applying the set concept to a basis set to arrive at the cardinality of the basis set . after checking that all bases have the same cardinality , this yields the vector - space notion of _
dimension_. thus the cardinality of a set lifts not to the cardinality of a vector space but to its dimension .
some of the lifting is accomplished by the free vector space functor from the category of sets to the category of vector spaces over a given field @xmath132 .
a set @xmath2 is carried by this functor to the vector space @xmath135 spanned by the kronecker delta basis @xmath136 where @xmath137 for @xmath138 and @xmath139 . a set @xmath2 of a certain cardinality thus generates a vector space @xmath135 of the same dimension .
a partition @xmath107 on a set @xmath2 is a set of subsets whose direct sum ( i.e. , disjoint union ) is the whole set , i.e. , a direct sum decomposition of the set .
the corresponding vector space concept is a set of subspaces of a vector space whose direct sum is the vector space , i.e. , a _
direct sum decomposition _ of the vector space . in terms of the basis principle , we could apply the set partition @xmath107 of a set @xmath2 to a basis set @xmath140 , then each block @xmath45 generates a subspace @xmath141 and the set of subspaces @xmath142 is a direct sum decomposition of the vector space spanned by the basis set .
thus the lift or transport of the concept of a set partition is a direct sum decomposition of a vector space . in particular , it is _ not _ a set partition of a vector space that is compatible with the vector space operations , i.e. , a quotient space @xmath143 as would be defined by each subspace @xmath144 with the equivalence relation @xmath145 if @xmath146 .
while a partition on a set is essentially the same as a quotient set ( or equivalence relation on the set ) , the vector - space lift of a set partition is not a quotient vector space but a direct sum decomposition of a vector space . in lifting or transporting the partitional concepts for sets to vector spaces
, we are making the choices guided by the set - to - basis - set connection which yields the mathematical machinery of quantum mechanics .
this is not particularly new ; it is part of the mathematical folklore .
hermann weyl outlined the lifting program by first considering an attribute on a set , which defined the set partition or `` grating '' @xcite of elements with the same attribute - value .
then he moved to the quantum case where the set or `` aggregate of @xmath31 states has to be replaced by an @xmath31-dimensional euclidean vector space '' @xcite .
becomes dimension @xmath31 .
] the appropriate notion of a partition or `` grating '' is a `` splitting of the total vector space into mutually orthogonal subspaces '' so that `` each vector @xmath147 splits into @xmath148 component vectors lying in the several subspaces '' weyl : phil , i.e. , a direct sum decomposition of the space , where the subspaces are the eigenspaces of an observable operator .
weyl s grating metaphor also lends itself to ( our own example of ) seeing measurement of the , say , regular polygonal shape of an indefinite blob of dough as it randomly falls through a opening in a grating to take on that polygonal shape ( with the attribute - value or eigenvalue being the number of regular sides @xmath149 ) . fig5-grating.eps figure 5 : imagery of measurement as randomly giving an indefinite blob of dough a definite eigen - shape .
note how the blob of dough is objectively indefinite between the regular polygonal shapes and does not simultaneously have all those shapes even though it might be mathematically represented as the set @xmath150 or the superposition vector @xmath151 in a certain space .
a set attribute is a function @xmath115 ( where the set of values is taken as the reals ) .
the inverse - image @xmath152 of each value @xmath153 is a subset where the attribute has the same value , and those subsets form a set partition .
given a basis set @xmath140 of a vector space @xmath154 over a field @xmath132 , we can apply a set attribute @xmath155 to the basis set and see what it generates .
one possibility is to linearly extend the function @xmath156 to the whole space to obtain a linear functional @xmath157 . but a linear functional defines a quotient space @xmath158 , not a vector space partition .
the same information @xmath159 _ also _ defines @xmath160 which linearly extends to a _ linear operator _ @xmath161 . the given basis vectors @xmath162 are eigenvectors of the operator @xmath163 with the eigenvalues @xmath164 , and the eigenspaces are the subspaces where the operator has the same eigenvalue .
the eigenvectors span the whole space so we see that the lift or transport of a set attribute , which defines a set partition , is a vector space linear operator whose eigenspaces are a vector space partition ( i.e. , direct sum decomposition ) of the whole space , i.e. , a _ diagonalizable linear operator_. that is a total function , so a non - diagonalizable linear operator is the lift of a partial function @xmath72 . ]
given a diagonalizable linear operator @xmath165 , where @xmath154 is a finite - dimensional vector space over a field @xmath132 and where @xmath166 are the distinct eigenvalues , then there are projection operators @xmath167 for @xmath36 such that : 1 . @xmath168 ; 2 .
@xmath169 ; 3 .
@xmath170 for @xmath171 ; and 4 .
the range of @xmath167 is the eigenspace @xmath172 for the eigenvalue @xmath173 for @xmath36 .
* theorem 8 , p. 172 ) what is the vector space partition _ canonically _ defined by a diagonalizable linear operator ?
any basis of eigenvectors could be seen as defining a direct sum of the one - dimensional subspaces spanned by those eigenvectors . but those subspaces are far from unique .
but if we group together all the eigenvectors with the same eigenvalue ( i.e. , use the top - down method to define a vector - space partition ) , then they span the eigenspaces .
it is the set of eigenspaces @xmath174 that gives the unique canonical direct - sum decomposition or vector - space partition defined by a ( diagonalizable ) linear operator .
this standard linear algebra result holds for any base field , but for qm , the base field is the complex numbers @xmath0 . in order for the eigenvalues to always be real ,
the diagonalizable linear operators are required to be _ hermitian _ ( or _ self - adjoint _ ,
i.e. , equal to their conjugate transposes ) .
a _ vector - space representation _ of an abstract group @xmath85 is a group homomorphism @xmath175 where @xmath176 is the group of invertible linear transformations @xmath177 of a vector space @xmath154 over the complex numbers . here again , the idea is to define a ( vector - space ) partition by a ( linear ) group of transformations @xmath178 that map elements @xmath179 to similar or symmetric elements @xmath180 .
a subspace @xmath144 is _ invariant _ if @xmath181 for all @xmath182 . and
again , it is the minimal invariant subspaces , the _ irreducible subspaces _ , that are of interest .
the irreducible subspaces @xmath183 are the carriers for the _ irreducible representations _
@xmath184 or _ irreps_. and
the representation space @xmath154 is a direct sum of some set of irreducible subspaces @xmath185 so the vector - space representation of a group defines a vector - space partition of the space . but these vector - space partitions are not unique and are thus not canonically defined by the representation . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ finding such a decomposition [ of irreps ] is an exact analogue of finding a basis of eigenvectors of a single operator . in neither case
is the decomposition unique .
however , in the operator case the eigenvalues and the multiplicities of occurrence are uniquely determined .
moreover the linear span of these basis vectors with a common eigenvalue is just the total eigenspace for that eigenvalue and is uniquely determined .
the decomposition as a direct sum of eigenspaces is unique .
@xcite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ hence the problem in this bottom - up approach is `` finding an analogue for equality of eigenvalues '' @xcite to group the irreps together .
suppose @xmath109 is a representation of @xmath85 acting on a space @xmath154 and @xmath186 is a representation of the same @xmath85 acting on a space @xmath187 .
then a linear map @xmath188 is said _ morphism of representations _ or _ intertwining map _ if for all @xmath182 and all @xmath179 : @xmath189 , i.e. , @xmath190{rcl}v & \overset{t_{g}}{\longrightarrow } & v\\ \phi\downarrow & & \downarrow\phi\\ v^{\prime } & \overset{t_{g}^{\prime}}{\longrightarrow } & v^{\prime}\end{array } $ ] commutes .
if @xmath191 is also invertible , then @xmath191 is said to be an _
isomorphism _ of representations , and the representations are said to be _ isomorphic _ or _
equivalent_. the remarkable fact is that each group has a fixed set of inequivalent irreps , so the distinct irreps are a characteristic of the group itself , not of a particular representation .
the uniqueness and canonical nature of the partition obtained in the operator case by equality of eigenvalues is now obtained using equivalence of irreps and their underlying irreducible subspaces .
all the irreducible subspaces @xmath192 for irreps equivalent to an irrep @xmath193 in any such direct sum @xmath185 are grouped together ( by direct sum ) to obtain the invariant carrier @xmath194 for a primary representation where a representation is _ primary _ if all its irreducible subrepresentations are equivalent and the underlying carrier space is also called _ primary_. note that some of the inequivalent irreps of the group @xmath85 may not be involved in a particular representation .
the decomposition of @xmath154 as the direct sum @xmath195 of the invariant primary subspaces for the primary representations is unique .
`` it is the invariant subspaces [ @xmath194 ] which are the analogues of the eigenspaces of a single operator . ''
@xcite in terms of representations rather than their carrier subspaces , it is the unique `` _ _ canonical decomposition into primary representations__. '' @xcite thus we have the top - down construction of the vector space partition @xmath197 of eigenspaces @xmath172 given by an operator ( or vector - space attribute ) and the bottom - up construction of the vector - space partition @xmath198 of the carriers @xmath194 for primary representations given by a vector - space representation of a symmetry group .
the following table brings out the analogies between the top - down and bottom - up determination of vector - space partitions .
fig6-top-bottom.eps + figure 6 : analogies between top - down and bottom - up determination of partitions to represent indefiniteness , we first need to specify the `` universe '' of fully definite eigen - alternatives , and then indefiniteness can be described by collecting together or superposing the `` potential '' eigen - alternatives . in the vector - space case , the eigen - alternatives determined by an operator are the eigenvectors and the eigen - alternatives determined by a representation of a symmetry group are the minimal invariant subspaces that are the carriers for the irreducible representations of the symmetry group . for state - dependent ( or extrinsic ) attributes of a quantum particle like the linear momentum or angular momentum ,
the fully definite eigenstates are determined by the irreducible representations of the linear - translation or rotational - translation symmetry groups respectively . for the state - independent ( or intrinsic ) attributes of quantum particles , like the mass , charge , and spin of an electron
, they are determined in particle physics by the irreducible representations of the appropriate symmetry groups .
the set notion of compatibility lifts to vector spaces , via the basis principle , by defining two vector space partitions @xmath199 and @xmath200 on @xmath154 as being _
compatible _ if there is a basis set for @xmath154 so that the two vector space partitions are generated by two set partitions of that common or simultaneous basis set .
if two vector space partitions @xmath201 and @xmath200 are compatible , then their _ vector space join _
@xmath202 is defined as the vector space partition whose subspaces are the non - zero intersections @xmath203 . and by the definition of compatibility , we could also generate the subspaces of the join @xmath204 by the blocks in the set join of the two set partitions of the common basis set .
since real - valued set attributes lift to hermitian linear operators , the notion of compatible set attributes just defined would lift to two linear operators being _ compatible _ if their eigenspace partitions are compatible .
it is a standard fact of linear algebra @xcite that two diagonalizable linear operators @xmath205 ( on a finite dimensional space @xmath154 ) are compatible ( i.e. , have a basis of simultaneous eigenvectors ) if and only if they commute , @xmath206 . hence the _ commutativity _ of linear operators is the lift of the compatibility ( i.e. , defined on the same set ) of set attributes .
that explains the importance of the notion of commutativity in qm and that is why the repeated compatible measurements , described mathematically as the join operation , requires commutativity .
the join of two operator - eigenspace partitions is defined iff the operators commute . as weyl put it : `` thus combination [ de : join ] of two gratings [ eigenspace partitions of two operators ]
presupposes commutability ... '' .
@xcite two commuting hermitian linear operators @xmath193 and @xmath207 have compatible eigenspace partitions @xmath208 ( for the eigenvalues @xmath209 of @xmath193 ) and @xmath210 ( for the eigenvalues @xmath211 of @xmath207 ) .
the blocks in the join @xmath212 of the two compatible eigenspace partitions are the non - zero subspaces @xmath213 which can be characterized by the ordered pairs of eigenvalues @xmath214 .
the nonzero vectors @xmath215 are _ simultaneous eigenvectors _ for the two commuting operators , and there is a basis for the space consisting of simultaneous eigenvectors . due to the problem of degeneracy . ]
a set of commuting linear operators is said to be _ complete _ if the join of their eigenspace partitions is nondegenerate , i.e. , the blocks have dimension @xmath127 .
the join operation gives the results of compatible measurements so the join of a complete set of compatible vector space attributes ( i.e. , commuting hermitian operators ) gives the possible results of a non - degenerate measurement .
the eigenvectors that generate those one - dimensional blocks of the join are characterized by the ordered @xmath31-tuples @xmath216 of eigenvalues so the eigenvectors are usually denoted as the eigenkets @xmath217 in the dirac notation .
these _ complete sets of commuting operators _ are dirac s cscos @xcite ( which are the vector space version of our previous cscas ) .
since the eigen - alternatives determined by an operator , i.e. , eigenvectors , can be obtained by the complete partition joins defined by a csco , one might ask if the eigen - alternatives determined by a group representation , i.e. , the irreps and their irreducible carrier spaces , could also be obtained by the partition joins defined by some csco . jin - quan chen and his colleagues in the nanjing school
have developed a little - known csco method to systematically find the irreducible basis vectors for the irreducible spaces that works not only for all representations of finite groups but for all compact lie groups as needed in qm ( @xcite , @xcite ) . ``
[ t]he foundation of the new approach is precisely the theory of the complete set of commuting operators ( csco ) initiated by dirac ... '' @xcite thus the linearized partition joins of the csco method extends also to all compact group representations to characterize the maximally definite eigen - alternatives .
the partitional mathematics for sets and vector spaces is summarized in the following table .
fig7-liftingtable.eps + figure 7 : summary of partition concepts for sets and vector spaces
in the tradition of toy models for quantum mechanics , schumacher and westmoreland @xcite have recently investigated models of quantum mechanics over finite fields . one finite field stands out over the rest , @xmath1 , since vectors in a vector space over @xmath1 have a natural interpretation , namely as _ sets _ that are subsets of a universe set .
but in any vector space over a finite field , there is no inner product so the first problem in constructing a model of qm in this context is the definition of dirac s brackets .
which aspects of the usual treatment of the brackets should be retained and which aspects should be dropped ?
schumacher and westmoreland chose to have their brackets continue to have values in the base field , e.g. , @xmath218 , so their `` theory does not make use of the idea of probability''@xcite which certainly constrains the relation to qm .
instead , the values of @xmath219 and @xmath127 are respectively interpreted modally as _ _ impossible _ _ and _ possible _ and hence their name of `` modal quantum theory . ''
a number of results from full qm carry over to their modal quantum theory , e.g. , no - cloning , superdense coding , and teleportation , but without a probability calculus , the connection to full qm is rather limited . and important results such as bell s theorem do not carry over ; `` in the absence of probabilities and expectation values the bell approach will not work . ''
@xcite but all these limitations can be overcome by the different treatment of the brackets based on crossing the sets - to - vector - space bridge in the other direction ( essentially using the basis principle in reverse ) . that yields a full probability calculus for a model of _ quantum mechanics over sets _ ( qm / sets ) using the @xmath1 base field .
qm / sets yields a probability calculus and it is a familiar calculus , logical probability theory for a finite universe set of outcomes developed by laplace , boole , and others . the only difference from that classical calculus is the vector space formulation which allows different ( equicardinal ) bases or universe sets of outcomes and thus it is the non - commutative version of classical logical finite probability theory .
this allows the development of the qm / sets version of qm results such as bell s theorem , the indeterminacy principle , double - slit experiments , and much else in the clear and distinct context of finite sets . , the category of finite - dimensional vector spaces of a field @xmath132 and linear maps .
it is thus tempting to expect that qm / sets will be the special case of @xmath220 .
but this is not the case for a variety of reasons ; the brackets in qm / sets take values not in @xmath1 but in the non - negative integers , and the attributes take their `` eigenvalues '' in the reals , e.g. , real - valued random variables .
that is how qm / sets turns out to be the non - commutative version of laplace - boole logical finite probability theory .
that is very different from a formal model of qm where the scalars ( e.g. , values of brackets and eigenvalues ) are in @xmath1such as schumacher and westmoreland s modal qt over @xmath1 @xcite . ] by developing a sets - version of qm , the concepts and relationships of full qm are represented in a pared - down ultra - simple version that can be seen as representing the essential `` logic '' of qm .
it represents the `` logic of qm '' in that old sense of `` logic '' as giving the basic essentials of a theory , not in the sense of giving the behavior of propositions in a theory which is the usual `` quantum logic '' @xcite that was , in effect , based on the usual misdescription of boolean subset logic as the special case of `` propositional '' logic .
qm / sets is said to be `` over @xmath1 '' or `` over sets '' since the power set @xmath221 ( for a finite non - empty universe set @xmath2 ) is a vector space over @xmath218 where the subset addition @xmath222 is the _ symmetric difference _ ( or inequivalence ) of subsets , i.e. , @xmath223 for @xmath224 . given a finite universe set @xmath225 of cardinality @xmath31 ,
the @xmath2-basis in @xmath226 is the set of singletons @xmath227 and a vector in @xmath226 is specified in the @xmath2-basis by its @xmath1-valued characteristic function @xmath228 for an subset @xmath42 ( e.g. , a string of @xmath31 binary numbers ) .
similarly , a vector @xmath229 in @xmath230 is specified in terms of an orthonormal basis @xmath231 by a @xmath0-valued function @xmath232 assigning a complex amplitude @xmath233 to each basis vector .
one of the key pieces of mathematical machinery in qm , namely the inner product , does not exist in vector spaces over finite fields but brackets can still be defined using latexmath:[$\left\langle \left\ { u_{i}\right\ } norm can be defined to play a similar role in the probability algorithm of qm / sets .
seeing @xmath226 as the abstract vector space @xmath235 allows different bases in which the vectors can be expressed ( as well as the basis - free notion of a vector as a ket ) .
consider the simple case of @xmath53 where the @xmath2-basis is @xmath59 , @xmath58 , and @xmath57 .
but the three subsets @xmath236 , @xmath60 , and @xmath237 also form a basis since : @xmath238 ; @xmath239 ; and @xmath240 .
these new basis vectors could be considered as the basis - singletons in another equicardinal universe @xmath241 where @xmath242 , @xmath243 , and @xmath244 . in the following _ ket table
, each row is a ket of @xmath245 expressed in the @xmath2-basis , the @xmath246-basis , and a @xmath247-basis .
[ c]|c|c|c|@xmath53 & @xmath248 & @xmath249 + @xmath250 & @xmath251 & @xmath252 + @xmath236 & @xmath253 & @xmath254 + @xmath60 & @xmath255 & @xmath256 + @xmath257 & @xmath258 & @xmath259 + @xmath59 & @xmath260 & @xmath261 + @xmath58 & @xmath262 & @xmath263 + @xmath57 & @xmath264 & @xmath265 + @xmath63 & @xmath63 & @xmath63 + vector space isomorphism : @xmath266 where row = ket . in a hilbert space ,
the inner product is used to define the amplitudes @xmath233 and the norm @xmath267 where the probability algorithm can be formulated using this norm . in a vector space over @xmath1
, the dirac notation can still be used to define a norm even though there is no inner product . for a singleton basis element @xmath268 , the _ bra _
@xmath269 is defined by the _ bracket _ :
@xmath270{c}1\text { if } u\in s\\ 0\text { if } u\notin s \end{array } \right .
= \chi_{s}\left ( u\right ) $ ] then @xmath271 is the set - version of @xmath272 ( for an orthonormal basis @xmath273 ) . assuming a finite @xmath2
, the bracket linearly extends to the more general form ( where @xmath274 is the cardinality of @xmath28 ) : @xmath275 for @xmath276 . takes values outside the base field of @xmath1 just like the hamming distance function @xmath277 on vector spaces over @xmath1 in coding theory .
@xcite ] the basis principle can be run in reverse to transport a vector space concept to sets .
consider an orthonormal basis set @xmath273 in a finite dimensional hilbert space .
given two subsets @xmath278 of the basis set , consider the unnormalized superpositions @xmath279 and @xmath280 .
then their inner product in the hilbert space is @xmath281 , which transports ( crossing the bridge in the other direction ) to @xmath275 for subsets @xmath276 of the @xmath2-basis of @xmath282 . in both cases ,
the bracket gives the size of the overlap or indistinctness of the two vectors or sets . the _ ket - bra _
@xmath283 is the one - dimensional projection operator : @xmath284 and the _ ket - bra identity _ holds as usual : @xmath285 where the summation is the symmetric difference of sets in @xmath226 .
the overlap @xmath286 can be resolved using the ket - bra identity in the same basis : @xmath287 .
similarly a ket @xmath288 for @xmath42 can be resolved in the @xmath2-basis ; @xmath289 where a subset @xmath42 is just expressed as the sum of the singletons @xmath48 .
that is ket - bra resolution in sets .
the ket @xmath288 is the same as the ket @xmath290 for some subset @xmath291 in another @xmath246-basis , but when the bra @xmath292 is applied to the ket @xmath293 , then it is the subset @xmath42 , not @xmath291 , that comes outside the ket symbol @xmath294 in @xmath295 . ''
is not even defined since it is the intersection of subsets of two different universes . ]
the @xmath2__-norm _ _ @xmath296 is defined , as usual , as the square root of the bracket : for the @xmath2-norm of a set to distinguish it from the single - line notation @xmath274 for the cardinality of a set , whereas the customary absolute value notation for the norm of a vector in full qm is @xmath297 . ] @xmath298 for @xmath299 which is the set - version of the norm @xmath300 . note that a ket has to be expressed in the @xmath2-basis to apply the norm definition so in the above example , @xmath301 since @xmath302 in the @xmath2-basis .
for a specific basis @xmath273 and for any nonzero vector @xmath229 in a finite dimensional complex vector space , @xmath303 ( @xmath304 is complex conjugation ) whose set version would be : @xmath305 .
since @xmath306 and @xmath307 , applying the born rule by squaring the coefficients @xmath308 and @xmath309 ( and normalizing ) gives the probability sums for the eigen - elements @xmath310 or @xmath49 given a state @xmath229 or @xmath28 respectively in qm and qm / sets : @xmath311 and @xmath312 where @xmath313 is a ` mysterious ' quantum probability while @xmath314 is the unmysterious laplacian equal probability latexmath:[$\pr\left ( \left\ { u\right\ } @xmath28 .
( another consequence of the lack of an inner product ) .
the normalization is , as it were , postponed to the probability algorithm which is computed in the rationals . ]
an observable , i.e. , a hermitian operator , on a hilbert space has a home basis set of orthonormal eigenvectors . in a similar manner ,
a real - valued attribute @xmath115 defined on @xmath2 has the @xmath2-basis as its `` home basis set . ''
the connection between the numerical attributes @xmath115 of qm / sets and the hermitian operators of full qm can be established by `` seeing '' the function @xmath72 as a formal operator : @xmath316 . applied to the basis elements @xmath128 , we may write @xmath317 as the set - version of an eigenvalue equation applied to an eigenvector , where the multiplication @xmath318 is only formal ( read @xmath319 as the instruction : ` give ` @xmath72 ` the value ` @xmath148 ` on ` @xmath49 ) . then for any subset @xmath320 where @xmath72 is constant , we may also formally write : @xmath321 as an eigenvalue equation satisfied by all the eigen - sets or eigenvectors @xmath28 in the eigenspace @xmath322 , a subspace of @xmath226 , for the eigenvalue @xmath148 .
the eigenspaces@xmath323 give a direct sum decomposition ( i.e. , a vector - space partition ) of the whole space @xmath324 , just as the set partition @xmath325 gives a direct sum decomposition of the set @xmath326 .
since @xmath327 is the projection operator is now interpreted as a vector space , it should be noted that the projection operator @xmath328 is not only idempotent but linear , i.e. , @xmath329 .
indeed , this is the distributive law when @xmath330 is interpreted as a boolean ring . ] to the eigenspace@xmath331 for the eigenvalue @xmath148 , we have the spectral decomposition of a @xmath2-attribute @xmath115 in qm / sets analogous to the spectral decomposition of a hermitian operator @xmath332 in qm : @xmath333 : \wp\left ( u\right ) \rightarrow\wp\left ( u\right ) $ ] @xmath334 spectral decomposition of operators in qm / sets and in qm .
qm / sets is a pedagogical model where the internal workings of qm math are laid out in a simplified and `` externalized '' form .
think of a simplified laboratory model of a complex machine where the parts are visible and easily laid out to clarify the workings of the actual machine . to recover qm math from qm / sets ,
the base field is lifted from the sets - case of @xmath1 to qm - case of @xmath0 , and the externalized forms become _ internalized _ ( or `` encoded '' ) within the vector space .
the formal multiplication @xmath335 $ ] is internalized as an actual multiplication of a scalar times an operator @xmath336 on a vector space over @xmath0 .
the operator representation @xmath332 of an observable is just the lifted internalization or encoding of a numerical attribute @xmath337 $ ] made possible by the enriched base field @xmath0 .
the set brackets @xmath338 taking values outside the base field @xmath1 become internalized as an inner product with the same enrichment of the base field to @xmath0 , and similarly for the @xmath2-norm that is the square root of the brackets . with the brackets taking values in the base field @xmath1 @xcite
can thus be seen as an example of premature internalization . ]
it is the comparative poverty of the base field @xmath1 that requires the qm / sets brackets and norm to take the externalized values outside the base field and for a formal multiplication to be used in the `` operator '' representation @xmath339 $ ] of a numerical attribute @xmath115 .
the only numerical attributes that can be internally represented in @xmath221 are the @xmath340-attributes or characteristic functions @xmath228 that are internally represented in the @xmath2-basis as the projection operators @xmath341 . in the engineering literature ,
eigenvalues are seen as `` stretching or shrinking factors '' but that is _ not _ their role in qm .
the whole machinery of eigenvectors [ e.g. , the eigen - sets @xmath321 for @xmath123 in sets ] , eigenspaces [ e.g. , the space of all eigen - sets @xmath323 ] , and eigenvalues [ e.g. , @xmath153 ] in full qm is a way of lifting and internalizing or encoding numerical attributes [ e.g. , @xmath115 in the set case ] _ inside _ a vector space that has a rich enough base field . the old question `` why do attributes in classical physics ( like the position or momentum of a particle ) become operators in qm ? ''
is addressed by _
internalization_. the observable operators of qm _ are _ the lifted vector space internalizations or encodings over @xmath0 of the concept of real - valued attributes ( or random variables ) on sets
. moreover , for the internalization of attributes as operators to always be possible , the secular equations for eigenvalues have to have a complete set of solutions so the base field has to be algebraically closed which addresses another old question of why full qm has the complex numbers @xmath0 as its base field
. the usual completeness and orthogonality conditions on eigenspaces also have set - versions in qm over @xmath1 : 1 .
completeness : @xmath344 has the set - version : @xmath345 , and 2 .
orthogonality : for @xmath346 , @xmath347 ( where @xmath219 is the zero operator ) has the set - version : for @xmath348 ,
@xmath349 \left [ f^{-1}\left ( r^{\prime}\right ) \cap()\right ] = \emptyset\cap():\wp\left ( u\right ) \rightarrow\wp\left ( u\right ) $ ] .
note that in spite of the lack of an inner product , the orthogonality of projection operators @xmath350 is perfectly well defined in qm / sets where it boils down to the disjointness of subsets , i.e. , the cardinality of their overlap ( instead of their inner product ) being @xmath219 .
an orthogonal decomposition of a finite set @xmath2 is just a partition @xmath107 of @xmath2 since the blocks @xmath351 are orthogonal ( i.e. , disjoint ) and their sum is @xmath2 .
given such an orthogonal decomposition of @xmath2 , we have the : @xmath352 pythagorean theorem for orthogonal decompositions of sets .
another old question is : `` why the squaring of amplitudes in qm ? ''
a state objectively indefinite between certain definite orthogonal alternatives @xmath44 and @xmath45 , where the latter are represented by vectors @xmath353 and @xmath354 , is represented by the vector sum @xmath355 . but what is the `` strength , '' `` intensity , '' or relative importance of the vectors @xmath353 and @xmath354 in the vector sum @xmath356 ? that question requires a _ scalar _ measure of strength or intensity .
the magnitude given by the norm does not answer the question since @xmath357 .
but the pythagorean theorem shows that the norm - squared gives the scalar measure of `` intensity '' that answers the question : @xmath358 in vector spaces over @xmath1 or over @xmath0 . and
when the objectively indefinite superposition state is decohered by a distinction - making measurement , then the _ objective probability _ that the indefinite state will reduce to one of the definite alternatives is given by that objective relative scalar measure of the eigen - alternative s `` strength , '' `` intensity , '' or importance in the indefinite state and that is the born rule . in a slogan ,
born is the son of pythagoras . the pythagorean results ( for the complete and orthogonal projection operators ) : @xmath359 and @xmath360 , give the probabilities for measuring attributes . since by the pythagorean theorem : @xmath361 , we have in full qm and in qm / sets : @xmath362 and @xmath363 .
here @xmath364 is the mysterious quantum probability of getting @xmath209 in an @xmath193-measurement of @xmath229 while @xmath365 has the rather unmysterious interpretation in the pedagogical model , qm / sets , as the probability @xmath366 of the random variable @xmath115 having the eigen - value @xmath148 when sampling @xmath42 .
thus the set - version of the born rule is not some weird quantum notion of probability on sets but the perfectly ordinary laplace - boole rule for the conditional probability @xmath367 , given @xmath42 , of a random variable @xmath115 having the value @xmath148 .
the collecting - together of some eigen - elements @xmath368 into a subset @xmath42 to form an `` indefinite element '' @xmath28 has the vector sum @xmath369 in the vector space @xmath226 over @xmath1 giving the superposition version of the indefinite element .
this cements the interpretation of collecting together in sets as superposition in vector spaces .
the indefinite element @xmath28 is being measured using the observable @xmath72 where the probability @xmath366 of getting the eigenvalue @xmath148 is @xmath370 and where the `` damned quantum jump '' ( schrdinger ) goes from @xmath28 by the projection operator @xmath371 to the projected resultant state @xmath372 which is in the eigenspace @xmath331 for that eigenvalue @xmath148 .
the partition operation in qm / sets that describes measurement is the partition join of the partition @xmath373 and @xmath374 so that the initial pure state @xmath28 ( as a mini - blob ) is refined into the mixture @xmath375 of possible resultant states .
the other states @xmath376 in the join @xmath377 are not possible or `` potential '' states starting from @xmath28 .
the state resulting from the measurement represents a more - definite element @xmath372 that now has the definite @xmath72-value of @xmath148so a second measurement would yield the same eigenvalue @xmath148 with probability @xmath378 \right\vert } { \left\vert f^{-1}\left ( r\right ) \cap s\right\vert } = \frac{\left\vert f^{-1}\left ( r\right ) \cap s\right\vert } { \left\vert f^{-1}\left ( r\right ) \cap s\right\vert } = 1 $ ] and the same vector @xmath379 = f^{-1}\left ( r\right ) \cap s$ ] using the idempotency of the set - version of projection operators .
this is _ all _ just the qm over sets version of the treatment of measurement in standard dirac - von - neumann qm where the probability calculus of logical probability theory is lifted and internalized by the born rule and where the real attributes or real random variables @xmath115 are internalized as observable ( hermitian ) operators .
these set - versions are summarized in the following table for a finite @xmath2 and a finite dimensional hilbert space @xmath154 with @xmath231 as any orthonormal basis .
[ c]|c|c|vector space over @xmath1 : qm / sets & hilbert space case : qm over @xmath0 + projections : @xmath341 & @xmath380 + spectral decomp . :
@xmath381 & @xmath332 + compl .
: @xmath345 & @xmath382 + orthog .
: @xmath348 , @xmath383 \left [ f^{-1}\left ( r^{\prime}\right ) \cap()\right ] = \emptyset\cap()$ ] & @xmath346 , @xmath384 + brackets : @xmath385 = overlap of @xmath224 & @xmath386 overlap of @xmath387 and @xmath388 + ket - bra : @xmath389 & @xmath390 + resolution : @xmath391 + norm : @xmath392 where @xmath42 & @xmath393 + pythagoras : @xmath394 & @xmath395 + laplace : @xmath396 , @xmath397 & @xmath398 , @xmath399 + born : @xmath369 , @xmath400 & @xmath401 , @xmath402 + @xmath403 & @xmath404 + @xmath396 , @xmath405 & @xmath406 , @xmath407 + measurement : @xmath408 & @xmath409 + probability mathematics for qm over @xmath1 and for qm over @xmath0 since the probability calculus on the left - side of the table is a non - commutative version of the old laplace - boole _
logical _ finite probability theory @xcite , the correspondence with the right - side of the table gives precision to the thesis that the mathematics of qm is a type of _ logical probability calculus complexified in hilbert spaces_. for instance , the equiprobability or indifference principle of that classical logical finite probability calculus that is , the equality of all non - zero coefficients in a vector over @xmath1generalizes to the qm probability calculus using the coefficients of vectors over @xmath0 , and the born rule applies to orthogonal decompositions in both cases . crossing the sets - vector - space bridge the other way , we have seen that the classical logical probability calculus ( in its non - commutative version ) is a type of quantum mechanics over sets .
when some particularly mysterious process like measurement can be clearly and distinctly modeled in qm / sets , then it casts some sense - making light back on full qm .
a good example is von neumann s distinction between type 1 measurement - like processes and type 2 processes of unitary evolution @xcite . in qm / sets ,
we have seen that measurement is a distinction - making process described by the partition join operation . in terms of the lattice of set partitions , such a `` type 1 '' process moves up in the lattice to more refined partitions .
is _ more ( or equally ) refined _ than @xmath108 , denoted @xmath410 , if for each @xmath411 , there is a @xmath412 such that @xmath413 , _ is _ just the inclusion relation on distinctions , i.e. , @xmath414 iff @xmath415 , so moving up in the ordering means making more distinctions . ]
this means in qm / sets that a `` type 2 '' evolution would be a distinction - preserving process that , as it were , moves horizontally in the lattice of partitions .
fig8-type1-2processes.eps figure 8 : `` type 1 '' distinction - making and `` type 2 '' distinction - preserving processes in qm / sets a linear transformation @xmath416 that keeps distinct vectors distinct ( i.e. , preserves distinctions ) is just a non - singular transformation .
are the non - singular linear transformations ( @xcite and @xcite ) . ]
this means that a type 2 process in full qm should be a process that preserves the degree of distinctness and indistinctness .
given two normalized quantum states @xmath387 and @xmath388 , the brackets @xmath417 can be interpreted as the degree of indistinctness ( or identification ) of the states with the extreme values of @xmath418 for full indistinctness or identification , i.e. , @xmath419 , and @xmath420 for zero indistinctness , i.e. , the full distinctness of orthogonality .
hence under this partitional approach to understanding or making sense of qm , the distinction - preserving type 2 processes are the ones that preserve the degree of indistinctness @xmath421 , i.e. , the unitary transformations . thus by this approach
, we can philosophically derive the mathematical form of the indistinctness - preserving transformations in full qm .
moreover , by stone s theorem in mathematics , those unitary transformations are given by ( the complex exponential of ) a hermitian operator @xmath422 that would describe how the `` substance '' changes to preserve indistinctness .
the partitional follow - the - math approach to understanding qm shows that the mathematical form of full qm is a type of logical probability system expressed in terms of vector spaces rather than sets ( the usual setting for logic and the laplace - boole logical probability theory ) .
but at some point this mathematical metaphysics has to pass the torch to physics to give empirical content to the formalism .
as previously noted , heisenberg tells us that `` substance '' is energy , but this `` follow the partitional math '' approach to making sense out of qm of course can not derive that physical fact nor the form of the operator @xmath422 ( `` h '' as in hamiltonian ) for a physical system
. there has been much concern and mystery in the foundations of quantum mechanics about the type 1 measurement processes in contrast to the clarity of describing the type 2 processes as unitary transformations .
that is another old question .
we have seen that this question can be answered at the _ mathematical _ level by the partition join operation .
the mathematical description of a measurement in qm / sets as the join of compatible set - partitions lifts to the mathematical description of a measurement in full qm as the join of compatible vector - space partitions where one partition describes the distinction - making measurement apparatus representing the observable being measured and the other partition is the indiscrete ( i.e. , one block ) partition representing the given pure state to be measured or , better , to be decohered . using
the respective partition join operations , a complete set of compatible attributes ( csca ) gives a non - degenerate measurement in qm / sets , and a complete set of commuting operators ( csco ) gives a non - degenerate measurement in full qm .
thus the clear and distinct distinction between `` type 1 '' distinction - making and `` type 2 '' distinction - preserving processes in the pedagogical model of qm / sets makes sense of the von neumann type 1 distinction - making measurements and type 2 distinction - preserving unitary transformations in full qm .
there are two meta - physical visions of reality suggested by classical physics ( objectively definite reality ) and by quantum physics ( objectively indefinite reality ) .
the problem of interpreting qm is essentially the problem of making sense out of the notion of objective indefiniteness . our sense - making strategy was to follow the lead of the mathematics .
the definiteness of classical physics is associated with the notion of a subset and is logically expressed in the classical boolean logic of subsets .
the indefiniteness of quantum physics is associated with the notion of a quotient set , equivalence relation , or partition , and the corresponding logic is the recently developed logic of partitions @xcite . moreover ,
those associated notions of subsets and quotient sets are category - theoretically dual to one another , so _ from that viewpoint _ , those are _ the only _ two possible frameworks to describe reality .
common sense and classical physics assumes the objectively definite type of reality , but quantum physics strongly indicates an objectively indefinite reality at the quantum level .
hence our approach to interpreting quantum mechanics is not flights of fantasy ( e.g. , about many worlds or realms of hidden variables ) but is trying to make sense out of objective indefiniteness . our sense - making strategy
was implemented by developing the mathematics and logic of partitions at the connected conceptual levels of sets and vector spaces .
set concepts are transported to complex vector spaces to yield the mathematical machinery of full qm , and the complex vector space concepts of full qm are transported to the set - like vector spaces over @xmath1 to yield the rather fulsome pedagogical model of quantum mechanics over sets or qm / sets .
abramsky , samson and bob coecke 2004 . a categorical semantics of quantum protocols . in _ proceedings of the 19th ieee symposium on logic in computer science ( lics04)_. ieee computer science press : 415 - 425 .
brading , katherine and harvey r. brown 2003 .
symmetries and noether s theorems . in _ symmetries in physics : philosophical reflections_. katherine brading and elena castellani eds . , cambridge uk : cambridge university press : 89 - 109 .
mittelstaedt , peter 1998 .
the constitution of objects in kant s philosophy and in modern physics . in
_ interpreting bodies : classical and quantum objects in modern physics_. elena castellani ed . , princeton : princeton university press : 168 - 180 .
shimony , abner 1989b .
search for a worldview which can accommodate our knowledge of microphysics . in _ philosophical consequences of quantum theory : reflections on bell s theorem_. james t. cushing and ernan mcmullin eds .
, notre dame , in : university of notre dame press : 25 - 37 .
teller , paul 1989 .
relativity , relational holism , and the bell inequalities . in _ philosophical consequences of quantum theory : reflections on bell s theorem_. james t. cushing and ernan mcmullin eds .
, notre dame , in : university of notre dame press : 208 - 223 . | arxiv |
in spite of the amount of precise cosmological data and good concordance between different observations , understanding the two dominant cosmic components , dark matter and dark energy , is still in order .
there are suggestions of unifying the dark sector , and a known example is the generalised chaplygin gas model , in which the dark sector is described by a unique component with density @xmath6 and negative pressure @xmath7 where @xmath8 and @xmath9 are constants @xcite . in early times
it behaves like pressureless matter , and tends to a cosmological constant in the asymptotic future .
however , the presence of unobserved oscillations and instabilities in the gas power spectrum was soon realised @xcite .
the possibility of unified descriptions of the dark sector is related to the so called dark degeneracy , i.e. the fact that the dark components are not uniquely defined @xcite .
nevertheless , in a recent paper @xcite it was argued that in observational tests it is necessary to properly define the clustering component of the dark sector , the component observed in large scale structures .
any dark fluid , unified or not , can be mapped into two interacting components , the first with zero pressure ( here named dark matter ) and the other with equation of state @xmath10 ( here called dark energy ) .
it was shown that , if the former is non - relativistic , the latter does not cluster and , hence , the defined dark matter can be identified with clustering matter . in this case , the dark matter power spectrum does not suffer from oscillations or instabilities , which are avoided owing to the presence of late - time entropic perturbations related to the energy flux between the components .
these results apply in particular to the generalised chaplygin gas ( gcg ) .
its split into two interacting components permits the identification of its clustering part and hence a proper analysis of observations @xcite .
the clustering component has no oscillations or instabilities in its power spectrum .
the gcg parameter @xmath1 determines the rate of energy flux between the components , with a negative @xmath1 meaning creation of dark matter at the expenses of dark energy .
in this paper we perform an observational analysis of the non - adiabatic gcg , by testing it against precise cosmological observations , namely the hubble diagram of type ia supernovas ( sne ia ) , the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background ( cmb ) and the distribution of large scale structures ( lss ) . for the latter we will consider the data from the 2dfgrs catalogue @xcite . for supernovae we will take two different compilations , the constitution and sdss samples , both calibrated with the mlcs2k2 fitter @xcite .
this choice is to avoid any bias resulting from the use of a fiducial @xmath3cdm model in the supernovae calibration , the case for instance of the union2 compilation that is calibrated with the salt2 fitter @xcite .
our joint analysis leads to the best - fit value @xmath11 .
this corresponds to a constant - rate dark matter creation , with the dark energy density decreasing linearly with the hubble parameter @xcite . on the other hand , the value @xmath4
, corresponding to the @xmath3cdm model , is comparatively rulled out , standing outside the 3@xmath12 confidence interval .
this might constitute , possibly for the first time , an evidence of particles creation at cosmological scale .
the paper is organised as follows . in the next section
we discuss the dark degeneracy and the mapping of any general model of the dark sector into interacting two - component models . in section [ gcg ]
we particularise these results to the non - adiabatic gcg . in section [ observations ]
we describe the performed observational tests , and the results are presented and discussed in section [ results ] , followed by conclusions in section [ conclusions ] .
consider a dark fluid with equation of state @xmath13 , with @xmath14 .
split this fluid into two components , one called dark matter , with zero pressure , and the other named dark energy , with equation of state @xmath15 .
with help of the friedmann equation . ]
@xmath16 , it is not difficult to show that @xmath17 these components will in general interact .
let us define the rate of energy flux between them as @xmath18 where @xmath19 is the scale factor and @xmath20 defines the dark matter particle number density . for non - relativistic matter , ( [ rate ] )
can also be written as @xmath21 where @xmath22 is the dark matter density . by using ( [ 11 ] ) ,
@xmath23 and the energy conservation equation @xmath24 it is possible to show that the energy - flux rate is @xcite @xmath25 the momentum transfer between the components is null in the isotropic background .
if it is negligible at the perturbation level , we can prove that the dark energy component does not cluster @xcite .
this is true , in particular , if dark matter is non - relativistic .
therefore , the dark matter component can be identified with the observed clustering matter .
this identification is necessary for observational tests involving the distribution of lss , as we shall discuss in section [ observations ] .
this result also guarantees that the dark matter power spectrum will not have oscillations or instabilities caused by pressure perturbations .
indeed , for any perfect fluid the evolution equation for the gravitational potential is given by @xcite @xmath26\phi_b = 0\,,\ ] ] where the prime means derivative with respect to @xmath19 , @xmath27 is the bardeen gauge - invariant potential , @xmath28 , @xmath29 is the perturbation comoving wavenumber , @xmath30 defines the adiabatic sound velocity , and @xmath31 is the effective sound velocity . if the dark energy component does not cluster , we have @xmath32 , leading to @xmath33
. therefore , the term proportional to @xmath29 in ( [ tam ] ) will be zero and the spectrum will be smooth .
the difference between @xmath34 and @xmath35 means that the decomposed dark fluid is non - adiabatic .
using ( [ eos ] ) in the energy conservation equation ( [ 26 ] ) we obtain @xmath36^{\frac{1}{1+\alpha}},\ ] ] where @xmath37 is the present gcg energy density and @xmath38 .
this density scales with @xmath39 for @xmath40 and tends to a constant when @xmath41 .
that is , at early times the gas behaves like dust matter , and tends to a cosmological constant in the asymptotic future .
with @xmath4 we reobtain the @xmath3cdm model , with @xmath42 . from ( [ eos ] )
we can derive the equation - of - state parameter @xmath43 and hence the adiabatic sound speed @xmath44 by differentiating @xmath13 we obtain @xmath45 substituting into ( [ 26 ] ) it follows that @xmath46 the gas can now be split into two interacting components like in the previous section , @xmath47 , @xmath48 . substituting ( [ 27 ] ) into ( [ 14 ] ) we obtain the rate of matter creation , @xmath49 since @xmath23 , we have , from ( [ 29 ] ) and ( [ 28 ] ) , @xmath50 while , from ( [ 11 ] ) and ( [ 29 ] ) , it is easy to obtain @xmath51 since @xmath52 ( from ( [ eos ] ) ) , we can see that @xmath53 and , therefore , @xmath54 . for @xmath4
we reobtain the @xmath3cdm model , with @xmath55 and a constant @xmath56 . when @xmath57 we have energy flux from dark energy to dark matter , since @xmath58 .
for @xmath59 we have the particular case of a constant @xmath60 , and @xmath56 decreases linearly with @xmath61 .
it was shown in @xcite that the split gas presents late - time non - adiabatic perturbations owing to the interaction between the components .
this prevents the appearance of oscillations and instabilities present in the power spectrum of the adiabatic gcg @xcite , provided that the dark energy component is unperturbed @xcite .
it was explicitly shown in @xcite that this is true in the case @xmath59 .
when testing the gcg against observations , we have to identify the clustering part of the gas to be compared to the observed amount of matter in galaxies and clusters . as discussed above
, this identification is unique if we split the gas as in sections [ dd ] and [ gcg ] .
we have seen that in this case the evolution equation ( [ tam ] ) does not depend on @xmath29 , which means that the profile of the dark matter power spectrum will depend essentially on the value of @xmath62 , the comoving horizon scale at the time of matter - radiation equality . by taking the limit @xmath63 in ( [ rho ] )
we obtain , for the early - time matter density , @xmath64 comparing with the standard expression @xmath65 ( case @xmath4 ) we see that , for the same amount of matter at high redshifts , we have more ( less ) matter today for a negative ( positive ) @xmath1 .
this is expected because of the late - time matter creation ( annihilation ) . with ( [ highz ] ) and by using for radiation @xmath66 , we obtain the redshift of matter - radiation equality , @xmath67 hence , with the use of @xmath68 , we have @xmath69 where @xmath70 mpc is the present hubble radius , and we are fixing the present radiation density parameter at the standard value @xmath71 . for @xmath4
the above expressions are reduced to the standard model ones ( see , for instance , equation ( 7.39 ) of ref .
@xcite ) . the present power spectrum is , apart from a normalisation constant , given by @xmath72 , if we take the scalar spectral index @xmath73 .
neglecting baryons ( whose density is only about @xmath74 of the total density ) the bbks transfer function @xmath75 is given by @xcite @xmath76}{(0.171x ) } \left[1 + 0.284x + ( 1.18x)^2 + ( 0.399x)^3 + ( 0.490x)^4\right]^{-0.25}.\ ] ] this transfer function was obtained by precisely fitting the observed spectrum with the cdm model .
it gives the spectrum profile at the begining of the matter dominated era and , therefore , is valid for any model that differs from the cdm model only at late - times ) and in a case with matter creation ( say , @xmath59 ) . taking in the first case @xmath77 ( the best - fit given by lss observations ) and in the second case the best - fit value @xmath78 , the redshift of equality is @xmath79 in both cases . at this redshift
the matter densities differ by @xmath80 , and the hubble parameter in the two models differ by @xmath81 . ] . during the late - time expansion
the spectrum is just amplified , and for its normalisation we use the observed spectrum at small scales .
the observed position of the first acoustic peak in the cmb anisotropy spectrum is given by @xcite @xmath82 ) , where @xmath83 is the acoustic scale and @xmath84 here , @xmath85 is evaluated at the redshift of last scattering @xmath86 , @xmath86 differs only @xmath80 from the standard value . ]
. using again ( [ highz ] ) and @xmath87 , we have @xmath88 for calculating the acoustic scale , we use @xmath89 .
the density parameters of baryons and photons , to be used in the calculation of the sound speed in the baryon - photon plasma , will be fixed at the same values of the standard model , @xmath90 and @xmath91 .
finally , when testing the distance - redshift relation of type ia supernovae , the calibration method has special relevance .
the union2 sample was calibrated with the salt2 fitter , and for it a fiducial @xmath3cdm model was used @xcite , something that may lead to bias .
a model - independent calibration is provided by the mlcs2k2 fitter , used in the calibration of the constitution and sdss compilations to be considered here @xcite .
and @xmath92 . the blue line was obtained by integrating the perturbation equations @xcite .
the dashed red line corresponds to the use of the transfer function ( [ transfer ] ) . for comparison
, we also show the power spectrum of the @xmath3cdm concordance model ( solid red line ) .
data are from the 2dfgrs catalogue.,height=226 ] rcccc + & & & + + constitution ( mlcs2k2 - 17 ) & @xmath93 & @xmath94 & @xmath95 & + sdss ( mlcs2k2 ) & @xmath96 & @xmath97 & @xmath98 & + sdss ( salt2 ) & @xmath99 & @xmath100 & @xmath101 & + union2.1 ( salt2 ) & @xmath102 & @xmath103 & @xmath104 & + table i shows the joint analysis results after marginalising over @xmath105 , with @xmath5 confidence level .
the two first lines correspond to the sne ia samples calibrated with mlcs2k2 , and in both cases we obtain @xmath106 , which corresponds to a constant - rate production of dark matter and to a dark energy density decaying linearly with @xmath61 .
the corresponding confidence regions are show in fig .
the present matter density is in agreement with concordance tests with @xmath1 fixed as @xmath107 , which have given @xmath78 @xcite .
it is higher than the standard model best - fit , as antecipated above for the case of a negative @xmath1 . the power spectrum for @xmath59 and @xmath92 is shown in fig .
[ fig2 ] , together with the 2dfgrs data .
the blue line was obtained by integrating the perturbation equations from very high redshifts to the present , as in ref .
the dashed red line corresponds to the use of eq .
( [ transfer ] ) and leads to an error of @xmath108 at most . for comparison
we show the spectrum of the @xmath3cdm concordance model ( solid red line ) .
the gcg best fit corresponds to a universe age @xmath109 gyr ( for @xmath110 ) @xcite .
the value @xmath4 , which corresponds to the @xmath3cdm model , is rulled out in comparison with the best fit , standing outside the @xmath5 confidence interval ( see , however , ref .
this agrees with previous tests in which @xmath1 was fixed as zero and that gave high values of @xmath111 for the sdss and constitution samples @xcite .
this relatively poor concordance reflects the fact that the matter density obtained with lss alone is @xmath77 @xcite , while the best fit obtained with sne ia tests using the constitution and sdss samples calibrated with mlcs2k2 gives @xmath112 and @xmath113 , respectively ( see table ii of ref .
@xcite ) . as we have discussed in the previous section
, lss tests strongly depend on the matter density at high redshifts , while sne ia probes are sensitive to the matter density at low redshifts .
therefore , this tension between the lss and sne ia values of @xmath114 may suggest a late - time process of matter creation . in the last two lines of table
i we show , for comparison , the joint analysis results when we use the sdss and union2.1 samples of sne ia calibrated with salt2 .
as antecipated in the previous section , the results are moved towards @xmath4 . however , the @xmath3cdm model ( @xmath4 ) is still outside the @xmath5 confidence intervals . in fig .
[ fig3 ] we show the corresponding probability distribution functions after marginalising over @xmath115 and @xmath114 . for the joint analysis of sne ia + lss + cmb .
the solid ( dashed ) line corresponds to union2.1 ( sdss ) supernovae sample calibrated with salt2.,height=226 ] to finish this analysis we need to comment about the power spectrum normalisation .
since the dark energy component does not cluster , the dark matter production is homogeneous , and this causes a late - time suppression of the dark matter density contrast @xmath116 ( see the left panel of fig . 3 in ref .
so , why is the spectrum normalisation not affected ? to answer this question ,
let us remark that we observe the baryonic power spectrum , not the dark matter one .
since baryons are conserved , no suppression in their spectrum is expected , although it presents the same profile as the dark matter spectrum , determined by @xmath117 .
this can also be understood if we remember that the baryons distribution follows the gravitational potential , which is determined ( via poisson s equation ) by the dark matter perturbations @xmath118 , not by the contrast @xmath119 itself .
the reader can see in the right panel of fig . 3 in ref .
@xcite that the gravitational potential for @xmath59 presents approximately the same strength and evolution as in the @xmath3cdm model .
this guarantees , by the way , that the cmb power spectrum will also have the correct normalisation .
an analysis of the @xmath59 case with the inclusion of conserved baryons can be found in @xcite .
a study of non - linear collapse in this model was recently done in @xcite .
models with interaction in the dark sector have been proposed for a long time ( see @xcite and references therein ) . in ref . @xcite it was shown that , in fact , any dark sector model can be mapped into a non - adiabatic fluid with energy flux between the dark energy and dark matter components .
choosing , on the basis of observations , a specific interaction inside this class of models is a difficult task , since the rate @xmath60 is a general function , related to the function @xmath120 by eq .
. this task becames simpler if we particularise the dark sector to a non - adiabatic gcg , since now the rate @xmath60 , given by ( [ 30 ] ) , is known up to the constant parameter @xmath1 , which can be determined from observations .
our analysis has led to a constant rate of matter creation , which corresponds to a dark energy density that decays linearly with the hubble parameter .
interestingly enough , a linear dependence on @xmath61 is expected from estimations of the energy density of the qcd vacuum condensate in the flrw spacetime @xcite . on the other hand , from ( [ 28 ] ) it is easy to see that the obtained constant rate is equal to @xmath121 , where @xmath122 is the hubble parameter in the de sitter limit . in other words ,
the creation rate is equal , apart from a factor of the order of unity , to the gibbons - hawking temperature of the future de sitter horizon .
we have also seen that the @xmath3cdm model is comparatively rulled out , an evidence in favor of matter creation at cosmological scale . this evidence may be confirmed with future observations , in which the discrepancies between the standard and interacting models will be more evident .
for example , in ref .
@xcite a slightly higher number density of high mass structures is predicted for @xmath59 as compared to the standard case .
although inside the error bars of present observations , this difference may be tested in future surveys like j - pas @xcite and erosita @xcite .
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_ , phys . rev . * d84 * , 123501 ( 2011 ) . | arxiv |
Olfactory receptor 2F1 is a protein that in humans is encoded by the OR2F1 gene.
Olfactory receptors interact with odorant molecules in the nose, to initiate a neuronal response that triggers the perception of a smell. The olfactory receptor proteins are members of a large family of G-protein-coupled receptors GPCR arising from single coding-exon genes. Olfactory receptors share a 7-transmembrane domain structure with many neurotransmitter and hormone receptors and are responsible for the recognition and G protein-mediated transduction of odorant signals. The olfactory receptor gene family is the largest in the genome. The nomenclature assigned to the olfactory receptor genes and proteins for this organism is independent of other organisms.
See also
Olfactory receptor
References
Further reading
External links
Category:Olfactory receptors | wikipedia |
Why can't a primary cell be recharged?
The explanation I have found is that primary cells have irreversible reactions, so passing current in the opposite direction cannot recharge the cell. But as far as I understood it, no reaction is really irreversible - what one calls irreversible simply has very high values of the equilibrium constant, so for all intents and purposes proceeds to completion. Nevertheless, some small - maybe undetectable practically - amount of reactant does remain and the reaction does reach equilibrium. So even in a primary cell, when it is used up, equilibrium has been achieved, so recharging should be possible - it might take long to build up the initial value of potential since the required concentration of the electrolytes will be very different from that at equilibrium, but it should be possible. Why then is it not?
In some cases, a primary cell *can* be recharged, e.g. Mn-alkaline cells can take a partial charge. However, there are a number of reasons primary cells cannot be fully recharged, and that secondary cells have to be specifically designed to allow recharging.
1. Gas evolution: once most of a cell is charged (though all material has not been converted to its original state), the electrolyte is electrolyzed (apologies for the pleonastic redundancy), usually evolving hydrogen and oxygen, causing the cell to rupture. [Nickel-metal hydride cells](http://en.wikipedia.org/wiki/Nickel%E2%80%93metal_hydride_battery), for example, get around that issue by incorporating a catalyst to recombine them, $\ce{2 H2 + O2 -> 2 H2O + heat}$.
2. Physical change in the reactants: the standard "dry cell" ([Leclanché cell](http://en.wikipedia.org/wiki/Leclanch%C3%A9_cell)) is made with an outer shell of zinc. As the cell discharges, parts of the shell are dissolved, eventually leaving holes. Reversing the current flow will cause zinc to redeposit, *but not necessarily filling in the weakened areas.* Even lead-acid cells designed for storage have limited lifetime because of the buildup of large, insoluble crystals of lead sulfate ([sulfation](http://support.rollsbattery.com/support/solutions/articles/5964-battery-sulfation), aka sulphation in GB), which may break off from the lead plates, preventing reversal of the chemical reaction during charging.
3. Physical damage to the insulator: metal dendrite may grow during charge-discharge cycling, piercing the dielectric between cells, [even in well-designed secondary cells](http://www.mpoweruk.com/lithium_failures.htm).
*Irreversible* in this context isn't a thermodynamic or kinetic thing, necessarily. It simply means that applying a current in reverse doesn't result in the original reagents. It may be that there is another possible reaction at a similar redox potential that leads to a different compound being formed or that the manner in which it is deposited is not suitable, e.g. the zinc in an alkaline battery being plated back onto the anode unevenly or such that it damages the ion conducting membrane.
It's also possible that recharging may make a primary cell inoperative by some other mechanism, such as gas formation in the potassium hydroxide electrolyte of an alkaline cell deforming the case or damaging the half-cell separator. Primary cells are also typically constructed cheaply as they don't have to withstand the stresses of secondary cells, e.g. the steel casing of alkaline batteries is susceptible to corrosion.
Things like the various lithium battery chemistries make better secondary cells as they use organic solvents which reduce the problem of gas evolution and lithium can form intercalated compounds where the lithium can be evenly spread instead of growing dendrites of solid lithium which can damage the cell when recharged. That's the main difference between disposable and rechargeable lithium cells: disposable cells use solid lithium electrodes because the anode only has to dissolve once and the difficulty of replating the anode is not an issue, whereas a rechargeable cell needs to return the anode to its original state many times and an intercalated lithium compound, though more expensive, is far easier to replenish with lithium.
I have heard that technically, a dry cell CAN be recharged, but it takes a very long time to do it without rupturing the cathode - the zinc shell -, enough time that the electricity used costs more than replacing the battery, plus, when recharged, it does not have the life of a brand new battery, so it just is not worth the trouble.
| stackexchange/chemistry |
Sarah Wall born 16 October 1984 is an Australian netball player. She currently plays for Giants Netball in the Suncorp Super Netball competition, as an injury replacement player. She has previously played for the New South Wales Swifts. In 2005 she played her first year of elite netball, for the Melbourne Phoenix in the Commonwealth Bank Trophy. She played three years with the Phoenix until the competition was disbanded in 2007. She was not signed with a team in the new ANZ Championship in its inaugural season the following year. But in 2009 she received a callup to the Melbourne Vixens. In 2010 Wall transferred to the Queensland Firebirds, but towards the end of the 2010 season she injured her CL. In August that year she signed back with the Vixens on a two-year contract starting in 2011.
Experienced Victorian midcourter Wall was called into the NSW Swifts side in Rounds 4 and 5 of the 2014 ANZ Championship as a replacement player for Paige Hadley who suffered a season-ending knee injury prior to Round 2.
A wing attack with four years of ANZ Championship experience, Wall fitted seamlessly into the Swifts attacking line, and was named the permanent replacement for Hadley for the remainder of the 2014 ANZ Championship on 4 April 2014 - read the announcement. She was rewarded for her contribution to the team with the 2014 NSW Swifts Coaches' Award.
ANZ Championship accolades
2014 NSW Swifts Coaches' Award
2009 Premiership with the Melbourne Vixens
References
External links
2011 Melbourne Vixens profile. Retrieved 20 February 2011.
Category:1984 births
Category:Living people
Category:Australian netball players
Category:Melbourne Vixens players
Category:Queensland Firebirds players
Category:Melbourne Phoenix players
Category:New South Wales Swifts players
Category:Suncorp Super Netball players | wikipedia |
in the last years the field of topological states of matter has been subject to stunning progress following the theoretical prediction @xcite and experimental observation @xcite of topological insulators .
a paradigmatic role within this field is played by the quantum anomalous hall ( qah ) state in the haldane model@xcite a model of non - interacting spinless fermions on the half - filled honeycomb lattice giving rise to a quantized hall conductivity at zero field .
this model requires an intricate magnetic flux pattern as provided by a complex second - nearest neighbor hopping amplitude @xmath0 averaging to zero over the unit cell and breaking time - reversal symmetry .
later , raghu _ _ et al.__@xcite and further mean - field studies@xcite suggested that the qah state of spinless fermions on the honeycomb lattice can in principle also be obtained dynamically from a large repulsive second - nearest neighbor density - density interaction @xmath1 as mean - field decoupling of this term generates a ground - state solution with an effective complex second - nearest neighbor hopping @xmath0 .
recent elaborate studies in terms of exact diagonalization@xcite , infinite density matrix renormalization group@xcite have addressed the stability of the qah ground state upon inclusion of quantum fluctuations .
these studies have found an intricate competition of various phases in the plane of nearest- and second - nearest - neighbor interactions including , e.g. , a conventional charge density wave state and a kekul dimerization pattern@xcite . in the regime where the topological mott insulating qah state was expected , a charge - modulated ( cm ) density wave phase has been found to be the ground state in refs . .
the qah state , on the other hand , is completely expelled from the quantum phase diagram .
note , that numerical evidence for the persistence of the qah state has been presented in ref . .
further support for the scenario where the qah is suppressed in the model s phase diagram has been contributed by means of the functional renormalization group within a high - definition resolution of the momentum dependence of the interaction vertex in our ref . .
by now , the spinless model has been investigated in great detail by analytical and numerically exact methods . at the same time , the physically relevant spin-1/2 case remained elusive to studies operating at the same level of accuracy which can be attributed to the great amount of numerical effort that would be required , e.g. by exact diagonalization techniques .
further , in the spinless as well as in the spin-1/2 case , an analysis of the problem by means of quantum monte carlo ( qmc ) approaches is typically inhibited by the fermion sign problem .
on the other hand , recent qmc studies@xcite have also taken into account non - local density - density interactions on the honeycomb lattice , however , a definite statement about the quantum many - body ground state in the presence of sizable second - nearest neighbor interactions is hindered by limitations on the accessible parameter range . in the spin-1/2 case ,
a cousin of the qah state on the honeycomb the quantum spin hall state emerges from an intrinsic spin - orbit coupling as suggested by kane and mele@xcite in the context of a graphene model .
the qsh basically corresponds to two copies of the haldane model with opposite chirality for the two spin projections and is symmetric under time reversal . also here , a next - nearest neighbor repulsion @xmath1 was argued to potentially trigger a phase transition towards the topologically non - trivial qsh state@xcite . a qualitative difference to the spinless case
, however , is the possibility of a local interaction term , i.e. , the onsite repulsion @xmath2 , that can in principle affect the balance of the different fluctuations in the particle - hole channel . in this work ,
we address the role of the qsh state in the phase diagram of spin-1/2 fermions on the half - filled honeycomb lattice , and in particular , whether the onsite repulsion can drive an instability towards the qsh state through the additional energy penalty of charge imbalance throughout the lattice , as it occurs in the cm state . to that end
, we implement the refined multi - patch rg scheme as established in ref . for the spinless case where it supported the absence of a topological qah state in the phase diagram .
we find that the unbiased inclusion of fermionic fluctuations of the spin-1/2 fermions exhibits a cm density wave phase with finite wavevector transfer as the leading instability for interaction strength @xmath1 larger than some critical value @xmath3 depending on the values of onsite and the nearest neighbor interactions .
the qsh state never is found to be the leading instability in the range of interaction parameters where we consider our weak - coupling approach reliable .
the paper is organized as follows : in sec .
[ sec : model ] , we introduce the hamiltonian for the extended hubbard - model for spin-1/2 fermions on the half - filled honeycomb lattice with short - ranged repulsions . in sec . [
sec : frg ] , we present essentials of the frg method and discuss the multi - patch scheme employed to analyze the leading instabilities of the model .
further , we discuss the convergence of the results with increasing momentum resolution at the example of the critical onsite interaction strength @xmath4 for the quantum phase transition between the semi - metallic state and the antiferromagnetic spin - density - wave state . sec .
[ sec : res ] is then devoted to an analysis of the quantum many - body instabilities of the model within our frg approach .
first , we study an exclusive @xmath1 interaction term to compare to the spinless situation . then , we also include onsite and neares - neighbor interactions , @xmath2 and @xmath5 , respectively .
conclusions are drawn in sec .
[ sec : conclusion ] and some technicalities on the functional renormalization group approach can be found in the appendices .
we study spin-@xmath6 fermions on the half - filled honeycomb lattice with short - ranged density - density interaction terms .
the hamiltonian is composed of a single - particle hopping term @xmath7 and an interaction contribution @xmath8 , @xmath9 where @xmath7 is a tight - binding hamiltonian @xmath10 with hopping amplitude @xmath11 to the nearest - neighbors @xmath12 of the hexagonal bravais lattice with a two - atomic basis labelled by the sublattice index @xmath13 , cf .
[ fig : lattice ] .
the operator @xmath14 creates an electron at lattice site @xmath15 in the sublattice @xmath16 with spin projection @xmath17 .
diagonalization of @xmath7 gives rise to the formation of a spin - degenerate valence and conduction band , touching linearly and isotropically at the @xmath18 points of the brillouin zone ( bz ) . at half - filling
, the fermi surface shrinks to the two dirac points situated at @xmath18 . here
, the single - particle density of states vanishes linearly resulting in a semi - metallic behavior of the non - interacting system , eq . ,
which is robust against spontaneous symmetry breaking induced by weak interactions . and @xmath19 are indicated by empty and filled circles , respectively , connected by the nearest - neighbor vectors @xmath20 .
the second - nearest - neighbor vectors are given by @xmath21 and the bond dimerization corresponding to the qah and qsh ordering patterns is indicated by @xmath22 , see for example ref .
for a discussion of the mean - field order - parameters .
right panel : nearest - neighbor hopping on the honeycomb lattice provides the depicted energy dispersion with the conduction ( blue ) and the valence band ( red ) touching linearly at the @xmath18 points at the fermi level.,title="fig : " ] and @xmath19 are indicated by empty and filled circles , respectively , connected by the nearest - neighbor vectors @xmath20 .
the second - nearest - neighbor vectors are given by @xmath21 and the bond dimerization corresponding to the qah and qsh ordering patterns is indicated by @xmath22 , see for example ref .
for a discussion of the mean - field order - parameters .
right panel : nearest - neighbor hopping on the honeycomb lattice provides the depicted energy dispersion with the conduction ( blue ) and the valence band ( red ) touching linearly at the @xmath18 points at the fermi level.,title="fig : " ] for the interaction part @xmath8 , onsite , nearest - neighbor and second - nearest - neighbor repulsions are taken into account , @xmath23 where @xmath24 represents the local electron density operator and the sums @xmath25 and @xmath26 run over nearest neighbors and second - nearest neighbors , respectively .
each pair is counted only once .
resulting from the inclusion of these short - ranged repulsions , quantum phase transitions towards different kinds of ordered states occur when the interaction parameters @xmath27 exceed critical values , a subject that has been addressed previously by many different methods@xcite .
for example , sizeable pure onsite interactions typically trigger a phase transition towards a fully gapped antiferromagnetic spin - density wave ( sdw ) state@xcite whereas a dominating nearest - neighbor repulsion @xmath5 supports the formation of a charge - density wave ( cdw)@xcite . the effect of the second - nearest neighbor interaction @xmath1 is less well - understood even in the absence of other interaction terms .
mean - field calculations@xcite suggested the emergence of an interaction - driven topologically non - trivial quantum anomalous hall ( qah ) state in the spinless case and a time - reversal symmetric quantum spin hall ( qsh ) state@xcite in the case of spin 1/2 .
more recent numerical and analytical studies@xcite for the spinless case , however , have found a suppression of the qah in favor for a charge - modulated ( cm ) density wave phase with finite wavevector transfer @xmath28 . here ,
for the case of spin-1/2 fermions , we shall thoroughly investigate the fate of the qsh and cm states upon inclusion of the onsite and nearest - neighbor interactions @xmath2 and @xmath5 .
we investigate the quantum many - body instabilities of the model by means of the functional renormalization group ( frg ) approach@xcite for the one - particle irreducible vertices of a correlated fermion systems , see refs . for recent reviews .
the multi - patch frg scheme employed here allows for an unbiased identification of the leading instabilities in the presence of competing correlations@xcite by successively integrating out fermion degrees of freedom starting from an initial energy scale @xmath29 corresponding to the bandwidth down to the infrared @xmath30 .
we now set up the frg approach in a nutshell and give more details in app .
[ app : frg ] . consider the fermionic action corresponding to the model hamiltonian , eq .
, given by @xmath31 = -({\bar{\psi}},g_0^{-1 } \psi ) + v[{\bar{\psi}},\psi]\,.\ ] ] the first term is the quadratic part with the free propagator @xmath32 including matsubara frequency @xmath33 and wavevector @xmath34 . here
, we work in the band basis providing diagonalization of the quadratic part of the hamiltonian @xmath7 with single - particle energies @xmath35 and band index @xmath36 . the fermionic propagator is diagonal with respect to the spin quantum number . the interaction term @xmath37 $ ] in eq .
is quartic in the fermion fields and can be inferred from the interaction part of the hamiltonian , eq . by introducing grassmann fields for the operators and transforming to the band basis in line with the diagonalization of @xmath7 .
this adds a non - trivial momentum dependence to the coupling function . in the frg
, the bare propagator is regularized by an infrared momentum cutoff , with energy scale @xmath38 , @xmath39 here @xmath40 is a smoothened step function with softening length @xmath41 cutting off modes with energies @xmath42 .
the modified propagator @xmath43 is then used to set up the functional integral representation for the effective action @xmath44 , which is now scale dependent and generates the one - particle irreducible vertex functions @xmath45 .
the rg flow is generated upon variation of @xmath38 generating a hierarchy of flowing vertex functions and integration towards the infrared @xmath46 reproduces the full effective action @xmath47 , see apps .
[ app : frg ] and [ app : trunc ] . for our analysis
we use a standard truncation that has proven to be suitable for analyzing instabilities in two - dimensional correlated fermion systems . in this truncation
the flow of all @xmath48-point functions with @xmath49 and also self - energy feedback are neglected .
this amounts to following the rg - scale dependence of the effective interaction vertex @xmath50 which carries a multi - index @xmath51 gathering matsubara frequencies @xmath52 as well as wavevectors @xmath34 and the band index @xmath36 .
as the most singular part of this quantity comes from the zero matsubara frequency and we are interested in instabilities , we will also neglect the frequency dependence in the following .
then , the flow equation of the effective interaction vertex @xmath53 reads @xmath54 with a contribution @xmath55 from the particle - particle loop , the direct particle - hole loop @xmath56 and the crossed particle - hole loop @xmath57 .
all these contributions are bilinears in the scale - dependent vertex function @xmath53 and include a loop - momentum integration .
we give explicit expressions for the flow equation in app .
[ app : flow ] .
the wavevector dependence of the interaction vertex is approximated in a multi - patch scheme . to this end , the brillouin zone ( bz ) is divided into @xmath58 patches and each patch is equipped with a representative patch point , see fig .
[ fig : patching ] for a pictorial representation .
then , a given wavevector @xmath34 is projected onto its closest patch point @xmath59 .
the patching discretization implemented in this work is shown in fig .
[ fig : patching ] . a single patch is composed of all the wavevectors having the smallest distance to the corresponding representative patch point .
we then solve eq .
for the projected vertex function @xmath60 which additionally depends on the band indices @xmath61 of the external legs of the four - fermion vertex .
the fourth wavevector is determined by momentum conservation and is subject to an approximation in our scheme by allocating it to its closest patch point . and @xmath62 .
right panel : numbering of angular and radial patches according to the patching scheme.,title="fig : " ] and @xmath62 .
right panel : numbering of angular and radial patches according to the patching scheme.,title="fig : " ] for the half - filled honeycomb lattice , the fermi level is located at the @xmath63 points where the density of states vanishes linearly . for the unbiased determination of the instabilities of this model
, we have therefore extended the conventional fermi - surface patching scheme by a refined momentum resolution of the brillouin zone which additionally resolves momentum dependencies away from the fermi level , cf .
[ fig : patching ] . to this end
, the patching scheme employed here takes into account several patch rings around the @xmath63 points , following ref . .
in the vertex function @xmath50 , each independent momentum argument can then take @xmath64 values , where @xmath65 is the number of corners of the brillouin zone , @xmath66 is the number of angular patches in one corner of the brillouin zone , @xmath67 of patch rings around the @xmath63 points and @xmath68 is the number of energy bands .
therefore , the flow eq . has to be solved for a vertex function with @xmath69 components where the fourth band index is not fixed by momentum conservation . to evaluate the flow equation , we implement the initial condition @xmath70 set at scale @xmath71 which is given by the two - particle interaction in the bare action , eq .
the flow equations are integrated out numerically by decreasing the cutoff scale @xmath72 . in flows where the initial interactions @xmath70 are large enough
, some components of the effective interaction vertex grow large and diverge at a critical scale @xmath73 indicating a quantum many - body instability . in practice
, the flow has to be stopped at a scale @xmath74 .
such a divergence hints at an instability towards a symmetry - broken ground state by a flow to strong coupling and tells us in which channel the leading ordering tendency occurs .
further , we obtain a pronounced momentum structure of the vertex function @xmath50 near the critical scale which is used to extract an effective hamiltonian for the low - energy degrees of freedom and to determine the leading order parameter .
we note that for the half - filled honeycomb lattice our previous study@xcite has shown that an insufficient wavevector resolution of the brillouin zone can have an influence on the leading instability which is found as a result of the renormalization group flow , see also refs . .
in particular , for the half - filled single - layer honeycomb lattice , this affects the competition between charge - modulated density wave states and the topological mott insulator . here , as in ref .
, we overcome this shortcoming by employing the enhanced wavevector resolution of the brillouin zone , cf .
[ fig : patching ] . an alternative approach to this problem in terms of the truncated unity frg scheme
is presented in refs . .
an alternative regularization scheme in terms of the temperature flow@xcite is briefly discussed in app .
[ app : temp ] .
we have cross - checked our results with respect to their sensitivity of the cutoff scheme by evaluating both the momentum and the temperature cutoff and find that our qualitative predictions on the leading instabilities of the extended hubbard model on the half - filled honeycomb lattice do not depend on the choice of the cutoff .
studies of spinless fermions on the half - filled honeycomb lattice with non - local density - density interactions have revealed a competition between various ordering tendencies depending on the relative size of the different interaction parameters @xmath5 and @xmath1 .
especially , it has been reported that the suggested topological mott insulator state is destabilized upon inclusion of quantum fluctuations .
these findings are supported by our recent study within the multi - patch scheme with the refined momentum resolution of the vicinity of the dirac points , as introduced above . in the case of spin-1/2 fermions
, the onsite term @xmath2 adds another source for driving interaction - induced ground states which affects the balance of quantum fluctuations in the phase diagram .
while @xmath2 will primarily drive an antiferromagnetic spin - density wave instability , that is in itself detrimental to the formation of a time - reversal invariant qsh state , it might at the same time suppress charge - ordering tendencies , thus giving way to other momentum structures in the renormalization of the interaction vertex .
for this case , however , there are no calculations for the phase diagram operating at a similar level of reliability as , e.g. , the exact diagonalization results due to numerical limitations . here
, we intend to fill this gap by presenting a high - definition multi - patch rg study of this issue which , despite its approximations , has shown to provide results in agreement with exact methods in large parts of the phase diagram .
therefore , we map the appearing instabilities for a range of the coupling parameters @xmath75 in units of the hopping amplitude @xmath11 with @xmath76 $ ] which allows to draw tentative phase diagrams of the model . as a function of the number of patch rings . @xmath66 and @xmath67 denote the number of angular and radial patches , respectively .
we observe a smooth convergence in the value for @xmath4 for @xmath77 . in the following instability analysis we therefore use a patching resolution with @xmath78 . ] the half - filled hubbard model on the honeycomb lattice , eq .
, with @xmath79 exhibits an instability towards an antiferromagnetic spin - density wave ( sdw ) state for onsite interactions @xmath80**???**. for smaller values of @xmath81 , the system is in the semi - metallic ( sm ) phase and does not exhibit any signs of a flow to strong coupling .
we study the dependence of the critical interaction strength @xmath82 as a function of the momentum resolution of the patching scheme , cf .
[ konvergenz_uc ] .
therefore , we separately vary the number of angular and radial patches , @xmath66 and @xmath67 , respectively , and identify the corresponding critical onsite interaction @xmath83 for the instability . for all combinations of @xmath84 and large enough @xmath85
, we observe a clear instability towards an antiferromagnetic sdw with a sharply structured leading part of the vertex function in wavevector space which can be cast into the effective hamiltonian @xmath86 where we have introduced @xmath87 , @xmath88 , @xmath89 and the fourier transformed spin-1/2 operator is given by @xmath90 .
mean - field decoupling of @xmath91 yields antiferromagnetic spin alignment on the real space lattice .
we observe that for fixed @xmath66 the inclusion of more than one patch ring , @xmath92 , increases the value for the critical onsite interaction @xmath4 by about 10% .
further , for a number of angular patches of @xmath77 we obtain a smoothly converging @xmath93 as @xmath67 is increased
. the converged value of @xmath94 is reached at @xmath62 and a higher @xmath67 does not induce further shifts in @xmath4 .
therefore , the following analysis of instabilities with local and non - local interaction terms is carried out in the patching scheme with @xmath95 which is a trade - off between the accuracy of the momentum resolution and numerical cost . in total
this amounts to a momentum resolution of the bz in @xmath96 patches .
finally , we note that the numerical convergence we have discussed here exclusively refers to the convergence within the specified truncation and approximation scheme . for the case of a pure onsite interaction
@xmath2 the numerically exact value@xcite for the quantum phase transition lies at @xmath97 .
this is considerably larger than our multi - patch frg value of @xmath98 and hints towards an overestimation of fermionic fluctuation effects or the neglect of the fluctuations from collective degrees of freedom within our approach .
recently , a related high - performance frg implementation the truncated unity frg ( tufrg)@xcite which operates at the same level of approximation to the flow of the vertex function has reported@xcite a value of @xmath99 .
this is considerably higher than our value and can be attributed to heavily increased momentum resolution of the exchange propagators in the tufrg and suggests a sizeable sensitivity of quantitative results to the momentum resolution .
further , the tufrg employs a different regularization scheme
the @xmath100 scheme@xcite which can also be expected to have an impact on quantitative findings . for our present purposes ,
we therefore consider the multi - patch frg employed here as a tool to qualitatively detect the leading instability of a correlated fermion system in an unbiased way as it treats all the appearing fermionic fluctuations on equal footing within a infinite - order resummation of all fermionic 1-loop diagrams . instability
. left and middle panel : effective coupling in units of @xmath11 as a function of the incoming patch indices @xmath101 ( vertical ) and @xmath102 ( horizontal ) with the third patch index @xmath103 fixed at the patch point with @xmath104 in the left lower corner of the bz , cf .
[ fig : patching ] . for simplicity ,
the vertex structure is only shown for patch points on the second ring .
the two vertex pictures correspond to different sublattice combinations of in- and outgoing momenta . on the left : @xmath105 . in the middle : @xmath106 .
the calculations were performed with @xmath77 and @xmath62 .
the large components in this interaction vertex are used to extract the effective form of the hamiltonian given in eq . .
right panel : qualitative charge distribution of the cm mean - field state for @xmath107 . ]
next , we study a pure next - nearest - neighbor interaction @xmath108 term and setting @xmath109 as this interaction was suggested to trigger the topological mott insulator state .
again , for small values of @xmath1 , the semi - metallic behavior from the single - particle picture is stable against interactions .
beyond a critical value of @xmath110 , we observe an interaction - driven instability with a sharp momentum structure , cf .
[ v2line ] .
this indicates a quantum phase transition from the semi - metallic state to an ordered ground state with a charge ordering pattern .
explicitly , the sharp momentum structure can be cast into an effective interaction hamiltonian of the form , @xmath111 again with @xmath87 , @xmath88 and @xmath89 .
the density operator reads @xmath112 .
importantly , the effective hamiltonian , eq . , exhibits a finite transfer momentum @xmath113 . in real space
, the structure of @xmath114 corresponds to a infinitely - ranged interaction featuring a modulation with wavevector @xmath115 .
this state is the analogue to the charge - modulated state that has been discussed in detail for the case of spinless fermions * * ? ? ?
* * and has previously also been found in the context of honeycomb bi- and trilayer lattices where it was dubbed the cdw@xmath116 state@xcite .
the corresponding ground state energy is minimized by the finite complex order parameter @xmath117 with phase factor @xmath118 yielding a density modulation @xmath119 on the lattice sites .
a change of @xmath118 redistributes the charges on the half - filled lattice and at @xmath120 the ground state is minimized by opening a gap , cf .
[ v2line ] for a pictorial representation .
the range of interaction strengths @xmath1 where we find the instability to the cm state extends up to @xmath121 .
this interaction strength , however , already lies in a regime , where the weak - coupling approximation can be expected to break down as the initial interaction has components that are larger than the bandwidth of the non - interacting system @xmath122 .
we further note that at large @xmath123 we also find an instability towards the interaction - driven qsh , cf .
ref . , with an effective hamiltonian , @xmath124 where @xmath125 with the @xmath126-wave form factor @xmath127 . at moderate @xmath1 , however , this instability only shows up as an artefact of an insufficient momentum resolution of the bz , e.g. , by restricting the multi - patch scheme to a single patch ring close to the dirac points .
we interpret this finding as an indication for the absence of the qsh state from the phase diagram upon inclusion of sufficiently momentum - resolved fermionic quantum fluctuations . in the next step ,
we explore the leading instabilities as a function of independently varied interaction parameters @xmath128 and @xmath1 , cf .
to this end , we note that a dominating nearest - neighbor interaction @xmath5 is known to trigger a conventional charge density wave ( cdw ) beyond a critical @xmath129 which we find to be @xmath130 .
we note , that this is close to the critical value obtained from monte carlo methods @xcite .
this might point to a weak influence of collective fluctuations close to the phase transition , in accord with the expectation that collective fluctuation effects are less pronounced in the spontaneous breaking of a discrete symmetry . for @xmath131
, we observe the cdw instability that can be cast into the effective hamiltonian @xmath132 with the same conventions for @xmath133 and @xmath134 as above .
this corresponds to a infinitely ranged density - density interaction on the lattice with a sublattice modulation on the @xmath135 and @xmath19 sublattices representing a conventional cdw where , e.g. , sublattice @xmath135 is occupied and @xmath19 is empty or vice versa .
the resulting tentative phase diagrams are shown in fig .
[ fig : uv1v2 ] as a function of the short - ranged interaction parameters @xmath5 and @xmath1 for four choices of the onsite interaction @xmath136 .
most importantly , we see that for @xmath137 , the phase diagram is completely dominated by the semi - metallic state , the cdw state and the cm state .
interestingly , for increasing @xmath2 the critical value @xmath138 is shifted towards larger values indicating a competition between the spin - density wave correlations and the cm correlations , see the panels for @xmath139 and @xmath140 in fig . [
fig : uv1v2 ] . on the other hand ,
despite enhanced correlations in the spin channel which support the formation of the qsh state , we do not find an indication for a stabilization of the qsh state as the leading instability due to finite onsite interactions .
in fact , in the region of larger @xmath1 , the correlations in the charge channel are always dominant and the cm state turns out to be the leading instability . for the largest onsite interaction we have explored , i.e. @xmath141 , the sdw state reemerges as an instability for small @xmath142 . also here
, we do not observe a stabilization effect of the topological qsh state due to the onsite interaction for any choice of interaction parameters @xmath143 which is in qualitative agreement with the related study in ref . .
we note , however , that our critical scales and interaction parameters turn out different due to the different wavevector resolution and regularization scheme .
in contrast to ref . , we do not find a strong suppression of the critical scale at the transition between the sdw state and the cm state to give rise to an intermediate semi - metallic region . within our data
, however , we can support the statement of a competition between the ordered states due to the increase of the critical value @xmath138 to larger values . [ [ wehling ] ] graphene parameters .
+ + + + + + + + + + + + + + + + + + + + in the setup above the short range repulsion parameters @xmath75 are completely independent of each other . in a real material electrons
interact via a ( screened ) coulomb potential which leads to a hierarchy in strength of the parameters . using
_ ab initio _
calculations for graphene s interaction parameters within the constrained random phase approximation from ref .
, we can provide an estimate for the leading instability for graphene - like systems as a result of short - ranged interaction potentials .
explicitly , these parameters read @xmath144 in units of the hopping amplitude @xmath145 ev . to account for the overestimation of fermionic fluctuations within our approach , cf . [
sec : afm ] , we consider variations in the absolute scale of the _ ab initio _ parameters , maintaining the shape of the potential , i.e. @xmath146 with @xmath147 $ ] . for @xmath148 , we do not observe indications for a flow towards strong coupling as all the vertex components remain finite during the flow for @xmath149 .
this indicates that the system remains in the semi - metallic state . in case
@xmath150 the flow develops an instability towards the antiferromagnetic sdw as given in eq . .
no other instabilities occur for this choice of parameters . following a coulomb - inspired shape of the interaction potential , eq . , with onsite repulsion strength
@xmath151 and screening parameter @xmath152 .
again , we evaluate the flow equations with a patching resolution of 144 patches in the bz . ]
further , to account for possible modifications of graphene and graphene - like systems affecting the interactions between the electrons , we studied variations of the shape of the screened coulomb potential in terms of the short - range parameters . therefore , we choose an _ ad hoc _ shape of the potential , reading @xmath153 with the lattice constant @xmath154 and @xmath155 as the strength of the onsite repulsion .
the parameter @xmath152 serves as the screening parameter and in the following we vary @xmath151 and @xmath152 . for this choice of the potential ,
the _ ab initio _ short - range parameters @xmath156 and @xmath157 from ref .
are approximately reproduced by @xmath158 and @xmath159 .
we note , that we use the suggested form of the potential only for the three short - range interaction parameters and no further interaction terms with @xmath160 are taken into account in our calculation to account for the finite momentum resolution of the brillouin zone .
the tentative phase diagram is presented in fig .
[ uepsilon_phasediagram ] .
again , the quantum spin hall state is absent , but we find the sdw and cm states next to the semi - metallic phase .
we studied interacting spin-1/2 fermions on the honeycomb lattice with repulsive onsite , nearest- and next - nearest neighbor interactions via the functional renormalization group ( frg ) for correlated fermions with a focus on the detection of a possible interaction - driven topological quantum spin hall state .
this was motivated through recent studies of interacting spinless fermions by means of exact diagonalization , the infinite density matrix renormalization group and the frg that supported the suppression of a topological mott insulating phase in the whole phase diagram of interaction parameters .
based on the findings in ref . , we used a refined multi - patch rg scheme where fluctuations further from the fermi surface are considered to overcome the residual influence of an insufficient wavevector dependence on the leading instability in the renormalization group flow . here , we complemented these previous studies by investigating the physically relevant case of spin-1/2 fermions additionally featuring onsite interactions which can potentially have an enhancing effect on the correlations in the spin channel supporting the topological qsh state .
for dominating next - nearest neighbor interactions , however , our frg results favor ordering tendencies towards a charge - modulated ground state over the topological mott insulating state in agreement with the spinless case .
further , our results are in qualitative agreement with a recent related frg study@xcite concerning the absence of the topological mott insulator state in the phase diagram and the appearance of charge - modulated states in the large @xmath1 regime . on the other hand , we do not find any sign for an incommensurable charge - modulated state reported in ref . .
this would require a much higher wavevector resolution .
this is beyond the applicability of the present multi - patch approach as it requires a much higher numerical cost . to summarize , an independent variation of the interaction parameters for the onsite , nearest - neighbor and next - nearest - neighbor repulsions does not reveal any spot in the tentative weak - coupling phase diagram , where the interaction - driven qsh state represents the leading instability .
also , for interaction profiles inspired by ab initio parameters for graphene no indication for an topological mott insulator state is found .
instead , we identified large parts of the phase diagram where a charge - modulated density wave order is the leading instability and we have found evidence for a competition between the spin correlations and the charge correlations . [ [ acknowledgments ] ] acknowledgments + + + + + + + + + + + + + + + we thank c. honerkamp , j. lichtenstein , d. snchez de la pea for useful discussions .
d.d.s . acknowledges support by the villum foundation .
is supported by grant no .
erc - adg-290623 and dfg grant no .
sche 1855/1 - 1 .
the connected correlation functions of a system of interacting fermions are given by the generating functional for the fully connected correlation functions@xcite , @xmath161=-\ln\int\mathcal{d}\psi\mathcal{d}\bar\psi \,e^{-s[{\bar{\psi}},\psi]+(\bar\eta,\psi)+(\bar\psi,\eta)}\,.\end{aligned}\ ] ] in the frg approach@xcite , we consider the generating functional for the one - particle irreducible ( 1pi ) correlation functions or effective action @xmath162=(\bar\eta,\psi)+(\bar\psi,\eta)+\mathcal{g}[\bar\eta,\eta]$ ] , which is the legendre transform @xmath163 $ ] and the field arguments in @xmath47 are given by @xmath164 and @xmath165 .
note that we use @xmath166 for both , the fields in the micrscopic action as well as for the field arguments of the effective action for notational convenience .
the modification of the microscopic action by means of the regulator function , cf .
eq . , in the action entering the functional integral yields the scale - dependent effective action @xmath167 .
the functional flow equation for this version of the effective action is obtained upon the variation of @xmath167 with respect to @xmath38 and reads @xmath168 = & - ( { \bar{\psi}},\dot{g}_0^{-1 } \psi ) \nonumber\\ & - \frac{1}{2 } \text{tr } \left ( ( \mathbf{\dot{g}}_0^{{\lambda}})^{-1 } \left ( \mathbf{{\gamma}}^{(2){\lambda}}[{\bar{\psi}},\psi ] \right ) ^{-1 } \right)\,,\end{aligned}\ ] ] where ( @xmath169 and @xmath170 = \left ( \begin{array}{cc } \frac{\partial^2 { \gamma}^{{\lambda}}}{\partial { \bar{\psi}}\partial \psi } & \frac{\partial^2 { \gamma}^{{\lambda}}}{\partial { \bar{\psi}}\partial { \bar{\psi } } } \\ \frac{\partial^2 { \gamma}^{{\lambda}}}{\partial \psi \partial \psi } & \frac{\partial^2 { \gamma}^{{\lambda}}}{\partial \psi \partial { \bar{\psi } } } \end{array } \right)\,.\ ] ] the initial condition at the scale @xmath171 reads @xmath172 , where @xmath171 is typically chosen as the bandwidth of the model . in the limit
@xmath173 one successively integrates out all fermionic fluctuations and obtains the full quantum effective action .
we expand the effective action @xmath167 in fields , @xmath174&=\sum_{i=0}^{\infty}\frac{(-1)^i}{(i!)^2}\sum_{\substack{k_1, ... k_i \\ k_1^\prime, ... k_i^\prime}}\gamma^{(2i)\lambda}(k_1^\prime, ... k_i^\prime , k_1, ... k_i)\nonumber\\ & \quad\quad\quad\quad\times\bar\psi(k_1^\prime) ... \bar\psi(k_i^\prime)\psi(k_i) ... \psi(k_1)\,,\end{aligned}\ ] ] and insert it into the flow equation .
then one obtains an infinite hierarchy of flow equations for the 1pi vertex functions . to use these equations in applications and integrate the flow equations
numerically one has to truncate the tower of equations at a certain level and employ approximations . for our analysis
we follow the rg - scale dependence of the two - particle interaction @xmath175 only , which carries spin indices @xmath176 and a multi - index @xmath51 gathering matsubara frequencies @xmath52 as well as wavevectors @xmath34 and the band index @xmath36 . for our spin - rotation invariant system , we can write the two - particle interaction as @xmath177 where we have suppressed the @xmath178 and introduced the effective interaction vertex @xmath179 .
the flow equation for the vertex is given in eq . and
the particle - particle channel the explicitely reads @xmath180 with @xmath181 .
the direct and crossed particle - hole channels are given by @xmath182\,,\\ \phi_{\text{ph , cr } } & = \operatorname*{\mathchoice { \ooalign{$\displaystyle\sum$\cr\hidewidth$\displaystyle\int$\hidewidth\cr } } { \ooalign{\raisebox{.14\height}{\scalebox{.7}{$\textstyle\sum$}}\cr\hidewidth$\textstyle\int$\hidewidth\cr } } { \ooalign{\raisebox{.2\height}{\scalebox{.6}{$\scriptstyle\sum$}}\cr$\scriptstyle\int$\cr } } { \ooalign{\raisebox{.2\height}{\scalebox{.6}{$\scriptstyle\sum$}}\cr$\scriptstyle\int$\cr } } } v^{{\lambda}}(k , k_2,k_3,b')l^{{\lambda}}(k , q_{\text{cr}})v^{{\lambda}}(k_1,q_{\text{cr}},k , b_4)\,,\label{eq : phc}\end{aligned}\ ] ] and we define @xmath183 , @xmath184 and @xmath185 .
@xmath186 denotes the are of the first brillouin zone and the loop kernel reads @xmath187\ ] ] with the free propagator @xmath188 due to the neglect of the self - energy .
instead of the momentum cutoff , cf .
eq . , the temperature @xmath189 can also serve as a flow parameter@xcite . in this scheme ,
the complete temperature dependence is shifted into the quadratic part of the action by rescaling the fields providing a modified regularized propagator , @xmath190 the structure of the flow equations , eqs .
, and , remains the same , for details see ref . .
we used the temperature cutoff scheme to test the reliability of our results upon variation of the cutoff procedure .
our results are stable with respect to variations of the regulator scheme . | arxiv |
Wallon-Cappel (niederländisch: Waalskappel) ist eine Gemeinde im französischen Département Nord in der Region Hauts-de-France. Sie gehört zum Kanton Hazebrouck (bis 2015: Kanton Hazebrouck-Nord) im Arrondissement Dunkerque. Sie grenzt im Nordwesten an Staple (Berührungspunkt), Hondeghem im Norden, Hazebrouck im Osten, Morbecque im Süden, Sercus im Südwesten und Lynde im Westen. Die Bewohner nennen sich Wallon-Cappelois.
Bevölkerungsentwicklung
Sehenswürdigkeiten
Siehe auch: Liste der Monuments historiques in Wallon-Cappel
Kapelle Notre Dame de Consolation
Kirche Saint-Martin
Literatur
Le Patrimoine des Communes du Nord. Flohic Editions, Band 1, Paris 2001, ISBN 2-84234-119-8, S. 854–855.
Weblinks
Ort in Hauts-de-France
Ersterwähnung 1149 | slim_pajama |
Is there proof gravity bends space or is it just the most convenient explanation? [duplicate]
**This question already has answers here**:
[General relativity: is curvature of spacetime really required or just a convenient representation?](/questions/159171/general-relativity-is-curvature-of-spacetime-really-required-or-just-a-convenie)
(3 answers)
Closed 3 years ago.
I have read this sentence in an [article](http://www.nature.com/news/the-quantum-source-of-space-time-1.18797):
>
> The theory [of general relativity] holds that gravity is geometry: particles are deflected when they pass near a massive object not because they feel a force, said Einstein, but because space and time around the object are curved.
>
>
>
Do we have a physical evidence that this is in fact true? By evidence I mean stronger explanation than just [Occam's Razor](http://en.wikipedia.org/wiki/Occam%27s_razor), that dictates that bent curvature of space is more plausible/shorter/elegant explanation than let's say gravitational pull being mediated by graviton particle?
**EDIT: I understand now that my question does not make the sense I thought it did. Gravity explained by a force between two objects manifests differently than gravity explained by curvature of space and we have measured the difference. Maybe the first part of my question may be of some interest - whether there are other indication of curved space - but I understand now it is the ONLY valid metaphor we have.**
I found the Weinberg passage, but to quote it I need to do it in an answer (too long). So here it goes.
>
> We have seen in this chapter that the nonvanishing of the tensor $R\_{\lambda \mu \nu \kappa}$ is the true expression of the presence of a gravitational field. We also saw in Chapter 1 that Gauss was led to introduce the Gaussian curvature $K = -R/2$ as the true measure of the departure of a two-dimensional geometry from that of Euclid, and that Riemann subsequently introduced the curvature tensor $R\_{\lambda \mu \nu \kappa}$ to generalize
> the concept of curvature to three or more dimensions. It is therefore not surprising
> that Einstein and his successors have regarded the effects of a gravitational field
> as producing a change in the geometry of space and time. At one time it was even
> hoped that the rest of physics could be brought into a geometric formulation, but
> this hope has met with disappointment, and the geometric interpretation of the
> theory of gravitation has dwindled to a mere analogy, which lingers in our language
> in terms like "metric," "affine connection," and "curvature," but is not otherwise
> very useful. The important thing is to be able to make predictions about images
> on the astronomers' photographic plates, frequencies of spectral lines, and so on,
> and it simply doesn't matter whether we ascribe these predictions to the physical
> effect of gravitational fields on the motion of planets and photons or to a curvature
> of space and time. (The reader should be warned that these views are heterodox
> and would meet with objections from many general relativists.)
>
>
>
I could complement what Weinberg said, but... Well, I don't see why. I think it's pretty clear and awesome.
There is no %100 proof in science; at least not for good science. It's always a question of being the most accurate / descriptive / useful theory. For example, Newtonian gravity is 'true' to the extent that it is very effective in a huge diversity of situations. General Relativity (GR) includes all of the accuracies of Newtonian Gravity, and then also explains a huge variety of additional phenomenon where Newtonian Gravity fails. [We think that there are places where GR is incomplete: when you need to also describe things on the quantum mechanical scales](https://en.wikipedia.org/wiki/Theory_of_everything). There are also some quirks about the 'dark sector' ([Dark Matter](https://en.wikipedia.org/wiki/Dark_matter), and [Dark Energy](https://en.wikipedia.org/wiki/Dark_energy)) that we don't really understand. But, for all intents-and-purposes, GR can satisfactorily explain all observed gravitational phenomenon, including a wide variety of ['Tests of GR'](https://en.wikipedia.org/wiki/Tests_of_general_relativity) --- which, very importantly, ***no other theory is able to do***.
At the same time, the description of gravity through General Relativity is intrinsically that of 'curved' spacetime. The '[metric](https://en.wikipedia.org/wiki/Metric_tensor_(general_relativity))' of GR is fundamentally, and inextricably, a description of the very geometry of 3+1 spacetime which, purely from that, describes all of the resulting gravitational dynamics. A GR description is effectively synonymous with a curved-space-time description. To my knowledge, this is also unique to GR. Thus, by demonstrating the accuracy of GR, the validity of viewing gravity as curved spacetime is demonstrated. As described in this first paragraph, this should still subject to the same interpretation that this is currently the best description of observable properties of the universe.
**Tests of General Relativity** (brief summary, see wikipedia for details)
--------------------------------------------------------------------------
* "Perihelion Precession of Mercury" (dynamics) : Mercury's orbit is not perfectly closed ellipses, but instead 'precesses' (rotates slightly). The exotic dynamical effects have also been [observed by space missions](https://en.wikipedia.org/wiki/Gravity_Probe_B), and in the [dynamics of stars moving near the massive black-hole in our galactic center](https://en.wikipedia.org/wiki/Sagittarius_A*#Central_black_hole).
* "Deflection of light by the sun" (lensing) : the path of light is observed to be deflected by massive objects. This was observed in the light of single stars moving behind the sun, but has since been extended to examples of [completely distorted or duplicated images of galaxies](https://en.wikipedia.org/wiki/Strong_gravitational_lensing), or [subtle statistical effects to large fields of distant galaxies](https://en.wikipedia.org/wiki/Weak_gravitational_lensing). The cause of the deflection (as read by GR) is very literally *curvature of spacetime* --- causing all objects (even photons, without rest-mass) to be deflected.
* "Gravitational Redshift" (light travel) : The frequency of light is 'redshifted' as it changes it's depth in gravitational potential wells. Similarly, [the delaying effects of *warped spacetime* have long been observed](https://en.wikipedia.org/wiki/Shapiro_delay), and is a [very important component of how GPS works](http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html).
* Binary Pulsar (Gravitational Waves) : The orbital decay of the ['Hulse-Taylor' Binary-Pulsar](https://en.wikipedia.org/wiki/PSR_B1913%2B16) is consistent with the emission of gravitational waves to an *incredible* precision, and won a Nobel prize. Gravitational waves are, very literally, traveling ripples in space-time which are able to carry energy.
* Cosmology : The expansion of space, and especially inflation, fit very nicely and naturally into the GR context --- because it describes the space-time itself, explicitly, instead of only the objects inside of it. The only alternative explanations we have for these observations are *extremely* convoluted - and require many different tools for different regimes (i.e. changing mass/light-speed etc may *kind-of* explain expansion observations, but you need something else to explain homogeneity and yet another thing for the horizon or monopole problem, etc). This is another example of a *dynamic, flexible spacetime* being employed.
In the very near future we expect to *directly* detect gravitational waves using [Pulsar Timing Arrays](http://www.ipta4gw.org/) and [ground-based Laser Interferometers](http://www.ligo.org/). This would be a 'nail in the coffin' for interpretation of gravity as spacetime.
There's a very real phenomenon called 'Gravitational Lensing', in which light is bent from its original trajectory by a massive enough cluster of matter (which curves the space-time around it). Moreover, it's bent by a different amount than predicted by a simply application of Newtonian ideas, as kindly pointed out by Rob Jeffries.
Is this evidence enough? =]
<https://en.wikipedia.org/wiki/Gravitational_lens>
One must distinguish between the common meaning of curvature (called extrinsic curvature) from the mathematical meaning of curvature used in general relativity (intrinsic curvature). Intrinsic curvature can *sometimes* be represented as extrinsic curvature, but generally speaking this is unhelpful, and it is unfortunate that popular accounts tend to focus on this kind of representation.
Intrinsic curvature does not imply that anything is "bent" in the usual sense. It means that the theorems of Euclidean geometry do not apply to space, and those of special relativity do not apply in spacetime (except in local approximation).
We can see the truth of this by recognising the daily fact that clocks on GPS satellites do not keep time with identical clocks on Earth. The laws of physics are the same on GPS satellites as they are on Earth, so the local speed of light is the same on a GPS satellite as on Earth. It follows that the metre is affected, and that the circumference of the satellites orbit cannot be exactly $2\pi R$, as would be the case for a circular orbit in Euclidean geometry. This is precisely what we mean by intrinsic curvature.
Science does not allow us to be sure of what things **are**, but rather of **what will happen**: scientific knowledge, and "truth", is about *consequences*, *implications*, and *relations* more than it is about "what things really are".
The purpose of building theories is to try and describe *patterns of cause and consequence*, so that we may extrapolate them to domains where we have not yet explored and/or better understand how that what we get when we do explore those domains relates to what we have already explored. That is, so that we can ask a question of the form "what will be the consequence if I do X?" and be able to have a trustworthy answer even without necessarily actually going and doing X (which may not be feasible).
Hence while it's common to hear it, ideas that there are "true" and "false" theories aren't really correct: there's only *better* and *worse* theories in terms of being able to cover a larger domain and make fewer incorrect inferences regarding those consequences - but no theory can be assured of capturing everything for the totality of all empirical investigations is only ever going to be finite. It is entirely possible (though we have no *a priori* reason to *assume*) that, say, the model of things as "spacetime" actually fails if you could somehow manage to "get over the cosmic horizon" - or even just if we were to set out suitably long into space *now*. It is possible that subatomic particles may *really* be little gnomes. It's just that there isn't anything unambiguous to be gained in terms of extrapolating the patterns of consequences we see.
You can also think of it as a form of "data compression" that we perform using our intelligence: a theory *compresses* a large sum of empirical data - perhaps imperfectly - into a small, cogent set of generating rules. Indeed, this is how proper, dumb, data compression algorithms work: they try to find patterns they can use to shrink the size of a piece of input data. And just as with data compression, the more fidelity and more data they can get while still retaining a reasonable size output, the better. But the compression is not unique: different algorithms may produce very different compressed outputs, and likewise there may be a variety of very different theories that we can use for "compressing" what we have now.
Hence, if there's anything that science does say about "what things are", it's that they *are*, in fact, compressible as such with such good fidelity.
So back to the question - does "space" get "bent" by gravity or not? Well, space - or more properly *space-time* - is a *human construct*, an intellectual construct, or a social construct: it's something that we humans made up to try and compress our empirical data and it works pretty well and lets us extrapolate those consequential relations. In that regard, its behavior is fully defined by the theory we construct, so the answer to your question is **yes**, gravity bends - or better - *is* a bending of - spacetime, because that is part of what "spacetime" as we've defined it, and found makes it useful in this regard, *is.* **And** it's also the most *widely-applicable* such construct we have so far - but not necessarily the most convenient or most useful: in day-to-day work, the simpler Newtonian system is entirely adequate.
The post by Dilithium Matrix is rather helpful and fairly informative if what you truly care about here is the epistemological (experimental) value of general relativity. No physicist should be too worried about the experimental falsification of general relativity given the many numerous experiments that have been conducted in which it passed with flying colors. If your concern was more about the coherency of the mathematics then any mathematician worth their degree would of found that discrepancy in the mathematics long by now.
What you really care about seems to be the interpretation of the theory in question which is closer to a philosophical question than it's a physics one (though physics and philosophy frequently overlap). There has been a long history among philosophers and physicist who have discussed the reality of space-time as well as the relationship of that discussion to more modern theories such as general or special relativity. There have been philosophers in regards to general relativity who have argued both ways in how to interpret general relativity whether there **really** is an existent spacetime that curves or if its a more complex set of relationships between material particles. The most I could glean from these discussions was that it was indeterminate whether we should interpret general relativity in such a way that spacetime exists and explains the motions of material objects or it does not exist but it's the physical relations between material objects that gives raise to this phenomenon.
Here is an encompassing book [here](http://strangebeautiful.com/other-texts/earman-world-enough.pdf) which outlines that discussion both historically but also in regards especially to general relativity. Here is a post from [stanford encyclopedia of philosophy](https://plato.stanford.edu/entries/spacetime-theories/) which also covers this discussion up to even a more recent investigation into dynamics without getting too preoccupied with the mathematics.
Sincerely, a college freshman going on sophomore year
| stackexchange/physics |
Biografia
Nato a Leeds, nello Yorkshire, studiò alla Harrow School, dove ha avuto per i contemporanei Lord Byron e Robert Peel. Dopo aver terminato gli studi, trovò impiego nell'ufficio di un avvocato a Calne nel Wiltshire, rimanendo lì fino al 1807 circa, quando tornò a Londra per studiare legge. Alla morte di suo padre, nel 1816, divenne proprietario di una piccola proprietà e subito dopo entrò in società con un avvocato; ma nel 1820 la società fu sciolta e iniziò a scrivere con lo pseudonimo di "Barry Cornwall".
Dopo il suo matrimonio nel 1824 con la signorina Skepper, figlia della signora Basil Montague, tornò alla sua professione di avvocato immobiliarista, iscritto all'ordine nel 1831. L'anno seguente fu nominato commissario metropolitano per i malati psichiatrici, incarico rinnovato annualmente fino alla sua elezione come uno dei Commissari in Lunacy costituiti dal Lunacy Act del 1845. Si dimise nel 1861.
La maggior parte dei suoi versi fu composta tra il 1815, quando iniziò a contribuire alla Gazzetta letteraria, e il 1823, o al più tardi nel 1832. Anche sua figlia, Adelaide Anne, fu poetessa.
Charles Lamb, critico forze non del tutto imparziale, elogiò al massimo i Dramatic Sketches del suo amico, affermando che se li avesse trovati come manoscritti anonimi nella Collezione Garrick non avrebbe avuto alcuna esitazione a includerli nei suoi Dramatic Specimens. Le canzoni di "Barry Cornwall" hanno catturato alcune note dai testi elisabettiano e cavalier e le hanno mescolate con altre dei principali poeti del suo tempo; e i suoi drammatici frammenti mostrano un'infusione simile del primo spirito vittoriano in forme e cadenze pre- restaurazione. I risultati sono vari e mancano di unità, ma abbondano di tocchi piacevoli, con qua e là il lampo di un'ispirazione più alta, sebbene casuale.
Quasi sconosciuto al di fuori della Gran Bretagna ai suoi tempi e considerato in gran parte come un imitatore di maggiori autori romantici, Barry Cornwall ispirò comunque Aleksandr Puškin ad alcune traduzioni e imitazioni nel 1830. Poche ore prima del suo ultimo duello nel 1837 Puškin inviò una raccolta di Cornwall ad una collega autrice, la signorina Išimova, suggerendole di tradurre alcune poesie da lui selezionate.
William Makepeace Thackeray dedicò La fiera delle vanità a BW Procter. Wilkie Collins ha dedicato La donna in bianco a BW Procter.
Opere
Le sue principali opere poetiche furono: Dramatic Scenes and other Poems (1819), A Sicilian Story (1820), Marcian Colonna (1820), Mirandola (una tragedia rappresentata nel 1821 al Theatre Royal di Covent Garden con William Charles Macready, Charles Kemble e Miss Foote nelle parti principali), The Flood of Thessaly (1823) e English Songs (1832).
Fu anche autore di Effigies poetica (1824), Life of Edmund Kean (1835), Essays and Tales in Prose (1851), Charles Lamb; a Memoir (1866), e di memorie di Ben Jonson e William Shakespeare per le edizioni delle loro opere.
Un frammento postumo autobiografico con note dei suoi amici letterari, un'ampia rappresentanza da William Lisle Bowles a Robert Browning, fu pubblicato nel 1877, con alcune aggiunte di Coventry Patmore.
Note
Altri progetti
Collegamenti esterni
Works by or about Barry Cornwall
Works by or about Bryan Waller Procter
Works by Bryan Procter
"Marcian Colonna: una storia italiana; con tre scene drammatiche e altre poesie", 1821, su Internet Archive.
"Second only to Byron" : un saggio su "Barry Cornwall" e Keats di TLS, 3 settembre 2008. | slim_pajama |
bayes theorem ( 22 ) links the probability of an event happening given a particular circumstance with the unconditional probability of the same event and the conditional probability of the circumstance given the event .
if the event of interest is a particular cause of death , and the circumstance is part of the events leading to death , then bayes theorem can be applied in terms of circumstances and causes of death .
specifically , if there are a predetermined set of possible causes of death c1 cm and another set of indicators i1 in representing various signs , symptoms and circumstances leading to death , then bayes general theorem for any particular c
i and i
j can be stated as : p(ciij)=p(ijci)p(ci)p(ijci)p(ci)+p(ij!ci)p(!ci )
where p(!ci ) is ( 1p(ci ) ) . over the whole set of causes of death c1
so that the total conditional probability over all causes totals unity : p(ciij)=p(ijci)p(ci)i=1mp(ci )
using an initial set of unconditional probabilities for causes of death c1 cm ( which can be thought of as p(cii0 ) ) and a matrix of conditional probabilities p(ijci ) for indicators i1 in and causes c1 cm , it is possible to repeatedly apply the same calculation process for each i1 in that applies to a particular death : p(cii1 n)=p(ijci)p(cii0 n-1)i=1mp(cii0 n-1 )
this process typically results in the probabilities of most causes reducing , while a few likely causes are characterised by their increasing probabilities as successive indicators are processed .
interva-4 aims to be a tool for interpreting va data which can be applied simply , quickly and cheaply to generate cause of death data , compatible with the international classification of diseases version 10 ( icd-10 ) .
it offers the consistency and reproducibility that is characteristic of mathematical models and thus facilitates comparisons of va cause of death between different places and over time .
furthermore , as a public - domain resource it is freely available and runs on any windows - based personal computer , or under the mac os as a virtual windows instance .
it builds on experience with previous interva models but brings a new standard of va interpretation by conforming to the 2012 who va instrument in terms of cause of death categories and input indicators .
indicators relating to durations in the who instrument are split into pre - defined categories for processing in interva-4 .
tables of cause of death categories and input indicators from the 2012 who va instrument as handled by interva-4 are included in the interva-4 user guide ( supplementary material ) . for deaths among women of reproductive age ,
a separate sub - model is incorporated which uses exactly the same methodology over three pregnancy status outcomes to assess the likelihood of pregnancy being associated with the death ( but not necessarily in a causal sense ) .
this was previously implemented in interva - m and is important in cases where pregnancy status at death may be ambiguous in the va data ( 16 ) .
apart from the mathematics , the major challenge in building a probabilistic model covering all causes of death to a reasonable level of detail lies in populating the matrix of conditional probabilities p(ijci ) .
there is no overall source of data available which systematically quantifies probabilities of various signs , symptoms and circumstances leading to death in terms of their associations with particular causes .
therefore , these conditional probabilities have to be estimated from a diversity of incomplete sources ( including previous interva models ) and modulated by expert opinion . in the various versions of interva that have been developed ,
expert panels have been convened to capture clinical expertise on the relationships between indicators and causes ( 23 ) . in this case ,
an expert panel ( dc , ah , sh , ak , kk ) convened in geneva in december 2011 and continued to deliberate subsequently , particularly considering issues that built on previous interva versions . experience has shown that gradations in levels of perceived probabilities correspond more to a logarithmic than linear scale ( 24 ) , and in the expert consultation for interva-4 , we used a perceived probability scale that was subsequently converted to numbers on a logarithmic scale as shown in table 1 .
this was similar to scales used previously but was extended into additional low probability categories .
we have also demonstrated by means of sensitivity analyses within the probability matrix that although the conditional probability values are important , the model does not require a high level of precision for these estimates ( 25 ) .
qualitative probability scale used as the basis for eliciting expert opinion on probabilities as was the case in interva-3 ( 5 ) , there are special arrangements for two causes of death ( hiv / aids and malaria ) , the occurrences of which vary appreciably in different locations . as described in the interva-4 user guide , the model has a facility for setting the unconditional probabilities for each of these causes to reflect their occurrence in a particular population .
conceptually , this is analogous to a physician 's background knowledge of local disease profiles , irrespective of the details of a particular case . in the new model ,
the setting for malaria is also applied to the unconditional probability for deaths due to sickle cell disease , because of the genetically determined geographical overlap between the two diseases ( 26 ) .
having experienced difficulties in previous versions of the software with proprietary data file formats , which tend to change in unpredictable ways over time , interva-4 has reverted to text with comma - separated values ( csvs ) for data input and output , as the lowest common denominator in file formats .
csv data can be relatively easily read and written by most analysis software packages , and examples of stata scripts for generating interva-4 input and processing output from interva-4 in a standard way , deriving cause - specific mortality fractions ( csmfs ) , are included in the user guide .
n ) for causes c1 cm for each case , methods have to be applied for interpreting the output in ways that make sense from medical cause of death and public health perspectives . in the interests of transparency
n ) data grid for all causes and cases in a batch as a csv file .
however , this is not a very convenient format for routinely analysing cause of death data ; hence , the interva-4 software also undertakes basic post - processing of the basic cause of death data into a more readily useable format .
although experience shows that the majority of cases arrive at a single overwhelmingly likely cause , some cases , particularly if there is scanty or somewhat contradictory information available , may end up with two or three causes of comparable likelihood .
this is analogous to a physician 's differential diagnosis in which ambiguity remains between multiple likely causes . in a further minority of cases ,
there is no high likelihood cause , amounting to no clear conclusion on cause of death . to handle all this in a standardised way
, interva-4 post - processes likely cause data in the same way that we have previously discussed in relation to interva-3 ( 5 ) .
if no single cause has a final likelihood of at least 0.4 , the cause of death is considered to be indeterminate .
the 0.4 cut - off is considerably higher than the unconditional probability of any cause , and conceptually includes a level approaching a 50:50 possibility for a particular cause , while leaving scope for other likely causes to be included in the overall consideration of the case .
multiple causes are only reported if they reach half of the likelihood of the leading cause .
any residual margin of likelihood not accounted for by the likelihood of the first and , where applicable , second and third causes can then be considered as a partial indeterminate component in analysing overall cause of death and csmf patterns .
we suggest that this is a much more appropriate approach than aggregating the sums of small residual probabilities of unlikely causes , which can lead to misleading results over large numbers of cases .
since an important part of the objectives behind this model is to extend the use of va into routine death registration procedures , additional non - medical questions about circumstances of death have been included in the 2012 who va instrument to facilitate the interpretation of cause of death in non - enumerated populations .
although these are not in any way intended to replace the developing role of social autopsy ( 27 ) , future developments in describing and modelling non - medical factors associated with cause of death are anticipated and will be reflected in future developments of interva .
as with any software tool , one of our aims in developing this new version of interva was to improve the scope of the tool and address known shortcomings of the previous version .
the differences between interva-3 and interva-4 are considerable , even though the same basic mathematical model lies at the heart of both versions .
both the range of causes of death and the scope of input indicators are considerably expanded in the new version and brought into line with the 2012 who va instrument , but this makes a direct and meaningful comparison between the versions difficult . to demonstrate the similarities and differences , we have taken a random sample of 1,000 cases from the agincourt , south africa , dataset previously analysed ( 5 ) .
these cases have been run with the interva-3 and interva-4 models , but without adding data for the additional interva-4 indicators .
age - specific csmfs from both models for these same 1,000 cases are shown in table 2 .
this demonstrates the more detailed classification of neoplasms in the new model , as well as the detailed maternal causes brought in from interva - m .
this illustrative dataset included 44/62 of the 2012 who va instrument possible causes of death .
comparison of age- and cause - specific mortality fractions ( csmf ) using the interva-3 and interva-4 models on 1,000 randomly selected va records from a previous analysis of data in agincourt hdss , south africa ( 12 )
these demonstration data included 44/62 of the cause of death categories in the 2012 who va instrument and interva-4 .
the new interva-4 model presented here represents a substantial advance in automated cause of death modelling .
it is specifically aligned to the new who 2012 verbal autopsy instrument ( 21 ) , although it can be used retrospectively for processing archived va data , provided a reasonable spread of the necessary indicators are available .
it offers the advantages of standardised interpretation over time and place ; is freely available as a public - domain resource ; and on a typical computer can process around 10,000 cases per hour .
these attributes mean that it offers new opportunities for cause of death data to be gathered routinely in settings where hitherto there have been few or no such records and where physicians to assess vas are few .
the speed of processing can yield cause of death information with the potential to feed into local and national health policy development in a timely fashion .
standardised assessment means that trends in causes of death can be tracked over time and can be compared across different settings .
we have previously shown that using a standard model across a wide range of settings yields appreciably different , and plausible , cause of death profiles ( 28 ) .
the potential disadvantage of using any mathematical model for interpreting cause of death is that some subtlety and nuance may be lost as compared to routine physician certification of cause of death ( either from attending physicians or from physicians coding individual va cases ) .
it is certainly true that mathematical models will fail to identify very unusual or complex causes of death .
however , such cases tend to be of more local or esoteric interest rather than contributing significantly to the public health understanding of population mortality patterns .
va is normally used in settings where other sources of information on circumstances of death are lacking , precluding many direct comparisons .
the va interview stage carries inherent uncertainty as the quality of information obtained depends on a variety of factors including relationship of respondent to deceased , knowledge of signs and symptoms during terminal illness , recall and willingness to disclose information , especially for conditions that are stigmatised or have culturally sensitive connotations ( 29 ) .
the absolute validity of deaths certified by attending physicians is by no means a given , and studies have shown considerable inconsistencies between hospital causes of death and pathologists findings ( 30 , 31 ) . the validity of physician interpretation of va material has also been shown to be questionable ( 3 ) and subject to inter - observer variation ( 12 ) .
it is also clear that any approach to va data must involve some degree of capturing expert opinion , alongside the use of established information ( 32 ) .
previous interva models have been extensively evaluated against local physician interpretations , with generally concordant findings ( 5 , 7 , 10 , 12 , 14 , 15 ) .
one evaluation suggested that interva-3 did not perform well against va data from tertiary health facilities ( 33 ) , but those data were not available for further study .
nevertheless , certain shortcomings have been identified in interva-3 , including over - diagnosis of meningitis , under - diagnosis and lack of differentiation between various cancers , and fairly high levels of indeterminate cases .
interva-4 is designed to handle these more effectively , and we will continue to explore realistic opportunities for further validations .
the comparison between interva-3 and interva-4 demonstrated in table 2 says nothing about the absolute validity of either model or about the mortality profile in the agincourt population .
it does demonstrate , however , the general continuity in results between the two versions of the model , when using exactly the same input data , as well as evidence of deliberately introduced changes in response to some of the shortcomings identified in interva-3 .
this comparison does not necessarily make the most of some of the new aspects of interva-4 , since data for new indicators were not included in order to demonstrate continuity
. we will continue to make interva-3 and interva - m available as legacy downloads , but we recommend the use of interva-4 wherever possible .
it offers substantial benefits over the default situation of not routinely capturing cause of death data ( which is the de facto standard in many resource - limited parts of the world ) , considerable improvements over previous versions and the ability to more reliably compare causes of death across different settings and over time .
this is important for research , for example , as indepth cross - site research accelerates ( 20 ) , and also offers new opportunities for cause - specific civil registration of deaths on a much wider scale .
work is in progress on a portable electronic version of the model which will be particularly useful for routine registration . in the longer term
, there will undoubtedly be further evaluations and developments as the science and methods of attributing cause of death improve
. we will continue to work with old and new collaborators on further refinements in this process .
the authors have not received any funding or benefits from industry or elsewhere to conduct this study . | pubmed |
Lester Ryan born 1 May 1988 is an Irish hurler who plays as a midfielder for the Kilkenny senior team.
Born in Clara, County Kilkenny, Ryan first arrived on the inter-county scene when he first linked up with the Kilkenny under-21 team, before later joining the intermediate side. He joined the senior panel for the 2011 championship. Ryan has since become a regular member of the team and has won four All-Ireland medals, four Leinster medals and four National Hurling League medals. He captained the team to the All-Ireland title in 2014.
At club level Ryan is a one-time championship medallist at senior level with Clara. In addition to this he has also won All-Ireland, Leinster and championship medals in the intermediate grade.
Ryan's uncles, Lester and Harry Ryan, also played with Kilkenny.
Playing career
Club
Ryan was just out of the minor grade when he enjoyed his first success with the Clara intermediate hurling team in 2007. A 115 to 012 defeat of St. Lachtain's in the championship decider gave him his first winners' medal in that competition.
Five years later in 2012, Ryan added a second intermediate championship medal to his collection following a 17 to 04 defeat of St. Patrick's Ballyragget. Clara subsequently faced Oylegate/Glenbrien in the provincial decider. An incredible game followed, which saw Oylgate having four men dismissed for second-yellow card offences. Clara powered to a 320 to 05 victory, with Ryan collecting a Leinster medal. The subsequent All-Ireland decider saw Clare face London-based St. Gabriel's. Clara were convincing 116 to 011 winners, with Ryan picking up an All-Ireland Intermediate Club Hurling Championship medal.
A year after making the step up to the top flight, Clara faced hot favourites Carrickshock in the senior championship decider in 2013. With four minutes of normal time left, Carrickshock looked the likely winners as they went two points ahead. Clara then won a free with just four minutes left. Ryan took the ball off regular free-taker Keith Hogan and decided to go for goal. Ryan fired to the net from 20 metres with a style similar to Anthony Nash. Two minutes later he popped over a point to extend Clara's lead. A 115 to 210 victory gave Ryan his first championship medal in the senior grade.
Inter-county
Ryan made his first impression on the inter-county scene in 2008 as a member of the Kilkenny under-21 team. He won his first Leinster medal that year as Kilkenny trounced Offaly by 221 to 29. Ryan later added an All-Ireland Under-21 Hurling Championship medal following a 213 to 015 defeat of Tipperary in the decider.
Kilkenny retained the provincial under-21 crown in 2009 following a 220 to 119 defeat of Dublin, giving Ryan a second Leinster medal in that grade. Kilkenny subsequently had the chance to retain the All-Ireland crown, however, Ryan's side faced a narrow 015 to 014 defeat by first time champions Clare.
Ryan joined the senior team after the 2011 National Hurling League and was a member of the panel for the subsequent Leinster and All-Ireland victories.
The 2012 National Hurling League was Ryan's first full campaign with the Kilkenny senior team, however, a knee cartilage injury after the first two rounds resulted in him facing a month-long lay-off. He was later restored to the starting fifteen and was once again a member of the panel as Kilkenny claimed All-Ireland honours.
Ryan was a regular member of the starting fifteen in 2013. He won a National Hurling League medal on the field of play that year as Kilkenny defeated Tipperary by 217 to 020. He finished off the campaign by being named GAA-GPA Hurler of the League. Ryan made his senior championship debut on 9 June 2013 in a 026 to 49 defeat of Offaly.
In February 2014 Ryan was appointed captain of the Kilkenny senior hurling team. In the League Final he was introduced as a substitute during the team's 225 to 127 extra-time defeat of Tipperary in the final. It was his second National League medal while he also had the honour of lifting the cup. He made a number of appearances in the championship, including in Kilkenny's 024 to 19 trouncing of Dublin in which he claimed his first Leinster medal on the field of play. On 7 September 2014, Kilkenny faced Tipperary in the All-Ireland decider. In what some consider to be the greatest game of all-time, the sides were level when Tipperary were awarded a controversial free. John O'Dwyer had the chance to win the game, however, his late free drifted wide resulting in a draw. The replay on 27 September 2014 was also a close affair. Goals from brothers Richie and John Power inspired Kilkenny to a 217 to 214 victory. It was Ryan's third All-Ireland medal, while he also had the honour of lifting the Liam MacCarthy Cup.
Honours
Team
Clara
Kilkenny Senior Club Hurling Championship 2: 2013, 2015
All-Ireland Intermediate Club Hurling Championship 1: 2013
Leinster Intermediate Club Hurling Championship 1: 2012
Kilkenny Intermediate Club Hurling Championship 2: 2007, 2012
Kilkenny
All-Ireland Senior Hurling Championship 4: 2011, 2012, 2014, 2015
Leinster Senior Hurling Championship 4: 2011, 2014, 2015, 2016
National Hurling League 4: 2012, 2013, 2014 c, 2018
Walsh Cup 1: 2012
All-Ireland Under-21 Hurling Championship 1: 2008
Leinster Under-21 Hurling Championship 2: 2008, 2009
Leinster
Interprovincial Championship 1: 2014
Individual
Awards
GAA-GPA Hurler of the League 1: 2013
References
Category:1988 births
Category:Living people
Category:Clara hurlers
Category:Kilkenny inter-county hurlers
Category:Leinster inter-provincial hurlers
Category:All-Ireland Senior Hurling Championship winners | wikipedia |
Kingdom Hearts, Sailor Moon 1. Surprises and more surprises
First of all, let me just assure you that I do not own Sailor Moon or Kingdom Hearts, or any of their characters. For those of you who ever thought how Sailor Moon and the Sailor Scouts would deal with the fact of being sucked into Kingdom Hearts world, well then, this is your lucky day. I hope you all like this story. And furthermore, to checkout illustrations from all of the Sailor Scouts dressed in Kingdom Hearts clothes, then check out Omen-of-Silverwing's webpage on DA. Well, on with the show…
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Chapter 1: Surprises and more surprises
"Kingdom Hearts. The worlds have given us this doorway. They want us to be the guardians of their destiny." (King Mickey, Kingdom Hearts II)
It was 13 pm in Tokyo. The day was sunny and the air was quite hot. In fact, it was too hot for a regular summer day, even in July. Very few people dared to be on the streets at that time of day, because the hot was almost unbearable. Still, the hot weather was not enough to keep Usagi Tsukino and her friends from meeting with each others in their usual hang out spot, Hikawa Shrine, which was also Rei's home. The white-marble floor was so hot that you could fry an egg on it. Usually, Usagi would wait for the others inside the shrine, but from some strange reason, that she could not explain, she wanted to wait for the others outside. She was leaning against a cherry-blossom tree that existed on the right side of the shrine, and next to her was her faithful feline companion, Luna, and her good friend, Rei. Usagi was wearing a blue and pale-pink cheerleader uniform, pink boots, and a pair of sunglasses. Rei, on the other hand was wearing her usual priestess clothes.
"Usagi, why do we have to wait for the others out here, in the sun?" –Rei asked her, as she waved a fan, trying to repel the hot.
"Since it's such a beautiful day, I thought it would be nice for us to wait for the rest of the gang out here." –She answered Rei with her gentle and sweet voice.
"But it's got to be like a 40ºC, Usagi! It's so hot that if I dropped an ice cube, it would melt before it touched the ground." –Rei complained.
"Rei is right, Usagi… It's quite hot. Why don't we wait for the others inside, where is fresh?" –Luna asserted, agreeing with Rei.
Usagi was about to answer to Luna, when she noticed that Ami, Makoto and Minako were climbing the staircase that lead to the shrine. Ami was wearing a white shirt, a cherry-red mini-skirt and a pair of white sneakers. On her hands, she was holding a copy of the latest book she had bought, "Quantum Physics: Mysteries of the Universe". Makoto was wearing a green sleeveless dress, which reached her knees, and a pair of black high-heel shoes. Usagi noticed that she was carrying a small package, which she hoped it was a box full of delicious treats that she had done for the group's reunion. As for Minako, she was wearing an orange tank top, a pair of jeans, a pair of orange tennis shoes and a pair of sunglasses. Accompanying them was Minako's faithful feline companion, Artemis. As soon as she saw them, Usagi waved at them.
"Girls, over here! –Usagi exclaimed.
In a matter of seconds, the girls got where Usagi and Rei were. Even though they saw each others everyday, Usagi was very happy to see them all, like if she had not seen them all in years.
"Hi, Usagi, hi, Rei, how are you today? –Ami asked, as she gave them a big hug, to which they answered that they were fine.
"Love your new look, Usagi! You look so pretty!" –Minako said, as she gave a closer look to the blonde girl's outfit.
"Really? You're sure it's not colourful?" –She asked –"I was afraid that it was too colourful, even for me."
"No, you're perfect, Usagi." –Makoto told her –"Those colours really suit you well, if you ask me. Are you trying to impress someone, besides Mamoru?" –She asked her, with a playful voice.
"Makoto, don't say that!" –Usagi exclaimed with a rather embarrassed voice-"You know that Mamoru is the only man for me. In fact, I'm counting the minutes for him to arrive… He promised me that he would meet us all here, so he should be arriving, any minute now."
"Okay, okay, I was just kidding with you…" –Makoto stated, letting out a girlish laugh, which was unusual for her, since she always tried to not show her most girlish side.
After that warm and cheerful reception, the girls all went to sit on the porch, where it was less hot, because the temperature was becoming unbearable. The sun was getting hotter by the minute. It was like if the gates of Hell had been opened, and the fiery flames that existed there were heating the air. But under the porch, it was fresh and cool, the perfect place for anyone to get out of the heat.
"It's not that I don't want to be here, Usagi, but why did you decided to call up this meeting?" –Ami asked her, as she sat down, always with her book in her hands.
"Yeah… You haven't told me either what was the occasion!"
"Well, I did not want to spoil the surprise, but, I guess I would have to tell it you soon or later… Chibiusa is coming to visit us!"
"What?!" –the four of them, including Luna and Artemis exclaimed, rather surprised with what they had heard.
"You heard me… Chibiusa is coming from the 30th century to visit us. She used the Silver Crystal to send me a message a couple of days ago, saying that she would arrive at exactly 14:30 p.m." –Usagi explained them. –"I wanted to tell you, but she made me promise that I would keep her arrival a secret."
"So that's why you were saying that today was a beautiful day to wait for them here… You were waiting to see if Chibiusa would arrive earlier than expected, weren't you?" –Rei asked Usagi.
"Okay, you got me… I was never a good liar, you all know that."
"We understand, Usagi. It'll be nice to see Chibiusa again." –Ami stated with a joyful smile in her face. –"But, have you also told Haruka and the others that she was coming to visit us?"
"Well, yes… I told them this morning about it, and from what I've heard through the phone, Hotaru was really excited about seeing Chibiusa again."
"No wonder… Those two were best friends, and will always be." –Minako said, as she grabbed Artemis and put him on her lap. –"But, where are they? If you told them that this morning, they should have arrived by now…"
Minako was not even able to finish that sentence, when they started to hear a strange noise. It sounded like something big was approaching them. Then, wind started blowing and leaves from the trees flew everywhere, like if a windmill had been magically conjured. Then, they all looked up and understood what was really going on. A white helicopter was flying up in the air. A few seconds later a rope ladder was tossed from it, and someone started climbing it down. The sun was too bright for them to see who it was at first sight, but after a couple of seconds, they all saw that it was Haruka and the rest of the girls who were coming down. The first one to reach the ground was Haruka, who was dressed in her usual tomboy outfit. She was wearing a white shirt, a pair of jeans and a pair of army boots. The second one to touch the ground was Michiru. She was wearing a beautiful floral dress and a pair of green matching high-heels. All in all, she was dazzling as always. Next, it was Setsuna who reached the ground. She was wearing a red t-shirt, black shorts and a pair of mountain-climbing boots. Finally, it was Hotaru who stepped out of the ladder. She was wearing a lavender mini-skirt, a yellow shirt, a pair of tennis shoes, and she was wearing a matching lavender bow on her head. They all smiled at the girls, as the ladder was pulled up and the helicopter got out of there, heading north.
"Only you would come up with an entrance like that one…" –Rei stated, as she got up.
"What did you expect? At least we have style." –Haruka said, as she and the others approached the group.
"Hello, girls. How are you?" –Michiru asked them with her sweet voice.
It did not take much time for all of them to start talking with each others. Haruka and Michiru were mostly quiet as always, but they participated in the talk, saying a thing or two. They quickly found out that the four of them had been travelling all over Japan, seeing the marvels that their country had to offer them, over the last months, right after the defeat of Galaxia.
"We've been in Kyoto, in Osaka, in Yokohama…" –Hotaru excitedly reported them all, showing them pictures of the places she and the rest of the girls had been.
"Looks like you've been quite busy having fun, Hotaru." –Makoto said, as she picked up a photo where you could see Setsuna and Hotaru next to each other, with Yokohama bay behind them.
Time went by, and Usagi kept looking at her watch, waiting for Mamoru to show up, but also, waiting for Chibiusa. She was getting really nervous, because Mamoru was supposed to meet them there, but he had not showed up yet. Makoto managed to leave the conversation for a moment, and went to see what was going on with Usagi. She sat right next to her, and gently put her hand in her left shoulder. With a warm smile, she said:
"What's the matter, Usagi? Is something troubling you?"
"It's Mamoru… He's taking too much to get here." –Usagi answered her. –"Do you think anything bad might happen to him?"
"Don't be ridiculous, Usagi. I'm sure he's just running a little late, that's all." –Makoto tried to cheer her up a little. –"You'll see… He'll be here in no time."
Minutes passed, and finally, at 14:30 p.m. they all waited for something to happen. At first, nothing happened, and all of them started to wonder what could have happened. Then, the sky over the temple got darker. The wind started to blow harder, like if a storm was passing through there. A bright light appeared in the middle of them, and little by little, not one, but three figures appeared. One of them as clearly Chibiusa, but the other two were complete strangers… The two strange figures were two boys, one of them from the same height and age as Setsuna, with dark spiky hair and white skin. He was wearing a pair of jeans and a red t-shirt, as well as a pair red and white of Converse-All's. As for the other one, he was the same height and age as Hotaru. He had dark hair, with a bowl cut, and he was wearing a pair of orange sneakers, black pants and an orange sleeveless shirt. As for Chibiusa, she was wearing a blue dress, with matching shoes. The group did not know how to react to that… They were waiting for Chibiusa, but they never thought that she would be accompanied, especially not by two boys.
"Hello, girls!" –Chibiusa exclaimed out loud, breaking the ice.
Usagi was the first one to hug her. She was so happy to see her, especially since it had been so long, since the two of them saw each other. A small of tear joy ran down her face, as she looked at Chibiusa. She had not changed a bit… She was taller no doubt about it, but her style had not changed a bit.
"Chibiusa, let me take a look at you… You've grown so much!" –Usagi exclaimed, as she took a closer look at the pink-haired girl.
"And you haven't changed a bit… In fact, none of you have. It's so good to see you all again."
"Hmm, aren't you going to present us your friends, Chibiusa?" –Minako asked her, as she looked at them very closely.
"Oh, I'm sorry, girls… Allow me to present you Johnny and George, they're my new bodyguards, if you can call them that. They are Sailor Pluto and Sailor Saturn" –she said, as they waved them.
"WHAT?!" –all of them chorused.
"Small Lady, I don't wish to be rude, but me and Hotaru are Sailor Pluto and Sailor Saturn." –Setsuna said with a rather confused voice and look, not understanding what was really going on there. Chibiusa hearing this let off a few laughs, and then said:
"No, no, no… You got it all wrong." –She said, between laughs. –"Maybe it's better if they tell you what is really going on."
The boys got near the group, and took a seat on the porch. The taller one took off his sunglasses and said:
"First of all, my name is Johnny Meioh and he's George Tomoe, and just like Small Lady has said, we are Sailor Pluto and Sailor Saturn… But we're not from this world. Or even better, we're not from this dimension."
"You're saying you're not from this dimension. Does that mean you came from another dimension?" –Ami asked.
"Exactly… We are from a parallel dimension." –George said, looking at Hotaru, who was trying to understand what they were saying.
"But, how did you ended up in the 30th century?" –Haruka asked them.
"In our dimension, our Sailor Mercury created a device which allowed us to cross between dimensions, and explore them. We were the first ones to use it… But, let's just say that things did not end up has we predicted." –Johnny explained. –"Our plan was to enter in your dimension for a few minutes, and then return to ours. Unfortunately, the device went 'Looney Tunes', and we ended up getting stuck in the 30th century. We contacted Queen Serenity from your dimension, and until we had any news from our dimension, we would serve as Small Lady's bodyguards."
"That means… You are me?" –Hotaru asked shyly to George.
"That's right, girl. I'm you, and you're me. Think of me as your twin brother from another dimension." –George said, as he got in front of Hotaru, noticing that they shared the same eyes.
"And, well, we also have other designations… While the two of you are Sailor Pluto and Sailor Saturn, we are Sailor Pluto FX Destroyer and Sailor Saturn Net Surfer. The reason why we have different codenames, is because in our dimension, we battle against bad guys using not only are powers, but also, every piece of modern technology that we come up with."
The entire group was astounded and confused with those explanations. Ami, Minako, Makoto and Rei, as well as Usagi seemed to accept their new colleagues, but as for Haruka and the rest of the girls, they still had their doubts about them. Luna and Artemis were also looking at them with rather suspicious looks.
"And how do we know if you're not some kind of fiends?" –Haruka asked them, giving them a really cold look.
"Your future version also gave us the same look, and asked them same thing, you know?" –George stated.
"And you know what we told her? We told her that if she didn't want to believe in our story, that was her problem, not ours… So, we give you the same answer, okay?" –Johnny said, as he looked her in the eyes. For a few seconds, their eyes kept looking onto each other.
Seeing that if they did not do anything, Haruka and Johnny would probably start fighting right over there, Usagi decided to break the tension, by reminding them why they were there, trying to smooth things a bit.
"Come on, guys. This isn't the time for us to fight… It's time to celebrate!"
Both Haruka and Johnny sighed, and silently agreed that the reason why they were there was to celebrate Chibiusa's visit. Still, what their mouths could not say out loud, their eyes could express it. They said: "We'll finish this later."
Trying to give them a chance, Setsuna and Hotaru sat next to the 'new' Sailor Scouts. Makoto decided to reveal what was inside the box she had brought with her. Inside it, there were delicious cookies that she had been baking all night, for that encounter. They all looked at the cookies and smiled, especially Chibiusa, who missed Makoto's cooking while in the 30th century, she said that although Makoto's future self was an awesome cook too, she could not surpass her.
"It's true. You're a much better cook, than your future self, Makoto." –Chibiusa stated.
"Thanks, Chibiusa, although I think it's a little bit difficult for me to accept that my future self is a worst cook than me…" –Makoto giggled, as she gave her the first cookie.
Chibiusa was just about to grab the cookie, when the earth shook for a few seconds. They all felt it, and at first thought it was just a small earthquake. But then, they all noticed that the way the earth shook, was not the same as when it is an earthquake. Then, Johnny's wristwatch started beeping out loud, and he looked at it, making a rather serious face.
"What's going on with your watch?" –Rei asked him.
"Either my watch is broken, or we got trouble." –Johnny said. –"This watch is not just a watch, it's also a device which picks up the energy from any kind of enemy that might be near, and I think that something or someone is lurking by."
Hearing this, they all concentrated and tried to figure out where danger would come from. Artemis then heard something moving in the bushes, in front of them.
"Everyone, it's coming from there!" –Artemis exclaimed.
They all looked at the bushes, and waited to see what would happen. Seconds went by, and nothing happened. They all started to think that Artemis had heard things. Still, Johnny's watch kept warning them that an enemy was near them. Tired of waiting, Luna jumped from the porch and went to investigate. She got inside the bushes, only to be thrown out of them with such force, that if it was not for Minako, she would have hit the ground pretty hard. Minako looked at Luna, and saw that she had a huge scratch on her beautiful black hair. Something or someone had attacked her, and it looked like it had no mercy to whatsoever.
"Are you alright, Luna?" –Minako asked her, as she looked at the scratch, only to see that although the scratch was huge, it was just a superficial wound.
"Over there, guys… Watch out…" –Luna
From the bushes a horrific black monster with the huge claws appeared. It was no bigger than a garden gnome, but something in it made all of them fear for their safety. His huge white eyes, showed no emotion. It had no mouth, but somehow, it could produce a strange groan, which got louder and louder. It walked on the direction of Usagi and the others.
"What is that thing?!" –Usagi asked the others.
"I don't know. I've never seen anything like it before." –Setsuna stated, as she held Hotaru close to her, wrapping both her arms around her shoulders.
"The same thing goes for us. We never saw this kind of fiend in our dimension." –George said.
"Well, whatever he is, he is not alone, guys… Look!" –Makoto exclaimed, pointing out to similar creatures that had also appeared from nowhere.
In a matter of seconds, the entire Sailor Scouts group became surrounded by these strange enemies, and although the enemies did not look like they were going to attack them, they all felt that they were dealing with something unknown, and worst, something far more dangerous, than anything they had ever faced before.
2. Transformation Time
Chapter 2: Transformation Time
Surrounded by those enemies, the Sailor Scouts did not know what to do. If they moved, the strange fiends could attack them, but if they stayed still, they would probably be attacked too. When one of the fiends got closer to them, Makoto took her chances and kicked him away; making him fly through the air like if he was a football. Then, the rest of the enemies looked at them, and charged against them, making them jump out of their way. Usagi and Chibiusa were almost caught by one of them, who tried to grab their legs, but they easily managed to get rid of them. Ami and Rei were also able to get rid of the small group of fiends that jumped on them. They tried to run, but when they thought things could not get worst, a new kind of fiend appeared. They were quite similar to the previous ones, but these were blue and black, and had some kind of armour.
"I'm not liking this." –Ami said, as she looked at the new fiends that mixed with the previous ones.
Grabbing some of the ofuda scrolls she had with her, Rei decided that those enemies might be affected by them. Targeting them, she said:
"In the name of all powerful gods, Evil spirits begone!"
With a quick and sudden hand movement, she threw all of the ofudas at the fiends, getting every one of them, who stopped for a split second. She thought that she had been able to stop them, and a smile appeared in her face for a second, only to disappear in the next second, when the fiends grabbed the ofuda that had pinned to their heads and ripped them into shreds.
"Smooth move, Miss Superstition…" –Johnny said sarcastically.
"But I don't understand. These ofudas are the most powerful ones I have, and they worked every time I use them on enemies." –Rei replied.
"These guys obviously don't know that. We need to use brute force on them!" –George exclaimed.
"I agree with what he says. They seem to be quite difficult to kill, so we'll just have to use force to get rid of them, permanently." –Haruka said, as she kicked another enemy that was getting near to her and Michiru.
"Very well, guess there is no other choice. Everyone, transform!" –Ami agreed.
"Right!" –They all chorused.
"Mercury Crystal Power Make-Up!" –Ami exclaimed.
"Mars Crystal Power Make-Up!" –Rei exclaimed.
"Jupiter Crystal Power Make-Up!" –Makoto exclaimed.
"Venus Crystal Power Make-Up!" –Minako exclaimed.
"Uranus Crystal Power Make-Up!" –Haruka exclaimed.
"Neptune Crystal Power Make-Up!" –Michiru exclaimed.
"Pluto Crystal Power Make-Up!" –Setsuna exclaimed.
"Saturn Crystal Power Make-Up!" –Hotaru exclaimed.
"Moon Eternal Power Make-Up!" –Usagi exclaimed.
"Moon Crisis Make-Up!" –Chibisa exclaimed.
The transformations released an energy wave, which swept away the fiends that were closer to the group, giving them some manoeuvre space. After the girls all transform, the two male sailor scouts also decide to transform.
"Now that you transformed yourselves, it's time for us to do the same… Sailor Pluto FX Destroyer, Fighting Mode, Activation!" –Johnny cried out.
"Sailor Saturn Net Surfer, Fighting Mode, Activation!" –George also cried out.
Just like the other scouts, the two boys were enveloped in a strange kind of veil light, and in a matter of seconds they changed from their regular clothes, to their Sailor Scout outfits. Sailor Pluto FX Destroyer was wearing a long sleeve shirt, along with a black waistcoat featuring on his back Pluto's planetary symbol, and on the front a ribbon, just like the ones in Sailor Moon and the others' outfits. He also wore a pair of black pants and matching gloves. Red and black tennis shoes and was wearing a pair of black sunglasses. As for Sailor Saturn Net Surfer, he was wearing a similar outfit to his partner, but it was purple, his waistcoat featured Saturn's planetary symbol, and he was not wearing sunglasses. The others were a little surprised for they did not think that the uniforms wore by the boys were somehow similar to theirs, but at the same time, totally different.
"Okay, let's get this party started, or what?!" –FX asked them all.
"Right… Hold it right there! You evil creatures chose a really bad day to ruin the reception to our friend! In case you don't know, I'm the sailor warrior of love and justice… Sailor Moon!"
"And we are the Sailor Scouts, defenders of this galaxy and of every living creature that lives in it!" –Sailor Jupiter declared.
"And I say that in the name of the Moon and of the other planets, we will punish you!" –Sailor Moon exclaimed.
Without losing time, Sailor Uranus was the first one to engage an attack against the mysterious black fiends. Concentrating, she attacked with no mercy.
"World Shaking!"
Releasing a huge golden energy ball, mirroring the aspect of her guardian planet, Uranus was sure that the fiends did not stand a chance against her attack. When the energy ball hit the creatures, a huge cloud of dust and smoke, clouded their vision, and they were not able to see what happened. Everyone could see a smirk on Sailor Uranus' face, for she believed that she had triumphed. Unfortunately, when the dust settled, that smirk vanished instantly. The fiends that ad been hit by the attack did not even had a scratch on them.
"I don't believe it! My attack did not obliterate them…" –Sailor Uranus stated, still not believing what she was seeing with her own two eyes.
"Let me try!" –Sailor Mars shouted at her, as she prepared herself to launch her attack. –"Mars Fire Sniper!"
Unfortunately, Sailor Mars' attack also failed to destroy the enemies, just like Uranus had. They all tried their attacks. Sailor Mercury used her "Mercury Aqua Rhapsody" attack, while Sailor Jupiter tried to combine her "Sparkling Wide Pressure" attack with Sailor Venus "Venus Love-Me Chain" attack, but failed miserably. Instead of doing any harm to them, they just made them bigger and stronger. It was then time for Sailor Neptune, Sailor Pluto and Sailor Saturn to try their attacks on them, but not even they were able to do anything.
"You girls really need to come up with new and more powerful attacks." –Sailor Saturn Net Surfer stated.
"If you think you can do better, then, go ahead, destroy them!" –Sailor Mars yelled at him.
"Gladly… FX, let's show them what we are made of!"
"On it, Surfer… Let's see if you cretins like one of my attacks…" –Sailor Pluto FX Destroyer said, as he prepared himself to launch his attack. – "Freezing Inferno Blast!"
The "Freezing Inferno Blast" was similar to Sailor Uranus' "World Shaking" attack, but instead of being thrown at the enemies, there was an explosion that made huge ice crystals appear from beneath the floor, slashing and incarcerating them inside. It was a direct hit. Most of the enemies that were in front of the male Sailor Scouts were completely frozen.
"Beat that, my friends." –he rejoiced.
But then, the ice crystals started to break and the fiends came out uninjured.
"Okay, I take what I said before. Maybe it was not such a great approach." –Sailor Pluto FX Destroyer admitted, as he saw the fiends coming out from the ice crystals they were incarcerated in. –"Surfer, it's your turn!"
"Got it… Saturn's Toxic Storm!" –he said, as he fired a huge golden cloud at the fiends, which actually hurt them, but not enough to kill them. –"Drat! It didn't work either…"
"Help!" –they all heard someone crying for help.
All of them turned around and saw that Sailor Moon and Sailor Chibimoon were in trouble. A large group of fiends came out of nowhere and had cornered them. They were trying to get rid of them, by hitting and socking them, but it looked like they were not affected by those physical attacks. Sailor Mars used her "Burning Mandala" Attack on them, trying to make them disband, so that Sailor Moon and Sailor Chibimoon had a chance to get away. The effect of the attack was short, but it was more than enough for both Sailor Moon and Sailor Chibimoon to get away from danger. Just when Sailor Moon thought that she was not in danger anymore, one of the creatures jumped on her, and nearly grabbed her face. But, thanks to a well positioned punch from Sailor Pluto FX Destroyer, the creature flew away.
"Better be careful, Sailor Moon! These things might be small but they seem to be serious when it comes to fighting." –the male sailor scout said, as he punched yet another one that was coming towards him.
"If our attacks don't do them any kind of damage, than maybe we should just use plain old brute force on them." –Sailor Saturn Net Surfer yelled at the others.
"Sailor Moon and Sailor Chibimoon haven't used their attacks on them." –Sailor Saturn stated. –"Maybe their attacks are the only ones that can destroy these creatures."
"Saturn is right about that, Chibimoon. Let's give them a taste of our powers!" –Sailor Moon said.
"Yes, let's do it!" –Chibimoon agreed.
Positioning themselves, both leaders of the Sailor Scouts prepared to strike the enemies. First, it was Chibimoon who stroke them, using her "Double Starlight Honeymoon Therapy Kiss" attack. The effect of the attack was powerful enough to repel the enemies, but not enough to destroy them. Then, Sailor Moon tried her own attack on them, hoping that they would be blown into smithereens.
"Silver Moon Crystal Power Kiss!" –she cried out, as she released the energy attack on a huge group of enemies that were approaching on her and the other scouts.
The attack lifted a huge cloud of smoke and dust, seemingly vaporizing all of them. But when the cloud faded away, they all saw that even the most powerful of Sailor Moon's attacks had done nothing to those creatures, which seemed invincible.
"Not even a scratch!" –Neptune exclaimed.
"These things are invincible!" –Sailor Venus said.
"They must have a weak spot… We just have to find it!" –Sailor Mercury said, as she activated her Mercury Goggles and grabbed her micro super-computer, I order to scan the creatures and find out anything about them.
"Hang on, I'll give you a hand, Mercury!" –Sailor Pluto FX Destroyer stated, as he pushed a miniaturized button on his sunglasses, which activated a small that covered half of his arm until its elbow, and seemed to look like a small computer. –"You're not the only one with gadgets, girl friend."
That last comment made Mercury giggle. FX knew he had a certain charm, which helped him dating any girl he wanted, but right that moment was not the time to think about it. He knew they were in trouble, and needed to find a way to help Mercury finding a weak spot on those creatures. They both quickly ran a scan on them and were amazed with what they saw.
"This can't be right! According to my computer scanner these things don't even exist!" –Sailor Pluto FX Destroyer exclaimed, while checked the results again.
"The same goes for mine… They have no energy signature of any kind. It's like they were mere shadows of actual creatures." –Sailor Mercury stated. –"The infrared scope on my goggles doesn't even pick them up…"
"You're saying that these creatures are here, but it's like they weren't?" –Sailor Jupiter asked, as she punched yet another of those creatures.
"Exactly… Look out, everyone!" –Sailor Mercury warned.
From the sky, a new kind of creatures appeared, but these had wings on them. They were about twenty or more of them, and they plunged into ground, with one target in their mind, the Sailor Scouts. They all jumped out of the way of those creatures. Unfortunately, one of those creatures actually succeeded in capturing one of them, Sailor Chibimoon. The creatures had grabbed her, by using its claws and started to go up at full speed. When they realised what was going on, they knew they had to do something, but they could not try to shoot the creature out of the sky, for they might hit Chibimoon. At the creature took off with Chibimoon, going to the distance until you could not see it, the dark fiends started to disappear as fast as they had appeared before.
"They're getting way. It's like they had came here just for one purpose…" –Luna said, as she and Artemis got out of their hideout.
"And that purpose was probably to snatch Chibimoon. We need to save her!" –Sailor Moon exclaimed.
3. To the Rescue
Chapter 3: To The Rescue
What had started has a welcome party for Chibiusa had become one of the strangest battles that the Sailor Scouts ever faced. Strange creatures that resembled living shadows had appeared out of nowhere and attacked them, taking Chibiusa with them. With no time to spare, all members of the Sailor Scouts knew they had to worry for they did not know what those creatures, or whoever that was commanding them wanted with her.
"How are we going to follow them?! They disappeared into thin air." –Sailor Moon stated, as she looked around, looking for something that might give them a clue to where they had taken their friend.
"Take it easy, Sailor Moon. Whatever they wanted with Sailor Chibimoon, they probably need her alive." –Sailor Saturn said, trying to calm her down.
"She's right, you know? If they did not need Small Lady alive, they would have killed her right here." –Sailor Pluto agreed with her usual serene voice.
"And thank God they didn't, otherwise, we would not have a clue to follow." –Sailor Pluto FX Destroyer said, as he tapped on the buttons of the mini computer of his.
"What do you mean by that?" –Sailor Mars asked him, intrigued.
"Well, it just happens that the creature that carried off Sailor Chibimoon away left us an energy trail to follow, that I'm picking up on my computer scan. If we follow it, we'll find it." –He answered her.
"But you and Mercury said that these creatures don't have any kind of energy signature… How can that be possible?" –Sailor Mars asked them.
"The ones that attacked us don't have it, but the one that carried away Sailor Chibimoon had an energy signature, thus leaving an energy trail behind it, for us to follow." –He explained her with a rather calm voice, without taking his eyes of the sky.
"And where does that trail lead?" –Sailor Moon asked him.
"Somewhere into the centre of the city…" –Sailor Mercury answered.
"We have to get there fast, and for that we're going to need a transport to get there." –FX Destroyer stated.
"I think I can help out with that… Follow me, everyone!" –Sailor Saturn Net Surfer said, as he headed to the Shrine's stairwell.
The others followed him. Once in the street, they saw that he was looking for something. What was it that he was looking for, none of them knew. He walked through the sidewalk, looking around. Sailor Saturn, who was intrigued, ran towards him and asked him what he was doing.
"Could you tell me what you're doing?"
"Simple… I'm looking for a car… Aha! This one here should do the trick!" –He said, as he got something out of his jacket's left pocket. The rest of the Sailor Scouts caught up with them, and wondered what he was going to do… all, except for Sailor Pluto FX Destroyer, who knew already what his partner had in mind. The object that he had in his hands looked like a small ink ribbon, but it was larger and had some kind of pins attached to it. He gently put it on the red car's roof and pressed a hidden button in it. The device beeped as some kind of black liquid covered the car completely. In a few seconds, the car started to change, becoming bigger and larger. In a couple of seconds, the small car had been transformed into a car that resembled Batman's Batmobile from Tim Burton's films, but it was blue and red. You could also see that a few of its traces, reminded them about the Matrix movies. The girls all wowed.
"What just happened?" –Sailor Jupiter asked. –"How were you able to turn that small red car into this awesome machine?"
"Technology from our dimension, toots... In our time, thanks to a special substance called Chrysalisium, which was created during the war against the Black Moon clan, we are able to change anything into whatever we want… In this case, we pre-programmed the substance to turn the car into a car similar to the one that the Sailor Scouts use in our world. Try to imagine the kind of weapons we can create in our dimension, by using it." –Sailor Saturn Net Surfer explained them. –"Not only it's pretty, but it's also equipped with everything you can think of, everyone… weapons, tracking devices, and a very powerful engine. The perfect car for pursuits and fighting evil creatures"
"I just have to say two things, this is amazing, and don't call me toots, okay?! I hate it when people call me that!" –Sailor Jupiter hissed.
"Sorry… Guess I touched a weak point." –He stated.
"In that case, let me baptize the car as the "Moon Wheel"!" –Sailor Moon exclaimed with an enthusiastic voice, as the others gave her a look that would instantly melt an iceberg. –"What, what is it?! You don't like it? If you don't like it, we can always come up with another name…" –She said with her spontaneous voice.
"Why don't we come up with a name for it later, and go save Chibimoon, right now?" –Sailor Mars asked them all, who nodded affirmatively with their heads.
Entering the car, they all took their places, with Sailor Pluto FX Destroyer at the wheel. Usually, Sailor Uranus would have demand him to let her take the car, but when she looked inside, and saw its interior, with all those buttons and screens in it, she decided to just sit right next to Neptune, without complaining about it. Luna and Artemis hopped into Sailor Venus' lap. Once they were all inside the car, Sailor Mercury asked:
"You guys haven't explained us how are we going to find Sailor Chibimoon with this car?"
"One moment, please… We're going to use the signature tracking system, which is similar to the one you and I have in our personal micro supercomputers." –FX Destroyer said, as he pressed a great amount of buttons in the panel. Suddenly, the front-window changed colour, going from a mildly black to a light-blue, turning itself into what looked like a computer screen, beeping some kind of information. –"According to the computer, the energy signature of the creature that took Sailor Chibimoon is heading to the centre of the city, more precisely, Downtown, where there is a very peculiar energy field, which goes off the charts."
"Whatever it is, it must be really big, folks." –Sailor Saturn Net Surfer stated.
"Then, what are we waiting for?! Let's go after it and get Chibimoon back!" –Sailor Jupiter exclaimed.
"You read my mind, girl… Put on seat belts, and get ready… Next stop, Tokyo downtown, everyone!" –Sailor Pluto FX Destroyer said, as he turned on the car's engine.
Speeding through the streets, the Sailor Scouts were surprised by the speed the car was going. Even though the streets were packed with traffic, it looked like that did not stop the car from heading to its destination. They did not know if it was the car that was manoeuvrable, or if it was FX Destroyer that was a great driver. In a matter of minutes, they were arriving downtown, and now all they needed to do was pinpoint the exact location of the creature that had taken their friend. Another thing they all noticed was the fact that it was getting quite hot. The further they went, the hotter it got.
"Can you raise the air conditioner? I'm sweating as if I was in a sauna!" –Sailor Venus stated, as she used her left hand as a fan, trying to keep cool.
"Sorry, it's already on maximum, Venus…"
"This heat is not normal, even for July." –Sailor Moon said.
"I bet that it has something to do with the strange enemies that have been attacking us! They must be behind this strange phenomenon." –Sailor Saturn stated, as she looked through the window, realizing that they were people lying on the ground, fainted. –"People lying on the ground isn't normal. It has to be connected."
"According to the thermometer, temperature out there is almost 55ºC! This can't be right!" –Sailor Pluto FX Destroyer exclaimed, as he turned left.
"I don't think it's an error. Look outside, everyone!" –Sailor Jupiter pointed, as the others all looked through the window.
In fact, people lying on the ground was just one of the many examples of what was really going on. Tree leafs started to turn orange, yellow and brown, like if it was autumn already, and were falling into the ground. The shop windows started to shatter due to the massive heat. In conclusion, it was like the gates of Hell had been opened.
"It looks like it's so hot that you could fry an egg on the asphalt." –Sailor Saturn Net Surfer said.
"We need to stop this, right now, or people will die." –Sailor Moon thought to herself, as she watched to horrible show that was going on outside.
"Have you picked up where the signature is coming from?" –Sailor Mercury asked, as she also used her laptop to try and pinpoint its exact location.
"Almost… I'm calculating the coordinates, based on the energy signatures. Think you can help me with it?" –Sailor Pluto FX Destroyer asked her.
"Hmm… Sure, according to my computer the biggest energy peak is coming from 35° 39′ 31″ N, 139° 44′ 44″ E." –Sailor Mercury declared.
"Tokyo Tower in Shiba Park!" –Sailor Uranus exclaimed.
"Yeah, that's right, but how did you know that those coordinates belonged to the Tokyo Tower?" –Sailor Pluto FX Destroyer asked her, astounded with that.
"Didn't need to… I just looked through the window." –Uranus stated with a rather calm voice, as she pointed into the tower.
The Tower's base was covered in what looked like some kind of goo that was spreading rapidly, covering it.
"If Chibiusa was here right now, she would say that the tower looked like it was covered with black liquorish… And then we would laugh about it, without caring about anything else." –Saturn told herself, as a little smile appeared on her face, and a small tear rolled down her cheek. –"We're going to save you, Chibiusa, don't worry."
Taking the main roads, FX Destroyer did everything he could to get to Shiba Park. Unfortunately, this proved to be a wrong decision. Due to the extreme heat, people fainted while driving. Some of the cars had crashed into something, while others, just stood in the middle of the road. Still, he managed to use alternative routes, which made it easier for them to reach their destination. As they got nearer Shiba Park, things looked even worse than before. The thermometer continued to rise, as they advanced. They all stated to think that when they reached their destination and had to exit from the car, it would be almost impossible to bear that overheating temperature. Still, inside the car the temperature was starting to rise, even though the air conditioner was on max. But suddenly, the temperature started to drop off rapidly. They checked the thermometer and saw that the outside temperature was 20 degrees.
"But how is that even possible?!" –Sailor Mars asked.
"If my readings are right, there's some kind of invisible force field around the tower, which prevents the grounds surrounding it from being as hot as the rest of the city." –Sailor Mercury answered.
"If that's true, then, whoever is responsible for this has to be quite powerful, I mean, it can't be one of the monsters that we are always fighting against. Those are usually not powerful enough to accomplish something such as this." –Sailor Neptune declared.
"I agree. It must be someone as powerful as Nehelenia or Galaxia herself." –Sailor Uranus said, agreeing with her partner.
"Well, whoever, or whatever it is, we'll soon find out." –Sailor Saturn Net Surfer said.
After they parked the car, they all exited as fast as they could. Seeing it from up close, they found out that what was covering the tower was not some kind of goo. What was covering it were millions of those tiny black creatures that had attacked them earlier. They were so close to each others that from afar, they looked like a huge living mass. All the Sailor Scouts were amazed and stunned by what they were seeing.
"There must be millions and millions of these creatures covering the tower." –Sailor Moon said, as she looked up, trying to see just how many they were.
"But whatever it is that's generating this kind of energy, it's not them. With the exception of those flying creatures that are flying around the tower, which possess a small energy signature, like the one who took Chibimoon, the others don't present any kind of energy." –Sailor Mercury stated, using again her laptop. –"It's something else, something big… and it's coming from inside the tower."
"Can you detect if Chibimoon is inside the tower too?" –Sailor Venus asked.
With agile and quick moves, Mercury's fingers tapped on her microcomputer's keyboard. In a matter of seconds she had the answer that her fellow Sailor friend wanted. Sailor Chibimoon was inside the tower, along with a few more people.
"She's up there alright, and so are other people." –Mercury answered.
"Then, there's only one thing to do, we have to go up and save her!" –Uranus declared, tensely.
"But how are we going to get inside with these many creatures, impeding us from going up?" –Sailor Venus asked when something hit her directly on her left shoulder.
It was one of the creatures who had jumped on her and was not trying to hurt her by using its claws. The others saw what was going on, and quickly helped her out. Sailor Neptune ripped the creature of Sailor Venus' back with her both hands, quickly throwing it to the other side. Unfortunately, this proved to be futile, because the creature bounced again, trying to grab Venus, but this time it hit Sailor Saturn Net Surfer's fist, which through it even farther away from where it had first land. At the same time, dozens if not hundreds of those black creatures jumped out of where they were and attacked the unprepared group.
"Great! Now we have hundreds of them surrounding us!" –Sailor Mars cried out.
"How are we going to save Sailor Chibimoon and the people who are stuck up there, if they keep coming at us?" –Sailor Jupiter asked.
"Like this!"
With a well positioned kick, Sailor Mercury kicked one of the creatures with all her strength, making it fly up into the air. The others all looked at her, rather shocked and astounded, for they never had seen their friend act like that before, either as in her civilian form, or when transformed into a Sailor Scout. When she noticed that they all were looking at her, she asked them.
"What are you looking at?!" –she asked with an innocent voice.
"N-Nothing… It's just that we never saw you acting like that before…" –Sailor Moon said. –"Usually, it's Sailor Uranus who behaves like that."
"Hey! I don't behave like that all the time!" –She objected.
"Yes, you do, silly…" –Sailor Neptune giggled, as she looked at Uranus, who smiled back at her. –"You just don't realize that, because you have a really strong personality, that's all."
"Ladies… I don't want to break the romance, or anything, but…" –Sailor Pluto FX Destroyer said; as he punched two creatures, back to where they came. –"… we got a situation here!"
"He's right, come on!" –Sailor Mars said seriously, as she advanced through the huge amount of enemies that were now surrounding them, kicking every single one of them. The others all did the same thing. If their attacks did not work on them, the only thing they could do was to shove them aside, making it possible for them to enter the tower.
Sailor Jupiter and Sailor Mars took the lead, while Sailor Neptune and Sailor Venus took the rear, making sure that they would not get close to them. As for the others, they all tried to find a way to keep the enemies as far away as possible from them. Sailor Saturn even decided to use her Silence Glaive as a baseball bat. Making their way to the tower's interior, Sailor Moon kept only one thought in her mind.
"We're coming, Chibiusa! Just hang on a little bit more, because we're arriving!"
4. Sailor Earth's Awakening
Chapter 4: Sailor Earth's Awakening
On the Main Observatory, things did not look good for the people who were trapped there. Black creatures were jumping from on side to the other, trashing everything they could put their claws on. But the worst part of it, was the fact that there was a huge creature, bigger than the others and had the appearance of a black octopus. Its head was in blazes, making it look like a fire demon. Its eyes were of the same colour as the others creatures, but there was something in them that made them look different. The black and red tentacles were swirling around, grabbing everything and everyone that got in their path. After being captured by the tentacles, each person was enveloped by them, until they were encased in a dark sphere. These spheres looked like they were some sort of capsules, in which people were put in. What happened once they were encased, one could only guess. Sailor Chibimoon, who was brought to that place, was now chained, both arms and legs to one of the walls. The chains that were restraining her were made out of some kind of substance, similar to the one that the strange creatures were made of. She had tried to get free, but ever since the creatures had caught her, it looked to her as if her whole strength was being sucked right out of her. Each second it passed, she felt weaker and weaker. Her eyes were getting sleepy and her body heavier, like if she was about to fell asleep.
"What are these creatures, and what do they want from me?" –She asked herself, as she tried to stay awake.
That's when she felt something cold crawling over her leg, making her shiver. She looked down and saw that one of the creatures looked like it was seeing if she was still awake. The creature grunted when their eyes met just for a brief second, and then went away. Trying to stay awake, Chibimoon focused on what was happening around her. She saw the spheres where people were being put in by the huge creature, and wondered why they were doing that. She also noticed that there was still a person who had not been captured by the creatures. The Sailor Scout tried to figure out if it was a man or a woman who was hiding behind a counter, near where she was, but her eyes were too tired to see it. She once again tried to break free from the chains, but it was in vain. That's when she heard a loud noise. It looked to her like a shot, and had come from the elevators. It was the rest of the Sailor Scouts, looking for her. They had to use the elevators to get there, which did not prove to be an easy task. The shaft was also crawling with those creatures, and they had to get rid of them, as they tried to enter in the elevator. Thankfully, the two male Scouts had a couple of device, which enable them from getting too close. But just when they had reached the Main Observatory floor, the doors were shut, and did not open. Telling them all to get behind him, Sailor Pluto FX Destroyer used his version of the Time Sceptre, which was actually a futuristic black and silver shotgun, to open the elevator doors. The blast was as loud as you can imagine, making their ears buzz for awhile, as it opened a huge hole in the doors.
"Couldn't you use anything else to open the door?! Did you really have to use that weapon?!" –Sailor Uranus yelled at him.
"It was either this, or a pack of C4, Uranus, and besides, it worked didn't?!" –He exclaimed, irritably.
"Could you two argue later? We have trouble coming right at us!" –Sailor Jupiter hissed at them, as she needed to use her "Supreme Thunder Attack" to repel a bunch of enemies who were trying to enter in the elevator.
Both Uranus and Pluto FX Destroyer nodded silently, and quickly exited the elevator, followed closely by the rest of the group. Once out of the elevator, they all saw that their situation was way worst than they were expecting. The place was crawling with those creatures, but the worst part was the giant creature that was standing in front of them. It was way bigger than any of the ones they had seen so far, and it looked like 10 times more menacing than the ones they had faced to get there.
"This just keeps getting better and better." –Sailor Saturn Net Surfer said, sarcastically, as he also made appear a weapon of his own; a high-tech crossbow, which had a similar design to the Silent Glaive.
"Its times like this I would have rather stay home today." –Sailor Venus mumbled to herself.
"This isn't just your everyday monster, now is it?" –Sailor Mars drawled, showing no fear of what was surrounding her.
"Where is Chibimoon?!" –Sailor Moon asked, as she looked around, finally finding her, where she was chained against her will.
Creatures started jumping on them, but they managed to outsmart them, by evading their attacks. Knowing that they would never be able to take care of everything if they stuck together, Sailor Uranus decided to go against the giant creature by herself, hoping that her attack would at least hurt it. Sailor Neptune, realizing what she was attempting to do followed her. Sailor Pluto and Sailor Saturn also followed them. Knowing that the four of them usually liked to work alone, Sailor Moon decided that while they tried to attack the creature that looked the main responsible for what was happening all over Tokyo, she and the others would try to release Chibimoon. As for Sailor Pluto FX Destroyer and Sailor Saturn Net Surfer, they both decided to try and find a way to destroy the enemies that surrounded them, or at least, to keep them at a distance from all of them.
"Let's use our weapons to take out these suckers, dude!" –Sailor Saturn Net Surfer exclaimed, as he pointed his crossbow to one of the little creatures that was standing in front of him.
"Okay, let's do it!" –Sailor Pluto FX Destroyer agreed with a confident voice, as he also pointed his shotgun. –"You go first… I always like to save my attacks for last."
"Why's that?"
"Because my attacks are more powerful and far more dangerous than yours are, of course." –FX answered.
"Are not… and I'll prove that to you, right here, right now!" –Net Surfer replied, as he got ready to use his attack. –"Saturn's Light Arrow!"
The arrow was shot with an incredible velocity, hitting the ground, releasing a powerful blast of light that engulfed the enemies. Usually, that attack was powerful enough to destroy any kind of enemies, in those creatures case, it merely stunned them temporarily. Still, it was more than enough for both of them to counter attack.
At the same time, Uranus and her group tried everything they could think of against the huge creature that was standing in front of them. But each time they attacked it, it looked like it was growing stronger, like if it sucked the energy right off their attacks. Somehow desperate, they all agreed to combine their attacks into one single attack, that with some luck, it would at least cause that creature some pain.
"Space Sword Blaster!"
"Submarine Reflection!"
"Chronos Typhoon!"
"Silence Glaive Surprise!"
The four Sailor Scouts' attacks were fired at the same time, and united into a single beam of pure energy, which hit the monster. Unfortunately, this only caused the creature to grow bigger. This one also started to mutate. Its arms became larger and longer, and the flames that covered some parts of his body, were now starting to cover all of its body. But the worst part was that it revealed its huge mouth. When the creature opened it, something was shot at them. It was the energy of their attacks that had been used against them, making the four girls being blown away into the air, like if they were nothing but pieces of paper. They hit the ground pretty badly, and for a few seconds Sailor Neptune thought that she had broken her arm, because of the pain that she was feeling. Sailor Saturn almost lost consciousness, but was able to gather strength to stay awake. Holding the Glaive with both her hands, she pulled herself up, which proved to be a harder task than she thought.
"I-Is it possible that this monster doesn't have a weakness?!" –Sailor Saturn asked herself, as she looked at it.
Sailor Pluto got back on her feet, with the help of Sailor Uranus. Still holding the Garnet Orb in her left hand, she tried to focus on what was going on around her.
"That monster has an incredible strength, no doubt about it." –Sailor Uranus said. –"It used the energy of our own attacks to grow stronger, and then, turned it against us."
"At least, we won't be fooled twice by the same trick, which I can assure you." –Sailor Pluto said, as she tried to straighten up.
Then, she and Uranus saw that Sailor Pluto FX Destroyer was running towards them, with his shotgun pointed at their faces. His facial expression was as cold as you could get, which scared Pluto for a brief second. Not knowing what he was doing, or what he had in mind, she just asked:
"What are you doing?!" –Sailor Pluto asked him, as he got closer to them.
"Get down!" –He yelled.
"What?!" –Sailor Uranus asked.
"I said, get down! Hit the deck, you two!" –As he fired his attack. –"Charon Explosion!"
The Charon Explosion attack was in many ways similar to Pluto's Death Scream attack, but instead of being just an energy orb, it were three energy orbs, fired from the shotgun, which rotated at high speed, exploding when it came into contact with an object or an enemy. Both Sailors leapt into the ground, avoiding being hit by the attack. That's when they noticed that the one of the monster's tentacles was about to grab them, but thanks to FX Destroyer intervention, it had failed. Uranus grimed back at him, and said:
"Thanks…We owe you one." –She declared, meaning every word she said.
"No need to thanks, it was my pleasure. But you two better watch your back, next time." –he said as he fired once again the same attack at another tentacle. Unfortunately, this time, he failed his target, and ended up breaking up a few windows of the Main Observatory deck. The sound of shattered glass was heard by everyone, but not even that was enough to distract them from their mission, especially Sailor Moon. While Uranus and the others batted the giant creature, she Mercury, Venus, Mars and Jupiter were trying to release Sailor Chibimoon from the chains that were restraining her against her will.
"It's no use, Sailor Moon! These chains look like they are made of the same stuff these creatures are." –Sailor Jupiter declared, as she tried to pull the chains out of the wall.
"No! We have to keep trying! I'm not going to let Chibimoon chained to this wall… That's not an option!" –Sailor Moon cried out, as she herself started pulling the chains with her hands.
"Maybe we can try using one our attacks to try and destroy these chains." –Sailor Venus suggested, as she prepared to use one of her attacks. –"Crescent Beam!"
With surgical precision, Venus fired her attack, a single beam of light at the chains, and tried to cut them, like if she was using a laser to do it. Unfortunately, that proved to be a waste of time, for the chains were not even scratched by it. Sailor Jupiter and Sailor Mars kept trying to keep the creatures away from the others. Using the "Burning Mandala attack" and the "Supreme Thunder Attack", they were trying little by little gain some manoeuvre space.
"Come on, Chibimoon! Don't give up! We're right here with you, okay?" –Sailor Moon tried to keep her awake, which was proving a difficult task, since Chibimoon looked weaker every second it passed. Slowly raising her head, she used all the strength she still had within her to open her eyes. She tried to talk, but when she tried, not a sound came from her mouth. She tried harder to talk, but all she could do was whisper something, that only Sailor Moon, who was close to her was able to hear.
"T-There's someone… someone hidden, behind… behind the counter, o-over there…" –She whispered, while pointing out the place with her eyes.
Sailor Moon looked to the counter and saw that someone was really behind it, hiding from the creatures. All of a sudden, one of the creatures was able to escape Sailor Jupiter's and Sailor Mars' attacks and jumped on her, with its razor-sharp claws, trying to shred her into pieces. Sailor Mercury and Sailor Venus saw it, and prepared to help her, when something hit the creature, knocking it into the ground. They all looked to the object that hit the creature, and found out that it was a rose… a red rose. Sailor Moon recognized it as being one of the roses of their most trusted ally, who was now standing on the porch of one of the shattered windows.
"Tuxedo Mask!" –She exclaimed, as she watched him, smiling at her, with his usual mysterious smile.
The others hearing Sailor Moon yelling his name, all turned their attention to where he was standing.
"You foul creatures should not attack a girl, especially if that girl is risking her life to save another life! I, Tuxedo Mask will not allow you to do as you please!" –he declared, as he jumped, landing right next to Sailor Moon.
"About time he decided to show up!" –Sailor Uranus said, as she punched another creature.
"I'm sorry if I'm late, but I got stuck by these creatures at the entrance." –He stated, as he looked to Chibimoon. –"What happened to her?"
"These creatures have chained her up to the wall. She's getting weaker by the minute, and has told me that there's someone who's hiding behind that counter." –Sailor Moon said. –"Take Sailor Venus with you, and see if you can rescue that person and get her out of here, safely, while I, Sailor Mercury and the others try to break these chains.
Tuxedo Mask nodded affirmatively at her and then proceeded to do as he was told. Venus followed him close. The creatures, decided to make him as their main target. Charging at him, he was forced to use all of his tricks to secure a path for him and Sailor Venus. That's when he noticed the two male Scouts that were with them. At first, he saw that as strange, but then assumed that whoever they were, if they were helping the girls, then they would have to be good guys. Finally, they reached the counter, and looked down to see who it was that was hiding there. It was a girl with reddish-brown waved hair with a dark-green ribbon on top of her head. Her eyes were light-blue, just like Usagi's. She was wearing an orange shirt and a pair of blue jeans, as well as a pair of white sneakers. For a moment, he did not recognize her, but then, Tuxedo Mask looked more closely and saw who she really was… It was Naru, one of Usagi's oldest and dearest friends. It had been almost a year since they had seen each other, but Usagi still considered her as one of her best friends, and the same thing could be said about Naru. Their paths diverged just right after Haruka and Michiru appeared for the first time. Ever since then, their lived took different paths, but it looked like, their paths had crossed again, after all this time. Mamoru even remembered that Usagi once told him that Naru seemed to always get herself into trouble, all because of the enemies that were after her and the other Sailor Scouts. Being called back to reality by Sailor Venus, Tuxedo Mask snapped out of that momentary flashback, and asked:
"Are you okay, Miss?" –He politely asked her.
"Y-Yes… I think I am. T-Tell me, what are these creatures?" –Naru asked, tensely, as she looked at him.
"I don't know, but we need to get you out of here…" –He said, when he was interrupted by a crashing sound.
The huge octopus-like creature had decided to target Tuxedo Mask, and using one of his tentacles, he smashed it into the ground, making the ground tremble, and the rest of the windows to crack open, leaving it to many other creatures to enter in the Main Observatory. Then, another tentacle tried to grab Tuxedo Mask, but only managed to destroy the counter, in which Naru was hidden. Fortunately, she was able to get out of the counter, before it was cracked up like a walnut. If it was not for her quick reflexes, the girl would have been crushed, along with it. Tuxedo Mask and Sailor Venus were forced to also jump out of the way of the creature's tentacle, before being crushed by it. But, she ran out of luck, when one of the tentacles grabbed her by the ankles and started pulling her towards the creature. Seeing that the girl was in danger, Sailor Saturn tried to cast her Silence Wall attack on her, but failed. Sailor Venus tried to grab her hand, but was not fast enough. Tuxedo Mask on the other hand was able to grab her left hand. As soon as their hands touched, something strange happened. Their bodies shivered, like if a lightning had stroked them. Then, the creature pulled Naru, and they both let go each other's hands. Naru kept looking at Tuxedo Mask, as dozens of creatures pilled on top of him, trying to restrain him. She wanted to cry out for help, but it was like if her tongue had been cut out, and she could not pronounce a sound, no matter how high or low it was. Her eyes then looked around, and she saw Sailor Moon. For a moment, their eyes met, and they both looked to each other. Sailor Moon recognized her immediately.
"Naru…" –Sailor Moon whispered to herself.
She wanted to help her friend, but her body froze as she saw Naru being encased by the octopus-like creature, into the same kind of spheres that the other persons were in. Sailor Uranus and Sailor Neptune still tried to prevent it from happening, but were both repelled by it, only to be caught by Sailor Pluto FX Destroyer and Sailor Saturn Net Surfer. All of the Scouts looked as Naru was trapped in the sphere. The moment was almost surrealistic. But as soon as she was encased, a small crack opened in the sphere, letting out a bright light from inside. The crack began to get bigger, and all of them, including the creatures, looked closely at what was happening. Then, the sphere broke open, releasing a light as bright as the Sun itself, which continued to glow for what looked like an eternity. Not only that, it seemed that a strange wave of silence had been cast on that place, and not a sound was heard. Then, the silence was broken, when they heard someone yelling:
"Earth Crystal Power Make-Up!"
As the incandescent light began to fade away, slowly they all saw what looked like a silhouette, standing up on her feet. She was dressed with a Sailor outfit, being her skirt light-brown, and the ribbon on her chest was dark-green, mirroring the one she had in her head. And her boots were light-brown, just like the skirt. On her forehead you could see a tiara with a dark-green jewel stone carved in it. She had her arms crossed and her eyes looked like they had the ability of melt an iceberg just by looking at it.
"You vile creatures think you can get away with this kind of destruction, don't you?! And furthermore, you think you can hurt my prince and get away unpunished? Well, think again! I, Sailor Earth, protected by the power of planet Earth, my guardian, will not allow you to get away with it, you hear me?!" –She exclaimed.
None of the Sailor Scouts were prepared for what they just had witnessed, the awakening of an unknown Sailor Scout, Sailor Earth. And the most amazing thing was that they never even suspected that this Sailor Scout would be Naru, a girl, who the Inner Scouts had saved so many times, while fighting evil. Sailor Moon was the one who was more impressed with all that, and could not take her eyes of Sailor Earth, as she opened a path to where Tuxedo Mask was, and with a smooth move of her left arm, she made the creatures who were grasping to him, to let him go. She then gave her hand to him, and helped him to get up on his feet. As he got up, what looked to him like a flashback sequence appeared in his mind, making him remember of what happened, and why Sailor Earth had not been awakened like the other Sailor Scouts, when they were reborn in their earthly forms.
"Forgive me, my prince, for not been able to protect you." –She sighed, and bowed her head, asking him for his forgiveness, to which he put his hand on her shoulder and said:
"It was not your fault, Sailor Earth… None of what happened was your fault." –He said with a calm voice. –"But we'll discuss this matter later. Right now, another enemy is attacking our world, and more than ever, we need all the help we can get. You think you're strong enough to fight along our side?"
"Yes…" –She said, as she looked into the eyes of the other Sailor Scouts, who were watching the scene. After that, she ran towards where Sailor Moon was and told her with a calm voice: "Leave this to me, Sailor Moon… I'll free her from these chains."
Sailor Moon did not know what to say, so she merely got out of the way and let Sailor Earth do what she thought it would help Chibimoon. She placed her hands on the wall, and soon, what looked like roots started to come out of it. In a matter of seconds, the roots started to mesh with the chains, and then, these shattered. Chibimoon was caught by Sailor Earth, who smiled to her. Sailor Earth also smiled back, displaying a more tender side, something that Naru had always displayed with the ones who loved her.
"Are you alright, Sailor Chibimoon?"
"Y-Yes… A l-little weak, but I'll be a-alright." –Sailor Chibimoon replied, as she tried to keep her eyes opened.
"Don't worry. You'll be fine… Sailor Moon, take care of her, please."
"S-Sure… Naru, I mean, Sailor Earth, I…"
"You're wondering what is going on, and how come I did not appear before, am I right? There will be time for me to explain that… Meanwhile, we have a problem to solve." –Sailor Earth said, as she handed Chibimoon to Sailor Moon.
"You're right! Go get those creatures, my friend."
Nodding at her, Sailor Earth dashed away, with two objectives in her mind; to protect Tuxedo Mask and to beat the crud of every enemy that appeared in front of her. Although she did not know what was really going on, her suppressed memories started to fill the blanks in her head, and her body acted on instinct. Concentrating, she unleashed her full wrath on the creatures.
"Roots of Fate!" –Sailor Earth cried out.
Her attack unleashed a powerful sonic wave, through the ground, like an earthquake. Then, huge and thick vines ripped the floor beneath their feet, attacking any enemy that appeared in front of it, by grabbing them, and then, quickly squeezing them. But, even this attack, which amazed some of the Scouts by the kind of raw power that unleashed upon the creatures, was not enough to destroy them. Still, this did not discourage the new Sailor Scout. Whoever those creatures were, they would not stop her from carrying out her mission.
5. The Keyblade
Chapter 5: The Keyblade
The battle got fiercer than before. The creatures became restless, even more than before, like if something far greater than them was getting nearer. Helped by the newly awakened Sailor Earth, the Sailor Scouts were giving their best to repel the creatures, using all their attacks to do it.
"Mercury Aqua Rhapsody!" –Sailor Mercury exclaimed.
"Mars Fire Sniper!" –Sailor Mars exclaimed.
"Jupiter Oak Evolution!" –Sailor Jupiter exclaimed.
"Venus Love and Beauty Shock!" –Sailor Venus exclaimed.
"World Shaking!" –Sailor Uranus exclaimed.
"Deep Submerge!" –Sailor Neptune exclaimed.
"Dead Scream!" –Sailor Pluto exclaimed.
"Silence Glaive Surprise!" –Sailor Saturn exclaimed.
"Freezing Inferno Blast!" –Sailor Pluto FX Destroyer exclaimed.
"Saturn's Toxic Storm!" –Sailor Saturn Net Surfer exclaimed.
"Roots of Fate!" –Sailor Earth exclaimed.
Still, none of these attacks seemed to produce any kind of damage on the creatures that just kept appearing, from everywhere. In a matter of seconds, these creatures became so numerous that all Sailor Scouts started to converge into a small circle, surrounding Sailor Moon, Sailor Chibimoon and Tuxedo Mask. They all were ready to give up their lives, if that meant the survival of their Princess and the others. As they continued to fight, Sailor Moon kept trying to reanimate Chibimoon, who was still too weak. Whatever those creatures had done to her, it had depleted her of most of her energy.
"Chibimoon… Come on, wake up, please!" –Sailor Moon cried out to herself, as her fingers pass through the girl's cheeks. Her skin was as pale as white marble, and her breathing was quite weak.
All of sudden, all creatures stopped and ceased their attack. It was like if time had stopped, and nothing could move… Nothing, except for the Sailor Scouts.
"What just happened?" –Sailor Neptune asked, as she looked around and saw all the creatures standing still, like if they were statues.
"I don't know… It's like someone stopped time flux." –Sailor Mercury stated, as she tapped on her micro-computer, trying to find a logical explanation to what was going on.
When she said that, everyone looked towards Sailor Pluto and Sailor Pluto FX Destroyer with accusing eye looks.
"I have nothing to do with this, believe me." –Sailor Pluto declared with a serene voice.
"The same thing goes for me." –Sailor Pluto FX Destroyer stated with a defensive voice. –"I know that I have enough power to stop time, but I'm not allowed to do it… and I bet all my lucky charms that neither you are allowed to do it, am I right?" –He asked to Sailor Pluto, to which she nodded.
"Well, if it wasn't one of you, then, who stopped these creatures?" –Sailor Jupiter asked.
"IT WAS I WHO STOPPPED THEM!!!"
A deep inner voice was heard by all of them, and then, a sinister and evil laugh filled the entire floor, sending shivers up their spines. They looked around, trying to see from where that voice had come from. All of a sudden, the air became chilly, like if a snow storm had just break in there. Then, what looked like a portal made out of living shadows, which kept on swirling, giving the idea of being some kind of mist, appeared not far from where the Scouts were. They all observed it, waiting for something to happen. They just knew something was about to happen, but they did not have a clue of what it could be. Finally, something did happen. Coming out of that dark mist, a tall, thin, pale green skinned woman with yellow eyes and a horned headdress, presented itself in front them. She was wearing what looked to them like a black and purple robe with bat wing-like edges, wearing a gold ring with a large mysterious circular black stone in it. In her left hand, she was carrying a staff with glowing green crystal orb at the tip. Also, a raven rested on her right shoulder. The woman had a malicious smile in her face, as she looked around. The creatures that were near her, gave a step back, thus creating a small corridor towards the Sailor Scouts. Not taking any chances, the group never let their guard down. Walking towards them, the woman kept staring at them. To the group, it was like if her eyes pierced their bodies with the sharpest of the knives.
"Who are you?!" –Sailor Uranus asked her, snarling at her.
"Are you the one who is controlling these creatures?!" –Sailor Jupiter also asked her.
The woman's smile became even scarier then before. She let out a laugh that would freeze the souls of the bravest of the warriors. Still, none of the Sailor Scouts had intentions of showing her if they were afraid of her. Finally, her laugh ceased and she answered with a voice similar to what they all imagined to be a voice that a snake would have.
"My, my, what an impressive group you are." –She said as she stopped just a few a couple of meters away from where the group was. –"From all of the problems that I had to deal with, you certainly are one of the biggest. But, allow me to introduce myself. I am Maleficent and these are my loyal subjects and warriors, the Heartless."
"Heartless?! So that is the name of these evil creatures." –Sailor Mars said, as she looked to Maleficent.
"What do you want from us?" –Sailor Neptune asked her.
"From you, I don't want anything… It's that girl over there that I want. Her Heart is certainly one of the purest Hearts I've ever felt. It's not as pure as the Hearts of the 7 Princesses of Heart, but still, it will make a splendid acquisition in our attempt to create and open Kingdom Hearts." –Maleficent said.
None of them really understood what was going on. They did not understand what the woman was talking about… Hearts… Princesses of Heart… Kingdom Hearts? To them, they were nothing more than mere words.
"I don't know what you're talking about, but you're not taking Chibimoon away without a fight!" –Sailor Venus exclaimed, as her partner Artemis, who was right beside her, looked at Maleficent with.
"She's right! If you want Small Lady, you'll have to go through me, first!" –Sailor Pluto declared, as she pointed the Garnet Orb.
"You'll have to go through all of us, you witch!" –Sailor Pluto FX Destroyer exclaimed, as he pointed his shotgun, targeting Maleficent. –"If you or any of those creatures want her, you'll have to kill us all first!"
"Very well, then… I'll get rid of you first, and then, I'll extract her Heart, personally! Heartless, kill them!"
Obeying their mistress' orders, the Heartless started to attack the Sailor Scouts. The number of creatures surrounding them grew with each second it passed. Sailor Pluto and Sailor Saturn cast their defensive attacks, the "Garnet Ball" and the "Silence Wall" in order to stop their advance. They all battled against those horrible creatures, while Sailor Moon and Tuxedo Mask tried to wake up Sailor Chibimoon, who was still unconscious.
Watching the battle that was taking place in front of her eyes, Maleficent saw that her Heartless were not causing them enough damage, so she decided to take the battle to the next level. She ordered them to fuse with the giant octopus-like Heartless, making this one bigger and stronger. The massive creature was now even bigger than before. Spikes appeared all over its body, giving it a more menacing look. Launching an attack, the new giant Heartless used all of its strength to break the force fields created by both Saturn and Pluto. The force fields withstood a couple of strikes from the monster's tentacles, but eventually, they shattered. The two Sailors tried to fight back, but having used most of their energy creating the force fields, had left them pretty weak. They were the first ones to be captured by the tentacles, and soon after, the other Sailor Scouts had also been captured by the horrible and gruesome creature. They all put up a little fight, but the adrenaline in their bodies had run its course, and they were now feeling tired and exhausted. And the worst part was that when the octopus-like Heartless grabbed them with its huge tentacles, they felt even worst, like if their vital energy was being sucked out right out of them. Even Luna and Artemis, who were doing their best to strike the monster, by slashing it with their claws, were caught by the tentacles. Sailor Neptune and Sailor Earth were the last ones standing between Sailor Moon, Tuxedo Mask and Chibimoon, and the gruesome monster. Seeing that if she did not do anything to help her friends they would all perish, Sailor Moon handed Chibimoon to Tuxedo Mask and joined her friends in battle. But when she was about to use her scepter to attack the monster, Neptune put herself in front of her and said:
"No, Sailor Moon… We'll handle this!"
"Yes, she's right! The Prince, you and Small Lady are much more important than us!" –Sailor Earth declared in a tone, which Sailor Moon recognized, whenever Naru told her something that was really important.
The two Sailor Scouts needed to get some maneuver space, so they cast their most powerful attacks on that Heartless.
"Submarine Violin Tide!" –Sailor Neptune exclaimed.
"Earth's Destroyer Rumble!" –Sailor Earth exclaimed.
Both attacks caused the Tower to shake like gelatin, and the floor beneath their feet to become all cracky. Still, none of them was powerful enough to hurt the beast in front of them. With yet another strike, the Heartless grabbed both Sailor Neptune and Sailor Earth. There was no one left to defend Sailor Moon, Tuxedo Mask and Sailor Chibimoon. Maleficent rejoiced as she saw what just happened; all of the Sailor Scouts had been captured and now she was free to do whatever she wanted with Chibimoon. She teleported herself to where the three of them were, and with a sinister grin in her face, she raised her hand to grab Chibimoon, when she something was pointed out at her face. It was Tuxedo Mask's cane. The cane itself was just a few millimeters from her face, but instead of being surprised or shocked with it, in her face, the sinister grin that she had, became even bigger, to the point that she burst out laughing at it.
"What do you think you are going to do with that?! Kill me?!" –she asked him, still laughing maniacally.
"If I have to, then, yes… I'll not allow you to touch a hair of Chibimoon or Sailor Moon…"
Before he could finish what he was saying, Maleficent used her scepter and cast some kind of force field around him, levitating him up in the air. She looked at him with an intriguing look in her eyes. There was something about him that fascinated her. Then, she felt it; it was his Heart. It was quite powerful and pure; not like Chibimoon's Heart, but it was still very powerful. Then, she also felt that Sailor Moon's Heart was as pure and powerful as Chibimoon's.
"I don't know how I didn't notice this before… The Hearts of the three of you are exceptionally pure and powerful. I thought that the little girl was the only one who had a Heart similar in purity to the Princesses of Heart, but I was wrong. Instead of just taking her Heart with me, I'll take the Hearts of you three." –She stated with her malevolent voice. –"It would be a shame to see such power not to be used."
Walking over to where Sailor Moon and Sailor Chibimoon were, she prepared herself to snatch their Hearts, when Sailor Moon, who was on her knees, grabbed her scepter and yelled:
"You let Tuxedo Mask go, and tell that monster to free my friends, you witch, or I'll…"
"Or you'll what?" –Maleficent scorned of her. –"Girl, I am the one who gives the orders around here, and you aren't in no position to give them to me." –She said, as she slapped Sailor Moon, making her fall on the ground. –"Be a good girl, and I'll take your Heart in last."
With her chest filled with nothing but pain and anger, Sailor Moon quickly stood up and grabbed Maleficent's dress, and pulled the wicked woman towards her.
"I told you to free my friends and to stay away from Chibimoon, witch!" –She yelled at her, this time with a very aggressive voice tone, demanding Maleficent to do what she told her to. This only made the wicked villainess to slap her once again, forcing the girl to let her go.
"You wretched girl! Don't tempt me… You don't know, or understand the true power of darkness, and believe me, when I say that you should thank me for dying without knowing it!"
"You don't know what I and the rest of my friends have faced during our battle against the forces of evil, so don't tell me what I understand or don't understand!" –Sailor Moon replied to her – "I will not allow you to win!"
Fed up of hearing her out, Maleficent decided that it was time to silence her, permanently. Lifting up her scepter, the crystal in it started to glow. She was going to strike her with it. Sailor Moon was able to evade the first blow, by dodging out of the way. Unfortunately, she was not so lucky, when trying to evade the second blow. She knew that when Maleficent's scepter hit her, she would probably be blown into smithereens. The only thing she remembered to do was using her own scepter, in an attempt to block the blow. She waited for the inevitable that was about to happen in a matter of seconds… seconds what looked to her like an eternity. Finally, when both scepters clashed, a light appeared and Sailor Moon's scepter turned itself into what looked like a key-shaped weapon. Its handle was golden, and you could see a small keychain on it. As for the key itself, it was silver, nothing special about it. But all in all, it looked amazingly beautiful.
"A Keyblade?!" –Maleficent yelled, shocked with what she had just saw. –"But that's impossible! After all my hard work to get rid of those pests, and still, that cursed object find a way to oppose me?!"
Still not knowing what was really going on, Sailor Moon felt that with that strange weapon, she could do anything. Strangely enough, she felt her strength coming back. It was like if her body had been immersed in pure energy. She swung the Keyblade left and right, and that just felt natural to her. Not exactly knowing what to do, she let her body move based on instinct. She pointed her new weapon at the evil woman's face, and this time, you could see that she had fear written on it.
"I won't ask you again! Let my friends go, as well as Tuxedo Mask, and go back to where you came from!" –Sailor Moon demanded.
"I think I have a better idea… Heartless, destroy her." –Maleficent ordered the giant Heartless, as she teleported to a safe distance. –"I'll enjoy watching this." –she thought.
The giant Heartless obeyed Maleficent's order, and started to swing his tentacles around, trying to pound Sailor Moon. The vibrations caused by this, made the tower shake even more than before… Sailor Moon, who tried to avoid being squashed like a pancake, started to jump around. Curiously enough, at first, she did not notice that she was leaping higher and longer than humanly possible. Even her Sailor powers did not grant her any kind of physical ability, such as that one. But she did not care. She was too busy trying to stay alive to care about it. Moving as fast as she could, the girl avoided every single strike by the giant Heartless, until, the floor beneath them finally collapsed. As they fell into the ground, chinks of concrete from what used to be the ground of the Main Observatory; were used by Sailor Moon to decrease her fall. Sailor Chibimoon and Tuxedo Mask, who were also falling, were captured by the Sailor Moon in mid-air. Holding them as hard as she could, she used the chunks of concrete as support points; she leapt from chunk to chunk as fast as she could, and in a matter of seconds, avoided a very nasty fall. The spheres where the people that had been trapped earlier also fell, but when they reached the ground, they just bounced a little. It looked like those spheres acted as some kind of protection to those encased in them. Finally, when the three of them reached the ground, the giant Heartless was already smashing more things as it moved towards one of the tower's feet. The smaller Heartless who were covering the rest of the tower, were now quickly descending it, running towards them. After being sure that both Chibimoon and Tuxedo Mask were safe, she ran towards the Heartless, holding the Keyblade with both her hands. As she got near them, one of the smaller Heartless tried to jump on her. Swinging the Keyblade, she hit it, and as soon as the Keyblade touched it, the Heartless blew up... Whatever that Keyblade was, it had the power not only to repel those creatures, but also to destroy them, permanently.
"Hang on, everyone! I'm taking you out of there… And then, then I'm going to get of all these creatures, with your help." –She said, as she ran towards the giant Heartless, wielding the Keyblade.
As she got nearer and nearer the giant creature, the other Heartless jumped on her, trying to block her path. But she did not mind, because inside her it was like something was burning as hot as the Sun, telling her to keep going, eliminating everything that got in her way. Each Heartless that put itself in her way was destroyed by the Keyblade's power. The creatures' eyes looked even more menacing than before to Sailor Moon, as they tried to shred her into pieces, but that did not stop the warrior of justice. Finally, she got close enough to the creature that was holding hostage in its tentacles, the rest of the Sailor Scouts. She used the Keyblade to strike it, and each time the Keyblade hit it, a howl was heard from the creature. Sailor Moon knew she was hurting the Heartless, so she kept hitting it successfully, over and over. After a few powerful blows to it, the creature let go one of the Sailor Scouts, who fell on the ground… It was Sailor Jupiter. She was amazingly pale, even paler than Chibimoon was when Sailor Earth broke the chains that were holding her. Seeing her friend like that, so fragile, so weak, just made the blonde girl even angrier than she was. She attacked the monster, giving everything she had in her, each time she swung the Keyblade. The smaller Heartlesses kept on crawling towards her, trying to hurt her, but she just gave them the same treatment she had given the others before them. One by one all of the Sailor Scouts were let go by the horrible creature, falling on the ground in the same state as Sailor Jupiter was. Powered by the adrenaline flow, she concentrated her energies on one last attack, which could be described as a single ray of light, which came out of the Keyblade and hit the giant-Heartless, making it roar in pain, before it dissipated itself into nothingness. The other Heartlesses also blew up, to her surprise. As this went on, the same ray of light kept on getting brighter, until the point that Sailor Moon had to let go the Keyblade and cover her eyes, to protect them from the intense light. As let go the Keyblade, she felt her strength fading away, and her body feeling wobbly and tired. The last thing she saw before passing out was her friends being engulfed by a strange light, which also engulfed her, and everything that was near.
6. The Awakening
Chapter 6: The Awakening
Sailor Moon felt like if her body had been dried of all of its energy. After being shrouded by the light, the girl only felt a warm feeling, taking over her being, like if she had died and her spirit had left her body. But if she was dead, how come she felt like she was still alive. She was so tired from the battle with the so-called Heartless that had been sent by the wretched woman named Maleficent, that she did not even had strength to open her eyes. She eventually fell asleep or at least that was what she thought had happened. But before that happened, she heard a voice in her head whispering something to her:
"Kingdom Hearts. The worlds have given us this doorway. They want us to be the guardians of their destiny."
For what looked like an eternity, Sailor Moon slept. Slowly, but steady, her body regained its energies back, growing stronger. She felt the floor underneath her was cold, almost icy, but strangely enough, it felt comfortable to her. That was the moment where she realized that she was not dead. She stayed there, without moving for quite some time. Inside her soul, she just wished to stay there forever, without being disturbed by anyone or anything. But she knew that that was not possible, because she needed to know what had happened to her friends, and more importantly, to Mamoru and Chibiusa. Finally, when she gathered enough strength, she opened her eyes and slowly turned her head around, looking at the place where she was... empty darkness and nothing more. Strangely enough was that although the place where she was surrounded by darkness, she could see as clearly as if it was daylight. Then, she looked down at the floor and was amazed with what she saw. The floor was actually a giant stained-glass window. It had a circular shape. She walked over to the edge, and saw that the place itself was a stained-glass pillar. The floor depicted the images of six characters, being three of them human, two boys and a girl, and the other three resembling anthropomorphic animals. All of them had their eyes closed, with the exception of the girl, and of one of the anthropomorphic animals, which looked to her like a mouse. All of them were over a navy-blue background. They were coloured with all kinds of colours. The boy with the golden-brown hair was in the middle of the stained-glass floor, and was much bigger than the other characters, which were inside smaller circles, surrounding a larger circle, where the boy was inserted in. He was holding a weapon similar, if not identical to the one she had used to destroy the Heartless in Tokyo Tower… a Keyblade. That's when she remembered that a huge bright light had engulfed her and the others who were near her.
"Where am I?" –She asked, looking around, trying to see if there was anyone else there. When she saw that there was no one in sight, she started to have second doubts about whether she was alive or dead. Could that be purgatory, or some kind of realm between Heaven and Hell? That was just one of the many questions that Sailor Moon had in her mind in that moment. –"Could this be a dream, or am I awaken? This is so strange…" –She stated, as she noticed that she was not wearing her Sailor Scout outfit anymore, but instead, she was wearing her regular clothes.
"Hello!!! Can anyone hear me?!" –She yelled, waiting for an answer which never came.
Not seeing any other alternative, Usagi looked for a way out of there. At first, she did not see it, but close to her was a staircase. This one was made out of crystal, and it loosed quite fragile, so the girl stepped in really carefully, to make sure that it was safe for her to walk on.
"If this thing would shatter, I bet Rei would tell me that the reason why that happened was because I am too fat…" –She giggled to herself, wondering where the others would be. –"Maybe if I follow these stairs, they will take me to where they are." –She thought as she walked through the staircase.
Usagi kept on climbing the staircase, without seeing the end of it. She wondered where she would end up. At first, she tried to count the number of steps, but she ended up losing the number after awhile. But one thing was for sure, that staircase looked endless. She went on, until finally she arrived at what looked like the same place from where she had departed. But then, she noticed that although the drawings on the floor were the same, the background was golden, and the Keyblade that the boy was holding was different from the previous one. She looked around, looking for something or someone, but she could not find anything. That's when she saw what looked like a shadow, moving on the ground, like if it had a life of its own. The shadow turned itself into a Heartless, which appeared in front of her. It looked like that even there those creatures would not let her go. Looking at it, her first thought was to transform herself, in hopes to defeat it. She reached for her brooch and yelled:
"Moon Eternal Power Make-Up!"
But nothing happened. She tried it once again, but still, the transformation did not happen. It was obvious to her on that point that the Silver Crystal did not work in that place. She started to move backwards, without knowing what to do. She first thought that she could try yelling for help, but who would listen to her? As far as she knew, she was all alone in that strange place. Then, she felt that she was trapped, when her left foot fell that she had reached the edge of the pillar. The menacing Heartless kept advancing towards her, and Usagi was running out of options. Either she tried to fight that thing, not knowing how to get rid of it or destroy it, or she could just wait for the inevitable death at the hands of the creature. It was right there, on that moment that she made up her mind. She took a deep breath and launched herself towards the horrible creature, with a fierce look on her eyes.
"If I die, then at least I won't die without fighting back, you monster!" –She thought to herself, as she threw herself in front of the Heartless.
Then, as a rather shocking development, something appeared in her right hand… the Keyblade. Seeing it in her hands once again, Usagi knew that now she had the power to get rid of the creature. Swigging it, she hit the creature with it, causing it to disappear, just like it had happened before. This time, she was surprised not by the fact that she was able to get rid of the creature, but by the fact that she made the Keyblade appear again, or at least that's what she thought. Another staircase appeared out of nowhere and she decided to climb it. This time though, her spirit kept telling her that she had to climb it, and she was determined to do it so. As she climbed it, more Heartless appeared, but she was not afraid of them, not anymore. Using the Keyblade, she made sure that none of them got near her. The way to the top seemed to her shorter than the previous one, though she did not know if it was the fact of her feeling somehow agiler than before, or if the staircase was shorter. Either way, when she finally reached the top, she did not feel tired at all. Once again she noticed the drawings on the floor, but this time she was surprised by what was laying over a navy-blue background. In the centre of it, there was her, inside the biggest of all the circles, dressed in her Sailor Moon uniform waving her staff in her right hand, and around her, there were other circles, and in each one of them there was one of her fellow Sailor Scouts. Even Sailor Pluto FX Destroyer and Sailor Saturn Net Surfer were depicted in there, as well as Tuxedo Mask. She looked at it and felt like if she was being watched by someone, or something. Who had been the person or persons who did those drawings, and how did they know about all of them, when even she did not know about the existence of FX Destroyer and Net Surfer, not to mention the fact of her old friend Naru Osaka being Sailor Earth? Then, once again she heard that strange voice again, but this time it was not just inside her head. This time, the voice was filling the dark void in which she was.
"Kingdom Hearts. The worlds have given us this doorway. They want us to be the guardians of their destiny."
"Who is there?! What do you want from me?!" –Usagi yelled at the mysterious voice, and waited for an answer. But the only thing she heard was the same sentence, said out loud by the same mysterious voice.
"Kingdom Hearts. The worlds have given us this doorway. They want us to be the guardians of their destiny."
Those words did not make any sense at all, at least not to the blonde girl, who was getting more confused by the minute.
"What does that mean?! What do you want from me and where are Mamoru and the rest of my friends?!" –She yelled in frustration.
There was silence. Not a word could be heard. Usagi kneeled down, and began to cry. She did not know exactly why she was crying about. Was it because she was alone, or because she did not understand why she was there, or maybe, just maybe, because she was all alone by herself? Tears ran down her cheeks. Tears of sadness, but also, tears of solitude and of despair. Then, all of a sudden she heard another voice.
"So much to do, so little time…" –another mysterious voice said –"Take your time. Don't be afraid. The door is still shut."
And with that, a door appeared out of nowhere, not far from where Usagi was. She wiped the tears out of her eyes with her fingers, and she saw how the door looked like. It was a little taller than her, and it was made of what it looked like wood, pink wood, with heart-shaped details magnificently carved in it. Slowly, she got nearer and nearer, and touched it. Her touch made the door open and she looked inside, to see what was on the other side. What she saw was a bright light, which made her blind for a couple of seconds. Although not sure of what she was about to do, she slowly headed into the light, not knowing what was on the other side. A warm sensation was felt by her, as she went through the light. She closed her eyes, and when she opened them, she looked around and saw that she had ended up in a similar place as she was before. The floor beneath her had the same drawings in it, but the background was diamond-white, instead of being navy-blue.
She heard the same voice as before, saying something which she did not understand at first. She closed her eyes once again, and focused on what the voice was saying.
"The closer you get to the light, the greater your shadow becomes." –it said with a firm tone.
This made Usagi look over her shoulder, seeing her shadow getting longer and longer. Then, without any sort of warning or whatsoever, her shadow started to rise from the floor. It possessed the same shape and form as Usagi herself, but it looked more like a Heartless, each second it passed. Then, it started to grow, until it was the size of a 7 floor-tall building. Its shape had also changed, not resembling with its original form. It now looked like a gruesome dark giant, with tentacles springing from its arms and legs. No doubt it was a Heartless, a giant Heartless, which was about to crush Usagi with its powerful arms. Looking at it, made the girl shiver with a strange kind of fear. A kind fear which she had never felt before in her life.
"But don't be afraid. And don't forget…" –the voice continued with the same tone.–"You hold the mightiest weapon of all. So don't forget: You are the one who will open the door."
The last words pronounced by the mysterious voice gave Usagi strength, but above all, they gave her courage to face the creature that was standing in front of her. Inside her, her heart told her that if she wanted to get out of there, wherever there really was, she had to stand up and face the creature that a few moments prior to that, had been her own shadow. Holding the Keyblade in her hands, she charged at the creature. Swinging, she made sure that each time she hit that thing, she felt it. Unfortunately, the giant Heartless was not going to let her hit it with all she had, without attacking her. Using its huge arms, it tried to grab her, but the girl was able to evade that by jumping into the air, and somersaulting over the creature's fist. This went on for a couple of more rounds, until finally Usagi was caught. Trapped in its fist, she started to feel like darkness was sucking her to someplace where light did not have place to exist.
"Now I know how the girl felt on King Kong feels when she's caught by the gorilla…" –she stated sarcastically to herself, as she tried to find a way to free herself from that tight situation.
Using all of her strength, Usagi managed to use the Keyblade and strike the creature on the palm of the hand, which forced it to release her. Somersaulting her way into the ground, she thought for a brief second that she was out of danger for the time being. What she did not expect was the fact that in the ground was something ready to snatch her. The ground was covered with a black liquid, much like the same kind of material that the Heartless seemed to be made of. A long arm emerged from the pond of black liquid, and grabbed her, wrapping itself around the chest, and started to pull her into the black liquid. The arm looked like if it belonged to a corpse or even a skeleton. Its touch was as cold as ice. Usagi tried her best to free herself from it, but when she managed to shake off that arm, another one emerged and wrapped itself around her, followed by another one, and then another one. In a couple of seconds, a dozen or more arms were pulling her into the ground, as she slowly sank into the black liquid. She fought back, but it was useless. She felt like if oxygen in her lungs was being sucked out of them… She felt like she was drowning. There were only two things she could; either she would let herself be absorbed or killed by that black liquid, or she could try fighting it, using more than just the Keyblade. A quick decision was made by her… She would try to combine the power of the Silver Crystal with the power of the Keyblade. She did not know if it would work, because the crystal had not displayed any kind of power, when she tried to transform herself, but what other choice she had? She used what was left of her strengths and tried to get to the surface.
"Don't give up! Don't give up! If you are to see Mamoru, and Chibiusa and the others, again, you have to struggle and not give up! Come on, just a little bit more!" –she told herself, as she struggled to get to the surface.
After what looked like hours, Usagi managed to get to the surface. She was covered in that black liquid, which was trying to pull her back into it. Her eyesight was somehow blurry, but she could see that the giant Heartless was still there, looking at her. Her arms were wrapped up by the viscous black liquid, so she had to use all of her strength to free herself from that tight situation. Managing to free her arms from that stuff, she reached them for the sky and it was revealed that in her left hand, she was holding her brooch. Opening it, it revealed the Silver Crystal. She united it with the Keyblade, which rested in her right hand and said:
"Silver Moon Crystal Power Kiss!"
Even though she had not been able to transform herself into Sailor Moon, Usagi figured that she could use the power of the Silver Crystal, channelling it through the Keyblade. An idea which proved to be right… the Keyblade channelled the attack of the Silver Crystal, firing it against the giant Heartless. It was a direct hit. The girl could hear the creature howl in pain, as the attack pierced its chest, making it explode. The explosion caused a shock wave that was so great, that all darkness surrounding Usagi was blown away like if it was nothing more than a layer of dust. It was also so great and powerful that the girl passed out. What happened next was a complete mystery for Usagi, because this time she woke up in a different place from where she was before. She felt something soft beneath in whole body. She slowly opened her eyes, to find she was lying in the grass, in what looked like a very peculiar garden. It had a couple of trees, all of them surrounded by small bushes. She slowly got herself up, which proved to be more difficult than she thought at first. Her legs felt wobbly, and the rest of her body was shaking like if she was cold. She looked around and there was no one around. The sky looked funny, because it looked like an Aurora Borealis, where you cold see colours like baby-blue, navy-blue and green, fusing into a beautiful light show. Then, she looked to her right and saw a very peculiar building. It had a surrealistic and crooked look, and it was golden-brown. Smaller towers were attached to it, and the windows were star-shaped. The towers were topped with greenish cone-shaped turret roofs, being the roof of the main tower which was blue, with white stars stamped on it. Usagi wondered if anyone lived inside. When she reached the entrance, a red door appeared. She knocked on the door, but no one answered, yet she could hear voices in the inside.
"Hello! Is anyone home?!" –she asked, as she knocked on the door, this time harder than before. Still, no one answered.
She pushed the door, forcing it to open, when she was surprised to see that it was unlocked. She looked inside, and the first thing she sees is Luna and Artemis, who were walking around in circles, as if they were worried about something.
"Usagi!" –Both Luna and Artemis exclaimed, as she walked in the tower.
"Luna! Artemis! You're alright!" –she exclaimed, as the two cats jumped on her, happy to see that she was alright. For a couple of seconds, Usagi forgot about everything that had happened, and did not care with what was really going on, because now she knew that she was not alone in that strange place.
7. Discoveries
Chapter 7: Discoveries
Usagi was so happy to the two cats, that a couple of tears dropped from her eyes… tears of happiness. But Luna and Artemis were also quite happy to see her. As she kneeled down, caressing both their heads, the cats smiled at her, making her also smile.
"Oh, you two don't have the slightest idea of how happy I am, for seeing both of you here." –she said, as she gave each one a kiss in the forehead. –"But, where are the others? Where are Mamoru and Chibiusa? What happened to you after I defeated that monster?"
Usagi kept bombarding both cats with questions, without even giving them a chance to answer them. Finally, when Usagi calmed down a little, Luna put her paw on top of the girl's right hand and said with her usual gentle and calm voice:
"Usagi… I'm afraid that we don't know exactly what happened to us. But we'll tell you what we know." –Luna said. –"When we got caught by the tentacles of that horrible and strange creature, and were encased into what I think were capsules of pure darkness, none of us have any memories of what happened after."
"What do you mean by "we", Luna? Who's here besides you?" –Usagi asked the cat.
"Please, let me finish, Usagi… After that, we woke up in this atrium, the girls, the boys and ourselves… But, Chibiusa and Mamoru, they were not with us, when we woke up."
"You mean that Chibiusa and Mamoru are gone?! They are not with you?!" –she asked, as panic stroke her heart. You could almost say that her voice gave the impression that an arrow had pierced her heart, filling it with despair. –"What about the Rei and Ami, and the rest of the group, where are they?!"
"When they saw that neither Chibiusa, or Mamoru or you were with us, they decided to explore this place, to see if they could find you." –Artemis explained –"They went up those stairs, and they never came back. We were just behind them, when they reached a wall. Ami, who was leading the group, touched the wall and then a light engulfed them, and they disappeared right in front of us."
"We called them for almost an hour, but none of them answered, and then you appeared, when we were trying to come up with another way to get to them, wherever they are." –Luna said.
"So, you say that they disappeared up there, and you haven't heard from them for almost an hour?" –Sailor Moon said, to which both cats asserted with their heads. –"Then, let's see if we can find out where they went."
As she got up, she took a look at the place where they were. Usagi was so happy in seeing her feline friends that she did not even care about where she was. Looking at the place, she was marvelled with the beauty of place. She was standing in the middle of a magnificent round entrance, but its decoration was rather simple, but that's what made it so magnificent. It was surrounded by an upward-spiraling staircase, which lead up. It was golden and it sparkled every once in awhile, giving it a feeling that it was magical. The girl went up, followed by the two cats. As she went up the stairs, inside her heart, she could feel the presence of her friends. Suddenly, they reached a dead end. In front of them was a wall. There was nothing weird or different about it, at least physically. Intrigued, Usagi decided to touch the wall, and see if anything happened. Raising her left hand, this one trembled as it got closer to the wall. Then, when fingers touched the wall, this one glowed for a brief second, and then the glow disappeared right after, revealing a door which was not there before. It was a door such as any other, but it had a golden crescent moon carved in it. Now, this golden crescent moon had a very peculiar detail… it had a key hole in it. The girl seeing this, instantly recalled what she had heard before in that strange place, where she had been before ending up in that tower: "You are the one who will open the door.".
Raising her right hand, she instantly made appear the Keyblade, which surprised both Luna and Artemis, who were not expecting that to happen. As for Usagi, she was already getting used to that, so it did not surprise her. She swung the Keyblade, and pointed it right into the keyhole. A beam of light was shot from the Keyblade, which hit the door. A noise was heard… a noise which was similar to a door unlocking. Both cats looked at each other, not realizing what just had happened. Luna then asked:
"Usagi, what is that, and just happened?"
"This is the Keyblade, or at least that's what I think they call it, and I think I just found a way to get to where the others are." –the girl answered a little unease, because not even her knew if what she was telling was really the truth or not. Before the cat could ask anything else, she said: -"Don't ask me how I know this… it's complicated. I just know it, and for now, that's good enough for me."
The black cat nodded with her head. Still holding the mysterious Keyblade in her hand, Usagi walked forward and pulled the door, opening it. The door creaked when she opened it, which gave both her, Luna and Artemis the chills. When they opened it, they saw they had entered in a circular room. And to their surprise, there they were, the Sailor Scouts. Usagi noticed that they were wearing their civilian clothes, which meant that they had de-transformed. When they saw who had opened the door, they rejoiced. Ami, Rei, Makoto and Minako quickly ran towards the blonde girl, giving her a big group hug, while giggling. Naru also joined the group hug, being quite happy to know that her friend was safe and sound. As for Haruka, Michiru Setsuna, Hotaru, Johnny and George, upon seeing her, they all smiled to her. Although it did not look like much, Usagi knew that that was their way to say that they were extremely happy to see her too… After all, at least Haruka and Michiru, as well as Setsuna and Hotaru had always been known for not showing their true feelings in a rather spontaneous way, like the rest of the girls.
"It's so good to see that you're alright!" –Minako exclaimed, as she once again hugged Usagi.
"I'm also happy to see that you are alright too…" –Usagi stated in her old fashioned cheerful voice.
"But, tell us… where did you go, and is Mamoru or Chibiusa with you?" –Ami asked her.
She quickly told them what she had been through and also showed them the Keyblade, telling them that it was thanks to that strange weapon that she had been able to apparently save them from the giant Heartless creature that attacked them.
"So, you're saying that that sort of key thing helped you saving us from that thing, an that it led you here?" –Rei asked, intrigued with all that.
"Yes… or at least, I think so." –Usagi answered her, as se showed them the Keyblade.
"But what is it, really? Is it a weapon, is it a key… or is it both?" –Naru asked her.
"I don't know, but I think it might be both things, combined into one." –Usagi answered. –"I don't even know how I make it appear and disappear." –she said, as she accidently dropped it.
When she was about to knee herself to grab it, the Keyblade flew back to her hand, like if it had been attracted to her like a magnet. All of them were quite surprised with that. Johnny decided to tae a closer look. Pressing a button on his watch, what looked like a miniaturized scanner scanned the Keyblade in just a blink of an eye. A few seconds later, his eyes could not believe what the report said.
"Unknown material? How is that even possible?" –he asked out loud, not believing in his on eyes.
"What do you mean by "unknown material"?" –Makoto asked him.
"What I mean is that this thing is made of some kind of material that does not resemble any kind of material that can actually exist." –he explained her, not knowing if what he was saying made any kind of sense.
But before anyone could ask him anything, the door behind them was sealed shut, and Johnny's watch started to beep once again, just like it happened at the Hikawa Shrine. That could only mean one thing: trouble. In a couple of seconds, Heartlesses appeared out of nowhere, surrounding the group. Not seeing any other option, the whole group, with the exception of Usagi, decided to transform, only to find out something unexpected.
"Mercury Crystal Power Make-Up!" –Ami exclaimed.
"Mars Crystal Power Make-Up!" –Rei exclaimed.
"Jupiter Crystal Power Make-Up!" –Makoto exclaimed.
"Venus Crystal Power Make-Up!" –Minako exclaimed.
"Uranus Crystal Power Make-Up!" –Haruka exclaimed.
"Neptune Crystal Power Make-Up!" –Michiru exclaimed.
"Pluto Crystal Power Make-Up!" –Setsuna exclaimed.
"Saturn Crystal Power Make-Up!" –Hotaru exclaimed.
"Sailor Pluto FX Destroyer, Fighting Mode, Activation!" –Johnny exclaimed.
"Sailor Saturn Net Surfer, Fighting Mode, Activation!" –George exclaimed.
To everyone's surprise, none of them transformed. Only Usagi was not surprised by that fact.
"Our transformations do not work in this place. Believe me, I know that because I tried to transform before, and my brooch didn't work." –the girl explained them. –"The only way to get rid of these things is to use the Keyblade.
She then proceeded to demonstrate the others what she was talking about. Swinging the Keyblade, she quickly took out the first wave of Heartlesses that jumped on her and the others. Then, when she thought that she had got ridden of all of them, a new kind of Heartless appeared. This one was similar to the ones that had first appeared, but they were taller and their limbs, as well as their claws were longer. They also were faster and agiler. One of them tried to attack Hotaru, but Usagi managed to repel it by shooting what looked like a energy dagger from the Keyblade, which hit the creature, making dissipate right in front of her eyes. Being a little scared of the amount of Heartlesses that appeared every time one of them was taken down, Hotaru held on to Setsuna, closing her eyes, just like small children do when they are afraid of things, waiting for someone to make it disappear or tell it to go away. Setsuna was also a little nervous with what was going on, but she tried to remain calm, so Hotaru did not get even more scared than she already was.
Johnny and George formed pairs with Makoto and Haruka respectively, and tried to attract the attention of the creatures to themselves, thus protecting the rest of the group. Even Luna and Artemis hissed at the creatures trying to scare them away. But the rest of the group quickly gathered enough courage to help the others. Punching and kicking them, did nothing to those creatures, because no matter how hard they attacked them, they just kept coming forward. Knowing that her friends were in danger, and that she would take too long to take care of all of them by ust using the Keyblade, Usagi decided to use once again the combined power of the Silver Moon Crystal and the Keyblade. Grabbing her brooch with her left hand, she wielded it in the air and then cried out:
"Silver Moon Crystal Power Kiss!"
With that, rays of light spanned from the Keyblade, striking all of the Heartlesses, making them disappear in front of their eyes. They were all amazed by the kind of raw, but subtle power that had been released by Usagi's Keyblade. When the last of the horrible creatures was destroyed a wave of light swept the whole room, thus revealing yet another surprise, a new door.
Michiru who was the one closest to the door that appeared right out of nowhere, went to examine it. It was similar to the one that they had used to enter in that same room, but instead of a crescent moon, a star was carved in it. She touched it, and the door slowly creaked, revealing what was on the other side. In front of her, there was another staircase, similar to the other which had lead them there, but this one was emerald-green, made of some kind of rock that reflected the supernatural and strange glow aura of that place. The others went to where she was, and were somehow amazed by the beauty of the place. If the other areas in which they had been were gorgeous, this one was certainly the most dazzling of them all. When the last one of them exited the room, the door closed behind them, disappearing right after. In its place, a wall of the same colour as the staircase appeared.
"This place is getting stranger and stranger by the minute." –Makoto stated as she looked to where the door had been a couple of seconds earlier.
"Not only that. It's getting scarier too!" –Minako pointed out. –"How are we supposed to get out of here now, folks?"
"Well, it's obvious that we can't go back, so we have no other choice but to keep moving forward, and hope that on top of this staircase there is a door which will lead us outside." –Johnny said.
"And what if there isn't a way out? What will we do then?" –Artemis asked.
"There's only one way to find out that. Let's keep moving forward." –Rei insisted, as she started climbing the staircase.
The others soon followed her. Like her, they did not want to stay in that strange place more than they needed to. As the group went up, Usagi and Naru decided to fall back a bit from the rest of the group. They wanted to catch up, because it had been more than year since they had last seen each other, and so much had happened to them. But furthermore, Usagi wanted to know the reason why she did not awake as a Sailor Scout when the others did. Still, this was a conversation that seemed strange to Usagi, because she had a million questions in her mind, but she did not know where to begin with.
"So… Are you still dating Umino?" –Usagi asked her, not really sure how to start that conversation.
"Yeah, I'm still dating him… he's a nice guy, you know? He may be a little annoying sometimes, but he's sweet and caring, and that's what I love about him." –Naru answered her with a sincere voice.
"That's go to know..."
"But that isn't the reason why you're talking with me, is it?" –Naru asked her. –"There's something else you want to talk about, right?"
"Well… yes, there is. I… I wanted to ask you about…"
"About me being Sailor Earth, right, Usagi?" –Naru asked, already knowing the answer to that question.
The others all heard that, so they slowed their pace, so they could also hear the conversation. Just like Usagi, they all had doubts and questions about their new ally, and they wanted to know the whole thing. Although Usagi did not notice what the rest of the group did, Naru did, but she did not mind, because she new it was only normal they wanting to know the truth. When she saw that they all of them were in her voice range, she said:
"It's only natural you wanting to know why I was only awaken now." –Naru stated. –"Please, give me your hand, so you might see what happen… don't worry, the rest of you will also see it, through the telepathic link that we all share with Usagi."
This last statement surprised the whole group, who were quite embarrassed with that situation, not expecting Naru to have noticed their previous action. Then, she held hands with Usagi, and the world around them went dark, like if they had been teleported to a place where darkness reigned. Looking around, Usagi only saw herself in the middle of that eternal darkness. At first, the blonde girl felt really scared about that, but then she heard Naru's voice, even though she could not see her.
"Do not worry, you cannot be harmed by my memories… you're perfectly safe. This is like a flashback of what really happened to me."
Darkness began to fade away, and what looked like a palace slowly appeared. At first, it felt like the majestic building was part of a blurry dream sequence, but little by little, the building gain a more distinct form, and it looked real. She saw herself outside, in a gorgeous garden. Not far from her, she saw two persons fighting. At first, she did not recognize any of them, but then she looked closely and recognized one of the persons. It was Tuxedo Mask, but he was wearing a different outfit than the one he usually wore. The suit was very much alike the one he wore in the 30th century. That's when Usagi assumed that that was really him, but in the 30th century. The other person was somehow harder to recognize, maybe because she would not stop somersaulting, giving the girl a good glimpse of who she really was. Still, she saw that she was wearing a Sailor outfit. Then, she finally got a good look on her face and saw who she was… it was Naru, or better yet, Sailor Earth.
"What you're seeing is me and Prince Endimion training." –Naru's voice said. –"I was responsible for the protection and well being of Prince Endimion."~
Suddenly, everything went black again, and the place where they were changed. This time, they were inside a beautiful white-marbled room with black stone columns. There were statues around a sumptuous shrine in the middle of the room. And there, right next to the shrine were two people that Usagi did not recognize, a man and a woman, and the woman was holding a baby in her hands, gently wrapped in a white blanket. Then, a double-door behind the blonde girl opened, and someone entered in the room. It was a young girl, dressed in a golden dress. She had brown waved hair tied up in a ponytail with an emerald-green ribbon, which matched her eyes. She slowly walked to the shrine, and bowed in the presence of the two figures. She then raised her head, as the man gently grabbed her left hand and said:
"Are you sure you want this?" –the man asked the little girl.
"Yes, Your Majesty… My only desire is to serve you and the Royal Family." –she said with a cheerful, yet serious voice.
"It is also your family, my dear." –the woman said.
"And that's why I must do it." –the little girl answered, this time with a serene voice, to which the couple agreed.
"If that's what you really want, my dear, then so be it." –the woman said. –"Before we begin, let me just tell you that I would not choose anyone else to carry out this task that you're being given, because I feel that there's something more about you than most people notice.
The words pronounced by the woman were spoken with such tenderness that a small tear fell from the little girl's eyes. What happened next was completely surreal. Some kind of ritual was performed by using a strange object, which looked like a sceptre, but it was much smaller. With it, the couple touched the baby's forehead and something appeared, as the light in the room slowly began to disappear. She recognized that object, which slowly rise up in the air. An object so familiar to Usagi, that its golden glow sent chills up her spine… the Golden Star Seed, Mamoru's Star Seed.
"As you can see, the baby is actually Prince Endimion, while the little girl is me. I was adopted by the Royal Family, and they gave me the position of guardian and tutor of the Prince, even though I was only a couple of years older than he was. I held that position and responsibility over the years." –Naru explained, as the ritual took place. –"But to do that, I would need to carry a piece of the Prince's true heart; the Golden Star Seed. That's why this ritual was performed… The King and the Queen with the help of a magic object were able to break a tiny piece of the Star Seed, and from it, create another Star Seed, which they gave me. That same Star Seed gave me the power to transform into Sailor Earth and also to protect the Prince from anyone or anything that could hurt him."
As her words filled in the room, Usagi's eyes focused on the ritual. On how a piece no bigger than a pin head was taken from the Golden Star Seed, and as it fell towards the shrine, a new Star Seed was created. This one had the same size and glow as the original one, but its colour was emerald-green. The King gently grabbed it and placed it in the hands of young Naru, who then lift it up and allowed it to be absorbed into her chest. An energy outburst originated from the girl, which demonstrated that the Star Seed was now part of herself, part of her body, but more importantly, part of her heart and soul.
All of a sudden, everything around her started to dissolve, like when a paint brush is dipped in water, and Usagi felt like she was being pulled off a dream. She opened her eyes, and saw that she was still in the staircase, alongside Naru and the rest of the group, who had seen Naru's memories just like Usagi. They all felt somehow dizzy, like if they had been inside a whirlwind. Naru was the one that looked worst, because she was quite pale. Ami grabbed her by the waist before she fell on her knees. She closed her eyes for a second and then opened them, sighing.
"Sorry, but I guess the rest of the story will have to wait, everyone." –Naru declared, as she gathered strength to stand up on her feet.
"Are you alright?" –Hotaru asked her, worried about her being so pallid and so fragile.
"I'll be alright, Hotaru… It's just that showing these memories to all of you drains a lot of my energy."
"You could have just told us what really happened, without the need to use your powers, you know?" –George stated, to which the others all agreed, by nodding their heads.
"No… You all had to see for yourselves, with your own eyes what really happened. But I guess the rest of the story will have to wait."
"Don't worry, we'll wait for you to sow us chapter 2, when you feel like you're strong enough." –Minako declared, giggling about it.
This made Naru also giggle, making her feel a little better already. The others also giggled about it. It was not the first, and it would probably not be the last time Minako would make them giggle or laugh about one of her commentaries. After that moment, Usagi and Ami made sure that Naru was strong enough to keep up with them, before resuming their climb. To show them that she was feeling much better, she gently picked up Luna and Artemis, ad decided to carry them with her while climbing. She had always been very fond of cats, and found that that would be a way for her to also help the felines climbing that huge staircase. Haruka and Michiru kept on leading the way. Their footsteps echoed, a noise which was not bad, but it was rather uncomfortable, because it felt like they were not the only ones there and they were probably right about that.
"Are you guys starting to think that this staircase goes on forever?" –Makoto asked them, not knowing what the others were going to say about it.
"I don't think so… We're bound to find the end of them sooner or later." –Setsuna said.
"I agree with you. There is no way these stairs can go on forever." –Rei agreed.
"Actually, they might go on forever." –Ami said with a voice which looked more like a whisper.
"What are you talking about, Ami?" –Usagi asked her. –"These stairs have to lead somewhere. This is not the Twilight Dimension… I think."
"No. I'm afraid se might be right about it… It's clear that the laws of physics do not apply here. And if they don't, then according to my calculations, I'm afraid that these stairs might go on forever and ever." –Johnny said.
"Or not, look! –Haruka exclaimed, as she pointed to something.
Up above them there was another door. None of them knew how that door appeared, because it was not the re before, but they did not care about that fact. As they looked to the door, they saw that this one was different from the previous ones that they had found. This one was a tall wooden double door, somehow similar to the one that gave entrance to the tower, but different. The handles were shaped like Stars, and had a small Crescent Moon carved in them. They quickly climbed the rest of the stairs that separated them from the door, and once in front of it, they knock on it and waited for an answer. Seconds passed, but no one answered, so they knocked once again. Still, no one answered.
"Maybe we should just push it, and see if we can open it." –Michiru suggested.
"Okay. When I count to three, we all push the door, alright?" –Johnny declared, to which the others promptly agreed. –"Alright, we're we go… one, two, three!"
They all pushed the door at the same time. Slowly and steady the door creaked and opened. When they finally got it open, they all looked inside and saw that the room they were entering was the largest room that they had seen, since entered in the building. The round walls had several shelves containing many books, all of them regarding multiple subjects. There was a large wooden desk with a matching chair, and behind it, two large windows, one of them shaped like a star and the other like a moon, displayed the Countryside. On to their right, there was another door, this one smaller, which probably gave way to another room. They also noticed that there was someone near one of the shelves, holding a book in his hands. He was an old man with a long grey beard and blue robes that extended to the floor. He was also wearing a blue pointy hat, adorned with stars and a crescent moon. He closed the book and turned to the group, as they entered in the room, still not knowing who the man was, or if he had anything to do with what was happening to them.
"You're here… It took you time to get here." –the old man said with a serene voice.
Usagi immediately recognized the voice, has being the voice that she heard, when she ended up in that strange dark place.
"You're the voice I heard! Who are you?" –Usagi asked the old man.
"My name is Master Yen Sid, and I've been expecting you and your friends, Sailor Moon… or should I call you, Usagi Tsukino?" –he declared, surprising them all, with the fact that he knew Sailor Moon's real identity.
8. A New Adventure
Chapter 8: A New Adventure
They were all in pure shock. Whoever that strange man was, he seemed to know about their secret. Thoughts started to develop in the minds of all of them. If that man knew about Usagi's true identity, would he also know about the rest of them?
"How do you know about her identity, and what do you want from us?!" –Haruka asked him, not trusting him. In her mind, he could very well be a fiend.
"You are quite feisty one, aren't you, Sailor Uranus?" –Yen Sid asked her, revealing that he also knew her true identity.
"That still doesn't answer the question f how do you know about our true identities as Sailor Scouts, and what do you really want with us." –Michiru snapped, not trusting him either.
"You're quite right, my dear." –he observed. –"Very well, then, I better get to the point. I know who all of you are and what is your mission, but you only know my name. I thnk this calls for a more detailed presentation of myself. Like I said before, my name is Yen Sid and I'm the master magician of this world called Mysterious Tower. I'm also the one who brought you here, after Maleficent attacked you in your world, with the help of the Heartless."
Usagi and the others were somehow surprised by the fact that the man knew about the existence of Maleficent and her attack in Tokyo.
"You know that witch that attacked us?! And what do you mean about "our world"? What is that supposed to mean?" –Haruka asked him, yet again with the same aggressive tone as before.
"All in due time…" –Yen Sid said, as he got up from his chair and moved towards the group. –"First of all, let me apologize for the fact that not all of you are here. I tried to bring you all into here before being captured by Maleficent, but I was not successful in bringing two members of your group."
Usagi immediately reacted to that statement. He was talking about Tuxedo Mask and Sailor Chibimoon.
"Then, where are they?! Where are Sailor Chibimoon and Tuxedo Mask?!" –Usagi asked him. Her voice revealed fear. Part of her wanted to know what had happened to them, but the other just wanted to ignore that they might be I peril.
"I'm afraid that Tuxedo Mask has been taken by Maleficent. To where, I do not know, but he is alive, have no doubts about that. As for Sailor Chibimoon, I was able to use my powers to also get her out of there, before Maleficent could put her hands on her. But, while bringing you here, I used a lot of my energy, and unfortunately, I ran out of strength before I could bring her here." –Yen Sid declared, seeing fear and horror in Usagi's face. –"But do not worry, for I know where she is. She is in a world different from this one, and as far as I can feel she is not in peril… at least, for now."
"That's another thing! Why do you keep saying "worlds"? What do you mean by it?" –Rei asked.
"Yeah, there are already too many words and expressions which we don't know what people are talking about. First, that witch referred to a thing called Kingdom Hearts, and that she was there because of Sailor Chibimoon's heart." –Johnny stated. –"Maybe it's time to get some answers as to what that woman was talking about, who is she, and what do you have to do with her."
"Yes, you're entitled to an explanation, my friends. I'll try to simplify things, although the things I'm about to tell you might be hard to accept or understand at first."
"Try us; we're used to deal with strange and unbelievable things." –Haruka said, defying the old man.
Yen Sid returned once again to his desk. As he sat on his chair, he looked them in the eyes, and then he clapped his hands. All of a sudden, a sphere of bright light appeared, and started changing shape quite slowly. In a matter of seconds, it had assumed a different shape and different colours. It displayed what looked like a living planetarium, but this one was amazingly different from any kind of planetarium they had ever seen before. There were things that looked like small planets floating around, life if they were underwater. These small planets all had different shapes and sizes. They all look at them, wondering what they were.
"What you see are just some of the many worlds that exist. All these worlds were once connected by ways that most people do not imagine, or cannot understand. Pathways that could only be opened by the ones who wielded a special key… the Keyblade." –Yen Sid explained them.
"Pathways? What kind of pathways?" –Setsuna asked, intrigued with that fact.
"Pathways are in many ways similar to tunnels… links between these worlds. If the pathways are closed, no one can get in or out of a world, but if this one is unlocked through the use of the Keyblade, any being who knows about their existence can use them to travel into other worlds."
"So you're saying that our world is just one of many worlds which compose an even bigger world, similar to a Universe, and those worlds have multiple side-dimensions, also known as alternative realities, but one of these dimensions is like a Prime-reality, which shapes a world as it is… Is that it?" –Hotaru asked.
"In rather simple terms, yes."
That kind of knowledge was mind-blowing. To know that there were alternate realities to theirs was one thing, but to find out that their "world", or universe, was part of an even bigger universe, was something that none of the Sailor Scouts were exactly ready to know about. Luna and Artemis, who were both amazed and terrified with what they were hearing, decided to post themselves a question to Yen Sid.
"You also referred to others having used the Keyblade before. Does that mean that Usagi is not the first one to use it, and more importantly, she's not the only one who can use it?" –Artemis asked.
"Indeed, my feline friend." –Yen Sid declared. –"She's not the first one to bear the Keyblade's power, and she's definitely the only one who can use it."
"But, what is a Keyblade? What's its true purpose?" –Luna asked.
"A Keyblade is (transcrição do que é a Keyblade)
All of you who are here in this room can use it."
Once again, they all felt like they were struck by lightening. They had already seen that Usagi was able to conjure a Keyblade and to use it. But the fact of them also being able to do the same had not crossed their minds.
"You mean that we can all conjure a Keyblade?" –Naru asked.
"Why, yes, you can. All you need to do is to concentrate on that thought, and you will also be able to do it like you friend. Why don't you try it, now?"
Believing in Yen Sid's words of wisdom, Naru closed her eyes and focused her energies on that thought. Seconds passed, but nothing happened. She did not feel different or anything.
"Nothing's happening… I can't feel anything." –Naru said, with her still shut. She did not open them, because something inside her was telling her that she should keep them shut.
"Focus on your Heart, young one. Find your Heart and you'll find what you're looking for." –she heard Yen Sid saying.
Once again, she tried. Little by little, she finally found something inside her that wanted to come out… something that wanted to be free… to be unleashed… to fulfil its destiny. She found her Keyblade. It was an amazing object, floating in total darkness. Somehow, it had a mysterious glowing aura around it. Its guard was made out of what looked like crystal, and you could see a small keychain shaped like Earth's symbol on it. The blade was emerald-green and the tip, as well as the teeth was shaped like a stylized "N" from the same color as the key. Opening her eyes, she saw that the Keyblade was in her right hand. Everyone was amazed with what Naru managed to summon, just like when Usagi first summoned her Keyblade in their presence. But even more amazed and surprised was Naru herself. She looked at her Keyblade and wowed.
"My God! I don't believe it… One minute, I see it in my mind, and then, I'm holding it." –Naru said, as she lightly swung it, admiring its beauty.
"That is the power of your Heart, Sailor Earth." –Yen Sid said. –"And the same thing applies to all of you, my friends. You also have the power to summon a Keyblade… You just have to find it, within yourself, using the power of your Hearts. Why don't you also try and find it, right now?"
They all did as they were told. They all closed their eyes, and waited. They all tried to find their Keyblades. Little by little, they all started to feel something inside them. Some of them, like Rei and Setsuna were able to successfully find theirs, but others like Minako and Ami, found this task harder. Still, they all managed to find their own Keyblade and feel their power, while admiring their beauty. Ami's Keyblade had a very curious design, to say the least. The guard was shaped like a breaking ocean wave on both sides, while the blade was baby-blue and its teeth were shaped like a jet of water. The keychain in the handle was shaped like Mercury's symbol.
"Incredible!" –Ami exclaimed, as she gazed at her Keyblade.
Rei's Keyblade was also very peculiar. The guard was shaped like a ball of fire, and its blade was red with what looked like black kanji for fire and spirit, stamped in it. The teeth resembled the guard. The keychain in the handle was shaped like Mars' symbol. All in all, a rather peculiar Keyblade, which reflected tradition and mystique.
"Fantastic…" –Rei said, as she gazed upon the kanji stamped on the blade.
Makoto's Keyblade was rather complex. Its guard was shaped like a black cloud, from which two white blades shaped like lightening came out and were united by another lightening, this one being yellow. The teeth were shaped like a stylized M. Finally, its keychain was shaped like Jupiter's symbol.
"Wonderful." –Makoto sighed, passing her finger through the blade.
Minako's Keyblade looked like it had come out straight from a designer's mind. The guard was golden and shaped like a heart. The blade was white and had a golden chain around it, similar to the chain from her "Venus Love-Me Chain Atack". The key's teeth were shaped like a red heart. Its keychain was shaped like Venus' symbol.
"Wow… Mine's a work of art!" –Minako exclaimed, as she give a small kiss on the blade.
Setsuna's Keyblade resembled her Garnet Orb. In fact, the Keyblade's guard was exactly like it. The blade was black with a white stripe in the middle, and its tip resembled a skeleton key, with its red and black teeth. You could see that the keychain was shaped like Pluto's symbol.
"What an otherworldly beauty…" –Setsuna thought to herself, as she paid attention to the details of the guard.
Haruka's Keyblade was somehow different from the others, because of its shape. The guard was similar to her Space Sword, carved with jewels of all colours, while the blade was black and had two barbed shafts and teeth resembling a battle axe split into three almost claw-like protrusions. Sinister, but beautiful at the same time.
"Now this is a weapon…" –Haruka whispered to herself.
Michiru's Keyblade had a rather interesting design. Its guard was shaped like a violin, to which the blade was attached, having the same design as the handle. Its teeth were shaped like a black treble clef. The keychain was shaped like Neptune's symbol.
"So simple, yet so gorgeous." –Michiru stated, passing her fingers through black treble clef.
Hotaru's Keyblade was probably one of the scariest Keyblades of all. Its guard was shaped like a purple hourglass, while the blade was grey, and the teeth resembled the Grim Reaper's scythe. The keychain was shaped like Saturn's symbol. Still, even if it looked menacing, she liked it very much.
"It's really creepy, I suppose, but it has a sweet side, I suppose." –Hotaru commented, as she swung it, feeling its weight in her hand.
Finally, Johnny and George's Keyblades were very different from each other. Johnny's Keyblade was in a way similar to Setsuna's, but different. The guard resembled his shotgun but it had bat wings, and the blade was half black, half red. The teeth were shaped like a menacing black claw. As for George, his Keyblade was completely out of the ordinary. The guard was completely silver, as well as the blade, which was shaped like a sword. There was also a small detail about the guard, which was the fact that it was surrounded by a yellow ring, which kept floating around it, giving it an unusual look. What was more interesting was the fact that his, was the only Keyblade, which had no resemblance with a skeleton-key. Just like the Setsuna and Hotaru's Keyblades, theirs also had each one a keychain shaped like Pluto and Saturn's symbols.
"Outstanding!" –Johnny exclaimed.
"Wicked, but cool!" –George stated.
They were all marvelled with their Keyblades. They were not just weapons to them. They felt like those objects that they were holding in their hands, were like a part of their own soul. Usagi's soul could not stop rejoicing about the fact that their friends also had Keyblades, and that they were really happy about it.
"You see, now, that the power of your Hearts can accomplish any challenge that you might face in the near future, just like you have done in your home world."
"That's another thing… What exactly are "Hearts"? I mean, I known that they are not our physical hearts, but they are something that is referred to by that name. Can you tell us exactly what they really are?" –Johnny asked.
"A Heart is one of the three parts that comprise a being. The other two parts are the body and the soul. As for what a Heart is made of exactly, I'm afraid that not even I know the answer to that riddle. But I do know that a Heart is mainly made of light and darkness. There are of course 7 exceptions to the rule… the Princesses of Heart."
"That's another thing that Maleficent spoke of. Who are these Princesses and why they seem to be so important?" –Usagi asked.
"The Princesses of Heart are seven maidens' whose Hearts are made purely out of Light. Each one of them comes from a different world, and when the seven are gathered in one place, Kingdom Hearts might be unlocked." –Yen Sid explained. –"No, you're probably wondering what Kingdom Hearts is. Well, to explain you that, I'll be showing you something that happened."
Waving once again his hand, a book flew from one of the shelves right into his hands. Grabbing it, he opened it and a mysterious light appeared from it. Then, images started to appear, little by little. They all saw that the images were of a boy who was wielding the Keyblade in his hands. He was accompanied by two anthropomorphic animals, a duck and a dog. Usagi recognized them as being three of the characters that she saw when she woke up in that strange place.
"The boy you're seeing in these images is the Keyblade's Chosen One. His name is Sora, and the two characters that are by his side are Donald and Goofy, two of King Mickey's loyal subjects… Donald is the court's magician, and Goofy is the captain of the Royal Guard. King Mickey was my apprentice once, you know? I taught him everything I could in order to make him a better king, and he used those teachings to do what he thought it was right, and that was an attempt to stop Kingdom Hearts from being opened." –Yen Sid, as the whole group watched the holographic images of the countless battles. –"Still, he was not alone… Sora, Donald and Goofy helped him, along with many others, in his battle against many enemies. They prevented Kingdom Hearts from being opened twice."
"But, what is Kingdom Hearts?" –Michiru asked.
"Kingdom Hearts is what you would call the Heart of all worlds." –Yen Sid stated, as the image changed again, this time showing a Moon shaped like a Heart. –"It is a source of enormous power and knowledge. That's why so many have tried to gather Hearts in order to open it. It is said that the one who's able to open Kingdom Hearts will be given infinite power and wisdom, but all that will come with a terrible price… If Kingdom Hearts is opened, it will most likely unleash a huge amount of darkness, which will invade all worlds, dooming them forever. Sealing it off prevents that darkness to spread and contaminate other worlds."
"That's all very interesting, but that doesn't explain why we are here. I mean, don't get this wrong, because I'm incredibly thankful for getting us all out of that tight jam, but to bring us here, you probably want us to help you with something am I right?" –George asked.
"Indeed… I brought you here, because you are the only ones who can prevent Kingdom Hearts from being opened." –Yen Sid answered.
"But, you just told us that Sora, the other Chosen One and your former apprentice had been able to prevent it from being opened. So what's the problem with it? Why don't you just call them here, so they can stop whoever it is from open it again?"
"I'm afraid that I can't do that, because they have disappeared from the world they were in, without a trace. The only one that has not disappeared is King Mickey."
The whole group reacted to this. This all lead Hotaru to comment about that fact.
"Well, maybe they just decided to use the Keyblade to go for a joyride in another world." –she commented with her rather cheerful voice.
"I don't think so. If this had happened, I would have been able to locate any of them, wherever they were. I even thought that they might have been accidentally transported into the past or the future, when using the Keyblade's power, but I could not sense their presence there either. I think that someone has managed to somehow, erase their existence from the time flux. It's as if they never even existed in the first place… which would explain why the Keyblade chose Sailor Moon to be its new wielder, as well as the rest of you." –Yen Sid stated.
"But, who could have done that in the first place? Who would have power to eradicate someone from the time flux itself?" –Minako asked
"That's impossible… I mean, it's not impossible to eradicate a person from existence, but if there is one thing that I know, is that the consequences of that act could compromise Time itself. I believe that they must have been removed from the time flux current. It is impossible to eradicate someone from the time flux current, without creating massive disturbs in the Past… whoever did that, must have known that the acts of such action could also prevent it from reaching its goal." –Setsuna declared. –"Removing a person from the time flux current is actually safer, than trying to mess up the whole time flux current." –Setsuna declared.
"Yeah, it's actually quite easy to do that… You only need to know which person you want to get rid of, find a place where time does not exist, and put that person in there, making sure that it won't have a chance to escape from there… end of story. As for the kind of power needed to do that, well, you would need to have some kind of artefact that enabled you to travel through time and space as it is. Not exactly your average trip to the shopping mall, that's for sure." –Johnny agreed.
"I bet that witch Maleficent is the one behind all this!" –Makoto exclaimed.
"My thought exactly... But I do believe that she's not the only one behind it… Her powers over Darkness are very great, but, I do believe that someone else might be helping her. Still, if she really is behind all this, then there's only one way to get Sora, Donald and Goofy back from wherever they are. You'll have to go back in time, and make sure that what they made to prevent Kingdom Hearts from being opened really happens." –Yen Sid declared.
"You mean, we have to go back in time and do whatever it takes to make sure that their actions really happen, but instead of being them doing those actions, we will be the ones doing them, is that it?" –Haruka asked, to which Yen Sid complied, by waving his head affirmatively. –"But, how is that going to help us finding those three guys?"
"You see, if you're able to make sure that Kingdom Hearts is never opened, you'll be able to follow their footsteps, and maybe, by doing that, you'll make contact with those who helped them, and furthermore, with those who they fought against. That way, you'll be able to gather clues to the place where they really are, and get them out of there."
"Great…" –Haruka sighed, knowing that the task they had been assigned for was not going to be easy.
"Come on, Haruka, it'll be fun. Besides, you should see this as another adventure, you know?" –Michiru declared, as she tried to flirt a little with Haruka, who answered back with a little, but cute smile in her lips.
"Okay, you can count on us, right, everyone?!" –Usagi asked them, to which they all said yes. –"But before that, can you tell me where exactly Chibiusa is?" –she almost pleaded to Yen Sid.
"You'll find out where she is soon enough, Sailor Moon… I ca guarantee you that you will see her very soon. But before you all go, I must give you a little present, as well as instruct you in a few more things you should know, before starting this new adventure of yours." –Yen Sid said, as he signalled them all. –"Follow me, please."
9. New Clothes
Chapter 9: New Clothes
Following Yen Sid, the group went through the door that was on their right when they entered. The door led them to another room. This one was smaller than the study where they were previously. Inside it there were also a large wardrobe, and several mirrors, which were covered with white sheets. In the middle of the room there was a small round table, with matching chairs. There were three women right next to the table. Although they looked smaller than them all, the three women were imposing figures just like Yen Sid was, and they all could sense it. One of them was dressed in red with a matching pointy hat, while the other two were dressed in green and blue, also with matching pointy hats. All of them had a pair of small wings. This made them looked like fairies, they all thought. When the three characters saw that they had company, they quickly turned around to meet the visitors.
"Oh… hello there, dears." –the woman dressed in red said. –"My name is Flora, and these are Fauna and Merryweather."
The other two women waved at them, always with a smile in their faces. The Sailor Scouts all waved back, feeling a little unease with that situation. They did not know what they were doing there, and asked themselves if those three women, who looked like fairies, had anything to do with it. Yen Sid broke the creepy silence that filled the room, by clearing his throat.
"Dear ladies, these here are the Sailor Scouts. They are the Keyblade's new chosen ones. But before I give them a few last pieces of vital information, I thought that you could help them, by giving them something which will help them in their quest." –Yen Sid stated.
"Oh, certainly, Master Yen Sid." –Fauna declared. –"I think I know exactly what you mean… This group really needs an upgrade."
"That's for sure… and nothing better than a pair of new clothes for each one of them to give them the perfect upgrade." –Merryweather said, as she looked at them.
None of them really understood what they were talking about. Already fed up with that gibberish, Minako finally said:
"What's wrong with our clothes?! I don't know about you, but from where we come, these clothes are the high from this year's fashion." –She said, like if what they had said was an offense.
"Oh, I'm sorry, dear; it's not that your clothes aren't pretty." –Fauna declared.
"But the clothes you are wearing right now are just regular clothes, and that will not help you in this journey of yours." –Flora stated.
"That's why you are all going to need special clothes, which will shine your personality, but above all, which will help you managing the power of your Keyblades, as well, as gathering and mastering techniques and movements." –Merryweather explained. –"And without any delays, we're going to start with you, my dear."
"I'll do the designing." –Fauna said.
"We'll do the designing together, Fauna." –Merryweather stated, with a somehow bossy voice.
Finishing that sentence, Merryweather approached Usagi and gently grabbed her by the hand, pulling her closer to her and the other fairies. Telling her to stand straight, and to relax, the three women grabbed what looked like wands and pointed them.
"Very well, girls, let's do this… all together now." –Flora said, as Fauna, Merryweather and herself, focused.
With a gentle twist of the wand, the three of them shot a beam of light, which hit Usagi. As soon as the beams hit her, a veil of light enveloped her. Then, it disappeared, revealing Usagi now dressed with new clothes. Her clothes had been replaced by a hooded pink strapless mini-dress, made up with three zippers, although two of them looked just decorative, as well as a white halter top, underneath her mini-dress, a black belt reminiscent of suspenders around her waist, and matching pink shoes. Around her neck, she had a silver necklace shaped like a crown. You could also see pink wristbands in her wrists, and moon-shaped earrings, similar to the ones she wore when transformed. They all noticed, including her, that she was holing her broche, containing the Silver Moon Crystal, in her left hand. She stared at herself in the nearby mirror, looking at every detail of her new clothes.
"This is really gorgeous! A little unusual, I admit it, but it's gorgeous." –Usagi said as she looked herself in the mirror.
"Indeed, the pink suits you nicely, dear." –Merryweather said. –"Come now, don't be shy, everyone. I'm sure we can all give you clothes as pretty as your friend's."
Ami was the next one. Flora looked at her, like if she was looking for something. Fauna looked her deeply in the eyes, and suddenly said:
"I know what will look nice on you, my dear. Please, try to stay still."
Once again, the three of them, with a quick twist of their wands, shot a beam of light, enveloping Ami in a veil of light. The others looked patiently, waiting to see the kind of clothes that they were going to give Ami. As the light veil faded away, they saw the final result. Ami was now wearing a beautiful blue plaited, flower-patterned dress, a pair of black boots and a black spaghetti-string camisole under a white sash of material that wrapped around her neck and over her chest. She was also wearing a yellow patterned Obi with a Chōchō musubi knot and a decorative Obidome to synch the cords. Two separate, kimono-like, sleeves hanging from her upper arms complete the white and blue ensemble, giving the impression that she really looked like a princess. As she looked herself in the mirror, amazed with everything, and with the fact that the dress she was now wearing matched the color of her eyes.
"Now that's a dress…" –Johnny whispered to Setsuna who was near him, when he was grabbed by the arm by Flora. –"Hey, what's the big idea?"
"Oh, come on, young man, I know you're quite anxious to see what we have stored for you, so let's get started." –Flora stated, as she brought him near the other fairies.
"Okay, but don't have any ideas, okay? I don't want to look foolish, get it?" –Johnny declared, still thinking that the three of them had something on their minds, which he did not like.
"Now, don't you worry, the last thing we want is to make you look silly… Stand still, and close your eyes." –Fauna said.
Repeating the same gesture as before, they changed his clothes in a matter of seconds. Johnny was now wearing white shirt, over a short leather jacket with a fur along the collar, as well as small white wings on the back, as well as a light-blue and white symbol that looked like an iceberg on the left sleeve. His pants were black with three shown buckles, to on his left leg, and the other in his right leg. He was also wearing black and red tennis shoes. All in all, his clothes were sort of his style.
"Not bad, not bad at all… You ladies must have been able to read my mind, because this is just the kind of clothes I like." –he said, with a happy voice, as he looked in the mirror.
"We knew you would like it." –Flora said.
"So, who's next in line?" –Merryweather asked the whole group, seeing if she had any volunteer.
This time, it was Makoto who decided to go. She was anxious, as to what the fairies were planning for her. Already knowing what would happen to her, as soon as they used their magic, the girl tried to imagine what kind of clothes she would end up with. The veil of light had not completely disappeared yet, her eyes marveled at the result. Her clothes had a Hawaiian motif; she was wearing an orange with the design of a white flower on the side, light-brown Capri's, orange socks with a white trim at the top, and finally, a pair of yellow, black, brown and white sneakers She also noticed that she had a necklace with a light green sphere, around her neck, which matched her eyes.
"Simple, but very pretty… my kind of clothes, without a doubt." –Makoto thought to herself.
Next, Minako was chosen for the makeover. Even though she first thought that they were saying that her clothes were awful, now she was really excited, because she never thought she would have anyone design unique clothes, just for her.
"Okay, I'm ready! Now, I don't want anything ostentatious, because I like simple things, but you could give me some cool accessories to match my new clothes." –Minako suggested.
"Now, don't worry, dear. As fairy-godmothers, were used to satisfy a person's wishes. Just stand still, and let us do our magic." –Fauna declared.
In a matter of seconds, Minako had what she wished for. She was now wearing a white apron-like shirt with a violet line across the chest, a black shirt underneath the apron-like shirt, a violet mini-skirt which matched the shirt and a pair of white and violet shoes, with purple lines in them. As for the accessories she had asked, the three fairies had given her a yellow wristband to wear in her left wrist, two bracelets, one yellow, and the other black in her right wrist. She was also wearing heart-shaped hearings, and finally, around her neck, she had a necklace with a beautiful amber gem. Looking herself in the mirror, she was speechless.
"I… I… I don't even know what to say… This is the most beautiful outfit that I ever wore." –Minako said, every last bit of it being true about how she felt.
"We're glad we surpassed your expectations." –Flora said.
"Surpassed? You practically vaporized them… This is much more than I expected." –Minako declared, not being able to stop looking at herself in the mirror.
"Come on, Minako! Stop looking at yourself in the mirror, and let one of us also change clothes." –George said, to which she complied.
"Your friend is right. Time is short, so we must go on." –Flora said. – "Okay, now let's see… who will be next?"
Flora looked at them, and decided that the next one would be Michiru. Trying not to move, the aqua-marine-haired girl stood still, as Fauna, Flora and Merryweather used her magic. When the veil of light disappeared, she saw that she was wearing a beautiful long Red Bordeaux wine and pearl cetin dress, with matching shoes. Around her neck, she had a gorgeous choker with marine-blue jewels in it, which matched the color of her hair and eyes. Haruka looked at Michiru and was really impressed, for she never thought that her partner and lover could look even more beautiful than she already was.
"You look dazzling..." –that was all Haruka could say, even though she wanted to say so much more about Michiru's new appearance.
"Oh, don't worry, dear... You will look just as dazzling as her." –Merryweather said. –"By the looks of you, I would say that you are quite the rebel one, although you are loyal to those who are dear to you, and I think me and the girls have just the right clothes for you."
Using their magic, they quickly changed Haruka's clothes. She was now wearing a sleeveless navy blue jacket, with beige Capri pants, which had irregularly placed pockets; one on her right thigh and one on her lower left leg. She was also using violet crocs. All in all, her clothes were simple, but beautiful, not mention quite convenient for using during a battle.
"You're not half bad yourself, you know?" –Michiru declared.
"You don't think they make me look too girlish?" –Haruka said, as she looked herself in the mirror.
"Girlish? Girl, you got to be kidding us!" –Johnny exclaimed. –"There's nothing girlish about your outfit."
"Got that right." –Minako whispered to Makoto, who giggled about it.
"Come now, enough with the gibberish, everyone. There are still some of you, who need new clothes." –Flora said.
This time, Setsuna was the one chosen by the three fairies. With their magic, they changed the girl's clothes, giving her new garments, which she liked a lot, because they were simple, but stylish. She was wearing a black, leather tank top with a zipper down the front overtop a slightly longer, white tank top, along with a black, leather skort with two black ribbons tied on either leg. The back of the skort is quite long and reached the floor. She was also wearing black and white shoes, with black ribbons tied around each.
"Fabulous, don't you agree, girls?" –Flora asked Merryweather and Fauna, to which they agree.
"It's very beautiful indeed. Thank you ever so much." –Setsuna thanked the fairies.
Hotaru looked at Setsuna, and fell a little bit jealous about her, even if it was just for mere moment. As she tried to put away that feeling, which she found evil and rather despicable, Fauna grabbed her by the hand and told her that she would be next. Although she only expressed her happiness by making a little smile appear on her face, inside her, her heart was pounding with so much excitement and happiness, that she thought she was going to explode. Standing still like they told her to, the girl closed her eyes, because she wanted to have a huge surprise when she opened them.
The magical beams of light flew from the fairies magic wands and hit Hotaru, involving her in that mystical light shroud. A warm feeling invaded Hotaru, as she felt her new clothes replaced the ones she was wearing. Finally, the warm feeling eventually faded away, and she slowly opened her eyes to see her new set of clothes. To her own amazement, she was now wearing a black, high-collared jacket with a zipper. Over this, she wore another jacket, this one unzipped and white, with several black block designs and a grey hem on the end of each sleeve. The jacket's collar was red and pleated and folded back. She was also wearing two-colored pants; the legs of the pants were light grey with several of what looked like buttons on the hem that appeared to attach the legs to the rest of the cloth, which were dark-colored. Her shoes were colored in shades of grey and black, and had red straps in place of laces. She was really happy about the result, but she could feel that something was missing; something that would make her new outfit perfect.
"It's very beautiful and I really like it, but… I think that in needs something more, if you know what I mean?" –Hotaru stated.
"Well, maybe you could make a suggestion, dear. What would you like us to add to your outfit?" –Flora asked with her gentle voice.
Hotaru thought for a second, and then she said:
"I know a French bonnet! Those are my favorite hats... Do you think you can give me one?" –she asked them, while making sad puppy eyes, which no one could resist.
"Not a problem." –Merryweather said, as she waved her wand, giving Hotaru a beautiful light-orange French bonnet.
This time Hotaru looked herself in the mirror and told herself, that this time everything in her new outfit was perfect. You could see by her eyes that she was really happy about her bonnet.
"It's perfect! I love it." –she said, as she gave both of the fairy-godmothers a big hug. The three of them were surprised by this way of expressing her gratitude. –"I mean it, it's beautiful."
"Oh, my dear, it was nothing." –Fauna declared, as a small tear of happiness dropped from her eyes. –"It was our pleasure to give you such nice garments."
After that tender and emotional moment, Flora, Fauna and Merryweather went on with their duty. This time, Naru was the one chosen. In a matter of seconds, her clothes were replaced by a black and silver overjacket, over a marine-blue shirt, as well as a black jumpsuit, with red pockets in her legs, and gloves of the same color as the rest of the suit. She was also wearing a pair of black and yellow shoes. Naru was very surprised with the outfit they had given her, because she was expecting something a little simpler. That transformation made her remember of the moment that she revealed herself as Sailor Earth, and of her mission of protecting Prince Endimion... a mission that until that moment, she had failed to fulfill. In her mind, she wondered where he could be, becoming detached of everything else surrounding her. It was only when Rei called her name that she remembered of what was going on.
"Naru, are you alright?" –she asked her, as she touched her shoulder.
"Oh, I-I'm alright, I was just thinking to myself." –Naru said, as she looked once again to herself in the mirror. –"Thank you for this outfit, it's very beautiful."
"Indeed it is." –Rei said, to which the others agreed. –"Well, there are only two of us left. Do you want to go first?" –She asked George, to which he answered:
"Of course not, I'm gentleman. Ladies first, I insist." –he said with a polite voice, as he bowed in her presence.
That gesture made Rei giggle. She was really not used to that kind of treatment, but she liked it. Trying to relax, she let Flora and the others do their magic. They gave her a yellow dress with overall straps and a pair of high-heeled sandals. The color of her dress contrasted with the color of her hair, and although she was not used to wear that color, she admitted that it was a color that suited her fine.
"Not bad, not bad at all." –Rei said, as she looked into the mirror. –"It's not really my style, but I like it very much. Thank you."
"You're welcome, dear..." –Flora said.
"And now, you, young man! You're the last one, and I think a handsome boy like you, will love what we have in mind for you." –Merryweather said. –"Come on, girls, one more time!"
And with that, they used their magic and changed George's clothes. He was now wearing a camo shoes and pants as well as a light brown vest over a black muscle shirt. He also wearing a small necklace that had a golden X around his neck. As he looked at himself in the mirror, he felt really good about himself, because his clothes suited him like a glove.
"Okay, now you got me impressed. Nice work, I really dig this new outfit, ladies." –George said, complimenting on their magic.
"It was our pleasure. Remember, just like we said, these new clothes that we gave you all are not just fancy. They are special, and enable you to master different kind of powers. You will eventually find out what these powers are, in time. Oh, and before I forget it. Your old transformations won't work in this journey, but these garments will allow you to use your old attacks on enemies… But remember that using those attacks will consume your energy, so you must be very careful when you use them." –Flora explained them. –"And well, I guess that's that, Master Yen Sid. They are ready."
"Not yet, they aren't… we forgot about two of them." –Merryweather stated, as the other two looked at her, not knowing who she was talking about. – "We forgot about their feline friends."
She was right. All of them had had their clothes renewed, all but Luna and Artemis. The two cats were next to Usagi. When they heard their names, they went to where the three fairy-godmothers were. Flora looked at them and said:
"Hmm… I guess you two also need a little upgrade, if you're going to accompany them in their journey."
That said, the three women used their magic and gave Luna and Artemis a collar each. Luna's collar was red and had a beautiful jewel from the same color as her fur, while Artemis had been given a dark spike collar. The cats were also now wearing what looked like metallic bracelets in their paws. Although the metallic bracelets looked strange, they were incredibly beautiful.
"The collars that we gave you will enable you to cast magical attacks on the enemies, and the bracelets will enhance your strength, stamina and speed." –Fauna said.
"Thank you!" –Both of them exclaimed in chorus, really happy about it.
"Well, I guess now we're all ready, right?" –Minako asked.
"Not just yet." –Master Yen Sid said. –"Before I send you on your way, I need to talk about the enemies that you will face in your journey.\"
10. Let the Adventure Begin
Chapter 10: Let the Adventure Begin
They all followed Yen Sid into his study. He went near one of the crescent moon-shaped windows and told them to approach. They all gathered around the old sorcerer, as he looked into the horizon. He sighed and then said:
"You know that the trip that you are about to venture on won't be an easy one. That's why I must warn you to the dangers that you are about to engage yourselves in." –Yen Sid stated. –"You all have seen the Heartless, but you don't know from where they come from or what they truly are, and that is something that you all need to know if you are to succeed in your mission."
"Then, please tell us what the Heartless are and why they do the bidding of that awful witch." –Usagi said.
"Very well, I shall tell you everything that I know about them, but before I do, et me remind you that the information that I give you might not be entirely correct, and that throughout your journey you will most certainly find new information regarding your enemies."
That said, he raised both his hands in the air and clapped them. From his hands a cloud of smoke appeared, and started to shape itself in the form of something they all had seen before… a Heartless.
"The Heartless are beings of darkness which manifest themselves in two forms; the _Pureblood Heartless_ and the _Emblem Heartless_." –He stated.
"What is the difference between them?" –Ami asked, intrigued by the nature of the subject. –"I mean, there has to be a difference between them, right?"
"That is true, Sailor Mercury, there is more than one difference between them." –The old sorcerer asserted. –"The Pureblood Heartlesses are natural Heartless, born when people's hearts are been consumed by darkness. As for the Emblem Heartless, those were created by machines that reproduce the processes of a Heart being consumed by darkness."
The cloud of smoke changed yet again, this time shaping itself into a different Heartless. This one looked like a pink monkey, although its torso was reddish brown, and its claws were black, while its tail was pink. It was wielding in its hand some kind of slingshot.
"This here is a Heartless called Sniper Wild, and it's only one of the many Emblem Heartlesses that exist. Unlike the Pureblood ones, these usually mimic the shape of creatures or objects within a world, and they all brand a symbol which differentiates them from the Pureblood Heartless. These are much more dangerous than the Pureblood Heartlesses, because not only they can mimic almost anything, but they are much more powerful." –Yen Sid concluded.
"We already battled the Pureblood ones, and they were tough, no doubt about it." –Makoto thought to herself. –"I wonder just how powerful the Emblem ones might be."
"But just like the Pureblood Heartlesses, the Emblem Heartlesses can also be eliminated by using our Keyblades, right?" –Rei asked.
"Yes, that is correct. Your Keyblades enable you to also destroy this kind of Heartlesses." –Yen Sid answered.
Well, it is clear what we are up against, but that still does no answer a question… Where do the Heartless come, and how can they exist?" –Michiru asked.
"To answer that, I shall tell you a legend, as I know it. According to this legend, the people of the Universe once lived in harmony on one world, with their hearts full of light. Unfortunately, as time passed on, they began to selfishly fight over the light, and darkness grew within their hearts, covering everything and destroying that world. The light survived in the hearts of children, who were able to rebuild the broken fragments of the one world into many, smaller worlds. However, the true light was still hidden in the darkness, so the worlds remained separate."
"So, according to that legend, the Heartless originated from a world which was a world that combined every world there is in the Universe, all because greed invaded people's hearts." –Usagi said. –"So, that means that our own world originally was part of this giant unified world."
"You're assumptions are correct, Sailor Moon."
"But, Master Yen Sid, if the world's remained separate, how come Sora and the others were able to travel to them, as well as the Heartless?" –Hotaru asked.
"That my dear, I'm afraid that not even I know exactly how it came to happen." –He answered her with a serene voice. –"But my theory is that with time, the barriers around the worlds aged and became frailer and the Heartless managed to create ways to enter in them. As for Sora and the others, being the wielders of the Keyblades, has given them the power to travel into other worlds, by using the Keyblade's power to do it… just like you."
"Well, that certainly explains many things, but now that 'm thinking about it, different Heartless must have different weak points and different powers." –Minako declared. –"How are we all going to know what kind of attack we should use against them?"
"Yeah, we won't have to know every name of them and their powers and weaknesses by heart, right?" –Johnny asked.
"For that matter, I give you this."
Yen Sid once again clapped his hands and what looked like a wristwatch appeared in everyone's right wrist. This object was similar to a digital wristwatch in shape, but when you looked at it closely, you could see that it looked like a mini-computer.
"These are the "Informants", powerful devices which will allow you to identify various kinds of Heartlesses, as well as other enemies." –He explained. –"You just need to point it to an enemy, and the information regarding it will show up, telling you what you need to know about it, in order to stop it.
"Radical!" –George exclaimed.
"Anything else we need to know about the dangers that await us?" –Haruka asked.
"Well, there is one last thing that you will need to know about before you start your journey." –Yen Sid declared. –"You see, Maleficent is not the only one that seeks power by controlling the Heartless, so it is most likely that you will encounter other creatures that also seek that power. My advice to you is to always be on the lookout, and follow your Heart at every time, for it will give you the answers you need in order to accomplish your goal. And most importantly, always trust each others."
"We will, Master Yen Sid, sir." –Usagi declared, bowing her head in respect to the great sorcerer. –"But before we go, I would like to ask you one last thing. Are we ever going to be able to go back home?"
"That is up to you to decide. When the time comes, you will all know what to do in order to return to your world."
Seeing this, the rest of the Sailor Scouts all nodded to that statement, a little smile appeared in Yen Sid's face as he also bowed in respect to them, also showing his mutual respect towards them.
"Now that I have given you all the information that you need, your journey may start."
"We're ready…" –Hotaru said, as she gave hands with Setsuna and George. –"Whatever happens, we will accomplish our mission." –She whispered to herself, gathering all the courage that she could find in her heart and soul.
"Very well then, let me open the path that it will take you to where your journey starts, and most importantly, to where your friend Sailor Chibimoon is."
When Yen Sid said those words, a warm feeling invaded Usagi's heart, because in a matter of minutes, she and the rest of the group would be one step closer to find Chibiusa, wherever she was. Everyone assumed that she was happy, not only because Usagi, probably more than anyone in the group cared about Chibiusa's safety, but because she had the biggest smile that they ever saw in her face. Luna and Artemis look to each other and also smiled.
Yen Sid used his magic and opened some kind of portal which covered the door from where they first entered. This one was formed of what appeared to be light in a liquid state, similar to the darkness that tried to envelop Usagi earlier. A mysterious glowing came out of it, and unlike the darkness, this one delivered a warm feeling. The light in it became stronger as the seconds went by. Looking to one another's, the group wondered where that would lead them.
"This portal will lead you to where your friend Sailor Chibimoon is… a world called Traverse Town. There, you will find people that will help you on your journey, but be careful because danger lurks everywhere." –Yen Sid said, answering to their question.
"Thank you so much for everything, Master Yen Sid. We won't disappoint you, believe us." –Michiru said.
"I know you will, and I have faith that you will be able to find Sora and the others, while preventing Kingdom Hearts from being opened." –Yen Sid declared. –"I just wished I could help you more."
"Don't worry; we can take care of ourselves. After all, the Keyblade wouldn't have chosen us for the job if we could not handle it, right?" –Makoto said.
"Yeah, just leave everything to us!" –George said.
"Very well, then. Good luck and have a safe journey."
As they all went through the portal, they were enveloped in the same kind of light that it had enveloped them, when they were in Tokyo. Through their minds, all kinds of thoughts went by. What kind of enemies awaited them? What friends and allies would they meet?
The journey had just begun, and they all knew that it would not be easy. But if that was the only way for them to ever go back to their own world; they would face anyone and anything that would dare try to get in to their path.
11. Traverse Town
Chapter 11: Traverve Town
She slowly opened her eyes to see where she was. Her body felt like if she weighted a couple of tons. She tried to move, but she could feel that she did not have the strength to move finger, much less her whole body.
"S-Sailor Moon, w-where are you?" –she lightly whispered.
There was no answer. Wherever she was, Sailor Moon or the others were not there. She noticed that she was wearing her regular clothes. Gathering all the strength she still possessed in her body, she tried to get up. This proved to be a hard task, because her body felt like it was going to shatter into pieces. After a few minutes, she managed to sit on the bed and looked around. The walls were coloured in light pink, while the ceiling was white and the wooden floor was covered with a red carpet. The furniture looked like it had been bought very recently. In fact, the only piece of furniture that looked quite old was the bed where she was. That's when she noticed that there was a door on the opposite side of the room. The door slowly opened itself, revealing who was entering in the room. A tall young woman with green eyes, white skin, long brown hair braids; two short ones on either side of her head and one long one in the back, the latter sporting a cherry-red bow. She was wearing a pink dress with magenta lining and buttons going down the front, all of which were buttoned except for the last two. She also had a black string tied in the same fashion as the one on her belt around her neck like a necklace. She had a warm smile in her face, as she asked.
"Hello there… Did you sleep well?" –the young woman asked her.
"I-I-I think so… Where am I?" –she asked, not knowing where she was, or how did she got there.
"Don't worry, you're safe. My name is Aerith, and you are at my house." –The woman stated. –"What about you, what is your name?"
"I'm Chibiusa." –the pink haired girl answered.
"Chibiusa… that's a very beautiful name you got, you know? So, tell me, you're not from around here, are you?"
"Well, that depends on where am I… the last thing I remembered was being in a battle against creepy black creatures with razor-sharp fangs, and feeling like if I was being involved by a warm light." –Chibiusa explained.
"Well, I don't know what that strange light that you're talking about really is, but I can tell that the creatures you fought against were Heartless; the way you described them, there is no doubt about it." –Aerith declared.
"Heartless? So that's the name of those creatures that attacked me and my friends." –Chibiusa exclaimed. –"Tell me, did you found anyone else besides me?"
"No… I'm afraid that you were the only one that we have found, Chibiusa."
"We?" –Chibiusa asked intrigued.
"Oh, yes, it was not I who found you, it was someone else… Don't worry; you'll have the chance to meet them. But first, you need some new clothes. Those that you are wearing will call too much attention on you, and we certainly don't want that, now do we?"
Opening the closet that was right next to her, Aerith grabbed a beautiful long pink and red cetin dress. She also grabbed a pair of matching red shoes and put them right beside Chibiusa.
"I don't know if it's your colour, but if definitely is your size. I hope you like it." –Aerith said. –"I'll be waiting for you in the kitchen, alright?"
Chibiusa nodded, as Aerith exited the room. She took a look at the dress and admired it simplicity, and also how the colours created such a peculiar colour pattern. She quickly changed into that dress. Looking herself in the large mirror that existed in the room, she was surprised to see that she looked as pretty as a china doll, while wearing the dress. She giggled and put on the shows, which made her look taller than she was. After getting dressed, she left the room and made her way to the kitchen, where Aerith was cooking something. She could not tell what it really was, but it smelled good. Aerith hearing her footsteps tuned around and looked at her, amazed by the transformation.
"You're picture perfect, Chibiusa. The dress really suits you well."
"Thank you, Aerith." –Chibiusa said, as she sat by the table. –"What are you making?"
"Pancakes with Paopu Fruit jam, I hope you're hungry."
"Paopu Fruit? I never heard of that fruit before." –Chibiusa declared.
"It's a fruit that comes from another world." –Aerith explained, with a warm smile in her lips.
"Another world? That's too much information for me, you know?" –she joked about.
"I understand that all of this might seem strange and inexplicable to you… It was all strange for me, hen I first came to this world." –Aerith stated.
While Chibiusa ate, Aerith decided to ask her a few questions.
"So, tell me, from what you remember, how did you end up in this world?"
"I don't really know. Like I told you before, the last thing I remember was being in the middle of a fight with some really disgusting black creatures, and then, some sort of light engulfed me, and then, nothing." –Chibiusa explained.
"Looks like your world has been attacked by the Heartless." –Aerith said.
"Heartless? So that's the name of those disgusting creatures." –Chibiusa said.
"Well, let me tell you something; most people don't come to this world the way you did… not even when their worlds are destroyed." –Aerith declared.
"What do you mean «when their worlds are destroyed», huh?" –Chibiusa asked, as she ate another bite.
"Well, that's what ultimately happens when the Heartless take over a world. It might take longer for some, but in the end, they all suffer the same fate. The Heartless feed on people's emotions, especially anger, greed, lost and despair." –Aerith answered with a melancholic, almost morose voice. –"And when they end they all go to another world and start all over again."
"And the inhabitants of those worlds, what happens to them?"
"Most of them just disappear into nothingness, but some manage to save themselves and get to other worlds, like this one. You could almost say that Traverse Town is like a meeting point to anyone whose home world has been destroyed by the Heartless." –Aerith explained.
"Was your world destroyed, Aerith?" –Chibiusa asked, even though something in her already knew the answer.
"Yes… Just like so many people around here, I'm also one of those people whose world has been destroyed. But, I do have hope that someday, somehow, my world and the other worlds that have been destroyed, might be rebuild once again." –Aerith said. –"But, let's not talk about this, I don't want you to feel sad." –she said, as she tried not to cry. –"When you woke up, I heard you calling someone's name. Who were you calling?"
"I was calling one of my friends, Sailor Moon. Just so you know it, that's not her real name, that's just the codename that she uses when she becomes a warrior who stands for justice, love and truth."
"Interesting. I've never heard of anyone who wore a codename like that one before. Is she the only one?"
"Oh, no, there are more Sailor Scouts like her… I'm also one of those Sailor Scouts, you know? I'm Sailor Chibimoon." –she said, though she somehow thought that Aerith was not entirely believing what she was telling her. –"Here, let me show you."
Chibiusa went back into the room and grabbed something that she had in one of her pockets. That something was the small brooch where she had her Pink Moon Crystal. She went back to the kitchen, and showed it to Aerith. When she opened the brooch, a small amount of light came out of it, although not as intense as it usually was.
"You see? This is the Pink Moon Crystal, my version of the Silver Crystal, which is the universe's most powerful weapon… or at least, the most powerful weapon from the universe from where I come." –Chibiusa explained. –"Ill transform so you can see for yourself what I'm talking about."
Grabbing the brooch with her right hand, she raised it up and exclaimed:
"Moon Crisis Make-Up!"
But nothing happened. She was standing in the same place, and she had not transformed herself. It was as if the Pink Moon Crystal had lost his power, or something similar. She looked at it, and asked herself what was really going on.
"I don't understand… Why isn't it working?" –Chibiusa said out loud.
"Maybe it doesn't have any sort of power in this world, my dear. But don't worry; you don't have to prove anything to me. If you say that you and your friends are warriors who fight for love, truth and justice, then, I believe you." –Aerith said, as she got up and stood up in front of Chibiusa, looking her directly in the eyes. –"Now, I know that you want to know the rest of the group who found you. Come on, I'll take you to see the. I'm sure that they are eager to know you."
Meanwhile, in the _First District_ of Traverse Town, a mysterious portal made out of light appeared. From it, a group came out. First enveloped by the light, the people who were walking through there could not see exactly who they were, or what they looked like. But as soon as they were out of the portal, their appearance was revealed. Looking around, their eyes contemplated the new world they had just arrived. It bared a Victorian-style design. At first sight, they saw a building which had a sign saying _Accessory Shop_, another building which had a sign saying Item shop. To their left there was a restaurant, and finally to their right there was a door leading into what it was called the _Third District_, according to the sign on top of the door. Behind them was a large set of double-doors, which appeared to be closed tight. There was the smell of burning wood in the air, probably coming from the chimneys on the roofs. It was not a bad smell, but it felt strange to them.
"Well, this is something." –Makoto said, as she looked around.
"It's hard to believe that we are in another world, far away from our own." –Luna stated.
"You're right." –Minako said, as Artemis stood by her right. –"We've travelled to other locations on our planet, we've travelled to the 30th century, heck, even travelled to the Moon once, but that is nothing compared to what we just did."
"This place looks so different from our world. People seem to not even care about the fact that we just stepped out of a magical portal." –Usagi declared.
"Back on Earth, they would have been surprised, but mostly terrified by that fact." –Ami said.
"Indeed... this is a strange place." –Haruka said, as her eyes looked around.
"We'll have time to sightseeing, everyone." –Johnny said.
"He's right; we have to find Small Lady." –Setsuna agreed, as she reminded the others of what they had to do.
"Right… I think we should split up and see if anyone has seen her." –Michiru suggested. –"Who knows, maybe someone has seen her, or we might even find her ourselves."
"I agree with her, we should split up." –Usagi said. –"We'll split up I groups of three. The first ones to find Chibiusa call the others, and wait until the rest of us get there. Always keep your eyes peeled for any trouble, and be careful."
Decided to find Chibiusa, they split up in to four groups of three. Usagi, Rei and George went one direction, Setsuna, Hotaru and Johnny went together, Ami, Makoto, Naru, Luna and Artemis stayed together and paralleled George and the girls, while Haruka, Michiru and Minako decided to parallel Setsuna's group.
At the same time, Aerith and Chibiusa walked through a deserted street. In the pink-haired girl's mind, she wondered how the people who saved her would look like. After awhile, Aerith stopped in front of a door. She quickly opened it with a she had with her, and both of them entered, where they were immediately greeted by a tall handsome man. He had long, brown hair and blue eyes. He also had a distinctive scar, which ran diagonally across the bridge of his nose. He was wearing a pair of black gloves, black shoes, each with a zipper lining it, silver necklace a white undershirt and a short, black short-sleeved jacket, bearing red wings on the back a strange symbol on each shoulder. He also wore three brown belts on his left forearm, as well as three buckles on his right thigh. His black pants also sported a vertical zipper going down the side of each leg.
"I see our visitor has awakened." –he said, while looking to Chibiusa.
"Chibiusa, this is Leon. He was the one who found you." –Aerith told her.
"Nice to meet you, Leon." –Chibiusa said.
"It's also nice to meet you, Chibiusa." –Leon said. –"I'm glad to see that you are alright. The others and I were afraid that you might have been hurt… But, where are my manners? Come in, the rest of the gang will also want to know how you are." –He said, leading both Chibiusa and Aerith through a long corridor, which reminded her of the corridors of Hikawa Shrine, Rei's home.
When they finally arrived at a door, this one was opened by a girl with short, black hair and violet eyes, wearing a metal headband with two green tassels, as well as a yellow scarf. Her clothes were interesting to ay the least, as she was wearing a green tube top with two blue belts holding it up, tan short-shorts with another loose blue belt around her waist, white socks that reach about mid-thigh, orange shoes, and mesh sleeves on her arms that disappear into orange and fingerless gloves with black bands constricting the ends. Chibiusa also noticed that she was carrying on her back a 4-Point Shuriken, which strangely enough, seemed to suit her well as a weapon, given her outfit.
"Hey, there! So has our guest waked up yet?!" –the girl asked with a jovial voice, seeing that Chibiusa was already awake, taking a look at her. –"My name's Yufie, and let me just tell you that I'm very happy to meet you, and that that dress looks amazing on you!"
"T-Thank you, Yufie. I'm Chibiusa… please to meet you."
As they entered in the room, Chibiusa noticed that it was fully decorated with all sorts of interesting stuff. They looked like some kind of gizmos or something else. The walls were colored green, as well as the floor, which she then noticed that it was actually a carpet, and that the floor was made out of wood. She also noticed that there exsted two windows that were sealed shut. She looked around and saw a man leaned against the wall. Unlike Leon, Yuffie and Aerith, he looked a little older, like if he was in his early forties. He had short blond hair, albeit styled, blue eyes as well as some stubble on his chin. She also noticed that he was chewing on a toothpick. He was wearing a white T-shirt with two buttons that descended from the neck; baggy blue pants and had a very wide, orange waistband with thin, vertical stripes on it. Finally, he was wearing grey socks and black shoes. As soon as he saw them entering, he smiled.
"Hey Cid, our guest has arrived! Come say hello to her!" –Yuffie exclaimed.
Cid approached Chibiusa and smiled. She looked into his eyes, and saw only kindness in them, revealing that although he looked a little meaning because of his physique, something in her knew he had golden heart.
"Hello, I'm Chibiusa."
"The name's Cid, girl, and it is a pleasure to meet you." –Cid said, always with a smile in his lips. –"I have to say that you gave us all quite a scare, when we first found you, you know that?"
"Yeah, you were on the ground, and we thought you weren't breathing. For a moment, we thought that you were dead. But then Leon here noticed that you were only sleeping, and let me tell you, that that was a relief, because I would not want such a pretty girl like you to be harmed or worse." –Yuffie said.
"Over our stay in this world, we saw many people entering in it, but you're the first one we found fainted on the ground." –Leon said.
"Yeah, he's right. What happened to you, when your world was destroyed?" –Yuffi asked her.
While Chibiusa told Leon, Yuffie and Cid the same thing she told Aerith, the Sailor Scouts were searching for her. The groups used different means to gather information about her location. They knew she was there, they just did not know where exactly. Usagi, Rei and George had decided to ask people if they had seen anyone with Chibiusa's description, while Haruka's group decided to use Michiru's hand mirror to look for her.
"So, can you see her?" –Minako asked her, as Michiru tried concentrated herself.
After a few seconds, she sighed, as if she was tired. Through her eyes, the other two already knew the answer she was going to give them.
"No. There is too much interference in this world, like some kind of force field that prevents me from seeing a person."
"Don't give up." –Hauka said, as she gently ran her fingers through Michiru's delicate face. –"She needs us."
"You're right, she needs us, and we have to find her." –She sad with a strong and determined voice. –"Let me try once again."
She continued trying, while Setsuna's group had entered the Second District. Johnny was convinced that he could track Chibiusa by using the technology of his dimension. Using his wristwatch, he started pushing buttons, until he finally found something that looked like some kind of radar.
"What exactly do you think you're doing?" –Setsuna finally asked him, fed up with the fact that he did not tell them anything.
"I'm trying to see if I can pick up any kind of energy signature that Chibiusa might have left behind her." –Johnny answered. –"In theory, when we cross into other worlds, we leave trail of residual energy from the world where we previously were. If that is true, I might be able to find her by following that energy trail."
"Just like the trail of pebbles from "Hansel and Gretel", right?" –Hotaru asked.
"Yeah, just like that trail, Hotaru."
They walked around, but did not find anything that would help them fining Chibiusa's position. Finally, they ended up in front of a house with a white door with blue stained-glass. Since the door was open, Hotaru decided to enter in it. She thought that maybe she would have better luck than Setsuna and Johnny, if she just asked whoever lived in that house if they had seen Chibiusa. When she entered, she did not see anyone. But then, there were two Dalmatians that appeared from behind a sofa. Hotaru smiled as she kneeled right next to them. She gently petted them in the head. They barked, but surprisingly, that bark was not just a bark. Somehow, Hotaru understood what they were saying, like if they were talking like humans do. She heard them saying that their names were Pongo and Perdita, and that they had lost their 99 puppies when they came into that world, right after their own world was destroyed by the Heartless. They told her that the puppies were scattered through other worlds, and they were asking her to find them. She smile tenderly to them, and said:
"Me and my friends will find them all, I promise."
As she gave her word to both Dalmatians, Ami's group had entered in a hotel, looking for any clues as to where Chibiusa would be. There was no one in the corridors, so they decided to knock on the doors, hoping that someone would answer. Normally, they would not do that sort of thing, but this was a delicate situation.
"It's strange. Nobody answers." –Naru said.
"It's hard to believe that this is actually a hotel." –Makoto declared. –"Where is everybody?"
"I agree; something smells fishy around here, and it's not tuna." –Artemis said.
"What do you mean?" –Luna asked him.
"Don't you see it? Since we passed through that double door and entered this section of this world, we haven't seen anyone."
"I'm afraid that Artemis is right. We haven't seen any person in this part of the world. It's like they knew something really bad was here, waiting for attack whoever decided to appear around here." –Ami said.
"Now that you mention it, it's really strange." –Luna said. –"Still, we have a job to do."
Then, all of a sudden, they heard a loud noise coming from one of the room, like an explosion, or something of the kind. Approaching carefully, they tried to open the door, but as soon as they touched the doorknob they were shocked.
"Transform, everyone!" –Artemis exclaimed.
"They can't transform into their Sailor Scout forms, remember? They lost the ability to do that when we were transported from our world." –Luna said.
"Oh, yeah, I completely forgot about it." –Artemis nodded, knowing that that it was truth.
"But we don't need to transform ourselves to use our powers. Step aside, I'll open the door." –Makoto said as she told everyone to stay behind her. Concentrating, she decided to try out one of her attacks on the door. –"Sparkling Wide Pressure!"
With that, a sphere made out of electrical energy came out of nowhere and smashed against the door, blowing it apart. From inside, Heartless started to come out, and they looked even more vicious than before. Without losing time, Ami decided to use her "Informant" to identify the different kinds of Heartless, and to know what the best way to stop them was. Scanning took no longer than a few seconds, and it took even less to show her the information she wanted to know.
"Okay, we got three kinds of Heartless surrounding us, everyone." –Ami exclaimed. –"Two of them we already know that are "Shadows" and "Soldiers", but the new kind is completely different… It's not a Pureblood one, but an Emblem Heartless, called Large Body!" –Ami said, as she pointed to the big round Heartless, who also possessed chains on his wrists.
"Can you give us the good news now, Ami?" –Makoto asked her.
"Those were the good news, Makoto." –Ami stated with a slightly nervous voice.
"Then, I think it's time for us to show these guys, just how we Sailor Scouts fight enemies who stand in our way." –Naru declared, as she made appear her Keyblade and prepared to fight.
"She's right, let's give these guys a taste of our powers, Ami!" –Makoto exclaimed, as she too made her Keyblade appear in her hands.
"You're right, let's do it! Aim for its head, that's its weak point. And by the way, don't call me by my real name… Call me Sailor Mercury." –she said, as her Keyblade also appeared, and she charged against one of the "Soldiers".
"Okay, I got it." –Makoto laughed about it.
Luna and Artemis looked to each other and then charged against one of the "Shadows". Truing to call for backup, Naru turned on her "Informant" and tried to use it to contact with the other groups.
"This is Sailor Earth, can anyone hear me?"
"This is Sailor Mars, I'm hearing you, what's the matter?" –Rei asked her, breathlessly.
"We're being attacked by Heartless! I think they set us an ambush and we fell in it.. Think you guys, or one of the other groups can give us a hand?"
"Sorry, but you're not the only one who fell on to a trap, Sailor Earth. The other two groups are fighting against groups of Heartless that appeared out of nowhere, and so are we." –Rei said.
While the Sailor Scouts faced the Heartless, Chibiusa continued explaining to Leon, Yuffie and Cid what had happened to her. She told them everything she said to Aerith.
"So, in your world you're some kind of vigilante who fights for love, justice and peace, is that it?" –Cid stated.
"That's so cool! You really must have an exciting life, that's for sure." –Yuffie said. –"Fighting those bad guys must be really tough, but it also is a way to pump up the adrenalin into your body."
"Still, it is a dangerous life." –Leon said.
"Yes, it is a little dangerous, but my friends and I have to stop those evil creatures, otherwise, our world will be in great peril." –Chibiusa said. –"The world might never know what really happened, but that doesn't matter, because what is important is that the evil shouldn't prevail."
That's when they heard a loud noise coming from outside. Yuffie went to open one of the windows, when something just thundered in from it, making her lose her balance. It was a Heartless... a Shadow to be more exact. Yuffie tried to retreat, but the creature grabbed her foot. Chibiusa seeing Yuffie being attacked felt something burning in her chest. Something that wanted out; she closed her eyes, and opened them a split second later, and saw that she was holding in her hand a key-shaped weapon. Its handle was heart-shaped, as well as the blade. The tip was shaped like the head of a white bunny rabbit. She recognized the kind of weapon, bearing in mind that Sailor Moon used a similar one in their battle against the Heartless in the Tokyo Tower. Not knowing how, her body moved instinctively and with an incredible somersault, she positioned herself right next to Yuffie, as she swung her weapon, and destroyed the Heartless that was grabbing her leg. Seeing that, Leon became surprised.
"A Keyblade?! You are actually a Keyblade wielder?"
"A Keyblade wielder?" –Chibiusa asked him. –"If by a Keyblade, you mean this strange weapon, then I guess I am. Although, I don't know how this came to be. I never saw this thing before, in my life."
"And looks to me she's not the only one, Leon! Come take a look at this!" –Yuffie exclaimed, as she looked through the window.
Leon quickly went to the window, and saw that Yuffie was right. Outside, there was a group of Keyblade wielders fighting an enormous group of Heartlesses. He never thought he would see many Keyblade wielders in one place at the same time. Chibiusa joined him and the rest of the group, to see what was going on, when she recognized them. It was Usagi, Rei and George.
"I don't believe it!"
"You recognize them?" –Cid asked Chibiusa, who was still in shock.
"It's Rei, Usagi and George! They are the friends I was telling you about." –Chibiusa answered, watching her friends fighting against the awful creatures. –"I have to help them!" –She exclaimed, as she quickly headed for the door.
"Wait for us! We'll help you!" –Yuffie said, as she and Leon followed the pink-haired girl outside.
12. Fighting the Guard Armor
Chapter 12: Fighting the Guard Armor
As the Heartless came out from the shadows, the Sailor Scouts tried their best to get rid of them. But no matter how many they were able to destroy, more and more kept coming towards them, like if they were attracting them like a magnet.
"There's no way we can keep up like this!" –Rei said.
"I know, but there's no way for us to run. We can't go forward, but we can't go back either." –George said, as he sliced yet another Heartless.
Suddenly, three Heartlesses came out of nowhere and attacked Sailor Moon. They were about to grab her with their claws, when something hit them. That something was Chibimoon's Keyblade, who performed a somersault in order to get them, just before they could harm Sailor Moon. When she saw Chibimoon, her heart almost jumped out of her chest. The pink haired girl landed right next to her, and smiled.
"What took you all so long to find me?" –She asked Sailor Moon.
"Long story, I'll tell you everything later. Right now we have to get rid of these ugly creatures!" –Sailor Moon said, smiling back to her.
"Need a hand?" –she heard a voice.
It was Leon and Yuffie who came after Chibimoon. The Sailor Scouts noticed that he was wielding a Keyblade too. This one looked like a silver revolver, which was kind of strange, for they had never seen a weapon such as that one, which combined elements of both a Keyblade and a fire gun. As for Yuffie, she was wielding a 4-Point Shuriken, which she used to repel the many Heartless that kept appearing.
"Thanks!" –Sailor Moon said, as Leon sent a nearby Heartless flying through the air. –"But who are you?"
"Introductions can wait, these guys can't!" –Leon declared.
"He's right, we got to keep moving, and try to find the rest of the group." –George said, as he executed a somersault taking care of three Heartlesses in the process.
"I'll lead the way, follow me!" –Yuffie said. –"Nobody knows these streets like I do. If your friends are nearby, we'll find them in a jiffy." –She exclaimed as she somersaulted, ending right in front of Rei, so she could lead them out of there.
At the same time, Michiru and Haruka were having a few problems of their own. They tried to repel all of the Heartlesses that appeared in front of them. Minako who was with them, tried to help them, but they were just too many for the three of them, especially because the kind of Heartless that started to appear were capable of shooting lightning, fire, and ice at them. Using their acrobatic skills, and combining them with their ability to swing the Keyblade they all manage to gain some manoeuvre space, in order to get out of there.
"This is getting stupid!" –Haruka stated as sliced yet another Heartless.
"I know. These creatures just keep coming. We have to come up with a plan to get rid of them." –Michiru said.
"I think I have one! We need to concentrate them all into one place." –Minako said, swinging her Keyblade at another Shadow, blasting him.
"It's a good like any other, but it's worth a shot!" –Michiru exclaimed, as she dodged an attack.
"Okay! Let's concentrate our attacks into a single one, and try to direct them to somewhere where we have enough space to manoeuvre at will!" –Haruka said, as she positioned herself between Michiru and Minako, trying to mimic their movements.
Setsuna, Hotaru and Johnny were also having troubles of their own. Not only they had been cornered, but the Heartlesses that had cornered them were none other than Large Bodies, and were blocking the passage.
"Out of our way!" –Johnny exclaimed as he managed to destroy one of the Large Bodies.
"It's no good! These things just keep coming, no matter how many we destroy!" –Hotaru said, as she fell into the ground, after being pushed by one of the Heartless.
Seeing that, Setsuna quickly evaded an attack, and slide over to where Hotaru was, helping her to get up. You could see a little fear in the young warrior's face, and if it was not for her friends who were there to protect her, she would probably be consumed by it. Still, she tried to look strong, also in order not to discourage Setsuna and Johnny. Just as Hotaru managed to stand up, a Soldier Heartless jumped over her, and if it was not for Johnny's agility and quick reflexes, it would have hurt the purple-haired girl.
"Keep swinging your Keyblades, and don't let your guard down! We have to find the others!" –Setsuna said, as she destroyed another Heartless.
Out of the blue, something sliced and diced more than ten Heartlesses at once. Once it hit the ground, they all saw what it was… a 4-Point Shuriken. They looked and saw a couple of strangers, one of them wielding what looked like a Keyblade. Then, they saw Chibimoon, as well as Sailor Moon, Sailor Mars and Sailor Saturn Net Surfer right behind them, as a small army of Heartless chased them through the narrow streets, trying to grab them.
"Look, it's our friends!" –Chibiusa exclaimed, as she saw Hotaru and the others.
"And looks like, they are in need of a little hand." –Rei pointed out, as she prepared herself to give them a hand. –"Burning Mandala!"
Using her attack, she managed to create a temporary corridor through the blasted creatures that were on to get them. Even though they were in the middle of the battle, Chibiusa and Hotaru just could not help, but to hug each other. As they hug, it seemed to them that time stood still, and nothing else mattered. Unfortunately, this feeling did not last long. Breaking the hug, both girls managed to get rid of a Heartless who was about to attack them. Focusing on the battle, they knew they would have time to talk about what happened to both of them. Right now, they had to focus on what was happening.
"I'm glad to see that you decided to come and help us." –Johnny declared. –"Who's the guy who's also wielding a Keyblade, and the girl who's holding a shuriken?" –He asked to Usagi.
"We don't know either! The only thing we know is that they helped Chibimoon, and that they don't like the Heartless!" –Usagi answered him, as she took out another Heartless.
"Less chit-chat, more action!" –George said, as he somersaulted over a Heartless, lading right next to Leon who had solely dispatched seven Heartlesses through the air, with one blow.
"Couldn't have said better myself. Let's keep moving… everyone follow Yuffie!" –Leon warned the others. –"Yuffie, you know what to do!"
"Roger that! Come on, everyone, follow my path!"
In the meantime, Naru, Ami, Makoto, along with Luna and Artemis had managed to get out of the hotel, and were now outside, battling every Heartless they could lay their eyes on.
"Roots of Fate!" –Naru exclaimed.
"Shine Aqua Illusion!" –Ami exclaimed.
"Supreme Thunder!" –Makoto exclaimed.
Their attacks combined with the power of their Keyblades had a devastating effect on the creatures that were attacking them. Still, the more Heartlesses they took out, the more appeared, replacing the ones they got rid of. Luna and Artemis were making use of the new abilities that their special garments were giving them, and attacked the every Heartless they laid their eyes on with an incredible speed and agility. With quite some difficulty, they managed to get to the Second District square.
"How many of these creatures are they?" –Luna asked out loud.
"Don't know, I lost count of them already…" –Artemis said, as he managed to take down another one.
"If only we knew a way to keep them from appearing." –Makoto said.
"Keep fighting everyone! We must do whatever we can to prevent these creatures from hurting innocent people." –Ami declared.
"We're with you, Ami!" –a voice exclaimed.
Running through the middle of the ocean of black creatures, came Minako, Michiru and Haruka, who had adopted a technique to repel the attacks of the Heartless, by coordinating their attacks at the same time. When they got to where Ami's group was, they were completely exhausted, still, they knew that there was no time to rest.
"Maybe it was a bad idea for us to split up." –Minako said. –"Maybe if we had stuck together, these icky creatures wouldn't be so tough to handle."
"I got to agree with you. This would be much easier if we hadn't split up." –Makoto said.
"Have you tried to contact the others?" –Michiru asked, as she managed to repel another Heartless.
"We have tried, but they were already having problems of their own." –Ami answered back.
"We could really use some reinforcements, that's for sure." –Makoto said.
"Then wait no more, because the cavalry has arrived!" –someone shouted, from the middle of the sea of black creatures.
From the middle of that living sea of darkness, Usagi and the rest of the gang appeared, leaded by two individuals. Using the Keyblade's power, they also opened a path through that madness, and joined Ami and the others. When they saw that Chibiusa was with them, they all felt better, knowing that their friend was safe and sound.
"What took you so long?" –Haruka asked sarcastically, with a smirk n her face.
"The traffic around here is a complete madness." –Rei said, between a couple of laughs, trying to relief the pressure.
"Does anyone of you have an idea for us to get rid of these things, braniacs?" –George asked, referring to both Ami and Johnny.
"No." –Ami answered.
"I wish I had one, but unfortunately I don't, and I don't think these creatures are going to give me enough time to come up with something." –Johnny answered, as he stroke another Heartless, with his Keyblade.
"I think I got one!" –Leon exclaimed. –"Everyone form a circle and start advancing towards the Heartless, very slowly, in order to get us more space to manoeuvre, and it's also a way for us to be sure that they don't jump on us.
The whole team quickly assembled themselves into a circle, and on Usagi's mark, they started to take out as many Heartless as they could, never breaking the formation. Incredibly enough, it all worked fine, and they were able to reduce the number of enemies that surrounded them. But when they thought they had things under control, something happened. The Shadows, the Soldiers, the Large Bodies, and all the other kinds of Heartless that were attacking them, they simply vanished into thin air, leaving no trace whatsoever of their early presence there. Everyone looked around, trying to spot any kind of threat that could have made the Heartless just disappear, but did not see anything.
"Do you think we won?" –Minako asked out loud.
"I don't know… it looked too easy. Just when we were gaining the upper hand of things, the Heartless disappear." –Rei said. –"It's as if they had been told to retreat."
"Maybe they got chicken…" –Yuffie kidded.
"Don't count on it, Yuffie. These creatures are as vicious as vicious can be. They wouldn't retreat without someone ordering them." –Leon said.
"He's right, everyone. My watch is picking up something… something big…" –Johnny said.
All of a sudden, a giant Heartless appeared in the middle of the Second District square. It was about 100 feet tall, and it resembled an old armour. It was purple, silver and black, with a couple of traces of red in its junctions. Its arms and legs were separated from the metallic hourglass-shaped torso, where you could see the Heartless' symbol in it. Its metallic claws were sharp and menacing, resembling the claws of a giant tiger. From all Heartlesses that they had faced so far, including the one that had attacked them in their home world, this was the biggest of them all.
"What is that?" –Haruka asked as she looked at the Heartless, trying to figure out what would be the best way to defeat him.
"It's a Guard Armor!" –Ami said, as she checked her "Informant" for that particular Heartless. –"This guy is an Emblem Heartless. His main attacks are physical, and it says here that its arms and legs are not attached to its torso, and that can move and attack independently.
"Well, no matter what it is, the bigger they are, the harder they fall. Attack!" –Johnny exclaimed, as he launched himself, attacking the huge Heartless.
Following Johnny's example, they all attacked the Guard Armour. This one was considerably stronger than the other Heartlesses, and it seemed that it did not even fell the attacks. Every time they were able to hit him with their Keyblades, it did not react. It was like if they were mere insects to it. But out of the blue, it started to swing his arms all around, trying to punch the Sailor Scouts. Makoto tried to hit one of the arms, but it was her who got hit by it, and she flew a couple of feet, before landing on the ground. She quickly got up and went up against it again, not caring for whatever might happen to her. Michiru decided to combine one of her attacks with Haruka's, and tried to strike the creature's torso, in an attempt to unbalance it, and make it fall on his back.
"Now, Haruka! Submarine Violin Tide!" –Michiru cried, as she pointed her Keyblade to the monster.
"World Shaking!" –Haruka yelled, making the same movement as her partner and lover.
The combined strength of both attacks was quite great and the creature felt it, unlike the attacks inflicted just by the Keyblades. Unfortunately, it was not enough to make it fall on his back. Seeing them failing, Hotaru came up with a strategy of her own.
"If I can hit it on the head, I'm sure I'll be able to at least knock it down." –she told herself.
Stepping back a couple of feet she than ran as fast as she could, each step bringing her close to her purpose. She then used her Keyblade, and used the magical ability that it possessed to shoot fire. Using it as a way to propel herself in the air, she mimicked her favourite Olympic athletes and jumped as high as she was able to. While in mid-air, she became amazed with herself, for she did not know that she could do that. Coordinating her landing, she landed right on top of the creature's head and swung her Keyblade, banging it on its head. The other Scouts looked up and saw what she was doing, and decided to give her a hand. But just as they were about to help Hotaru, she slipped and started to fall. Trying to get a hold on something, she thrust her Keyblade into the creature's arm, making it scream in agony. As the Heartless screamed, its arm just crumbled and disappeared. Thanks to that movement, not only Hotaru was able to land safely, without injuring herself, but she also managed to destroy one of the creature's arms.
"How did you do that?" –Leon said, as he fired a fire ball with his Keyblade, targeting the Heartless' torso.
"I.-I don't know… I just used all my strength into that attack, not because I did want to destroy it, but because I did not want to injure myself in the fall." –Hotaru said.
"The Heartless are creatures of pure evil, maybe it was something you were thinking about, that its energy got transferred to that blow, which was incredibly powerful. What were you thinking when you were falling?" –Leon asked her, desperate to find a way to destroy that thing.
"I was thinking about my family, and my friends, I guess." –Hotaru answered him.
"That must be it. Good memories are something that is essentially dear to someone, because they reflect the love that a person has for something. If Heartless are born from the evil and darkness from people's hearts, then, good memories most counteract as the opposite to Heartless." –Chibiusa suggested.
"It must be that." –Usagi agreed. –"Everyone, when you strike this creature, I want you to think about the thing that you consider the dearest to you, okay?"
Needless to say, that all of them did as Usagi told them. Ami thought of her mom and how she really missed her, while Rei thought of her grandfather and about the great friendship that all of them nurture for each others. As for Makoto, she thought about her passion for cooking, as she thrust her Keyblade into the creature's feet. Minako also thought about her parents, and also thought about Artemis. Haruka and Michiru thought about each other and the love bound that linked them, while Setsuna thought about how Hotaru and Chibiusa made her feel happy whenever they were near her. As for Hotaru, she once again thought about her family and friends, while Chibiusa thought about all her friendships, and how her friends had always been there for her, even when she thought she was all alone. Naru thought about the good moments she had with Usagi and Umino in the past. Johnny and George thought about their home dimension, and the hope they both had that one day they would be able to go back there. Finally, Usagi thought about Mamoru and Chibiusa. As if it was magic, their attacks started to affect the Guard Armor. Soon it had lost one of his legs, and it was starting to give in. Being pumped by the adrenaline in his blood, Johnny reached for his pocket, and hoped that what he was looking for was inside his pockets. Luckily, he found it. He took out yet another of his futuristic gadgets of his pocket, thanking for the fact that when the Flora, Fauna and Merryweather gave them new clothes, they had put everything they had with them in the pockets of their new garments. Pressing a couple of buttons, the little device soon turned into what it looked like a radio. He had decided to put on some music, to help everyone relax while in battle.
"This might help us!" –he said, as he jumped in the air and threw the radio into the ground and this one started to pump out music.
"How is this going to help us?" –Haruka asked him sarcastically, not really believing that a radio could help them.
"Feel the music! We, the Sailor Scouts, in out home dimension tend to fight against all kinds of bad guys to the rhythm of them music! Let's see if you guys can also do that!" –Johnny declared, as the music started. – "Music, maestro!"
_It's been a long, rough road
And I'm finally here
I move an inch forward,
Feels like a year_
Everything you feel,
It's so unreal
Is it true?
Is it true?
"Man! I just love this music!" –George exclaimed.
"I know; that's why I put it on the radio's memory card, genius." –Johnny commented, as he fired way an ice sphere with his Keyblade.
_I take one step forward
Two steps back
I have a hundred-thousand pounds
Sitting on my back_
Up, down
All around
Don't know quite what to do
To get through
Well I'm on my way
On my way
On my way
On my way
Here I am (Here I am)
Made it to
The end of you
Never had a chance when I'm around (No, No)
No No No No
"Hit this guy with everything you got!" –Naru yelled, as she hit the Heartless with her Keyblade, while also kicking it, in the leg.
_Well now I'll never turn back (Never turn back)
I'll never turn that way
No matter how life tries to face me,
I turn the other way_
Now and then (Now and then)
My head starts to spin (Starts to spin)
I'll never turn back....again!
"We're hurting it! Everyone jump and attack its arm!" –Rei said, as she also jumped, wielding her Keyblade in her hands.
"You heard her! Target that bastard's arm and tear it apart!" –Haruka exclaimed in rage.
_From this moment on (Moment on)
I am moving on (Moving on)
And I'll never turn back!_
I guess I'm doing alright
I'm on my way
Facing every moment
Day by day
Take a chance on black
Or tunnel into light
Head straight
Head straight
What will I become if I don't look back?
Give myself a reason, for this had lack
I can learn
I can turn
I can stay right here
Where I'm at
Where I'm at
Well I'm on my way
On my way
On my way
On my way
Well here I am (Here I am)
Made it to
The end of you
Never had a chance when I'm around (No, No)
No No No No
"We're almost there! Just a few more hits, and I think it'll go down!" –Usagi said.
_Well now I'll never turn back (Never turn back)
I'll never turn that way
No matter how life tries to face me,
I'll turn the other way_
Now and then (Now and then)
My head starts to spin (Starts to spin)
I'll never turn back....again!
_From this moment on (Moment on)
I am moving on (Moving on)
And I'll never turn back !_
I
I
I'll never turn back!
As the music faded away, the Guard Armor shrieked in pain, as Usagi somersaulted and thrust the Keyblade in the Heartless' torso, making what looked like veins of light appear in it. From them, beams of light started to come out, and suddenly, the creature's torso blew up, and what's left of the Guard Armor disappeared into thin air. Panting, trying to regain their breath, all the Sailor Scouts looked to each others and smiled, as their heart beat went back to normal. Luna and Artemis approached Usagi.
"Nice work, Usagi." –Luna said happily.
"Thanks, but I wouldn't have been able to stop it if you all hadn't helped me. " –she answered her, as all of a sudden something really magic happened.
In front of the girl's eyes, something began to materialize, enveloped in tiny sparkling stars. At first, she did not know what it was, and neither the others. Little by little, the object materialized in front of everyone's eyes, turning into a new Keyblade. This one was extremely simple, yet beautiful. Its handle was shaped in the form of a crescent Moon, while its blade was pink. At the tip of the blade, the teeth were also shaped in the form of a crescent Moon, but unlike the other that it was yellow, this one was silver. Finally, the Keychain was shaped as a small pink rose bud. Usagi gently grabbed it, and as soon as her fingers touched it, she felt its power flowing through her body, the same kind of power that she had felt when se first used the Kingdom Key.
"Whoa, a new Keyblade!" –Minako exclaimed. –"Please, let me have it, Usagi, please."
"Sorry, young lady, but I'm afraid that a Keyblade chooses its master, and it looks to me that it chose your friend." –Leon declared, with a gentle voice.
"By the way, now that we got rid of all the Heartlesses, we would at least like to know how you are, if you don't mind presenting yourselves, of course." –George said.
"Of course… My name is Leon, and this here is my friend and companion, Yuffie." –he said.
"And those over there are Aerith and Cid!" –Yuffie exclaimed, with her joyful voice, as she pointed out to the last two, who waved back at the group, were arriving at the square right at that moment.
"Well, you already know Chibiusa… I'm Usagi, also known as Sailor Moon, and this one over here is Minako, known as Sailor Venus." –Usagi said, as she presented them.
"I'm Ami, but you can also call me Sailor Mercury." –Ami waved.
"I'm Rei and she's Makoto, we're Sailor Mars and Sailor Jupiter." –Rei said, as she and Makoto waved.
"Those two lovebirds over there are Haruka and Michiru, Sailor Uranus and Sailor Neptune respectively, and I'm Johnny, Sailor Pluto FX Destroyer, if you prefer." –he said, as he cleaned his sunglasses.
"I'm Setsuna, also known as Sailor Saturn; this is Hotaru, also known as Sailor Saturn." –Setsun said, as Hotaru waved shyly.
"I'm George, also known as Sailor Saturn Net Surfer." –he said.
"I'm Naru, also known as Sailor Earth." –Naru said.
"And these two here, are Luna and Artemis." –Chibiusa said, as she held both of them in her arms.
"Well, it seems that we'll have lots of people to have tea with us, today." –Aerith said, with her sweet caring voice.
13. Blast Off!
Chapter 13: Blast off!
After a nice cup of tea, Chibiusa told the whole gang how she had met Leon and the others, and Usagi and the gang explained to her how they ended up there, and what their mission was.
"So, let me get this straight. You're saying that an old wizard called Yen Sid has told you that we were chosen to be new bearers of the Keyblade, the weapon that we all used to fight off those awful creatures, which are called Heartless, is that it?" –Chibiusa asked Usagi, as she finished her cup of tea.
"Pretty much. Three fairies called Flora, Fauna and Merryweather also gave us these cool clothes, which they say amplify our powers, and that we have to prevent something called Kingdom Hearts from happening, while looking for the last Keyblade bearer and his companions, who disappeared from existence." –Usagi completed her explanation.
"That's a lot of work you got there to do, kiddos." –Cid said.
"I know, and well, all the help we can get is welcome. Yen Sid said that the Heartless have infiltrated in every world that exists, and so, we need to visit other worlds and make sure that those creatures don't hurt any more innocent people." –Usagi said.
"And do you know how to get there?" –Cid asked.
"Well… not really." –Usagi declared. –"Yen Sid didn't tell us exactly how we are going to get to the other worlds. He only told us that the Keyblade would point us the way, just like it did to the previous Keyblade wielder, Sora."
When Usagi said Sora's name, something inside Leon's head called his attention.
"Sora? Why is that name seems so familiar?" –Leon thought to himself.
"What is it, Leon?" –Yuffie asked him.
"It's the name of the previous Keyblade wielder… It's like if I had heard it before." –Leon answered his partner.
"Now that you mention it, the name also seems familiar to me. But I think none of us ever heard it before." –Yuffie said.
"I do believe that you might be some of the people that he must have met during his adventures, but because he was removed from the time flux current, everyone who met him and his companions, must have forgotten about them." –Johnny explained.
"And that's not all; we're also looking for the only member of his group that is still out there, an anthropomorphic mouse, named King Mickey. Do you remember of him, or have seen him?" –Setsuna asked them.
"I'm afraid not…" –Aerith said.
"The name is also familiar, but we haven't seen anyone that resembled that description. Maybe he's in another world, and hasn't been able to get to this one yet." –Yuffie said.
"I guess we're no where near of finding any of them, everyone." –Rei said.
"Anyway, we have to get going. But how do we get out of this world in this first place?" –George asked. –"I knew we should have asked that old wizard!" –he said, cursing that fact.
"Well, cursing our luck isn't going to get us anywhere, George." –Haruka said.
"You know, maybe I can help you out with that little detail."-Cid said. –"You guys need a way out of this world, and the only way to do that is to travel in a space ship, a Gummi ship."
"A Gummi ship?" –Naru asked.
"What is that?" –Hotaru asked him.
"A Gummi ship is a special space ship that enables people to travel through dimensional rifts, and so, get to other worlds safely… and it just happens that the one that me and the others used to escape from our own world, just before this own disappeared, is still operational. If the rest of the gang doesn't oppose it, you guys could have it." –Cid declared, while looking to Leon and the others, whose eye look said that they agreed.
"And, is it fast?" –Johnny asked.
"Are you kidding, kid? Of course it is! In fact, it's probably the fastest Gummi ship to ever been build! Why don't I show it to you, right now?"
That said, Cid told them to follow him. The whole group agreed immediately that they wanted to see the ship. Everyone was excited; all, except for Johnny and George, who were already used to see space ships in their home dimension.
"I wonder how the ship is." –Chibiusa said out loud.
"Me too, Chibiusa, me too… But one thing is for certain, it has to be really big to transport lots of people." –Hotaru said, smiling to Chibiusa, who replied to Hotaru's smile, with a smile of her own.
After almost ten minutes, they stopped in front of what looked like a warehouse. Cid opened the door, and revealed what was inside.
"Amazing…" –Ami said, as she looked at the space ship.
"She's a beauty, isn't she? I made her from scratch… You know, it took me only a couple of minutes to come up with the plans for it, but it took me more time than I thought to perfect it in every detail." –Cid admitted.
"Does it work?" –Johnny asked Cid, not convinced that that Gummi Ship could actually fly.
"Are you kidding me, boy? This ship is one of the best in this universe. It can take you wherever you want!" –Cid told him, showing off a little temper.
"I just have one question. When can we depart?" –Usagi asked him.
"As soon as finish a couple of modifications. It's been a while since she flew, and if you're going on a long trip, you're definitely going to need a couple of extras in it." –Cid said. –"In the meantime, Leon there can take you to the Moogle Synthesis Shop." –he said, as he approached the Gummi Ship, ready to make a couple of modifications.
"The Moogle Synthesis Shop? What's that shop and what is a Moogle?" –Minako asked, not understanding a word of what they talked about.
"You'll see." –Leon said.
Leaving Cid in the warehouse, everyone followed Leon through the narrow streets, until they reached _First District_. Leon walked into a store that was located on a small building, with the rest of the group following him. As soon as they entered in a shop, the first thing they noticed was that the walls were yellow; a canary-yellow, which was a colour that gave away a warm thought. There were wooden tables all over the place, where strange materials rested, and they were met by a strange creature. It was just one of many that were flying around the place. They were small, white creatures resembling plush toys, with large, spherical heads, small ears sprouting out of the sides of their heads, and stubby hand and feet that lack distinct digits. Their eyes were constantly narrowed into brown slits and their noses were bulbous and pink. The creatures also sported tiny, purple wings like those of a bat on their backs, but, perhaps their most distinctive traits were large, red, spherical "pom-poms" on attached to the tops of their heads by a thin, brown, antenna. Hotaru looked at them and found them extremely cute, comparing them to one of the plush animals that she loved to collect.
"Are these the Moogles?" –Setsuna asked Leon.
"Yes, they are. Don't let their appearance fool you. They are all experienced artisans when it comes to the art of synthesis." –Leon said.
"Synthesis?" –Makoto asked them.
"It's not exactly an art, it's almost a science, which allows you to create new objects from raw materials." –Yuffie told her.
"Oh, in our world, we have something similar. It's called alchemy, and of course, let's not forget that we also have chemistry, even if it's a little different from alchemy." –Michiru said.
"But, what exactly are we doing here?" –Haruka asked, as she pulled Michiru closer to her, and then putting her arm around her waist.
"Moogles are known to be able to synthesize all kinds of materials, like I said. But they are also known to be able to examine objects like weapons, such as shields, staffs and of course, Keyblades. If you want to, and I'm sure you all want to, they can tell you the characteristics of your Keyblades; their weaknesses, their attacks, and of course, if they are resistant to an element, or to many, and even tell you the name of your Keyblades… you know, the full characteristics of your Keybades." –Leon explained them.
"The Keyblades have names?" –that was the first thing that Usagi asked.
"Of course they have. Just like every powerful or important weapon, the Keyblades also are given names." –Leon said. –"Just give me a couple of seconds to talk with them."
They all heard Leon talking a strange language, which they tried to figure out what it was, but it seemed that it did not resembled any kind of human language that existed on Earth. Finally, Leon finished talking with the Moogle, he turned to the group with a little smile on his face.
"He says that there won't be a problem, and that he would love to tell you all the characteristics from each one of your Keyblades… In fact, he considers it an honor doing that."
"Great. This ought to be fun." –George said.
"That was some strange language you were talking with the Moogle, you know?" –Chibiusa said. –"What's its name?"
"It doesn't have a name, but it's one of the most ancient languages from our home world." –Leon said.
"It looks and sounds strange, at least to me. It must be very hard to learn it." –Minako declared.
"Not really. It just looks harder than it really is, just like Al Bhed, which is another language from our world. Once you learn the basics, the rest is pretty easy." –Aerith told them.
"Could you teach us?" –Hotaru asked, always with a cute smile and a warm smile, making her look incredibly adorable.
"Sure, I would be delighted to teach you." –Yuffie said. –"But right now, let's find out a couple things about your Keyblades."
They started by taking a look to Usagi's newest Keyblade. In a matter of seconds they examined it and told her that its name was the "Crescent Moon" and that it had Orichalcum Crystals in its composition, a very rare element, which made a person's magic flow through the blade much easier. The same thing was said about Chibiusa's, whose Keyblade was named "Pink Sugar". They then examined Ami's, and told her that this one was named "Enchanted Wave" and that it had been forged using Blizzard Gems and Dark Gems, which enabled its wielder to perform stronger ice attacks, giving the user greater speed. Rei's Keyblade was next. It was called the "Blazing Spirit" and it had been forged using Flame Crystals and Flame Gems, which allowed its wielder to cast powerful fire attacks.
"Figures… I mean, she's the Fire Scout, so her Keyblade had to be forged to help her cast fire attacks." –Michiru commented with Haruka.
Makoto's Keyblade was the next one to be examined by the Moogles. They told her that her Keyblade's name was the "Rumbling Thunder" and it had been forged, using Lightning Crystals and Light Gems, which enabled her to cast more powerful electrical attacks and superior stamina. Minako was so thrilled to know the details of hers that she literally made it appear right in front of one of the Moogles, and begged him for any kind of details. In just a couple of minutes, they told her its name, which was the "Passionate Kiss" and that it had been forged using Lightning Gems and Energy Crystals, which gave her superior agility and the ability to cast her attacks faster than before. Then, Haruka's Keyblade was the one to be examined. They told her that it was named "Mortal Blade", which had been forged using Dark Shards and Lightning Gems; a combination which gave the Keyblade's wielder the ability to use more powerful attacks. All that made Haruka feel even prouder of her Keyblade than before. Next, Michiru's Keybalde was examined. They told her that its name was the "Musical Symphony" and that had been forged by using Blizzard Gems and Twilight Shards, which allowed her to use stronger water attacks.
"Musical Symphony? What a beautiful name for such a weapon." –she thought to herself.
After Michiru, it was Setsuna's turn. Even though she was excited to know the details of her Keyblade, she kept her composure, and waited for them to tell her everything in due time. They told her that her Keyblade was called the "Time Sweeper", a name which she loved, and that had been forged using Dark Gems and Blizzard Crystals. It gave its wielder more stamina and velocity, not to mention a greater control of the powers of time. Then, it was Johnny's turn. His Keyblade was called the "Dark Necromancer" and had been forged Dark Crystals and Blizzard Crystals, similar to Setsuna's, but this one enabled its wielder to use more powerful ice attacks, as well as giving him much more strength. After him, it was Naru's turn. She was a little nervous, even though she did not know why. The Moogles told her that the name of her Keyblade was "Emerald Core", a suitable name for a Keyblade such as hers. It had been forged using Energy Crystals and Dark Shards, and it granted its wielder more strength and velocity. Hotaru was next. The Moogles had a hard time examining hers, probably because it was quite complex, and undoubtedly, one of the most powerful Keyblades that they had ever seen. After a while, they finally told her that the Keyblade's name was the "Grim Reaper", which suited her, since she was supposedly the Soldier of Chaos and Destruction. It looked like hers had been forged by using Dark Crystals and Dark Shards, which gave her more power and strength. Finally, it was George's turn. His Keyblade was named the "Razor's Edge", which had been forged by using Dark Shards and Twilight Gems, giving its wielder more agility and velocity.
They also gave the original Keyblde for the Moogles to examine, but these were not able to tell them anything regarding this particular one. The only thing they could tell them was that it had been forged by using unknown materials, and whoever had been able to forge it must have been a genius or a master when it came to create those weapons. After that was taken, the Moogles told the whole group that during their adventures, whenever they manage to collect enough items, they could take them to a Moogle in order to turn them into other objects, which would help them on their quest.
A couple of hours went by, when finally Cid reappeared, to tell them that the ship was good to go. He had been making a couple of modifications to the ship, which he thought were necessary.
"Well, I think that's that. I modified the navigational system so you guys don't have to worry about getting lost. Just point out the world that you want to visit and the ship will take you there." –Cid explained them. –"Plus, I've upgraded the weapons system. It still has a couple of bugs in it, but other than that, it's operational and ready to take on any kind of enemy that crosses your path out there."
"Cool." –Johnny said, as he checked out the control panel.
"Thank you ever so much, all of you. I don't know how to repay you for all that you did for us and for Chibiusa." –Usagi said.
"No need to thank us. We're happy to help anyone who's fighting the Heartless, and besides, you guys taught that old witch a lesson." –Yuffie said.
"You guys just take care of yourselves, and watch out for whatever comes your way." –Leon said. –"And remember, you're always welcomed back here."
"We'll remember that, you can bet that." –Haruka declared.
"Oh, and one more thing… If you guys have any more troubles with the Heartless, or, if you find anything that helps us in our quest, let us know, okay?" –Minako stated.
"Don't worry about that. If we find out anything that can help you, guys, we'll contact you through the radio." –Leon said.
After saying their goodbyes, everyone hoped aboard the Gummi Ship, and they started it. Since they were used to drive vehicles similar to that one, back at their home dimension, Johnny and George took the controls of the Gummi Ship. In a matter of minutes, they had left the gravitational field of that world, and were now floating in what looked like deep space. They all looked at the world they had left behind, and saw that this one had a curious shape, nothing like a planet, but something entirely different.
"Okay, we're good to go, everyone." –George said. –"My only question now is, where to?"
"I don't know. I mean, Yen Sid told us that there are numerous other worlds, but we don't know where they are." –Setsuna said.
"Why don't you check if this thing has a map or something that can help us, navigate through here?" –Ami suggested them.
"Good idea! Let's see if Cid put something like that in this giant central computer" –Johnny said, as he pressed countless buttons, looking for the right one. –"There's got be one around here."
"Just try and not push the auto-destruction button, okay?" –Haruka commented sarcastically.
"Very funny, ahahah, very funny…" –Johnny said.
Finally, he managed to find a map, where you could see the names of numerous worlds. All of them had different shapes, colors and sizes, not to mention that they all had rather curious names.
"Well, which one should we pick?" –Makoto asked out loud.
"Why don't we visit the ones that are nearer to us, and then proceed to the ones that are farther from us?" –Artemis suggested them.
"Good idea, Artemis." –Minako said. –"Well, then our first stop should be this one here." –She pointed in the holographic map.
"Wonderland? Funny name for a world." –Hotaru commented. –"I wonder what kind of world, will that one be?"
"Will soon find out, because that will be our next stop. Strap yourselves to your seats and enjoy the ride… oh, and thanks for choosing Air Sailor Scouts." –George said, causing everyone to laugh over the last sentence, as he activated the thrusters.
Unknown to them all, someone was watching their every move, and was getting ready to attack them, when they least expected.
14. Bridge to Wonderland
Chapter 14: Bridge to Wonderland
Unknown to all of the Sailor Scouts, someone was watching them. And that someone, were actually several people. Somewhere inside a dark and spooky chamber, a group of sinister figures gathered around some kind of portal, created by the most powerful witch in the universe, Maleficent. They were eight, all different in aspect, but, their evilness was on the same level as the despicable and dastardly olive-skinned witch. By her left side, was a tall and bony man dressed in extravagant clothes. He was dressed in black robes that reached the ground overtop a red-violet garment with bell sleeves. Underneath that second garment, he was wearing yet another shirt, this one black with very close-fitting sleeves that reached his wrists. The shoulders of his outer robe were pointed and connected to a long, billowing black cape with a blood red interior. His shoes were brown and the tips curl inward. A red-violet sash was tied around his waist. He was also wearing an odd, light-coloured garment that covered his neck, the back of his head, and his chest. He had a twisted, black goatee and a faint moustache, as well as grey eyeliner. He also sported a distinctive black headdress, seemingly a type of mitre, with a thin, yellow pattern, wrapped around the middle, what seemed to be a ruby set in the front, and a bright red feather placed just above it. More red-violet cloth hanged from the mitre, draping over his shoulders. He was also carrying a gold, ruby-eyed cobra sceptre on his left hand, while on his right shoulder rested a red plump parrot, being his tail and the tips of the first four feathers on each wing the exception, which were blue. These were Jafar, Agrabah's grand-vizier, and his parrot, Iago.
By their right side was yet another villain, this one being an obese cecaelia, a mythical being with the upper body of a woman and the lower body of an octopus, with lavender skin. The top side of her octopus half was pitch-black and reached up over her chest, resembling a shoulder less, backless gown. The underside was a bright violet colour, while her short hair was stark white with a few grey streaks that stands on end. She also sported a widow's peak hairline. She wore various forms of make-up, including purple nail polish on her pointed nails, light blue eyeliner, dark purple eye shadow, bright red lipstick, and seemingly pencilled-on black eyebrows, not to mention a small beauty mark near her chin on the left side of her face, as well as a yellow spiral shell necklace on a thin black cord, and two violet, thinner spiral shells as earrings, one on each ear. She was Ursula, the sea-witch.
On her left side was a man with blue skin and blue flaming "hair". His eyes were completely yellow, except for his black pupils. He had very sharp teeth and an unnatural black mouth. His face was quite long and thin, with his chin jutting out abruptly. His fingers were long, thin, and clawed. He was wearing what appeared to be a dark grey shirt underneath a black toga, the latter of which seems to be held up by a small skull pin on his right shoulder. He was Hades, God of the Dead and Lord and Master of the Underworld.
On his left side was a tall, slender man with pale skin and black short hair, though he had a few grey hairs on his temples and a black goatee. He was dressed in an ash-grey suit, white shirt, black tie and black shoes. At first sight, you would think that he was just a bank manager or perhaps an executive. But if you looked into his face, you would see his most distinctive mark; his right eye, which was a green eye, was shaped like the eye of a feline. He had a menacing grin, which gave the creeps to anyone who looked at him, when he was smiling, all because of his razor-sharp teeth. He was Dr. Calico, one of the most devious and evilest beings that ever existed, as well as a calculating man, who's only goal was world domination.
On Maleficent's right side there was a creature quite rotund with stumpy legs and fingerless arms, covered from head to toe in a grey burlap sack, and an obvious seam along the sides. His eyes and mouth were featureless black holes, while the tip of his head extended outward and flopped down. He was Oogie Boogie, the meanest and most dangerous creature of Halloween Town.
By his left side, there was a thin man with curly, black, shoulder-length hair that draped over his shoulders, a large, hooked nose, a thin, black moustache that angled upward sharply, and a large chin. He was dressed in a frilly, white shirt underneath a red coat with gold lining and maroon cuffs. Each of those cuffs sported two yellow buttons. He also wore an orange sash over his right shoulder that held his sword scabbard at his left hip. On top of that, he was wearing maroon pants and white, knee-high socks, as well as black shoes with a pink circle decorating each one. The tongues of his shoes were enormous, reaching halfway up his shins. On the top of his head, he was wearing a large, maroon hat with a huge, white feather stuck in it. He carried a rapier with a gold handle and guard as a weapon. But the most distinctive feature of this man was the fact that instead of having a left hand, he sported a hook. He was none other than the infamous Captain James Hook, the most feared pirate in all seven-seas, or at least that is how he entitled himself.
And last, but not the least, to Hook' left was an icily beautiful woman with a serene and unfeeling face and a slender figure. She was pale-skinned with green eyes, red lipstick, and seemingly penciled-on eyebrows. She was wearing a purple gown with long sleeves and a rope belt tied around her waist, as well as a black balaclava that covered her ears, neck, and raven hair, leaving her face exposed. She also wore a long black cloak that appeared to be part of the cowl. The cloak was lined with red inside and the bottom of the cloak was lined with white fur. She also had a high white collar attached to her cloak. On top of that, she wore a golden pendant that seemed to connect with the collar. Atop of her head, she was wearing a golden crown with five spikes on the front and a jewel on the tip of the middle and tallest spike. She was Queen Grimhilde.
"So, you're saying that you managed to get rid of those scurvy kids, and the king's fellow companions, but the Keyblade managed to find another wielder… that wretched girl, and her friends?" –Captain Hook asked, as he visualized Usagi and the rest of the Sailor Scouts in the portal.
"I'm afraid so. I shouldn't have, but I underestimated the power of the Keyblade. I thought that by removing that wretched Sora and his friends from the time flux stream would give us the opportunity to open Kingdom Hearts without any kind of interference, but it seems that the Keyblade had other plans."
"And can't you just make them disappear from the time flux stream just like you did with those show-offs?" –Oogie Boogie asked her.
"I don't think your careless brain understands what I'm saying, Oogie Boogie. If I did that, the Keyblade would simply find another wielder, and then we would be back at square one. The only thing I can occur right now is to go on with our plans, and leave them to the Heartless. They'll make sure that they stay busy enough for us to conquer every world, and believe me when I say that this time we will succeed." –Maleficent said.
"So, you mean that in the meantime, we'll just leave those pipsqueaks to walk around wherever they want?" –Ursula asked.
"I'm afraid that's the only thing we can do for now. Still, there is one thing that none of us remembered so far… it's not these kids who represent the danger; it's their Keyblades. If we find a way to prevent the Keyblade from choosing anyone to be its new bearer, then nothing will stop us from achieving our goal" –Queen Grimhilde explained.
"I don't think such a group will pose any treat to us or to my organization." –Dr. Calico said with a polished tone. –"I have experience when it comes to handle such threats… they will be exceedingly easy to dispose off, I can assure you. If the Heartless fail to accomplish that, my troops will make sure that that happens."
"Come on, people, right now we can't loose our temper with these things. We got more important things to worry about… they're just a bunch of chicks and guys who happen to have a little luck until now. Let's just do what Maleficent is saying, leave them for now and then, if we find a way to get rid of them permanently, we'll show them no mercy." –Hades said with his calm and usual voice.
"Show them no mercy? Hahahah, I like your style, Hades." –Oogie Boogie declared.
"What can I say, I'm the hottest guy in the Underworld, get it? The hottest guy…" –he laughed, as he pointed to his flaming hair.
As everyone talked among themselves, Jafar stood still, with only Iago, his parrot, talking with him.
"Do you believe these guys, Jafar? I mean, we already had enough trouble with Sora and the rest of the brats last time, and now we have to worry about these new ones? I hope you have a good idea, because I…" –Iago exclaimed, when Jafar shut his beak with his fingers, preventing him from talking.
"Yes, I'm afraid you may be right about it, Iago. These new brats will certainly become a thorn on our side, even though some of us think the opposite. But believe me when I say, that this time I'll be ready to deal with them." –Jafar told him, with a calm and serene voice. –"They won't even know what hit them, when I'm through with them."
At the same time, aboard the Highwind, the Sailor Scouts continued their voyage to the strange new world that headed into. The ship was incredibly spacious and comfortable in almost every way, but the trip was taking too long for them. In fact, it did not take long for them to get bored.
"This is taking too long… Can't we go any faster?" –Usagi cried to Johnny, who was piloting the ship.
"Don't you think that if there was a way to go faster I wouldn't have found it by now, Usagi?" –Johnny asked her. –"This is the fastest this ship can go. Why don't you go and take a look around the ship, maybe you'll find something that amuses you… you don't have to stay here in the cockpit with me and George, you know?"
"Maybe you're right. I'll go and take a look."
Following Johnny's advice, Usagi want to take a look around the ship. She quickly found Ami coming out of a room, with a stack of books in her hands, all of them huge books… Usagi always knew that Ami was the kind of girl who read huge books. Heck, she would read a whole encyclopaedia if anyone asked her. But she never thought that she would try and read anything while on this adventure.
"Hey, Ami!" –Usagi exclaimed.
"Oh, hi, Usagi." –she said.
"Where did you get all of those books?" –Usagi asked her, while she walked over to her.
"Over here. The ship has a huge library, with books on almost very subject, so I decided that it would be best if I could find out any information regarding our enemies… lucky for me, there are a few books on the matter." –Ami explained. –"Why don't you go check it out? Maybe you'll find something that you like. Haruka and Michiru are also inside reading something."
"Hmm… No, I guess I'll pass. You know that reading it's not really my thing. Tell me, have you seen the rest of the gang?" –Usagi asked her.
"Well I think Makoto was on lower deck with Rei and Minako, as well as Luna and Artemis. Chibiusa and Hotaru were here at the library a while ago, and I haven't seen them since, and Naru… well, I haven't seen Naru since we boarded the ship." –Ami said. –"I'm going to the cockpit, and see if George or Johnny need any help. Coming?"
"Oh, no, I just came from there. I'll go check on the others… catch you later." –Usagi said.
Walking through the ship's white corridors, her footsteps echoes in the air as she walked by them. Following the distant sound, she soon found Makoto, Rei and Minako. Makoto had found some kind of video arcade machine and was going for the highest score, while Minako and Rei cheered for her. At the same time, Hotaru and Chibiusa were seated in a couch, not far from the others, reading a book together. From where she was, Usagi could not see what the book was about, but from the way both of them were laughing, she assumed that it was a book about something funny.
"Come on, jump!" –Minako said.
"I'm trying, but the enemies are too fast for me!" –Makoto said.
"Hurry, here comes another wave!" –Rei warned her. Unfortunately, it was too late and Makoto lost. She screamed on top of her lungs, as the words "Game Over" appeared on the screen.
"Drat! I can't believe it… Okay, two out of three!" –Makoto said, as she pushed the button to begin a new game.
Usagi smiled seeing her friends having fun. Even knowing that they all faced a dangerous and still unknown enemy, they still managed to laugh and cheer. And that, that gave Usagi hope that everything would turn out okay in the end. All of a sudden, she felt something rubbing against her leg. She looked sown, and saw that it was Luna and Artemis.
"Hey, so what are you two doing?" –Usagi kneeled, petting both cats.
"Nothing. We had to get out of there before they killed us." –Luna said.
"Indeed, Minako almost strangled me, when she lost the first round." –Artemis stated.
"Yeah, she can't control her strength sometimes, especially when she gets mad." –Usagi said. –"Tell me, have you seen Naru?"
I thin she was on the observatory deck; up there. Why do you ask, Usagi?" –Luna asked her.
"No special reason at all. I just want to see if she's alright… after all, unlike the rest of us, she's not used to this. She did not even know that she was Sailor Earth, until that attack of the Heartless back at our world."
"Indeed… Maybe you should really talk with her and make sure she's taking all of this right." –Artemis said. –"The last thing we need now, is for one of us to become confuse about their mission.
"You're right, I should go and talk with her." –Usagi said. –You said she's in the observatory deck, right?"
That said, Usagi headed to the observatory deck, to talk with Naru. When she got there, she saw that Naru was leaned against the glass dome, looking at the immense stars and what seemed like constellations in space. She had a little smile on her lips, and you could see that she was thinking about something happy. The fact of have been her best friend for so long, Usagi knew her too well.
"Hey, Naru!" –Usagi called, but Naru did not answer her. –"Naru! Earth to Naru, Earth to Naru… Are you there?"
"Oh… it's you, Usagi. Sorry, my head was a million miles away. " –Naru said.
"I noticed. Do you mind if I sit here with you?" –Usagi asked her.
"Sure, be my guest." –Naru answered, as Usagi sat a couple of feet from her.
"So… what's on your mind right now?" –the blonde asked her.
"Oh, nothing… I mean, I was just thinking about how many times you saved my life ever since you became Sailor Moon." –Naru said.
"I still remember those early days, too, you know? Things were so less complicated back then. We had so little to worry about."
"Yeah, the way you managed to always arrive late at class, and how Miss Sakurada punished you, by giving you detention." –Naru laughed.
"Indeed… You know, I never knew what happened to her after we left Juuban Municipal Junior High School."
"Oh, that I think I can answer, Usagi. She ended up marrying a man she met when she was on vacation in Yokohama, and she still teaches at our old school. She happens to visit me and my mom at the jewellery. She wonders if you're still the same girl that you were a couple of years ago, always arriving late at class, eating when you're not supposed to… In a way, I think she misses you." –Naru said.
"Well, she could be a little mean to me sometimes, but, I actually liked her a lot. When we get back, I have to pay her a visit." –Usagi declared.
"I believe that she'll be very happy about it." –Naru said. –"But, that's not why you are here, is it, Usagi? You're here because of something else, am I right?"
"Well…" –Usagi hesitated.
"Don't pretend that you don't know what I'm talking about, Usagi. I know you too well for you to keep anything from me." –she chuckled. –"Come on, tell me, what is that you want to talk with me?"
"Well, it's because of the fact that you're not used to all of this, like all of us are. After all, you were awakened from your sleep as Sailor Earth recently, and well, I understand that you might be confused with all of this." –Usagi said.
"You want to know if I'm alright, is that it?" –Naru asked her friend, to which she nodded with her head. –"I'm alright, Usagi. I'm stronger than most people think, and besides, having you and everyone by my side, it certainly makes me feel safer. What about you, are you alright?"
Usagi took a moment to think about it. Ever since that all started, she had not a moment to think about that matter. Then, she took a deep breath and said:
"I don't know… I mean, I must be strong, because everyone depends on me for guidance, but I'm really scared. I'm scared because I don't know what awaits us in this new journey of ours… and worst of all, I miss him… I miss Mamoru…" –Usagi said, as a tear rolled down hr cheek. –"I can't help but think about him, and where will he be, right now."
"Don't worry; I'm sure he's fine, wherever he is. The prince is a talented warrior, and besides, he can take care of himself." –Naru said. –"You'll see, we'll eventually find him. But right now, what you need is to focus on your mission, which is to guide everyone. You need to be strong… just like you have been."
"How do you even know that I was strong all this time?" –Usagi asked her.
"Because if you hadn't, you wouldn't been able to save the world countless times from the forces of evil… and just so you know it, yes, I'm aware of everything that happened while I was "sleeping", thanks to the link that I have with Prince Endimion. His memories have become mine, you know?"
"Then… you know bout all our confrontations… Queen Beryl, Queen Metalia, Alan and Ann, the Black Moon Clan, the Witches 5, Pharaoh 90, Amazon Quartet, Queen Nehelenia, Sailor Galaxy, and well, the rest…"
"Yes… and I know that you needed all the courage you needed to face them. You're very brave, even if you don't admit it, and I think that…" –Naru said, when she was interrupted by a shaking. –"What was that?"
"I don't know, but I bet all the cookies you can eat that Johnny and George know what's going on… come on!" –Usagi said, as she grabbed Naru by her wrist and guided her through he corridors, back to the ship's bridge.
When they got to the bridge, everyone was already there. The amount of noise was practically infernal. The buttons in the panels were all buzzing and beeping. It was total chaos.
"What happened?" –Usagi asked.
"We were hit, that's what happened!" –Johnny answered her.
"But, were we hit by what?" –Rei asked him.
"We don't know yet, and that's what we're trying to figure out, as in now." –George said.
"I think I know what hit us… it was that!" –Hotaru exclaimed, pointing something out of the window.
Everyone looked to where she was pointing, and they all saw some kind of ship outside. Then, they saw another one, and then another one… in a matter of five seconds, about twenty ships, from about a quarter the size of the Highwind, surrounded it. And the worst part about that, was the fact that they had the emblem of the Heartless stamped on them, and that they were about to use the Highwing for target practice.
"They're going to blast us into smithereens!" –Minako panicked.
"Not yet, they won't. Our shield will make sure that we won't get blasted just yet. But we have to find a way to counter attack them, because the shield won't last forever, and those guys look like they want to make mincemeat out of our ship." –Johnny said. –"Take the controls, George, while I try and find something for us to shoot back. Try to evade them."
"Roger that!" –George said, as he took over the controls of the ship.
"What do you want us to do?" –Michiru asked.
"Yeah, give us something to do!" –Haruka exclaimed, impatiently. Everyone knew that she was never the kind of person to stand still when on a dangerous situation.
"If you want to do something, help me find either an instruction booklet that tells me how to activate the ship's weapons system… there has to be one around here! Or if you prefer, find the weapon system itself. Cid told us that the sip had a really powerful weapon system. All we have to do is find it… Everyone, start looking for either the booklet or for the button that activates the weapons! –Johnny ordered them all.
Obeying his orders, everyone started pressing every button they saw. At the same time, George did his best, manoeuvring the ship from starboard to portside, avoiding most of the lasers shot from the Heartless ships.
"Hurry up, finding that weapon system! These guys are starting to annoy me!" –George warned them all.
"A little patience, please…" –Setsuna said, as she pressed one of the buttons on the panel.
"I wonder what this does." –Chibiusa said, as she pushed a big green button, only to find out that when someone pressed that button, a little robot would appear and would serve a cappuccino. –"This is definitely not what we're looking for."
Makoto did her best, looking for an instruction booklet that would help them. Unfortunately, she was not having any luck at it. Minako decided to help her out. Setsuna and Hotaru were busy pressing every button that they could find.
"Maybe it's not just one button, guys. Maybe it follows a partner, where we have to push multiple buttons in order to activate the weapon system." –Ami said.
"Hope not. If that happens to be true, we'll take years just to figure out the pattern." –Naru said.
"Well, there is another option…" –Ami said.
"What? Tell us, there's not time to lose!" –Johnny insisted.
"What if the weapon system is voice activated? I mean, being so important, it would have to be made so anyone could control it, without needing to use any buttons." –Ami explained.
"Maybe she's right…" –Setsuna said. –"Why don't we try it?"
"Okay, let's try it… Activate weapon system!" –Johnny shouted, when all of a sudden, the ship's computer beeped, and an attack grid appeared in front of their eyes. –"Okay, now that's better! Fire a 21 guns salute against the enemy ships!"
With the order given, the ship's computer targeted the Heartless ships, and fired against, quickly taking them out of the sky. Once again, they managed to eradicate yet another menace.
"Wow! What a rush!" –George said, exhausted from all that commotion.
"You can say that again! There's nothing better than a rush of adrenaline pumping through our veins and heart, to make you feel alive!" –Johnny exclaimed, as he got back to his seat.
"We were really lucky this time." –Artemis said. –"We better prepare ourselves for future encounters with those things."
"I'm afraid he's right. Next time, we may not be so lucky." –Luna concurred.
"Yes, we must be ready. A good soldier is always prepared to face any kind of danger, on any occasion and on any circumstance." –Setsuna declared.
"Agreed." –Johnny said as he got out of his chair. –"We'll have to find a way to know every system of this ship, even if it kills us…"
Tripping over something, Johnny fell on his face onto the floor. Everyone gathered around him, to see if he was alright. Turns out he was fine. And that was not all. He saw something underneath one of the chairs. He reached his arm for it, and grabbed it. It had a red cover with something written in it, it was all dusty and a little crumpled, but you could definitely see what it was. It was the ship's instruction booklet, where it explained how every system on the ship worked.
"Figures… When you're looking for something, you can't find it. But when you're not looking for it, then you find it." –he said as he studied the booklet's content.
"We all better start studying what's written in there, so we can operate this ship more easily." –Rei said when the alarm went off again. –"Now what? Don't tell me that we're being attacked again!"
"Nope, we're not under attack, Rei. The alarm was just telling us that we have arrived to our destination." –George explained. –"Look at that… it's Wonderland!"
In front of them, was a new world. This one was shaped like a heart, and it was all red and pink. Chibiusa giggled, while looking at it.
"It looks like a heart-shaped lollypop." –Chibiusa kept giggling. –"I wonder how the inhabitants of this world look like?"
"There's only one way to find out, Small Lady… we'll have to go there." –Setsuna answered her.
"There's only one problem with that… we can't land this ship. Looks like Cid forgot to put on a landing gear on it." –Johnny stated, as he read through the instruction booklet.
"So… how are we going to get there?" –Hotaru asked.
15. Down the Rabbit's Hole
Chapter 15: Down the Rabbit's Hole
Studying the ship's instruction booklet, Johnny attempted to find a solution to the problem they had… how to visit a world, without landing the Highwind. Time went by, and he still had not found anything that could help them. To say that everyone grew impatient by the minute was little, which bothered Johnny even more, because he did not like feel under that kind of pressure or stress.
"So, have you found anything?" –Rei asked him, as he paced through the cockpit, reading the booklet.
"No, and stop asking me that. It's the fourth time you ask me that question in five minutes…" –Johnny replied. –"Asking me that, won't help me finding the information we need faster, believe me."
He continued to read, when he finally found something that might be just what they needed to know. He read the paragraph as fast as he could and then said:
"Hmm… interesting… According to this, there is in this ship a room which possesses some kind of teleportation device. I think we could use it to our benefit. All we have to do is find that room." –Johnny declared.
"Then, let's not waste another minute. That world might have been invaded by the Heartless already... if so, we have to help its inhabitants." –Ami said as she looked through the glass canopy, contemplating the strange new world that was in front of them. –"Computer, where is the room with the teleportation device?"
"The room which you are seeking is on Deck D, sub section 3." –the computer said, at the same time in one of the monitors a map was traced, using the ship«s schematics.
Following the path given by the ship's computer, they managed to find the room they were looking for. The room was completely white. In fact, you could almost say that was similar to the TV Room, from the movie "Charlie and the Chocolate Factory". As they stepped into the room, they all felt that the air was rather chilly, almost frozen. Everyone felt as if they were inside a huge freezer.
"So, how do we use this?" –Haruka asked, as she looked around the room.
"Don't know… But, I suppose we have to use that sort of tube." –Ami said, pointing to the huge glass tube that existed in the middle of the room.
They all approached it, not knowing what to do exactly. Observing it, they concluded that glass tube was probably the teleportation device. But how they were going to use it was a problem. It did not have any buttons or any sort of thing to start it. Puzzled, they asked the ship's computer for help.
"Computer, how do we start the teleportation device?" –Usagi asked.
"To use the teleportation device, simply touch it, introduce the coordinates in the teleportation device and enter in it. To come back to the ship, just press the blue gem in these bracelets once." –the computer said, at the same light a light appeared on the floor, to reveal a hidden compartment, where there were many bracelets. These looked like ordinary metal bracelets, with a blue gem incrusted on them. Each one of them picked one of the bracelets and slipped in on their right wrist.
Then, they touched the glass and as if by magic, a bunch of holograms appeared floating around the glass. Most of them displayed what could be called Matrix codes, while others displayed images of several different worlds. Feeling curious Chibiusa touched one of the window screens and in a microsecond, multiple smaller window screens with information of that world. Looking for the world of Wonderland in the holograms, they eventually found it. Touching it, the same thing that had happened when Chibiusa had touched the window screen happened.
"Interesting information… so, shall we go?" –Rei asked.
A little anxious, one by one, all of the Sailor Scouts entered the teleport device. The way the teleportation process worked was curious to say the least. They felt that their bodies were being dismembered limb by limb, then, they felt like they were being swirled inside a huge blender. After that, everything just went white, and when they opened their eyes again, they were somewhere else.
"W-Where are we?" –Rei asked with a bleary voice, as she looked around.
"I don't know… but one thing is for certain, we're not aboard the ship anymore." –Makoto said, also with a bleary voice.
"Which means that the teleporting device worked…" –Haruka said.
"No kidding, Sherlock?" –Johnny grumbled, as he made everything in his power not to throw up. –"Am I the only one who's feeling a little nauseated after this crazy trip?"
"No, you're not. I'm also not feeling quite myself now." –Usagi said, as she counted her fingers, fearing that she might have lost one of them during the teleportation. –"Nope, they are all here." –she thought to herself.
"Is everyone here?" –Artemis asked, as he looked for Luna, who was a few feet from him, still unconscious.
"Let me see…" –George said, as he looked around, counting the ones he saw. –"… yeah, I guess we're all accounted for."
"I think it's safe to assume that we were teleported to the world that is called Wonderland." –Minako said. –"But I don't know why it's called Wonderland. It doesn't look that wonderful to me."
Minako was right. That place did not look that wonderful. The only thing that existed around them was trees…Trees and more trees. It looked like they were in the middle of a wood or a forest perhaps. The grass was emerald green and it covered most of the ground, existing very few spots were there was not an inch of grass. It was a magnificent forest, no doubt about it, but it looked like so many forest that existed back on their home world. A stream with crystal water was running not far from where they appeared. In its bottom, there were countless beautiful grey pebbles, and you could see a couple of blue birds chirping happily, while bathing in the crystal waters.
"True. All these trees don't look so wonderful to me. But then again, I was always a city lover." –Johnny said.
"I hate to agree with him, but he's right. The only things I see around here are trees and… Is that a rabbit wearing a jacket?" –Haruka pointed out.
Everyone looked to where the tomboyish Sailor Scout was pointing to, and at first they thought it was just a joke, but then, they also could not believe their own eyes. A white rabbit with a large red nose, short ears and bright pink eyes… He was wearing spectacles, grey pants with a hole in the back for his tail, and a red over-coat and bow tie, worn over an orange button-up shirt with a white collar.wearing, and was holding in his left hand a golden pocket watch as big as his head, with a golden chain attached to it. Of all the strange things they were expecting to see on their journey, that one was clearly was not one of them.
"Oh, I'm late, I'm late, I'm late! The Queen will have my head for this!" –he said, as he hopped through the middle of the grass.
"Now there's something you don't see everyday… a rabbit who dresses like a person and talks like one too." –Rei said, as she looked at the rabbit jumping for his life, heading deeper into the forest.
"I don't know about you, but I'm following that rabbit." –Chibiusa said, as she started running after him.
"Wait for me, Chibiusa!" –Hotaru said, as she raced after her best friend, trying to catch up to her.
"Hey, don't leave us here! Wait for us!" –Makoto yelled at them, as she and the rest of the Sailor Scouts tried their best not to let them out of their sight.
Since the rabbit would not stop, Chibiusa tried to call him. Maybe that way, he would stop. She was certain that he might help them by giving them some information about the world itself. But more importantly, to ask him if there were any sign of the Heartless in that world, of if he knew anything about Sora and his companions, or King Mickey for that matter.
"Mr. Rabbit, please! Could you slow down a little bit? We have some questions to ask you!" –Chibiusa said.
"I'm late, I'm late, for a very important date. No time to say "Hello.", "Goodbye". I'm late, I'm late, I'm late!" –he said as he kept running between the trees.
"He's a fast runner!" –Michiru said, as she ran side by side with Haruka.
"What did you expect? He's a rabbit, and rabbits are fast runners. Otherwise, they would get caught by every single fox, wolf, or whatever carnivore that tried to catch them for supper." –George said.
"Why don't you stop talking about those things and save your breath? If that rabbit doesn't stop soon, we're all going to need every bit of air just to keep up with him." –Setsuna stated the obvious.
Finally, the white rabbit arrived at a tree which had a rabbit hole in it. He quickly entered in it, and disappeared. Determined to get a couple of answers, Chibiusa and Hotaru, who were the first to get there, decided to go after him. Since the hole was big enough for either one of the girls, they entered it, followed by Luna and Artemis. Chibiusa went first, but as soon as she got inside the rabbit hole she falls into what seemed to her like a huge well. Hearing her friend screaming, Hotaru entered in the rabbit hole, only to suffer the same fate. Luna and Artemis also followed her, but were luckier and did not fall through the huge well-like hole.
"Hotaru! Chibiusa!" –Artemis yelled, as he looked down, only to see Hotaru disappear into the darkness.
The rest of the Sailor Scouts arrived to the site soon after. They looked around, looking for either the White Rabbit and the Chibiusa and Hotaru. Luna and Artemis hearng them quickly appeared from inside the rabbit hole.
"Where are Hotaru and Small Lady?" –Setsuna asked both cats.
"They went through the rabbit hole in pursuit of that rabbit. Beneath this mount of dirt there's a huge whole that resembles a well, and they fell through it." –Luna said.
"Then, what are we waiting for? We have to save them. God knows where that hole leads to." –Usagi said, trying not to panic.
"But the hole is too small for us. Chibiusa and Hotaru managed to get in it because they're smaller than us, but we won't be able to fit in." –Makoto stated.
"Not a problem. Everyone step away from the rabbit hole." –Johnny warned them, as he made his Keyblade appear in his hand.
"What are you going to do?" –Rei asked him, not understanding what he had up his sleeve.
"What do you think I'm going to do? I'm going to blast this rabbit hole, so I can make it big enough for us to fit in." –he said, as he pointed the Keyblade. With a quick move he used one of his attacks to blow up a whole. –"Charon Explosion!"
The blast sent pieces of rock and dirt flying into every direction. There was a cloud of dirt and powder in the place where the small rabbit hole was just a couple of seconds earlier. When the cloud finally disappeared, they all saw that there was a huge hole on the ground, big enough for them to go through in search of their friends and the rabbit.
"Well, ladies first…" –Johnny said, as he let Usagi and the rest of the girls pass.
"You're such a gentleman…" –Haruka mocked sarcastically, as she followed the others.
Not exactly knowing what would happen next, one by one, they all jumped into the hole. Usagi went first. She closed her eyes as she jumped into the unknown. She felt herself falling at an incredible speed. Her body began to twirl while in midair, making her feel a little nauseous. When she finally opened her eyes, she saw the strangest things. The sides of that well were filled with the most amazing objects. For example, there were book helves crammed with books of all sorts; cupboards filled with the most amazing objects, like jars of jam, knives and forks, little ragdolls… There were also huge mirrors on both sides.
"What an interesting place… I wonder how many miles have I must have fallen by now?" –Usagi thought to herself.
When she almost hit a rocking-chair that was in her way, she looked up and saw Rei and the others, all falling down after her. They ended up in a heap of sticks and dry leaves. Thanks to their new abilities, they landed on their feet without making much effort. A couple of feet from where they all landed were Chibiusa and Hotaru, who looked perfectly well, without a single scratch.
"Are you girls alright?" –Naru asked both Hotaru and Chibiusa.
"We're fine; why do you ask?" –Chibiusa stated.
"Well, after we saw you falling down that well, we thought that you might have been in trouble." –Luna said.
"Oh, don't worry, were both fine. The fall was actually funny; it felt like we were in a carnival ride." –Hotaru declared.
"Well, now that we know that you're alright, I have two questions… where are we, and where did that rabbit go?" –George asked them.
"The white rabbit disappeared. When we got here he wasn't here anymore, and as for where we are, I don't have the sightless idea." –Chibiusa said, as all of the others started to look around.
"What is this place?" –Naru asked out loud.
"I don't know, but one thing is certain, it looks very pretty and funny." –Minako said, as she noticed the walls on that seemingly strange room.
Indeed the room looked pretty and funny. The whole place looked like something pulled out of a dream sequence, or something of that kind. The walls were made out of red bricks, making it look like the inside of an oven. In them, there were many mirrors; some of them as small as a pocket mirror, while others were as tall as the mirrors that you only see in palaces and reception halls of fancy hotels. Plus, there were multiple paintings hanging in the walls. Some of them were portraits, while others looked like something painted by a cubist artist. The floor looked like it had a huge spiral stamped on it. But from all strange things, the way the place was illuminated was the strangest, because there were no windows, lamps or torches to light the place. Still, it was as clear as if they were outside.
"I've seen crazy things over the years, but this place takes the 1st place." –George said.
"Hmmm… guys, I'm afraid I know why this place looks like this." –Ami said.
"What do you mean, Ami?" –Rei asked her.
"Well, I'm not entirely sure, but, I think I know why this world is called "Wonderland"; I think it's because somehow, this world is modelled after Lewis Carroll's book _Alice in Wonderland_." –Ami answered.
Nobody spoke for what looked like an eternity. Ami's explanation looked a bit strange to say the least. Usually she would come up with a reasonable explanation, but this time, there seemed to be none. That was the best she could come up with on such short notice. No one wanted to say that that explanation was a little farfetched, not to mention crazy, but then again, they all had seen their share of strange places and things during their adventures, and nothing they had seen was as bizarre as what they just had experienced.
"But, why do you think that?" –Makoto asked Ami, breaking the wall of silence that had been formed.
"Well, we are pursuing a white talking rabbit, who so happens to be able to talk like a human being; we went through a rabbit hole, and fell down a well where we saw things that are impossible to see inside a well… it all fits. It's as if we're retracing what happened to Alice in the book." –the blue haired Sailor Scout explained.
"It's entirely possible. Let's say that we are in a world such as the one you just told us; what happens now?" –Minako asked Ami.
"Well, we don't have much choice but to follow the white rabbit, just like Alice did. Who knows, maybe we end up finding Alice on our way." –Ami answered, not entirely sure that that would be the best course of action.
"Bearing in mind that in the book she was the only character that did make sense in that strange world that was Wonderland, she might be the only one who can answer our questions." –Johnny said.
"Maybe, but then again, all of the characters in the book weren't that crazy, you know? All of them were right in their own away about something." –Setsuna said.
"I personally don't agree with that, but whatever." –Johnny said.
"So, where should we go now?" –Makoto asked.
The answer was obvious. They had to follow a small corridor, which led them out of there. This one ended abruptly in a long, low hall, which was lit up by a row of lamps hanging from the roof. The only way out of it was a door. They turned the door's knob, and easily exited, only to find themselves in an even stranger place than before. This time they were in a room which had its walls covered with pink wallpaper and tilted bright red and light pink floor. The furniture looked odd, many of it being bunny-shaped. In the middle there was a three-legged steel table, and next to it a chair.
"This place just keeps getting stranger and stranger by the minute. Now what do we do?" –Rei asked.
"We have to keep moving… I'm hearing the White Rabbit, so that means he's close." –Usagi said.
"But where did he go from here? There's no exit from this room." –Luna said, as she jumped on to the three-legged table.
"I think I have the solution to that problem." –Hotaru said, as she kneeled down and pointed to something behind a small red velvet curtain. –"Look at this."
The Soldier of Silence was pointing to a small red door with a golden doorknob. It was even smaller than a doggy-door.
"And, how are we supposed to fit through there?" –George asked her. –"Not even Luna and Artemis will fit through it."
"I can always blast it, just as I did with the rabbit hole." –Johnny suggested it.
"No, it's too dangerous… we don't know how that might affect this place." –Naru warned him.
"First, let's see where it leads to. I'm going to try and open it, and I'll peak inside to see what's on the other side." –Hotaru said.
She tried to turn the knob, but when she tried to, a pair eyes appeared over the doorknob, and this one yelled, catching them all by surprise.
"Ouch!" –the Doorknob yelled in pain.
"Oh my, sorry." –Hotaru said.
"T-That's okay, my dear. I'm actually used to that happening. After all, I'm a door." –the Doorknob said, while giving a great yawn.
"I'm terribly sorry, but I thought that you were a door… I mean, a regular door." –the purple-haired girl said, excusing herself.
"Well, as you see, I'm no ordinary door." –the Doorknob said defensively. –"Either way, I suppose that you want to pass to the other side, am I right?"
"Yes, sir, we want to. We're following the White Rabbit." –Usagi answered, while
"Oh, him again… I say, that rabbit sure has a lot of admirers." –The Doorknob stated.
"What do you mean by that?" –Johnny asked the Doorknob.
"Well, you're not the first ones to come through here looking for him, you know? There is that little blonde girl named Alice, who came by here also looking for him." –the Doorknob answered.
Hearing that, they all found out that they were on the right track. There was only a little problem, to which Michiru posed a question.
"Still, how do we enter through you? You're too small for us to pass through." –Michiru asked.
"Well, actually you are the ones who are too big… but don't worry, there is a way you can shrink until you are the right size. Why don't you try and drink what's in that glass bottle." –the Doorknob suggested.
They all looked to the table, but saw nothing. Then all of a sudden, a glass bottle with a small tag appeared a few inches from where Luna was laid. They all got closer and looked at the bottle, taking in special attention the little tag that was wrapped around it, which said "Drink Me". For those who knew the story of the book, it was like seeing a ghost or a spook.
"Drink Me? What's in it? –Artemis asked, because he did not know the story, and of course, did not know what the potion was supposed to do.
"It's called Pishsalver. It's a potion that makes you shrink. But I warn you, you mustn't drink more than a tea spoon of it, or you'll shrink to the size of an ant, and you don't want that, now do you?"
Hearing that warning, almost everyone trembled all over with fear. Still, they knew that if they wanted to find out if there were any Heartless in this world, they had to inspect it, and more importantly, they had to follow the White Rabbit to find Alice. Everyone took a little sip from the bottle, and started to feel the effects right away. The strange translucent liquid had a different taste to every single one of them. To Usagi, the potion tasted like sweet potatoes, while to Ami it tasted like tuna sandwiches, and to Rei it tasted like sushi. As for Makoto, the potion tasted like cherry tart, and to Minako it tasted like whipped cream. To Haruka it tasted like pineapple, as for Michiru, the potion tasted like grilled tomatoes with oreganos In Setsuna's case, the potion tasted like orange jam, and Hotaru felt that the potion tasted like lemonade. To Naru, it tasted like blueberry pie. Finally, the potion tasted like French fries to Johnny, and like chocolate ice-cream in George's case. The potion tasted like fish to both Luna and Artemis. Slowly and steadily, they all began to shrink, until they were the right size to fit through the door.
"Well? Are we small enough to fit through you?" –Chibiusa asked the Doorknob.
"Indeed you are, and I shall be glad to open up for you."
But when they were about to get ready to go through the door, a dark creature appeared in front of them, and then another one, and another one… Heartless, a whole swarm of Heartless appeared out of nowhere and was now blocking their way.
"Heartless!" –Hotaru exclaimed.
"Finally, some action!" –Haruka declared, as she made her Keyblade appear in her hand.
Everyone mimicked Haruka. In a matter of a split second, they were armed with their Keyblades and ready to fight. This time, Usagi decided to use her new Keyblade, The Crescent Moon, to see how she wielded it battle.
"Okay, let's see what the Informants say about these new guys. " –Rei said, as she turned on her Informant. –"We got Shadows and Soldiers, and there are two new kinds of Heartless, the Crescendo and the Creeper Plant."
The Crescendos were Heartless that looked similar to a vehicle horn, the round, black body resembling a squeeze bulb, while its golden mouth resembled the bell of an instrumental horn. Their black head and antenna resembled a musical note, notably a quaver or an eighth note. A red collar separated the head and body. Two yellow eyes could be seen on their faces, and they seemed to be wearing earmuffs on their heads, which were light and dark blue in colour. The Heartless emblem could be seen clearly on the front of their bodies.
The Creeper Plant were Heartless that had round, silver-lined head, in it a small face, with two glowing yellow eyes and a jagged maw. Four large flower petals border the head, two of which were orange, and two of which were yellow. Four orange and yellow spikes could be seen protruding from the head, the orange ones appearing in front of the yellow petals, the yellow ones appearing in front of the orange petals. A thin, green, vine-like neck extended from the back of the head to the small, blue-green body, where four root-like legs extended from the corners and into the ground. All in all, they were very creepy Heartless.
"You guys picked the wrong people to mess with." –Haruka stated, as a Creeper Plant jumped in front of her. –"Take this!"
And with that, the fight began. The new Heatless looked a little stronger than the ones that they had faced until then, but in the end they were no match for the Sailor Scouts teamwork. The last one was defeated by Usagi, who felt that her new Keyblade, the Crescent Moon was in some ways better than the Kingdom Key, even though she did not tell anyone about it.
"Phew… now that wasn't so hard, now was it?" –Johnny sighed in relief.
"More or less, these new Heartless were a somehow tougher than the ones that we faced in the previous world." –Setsuna said.
"Yeah, but in the end, we showed them, didn't we?" –Minako said with a proud and somehow pompous voice.
"I must congratulate you on your fighting skills. These creepy creatures have been causing nothing but trouble around here." –the Doorknob declared.
"Tell us, how long have they been appearing in this world?" –Ami asked it.
"Don't know exactly for how long, but they have been causing a lot of troubles." –the Doorknob answered, when something was heard at the distance… the sound of a trumpet. –"Oh ho, someone is bound to lose its head…"
"What do you mean lose its head?" –Chibiusa asked.
"The White Rabbit only plays his trumpet like that, when someone is about to be trialled by the King and the Queen of Hearts in a trial." –
"That doesn't sound so bad…" –Artemis said.
"Oh, but it is. You see, it doesn't matter what the person who's being judged says, the Queen will consider it guilty, and will demand that they cut off its head."
Ami instantly remembered that person being judged in the book was Alice, so it was only logical that the person who was being judged right then was none other than Alice. Fearing that she might be right about it, the blue-haired girl said:
"We have to get to where the trial is being held!" –Ami said.
"Then, you must not waste another second… Go right through the Lotus Forest and then turn into the Queen's Gardens. The trial is usually held in the centre of the gardens, in the Queen's Court." –the Doorknob explained to them, as he unlocked himself and pulled to the side, letting them in.
Following the instructions given by the Doorknob, they all quickly went through the Lotus Forest, which was not a forest like so many they have seen, but a rather strange one. There were not tees or grass, but instead the plants looked like grass and there were many flowers, some of them were blood red, while others were as yellow as the Sun itself. Another particularity of that forest was the fact existing giant mushrooms growing around the place. The floor was made of dirt. All in all, it looked more like a huge flower bed in a garden, than a wood.
"Where to now?" –Hotaru asked.
"Just follow the sound of the trumpet; it will lead us right to the where the trial is being held." –Chibiusa said.
After awhile, they were already in the Queen's gardens, and were caught by surprise when they saw themselves inside this huge hedge maze. The tall bushes formed the walls of that hedge maze. There were rose bushes; all of the roses in them were red, blood red, and its shape made them some of the finest and most beautiful roses that any of them had ever seen in their life. Needless to say that those roses reminded Usagi and Naru, as well as the rest of the gang of Tuxedo Mask.
"These roses remind me of Mamoru… my sweet Mamoru, where are you now?" –Usagi asked herself.
"Wherever you are, my prince, I hope that you are well and that you manage to join us soon enough." –Naru told herself, as they continued to sprint through the hedge maze, following the trumpet's sound.
Finally, they arrived at the centre of the hedge maze, where the Queen's court was, they found Alice being trialled, just as Amy predicted earlier. They immediately recognized Alice as being the blonde girl, with the age of 10 or 12. She was a beautiful and fair skinned girl with blonde hair, a black ribbon in her hair with a bow top centred, blue eyes, and was wearing a light blue dress with a white pinafore apron, white stocking over bloomers and an underskirt and black Mary Jane shoes.
Then, they recognized the White Rabbit, which they had been after. He was blowing his trumpet signalling that the trial was about to begin. Seated on their thrones were the Queen and the King of Hearts.
When they looked at her, they saw that the Queen of Hearts was a large woman dressed in regal attire and was carrying a small wand with a red heart on the tip. Her collar was white and very tall, reaching her ears. Her gown had a white lining (rather like the border of a playing card), with the rest of it being coloured red and black. The left half of her dress had a short, black sleeve with a red cuff, a red abdomen, with everything below that being black. The right side was identical, but with inverted colours; a red sleeve, black cuff, black abdomen, and red lower half. She was also wearing a second dress or skirt with a similar split design, the left side being an alternating thick black line, thin yellow line pattern, while the right side is identical, but with inversed colours. The right side of this second skirt is actually a darker shade of yellow than the left, appearing more gold. She also had a round nose, gold earrings, and a small gold crown on her head. Her hair was black and tied into a tight bun on the back of her head with a red ribbon, though a few loose bangs dangle in front of her forehead. As for the King of Hearts, he was the complete opposite of his wife, not only physically, but also in the way that he was dressed. He was a short, skinny man in a big golden crown and small moustache. He was wearing a long red gown with a white lining.
There were also soldiers spread through the court patrolling it, which could be divided into two different kinds, the Heart soldiers and the Spade soldiers. The Heart soldiers had red heads shaped like an upside-down heart. They had a pale-skinned, heart-shaped face showing, indicating that the red is some sort of helmet, a bright red, vaguely heart-shaped nose, and a small, heart-shaped mouth. Two red semi-circles were present on either "shoulder". They had spindly arms and large red gloves, when in comparison to their arms, as well as floppy red shoes. They were seen carrying red lances as weapons, each lance tipped with an upside-down heart.
The Spade soldiers shared the same structure as their red counterparts, sporting the same physical characteristics, albeit theirs were coloured black. Their noses were also black and shaped like an upside-down heart, which could be described as a spade without the "handle". Their mouths shared this upside-down heart shape. Their faces are pale like the Heart soldiers, while their "helmets" were shaped like spades, with parts of the design, specifically the handle and lower half of the spade, continuing onto their card bodies. Their black gloves were slightly closer-fitting than their red-coloured brethren. Finally, they were seen carrying black axes as weapons.
None of the soldiers, or the people taking part in the trial had seen any of the Sailor Scouts yet, and they all thanked for that, for they did not know what to do next. Getting there had been easy, but now came the hardest part… what were they going to do?
"Mmm, now how do we help her?" –Usagi asked her friends.
"Don't speak so loud!" –George gritted his teeth.
"He's right; don't speak so loud, Usagi. First, let's see how the trial goes, before we make any assumptions about what's going on." –Rei said
"I agree with Rei. Let's see what happens, and then, if we're needed to fight against these guys, so we can protect Alice, we'll do it. But for now, let's just watch." –Michiru said.
Alice was feeling quite nervous, for she had never been in that position.
"Court is now in session!" –the White Rabbit exclaimed, while trying to catch his breath.
"I'm on trial? But why?" –Alice asked.
"Her Majesty, the Queen of Hearts, presiding!"
The Queen of Hearts looked at Alice from top to bottom with a menacing look, and then said:
"This girl is the culprit. There's no doubt about it. And the reason is… because I said so, that's why!" –the Queen exclaimed, with a positively delightful voice, which meant that she was actually enjoying accusing the blonde girl, just for the sake of it.
"That is so unfair!" –Alice exclaimed, not believing what she was hearing.
"Well, have you anything to say in your defense?" –the Queen asked her, granting her at least the right to defend herself on trial, which she usually did not grant.
"Of course! I've done absolutely nothing wrong!" –Alice told the Queen, with an uprising voice. –"You may be Queen, but I'm afraid that doesn't give you the right to be so… so mean!"
The White Rabbit and the King of Hearts all listened and were starting to panic. Nobody had ever said that to the Queen before. Everyone in Wonderland knew that they should not talk like that with the Queen, because they knew that she was royalty, but mostly because they knew that she had a very hot temperament, and whenever anyone insulted her, she would just get mad about it.
"Silence! You dare defy me? I'll have your head for this!" –the Queen yelled in rage.
Hearing that, Usagi and the rest of the Sailor Scouts knew that things were not going so well for Alice.
"Maybe it would be best if we did help her." –Luna suggested. –"I don't like where this is going."
"Usually, I would say that we should not interfere with these affairs, at least until we know exactly what is going on, but in this case, I think we should and must interfere, before that poor girl gets into more trouble." –Artemis said, agreeing with Luna.
It was then that the Queen proclaimed Alice's sentence, and it was everything but good.
"The court finds the defendant… guilty as charged!" –the Queen yelled. –"For the crimes of assault and attempted theft of my heart!"
The Sailor Scouts all gasped after hearing those words. Alice was being trialled on something which the Heartless were responsible for.
"B-Bravo, dear! Bravo!" –the King of Hearts said, with an uneasy voice, while clapping his hands, for he knew that if he did not do it, his wife would get even madder.
"Off with her head!" –the Queen ordered.
The card soldier all moved forward to where Alice was standing, ready to oblige to the orders of their Queen.
"No, no! Oh, please!" –Alice begged.
Alice's plea for mercy was the last straw. Knowing that she was innocent, Ami was the first to jump right into action. Jumping into the air and propelling herself with a somersault, she landed right in front of Alice, shielding her from the soldiers and their weapons. The other Sailor Scouts also went to help, pushing the soldiers to the side, while trying to get where Ami and Alice were. All of them had their Keyblades pointed to the soldiers, while surrounding the little blonde girl.
"Don't worry, Alice, we're here to protect you." –Ami said, as she looked to the Queen of Hearts, who did not like what she was seeing.
16. Wonderland Surprises
Chapter 16: Wonderland Surprises
They had all got themselves into a tight jam. Surrounded by Card Soldiers, the Sailor Scouts knew that if they did not do anything, they would just turn them into sis kebab. Ami, who had been the first one to jump into action, in order to protect the blonde girl, was starting to feel that that had been a bad move, even though she did not want to admit it in front of the others.
"What is the meaning of this?" –the Queen yelled at the Sailor Scouts.
"We know who the real culprits of the attempted attack to steal your heart are." –Ami said.
"It's the Heart…" –George tried to say that the culprits were the Heartless, but Haruka stopped him, by placing her hand in front of his mouth, shushing him.
"Either way, Alice is not the culprit!" –Michiru stated.
"And, do any of you have any proof of what you are saying?" –the Queen asked them, not believing what they were saying.
None of them were expecting that from the Queen. She clearly looked like the kind of person that would just ignore any kind of evidence, even if these evidences worked in her favour. They quickly exchanged looks, and felt like cockroaches trapped in a roach motel.
"N-No, not really." –Ami answered her.
"But that doesn't mean we can't find anything to prove her innocence." –Makoto declared with a challenging voice. She did not have any intention of letting the Queen think that they were in what looked like a hopeless situation, given the situation.
"Very well, then. I will allow you to scatter the Lotus Forest for any clues. But the defendant will stay here, waiting for your return." –the Queen said, as two Card Soldiers managed to break the circle that they had create around Alice, grabbed her by the wrist and took her to a golden cage, which was shaped like a birdcage. George and Minako just wanted to jump on those two and beat them to a pulp. Still, they knew that if they did that, they would just get into a lot more trouble. They opened the cage's door and put her inside, locking the door. Then, the cage was lifted up in the air, and covered with a red cape, just like a magician's.
"How much time do we have?" –Johnny asked the Queen of Hearts.
"You have until I think you had enough time to look for them."
"Ask a smart question, and you get a smart answer. Ask a stupid question and you get a stupid answer… but in this case, you ask a smart question, and you get a stupid answer." –Haruka thought to herself. –"I'm so not liking where this is heading to."
"As you wish." –Johnny answered back.
They all round up and began to decide what to do next. The logical thing to do was to look for evidence to prove that Alice was innocent, but how were they going to do it? Should they all go together, or should some of them stay there, keeping an eye n the Queen, while the others would go and find the evidence? Decisions, decisions, decisions…
"I'm not a fan of us going into separate ways." –Rei said.
"Well, I like the idea." –Haruka said.
"But you and Michiru are used to work alone. Most of us aren't." –Makoto stated. –"Now, I'm talking for me and for Rei, Usagi, Minako, Chibiusa and Ami. What about you, boys, how do you usually work where you come from?"
"We usually work together, but we also work in pairs. Let me just state that back on our home dimension, we don't deal with bad guys, the same way you girls do." –George answered.
"And in this case, I think half of us should go after the evidence, while the other half keeps an eye on the Queen. I trust her as much as I trust a rookie defense attorney, which is close to zero, null, cero, nolla, zéro, noll." –Johnny said.
"Maybe it would be best if we follow that idea. We can communicate with each others, and if there was trouble, we would know right away." –Artemis suggested.
"Okay, but, who will go and who will stay?" –Hotaru asked.
"Well, the ones who should do should be the ones who are best to know how to locate anything that looks remarkably to a clue, and for course, the best fighters, in case they run into trouble." –Luna said.
"Okay, then Ami and Johnny should go, because with their computers and technological gizmos, they should be able to find whatever clues there are in that forest." –Usagi said. –"As for the best fighters, Rei and Makoto should go, as well as Haruka and Naru. The rest should stay here, keeping an eye on the Queen and her guards, as well on Alice. Luna and Artemis should also go."
"I agree. As soon as we find enough clues, we come back here." –Rei said.
"Good luck, everyone." –Setsuna wished them.
While Ami and the rest of her group made their way to the Lotus Forest, Usagi and the others who stayed with her tried to talk with Alice, who was still locked on the cage, up on the air. In order to talk with her, they had to yell into the air, which was not the best way to have a conversation, especially because they needed to ask a couple of questions to the blonde girl, and could not, without alerting the soldiers or the King and the Queen, who would certainly ask questions. Given that, they had to make sure that whatever the conversation subject was, it would not reveal too much about the Heatless, or Maleficent, or anything else.
"Alice, are you alright?" –Usagi asked her.
"More or less. I think I could be better, given the situation." –the little blonde answered her. –"May I ask you, who are you and how do you know me?"
"Oh, of course. I'm Usagi, and here with me are Minako, Michiru, George, Setsuna, Chibiusa and Hotaru." –Usagi answered her, -"As for how we know you, well… it's a little complicated. The thing is we're here to help you."
"Yes, our friends have gone looking for clues to help you get out of here." –Chibiusa told her.
"Well, I do hope they find something that might help me." –Alice told them. You could sense through her voice that she was rather worried.
"Don't worry, Alice. If there's anyone who can find any clue that will help you, it's them." –Hotaru told her with a soothing voice, trying to calm her down.
Looking for something that would remotely be a clue in that strange forest was like finding a needle in a haystack, and the group that had been chosen for that task knew it.
"We don't even have a clue of what were looking floor" –Haruka said.
"It will be like finding a needle in a haystack." –Makoto stated.
"Actually, a needle would be easy to find in a haystack, because a needle is made of metal, and so, it would be easy to spot in a haystack." –Ami declared. –"Now if it was needle in a needle stack, now that would be different…"
"We get the point the Ami." –Makoto told her with an uneasy voice. –"Still, that doesn't tell us what were looking for, or where should we go."
"Maybe I can be of some assistance…"
Everyone heard the voice, but did not know from where it came. They looked around, looking for whoever said that. Still, they did not find anyone.
"Who said that?" –Haruka yelled, as she looked around, trying to find who had spoken. –"Where are you? Identify yourself!"
On a rock near them, a large grin appeared in the middle of the air. Then, a pair of yellow eyes, which composed a smiley face. Little by little, a pink and purple creature began to appear in front of their eyes. Finally, they saw who it was… the Cheshire Cat.
"Who are you?" –Haruka asked, demanding to know who or what that creator was.
"Who, indeed." –the Cheshire Cat said. –"I'm the Cheshire Cat, and I must say, that I wasn't expecting that to happen. Poor Alice. Soon to lose her head, and she's not even guilty of a thing."
"Then, in that case, we're going to need to prove Alice's innocence. Can you help us, please?" –Naru asked the strange pink and purple Cheshire Cat.
"The Cheshire Cat has all the answers… but doesn't always tell. You seem to already know who the culprit is." –the Cheshire Cat said. –"They have already left the forest. I won't tell which exit. Still, they have left four pieces of evidence behind. Three are a cinch to find, but the fourth is tricky. I will tell you something, which might interest you, if you can find them all."
Makoto frowned her eyebrow looked at Ami, and whispered to her ear:
"Should we trust him, Ami?"
"To trust or not to trust? I trust you'll decide! And with that, I'm off!" –he said, as his body disappeared into thin air, as if it never had been there.
"Well, in the book, the Cheshire Cat tells Alice where to go, so, I think we can trust him." –Ami told Makoto.
"So, let's start looking for the clues. Spread out and look for them. Whoever finds one tells us the others, through the use of the Informants. And one last thing, be careful." –Hauka said, as she and Rei went one way, and the rest of the Scouts went in different ways.
Even though they now knew how many clues they were looking for, they still did not know where they were and the Lotus Forest was quite big. The first ones to find something were Ami and Naru, who found a set of footprints on the ground. They analysed them, and quickly saw to which kind of Heartless it belonged to.
"Soldiers. According to what the Informants say, after the Shadows, they are the base of the Heartless forces." –Ami said.
"It's only logical. In order to plunge this world into darkness, Maleficent would need to use an army. Even she couldn't have enough power to do it on her own." –Naru said.
"I wouldn't be so sure of it, Naru. The amount of energy that the creatures that attacked us in Tokyo was quite high; some of them even higher than any youma that we have faced before, so naturally, she needs to be even more powerful to control them." –Ami stated.
The next ones to find a clue were Rei and Haruka. They found what looked like a small crystal. After picking it up, they saw that it was really a crystal. This crystal was round and orange; more or less form the size of a tangerine, and inside it was some kind of living dark matter, floating.
"How do you know this is a clue? For all we know it, there could be thousands of those thing lying around the place." –Haruka told Rei.
"You're right, I don't know. Still, this place is so crazed up, that we can probably find a way to show this is a piece of evidence." –Rei explained to her, as she looked closer to the crystal.
Then, it was Johnny and Makoto's turn to find a clue. Examining the huge plants, they found claw marks, which belonged to the same kind of Heartless that Naru and Ami had had found footprints of.
"Nasty little creatures." Johnny said, as he inspected the claw marks, and used his Keyblade to cut the section of the stem where the claw marks were, in order to present it as a piece of evidence. –"According to the set of footprints that Ami and Naru found, these claw marks clearly belong to Soldiers."
"If that's true, then we have found already three clues… only one left to find." –Makoto stated, as she looked around. –"Still, it seems to me that this was too easy. It feels like… What was that?" –she turned her head behind, after hearing something moving.
"What was what?"
"I heard something." –Makoto told him.
"It was probably just the wind." –Johnny said when the noise was heard once again; this time he also heard it. –"Okay, now I've heard it."
The noise came from somewhere near. Paying attention to what surrounded them, trying to find the source of that intriguing noise. For a couple of seconds, nothing was heard. Complete and utter silence surrounded them. Then, they heard it again. It was coming from behind a bush near Makoto. She silently turned around and peaked inside the bush, only to be startled by what she saw, falling on her back. Something with big yellow eyes looked at her… it was a Heartless.
"H-Heartless!" –Makoto said, as she tried to get up on her feet.
"Now what do you know? This one must have stayed behind. Get him! We can use him as a piece of evidence!" –Johnny said, as he launched himself to the Heartless, trying to grab him with his hands. The little Heartless jumped more than a Jack-rabbit. Still, he was determined to catch it.
"But how are we going to cage it? These things can teleport themselves to where they want!" –Makoto exclaimed, as she sprinted after that Heartless.
"Leave that to me! Just try and catch it! Call the others and tell them that that creature can't get away! Even if it's not one of the clues that cat told us about, it will be enough to convince that crazy queen!" –Johnny said, as he looked around for something that could help them catch that thing.
Soon, all the Scouts that had gone after the clues to present as evidence of Alice's innocence were after that small Heartless, trying to catch it. It seemed the small Heartless was not going to let itself being caught by one of the Sailor Scouts. Naru almost grabbed it, but as she was about to grab it, it simply jumped onto her head and then kept jumping all the way through that immense forest.
"Blast it! I almost caught it!" –Naru exclaimed, as she kept running after it.
Eventually, that wild chase led them to a rather curious place. They saw themselves in a garden, surrounded by tall bushes and a white and pink house, with a red roof. On the centre of the garden, there was a long table set for tea. There were teapots, cups, sugar bowls and plates of all shapes and colours. All the teapots were smoking, indicating that there was hot tea in them. But even more interesting, was the fact that all of them were whistling and screeching in the most varied tones, almost sounding like an orchestra… a very fascinating orchestra.
"Stand still, you miserable creature!" –Haruka said, as she failed yet again to catch it.
"Try going around, and surround it! We need to cut its path!" –Makoto said.
"It jumps too high, it's impossible to keep up with it!" –Ami said.
"Remember, we can also jump pretty high, thanks to our clothes! Follow my lead!" –Rei said, as she somersaulted, cutting the Heartless' path.
This time, they managed to gain the upper hand. The Heartless fell on the table, knocking down a couple of teapots, which spilled tea all over the place, as well two sugar bowls, sprinkling the Heartless as if it was a donut or a biscuit, who seemed not to like that at all. Seeing this opportunity, Rei grabbed the creature by its legs, and in the following second, Haruka did the same with the arms.
"Hold it steady, while I capture it! I don't want that thing to get the chance to teleport itself out of here." –Johnny said, as he approached them, holding a strange object on its right hand. –"Get inside, you disgusting black cockroach, you!"
He slammed the object on his hand onto the Heartless, and the object opened in the same way a flower blossoms, enveloping the nasty creature in a glass cocoon.
"And that's that!" –Johnny said, as he looked around the place, noticing that everything around them was a complete mess. –"What a waste of good tea…"
"At least we got it, that's what it counts, right?" –Makoto asked rhetorically.
"Indeed it is" –they all heard. It was the Cheshire Cat, who once again appeared out of nowhere. This time, it was his tail that first appeared, and then the rest of his body. Before his head was completely visible, he began to talk again. –"I never thought that you would be able to find all the clues that those creatures left behind so fast… I usually don't say this, but you are very good."
"Thanks… I guess." –Makoto said.
"Now, what about that secret that you were going to tell us, if we found them all?" –Naru asked him.
"Oh, very well, I shall tell you it. But before that, I would like you to answer this little riddle… can you tell me why is a raven like a writing desk?"
The riddle was strange and unusual. Still, Ami, who had memorized every little bit of both Lewis Carroll's books, knew that there was an answer. In fact, there were multiple right answers, given by people over the years, even though initially Carroll himself did not have one.
"Because Poe wrote on both?" –Ami answered, not entirely sure; so she decided to give another answer. –"Or, is it because the notes for which they are noted are not noted for being musical notes?"
"Why… they're both right!" –the Cheshire Cat exclaimed, impressed with what Ami had done. –"Nobody has ever managed to give an answer to this riddle, let alone two at the same time."
"So… can you tell us that secret you were talking about?" –Haruka asked him, with a very imposing voice, showing that she was in no mood for jokes or pranks.
"Oh, if I must… a green faced witch called Maleficent, if I'm not mistaken was talking about something regarding 7 maidens of pure heart, and that one of them might be from this world."
Hearing that, they remembered about what Yen Sid had told them; about the 7 Princesses of Heart. If someone managed to put the 7 maidens in the same place, it would be able to open Kingdom Hearts, thanks to the purity of their hearts.
"How did you manage to hear that?" –Naru asked him, not trusting entirely on the Cheshire Cat.
"Well, when you have the ability to appear and disappear at will, like I do…" –he stated, as he began to disappear, very slowly. –"… you end up hearing some interesting things, from time to time."
Finally, when the only parts of his body that were still visible were his white grin and his yellow eyes, he said:
"If I were you, I would hurry up back to the Queen's Court, or Alice will surely lose her head, before you can actually help her."
Knowing that what he told them was true, they wasted no time returning to the Queen's Court, where the others awaited their arrival. They had been trying to cheer up Alice, who was still locked in that cage.
Everyone took their places, as the evidences were handed over to the White Rabbit, who carefully placed them in pink square boxes, and then put them all in front of the Queen and the King of Hearts. Usagi, determined to set things right, approached the Queen and the King and said:
"Your Majesties, like we promised, we have found evidences that will prove that the defendant is innocent."
"Very well, let's start." –the King said.
"Choose one of them and bring it to me."
"W-What about the other three?" –Usagi asked her, knowing that it was strange that she only wanted to see one of the evidences, and not all of them.
"Checking all of four would only be a waste of time. Choose the one you wish to present. I'll decide who's guilty based on that evidence." –the Queen answered.
"After all the trouble we had gathering all of them?" –Haruka said, outraged.
"You dare object? Then you will lose your head!" –the Queen exclaimed. –"Now, choose! One box!"
Not wanting to enrage the Queen more than she already was, she told Ami to go and pick one. Not knowing the order in which the boxes were placed, she decided to use her Informant as a scanner, in order to find out where the Heartless was. Scanning the boxes, she quickly found out that the creature was inside box number 3. Choosing it, one of the Card Soldiers opened it, and as soon as it was open, the Heartless jumped out of it, scaring everyone, especially the Queen, who immediately thought that it was yet another attempt to steal her heart, this time done by the Sailor Scouts.
"Seal the gardens and get them!" –the King said.
As soon as he said that, the Garden's exits all disappeared as if by magic, and two small yellow hexagonal towers, each one had three cranks in them, appeared out of nowhere as if by magic.
"Do not let them escape, or you will lose your heads for it!" –the Queen yelled at the Card Soldiers, who did not waste a second organizing themselves, in order to stop the Sailor Scouts from escaping the Queen's Court.
The situation looked dark for all of them. They were trapped, and they would have to fight their way out of there. Regrouping, Usagi quickly told the others to get closer to her, in order to find a way to get out of that tight jam. Whoever came up with an escape plan, needed to do it quickly in order to explain it to the others.
"Okay, everyone, I know this looks bad, but we can overcome this. We have faced a lot worst in the past." –Usagi said.
"No kidding…" –Johnny shot back at her, sarcastically.
"What's the plan?" –Minako asked Usagi, as she looked around, worried that they might not have a way to escape.
"Those towers with the cranks over there appeared, as soon as the other exits disappeared, which mean that they somehow are connected. My guess is, if we destroy them, we might make them appear again." –Setsuna suggested.
"Then that's the plan! Half of us will attempt to destroy those two towers, while the other half tries to repel the Card Soldiers!" –Naru suggested, to which the rest waved their heads in acknowledgement.
"What about Alice? We need to get her out of here too." –Chbiusa said, worried about Alice's welfare.
"You go and get her. Use your Keyblade to get her out of that cage!" –Hotaru suggested. –"I'll cover your back!"
"Alright, I'll go get her."
"Then, it's settled! On my mark! 5… 4… 3… 2… 1… Go!" –Usagi said.
Following Naru's plan, Usagi, Ami, Rei, Makoto, Minako and Naru herself began using their special abilities to destroy the towers, while the rest of the Sailor Scouts attempted pushing the Card Soldiers away from them, in order to give the others some manoeuvre space. Chibiusa and Hotaru, on the other hand, made their way through the Queen's Court, in order to break Alice free from that cage.
Using their abilities, all of them tried their best to stick to the plan. They knew that in order to get out of there, they would need to work as a team. The Card Soldiers were proving to be as tough as any Heartless they had faced until that point. Still, the Outer Scouts managed to keep them away, so as the Inner Scouts could destroy the crank towers.
"Mercury Aqua Rhapsody!" –Ami exclaimed.
"Mars Fire Sniper!" –Rei exclaimed.
"Jupiter Oak Evolution!" –Makoto exclaimed.
"Venus Love and Beauty Shock!" –Minako exclaimed.
"Roots of Fate!" –Naru exclaimed.
Their attacks began destroying the towers, making them crumble into pieces very slowly. The others, seeing that picked up the pace making sure that the Card Soldiers would not get even near of the Inner Scouts. Thanks to the power of their Keyblades, they still had the power to use their attacks, and they were making sure that they used them correctly against their enemies.
"World Shaking!" –Haruka exclaimed.
"Deep Submerge!" –Michiru exclaimed.
"Dead Scream!" –Setsuna exclaimed.
"Freezing Inferno Blast!" –Johnny exclaimed.
"Saturn's Toxic Storm!" –George exclaimed.
Haruka could not help but to smirk, as she saw the Queen and King of Hearts looking at them, seeing them literally obliterating any kind of attack that they pulled against the Sailor Scouts. Still, it was the same confidence that she had in her, that almost made her miss one of the Card Soldiers that managed to break through the blockage they had built around Usagi and the others. Fortunately, Luna and Artemis launched themselves towards the Card Soldiers legs, making him fall into the ground, giving Johnny the opportunity to grab him and literally punching him to the opposite side of the Queen's Court.
"Keep your eyes open!" –he yelled at Haruka.
"Sorry, I was distracted! Don't tell me you have never been distracted before during a battle?" –she yelled at him, clearly upset with the fact that he had to warn her about her mistake.
"Let's see… no, I have never been distracted during a battle, because back in my home dimension, if you get distracted, you'll end up without your head!"
"Stop yelling at each other! You sound just like a pair of siblings arguing about who broke a vase, after you've been playing soccer on the living room! Get a grip, and save that energy for these guys!" –George yelled at them, trying to stop them arguing with each other.
On the other side of the Queen's Court, Chibiusa and Hotaru did their best to get to where Alice was. Looking to the cage, they raced to see who got their first. Swinging their Keyblades at the same time, they managed to keep all the Card Soldiers out of their way. Finally, when they got in front of the cage, which was still suspended in the air, covered with the red curtain, Chibiusa kept going, while Hotaru stayed behind, in order to keep the Card Soldiers away form her.
"Keep going, Chibiusa! I'll take care of them! _Silent Wall_!" –she warned Chibiusa, as she used one of her attacks along with her Keyblade, in order to keep the enemies away from them.
"Got it!" –Chibiusa said as she somersaulted over a pair of Card Soldiers.
As soon as she got near the cage, she prepared herself to use the Keyblade in order to cut it down. But, before she could do what she had in mind, she was stopped by the Red Queen, who threw her wand at the pink-haired girl, trying to hit her in the head, unsuccessfully. Chibiusa looked at her, and saw that the Queen was boiling mad. Her face was completely red and her eyes looked as if they were about to be shot right out of their sockets.
"Stay away from me!" –she yelled at Chibiusa, as she grabbed the King's crown and threw it, trying to hit the girl, who simply tossed it back, using her Keyblade like a baseball bat. The King's crown ended up falling on top of the Queen's head, making her even madder than before.
Trying not to pay attention to the Queen and her attempts to hurt her, by throwing objects at her, Chibiusa, used her Keyblade and with a swift and slender move, she broke the golden chain that was hanging the cage up in the air. The cage where Alice was fell to the ground, ending on top of a rose bush. Seeing what had just happened, Hotaru joined Chibiusa, and helped her taking the red cape that was covering the cage, only to find something they were not expecting… Alice was not inside.
"She's gone!" –Hotaru said. –"Where could have she gone to?"
"I don't know, but do you want bet that the Heartless or that evil witch are behind this?" –Chibiusa said.
A few seconds after the youngest members in the team made that discover, Makoto managed to destroy what was left of the second tower, sending the metallic cranks flying through the air, one of them almost hitting the Queen of Hearts, who yelled at the Sailor Scouts:
"I will have your heads for this, even if I have to cut them myself!"
At the same time, all the exits reappeared, and none of them wanted to stay another minute there. Usagi looked at Chibiusa and Hotaru, expecting to see them accompanied by Alice, but when she saw that she was not with them, she instantly sensed that something was not right. Still, they had to escape before the Card Soldiers decided to make mince meat out of them, this time permanently. They all escaped into the Lotus Forest, where they hoped they would not be followed; they needed to regroup and think of what to do next. Finally, they stopped running when they felt that they had left the Queen's Court far behind them.
"Okay, I really wasn't expecting those guys to put up such a fight." –George said, still panting.
"I never thought that a bunch of cards could be so tough to beat." –Setsuna declared. –"Imagine if they were Heartlesses."
"Just pray we don't have that luck, okay?" –Haruka said.
"Now that you mention it, where did that Heartless go?" –Rei asked out loud.
"Last we saw of it, it was running around like a maniac on the Queen's Court, always appearing and disappearing… hey, there he goes!" –Minako pointed to the little Heartless that ran past by them.
"Come on, let's go after him!" –Johnny said, as he launched himself in pursuit.
"Oh, but I haven't had time to rest yet!" –Usagi cried out, as she had just sat on a huge pink mushroom that was on the ground. She was tired, and wanted to rest for a bit.
"Run now, rest later, Usagi!" –Makoto said, as she grabbed the blonde by the hand pulled her into that pursuit.
"But I'm dead tired!" –Usagi whined about it, not wanting to accompany the rest of the group, into what she considered a wild goose chase right then.
Determined to not let the Heartless escape, the Sailor Scouts tried to keep up with the little Heartless, who went through a hole in a rock. In order to follow it, they entered through the hole, which lead to a dark tunnel. They had crawl through the tunnel in order to follow the Heartless, which proved to not be an easy task for them.
"Where do you think this hole goes to?" –Makoto asked the rest of the gang, as her voice echoed.
"Who knows? It might end on the other side of these woods, or it might take us to a totally different place." –Minako said.
"As long as it doesn't end on a lake full of hungry piranhas or a tank with man-eating sharks, I'll consider myself quite happy about it." –Johnny said. –"We better move faster, otherwise that little rascal is going to get away."
Moving through the tunnel, Usagi who was up on front, could hear very vaguely the Heartless moving in front of them. The question was, how far behind were them from it? It could be just a couple of feet, but it could also be more than 20 metres. The only ones that were able to see anything in front of them clearly were Luna and Artemis, and both of them were walking side by side with Chibiusa, who did not want to confess, but was a little afraid of the dark. Still, they kept moving forward, hoping to catch the black creature and that this one would lead them to where Alice had been taken to. Finally, they saw a shiny bright light at the end of the tunnel. Crawling a little faster than before, they were soon out of the tunnel, and were rather surprised to see where the tunnel had taken them to. They were once again back in the room where they had shrunk to the size of a mouse. Looking around, they saw that the Doorknob was now sleeping, an there was no sign of the Heartless.
"Well, back to square one, I guess." –Rei said.
"I don't think so…" –Naru pointed to the other side of the room, where a huge group of Heartless was standing. –"We got company!"
The group of Heartless was composed by numerous types of Heartless, among them were Shadows, Soldiers and Large Bodies, which they had fought against before, as well as some new ones. There were some Heartless that looked like the Soldiers, but they had dark grey skin, large blue claws and wore tattered red boots with curled toes. Then, there were Heartless that had round, silver-lined heads, with a small face, two glowing yellow eyes and a jagged maw. Four large flower petals border the head, two of which were orange, and two of which were yellow. Four orange and yellow spikes could be seen protruding from the head, the orange ones appearing in front of the yellow petals, the yellow ones appearing in front of the orange petals. A thin, green, vine-like neck extended from the back of the head to the small, blue-green body, where four root-like legs extended from the corners and into the ground. Finally, there was a kind of Heartless that looked like it was based on the design of an old-fashioned vehicle horn. Their round, black body resembled a squeeze bulb, while its golden mouth resembled the bell of an instrumental horn. Its black head and antenna resembled a musical note, notably a quaver or an eighth note. A red collar separated the head and body. Two yellow eyes could be seen on its face, and it seemed to be wearing earmuffs on its head, which were light and dark blue in color. The Heartless emblem could be seen clearly on the front of its body.
"Let's see… the ones that look like plants are called Creeper Plants, while the ones that look like vehicle horns are called Crescendos. Oh, and the ones that look like the Soldiers, but aren't Soldiers are called Stealth Soldiers." –Ami told them, while looking at their names in her Informant. As she finished informing the rest of the group, the Heartless all turned to them, and began speeding towards them, with only one objective in their mind, to destroy the Sailor Scouts.
"Stand on your guard, everyone!" Usagi told hem, as she made her Keyblade appear on her hand, positioning herself in combat formation.
"Alright, it's playtime!" –Johnny exclaimed with an almost maniacal, yet comical voice, as he prepared himself to attack the Heartless.
The whole group did their best to get rid of the strongest and toughest Heartless, which were the Large Bodies and the Stealth Soldiers. These last ones proved to be quite hard to fight against, especially because of the fact that they were always appearing and disappearing, thanks to their ability to turn invisible. Still, thanks to a good coordination, Haruka and Michiru, as well as Chibiusa and Hotaru managed to get rid of them. Johnny was having the time of his life, while George, Makoto and himself played baseball with all the Shadows, using them as baseballs. Given the fact that they were all exhausted from their earlier battle, it was incredible just how suddenly they got their energy back. Usagi assumed that it was the power of the Keyblade or of the clothes they were wearing that enabled them to recover their energy in very little time.
In a matter of minutes, all of the Heartless that were attacking them, disappeared, and they were all alone in that strange room. But, they were not alone for very long. All of a sudden, the Cheshire Cat appeared on top of the chair. This time, his body was bouncing on top of his head, as if it was a beach ball, and as always, he was smiling with that big grin of his.
"Hello again to those I already know, and also to those I'm meeting now!" –he told them.
"Cheshire Cat, do you know where Alice is?" –Ami asked him.
"The shadows took her… she's not here anymore. She has gone with the shadows, into darkness." –he told her. –"And if I were you, I would get ready, because in a matter of seconds, you'll be having quite a surprise!"
With that, he disappeared, leaving all the Sailor Scouts, thinking about what was to come next.
End file.
| fanfiction |
semantic dementia ( sd ) is a clinical syndrome that is characterised by progressive , selective breakdown of verbal and non - verbal ( multimodal ) knowledge systems .
the disorder is associated with focal brain atrophy predominantly involving the anterior left temporal lobe1 and is distinct clinically , anatomically and pathologically from alzheimer disease .
music is a specialised dimension of non - verbal cognition;2
4 however , the effects of sd on music processing have not been studied . here
a 56-year - old right - handed female book keeper exhibited insidiously progressive deterioration of language , manifesting as reduced vocabulary and empty , circumlocutory but grammatical speech .
the patient subsequently developed impaired recognition of familiar faces and everyday objects , executive dysfunction and behavioural changes including sweet tooth and mild disinhibition .
she became increasingly interested in music , listening to cds of popular songs for many hours each day and singing or humming along to these songs and music on television .
brain mri and general neuropsychological assessments were undertaken 3 years and 5 years after clinical onset .
brain mri initially showed selective atrophy of the anterior left temporal lobe predominantly involving the temporal pole and the fusiform , inferior and middle temporal gyri
subsequently , there was extension of the atrophy to involve the right antero - inferior temporal lobe and orbitofrontal cortex .
at the first neuropsychological assessment , the patient displayed predominant impairments of naming and of single - word comprehension ( both < 5 percentile ) with surface dyslexia ( supplementary table 1 online ) . by the time of the second assessment , the patient had widespread deficits with profound impairment of both verbal and non - verbal semantic memory ( at floor on synonyms , famous faces recognition and easy british picture vocabulary scale rests ) .
the patient was asked to continue singing or humming familiar tunes after hearing a brief introduction .
forty tunes were chosen ( supplementary table 2 online ) : 10 popular songs of the 1960s and 1970s to which she listened regularly ( identified by her family ) , 10 common nursery rhymes and 20 other tunes well - known to british subjects ( e.g. auld lang syne , jerusalem ) .
the first four to eight musical bars of each tune were presented , whereas for the popular songs and nursery rhymes the first line was sung ( with lyrics ) by one of the authors ( jh ) . for the british tunes ,
another of the authors ( ro ) played the introduction on the piano as a single line melody without harmony or vocal accompaniment .
british tunes were also administered to three healthy non - musician female control subjects ( ages 6472 ) with no history of tone deafness , who were asked to demonstrate recognition of the tunes . to compare musical and verbal performance ,
the patient was assessed on verbal tasks analogous to the musical continuations ( supplementary table 2 ) .
she was presented with spoken first lines of the pop songs and nursery rhymes , and five sentences requiring high frequency terminal words ( e.g. she posted the letter without a [stamp] ) and six common idioms ( e.g. bread and [ butter] ) .
the patient sang an accurate ( unambiguous ) continuation of the melody for 25 of the 40 tunes ( figure 1 ; supplementary table 2 ) : 7 of the 10 pop songs , 6 of the 10 nursery rhymes and 12 of the 20 british tunes .
her performance on british tunes was comparable or somewhat inferior to recognition performance of the older control subjects ( mean control score 13 out of 20 , range 1216 ) .
do , producing accompanying lyrics for three pop songs ( average 5.3 words ) and five nursery rhymes ( average 1.6 words ) . in those cases where the patient did not continue the tune correctly , she produced an alternative continuation that was meaningful melodically ( ending on the tonic or the dominant of the key ) or rhythmically ( ending with a long or stressed final note ) .
she was able to provide a verbal continuation for only 5 of the 20 spoken song lyrics and nursery rhymes ( between 1 and 3 words in these cases ) and was unable to provide any high frequency sentence or idiom completions .
examples of musical continuations provided by the patient for pop songs , well - known british tunes and nursery rhymes . for each tune ,
melody ( the correct continuation ) is shown above and the patient s response has been transcribed below .
this case suggests that knowledge of music may be disproportionately preserved in sd compared with other modalities of knowledge .
debate continues regarding the nature of musical knowledge and the relative contributions of semantic , episodic and procedural factors.2
4 indeed , episodic and procedural ( motor activity ) memory are often spared in sd and might support some kinds of musical memory .
it is unlikely , however , that our patient s ability to continue familiar tunes depended entirely on episodic recall , since the tunes were presented in a non - standard form with both instrumental context ( sung or played on piano ) and harmonic context ( transposed in key ) altered .
this suggestion is consistent with other evidence that knowledge of familiar music does not depend on episodic memory.2
3 it is also unlikely that our patient s performance was driven solely by procedural memory : only around a quarter of the tunes were sung regularly by the patient , and half were presented on the piano , which she had never played .
rather than reactivating an episode from memory or a stored motor programme , the continuation of the tunes required , therefore , active translation of heard music into a new vocal output .
we argue that this translation process is mediated by brain knowledge stores ( semantic memory ) for music . besides retained knowledge of particular songs , the patient s ability to supply alternative musical continuations in accord with the melodic and rhythmic
the present case supports previous studies suggesting that knowledge of music has brain substrates that are partly separable from those mediating other forms of verbal and nonverbal knowledge.3
4 functional imaging evidence in normal individuals suggests that semantic memory for familiar tunes is mediated by a distributed network that includes the bilateral medial and orbital frontal cortex , the left angular gyrus and the left anterior middle temporal gyrus.3 we do not claim that musical semantic memory was entirely normal in our patient ; however , the present findings suggest that the anterior left temporal lobe may be less critical for musical than for other forms of semantic memory .
we propose that musical knowledge may be differently represented in the brain because musical objects ( such as melodies ) are essentially abstract , unlike visual objects , environmental sounds and other objects of sensory perception .
this differentiation could be functional as well as anatomical : it is likely that factors such as emotional content , arousal and context have an important influence on the encoding and retrieval of musical versus other kinds of memories .
moreover , knowledge for different kinds of musical information may have distinct substrates.4 relative sparing of musical knowledge may contribute to musicophilia in patients with frontotemporal lobar degenerations5 and may have implications for the use of music therapy and music - based cognitive rehabilitation . | pubmed |
laryngotracheal separation ( lts ) is the most immediately life - threatening airway injury caused by any of various injuries to the neck including automobile accidents , attempted hanging , and direct blows to the anterior neck [ 1 , 2 ] .
because lts is very so rare , emergency physicians and otolaryngologists have limited experience with it and there is no consensus on its management .
therefore , lts is a diagnostic and therapeutic challenge in airway injuries . a high index of suspicion and immediate reconstruction with restoration of the laryngotracheal framework and mucosal integrity enables patients to recover a patent airway , functional voice , and normal swallowing .
the patient had attempted to hang himself from a height of three stories and was immediately rescued by an eyewitness . on arrival ,
the patient had a hoarse voice but no other symptoms or signs of airway distress .
transverse linear abrasion by a clothes - line was visible on the anterior aspect of the neck at the location of the larynx , and subcutaneous emphysema without any penetrating wounds of the skin was detectible by palpation over an extensive area of the neck and upper chest wall .
cervical and chest x - rays revealed cervical and upper thoracic emphysema but no other abnormality .
multi - detector computed tomography ( mdct ) including multiplanar reconstruction images revealed a complete laryngotracheal separation without fractures of the thyroid and cricoid cartilage .
tracheotomy at the suspected site of separation was performed urgently , after which the patient was transferred to the operating room .
the neck was explored through a transverse incision formed by extending a tracheotomy incision laterally .
the patient had complete transection between the cricoid cartilage and the first tracheal ring , and stretching of the left recurrent laryngeal nerve was observed ( fig .
2 ) . however , the thyroid cartilage , cricoid cartilage , esophagus , and great vessels were intact . before anastomosis ,
release techniques such as suprahyoid release were not used in this patient because of the absence of tracheal cartilage loss .
right side tracheal wall was dissected to avoid damage to the right recurrent laryngeal nerve with great care because stretching injury of left recurrent laryngeal nerve was suspected strongly .
neck extension was eliminated with removal of shoulder roll and the trachea was anastomosed to the cricoid cartilage using interrupted 4 - 0 vicryl sutures .
each suture was passed from extraluminal side to intraluminal side submucosally , with the knot placed extraluminally to minimize the risk of infection , granuloma , and stricture formation . following complete closure ,
the wound was flooded with saline and a valsalva maneuver was performed after the deflation of the cuff of the endotracheal tube to assure an air - tight closure .
the strap muscles were re - approximated in the midline over suction drains , followed by closure of the platysma and skin . to lessen the tension over anastomosis in the postoperative period , the head was kept in flextion position with a nylon suture from the chin to the anterior chest wall .
the endotracheal tube was removed on day 3 in the intensive care unit , and left vocal cord paralysis was observed upon flexible laryngoscopy .
neck computed tomography ( ct ) scan taken at 10 days after the operation demonstrated complete resolution of subcutaneous emphysema and appropriate reconstruction of laryngotrachea ( fig .
the patient was discharged 2 weeks later without a tracheostomy and was lost to follow - up .
airway trauma may be life - threatening , immediately or within several hours after acute injury .
although laryngotracheal injuries represent less than 1% of all traumatic injuries , they account for more than 75% of immediate mortality .
motor vehicle accidents are the most common cause of blunt trauma to the airway , with hanging as a method of attempting suicide increasing in incidence [ 3 , 4 ] .
laryngeal injuries were observed in 35% to 45% of victims of hanging at autopsy . because laryngotracheal separation caused by hanging usually results in early death at the scene , the true incidence is unknown [ 2 , 3 , 5 ] .
typical lts occurs with clothes - line type injuries , as in the present case .
sudden neck extension , fixation of the larynx , and anteroposterior compression of tracheal rings creates shearing forces tearing the cricotracheal membrane .
direct upward pressure by hanging elevates the larynx superiorly and , as a result , larynx , and trachea are separated .
admitted patients with laryngotracheal injury exhibit characteristic signs including hoarseness , dyspnea , subcutaneous crepitus , and skin abrasions over the anterior neck , but their presence vary according to the degree and extent of injury . respiratory distress may be absent , as in the present case , if the separation between the cricoid cartilage and the ends of trachea is not large , allowing adjacent soft tissue around the trachea to form a pseudo - airway and make ventilation possible .
sudden airway obstruction may occur by trial of endotracheal intubation , neck extension or coughing [ 2 , 5 , 7 ] .
fiberoptic laryngoscopy of the upper airway may be helpful for evaluating the site and extent of injury .
however , in the case of highly suspected lts , fiberoptic laryngoscopy should be performed cautiously and with the preparation of a tracheotomy .
irritation by instrumentation may induce effortful cough and disrupt this unstable airway , resulting in abrupt dyspnea .
cephalocaudal separation between cricoid and trachea , abrupt change in position , diameter , and shape of the airway and an extraluminal position of the distal endotracheal tube are the suggestive ct findings of lts .
as shown in this case , sagittal reconstructive image may be useful to evaluate the integrity of laryngotrachea .
tracheotomy is recommended as the method of choice to secure the airway by many authors , because endotracheal intubation may pass into a false track at the site of tracheal separation and obstruct the airway completely [ 2 , 4 , 9 ] .
cricothyroidotomy is not recommended after blunt laryngotracheal injuries , as this may further injure the laryngotrachea .
tracheotomy at the suspected site of separation may be performed rapidly without further tracheal cartilage injury , as in the present case .
after airway is secured , definite surgical repair should be considered as early as possible .
early repair within 48 hours shows improved outcomes with respect to airway and voice and also lower incidence of subglottic stenosis [ 10 , 11 ] . in conclusion ,
a high index of suspicion , adequate imaging , prompt airway establishment , and early surgical repair are the most vital factors in managing the patient with lts ( fig . | pubmed |
Intercept of 2 moving objects at constant acceleration
I have to make a simulation in which a guided missile has to hit an incoming enemy missile.The enemy missile "T" is the one which has to be intercepted and is only affected by gravity, the guided missile "P" is moving by its own acceleration which is constant in magnitude with a variable angle and is also affected by gravity. I have to find the right angle to give to the acceleration vector of the guided missile "P" in order to be able to catch the enemy missile "T".
For $t = 0$ I have this situation:
Enemy missile "T":
$x\_t$ = random; $y\_t$ = fixed; $v\_{x,t}$ = random; $v\_{y,t}$ = random; $a\_{x,t} = 0$; $a\_{y,t} = -9.8$;
Guided missile "P":
$x\_p$ = fixed; $y\_p$ = fixed; $v\_{x,p} = 0$; $v\_{y,p} = 0$; $|a\_p|$ = fixed; $a\_{p,\theta} = 0$;
Starting from this i wrote this system of equations in which $a\_{x,p}$, $a\_{y,p}$ and $t$ are the variables (sorry I don't know how to write equations here).
$$x\_t + v\_{x,t} \* t = x\_p + (a\_{x,p} / 2) \* t^2 $$
$$y\_t + v\_{y,t} \* t + (a\_{y,t} / 2) \* t^2 = y\_p + (a\_{y,p} / 2) \* t^2$$
$$\sqrt{a\_{x,p} ^ 2 + a\_{y,p} ^ 2} = |a\_p|$$
Now what I really need is to solve this in a symbolic way, because I have to write the results in a C program to make this computation at runtime.
I tried to solve this with Matlab and Wolfram Alpha but I'm not able to get any result. Is there something wrong in the system? Is there any better way to get the result of this problem?
At the OPs request, here I suggest looking at the target and projectile as non-self propelled: once launched from their initial positions only gravity acts on them (air drag is neglected too).
Both target and projectile are assumed launched at the same time. If there is some lag $\Delta t$ between launch of target and projectile use $\text{Eq.1}$ and $\text{Eq.2}$ to calculate new initial positions for the target, then proceed from there, resetting time to $0$.
I'm using indices $1$ and $2$ resp. for target and projectile.
$$x\_1=x\_{1,0}+v\_{1,0,x} t...\text{Eq.1}$$
$$y\_1=y\_{1,0}+v\_{1,0,y} t-\frac{1}{2} g t^2...\text{Eq.2}$$
$$x\_2=x\_{2,0}+v\_{2,0,x} t$$
$$y\_2=y\_{2,0}+v\_{2,0,y} t-\frac{1}{2} g t^2$$
The objects collide when $y\_2=y\_1=y$ and $x\_2=x\_1=x$:
$$y\_{1,0}+v\_{1,0,y} t-\frac{1}{2} g t^2=y\_{2,0}+v\_{2,0,y} t-\frac{1}{2} g t^2$$
$$t=\frac{y\_{1,0}-y\_{2,0}}{v\_{2,0,y}-v\_{1,0,y}}$$
Use this expression in $\text{Eq.1}$ and $\text{Eq.2}$ to get expressions for $x$ and $y$ (the collision point).
Define the angle $\theta$:
$$\tan\theta=\frac{v\_{2,0,y}}{v\_{2,0,x}}$$
[From Wikipedia](https://en.wikipedia.org/wiki/Trajectory_of_a_projectile#Conditions_at_the_final_position_of_the_projectile):
$$y\_2=y\_{2,0}+x\_2\tan\theta-\frac{gx\_2^2}{2(v\_2\cos\theta)^2}$$
Where $v\_1=\sqrt{v\_{2,0,x}^2+v\_{2,0,y}^2}$
The objects collide when $y\_2=y\_1=y$ and $x\_2=x\_1=x$:
$$y=y\_{2,0}+x\tan\theta-\frac{gx^2}{2(v\_2\cos\theta)^2}$$
From this equation $\theta$ can be calculated but this isn't easy either. The equation can be re-worked to:
$$A\tan\theta-\frac{B}{(\cos\theta)^2}=C$$
I suggest to take this problem to MathOverflow of our network.
---
**Edit:**
If we assume that after launch the projectile motor simply provides enough force to combat gravity:
[](https://i.stack.imgur.com/R7MOD.png)
So $F=mg$, then no net forces act on the projectile and its initial velocity vector $\vec{v\_2}$ is maintained and:
$$x\_2=x\_{2,0}+v\_{2,0,x} t...\text{Eq.3}$$
$$y\_2=y\_{2,0}+v\_{2,0,y} t$$
$$y\_2=y\_{2,0}+ (x\_2-x\_{2,0})\tan\theta$$
Combining $\text{Eq.1}$ and $\text{Eq.3}$ allows to extract $t$. Use that value to determine $x$.
Again with Wikipedia:
$$y\_1=y\_{1,0}+x\_1\tan\alpha-\frac{gx\_1^2}{2(v\_1\cos\alpha)^2}$$
Where $v\_1=\sqrt{v\_{1,0,x}^2+v\_{1,0,y}^2}$
And $\tan\alpha=\frac{v\_{1,0,y}}{v\_{1,0,x}}$, $\cos\alpha =\frac{v\_{1,0,x}}{v}$:
At collision:
$$y\_{2,0}+ (x-x\_{2,0})\tan\theta=y\_{1,0}+x\tan\alpha-\frac{gx^2}{2(v\_1\cos\alpha)^2}...\text{Eq.4}$$
Since as all parameters except $\tan\theta$ are now known, $\tan\theta$ can be extracted from $\text{Eq.4}$.
[](https://i.stack.imgur.com/tieqk.png)
I can see why Mathematica has a problem with this. The result is ugly, and does not necessary have an analytical solution. I might as well say from the start that I think your best option here is to solve the system of equations partly analytically and partly numerically.
Here goes. Instead of $a\_x$ and $a\_y$, I use $a$ and $\theta$ as these are more natural variables when the magnitude of the acceleration is fixed.
The two equations to solve is then
\begin{eqnarray\*}
x\_{t}+v\_{x}t & = & x\_{p}+\frac{1}{2}a\_{p}t^{2}\cos\theta\\
y\_{t}+v\_{y}t-\frac{1}{2}gt^{2} & = & y\_{p}+\frac{1}{2}a\_{p}t^{2}\sin\theta
\end{eqnarray\*}
We can use the first to solve for the time until impact. We basically use completion of squares and get the solution
\begin{eqnarray\*}
t\_{\mathrm{impact}} & = & -\frac{v\_{x}}{a\_{p}\cos\theta}\pm\sqrt{\frac{2\left(x\_{t}-x\_{p}\right)a\_{p}\cos\theta+v\_{x}^{2}}{a\_{p}^{2}\cos^{2}\theta}}\\
& = & \frac{v\_{x}}{a\_{p}\cos\theta}\left(-1\pm\sqrt{1+\frac{2\left(x\_{t}-x\_{p}\right)a\_{p}\cos\theta}{v\_{x}^{2}}}\right)
\end{eqnarray\*}
This will only have one solution with $t\_{\mathrm{impact}}>0$ so you choose that. Note that $t\_{\mathrm{impact}}=t\_{\mathrm{impact}}(\theta)$ so for every value of $\theta$ you will have a differnt solution for $t\_{\mathrm{impact}}$.
Next you feed your solution $t=t\_{\mathrm{impact}}$ into the second equation. This, you will not be able to solve analytically (unless some magic simplification occurs).
Instead you solve it graphically/numerically by plotting both sides of the equation as a function of $\theta$. If the functions is relatively nice you should be able to use [Newton's method](https://en.wikipedia.org/wiki/Newton's_method) to solve for the desired angle.
NB: Remember to relcalulate $t\_{\mathrm{impact}}$ for every new $\theta$ as that will chage.
Note that the expression for $t\_{\mathrm{impact}}$ will still hold even if you introduce a gravitational pull on your projectile (as that only acts in the $y$ direction).
| stackexchange/physics |
one - loop calculations are important in the quest for discovering new physics beyond the standard model , especially for determining qcd backgrounds .
a number of significant improvements in the calculation of one - loop amplitudes , especially ones with massless particles , have been made in recent years .
these methods , which have recently been reviewed in ref .
@xcite , include the use of helicity @xcite , color decompositions @xcite , string - inspired ideas @xcite , recursion relations @xcite , unitarity @xcite and factorization @xcite .
besides allowing for the computation of certain infinite sequences of amplitudes , these techniques have been used in the computation of non - trivial amplitudes relevant for phenomenological applications @xcite .
a technique that has proven to be especially useful is that of using unitarity to determine the functional form of the amplitudes . by working to all orders in the dimensional regularization parameter , @xmath1
, one can determine the coefficients of all integral functions that may appear @xcite . for certain amplitudes that satisfy a power counting criterion , such as supersymmetric ones
, one can show that cuts with four - dimensional momenta are sufficient to determine the amplitudes through @xmath2 @xcite .
the case of an amplitude with massive internal legs has been considered in ref .
@xcite .
the efficiency of the unitarity method stems from the use of gauge invariant tree amplitudes in performing calculations . with the use of helicity and color decompositions
this can lead to enormous reductions in the complexity of intermediate expressions .
this may be contrasted against calculations of individual feynman diagrams that are gauge variant , where large cancelations must take place in order obtain simpler gauge invariant results . in this paper
we will show how to evaluate feynman diagrams so as to obtain efficiency of computation inherent in the unitarity technique .
this is done by performing feynman diagram calculations in a particular way so as to mimic the unitarity approach advocated in ref .
one may therefore start with feynman diagrams , yet obtain the advantages of the cutkosky approach .
this is useful since it explains the unitarity method from a conventional feynman diagram viewpoint .
this is of interest in , for example , the extension of unitarity methods beyond one loop , such as in ref .
@xcite . as an explicit example we have calculated the one - loop helicity amplitudes for @xmath3 .
this example has the desirable features that it contains both colored and colorless lines and massive internal and external legs .
this example is useful since it illustrates features beyond purely massless calculations , where most attention has been concentrated @xcite .
also it has already been evaluated via conventional methods by r.k .
ellis et al .
@xcite , allowing for an easy comparison to the correct result to be made .
we find agreement with their result .
we now briefly review some of the techniques that we shall use in this paper .
two important techniques that we utilize are spinor helicity and color decomposition .
the reader may consult review articles @xcite for further details . in explicit calculations with external gluons ,
it is usually convenient to use a spinor helicity basis @xcite which rewrites all polarization vectors in terms of massless weyl spinors @xmath4 . in the formulation of xu , zhang and
chang the plus and minus helicity polarization vectors are expressed as @xmath5 where @xmath6 is the momentum of the gluon and @xmath7 is an arbitrary null ` reference momentum ' which drops out of the final gauge invariant amplitudes .
we use the convenient notation @xmath8 \ , .
\equn\ ] ] these spinor products are anti - symmetric and satisfy @xmath9 .
one useful identity is @xmath10 \ket{b } \
, , \equn\label{polslash}\ ] ] where either @xmath11 or @xmath12 are spinors with four - dimensional momenta .
it is convenient to choose a dimensional regularization scheme that is compatible with the spinor helicity formalism .
we use the four - dimensional helicity scheme @xcite which is equivalent to a helicity form of siegel s dimensional reduction scheme @xcite .
the conversion between the various dimensional regularization schemes has been given in ref .
@xcite .
color decompositions @xcite have been extensively discussed in review articles @xcite .
here we only present the color decomposition for the @xmath3 amplitude .
for this one - loop amplitude the decomposition is@xmath13 \ , a^f_4 ( \si(1 ) , \si(2 ) , \si(3 ) , h ) \
, , \equn\label{decomp}\ ] ] where we have taken the loop to be in the fundamental representation .
the sum over @xmath14 includes all cyclic permutations of the indices @xmath15 ( i.e. @xmath16 ) and the @xmath17 are fundamental representation color matrices ( normalized so that @xmath18 ) .
we have abbreviated the dependence of @xmath19 on the outgoing momenta @xmath20 and helicities @xmath21 by writing the label @xmath22 alone .
we have also explicitly extracted the coupling and a factor of @xmath23 from @xmath24 , where @xmath25 is the renormalization scale .
for adjoint representation loops there is an analogous decomposition with up to two color traces in each term .
it is convenient to further decompose the partial amplitude in terms of _ primitive amplitudes _ ,
@xmath26 in the primitive amplitudes appearing on the right - hand - side we may treat the higgs as carrying color charge ( in the adjoint representation ) , which couples to gluons ; it is not difficult to show in the permutation sum all such additional terms cancel .
this is convenient since these primitive amplitudes are gauge invariant and have a fixed cyclic ordering of external legs .
a similar decomposition in terms of ` primitive amplitudes ' can also be performed for the case where some of the external particles are in the fundamental representation @xcite .
feynman diagrams , which have been essential for evaluating terms in the perturbative series for scattering processes , suffer from a number of well known computational difficulties .
firstly , individual feynman diagrams are inherently gauge dependent ; gauge invariance is restored only after summing over all diagrams . secondly , when evaluating loop momentum integrals using traditional techniques , such as passarino - veltman reduction @xcite , one encounters a large number of spurious denominators .
these spurious denominators typically involve gram determinants , @xmath27 raised to a power .
enormous cancelations must then take place before one obtains relatively simple results .
when using conventional techniques to evaluate feynman diagrams one reduces all tensor integrals into sums of scalar integrals multiplied by reduction coefficients .
( by a tensor integral we mean loop momentum integrals with powers of momentum in the numerator and by a scalar integral we mean integrals with no powers of loop momentum in the numerator , see . ) with the knowledge of how this reduction works , given any one - loop amplitude we can list all the scalar integrals that could potentially enter .
thus we have @xmath28 where the subscript @xmath29 is some index that labels the scalar integrals that contribute to this amplitude .
the heart of the calculation is in evaluating all the coefficients of the scalar integrals , i.e. the @xmath30 s . a conventional feynman diagram technique like passarino - veltman ( pv ) reduction evaluates all the necessary coefficients simultaneously .
if one could obtain these coefficients in a more efficient manner one would greatly improve the ability to calculate .
some of the features that are useful in improved calculational methods are : ( 1 ) that the building blocks be gauge invariant combinations of diagrams instead of individual diagrams ; ( 2 ) that wherever possible tensor integrals should not generate large powers of gram determinants in denominators ; ( 3 ) that large cancelations between diagrams be avoided as much as possible ; ( 4 ) and that calculations can be recycled when performing new ones .
the cutting method reviewed in ref .
@xcite has these above properties . in this method one
writes down the cuts in a given channel , depicted in , @xmath31 this equation is valid only for the cut channel under consideration .
the loop momentum is @xmath32 ; @xmath33 and @xmath34 are the momenta of the cut propagators , with masses @xmath35 and @xmath36 respectively and @xmath37 .
one then reconstructs the complete amplitude by finding a function which has the correct cuts in _ all _ channels . -1.75
cm since the loop integral in is composed of products of on - shell tree amplitudes , the basic building blocks are gauge invariant .
these tree amplitudes are inherently easier to calculate than loop amplitudes and in many cases have been previously calculated .
a key feature of the cutting method is that a specific subset of scalar integral coefficients are obtained in any given channel
. then one repeats this process for various channels thus computing the coefficients for all the scalar integrals .
there are integrals that do not appear in any channel , namely the tadpole and scalar bubble integrals , @xmath38 however , with prior knowledge of the infrared and ultraviolet behavior of an amplitude in many cases the coefficients of these integrals can be fixed , as discussed in ref .
@xcite .
it is generally convenient to express the tree amplitudes in using the spinor helicity formalism discussed in .
then one can evaluate the right - hand side of by constructing spinor strings of the form @xmath39 , and then commuting the @xmath40 towards each other .
this generates terms of the form @xmath41 , which may be rewritten as differences of inverse propagators and terms which do not depend on the loop momentum .
this type of reduction procedure has been previously used in a number of references @xcite .
we shall make use of it in the next section . -.75
cm when using spinor helicity one must take into account that the momenta of the intermediate on - shell lines are in @xmath42 dimensions while the helicity formalism is defined in four dimensions .
if one drops the @xmath43-dimensional components of the momenta , one could make an error in rational functions arising from @xmath44 terms . for five- and higher - point calculations it can be more convenient to use four - dimensional momenta in the cuts , but then to reconstruct the missing rational functions using collinear and multi - particle factorization properties @xcite . for four - point calculations it is convenient to keep terms to all orders in @xmath45 , since factorization is insufficient to fix all rational functions .
the cases of fermion or scalar lines with @xmath42 momenta in the helicity formalism have been extensively discussed in ref .
@xcite and do not present any difficulties .
although it is unnecessary for the specific calculation @xmath46 , a convenient strategy for handling channels with gluon lines is to subtract and add equivalent diagrams with internal gluon lines replaced by scalar or fermion lines , as depicted in . in some cases
one uses fermions so as to group particles together with supersymmetric partners .
such combinations of diagrams satisfy the power counting criterion that @xmath47-point tensor integrals should have ( for @xmath48 ) at most @xmath49 powers of loop momentum in the numerator of the integrand ; two - point integrals should have at most one power of loop momentum .
the required rearrangement of the diagrams to make the power count apparent is discussed in ref .
in particular , for the example portrayed in one should use background field feynman gauge @xcite .
the origin of this power counting criterion is from the requirement that all contributions due to the @xmath50 parts of loop momenta should not interfere with ultraviolet poles to yield @xmath2 contributions .
( one can also show that infrared divergences never interfere with the @xmath50 parts of loop momenta @xcite . )
this criterion also holds for the general massive amplitudes discussed in this paper .
this is useful since one can then take the sewed gluon lines to have four - dimensional momenta without any errors through @xmath2 .
we now describe how to perform a feynman diagram calculation so as to mimic the cutting method . in the next section we give an explicit example involving both internal and external masses .
the basic idea is rather simple . given that we know all the scalar integrals that could possibly enter a one - loop amplitude , suppose we target those scalar integrals that have a pair of scalar propagators @xmath51
where @xmath33 is the momentum of the scalar propagator between external legs @xmath52 and @xmath53 , and @xmath34 is between @xmath54 and @xmath55 of a general @xmath47-point amplitude , where the indicated propagators are each of a specific particle type . in order to generate a scalar integral with a specific propagator one
must necessarily have evaluated a feynman diagram that has the corresponding propagator .
we can define a channel ( this channel will correspond to the cut - channel when the cut is performed on the indicated legs ) as a subset of the terms in the full amplitude ; the terms being the scalar integrals which include the pair of scalar propagators mentioned above together with their corresponding coefficients , the @xmath30 s . in each feynman integral ( the tensor integral corresponding to each feynman diagram ) we explicitly extract a denominator that includes the pair of scalar propagators under consideration .
then if we impose the on - shell conditions @xmath56 to the numerators of all the feynman integrals contributing to the amplitude then the result would yield exactly what we defined as a channel in the previous paragraph .
the potential errors when imposing these on - shell conditions would necessarily be of the form @xmath57 where @xmath58 and/or @xmath59 , and @xmath60 .
since @xmath61 and @xmath62 are themselves inverse scalar propagators , anything of the form of could only generate terms which are not in the channel under consideration .
this is because one or both of the inverse propagators would cancel a scalar propagator in the denominator and generate a scalar integral not included in the specified channel , i.e. that does not include both of the indicated scalar propagators . setting @xmath56 only affects the calculation of those terms not in the specified channel . thus the evaluation of the @xmath30 s that are in the specified channel are not affected by imposing the on - shell condition .
by systematically stepping through a sufficient number of channels one can fix all the coefficients , the @xmath30 s in . in this way we can reconstruct the full amplitude . for some coefficients
the corresponding integrals appear in multiple channels ; for consistency these must coincide .
so how does using the on - shell conditions @xmath56 in the numerator help us in evaluating the feynman diagrams ?
all feynman diagrams in a specific channel can now be ` factorized ' using their on - shell legs into the sewing of two feynman tree diagrams ( see ) .
-.75 cm in figure the ` factorized ' feynman graph only contains intermediate on - shell fermions for the @xmath46 amplitude .
but in general this ` factorization ' process can be performed on any one - loop feynman diagram . with on - shell scalars or fermions
it is clear that this can be done . with intermediate massless gauge particles
one might worry that one has forgotten about the contributions of diagrams with ghosts on the right hand side of .
we know , however , that the net effect of the one - loop diagrams with ghosts is to cancel the unphysical polarizations of graphs with corresponding gauge particles .
this cancelation can be made apparent using the background field feynman gauge @xcite .
however , once one has ` factorized ' a feynman graph on a pair of propagators that includes a gauge particle then the contribution of the ghosts is not necessary as the sewing of the two on - shell feynman trees manifestly has no unphysical gauge degrees of freedom .
if one sums over all the feynman diagrams that contribute to a specific channel and we impose the on - shell condition then the equivalent equation to would have on - shell tree amplitudes sewed together instead of on - shell feynman trees : @xmath63 the sum on the right - hand side runs over all helicity states that can propagate across the ` cut ' legs . using the above equation one can compute all the coefficients of the scalar integrals that appear in this channel .
the above equation , , is the unitarity method mentioned earlier in this section .
originally the method was inspired by cutkosky rules , however , from the arguments presented here it is clear that one can evaluate feynman diagrams in a sophisticated manner so as to take advantage of the benefits inherent in the unitarity method . instead of performing the calculation of the scalar integral coefficients in parallel , we perform the calculation by targeting simultaneously only those integrals in a given channel . the notion of channels presented in this section is more general than that of just considering cutkosky rules because we may use the on - shell conditions on any propagator which does not collapse in the integral function under consideration .
( indeed , this observation has already been used in calculations of @xmath64 partons @xcite . ) in general we could construct a channel where we use the on - shell condition for any number of propagators ( it is even possible to construct a channel where the on - shell condition is used for a single propagator ) ; however , it is normally convenient to use only the two - propagator channel construction .
in this section we apply the procedure outlined in the previous section to the specific example of @xmath66 .
this amplitude has one massive external leg and all the feynman diagrams have a massive quark running in the loop .
see for the color - ordered feynman diagrams contributing to this amplitude .
-.75 cm in there are two feynman diagrams that involve a higgs - higgs - gluon coupling which does not exist in the standard model .
as mentioned in , although these diagrams cancel from the final result , they make the primitive amplitudes ( which have a fixed ordering of external legs ) gauge invariant . of course
, one does not need to include the extra diagrams , but then one would need to sum over the permutations with all possible external orderings of the higgs , as in , to recover gauge invariance . as mentioned in by observing the feynman diagrams in we can write down all the scalar integrals that can enter the amplitude , see . -.75
cm the integrals are two- , three- and four - point scalar integrals that have massive internal propagators and some combination of massive external kinematics .
one - point tadpole integrals do not appear since they are forbidden by power counting .
( when using passarino - veltman reduction one could encounter such integrals , but they must cancel in the final expressions for this amplitude since one does not encounter them when using feynman parameterization . ) the scalar integrals are found in .
in addition to the use of color decomposition , , it is also convenient to decompose the primitive amplitudes into all possible external helicity configurations .
so the objects that need to be computed are the color ordered gauge invariant primitive amplitudes .
there are three such objects ; they are @xmath67 , @xmath68 and @xmath69 .
the other primitive amplitudes ( e.g. @xmath70 ) can be obtained from the above three primitive amplitudes using parity and relabelings . since this amplitude has already been calculated by ellis et al .
@xcite the purpose of the calculation is to explicitly demonstrate that we may obtain the correct results by applying the unitarity method to massive amplitudes , starting from feynman diagrams . for illustrative purposes , only the calculation of @xmath67
is explicitly presented here the results of the calculation of the other two primitive amplitudes are shown for completeness . in order to compute the primitive amplitude @xmath67
we will construct it from multiple channels .
we will see that it is sufficient to only compute the @xmath71- and @xmath72-channels .
the mandelstam variables are defined as @xmath73 and @xmath74 .
these channels can be seen in .
-0.5 cm we begin by first constructing the @xmath71-channel by sewing together the two tree amplitudes on the left- and right - hand side of a. this corresponds to targeting the coefficients , @xmath75 , @xmath76 , @xmath77 and @xmath78 in .
the tree amplitude on the right of a is given by @xcite @xmath79 where @xmath80 is the helicity projection operator and the tree amplitude on the left is given by @xmath81 here @xmath82 is the vacuum expectation value of the scalar higgs field @xcite , @xmath83 is the mass of the fermion in the loop and @xmath84 is the scalar higgs mass
. capitalized momenta are @xmath42-dimensional , lower case momenta are four - dimensional and @xmath85 is the @xmath86-dimensional part of the loop momentum .
( see and . ) in these tree amplitudes we follow the conventions of ref .
@xcite for massive spinors , summarized in . in this convention
the distinction between fermion and anti - fermion spinors is suppressed . as depicted in a , for the @xmath71-channel the momenta of the on - shell legs are @xmath87 the second tree amplitude , , involving the higgs has been constructed from the tree level feynman diagrams including the additional fictitious higgs - higgs - gluon coupling ( this is the standard scalar - scalar - vector coupling of scalar qed @xcite ) mentioned earlier .
so sewing the two tree amplitudes together gives us the @xmath71-channel of the amplitude @xmath88 where the denominators are @xmath89[(\ell_1-k_1)^2-\mu^2-m^2 ] [ ( \ell_1-k_1-k_2)^2-\mu^2-m^2 ] \cr \d_4 = \ : & [ \ell_1 ^ 2-\mu^2-m^2][(\ell_1-k_1)^2-\mu^2-m^2 ] [ ( \ell_1-k_1-k_2)^2-\mu^2-m^2][(\ell_1+k_4)^2-\mu^2-m^2 ] \
, , } \equn\ ] ] and the numerators are @xmath90 the two terms in correspond to the two terms in .
first , concentrating on the numerator @xmath91 we can write it in the form of a trace @xmath92 \ , , \equn\ ] ] where we use the notation @xmath93=\tr[\omega_\pm\ldots]$ ] .
when expanding out the trace we first concentrate on the @xmath94 s since the final expression for the numerator can only depend on @xmath95 since the @xmath86-dimensional integral over @xmath85 vanishes for a integrand with a odd number of @xmath96 s .
thus , @xmath97 \cr = \ ; & 2m(m^2+\mu^2 ) + 2 m \ , \ell_1\cdot\ell_2 \cr = \ ; & 4m(m^2+\mu^2 ) - m s \ , .
\cr } \equn\ ] ] the numerator @xmath98 can also be written in the form of a trace @xmath99 \ , .
\cr } \equn\ ] ] so again first concentrating on the @xmath94 s we can write @xmath100 \cr = \ ; & \tr_+ [ ( m\s{\ell}_2-\mu^2-m^2)\s{\pol}_3^+(\s{k}_4 - 2 m ) ( \s{\ell}_1-m)]-\mu^2 \ , \tr_+ [ \s{\ell}_2\s{\pol}_3^+(\s{k}_4 - 2 m ) ] \cr = \ ; & 2m(m^2+\mu^2)(2\ell_1 + 2\ell_2+k_4)\cdot\pol_3^+ + m \ , \tr_+[\s{\ell}_2\s{\pol}_3^+\s{k}_4\s{\ell}_1 ] \ , . } \equn\ ] ] recalling that @xmath101 and choosing the reference momenta @xmath102 ( so that @xmath103 ) then @xmath104 \ , .
\equn\ ] ] we can evaluate the remaining trace in the expression for @xmath98 by using @xmath105 = \tr_- [ \s{\pol}_3^+\s{k}_4\s{\ell}_1\s{\ell}_2 ] = \frac{\sqrt{2}}{\bkmp{13}}\langle 1 ^ - | 4 \ell_1 \ell_2 | 3 ^ -\rangle \ , , \equn\ ] ] where for brevity we represent external momenta by their indices and neglect slashing the momenta inside the inner - product . using @xmath106 and momentum conservation the trace can be expressed as @xmath105 = \frac{\sqrt{2}}{\bkmp{13}}\left\ { ( m^2+\mu^2)\langle1 ^ -|4|3 ^ -\rangle + \langle 1 ^ -|4\ell_14|3 ^ -\rangle \right\ } \ , .
\equn\ ] ] but since @xmath107 @xmath98 can be expressed as @xmath108 the integral comprised of the numerator @xmath98 now only involves at most a single power of loop momentum @xmath109 in the integrand .
this can be readily evaluated with the use of feynman parameterization .
the feynman parameter shift is @xmath110 where @xmath7 is the shifted loop momentum . after feynman parameterizing the integral
the terms in @xmath98 involving @xmath33 can be evaluated by performing the momentum shift and next dropping terms containing a single power of @xmath7 which vanish .
so the two terms in @xmath98 involving @xmath33 become @xmath111 and @xmath112\langle 1 ^ -|4|3 ^ -\rangle \ , , } \equn\ ] ] after performing the momentum shift . as defined in ,
the integral function @xmath113 $ ] is a feynman parameterized form of the loop integral with a factor of @xmath114 in the numerator .
thus after feynman parameterization becomes @xmath115 - ( t - m_h^2)i_4[a_2 ] \cr & + si_4[a_3 ] + m_h^2i_4[a_4 ] -4i_4[(m^2+\mu^2)(1-a_3-a_4 ) ] \biggr\}\biggr|_{s-{\rm channel } } \ , , } \equn\ ] ] where @xmath116=-\epsilon i^{d=6 - 2\epsilon}_n[a_i]$ ] and @xmath117 is defined in .
the dimension label on @xmath118-dimensional integrals has been suppressed . then using the recursive formula for @xmath113 $ ] in and one can write the @xmath71-channel of the primitive amplitude as @xmath119 \cr & \hskip -1.3 cm -\frac{s - m_h^2}{2st}i_3^{(2)}[4(m^2+\mu^2)-m_h^2 ] -\frac{1}{2}i_4[4(m^2+\mu^2)-m_h^2 ] \biggr\}\biggr|_{s-{\rm channel } } \ , , } \equn\ ] ] where @xmath120 , also noting that @xmath121 is a scalar triangle integral dependent on the kinematic invariant @xmath71 and @xmath122 , while @xmath123 is a function of @xmath71 only .
then using the @xmath71-channel becomes @xmath124 -4\epsilon\biggl [ \frac{t - u}{2t(s - m_h^2)}i_3^{(4)d=6 - 2\epsilon } -\frac{s - m_h^2}{2st}i_3^{(2)d=6 - 2\epsilon}-\frac{1}{2 } i_4^{d=6 - 2\epsilon } \biggr ] \biggr\ } \biggr|_{s-{\rm channel } } \ , . }
\equn\label{scutanswer}\ ] ] now that we have the @xmath71-channel of this amplitude we need to calculate the @xmath72-channel ( corresponding to targeting @xmath75 , @xmath125 , @xmath126 and @xmath127 in ) in order to reconstruct the full primitive amplitude .
however due to the symmetry of the all - plus primitive amplitude it is not necessary to explicitly perform this calculation as the @xmath71- and @xmath72-channels are related up to an overall sign by a simple exchange of legs @xmath128 and @xmath129 which is equivalent to exchanging @xmath71 and @xmath72 in ( and also switching the @xmath128 and @xmath129 in the inner products in the pre - factor of the expression ) .
thus the @xmath72-channel of @xmath67 is given by @xmath130 - 4\epsilon\biggl [ \frac{s - u}{2s(t - m_h^2)}i_3^{(1)d=6 - 2\epsilon } -\frac{t - m_h^2}{2st}i_3^{(3)d=6 - 2\epsilon}-\frac{1}{2 } i_4^{d=6 - 2\epsilon } \biggr ] \biggr\ } \biggr|_{t-{\rm channel } } \ , , } \equn\label{tcutanswer}\ ] ] again recalling that @xmath131 is a scalar triangle integral dependent on the kinematic invariant @xmath72 and @xmath122 , while @xmath132 is a function of @xmath72 only .
it is also useful to observe that the coefficient of the @xmath133 integral in the @xmath72-channel matches that of the @xmath71-channel as expected .
if we refer back to , where all the scalar integrals that could possibly enter were listed , we notice that the coefficients , @xmath134 of @xmath135 and @xmath136 of @xmath137 have not yet been fixed . however , there are no other uv infinities in either the @xmath71- or @xmath72-channel expressions ( eqs .
( [ scutanswer ] ) and ( [ tcutanswer ] ) ) , so therefore since this primitive amplitude is uv - finite ( since it vanishes at tree level ) , it is not surprising that these coefficients are zero .
this may be explicitly verified by direct construction of the channel corresponding to using the on - shell condition on the two propagators adjacent to the massive external leg , showing that both @xmath134 and @xmath136 are individually zero .
we have not evaluated this channel , since this example is only for illustrative purposes .
thus with the two channels of the primitive amplitude we can construct the full primitive amplitude @xmath67 , which is @xmath138 -4\epsilon\biggl[\frac{s - u}{2s(t - m_h^2)}i_3^{(1)d=6 - 2\epsilon } \cr & \hskip 2 cm -\frac{s - m_h^2}{2st}i_3^{(2)d=6 - 2\epsilon } -\frac{t - m_h^2}{2st}i_3^{(3)d=6 - 2\epsilon } + \frac{t - u}{2t(s - m_h^2)}i_3^{(4)d=6 - 2\epsilon}-\frac{1}{2 } i_4^{d=6 - 2\epsilon } \biggr ] \biggr\ } \ , . } \equn\label{pppamplitude}\ ] ] note that this expression is valid to all orders in @xmath45 with four - dimensional external momenta .
since this amplitude has no ultraviolet or quadratic divergences , the primitive amplitude is well defined in the limit @xmath139 .
therefore can be simplified , since in this limit with the use of , @xmath140 and @xmath141 .
also with the intention of simplifying this expression we can use explicitly . thus @xmath142 -\frac{2u(m_h^4-ts)}{ts(s - m_h^2)(t - m_h^2 ) }
\biggr\ } \ , , } \equn\label{answer1}\ ] ] where all the integrals in this equation are in four dimensions . in a similar fashion to the all - plus helicity case the primitive amplitudes corresponding to the remaining two helicity configurations may be calculated .
the results are @xmath143 \cr & \hskip 2 cm - \frac{2u}{(t - m_h^2)^2}\left[\tilde{i}_2(t ) -\tilde{i}_2(m_h^2)\right ] + \frac{2u(t - s)}{t(s - m_h^2)(t - m_h^2)}\biggr\ } \ , , } \equn\label{answer2}\ ] ] and @xmath144i_4(s , t , m_h^2 ) \cr & \hskip 1.0 cm + \biggl[\frac{u-4m^2}{s - m_h^2}+\frac{4s}{u}+\frac{4um^2}{(s - m_h^2)^2 } \biggr]i_3(s ) + \biggl[\frac{u-4m^2}{t - m_h^2}+\frac{4t}{u}+\frac{4um^2}{(t - m_h^2)^2 } \biggr]i_3(t ) \cr & \hskip 1.0 cm + m_h^2\biggl[\frac{(u-4m^2)(st - u^2)}{st(s - m_h^2)(t - m_h^2)}-\frac{4}{u } -\frac{4um^2}{s(s - m_h^2)^2}-\frac{4um^2}{t(t - m_h^2)^2}\biggr]i_3(m_h^2 ) \cr & \hskip 1.0 cm -\frac{2(3u+2t)}{(s - m_h^2)^2}\left[\tilde{i}_2(s ) -\tilde{i}_2(m_h^2)\right ] -\frac{2(3u+2s)}{(t - m_h^2)^2}\left[\tilde{i}_2(t ) -\tilde{i}_2(m_h^2)\right ] -\frac{2u(u^2-st)}{st(s - m_h^2)(t - m_h^2 ) } \biggr\ } \ , , } \equn\label{answer3}\ ] ] where the @xmath145 s are bubble integrals with their @xmath146 poles removed ( since the poles cancel in the difference between the two @xmath147 s ) and all integrals are in four dimensions .
thus in equations ( [ answer1],[answer2],[answer3 ] ) we have the three necessary primitive amplitudes @xmath67 , @xmath68 and @xmath69 which are needed for the full @xmath46 amplitude .
we have compared these amplitudes to those of ellis et al .
@xcite and they agree .
this comparison is performed by dotting the tensor expressions of ellis et al . with spinor helicity polarization vectors .
in this paper we have explained the relationship of the unitarity method reviewed in ref.@xcite to feynman diagram calculations .
one may calculate feynman diagrams in a sophisticated manner so as to take advantage of the benefits of the unitarity method .
we have illustrated the usefulness of this method for the case of @xmath46 .
this example is general in that it incorporates both massive internal and external kinematics as well as a combination of colored and colorless external particles
. it should be evident from the explicit calculation presented in this paper that this method lends itself to making complicated analytical calculations more tractable .
this is because in this approach one is always dealing with gauge invariant constructions , which are generally significantly simpler than the gauge dependent feynman graphs in a conventional calculation . in the unitarity method one
targets the coefficients of a subset of scalar integrals contributing to the amplitude by computing a gauge invariant combination of feynman diagrams .
the notion of a channel as defined in this paper is more general than just the cut legs of a cutkosky calculation , where one is nominally computing the discontinuity of an amplitude in a certain cut channel .
the reason it is more general is that one defines a channel as a subset of the terms in the full amplitude ; those terms being the scalar integrals that include some pre - defined combination of internal propagators .
this notion of a channel has already been useful in the evaluation of @xmath148 @xcite .
it was also helpful in two - loop calculations in @xmath149 supersymmetric yang - mills @xcite .
one of the themes of this paper has been to explain the usefulness of the unitarity method to multi - point one - loop calculations .
the ideas discussed here will potentially be beneficial to the extension of these types of calculations to multi - loops .
initial steps have already been made @xcite , and more attention is being devoted to these pursuits .
.5 cm * acknowledgments * i thank z. bern for encouragement and many valuable discussions .
i also thank l. dixon , a.k .
grant , d.a .
kosower , e. marcus , a.g .
morgan and b. yan for helpful discussions and comments .
this work was supported by the doe under contract de - fg03 - 91er40662 .
in this appendix we collect expressions for the integrals @xcite we use in this paper . the @xmath150-dimensional loop integrals considered in this paper
are defined by @xmath151 = i ( -1)^{n+1 } ( 4\pi)^{d/2 } \int \frac { d^{d } p } { ( 2\pi)^{d } } \frac{p^{\alpha_1 } \cdots p^{\alpha_m } } { ( p^2 - m^2 ) \cdots ( ( p-\sum_{i=1}^{n-1 } k_i ) ^2 - m^2 ) } \ , , \equn\label{generalloop}\ ] ] where @xmath152 is a @xmath150-dimensional momentum and the external momenta , @xmath153 , are four - dimensional . our convention is to suppress the dimension label on @xmath154 when we are dealing with a @xmath60 integral , unless otherwise indicated .
we also suppress the square brackets when the argument is unity .
such integrals are referred to in the text as scalar integrals , while tensor integrals have @xmath155 .
given a four - point amplitude , we have two conventions for labeling the one- , two- and three - point integrals . the first , and more familiar one is to explicitly give the kinematic invariant upon which the integral depends .
for example , @xmath156 is the @xmath42-dimensional bubble that has an invariant mass square of @xmath157 flowing through its external legs .
the second convention for labeling the lower point integrals is to indicate , by a raised @xmath158 that the internal propagator between legs @xmath159 ( mod @xmath160 ) and @xmath29 has been removed .
if two indices are present as in @xmath161 then two propagators have been removed .
this follows the labeling convention of refs .
@xcite .
the bubble with an external kinematic invariant @xmath71 is @xmath162 where @xmath163 . for external massless kinematics ,
this may be written in closed form as @xmath164 the scalar triangle integral can either be a function of just one kinematic invariant @xmath71 @xmath165 or of two invariants @xmath71 and @xmath122 @xmath166 while the box with a uniform internal mass and a single massive external leg , with invariant mass - square @xmath122 is @xmath167 + \ord(\eps ) \ , , \equn\label{extmassboxdef}\ ] ] where @xmath168 , @xmath169 \ , , } \equn\ ] ] with @xmath170 , @xmath171 and the dilogarithm @xcite is defined by @xmath172 .
the scalar integral expressions quoted above are only valid in certain analytic regions .
these can be analytically continued , but are not presented here since related expressions , @xmath173 and @xmath174 . ]
are presented for all analytic regions in ref .
@xcite .
the higher dimension integrals are defined in with @xmath150 set to the appropriate value .
the relationship of these integrals to the usual four - dimensional ones has been extensively discussed in ref .
@xcite . for @xmath175 ,
@xmath176-dimensional integrals can be written in terms of @xmath42-dimensional integrals via the integral recursion relation @xmath177 \ , , } \equn \label{highertolower}\ ] ] where @xmath178 , @xmath179 and the matrix @xmath180 is @xmath181 higher dimension integrals arise naturally when performing the calculations described in this paper . in a typical primitive amplitude discussed in the text
we obtain integrals of the form @xmath182 = \cr & i ( -1)^{n+1 } ( 4\pi)^{2-\epsilon } \int \frac { d^{4}p } { ( 2\pi)^{4 } } \frac{d^{-2\epsilon}\mu}{(2\pi)^{-2\epsilon } } \frac{f(p^\alpha , k_i^\alpha , \mu^2)}{(p^2 - \mu^2 - m^2 ) \cdots ( ( p-\sum_{i=1}^{n-1 } k_i ) ^2 - \mu^2 - m^2 ) } \ , , } \equn\label{betterloop}\ ] ] where we have explicitly broken the @xmath42-dimensional momentum into a four - dimensional part , @xmath32 , and a @xmath43-dimensional part , @xmath85 . as noted by mahlon @xcite , using the definition ( [ generalloop ] ) , we can write @xmath183 = -\epsilon i_n^{d=6 - 2\epsilon } \ , . \equn\label{dseintegrand}\ ] ] note that although the loop momentum is shifted to higher dimension , the external momenta remain in four dimensions .
as discussed in the text , tensor integrals may be evaluated using feynman parameters .
we make use of the following formulae in the text . after feynman parameterization and the normal shift of momentum
we make use of the following , @xmath184 where @xmath180 is defined in . after integrating out the loop momenta we obtain integrals of the form @xmath185
\equiv \gamma(n - d/2)\int_0 ^ 1 d^na_k\ \delta ( 1 - { \textstyle \sum_r } a_r ) { f(a_k ) \over \left [ \sum_{i , j=1}^n s_{ij } a_i a_j - i\varepsilon \right]^{n - d/2}}\ , . \equn\ ] ] an integral reduction formula that is quite useful is @xcite @xmath186\ = \ { 1\over2 } \sum_{j=1}^n c_{ij}\ i_{n-1}^{(j ) , \ , d } \ + \ { c_i\over c_0}\ i^d_n \ , , \equn\label{linearintegralrelation}\ ] ] where @xmath187 and @xmath30 and @xmath188 are defined in .
another useful integral reduction formula for @xmath189 $ ] can also be found in @xcite .
to begin , we have a @xmath118-dimensional vector , @xmath190 , which we can express as a sum of a four dimensional piece @xmath191 and a @xmath86-dimensional @xmath192 ; @xmath193 .
( we have used the convention that upper - case momenta are @xmath118-dimensional and lower - case momenta are four - dimensional . ) here we summarize the rules for dealing with @xmath85 s given in ref .
@xcite .
we abide by the conventional dirac algebra , @xmath194 and @xmath195 , where @xmath196 and @xmath197 are @xmath198)-dimensional lorentz indices .
the metric is given by @xmath199 .
it follows that @xmath200 ( the negative sign preceding the @xmath95 is from the metric ) .
thus @xmath201 anti - commutes with four - dimensional @xmath202 matrices , @xmath203 .
so if we use the conventions of t hooft and veltman @xcite , and adopt the arbitrary dimension definition , @xmath204 , then @xmath205 and @xmath206 = 0 $ ] .
that is @xmath201 freely commutes with @xmath207 , since @xmath207 is constructed as a product of four - dimensional dirac matrices .
hence , @xmath208 and @xmath209 , where @xmath210 is the helicity projection operator . in calculations
it is important to first commute the @xmath201 s together before evaluating the remaining four - dimensional pieces . in the calculation presented in the momentum of the sewn fermion lines
. we will borrow the bra and ket symbols to represent the spinors , but as helicity is not a good quantum number we shall not label them with a helicity . since we always sum over all states across the cut
, there is no need to define a @xmath118 helicity notion . in sewing the @xmath118-spinors
together we implicitly sum over the spin degrees of freedom , that is @xmath211 this notation glosses over the distinction of spinors and anti - spinors .
however , as discussed in ref .
@xcite , this may introduce an overall sign which can be readily fixed by hand .
alternatively , one may easily use both particle and anti - particle spinors to obtain identical results .
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Photosynthetic rate calculation
>
> What are the steps in calculating the photosynthetic rate ($\pu{\mu mole}~ \ce{O2} \pu{m2/ min}$) for a leaf that has an area of $\pu{0.0025 m2}$ and a $\ce{O2}$ evolution
> rate of $0.096~\ce{O2}/\pu{min}$?
>
>
>
To do so , the first step is to convert it to $\mu L$ i.e. $\pu{960 \mu L} ~\ce{O2}/\pu{min}$.
The second step should be to convert it to $\pu{\mu moles}$. So, how do we do that ?
EDIT : In my textbook, the following calculation has been done but I am not able to understand it...
>
> $\pu{960 \mu L}~\ce{O2}~\pu{/L} / [(273+23)/273) \times 22.423]$
>
>
>
I know that $22.423$ is the volume of a mole of gas and $\pu{273K}$ is $\pu{0^\circ C}$ but I am not able to understand how that fits here.
Using the general case equation
$$\frac{P\_1V\_1 }{T\_1} = \frac{P\_2 V\_2} {T\_2}$$
and given that pressure is constant at $\pu{1 atm}$ in your experiment, the equation simplifies to
$$\frac{V\_1 }{T\_1} = \frac{ V\_2} {T\_2}$$
We know $V\_1=\pu{960 \mu L}$ and it appears that the experiment is being run at $\pu{(273+23)K}$, so we need to calculate what the volume ($V\_2$) would be at standard T ($\pu{273 K}$). This is given by
$$V\_2 = \frac{V\_1 T\_2}{T\_1}$$
if we next divide $V\_2$ by $\pu{22.423E6 \mu~L}$, we now know how many moles of $\ce{O2}$ we have.
| stackexchange/chemistry |
schur polynomials is an ubiquitous object in mathematics and mathematical physics , ranging from representation theory , combinatorics , enumerative geometry to knot theory .
being one of the most fundamental symmetric polynomials , extensive studies and numerous combinatorial identities have been found for the schur polynomials .
many mathematical objects are introduced for which the schur polynomials serves as a building block since one can use various properties found for the schur polynomials .
one typical example is a stochastic process called the schur process @xcite whose probability measure is given by the schur polynomials , from its property many useful combinatorial formulae can be employed to study the dynamics of the process .
the schur polynomials itself has many expressions .
one of the most famous ones is the jacobi - trudi identity which expresses schur polynomials in terms of elementary symmetric polynomials . besides these traditional identities , a very interesting formula called the tokuyama formula @xcite
was found which expresses schur polynomials in a combinatorial form .
the distinctive feature of the formula is that the expression is given in terms not only of the symmetric variables but also with an additional parameter which does not appear in the original definition of the schur polynomials .
specializing the additional parameter , the tokuyama formula reduces to the determinant formula , weyl character formula and so on . in this sense
, the tokuyama formula can be viewed as a deformation of weyl character .
recently , the tokuyama formula has found its interpretation in terms of integrable vertex models @xcite .
the idea to understand this tokuyama formula from the point of view of quantum integrability is to extend the @xmath1-operator for the free - fermion model ( the corresponding @xmath2-matrix is the trigonometric felderhof model ) to an @xmath1-operator including an additional parameter besides the spectral parameter .
the newly - introduced parameter plays the role of refining the combinatorial expression for the schur polynomials .
this idea of relating tokuyama formula which is a deformation of weyl character formula to integrable vertex models have been recently generalized to the factorial schur polynomials @xcite and other types of symmetric polynomials @xcite by introducing inhomogeneous parameters or changing boundary conditions . in this paper
, we present another type of combinatorial formula for the schur polynomials with an additional parameter by investigating a partition function of an integrable six - vertex model .
we find the following combinatorial formula for the schur polynomials @xmath3 where @xmath4 is an arbitrary parameter .
@xmath5 , @xmath6 are strict partitions satisfying the interlacing relations @xmath7 , @xmath8 is fixed by the young diagram @xmath9 as @xmath10 , and @xmath11 denotes the number of parts in @xmath12 which are not in @xmath13 .
we obtain this combinatorial formula from an integrable six - vertex model .
the six - vertex model we consider can be regarded as a certain degeneration of a @xmath0-deformed non - hermitian boson model introduced in @xcite .
the corresponding wavefunction seems to be analyzed by the coordinate bethe ansatz @xcite which at the degeneration point is given by the schur polynomials times a factor including an additional parameter . to obtain the combinatorial formula , we investigate the corresponding model from the point of view of the quantum inverse scattering method , i.e. , starting from the @xmath1-operator which is the most fundamental object in quantum integrable models .
we view the wavefunction as a partition function of a six - vertex model and evaluate it in two ways .
first , we evaluate the partition function directly to show that it is given by a schur polynomials times an additional factor .
another way of evaluation is to take the viewpoint that the partition function consists of a layer of @xmath14-operators , and calculate the matrix elements of a single @xmath14-operator to show a summation formula for the partition function . combining the two expressions give the combinatorial formula . besides the combinatorial formula
, we examine the scalar products and present an algebraic analytic proof for its determinant form , which combined with the wavefunction gives us the celebrated cauchy formula for the schur polynomials .
we also make an application of the domain wall boundary partition function to show a simple formula for a particular generating function of alternating sign matrices .
this paper is organized as follows .
we introduce the integrable six - vertex model as a particular degeneration of a non - hermitian @xmath0-deformed boson model in the next section .
we give an algebraic analytic proof for the scalar product in section 3 . in sections 4 and 5
, we evaluate the matrix elements and the wavefunction of the six - vertex model .
we combine the results of sections 3 , 4 and 5 to present the combinatorial formulae for the schur polynomials in section 6 . in section 7
, we give an application of the domain wall boundary partition function to a generating function of the alternating sign matrices .
we introduce the @xmath0-deformed non - hermitian boson model @xcite and its equivalent six - vertex model at the point @xmath15 .
the model is characterized by @xmath0-deformed boson algebra with generators @xmath16 satisfying the following relations @xmath17=t^{n}(1-t ) , \quad [ n , b]=-b , \quad [ n , b^\dagger]=b^\dagger.\end{aligned}\ ] ] these generators act on a fock space @xmath18 spanned by the orthonormal basis @xmath19 as @xmath20 the operators the dual orthonormal basis @xmath21 ( @xmath22 ) satisfying @xmath23 as @xmath24 we consider the following @xmath1-operator which is a slightly deformation of the one in @xcite @xmath25 acting on the tensor product @xmath26 of the complex two - dimensional space @xmath27 and the fock space at the @xmath28th site @xmath29 .
let us denote the orthonormal basis of @xmath27 and its dual as @xmath30 and @xmath31 .
the explicit forms of the matrix elements of in the orthonormal basis are @xmath32 in figure
[ boson - l ] , we depict the non - zero elements of the @xmath1-operator .
, scaledwidth=70.0% ] the @xmath1-operator satisfies the intertwining relation ( @xmath33-relation ) @xmath34 which acts on @xmath35 .
the @xmath2-matrix @xmath36 is a solution to the yang - baxter equation : @xmath37 from the @xmath1-operator , we construct the monodromy matrix @xmath38 which acts on @xmath39 .
tracing out the auxiliary space , one defines the transfer matrix @xmath40 : @xmath41 simplifications happen for the @xmath0-deformed boson model at @xmath15 . due to the matrix element ,
when we construct @xmath42-particle states from the vacuum , each site can only be occupied by at most one boson .
this is equivalent to the reduction of the @xmath0-deformed boson model to the six - vertex model whose @xmath1-operator is given by @xmath43 one can check that indeed satisfies the intertwining relation .
we analyze the structure of this six - vertex model in this paper .
we remark that at the other degenerated point @xmath44 of the @xmath0-deformed boson model , the model is called the non - hermitian phase model @xcite , whose wavefunction @xcite constructed from the @xmath1-operator is given by the grothendieck polynomials @xcite , which furthermore reduces to the schur polynomials by taking @xmath45 where the corresponding model is the _ hermitian _ phase model @xcite . on the other hand ,
the wavefunction at @xmath45 for generic @xmath0 is given by the hall - littlewood polynomials @xcite .
in this section , we first construct a state vector of the integrable @xmath0-deformed boson model following the standard procedure of the quantum inverse scattering method ( i.e. the algebraic bethe ansatz ) which is based on the yang - baxter algebra . the @xmath42-particle state @xmath46 is characterized by @xmath42 unknown numbers @xmath47 ( @xmath48 ) , and is not an eigenvector of the transfer matrix in general .
however , if the parameters @xmath49 satisfy a set of constraints called the bethe ansatz equation , the @xmath42-particle state becomes an eigenstate .
we call the state @xmath46 on - shell state if @xmath50 satisfies the bethe ansatz equation , and off - shell state if no constraints are imposed on @xmath50
. we then restrict the analysis to @xmath15 , which is equivalent to considering the six - vertex model , and prove the determinant form for the scalar products @xmath51 which is the inner product between the off - shell state @xmath52 and the dual off - shell state @xmath53 . from the @xmath1-operator
, we construct the monodromy matrix @xmath54 which acts on @xmath39 . here
we introduced the inhomogeneous parameters @xmath55 .
see figure [ abcdpic ] for the graphical description of the elements of the monodromy matrix .
associated with site @xmath28.,scaledwidth=90.0% ] taking the homogeneous limit @xmath56 ( @xmath57 ) , is recovered : @xmath58 as in the above equation , hereafter we will omit @xmath59 for the quantities in the homogeneous limit ( e.g. @xmath60 ) . tracing out the auxiliary space , one defines the transfer matrix @xmath61 : @xmath62 the repeated applications of the @xmath33-relation leads to the intertwining relation @xmath63 some of the elements of the intertwining relation are @xmath64 } = { [ } \mathcal{c}(u,\{w\}),\mathcal{c}(v,\{w\}){]}=0,\end{aligned}\ ] ] where @xmath65 the transfer matrix @xmath66 is then expressed as elements of the monodromy matrix : @xmath67 the arbitrary @xmath42-particle state @xmath68 ( resp .
its dual @xmath69 ) ( not normalized ) with @xmath42 spectral parameters @xmath70 is constructed by a multiple action of @xmath71 ( resp .
@xmath72 ) operator on the vacuum state @xmath73 ( resp .
@xmath74 ) : @xmath75 by the standard procedure of the algebraic bethe ansatz , we have the followings .
[ eigenstate ] the @xmath42-particle state @xmath76 and its dual @xmath77 become an eigenstate ( on - shell states ) of the transfer matrix when the set of parameters @xmath78 satisfies the bethe ansatz equation : @xmath79 where @xmath80 then the eigenvalue of the transfer matrix is given by @xmath81 for the case @xmath15 which we investigate extensively in this paper , the bethe ansatz equation is @xmath82 this is the bethe ansatz equation for free fermions in the homogeneous limit @xmath56 ( @xmath83 ) . in the analysis below , we do not impose these constraints between the spectral parameters @xmath50 and inhomogeneous parameters @xmath84 .
we remark that from this consideration on the bethe ansatz equation , one can imagine the wavefunction is given by the schur polynomials .
the amazing thing is that a detailed analysis of its realization as partition functions lead us to a new combinatorial formula for the schur polynomials itself .
the scalar product between the arbitrary off - shell state vectors , which is mainly considered in this section , is defined as @xmath85 with @xmath86 . from now on , we specialize the parameter @xmath0 of the @xmath0-deformed boson algebra to @xmath15 .
this is equivalent to considering the six - vertex model .
the following determinant formula in the homogeneous limit @xmath56 ( @xmath83 ) is valid .
[ scalarthm ] the scalar product in the homogeneous limit @xmath87 ( @xmath83 ) is given by a determinant form : @xmath88 where @xmath89 and @xmath78 are arbitrary sets of complex values ( i.e. off - shell conditions ) , and @xmath90 is an @xmath91 matrix with matrix elements @xmath92 here we will show the above determinant formula by using a method initiated by izergin - korepin @xcite for the domain wall boundary partition function and recently developed by wheeler @xcite in the calculation of the scalar product of the spin-1/2 xxz chain .
this procedure was applied to a family of integrable five - vertex model @xcite which , in contrast to the spin-1/2 xxz chain , there was no need to impose the bethe ansatz equation ( i.e. on - shell condition ) to show the determinant formula . for the six - vertex model
we consider in this paper , we also do not have to impose the bethe ansatz equation , i.e. , the determinant formula is valid for arbitrary off - shell states .
first let us introduce the following intermediate scalar products which plays the key role for the proof @xmath93 see also figure [ intermediatepic ] .
the term intermediate " stems from the fact that interpolates the scalar product ( @xmath94 ) and the domain wall boundary partition function ( @xmath95 ) ( see also figure [ initialpic ] ) .
associated with site @xmath28.,scaledwidth=60.0% ] we have the following lemma regarding the properties of the intermediate scalar product . [ property ]
the intermediate scalar product @xmath96 satisfies the following properties . 1 .
@xmath96 is symmetric with respect to the variables @xmath97 .
2 . @xmath98 is a polynomial of degree @xmath99 in @xmath100 .
the following recursive relations between the intermediate scalar products hold @xmath101 4 .
the case @xmath95 of the intermediate scalar products has the following form : @xmath102 property 1 follows from the @xmath33-relation @xmath103 holding in @xmath104 ) . here
@xmath105 is given by @xmath106 which intertwines the @xmath1-operators acting on a common auxiliary space ( but acting on different quantum spaces ) .
note the usual @xmath33-relation intertwines the @xmath1-operators acting on a same quantum space but acting on different auxiliary spaces .
the above @xmath33-relation allows one to construct the monodromy matrix as a product of the @xmath1-operators acting on the same quantum space ( see also appendix for an example of using its property to examine the symmetries of the domain wall boundary partition function ) , and rewriting the intermediate scalar products in terms of the resultant monodromy matrices makes one see property 1 holds .
property 2 can be shown by inserting the completeness relation into the intermediate scalar products @xmath107 and noting that the factor containing @xmath100 is calculated as @xmath108 property 3 can be obtained by setting @xmath109 in , or can be directly observed by its graphical representation that the top row is completely frozen . to show property 4 , we first note by the graphical representation ( see figure [ initialpic ] ) that @xmath110 where @xmath111
one can evaluate the domain wall boundary partition function @xmath112 by the standard procedure following the arguments of izergin - korepin @xcite , which is given in appendix .
, which corresponds to the domain wall boundary partition function.,scaledwidth=99.0% ] the result has the following simple factorized form @xmath113 which together with proves property 4 . [ uniqueness ] the properties in lemma [ property ] uniquely determine the intermediate scalar product . due to lemma [ uniqueness ] ,
the following determinant representation for the intermediate scalar product is valid .
[ determinantthm ] the intermediate scalar product @xmath114 has the following determinant form : @xmath115 with an @xmath91 matrix @xmath116 whose matrix elements are given by @xmath117 we can directly see that the determinant formula satisfies all the properties in lemma [ property ] . to show property 4
, we utilize the cauchy determinant formula @xmath118 finally due to lemma [ uniqueness ] , the determinant formula holds . taking @xmath94 in yields the determinant representation of the scalar product for the six - vertex model with inhomogeneous parameters : @xmath119 with @xmath120 further taking the homogeneous limit @xmath56 ( @xmath121 ) yields in theorem [ determinantthm ] .
in this section , we derive matrix elements for the @xmath0-deformed boson model for the generic parameter @xmath0 , and then we restrict ourselves to the case of the six - vertex model @xmath15 . consider the arbitrary off - shell state , i.e. , the parameters @xmath78 in the @xmath42-particle state are arbitrary .
the orthonormal basis of the @xmath42-particle state @xmath68 and its dual @xmath69 is given by @xmath122 and @xmath123 , where @xmath124 .
the wavefunctions can be expanded in this basis as @xmath125 there is a one - to - one correspondence between the set @xmath126 ( @xmath124 ) and the young diagram @xmath127 ( @xmath128 ) .
namely , each young diagram @xmath13 under the constraint @xmath129 , @xmath130 can be labeled by a set of integers @xmath131 as @xmath132 .
the following definition @xcite on the ordering on the basis of particle configurations is useful for later purpose .
@xcite for two configurations @xmath133 @xmath134 and @xmath126 @xmath135 , let @xmath136 and @xmath137 .
we say that the particle configurations @xmath138 and @xmath131 are admissible , if and only if @xmath139 ( @xmath140 ) , and write this relation as @xmath141 .
moreover we also define the ordering on the young diagrams . for two young diagrams @xmath142 and
@xmath127 , we say that @xmath12 and @xmath13 interlace , if and only if @xmath143 @xmath144 , and write this relation as @xmath145 .
[ admissible ] let @xmath146 and @xmath147 be the particle configurations described by the young diagram @xmath148 and @xmath149 .
then @xmath150 for @xmath138 and @xmath131 , we introduce @xmath151 to be the set of all integers @xmath152 such that @xmath153 , and @xmath154 to be the set of all integers @xmath155 such that @xmath156 . when @xmath138 and @xmath131 satisfy the admissible condition @xmath141 , @xmath157 and @xmath158 satisfy @xmath159 and @xmath160 ( @xmath161 ) .
from the matrix elements of the @xmath1-operator , one finds @xmath162 when the admissible condition is satisfied , one finds the following .
@xmath163 where @xmath164 . +
this can be shown by combining the following partial actions : latexmath:[\ ] ] first , substituting the completeness relation , one decomposes the scalar product as @xmath277 then substituting the determinant representation for the scalar product into the rhs of the above and utilizing the relations and yields the cauchy identity by changing the variables from @xmath278 and @xmath49 to @xmath279 and @xmath209 respectively .
in this section , we make an application of the domain wall boundary partition function to the enumeration of alternating sign matrices .
see @xcite for example of a huge literature on the relation between the enumeration of alternating sign matrices and integrable vertex models .
the presentation below for the explanation of the relation between alternating sign matrices and the six - vertex model follows the lines of @xcite .
we take the homogeneous limit of the domain wall boundary partition function or @xmath280 an algebraic analytic proof of is given in appendix .
it can also be obtained as a special case of the wavefunction . as a corollary of the domain wall boundary partition function ,
we derive a simple expression for a special case of the generating function of alternating sign matrices . alternating sign matrices are square matrices with the following properties : 1 .
each entry is either 0 , 1 or @xmath281 .
2 . there is at least one nonzero entry in each row and column .
the entries in each row and column sum to 1 . to satisfy the above conditions ,
the nonzero entries must alternate in sign along each row and column . for @xmath282 , there are 7 alternating sign matrices : @xmath283 let @xmath284 be the set consisting of all @xmath285 alternating sign matrices
. for @xmath286 , let us define @xmath287 @xmath288 as the number of @xmath281 s in @xmath289 and @xmath290 as the number of 0 s to left of 1 in the first row of @xmath289 .
the generating function of the alternating sign matrices is defined as @xmath291 each element of an alternating sign matrix @xmath284 has one - to - one correspondence with a particular configuration which makes a non - zero contribution to the domain wall boundary partition function of the six - vertex model . to simplify the explanation ,
we identify a particular configuration of the domain wall boundary partition function at the coordinate @xmath292 with the matrix elements @xmath293 be the set of all particular configurations making non - zero contributions to the domain wall boundary partition function of the six - vertex model . for @xmath294 ,
let @xmath295 be the number of vertex configurations latexmath:[${}_a
\langle 1| { } _ j \langle 1 | \mathcal{l}_{a j}(v_k ) @xmath166 , @xmath297 the number of vertex configurations latexmath:[${}_a \langle 1| { } _ j \langle 0
| \mathcal{l}_{a j}(v_k ) @xmath166 , @xmath299 the number of vertex configurations latexmath:[${}_a \langle 1| { }
_ j \langle 1 | \mathcal{l}_{a j}(v_n ) @xmath166 .
[ onetoone ] @xcite there is a bijection between the set of alternating sign matrices @xmath301 and the set of configurations making non - zero contributions to the domain wall boundary partition function of the six - vertex model @xmath302 by identifying the matrix elements 1 with @xmath303 @xcite let latexmath:[$\ # { } _ a \langle * | { } _ j \langle * | \mathcal{l}_{a j}(v_k ) latexmath:[${}_a \langle * | { } _ j \langle * | \mathcal{l}_{a j}(v_k ) configuration @xmath294 .
@xmath305 we use , theorem [ onetoone ] and proposition [ numberoftypes ] to show the following simple formula for a particular type of the generating function of alternating sign matrices : @xmath306 we first take the homogeneous limit @xmath307 , @xmath308 of the partition function of the six - vertex model : @xmath309 on the other hand , by the definition of domain wall boundary partition function and proposition [ numberoftypes ] , we have @xmath310 where @xmath311 , @xmath312 , @xmath313 , @xmath314 , @xmath315 , @xmath316 . + combining and and simplifying ,
one gets @xmath317 we make change variable from @xmath185 to @xmath318 .
finally , we use theorem [ onetoone ] on the one - to - one correspondence between the set of alternating sign matrices and the set of configurations of the domain wall boundary partition function to replace the sum over @xmath294 and the numbers @xmath295 , @xmath297 by the sum over @xmath286 and the numbers @xmath319 , @xmath288 .
then can be rewritten as , which concludes the proof . for @xmath282
, there are 7 alternating sign matrices as in . summing up all the corresponding factors
, we have @xmath320 we finally remark that it may also be possible to derive as a limit of the determinant representation for @xmath321 in @xcite .
in this paper , we derived a new combinatorial formula for the schur polynomials .
the quantum integrability is useful to derive a formula even for schur polynomials which is the most fundamental symmetric polynomials .
the formula expresses schur polynomials with an additional parameter besides the spectral parameter .
the other known formula in a similar sense is the tokuyama formula , which can be interpreted as a deformation of the weyl character formula and the determinant expression .
the representation theoretic meaning of the deformation parameter in our formula is unknown now which may be worth investigating .
there may be other possibilities to find combinatorial formulae to express schur polynomials and other symmetric polynomials in terms of additional parameters using the power of quantum integrability .
this may be achieved by dealing with partition functions consisting of different local @xmath1-operators or changing global boundary conditions for example .
besides the traditional problem of the application of partition functions of the six - vertex model to the enumeration of alternating sign matrices , one of the most active line of researches on quantum integrable combinatorics today is to derive combinatorial formulae for symmetric polynomials such as the cauchy identity , littlewood identity and so on by analyzing the transfer matrices or partition functions of integrable lattice models .
the power of quantum integrable combinatorics is that one can fuse combinatorics with algebraic analysis to find and prove identities which seems to be hard to show in a purely combinatorial or a purely algebraic way .
see @xcite for finite lattice and @xcite for infinite lattice for example of the recent progresses on this line .
this work was partially supported by grant - in - aid for scientific research ( c ) no .
here we derive the factorized form of the domain wall boundary partition function defined by @xmath322 where @xmath323 is given by and @xmath324 . 1 . @xmath326 is symmetric with respect to the variables @xmath327 .
2 . @xmath328 is a polynomial of degree @xmath329 in @xmath330 .
the following recursive relations between the domain wall boundary partition functions hold : @xmath331 4 .
the case @xmath225 of the domain wall boundary partition function following form : @xmath332 first note that the domain wall boundary partition function @xmath333 can be re - expressed using the transfer matrix @xmath334 propagating in the horizontal direction as @xmath335 where @xmath336 from the @xmath33 relation , one has @xmath337 combining and shows property 1 .
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proofs and new conjectures _ , [ arxiv:1405.7035 ] a. borodin , _ on a family of symmetric rational functions _ , [ arxiv:1410.0976 ] | arxiv |
Elisabetta Fontana attends the school of art "Castello Sforzesco" and begins to work with sculptural goldsmiths, Davide De Paoli with his school "Primateria", that impassions her to the study of all the ancient techniques, from chisel to incision, to fusion, from sketch to the ended object. She graduates in design and disciplines of fashion. With her partner, that has matured experience in theatre and music, they realized some creative laboratories in the schools: to play with the art, as Bruno Munari has taught us, to play with modulated pieces using ancient and recent techniques, to play with the symmetry and the asymmetry, with the translation, the rotation. She designs and draws new collection always careful to the world of fashion in the respect for the environment, thinking that through the conjunction and collaboration between all these different types of knowledge can lead to the ideation and realization of high quality products. | slim_pajama |
At least two ships of the Royal Navy have borne the name HMS Fiona:
was an armed boarding steamer in the First World War. She was wrecked in 1917.
was an armed boarding vessel in the Second World War. She was sunk by air attack in 1941.
was a water tractor akin to a tug in service during the 1980s
Category:Royal Navy ship names | wikipedia |
Raipur Araian is a village in Bhulath Tehsil in Kapurthala district of Punjab State, India. It is located from Bhulath, away from district headquarter Kapurthala. The village is administrated by a Sarpanch who is an elected representative of village as per the constitution of India and Panchayati raj India.
References
List of cities near the village
Bhulath
Kapurthala
Phagwara
Sultanpur Lodhi
Air travel connectivity
The closest International airport to the village is Sri Guru Ram Dass Jee International Airport.
External links
Villages in Kapurthala
List of Villages in Kapurthala Tehsil
Category:Villages in Kapurthala district | wikipedia |
in the standard approach to galactic cr propagation , the @xmath74-particle phase space distribution of crs is approximated as a macroscopic fluid . solving then the diffusion equation including cr interactions permits to model self - consistently primary and secondary fluxes .
however , the diffusion approach has several disadvantages .
first of all , the diffusion approximation itself breaks down in several interesting regimes @xcite .
moreover , the diffusion tensor is an external input in this approach .
it is only loosely connected to fundamental properties of the galactic magnetic field ( gmf ) . in this work ,
we apply therefore the trajectory approach where one calculates the path of individual crs solving the equations of motion of particles propagating in the gmf .
we use the code described and tested in @xcite , while we use for the regular and the turbulent component of the gmf the parameters described in @xcite . as we showed previously in @xcite ,
the resulting cr fluxes reproduce over a wide range of energies all available experimental data for individual groups of cr nuclei .
our numerical results for the propagation of crs emitted by a bursting source can be summarized as follows . in an initial period ,
crs propagate essentially one - dimensional , filling a filament - like structure around the magnetic field line going through the source .
after this rather short initial period , crs start to diffuse also perpendicular to the direction of the filament . in a realistic gmf model ,
the two perpendicular components of the diffusion tensor differ , @xmath75 , and thus crs diffuse mainly in the @xmath76 and the @xmath77 direction . in particular , we found for the case at hand in the jansson - farrar model @xcite the values @xmath78@xmath40/s for crs with energy @xmath79tev .
this behavior is illustrated in fig .
[ fig : s1 ] which shows the scaled cr density @xmath80 at the position of the earth as function of time for three different energies .
additionally , we used the relation @xmath81 valid for kolmogorov turbulence to rescale the @xmath82ev curve by @xmath83 to @xmath84ev and to @xmath85ev .
the approximate agreement of the two rescaled curves with the true result supports a kolmogorov - like scaling of the density .
moreover , it is visible that the density scales approximately as @xmath86 for intermediates times , 10kyr@xmath87myr .
such a scaling is characteristic for two - dimensional diffusion and reflects the observed hierarchy in the eigenvalues of the diffusion tensor . of crs at the position of the earth as function of time for three different energies ; also shown are the densities rescaled using @xmath88 ( grey lines ) and the @xmath89 behavior expected for @xmath90 diffusion . ]
the trajectories of charged crs depend on their rigidity @xmath91 .
the sign difference of the charge of protons and antiprotons becomes important only on distances of a few coherence lengths to the source , while on larger scales the diffusion of protons and antiprotons of the same energy proceeds in the same way . in this paper
we do not perform the full ( computationally expansive ) calculation of trajectories of the secondary particles . instead , we use a scaling relation to describe the spread of the secondaries , taking into account the shift of energy of the secondaries compared to the primary particles .
the density @xmath92 of antiprotons which are produced at the time @xmath93 by protons with the density @xmath94 is given by @xmath95 where @xmath96 is the green function describing the diffusion of antiprotons .
our numerical results show that the cr propagation from a bursting source can be modeled by two - dimensional diffusion in the time and energy range of interest for cr secondary production .
thus the proton density at the production time @xmath93 is given by @xmath97 \,,\ ] ] where @xmath90 , @xmath98 denotes the distance in the two - dimensional diffusion plane , @xmath99 the source spectrum and @xmath100 the effective diffusion distance , @xmath101 .
the corresponding green function @xmath102 has the same functional form , @xmath103\ ] ] with @xmath104 . for simplicity , we assume a one - to - one relation between the energy of protons and antiprotons , setting @xmath105 , where @xmath106 .
this results in the diffusion coefficient @xmath107 for kolmogorov turbulence .
the integral in eq .
( [ eq : green ] ) is of the standard gaussian type . in the limit of small @xmath98
the exponent is @xmath108\sim 1 $ ] and the ratio @xmath109 is @xmath110 where we introduced also @xmath111 . in particular , we see that the ratio does not depend on energy and satisfies as required @xmath112 .
integrating over the production time @xmath93 , we find @xmath113 for @xmath106 .
thus , using for cr antiprotons the primary proton trajectories we underestimate the antiproton flux by @xmath114% . since this enhancement is energy independent , we can use the following scheme for the calculation of the antiproton flux . in a first step ,
we calculate the proton flux at the position of the earth neglecting interactions . in the trajectory approach ,
we obtain the local cr flux at a given time interval recording the path length of crs spent in a sphere around this point .
we record also the grammage @xmath37 these crs crossed on their way to the earth .
then we calculate the average grammage @xmath115 summing up the gas density along the trajectories of the @xmath74 individual crs .
we employ @xmath116 as model for the gas distribution in the galactic disk , with @xmath117 as the distance to the galactic plane , @xmath118@xmath48 at the solar position and @xmath119kpc @xcite .
we set also @xmath120g/@xmath48 as minimum gas density up to the edge of the milky way at @xmath121kpc .
next we calculate the secondary antiprotons produced by crs interacting with gas using the modified version of qgsjet - ii-04 introduced in @xcite .
the antiproton flux is then given by @xmath122 where the @xmath53-factor is given by the inclusive spectra of antiprotons @xmath123 , @xmath124 , @xmath125 with @xmath126 as the average slope of the proton spectrum .
the factor @xmath127 accounts for the underestimate of the antiproton flux , while we include the effect of heavier nuclei in the interstellar medium using a nuclear enhancement factor @xmath128 .
note that it is a virtue of our model that the slope of the injection spectrum is the same for all cr nuclei . as a result
, the use of a nuclear enhancement factor is justified .
the same approach could be applied also to positrons , with a change @xmath129 to take into account their lower average energy .
the above simple picture has to be modified at the highest energies ( beyond the current measurements energy range ) where continuous energy losses of positrons become important .
the first estimate of the corrections due to the continuous energy losses could be found from the solution of the diffusion equation in the syrovatskii approach in @xmath90 @xcite , @xmath130 \,,\ ] ] where @xmath131 , @xmath132 the energy loss rate and @xmath133 denotes the energy at injection @xcite .
the effective diffusion coefficient for this solution is @xmath134 as determined from our simulations . for a fixed value of @xmath135 ,
this determines the electron and positron spectra formed at time @xmath93 .
the total electron and positron fluxes are then obtained summing over the formation time .
this approximation has to be verified by simulations of trajectories of secondary positrons taking into account continuous energy losses .
such simulations require however a considerable increase of computing resources and are therefore postponed to a future work . | arxiv |
we consider @xcite an isospin triplet pion field @xmath4 interacting with quark fields @xmath5 through the lagrangian density @xmath6 where @xmath7 is the isospin vector operator . the imaginary part of the amplitude for @xmath0 is considered at lowest order ( @xmath8 ) and obtained using cutkosky rules .
the coupling constant @xmath9 ( see fig . [
figure1].a ) is chosen to fulfill the number of particles sum rule ( @xmath10 ) .
the effects of the pion size are mimicked by the introduction of a cut - off ( @xmath11 ) on an observable quantity , _
i.e. _ @xmath12 for the process @xmath13 , thus in a gauge invariant way.
as seen in fig .
[ figure1 ] , @xmath9 exhibits plateaux for @xmath14 gev@xmath3 .
these plateau values are in reasonable agreement with those extracted in the njl model @xcite .
a similar behaviour is obtained for the momentum fraction @xmath15 derived from @xmath16 .
the structure function @xmath17 is shown in fig .
[ figure2 ] , which illustrates the effect of the parameters @xmath11 and @xmath18 , and the evolution for increasing @xmath1 .
the most striking feature of these distributions is the vanishing of @xmath17 for @xmath19 larger than some value @xmath20 .
this effect originates from the kinematical cuts .
indeed for a finite @xmath1 , when @xmath19 is large , there is no way to put the cut quarks on their mass shell : this requires at least an energy of @xmath21 . the vanishing at large @xmath19 is not obtained in similar works , in particular in ref . @xcite . in this reference ,
the bjorken limit is taken first and the kinematical constraint is not applied .
this procedure does not seem correct for evaluating cross - sections at finite @xmath1 .
we have presented the simplest model allowing to relate virtual photon - pion forward elastic scattering to quark distributions .
the introduction of a cut - off due to the pion size makes crossed diagrams appear as higher twists and thus allows us to define quark distributions .
however , the introduction of the cut - off breaks the momentum sum rule ( 2@xmath22 ) at @xmath23 because , in the case of the pion , constituent quarks can never be considered as free .
we motivated the cut - off as a manifestation of the pion size . the value @xmath24
gev@xmath25 is close to the hard core rms radius of the chiral bag model , 0.35 fm @xcite .
the cut - off has been imposed on the relative quark momentum .
this procedure is at variance with the double - subtraction pauli - villars procedure proposed in ref .
@xcite , or with other ones introduced in similar works based on njl models .
in addition , there is no need in our approach to consider additional diagrams with local pion - pion - quark - quark interactions . yet
, the pion - quark - quark coupling constant turns out to be the same in our approach and in njl models
. this may not be too surprising , as in both cases this coupling is determined by the requirement that the pion appears as made of two constituent quarks .
f. bissey , j. r. cudell , j. cugnon , m. jaminon , j. p. lansberg and p. stassart , arxiv : hep - ph/0207107 , to appear in phys .
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quantum correlations are in the heart of a number of quantum effects such as quantum nonlocality @xcite , the speedup @xcite , and unambiguous state discrimination @xcite . even more , quantum correlations are the key ingredient for implementing processes between distant particles , for instance , the teleportation of unknown state @xcite and the remote state preparation @xcite . thus , quantum correlations become fundamental resources for attaining novel quantum effects . in this context , quantum correlations have been well characterized hitherto by the so - called entanglement and quantum discord @xcite .
the discord can be generated by starting from a separable classical state and using local operations and classical communication @xcite ; whereas the preparation of a bipartite entangled state requires a direct interaction of the particles at their common past .
the entanglement - swapping @xcite procedure does not infringe the above statement since it simply redistributes quantum correlation between different parts of two composed systems .
the advantage of this process lies in the fact that two factorized parts can acquire entanglement even though they are away from each other and from the other parts .
numerous are the experimental realizations reported in the literature which account for some application of the entanglement - swapping process @xcite ; recently it has been demonstrated that entanglement can be swapped to timelike separated quantum systems @xcite . in this work
we propose a generalization of the basic entanglement - swapping scheme by considering two pairs of qubits being initially correlated via @xmath0-states instead of pure ones .
we start by showing that the basic entanglement - swapping process redistributes the entanglement when we consider pure and partially entangled states . in this case ,
two of the four outcome states are maximally entangled and the other two have entanglement smaller than the input one .
this motivates us to study the process by considering two pairs of qubits prepared initially in mixed states , specifically the @xmath0-types for which there is an analytical expression for the concurrence @xcite .
we focus with special interest on analyzing the entanglement redistribution accomplished in this process .
further and major motivations for studying @xmath0-states stem from the fact that they are usually encountered in different areas ; for instance , some decoherence mechanisms can take two qubits to an @xmath0-state @xcite , two two - level atoms in the tavis - cummings model can reach a dynamics @xmath0-state @xcite , the states with minimum and the states with maximum discord for a fixed entanglement value are @xmath0-states @xcite , in condensed matter the ground state of two @xmath1-symmetry sites of a lattice is represented by an @xmath0-state as well @xcite .
this article is organized as follows : in sec . [ pure state ]
we expose the principal aspects of the entanglement - swapping process with pure states . in sec .
[ x - state ] we describe the main properties of an @xmath0-state . in sec .
[ 2xstate ] we address the entanglement - swapping scheme starting with two different @xmath0-states . in sec .
[ x state entanglement ] we analyze the entanglement swapping in the special case where the two initial @xmath0-states are equal .
some interesting and particular examples are studied in sec .
[ rhodifferent ] where the entanglement is partially redistributed .
finally , in the last section we summarize our results .
in this section we describe the principal aspects of the entanglement - swapping schemes with pure states .
let us consider the simplest case of two pairs of qubits @xmath2 and @xmath3 prepared in the bell states @xmath4 and @xmath5 ; see fig .
[ figure0 ] .
the entanglement - swapping protocol can readily be read out of the identity @xmath6 where @xmath7 and @xmath8 are the bell states of the systems @xmath9 and @xmath10 , and @xmath11 are the eigenstates of the pauli operator @xmath12 of the respective system . from ( [ swapingpure ] )
we realize that by implementing a measurement process , which projects the qubits @xmath13 and @xmath14 onto one of their bell states , then the pair of qubits @xmath15 are projected also onto one of their bell states .
each one of the four results has the same probability @xmath16 .
therefore , by projecting onto the bell basis of the qubits @xmath17 the entanglement contained in the two pairs @xmath2 and @xmath3 is redistributed to the pair @xmath15 , even though there is no interaction between them . when the two pairs of qubits @xmath2 and @xmath3 initially are in partially entangled pure states the identity ( [ swapingpure ] ) becomes @xmath18 where @xmath19 with @xmath20 .
note that by projecting the qubits @xmath13 and @xmath14 onto one of the bell states @xmath21 the pair @xmath15 is projected as well onto one of the bell states @xmath22 with probability @xmath23 , otherwise when the pair @xmath17 is projected onto one of the bell states @xmath24 the composed system @xmath15 also is projected onto one of the partially entangled states @xmath25 with probability @xmath26 . thus , even though the initial entanglement @xmath27 is not maximal , there are two possible outcome states maximally entangled
. however , the other two resulting states have amount of entanglement @xmath28 smaller than the initial ; even more , the average outcome entanglement @xmath29 is smaller than the initial one @xmath27 .
we illustrate that behavior of the redistributed entanglement in fig .
[ figure1 ] , as functions of @xmath30 .
we note that the four outcome states are maximally entangled only for @xmath31 , which is the case of the identity ( [ swapingpure ] ) .
it is worth emphasizing three affairs ; i ) the outcome entanglement is maximal with probability @xmath32 , which vanishes only at the end values @xmath33
, @xmath34 where there is no input entanglement , ii ) the probability of increasing the entanglement is always smaller than the one for decreasing it , since @xmath35 , iii ) for having entangled outcome states it is required to have initial entanglement different from zero only . finally , we want to emphasize that there is an asymmetry in the distribution of the entanglement over the four outcome states , which in the identity ( [ swapingpure2 ] ) looks with favor on the @xmath22 outcome bell states .
and @xmath14 are in the same laboratory , whereas @xmath36 and @xmath37 are spatially remote from each other and from qubits @xmath13 and @xmath14.,scaledwidth=40.0% ] of the initial states @xmath38 ( solid line ) and of the outcome ones @xmath25 ( dashed line ) and @xmath22 ( dotted line ) . the dot - dashed line corresponds to the average entanglement @xmath29 of the four possible outcome states @xmath25 and @xmath22.,scaledwidth=40.0% ]
here we review succinctly the properties of a general @xmath0-state @xmath39 of two qubits @xmath40 and @xmath41 . in the logic basis
@xmath42 the state is represented by the matrix @xmath43 in order for ( [ xstate ] ) to describe a quantum state , the matrix elements must satisfy the normalization @xmath44 and the positivity conditions , @xmath45 in what follows we consider _ fixed diagonal elements _ and we do the analysis in terms of the off - diagonal elements .
the off - diagonal elements account for the coherence degree inside two orthogonal subspaces , say , @xmath46 spanned by the basis @xmath47 and @xmath48 spanned by @xmath49 . for instance , when @xmath50 there is absolute decoherence into @xmath46 , while for @xmath51 there is a pure state into @xmath46 .
the @xmath52 element has similar meaning in the subspace @xmath48 .
accordingly , depending on the moduli @xmath53 and @xmath54 the @xmath0-state ( [ xstate ] ) goes from an incoherent superposition of the four factorized logic states to an incoherent superposition of two partially entangled pure states .
there are two special features of an @xmath0-state : i ) the @xmath0 form in itself which arises because it populates the two subspaces @xmath46 and @xmath48 without having off - diagonal terms between the elements of those subspaces , ii ) the entanglement between the two involved systems
. the entanglement can be evaluated by the concurrence @xcite , which for the ( [ xstate ] ) state is given by @xcite , @xmath55 thus , there is nonzero entanglement when one of the two following inequalities is satisfied : @xmath56 otherwise entanglement is absent . complementing inequalities ( [ rhooverrho ] ) with those for positivity ( [ positivity ] ) , leads to the following two inequations for having entanglement : @xmath57 clearly only one or none of them can be fulfilled .
we extract in the following three sentences what the inequalities ( [ eqfore ] ) are saying to us : * for @xmath58 it is necessary that @xmath59 .
* for @xmath58 it is necessary and sufficient to have a certain nonzero coherence degree inside only one subspace @xmath46 or @xmath48 , i.e. , @xmath60 , with @xmath61 .
* the coherence degree into the other subspaces , @xmath62 , does not contribute to @xmath63 ; even more , @xmath62 can be zero and even then it does not affect the amount of entanglement of the @xmath0-state . *
the entanglement dies just when the @xmath64 .
we stress that , for fixed diagonal elements , the maximum amount of entanglement is reached by satisfying condition i ) and having total coherence into only one subspace @xmath46 or @xmath48 in agreement with condition ii ) .
the inequations ( [ eqfore ] ) define , in the composed hilbert space , the border between the entangled and the separable @xmath0-states .
let us consider two pairs of qubits @xmath36,@xmath13 and @xmath37,@xmath14 .
the qubits @xmath13 and @xmath14 are in the same laboratory , in this way local and joint operations can be applied on them .
the @xmath36 and @xmath37 qubits are spatially remote from each other and from qubits @xmath13 and @xmath14 , accordingly , it is not possible to perform joint operations onto @xmath36 and @xmath37 ; see fig .
[ figure0 ] .
we assume that , at the common past , both pairs of qubits @xmath2 and @xmath3 were prepared in the @xmath0-states @xmath65 and @xmath66 , which we call input states . in the respective logic bases @xmath67 and @xmath68 the input states are represented by the matrices @xmath69 now we consider that a projective measurement is performed over the qubits @xmath13 and @xmath14 .
specifically , onto the factorized state @xmath70 is applied a von neumann measurement , which projects the pair @xmath17 onto one of the four bell states @xmath71 consequently the pair @xmath15 also experiments a projection onto one of the states @xmath72 or @xmath73 , which we call outcome states . in the logic basis
@xmath74 the outcome states are represented by the matrices @xmath75 @xmath76 [ xrhoab ] where we have defined the normalization constants , @xmath77 the probabilities of obtaining each one of the four possible outcomes ( [ xrhoab ] ) are @xmath78 and @xmath79 .
we can note that the four possible outcomes , @xmath72 and @xmath73 , are @xmath0-states as well .
this means that the @xmath0-feature of the input states of pairs @xmath2 and @xmath3 is swapped to the state of the pair @xmath15 .
the diagonal elements of the outcomes ( [ xrhoab ] ) depend only on the diagonal elements of the input state , and the off - diagonal elements of ( [ xrhoab ] ) depend on the off - diagonal elements of the input states .
thus , both terms @xmath80 and @xmath52 affect and contribute to the coherence into both subspaces @xmath46 and @xmath48 of the pair @xmath15 .
the two states @xmath81 and @xmath82 are equivalent by means of local unitary operators , say , @xmath83 or @xmath84 ; this means that they have equal amounts of quantum correlation .
similarly , the states @xmath85 and @xmath86 are equivalent with the same local unitary operators
. however , the two states @xmath87 , in general , are not local - unitarily equivalent to the two @xmath88 states .
therefore , in this process the entanglement is distributed probabilistically with concurrence @xmath89 in the two outcomes @xmath87 and with @xmath90 in both states @xmath88 , which , in general , are different .
this asymmetric distribution is reminiscent of the case exposed in sec .
[ pure state ] for pure states . from eqs .
( [ xrhoab ] ) we realize that the matrix elements of @xmath65 are transferred to the outcome states of pair @xmath15 when the state @xmath91 . in this particular case ,
the states @xmath87 are local - unitarily equivalent with the @xmath88 states respectively by means of the local unitary transformation @xmath92 or @xmath93 .
this means that in this process , all the features of the @xmath0-state @xmath65 are transferred to the state of the two remote qubits @xmath36 and @xmath37 . in order to simplify the analysis and to shed some light on the principal aspects and the scope of this scheme , in the next sections we restring it to the case with elements of the matrices ( [ xstates ] ) equal , i.e. , @xmath94
in what follows we analyze the entanglement redistribution from @xmath2 and @xmath3 pairs to the @xmath15 system , when both initial @xmath0-states ( [ xstates ] ) are alike , i.e. , @xmath94 . in this case , the concurrences of the respective outcome states ( [ rhoabphi ] ) and ( [ rhoabpsi ] ) become @xmath95 [ cabs ] where we have defined the function @xmath96 with @xmath97 and @xmath98 being the phase of the off - diagonal elements , i.e. , @xmath99 . the concurrence @xmath100 does not depend on the phases @xmath98 and it is higher than @xmath101 for all values of @xmath102 . in addition to having asymmetrically distributed the entanglement over the outcomes , the probability @xmath103 of having @xmath100 is smaller than the one @xmath104 of having @xmath101 .
the concurrence @xmath101 reaches its maximal value at @xmath105 and the minimum for @xmath106 . taking into account that the relative phases @xmath98 can be managed by properly choosing the axes on the bloch sphere of the qubits
, we can assume @xmath107 , which leads to @xmath105 .
in this case the concurrences ( [ cabs ] ) become @xmath108 [ cpshi0 ] from these expressions we find that the four outcome states ( [ xrhoab ] ) are entangled if the matrix elements of the input states satisfy the inequality @xmath109 whereas the entanglement is present only in two outcome states ( [ rhoabpsi ] ) if the following inequalities hold : @xmath110 otherwise the four outcomes states are separable . by making a detailed analysis of the inequalities ( [ positivity ] ) , ( [ rhooverrho ] ) , ( [ eqfore ] ) , ( [ ineinf ] ) , and ( [ algo ] ) we can asseverate what follows : * if the input states @xmath65 and @xmath66 are not entangled then @xmath111 and @xmath112 . the suitably multiplication of the respective terms of these inequalities with those for positivity @xmath113 and @xmath114 leads to @xmath115 and @xmath116 . adding them we obtain that @xmath117 , which means that the right hand side inequality of expression ( [ ineinf ] ) is not fulfilled .
this means that , if the input states lack entanglement , then the four outcome states are separable .
+ additionally , the fact that the concurrence @xmath63 of the input states is different from zero does not guarantee that the outcomes states are entangled . specifically , by considering that @xmath118 , we find that : * only the two outcome states @xmath119 have entanglement different from zero if @xmath120 * the entanglement is present in the four outcome states @xmath119 and @xmath121 if @xmath122 the two threshold concurrence values are @xmath123 these threshold values are decreasing functions of the off - diagonal element @xmath124 , which does not affect the amount of @xmath63 .
therefore , we can realize that , when the input states have entanglement , the off - diagonal term @xmath124 now plays an important roll for achieving the task of having entanglement in the outcomes .
in fact , it allows to decrease the threshold values and to increase the outcomes entanglement . in other words
, the coherence degree inside the respective subspace helps to increase the entanglement of the outcome states , when the input states have entanglement , of course .
consequently , the outcome concurrence ( [ cpshi0 ] ) reaches the maximum value when there is maximal coherence inside both subspaces @xmath46 and @xmath48 , namely @xmath51 and @xmath125 .
therefore , in this case and for fixed diagonal elements , the highest outcome concurrence is @xmath126 and the smallest outcome concurrence becomes @xmath127 here , we easily note that @xmath128 is higher and @xmath129 is smaller than the input one @xmath63 .
note that ( [ cmax3 ] ) is different from zero when @xmath130 and @xmath131 or @xmath132 and @xmath133 , which are conditions for having initial entanglement , in agreement with inequality ( [ algo ] ) evaluated for maximal coherence .
it is worth emphasizing that , in order to get in the process maximal outcome entanglement , it is required to manipulate the initial states ( [ xstates ] ) in such a way that @xmath107 .
this can be done by applying the local unitary operation @xmath134 to the @xmath13 and the @xmath14 qubits , before performing the measurement procedure .
here we have found two threshold concurrence values , conditions for which this scheme allows redistributing entanglement onto two remote qubits .
the entanglement is distributed asymmetrically onto four possible outcomes , thus having probabilities different from zero of increasing and decreasing it with respect to the initial entanglement .
moreover , the probability of increasing it is smaller than the one for decreasing it .
we show two examples which illustrate the effect produced by the smallest module of the off - diagonal term of the input states on the outcome entanglement . in the cases with werner states and with @xmath135-states the module @xmath136 ; consequently the outcomes demand input states with finite entanglement . in the case with input @xmath137-states the module @xmath138 ; accordingly the outcome entanglement arises for all @xmath139 similarly to the input state .
the relation between discord , entanglement of formation ( eof ) , and linear entropy was addressed in ref .
a. al - qasimi and d.f.v .
james found the states for which discord takes extreme values for a given entropy or given entanglement .
the upper bound of entanglement - discord relation is given by the @xmath135-state for @xmath140eof@xmath141 .
the lower bound of that relation is satisfied by the @xmath137-state for @xmath140eof@xmath142 .
thus , in this section we analyze the outcome states ( [ xstates ] ) when input states are both @xmath135 or both @xmath137 . before developing these examples
, it is worth taking a gander to the case when the input states are the well - known werner states @xcite : @xmath143 , with @xmath144 . in this case
, the input states are not separable for all @xmath145 ; the two threshold concurrence values are equal , @xmath146 . considering the asseveration c ) of sec .
[ x state entanglement ] , the four outcome states are entangled when @xmath147 , which holds for @xmath148 . the @xmath135 state corresponds to an @xmath0-type given by @xmath149 where the @xmath135 real parameter goes from @xmath150 to @xmath34 and @xmath151 and @xmath152 are the bell states . at @xmath153 the @xmath154 state is an incoherent classical state and at @xmath155 is the bell state @xmath156 .
the concurrence @xmath157 of @xmath154 is @xcite @xmath158 the @xmath154 state is separable for all @xmath135 between @xmath150 and @xmath159 and is entangled for @xmath160 . in this case , the four outcome states ( [ xstates ] ) are local - unitarily equivalent and given by @xmath161|\phi_{ab}^{+}\rangle\langle\phi_{ab}^{+}| \\ & & + \left[\frac{\alpha^{2}+\left(1-\alpha\right)^{2}}{2}\mp\frac{\alpha^{2}}{2}\right]|\phi_{ab}^{-}\rangle\langle\phi_{ab}^{-}| , \\
\hat{\rho}_{ab}^{\psi^{\pm}}\left(\alpha\right)&=&\sigma_x^{(a)}\hat{\rho}_{ab}^{\phi ^{\pm } } \left ( \alpha \right)\sigma_x^{(a)}.\end{aligned}\ ] ] the common concurrence of them is @xmath162 on the other hand , for the input state ( [ alpha ] ) the two threshold concurrence values are equal , @xmath163 , with @xmath164 therefore , the outcome entanglement arises when @xmath165 , which holds for @xmath166 .
[ figure2 ] illustrates this behavior showing @xmath157 , @xmath167 , and @xmath168 as functions of @xmath135 . .
@xmath157 ( solid line ) , @xmath167 ( dashed line ) , and @xmath169 ( dotted line).,scaledwidth=40.0% ] the @xmath137-state is a particular @xmath0-type given by the expression @xmath170 where @xmath137 is a real number going from @xmath150 to @xmath34 ; at both ends it becomes a bell state and is separable at @xmath171 .
its concurrence @xmath172 is @xcite @xmath173 in this case , the outcome states ( [ xrhoab ] ) become @xmath174|\phi^\pm_{ab}\rangle\langle\phi^\pm_{ab}| \\ & & + 2\beta(1-\beta)|\psi_{ab}^\pm\rangle\langle\psi_{ab}^\pm| , \\ \hat{\rho}_{ab}^{\psi^{\pm}}(\beta)&=&\sigma_x^{(a)}\hat{\rho}_{ab}^{\phi^{\pm}}(\beta)\sigma_x^{(a)}.\end{aligned}\ ] ] we note that the four outcomes are @xmath137-states with the @xmath137 parameter changed by @xmath175 .
the common concurrence of the four outcomes states is @xmath176 which is just the square of the input one .
the threshold concurrence values for @xmath177 are equal , @xmath178 , and given by @xmath179 according to asseveration c ) of sec .
[ x state entanglement ] four outcome states are nonseparable when @xmath180 , i.e. , there is outcome entanglement for all @xmath181 .
[ figure3 ] shows the behavior of @xmath172 , @xmath182 , and @xmath168 as functions of @xmath137 . .
@xmath172 ( solid line ) , @xmath182 ( dashed line ) , and @xmath168 ( dotted line).,scaledwidth=40.0% ]
in summary we propose a generalization of the simplest scheme for entanglement - swapping beyond pure states . basically the generalization is based on performing a von neumann measurement on two local qubits , but in this case , each one being correlated through an @xmath0-state with a spatially distant qubit .
this process swaps the @xmath0 form of the input states without conditions .
when one of the inputs is a bell state then the other input @xmath0-state is swapped fully to the remote qubits .
the input entanglements are , in general , partially distributed in the four possible outcome states under certain conditions . when the input states are equal , we obtain two threshold concurrence values which have to be overcome by the input state entanglement in order for the outcome states to be non - separable . in addition , in this case , we find that there are two possible amounts of outcome entanglement , one is greater and the other is less than the input entanglement ; the probability of obtaining the greatest outcome entanglement is smaller than the probability of attaining the least one .
finally , we would like to emphasize that the asymmetric redistribution of the entanglement holds also in the case with pure states , but the _ threshold - concurrence - values _ effects are onset only for mixed @xmath0-states , thus being a consequence of the nonzero decoherence of the input states .
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a * 40 * , 4277 ( 1989 ) . | arxiv |
Above-the-ground pool slope pressure calculation
I'm not sure this is the right place to ask this "homework" question, but I have a real life problem that requires calculation and I do not have the math knowledge to make them myself.
I have bought an above-the-ground pool, with dimensions of 2x4 meters and water level of 1 meter. The image below describes exactly the model I have.
[](https://i.stack.imgur.com/mh4QQ.jpg)
The only place I have to install it has a slope that will result in a 10cm difference in water level. The difference is between the narrow side of the pool. In other words if I will fill the pool with 1 meter water level, on one 2 meter side the water will be 1 meter high and the other side it will be 0.9 meter high.
From my understanding this difference will create more pressure on the wall with the higher water level.
My question is, what water level should I achieve on the higher end so that the pressure on this wall would be as it would have to be if the pool would be on a flat surface with 1 meter water level
Thank you so much for the help.
The pressure on any part of the wall is solely dependent on the depth of the water ***at that point***.
Yes, the force on the "deep-end" wall **will** be greater. **Greater than the force on the shallow end wall.**
But if you keep the deep-end wall filled to the same $1$ metre depth, there will be exactly the same pressure at each point on the wall, no matter what happens in the rest of the pool.
Dimkin- I agree with your concern and have a similar situation. The problem isn't the pressure on the deeper end (which is actually the designed depth) but the LACK of horizontal pressure on the less deep end. This causes the deep end to force the top support ring outward while pulling the less deep end inward creating unequalized support which could force the wall to collapse towards the deep end.
| stackexchange/physics |
Cameron Kenneth Ward born February 29, 1984 is a Canadian former professional ice hockey goaltender. He played the majority of his fifteen-year professional career for the Carolina Hurricanes of the National Hockey League NHL. He most recently played for the Chicago Blackhawks during his final season before signing a one-day contract to officially retire as a Hurricane in 2019.
Ward was born in Saskatoon, Saskatchewan, growing up there and in the Edmonton suburb of Sherwood Park, Alberta. During his three-year junior career in the Western Hockey League with the Red Deer Rebels WHL, he was selected 25th overall by the Hurricanes in the 2002 NHL Entry Draft. After a season with the Hurricanes' American Hockey League AHL affiliate, the Lowell Lock Monsters, he won the Stanley Cup with the Hurricanes in 2006, winning the Conn Smythe Trophy as the most valuable player in the playoffs. He became the first starting goaltender to win the Stanley Cup as a rookie since Patrick Roy in 1986.
Playing career
Early career
Ward spent his junior career with the Red Deer Rebels of the Western Hockey League WHL. After appearing in one game for the Rebels in 200001, Ward played three full seasons with the team from 20012004, leading them to the WHL finals twice. Ward was drafted 25th overall by the Carolina Hurricanes in the 2002 NHL Entry Draft. Upon graduating from the WHL, Ward signed a multi-year, entry-level contract with the Hurricanes on May 13, 2004. Due to the 200405 NHL lockout, he was assigned to Carolina's American Hockey League AHL affiliate, the Lowell Lock Monsters, for the season.
Carolina Hurricanes
Joining the Hurricanes for the 200506 NHL season, Ward largely served in a backup role to Swiss goalie Martin Gerber during the regular season. He made his NHL debut on October 5, 2005, replacing Gerber after the starter injured his hamstring. He saved 10 of 11 shots in the third period, as the Hurricanes lost 52 to the Tampa Bay Lightning. He made his first NHL start the following game two days later in the club's home opener against the Pittsburgh Penguins. Ward turned aside Mario Lemieux, Žigmund Pálffy and Sidney Crosby in a shootout, as the Hurricanes won 32. Ward completed his NHL rookie season with 14 wins and 8 losses, along with a 3.68 goals against average.
In the opening round of the 2006 Stanley Cup Playoffs, the Hurricanes faced a two-win deficit against the Montreal Canadiens. With Gerber struggling in the series, Hurricanes coach Peter Laviolette turned to Ward. The goaltending switch prompted Carolina to a series comeback, advancing to the second round against the New Jersey Devils, where he played opposite his personal hero, Martin Brodeur. After eliminating the Devils, the Hurricanes defeated the Buffalo Sabres in seven games. Facing the Edmonton Oilers in the 2006 Stanley Cup Finals, he helped the Hurricanes to the franchise's first Stanley Cup. In doing so, he became the first rookie goaltender to lead his team to the Stanley Cup as a starter since Patrick Roy in 1986. Against Edmonton, he also became the first rookie goaltender to both play and record a shutout in the Finals since Roy. He tied the rookie record for wins in the playoffs 15, previously held by Roy and Ron Hextall, and became the first rookie goalie to win the Conn Smythe Trophy since Hextall in 1987.
After his heroics in the 2006 Stanley Cup Playoffs, Ward became the Hurricanes starting goaltender for the 200607 season. He recorded season stats of 30216 and 37255 in the 200607 and 200708 campaigns, respectively. The Hurricanes would miss the playoffs both years. The Hurricanes, however, would reach the Eastern Conference Finals in the 200809 season before bowing out to the eventual Stanley Cup champion Pittsburgh Penguins. Ward went 810 with a 2.67 GAA during the playoffs.
Ward and the Hurricanes struggled to begin the 200910 season, as Ward went 293 to start the campaign. On November 8, 2009, in a game against the Columbus Blue Jackets, Ward was injured when he was cut on the leg by the skate of opposing forward Rick Nash. As Ward was helped into the dressing room, he left a trail of blood on the ice. After returning from his injury, Ward finished the season with an 18235 record, a 2.69 GAA and .916 save percentage as the Hurricanes failed to qualify for the post-season.
Ward was selected to participate in the 2011 NHL All-Star Game, along with teammates Eric Staal, Jamie McBain, and Jeff Skinner. Ward was the first overall pick in the 2011 NHL All-Star Game Fantasy Draft, selected by All-Star Game captain, Eric Staal.
Ward was credited with an empty-net goal against the New Jersey Devils on December 26, 2011, when a misplaced pass from Ilya Kovalchuk found its way into the empty goal after a rebound from Ward. He is the tenth goalie in NHL history to do this.
Ward recorded his 500th game with the Carolina Hurricanes on February 27, 2015.
During the offseason, Ward re-signed with the Hurricanes to a two-year, $6.6 million contract on June 16, 2016.
On March 22, 2018, during a game against the Arizona Coyotes, the puck got stuck in his skate without his knowledge. His skates crossed the goal line when he went back into the net, ultimately resulting in an own goal. Despite this, the Hurricanes ended up winning that game 65.
Chicago Blackhawks
On July 1, 2018, Ward signed a one-year, $3 million contract with the Chicago Blackhawks. He went 16124 in 33 appearances for the team during the 201819 season.
Retirement
On August 28, 2019, Ward signed a one-day contract with the Hurricanes and subsequently retired from professional hockey. He retired as the Hurricanes' franchise leaders in wins 318 and shutouts 27.
International play
Ward's performance in his NHL rookie season earned him consideration on a list of 81 candidates to play for Team Canada in the 2006 Winter Olympics. He was one of nine goalies selected; he was not, however, named to the Canadian squad. Additionally, Ward was named a part of the summer camp roster for Team Canada in preparation for the 2010 Winter Olympics, but did not make the final roster cut.
Ward was a member of the Canadian team that won gold at the 2007 IIHF World Championship in a 42 win against Finland in Moscow, as well as a member of the team that won silver at the 2008 IIHF World Championship in a 54 loss to Russia.
Personal life
Born in St. Paul's Hospital in Saskatoon, Saskatchewan, Ward is the second child of Ken and Laurel Ward. He grew up in the Lakeridge neighbourhood of Saskatoon and the Edmonton suburb of Sherwood Park, Alberta, spending his adolescent years in the latter. He attended junior high at F.R. Haythorne Jr. High School and high school at Salisbury Composite High School in Sherwood Park, until he graduated.
Ward is a fan of his native province's team the Saskatchewan Roughriders of the Canadian Football League CFL.
On March 25, 2007, Ward shaved his head for the St. Baldrick's Foundation.
Ward and his wife Cody have a son and a daughter.
Career statistics
Regular season and playoffs
International
Awards and achievements
200001 Bill Ranford Trophy, Red Deer Rebels Rookie of the Year
200102 CHL Second Team All-star, Del Wilson Trophy
200304 CHL First Team All-star, Del Wilson Trophy, Four Broncos Memorial Trophy
200405 AHL All-Rookie Team
Conn Smythe Trophy NHL Playoff MVP 2006
2006 NHL Stanley Cup Champion Carolina Hurricanes
IIHF 2007 World Championship Gold Medal
NHL All-Star Game 2011
See also
List of goaltenders who have scored a goal in an NHL game
List of NHL goaltenders with 300 wins
References
External links
Cam Ward biography at The Goaltender Home Page - advanced statistics and game logs
Category:1984 births
Category:Living people
Category:Canadian evangelicals
Category:Canadian ice hockey goaltenders
Category:Carolina Hurricanes draft picks
Category:Carolina Hurricanes players
Category:Charlotte Checkers 2010 players
Category:Chicago Blackhawks players
Category:Conn Smythe Trophy winners
Category:Ice hockey people from Alberta
Category:Ice hockey people from Saskatchewan
Category:Lowell Lock Monsters players
Category:Members of the Christian and Missionary Alliance
Category:Memorial Cup winners
Category:National Hockey League All-Stars
Category:National Hockey League first round draft picks
Category:National Hockey League goaltenders who have scored in a game
Category:Red Deer Rebels players
Category:Sportspeople from Saskatoon
Category:Sportspeople from Sherwood Park
Category:Stanley Cup champions | wikipedia |
Lion King 1. No Blood, Just Dust
**A/N: I know i said i would wait, but i really wanted to do this story. I'll still finish up The Female Lands. Anyway, i won't keep you waiting long. I hope you enjoy!**
* * *
"There had been numerous incidents in the Pridelands about a rogue leopard killing the animals." Zazu said to Simba, flying right next to him. Simba had seen a resident almost near death telling him about the leopard. It's not unusual for a leopard to do this-due to their aggressive nature-but, this one had glowing red eyes. That's something really new.
He got to the spot that the resident told him about, but didn't see a leopard. Was it just their imaginations? He went inside of a nearby cave just in case. When, he was inside, there was an unearthly shrill. He looked around and didn't see anything. Then, out of nowhere, something tackled him down.
He looked up and saw the rogue leopard. Just like he said the leopard's eyes were a deep red. Simba kicked the leopard. It back flipped in the air and landed perfectly on the ground. Simba snarled, "What're you doing here?"
It growled in Swahili, "Je, udhi mimi, hali ya kufa! (Do not vex me, mortal!)"
Simba looked confused. _Why did he call me a mortal?_
The leopard roared and pounced at Simba. He tossed the leopard like he did with Scar, and pinned him down. He slashed the leopard's stomach and thick red dust came flying out. He coughed. After a little while, the leopard disappeared. Zazu came up to him and praised, "Good job, sire. You sent the leopard running off."
Simba sighed, "Yeah….I…d-d,"
Before he could finish, he passed out. Zazu flew up and exclaimed, "Oh gods, don't worry Simba; I'll go find help!"
He flew off and went back to the pride.
* * *
_Pride Rock-20 minutes later_
Simba woke up with everyone looking at him. Kovu looked over at him. He sighed in relief. "Thank the gods, you're fine. We had someone perform CPR on you, just in case."
Simba got up and looked at Nala. Before he could say anything, she shook her head. He then looked at Kiara. She also shook her head. The whole pride shook their heads. He looked down at Zazu. He just gave him a disgusted look. _Please, shake your head. _He hesitated ever so much, but managed to look at Kovu. Kovu just gave him a smile. Anger boiled inside of Simba than ever before.
He tackled Kovu down. Kovu gasped. Simba's eyes glowed red. He whispered, "Don't push me Kovu."
Simba slashed Kovu across the face. The cut burned badly. Nala gasped, "Simba, why did you do that?"
She pushed Simba off of Kovu and helped him up. She turned around. Simba's expression was just full of anger. But, it was kind of dark this time. He walked past her and went into the den. Kiara went up to her mother. She asked, "Are you okay? Is there something wrong with daddy?"
Nala kept a blank stare on her face. _What's wrong with him? Is it from stress? _
Kiara shouted, "Mom!"
That got her attention. She sighed, "I don't know, Kiara."
Kiara just looked down. She went over to Kovu and started cleansing his wound. Nala looked back at the den. She whispered, "You're taking a day off Simba."
* * *
_Next Morning_
Simba woke up and no one was in the den. _Oh no! I slept in!_ He quickly took off out of the den. Zazu got in front of him and greeted him, "Good morning, Sire. You seem to be in a rush."
Simba explained, "I slept-in. Have they started patrolling the borders or anything like that?"
Zazu nodded and informed, "Queen Nala decided to give you a break. She thought that you were working too hard. I don't blame her; you completely went berserk on Kovu."
"Well, I do that _all_ the time." Simba laughed. Zazu laughed along with him. He instantly got serious. "I do know that, but it was different. You usually wouldn't harm him or at least damage him _that_ badly."
Simba started getting confused. _I attacked him?_ He asked, "I attacked Kovu? I only remember getting on top of him and that's it."
He flew on to Simba's shoulder. "You see, your stress is making you forgetful. Just rest for today Simba."
He nodded. _Maybe they're right. I do need a break._ Zazu flew off. Simba sighed and went down Pride Rock. He decided to go to his favorite spot when he was a cub.
* * *
When he got there, there was a family of gazelles lying in the shade. He sighed, "Guess, I can forget about that."
_**What're you doing? You had that spot since you were just a prince. So, you basically own it!**_
"I guess I do. But, they're using it. I can give it up for _one_ day."
_**No you don't! Like Nala said, you need to relax. What better way to relax is taking back what's yours?**_
He thought for a few seconds and agreed, "You know what you're right!"
_**No that that's a big surprise. Now, go get 'em, champ. Also, no mercy.**_
Simba took a deep breath and walked over to the gazelles. He lowered his head and said as politely as he could, "Excuse me, I think you need to move."
The female looked at Simba. She smiled sheepishly. "Oh sorry, King Simba. We'll move as soon as we're ready."
He sucked his teeth. "That won't work, because I kinda need this spot, like, _now_."
"There are not really many shaded spots in the Pridelands, ever since the dry season came."
"Well, that's not my problem."
_**Good job, Simba.**_
The gazelle was now irritated. She snorted, "My patience is gone! We are **not** moving, Simba!" The two fawns went behind their mother.
A few feet away listening to the conversation was Kovu. He was crouched behind a rock. He couldn't believe what he was hearing. _What's up with Simba?_
Simba laughed, it was more demonic and crazy. "I'm the king. You follow _my_ orders."
"I don't care. Queen Nala, Queen Kiara, or King Kovu wouldn't agree with this. What do you have to say?"
Simba was taken aback. He didn't know what to do. The voice in his head spoke again:
_**Desperate times calls for desperate measures, Simba; even if it is graphic. Don't you agree?**_
Simba looked back at the gazelle. She smiled, knowing that she won. He whispered, "Absolutely."
_**Then do it!**_
He tapped the gazelle's shoulder. She gave him a glare. He apologized, "I'm sorry for the way I acted. Can I settle this with your husband?"
She looked kind of confused. She sighed, "Mu husband died. I'm sorry, for acting the way I did."
Simba nodded. He walked away from the family. Kovu smiled. _Oh thank the gods; I thought he was going to do something resentful. He was just being his regular douche self._ He was about to walk away, until he saw Simba crouch down out of the corner of his eye. He turned back around.
Simba smiled, evily. He sprinted at the mother gazelle. She barely even got to move. Simba got up to her and bit down into her neck, right in front of the two fawns. She struggled to get out the grip, but it was pointless. After a few seconds, her body went limp. He set her lifeless body down. The two fawns were shaking. He smiled at them. He got down and whispered coldly, "I'd run if I were you."
The two ran away. They saw Kovu and ran up to him. They wouldn't survive on their own. One of them asked, "What's wrong with King Simba? Is he ill?"
Kovu looked back at Simba. For some weird reason, a cold chill went up his spine.
_**Well done Simba. I couldn't have done it better. Doesn't it feel better this way? Everyone cowering at your paws. **_
Simba smiled. He chuckled, "Why didn't I do this before?"
He laughed evily to himself. Kovu stared at him with wide eyes. He looked down at the two fawns. He sighed, "I don't know what's wrong with him. But, I'm gonna find out."
* * *
**Did you like it? Should i continue on? Every little review counts.**
**Disclaimer: I don't own any Lion King characters.**
2. I'm Kifo
Kovu walked over to Simba calmly as possible. The two fawns followed behind him slowly. Kovu greeted, "Hey Simba! How are you?"
He answered, "I feel great! Why?" He started sounding more suspicious at the ending. Kovu hesitated, "Well, you see…these fawns told me you killed their mother," He pointed at the two babies, "I just wanted to make sure that fact was correct."
Simba glowered at the two fawns. He sighed, "Must've been a mistake."
One of the fawns shouted, "Liar!"
The other consoled, "Tara, calm down."
"He's lying!" Tara shouted.
Simba growled at them. Kovu has had enough. He growled, "Simba, I _know_ you killed their mother. You didn't need to do that! Do you honestly think that was the right thing to do?"
Simba thought for a little bit. _Was that the right thing to do?_
**_Of course it was! She wasn't obeying the king's orders. Say it!_**
Simba repeated, "Of course it was! She wasn't obeying the king's-I mean my orders!"
Kovu just stared at him. He was confused. He enunciated, "You, argued, over, a fucking, spot! Simba, stop being an idiot, and listen to yourself. This isn't the Simba I love to play pranks on, make fun of, call him names, smart mouth…what was I talking about?"
**_Clearly this idiot doesn't need to be in our presence. Command him to leave._**
Simba sighed, "Whatever Kovu. There's no way you can bring their mother back. Go away."
He shook his head. "This isn't you."
"I said leave, Kovu!"
"Just calm down and listen."
**_He's not listening, Simba! Now's our chance! You have to take back what's yours!_**
**_"Take back what's ours!"_** Simba said in a raspy demonic voice.
Kovu's eyes widened. "Holy fucking," He didn't get to finish. Simba made a half eagle screech, half lion roar noise. Then, his eyes started glowing red. _It wasn't my imagination._
Simba swung at Kovu. He backed up and ordered, "Go! RUN!"
The two started running away. Simba stepped away from Kovu and started running after the fawns. Kovu had to think quickly, so the cubs don't get killed. He called, "Hey, King Cunt!"
Simba turned around and glared at Kovu. He continued, "I bet your mother has a silicon butt!"
Simba growled, ran up to Kovu and swiped at him. He got out the way on time. He missed and hit the tree. The tree broke. Kovu stared at the tree and went back to Simba. _There's definitely something wrong with him._ It didn't take long for him to run away. Simba easily caught up with him. He pushed himself a little harder. Only to run into a cave and get stuck.
Kovu searched for an opening but, couldn't find one. Simba came in growling. He begged, "C'mon Simba, we're frenemies. You haven't acted _this_ murderous to me before. Then again, I remember one night, you tried choking me, but you fought back…behind a bunch of lionesses blocking you from me. You know what; I don't think this is helping."
He groaned, **_"I understand why Simba hates you so much. You're extremely irritating!"_**
"I'm not irritating." Kovu doubted.
**_"He's already thinking of million different insults for you. Not to mention different ways to kill you."_**
"That's kind of ironic, I tried killing him in the movie…I mean before I was welcomed in the pride."
Simba shouted, **_"ENOUGH!"_**
Kovu instantly got quiet. Simba advanced toward Kovu. He started crouching down, trying to get far away as possible. All the sudden, someone called, "Simba, Kovu? Where are you guys?"
Kovu recognized it as Kiara. He laughed, "Hah! You'll definitely get caught, especially with those glowing eyes and weird voice. And not to mention that weird screech. What's up with that? More importantly, where can I get one?"
Simba shut his eyes tightly and opened them up. The red glowing eyes disappeared. They were replaced by his normal color. He kicked Kovu forward; he looked back at him confusingly. He ordered, "Keep moving, mortal." His voice was back to normal to.
Kovu complained, "You changed back to Simba's douchey self. That's not fair. Now I _have_ to deal with you."
Kovu walked out of the cave, with Simba right behind.
* * *
_Outside_
Kiara hadn't seen them ever since the hunting party got back. She got bumped into. She looked over and saw Kovu and Simba. She smiled. "Oh there you guys are!"
She nuzzled Kovu. Simba started growling. He shook his head. He asked himself, "Why am I doing this?"
Kiara looked at her father weirdly. She asked, "Daddy, are you okay?"
Simba just blinked. Then, he realized she was talking to him. He chuckled, "Of course I am, why?"
She just shrugged. Kovu asked, "Kiara we'll go to Pride Rock in a few minutes, can you give us a minute?"
She nodded and started heading back. Kovu turned to Simba. Simba just smirked at him. He asked, "Okay. Who are you? What happened to Simba?"
He answered, "Simba's still here, he just realized what's best for him. As for me, I'm Kifo. Lord of the Dark Pits of Tartarus."
Kovu added, "You also Lord of the Really Long Names. Seriously, why don't you just say Lord of the,"
Kifo shouted, "**You will be silent!**"
"Okay, I'll shut up."
He sighed and continued, "I was using the body of a leopard, until I saw your precious king. Why didn't I use him before? He already is King. Basically, I can already command everyone to do my bidding."
Kovu spat, "So? You're king, big deal. Is that really your plan?"
Kifo laughed. It sent chills through Kovu's body. He explained, "I would reveal my plan to you, but you'll _have_ to do better than that. Now, if you don't mind I have a kingdom to rule."
He was about to walk away, until he forgot to mention something. "Oh and by the way, by the night of the full moon you'll never see your...gracious king again."
Kovu gasped. "But, that's only three days away. It doesn't matter, I'll awaken Simba."
He laughed again. "Oh please, _you_. Don't make me laugh."
Kovu whispered, "But, you laughed twice already."
With that, Kifo walked away. Kovu stayed there, thinking. _I have to get Simba back. But, how?_
* * *
**Will Kovu be able to break the curse in time? Or will Simba be lost forever? I guess you'll never know. Did you like this chapter? Please Review!**
**Disclaimer: I don't own any Lion King characters. I only own the two fawns and Kifo**
3. Need To Know More
**A/N: I want to say i'm extremely sorry for the wait. I had kind of a hard time updating this story. I've been trying to update my other stories. Hopefully, it won't take me so long to write another chapter. Also, i want to say school is about to start up soon for me, so it may take me longer to update any of my stories. Anyway, enjoy!**
* * *
_Next Morning_
Kovu paced around the den, trying to figure out how to free Simba. _I don't know what'll awaken him. I only have two days left. And what's his whole plan? Ugh! This is so much easier with Simba. _On cue, Simba/Kifo walked into the den. Kovu walked up to him and asked, "Is this Simba or Kifo?"
He asked, "I didn't think you could reach higher levels of being a retard."
"Oh thank the Great Kings! It's you Simba. I thought you were Kifo." He chuckled. Simba just gave him a lost look. Kovu noticed it. He asked, "Do you remember killing a gazelle and almost killing her fawns?"
Simba just laughed. "I don't remember doing something like that."
"Okay?" He was really confused. Does Kifo just come up randomly? It was one of those things that are hard to tell. He looked into Simba's eyes and he swore he saw a little evil glare. It could be just him. Simba pleaded, "Please, don't be gay."
He shook his and got back into reality. Seeing Simba's discontent expression, he just nodded to him. He gave him one last weird look and left the den. Kovu sighed, "I'm so confused. One minute, he's Simba. The next, he's Kifo. Well, I guess it won't be hard telling the difference. But, I'll worry about that later. Right now, I have-"
He got interrupted by a shout, "Why are you acting this way!" It was coming from outside. He started walking out.
* * *
_Pride Rock-Base_
Kovu went down, he saw Nala and Simba. _What's this all about?_ He hid into the shadows, but leaned in to hear it a little better. Simba answered, "I'm not acting any different; it's just that I think this is mostly a lioness' job. I mean, they do the work for me."
She growled, "Yes, but you must also pull your weight, Simba. Patrolling the borders is a king's duty."
He rolled his eyes. "Are there lionesses down there?" He asked. She restrained from choking the hell out of him. She mumbled a little, "Yes, there are."
"So, just let them do it. It won't make a difference. Plus, there are more of you, so that means you'll cover more ground." He explained.
Nala groaned in defeat. Despite the fact that she's queen, she still needed to follow some kingly orders. She sighed, "I'll go tell them. I hope you straighten your act."
She ran back to the borders to tell the others their duties. Simba sat there and just laughed. Kovu furrowed his brow. He scoffed, "Dumb lionesses. When I'm at my full power, they'll find their place." He paused for a bit and continued, "I know you're behind me Kovu."
Kovu jumped down and asked, "Simba, don't you know you're doing something wrong? You're nothing like this!"
Kifo laughed. He groaned, "Will you stop doing that? I know it doesn't seem like I'm the one to get Simba back."
"It seems like Simba knows that as well. You two aren't great friends, are you?" He asked. Kovu answered, "We have a complicated relationship."
"You're gay."
"NO! Why does everyone say we're gay?" He shouted. It seemed like everyone they crossed they would suspect them to be a couple. "It doesn't matter I will get him back."
Kifo rolled his eyes. "And how are you gonna do that?"
Kovu shouted, "Simba I fucked up your wife!"
Instantly, he got knocked back and the two went rolling across the ground. He roared, "**I'm gonna kill you Kovu!**"
He choked out, "Yes…you're back. Stop…choking….me"
"You had sex with Nala!"
"I lied!" He shouted/coughed. Simba got off Kovu and snarled at him. He growled, "Next time, whether it's a lie or not, I'll…fucking…kill you!"
Simba walked away from him, extremely pissed. He started following him. "Go away!" He shouted. But, he didn't listen to him. He said, "I need to make sure you don't…change. You also told Nala to tell the lionesses to patrol the borders, since it's their job."
His eyes widened. _Nala's gonna kill me! Then after she's done, the rest of the lionesses will do the same!_ He started sprinting towards the borders. Kovu started running after him, but he wasn't fast enough so he just let it go. He sighed, "I'll just leave him alone. I need to know who exactly this Kifo is. The only one who I know that can tell me this is…Rafiki."
He started sprinting off to Rafiki's home. If anyone knows anything about spirits and mythical weird things, it's that crazy shaman. Hopefully he'd get some answers.
* * *
**Do you think Kovu will get his answers? Will he stop Kifo before it's too late? Stay tuned! Please review!**
**Disclaimer: I don't own any Lion King characters, settings, or any of that jazz. I only own Kifo.**
4. Epic Ending
**A/N: SORRY! I'm very very sorry. I didn't mean to wait this long. Anyway, i want to thank everyone who reviewed and read this story. But, now it's ending. I hope you enjoy the epic conclusion.**_
_
* * *
_Rafiki's Tree_
Kovu had just told Rafiki what's been going on with Simba. Rafiki said, "I have heard of this spirit Kifo, in many different tales."
That made a tiny spark of hope for Kovu. "Do you know what he's planning? Anything?" He asked. Rafiki got some black powder from a gourd and threw it up. It made a figure of a menacing looking lion. He explained, "Kifo is the spirit of the dead. Usually, Kifo enjoys seeing others' lives end, but he thought it was too dreary just waiting for others to die. I've heard he's been planning to bring up a plague to the kingdom when he takes over. But, I didn't think it would ever happen."
Kovu interrupted, "Because it seems like an old legend."
"No, because it's you two kings that are in charge, and who would want to take over the place of two idiots." He joked. Kovu just rolled his eyes. He asked, "Can you think of way to bring Simba back?"
"Make him jog his memory. Do something that only Simba will react to." He suggested. Kovu nodded. He thanked him and left. He noted, "I will make sure Simba gets back here **today**!"
* * *
_Next day- 4 hours till Midnight_
Kovu walked through the savanna growling. "Dammit! It's already the next day and it's dark out! Stupid amusement park/resort! It's sad that the author had to skip that part. It was wild! Now what am I gonna do?"
He heard someone calling. "Kovu!"
He looked around and saw Kiara running up towards him. She looked very scared. She informed, "Something's wrong with Dad. He's down by the Water hole chanting something. And, it's really scaring me. I don't know what's going on."
He needed to figure out something and fast! He told Kiara to follow him. They both ran towards the Water hole.
* * *
_Water hole_
They hid behind a rock and looked over. Simba was chanting their native language. He seemed to be summoning something. Kovu just kept reminding himself that hopefully he's just practicing. Kiara asked, "What's going on?"
He didn't know whether to tell her the truth or not. He sighed, "What would you think of me, if I told you that your father is being controlled by an evil spirit that wants to take over all of Africa?"
"I would think, that I want to have whatever you're smoking or drinking." She answered, truthfully. He expected that answer. There has got to be a way for him to make Simba come back. He remembered what Rafiki said: _Do something that only Simba would react to._ Yes he knew that, but what? He already said that he fucked up his wife. What more could he-KIARA! Without warning, he pushed Kiara out and went out with her. She growled, "What are you doing!"
He ignored her. He shouted, "Hey, Kifo!"
Kifo turned around and laughed, "It's too late Kovu, there's nothing you can do that will bring Simba back."
"Wanna bet?" He questioned. He pounced down on top of Kiara and started kissing her. Kiara was taken by surprised, but she didn't make him stop either. Kovu started thrusting. All the sudden, the two heard a spine chilling roar. _HOLY SHIT!_ Kovu thought. He stopped and turned around. Red smoke exited out of Simba's body, he growled, tackled Kovu, and started choking him. He snarled, "You're fucking dead Kovu!"
He choked out, "It's great…to…see you back."
The two heard Kiara scream, she ran up to them and started hiding. Simba stopped choking him and Kovu got up. They saw Kifo laughing. Kifo has black fur, an equally black mane, gleaming fangs, soulless yellow eyes, and breaths out red dust. And he also has a score of battle injuries all over his body. He laughed, **_"Possessing a king or not, no one's standing in my way of taking over the kingdom. NOT EVEN YOU TWO!"_**
Simba whispered, "I think he's pissed at you."
Kovu turned around and ordered, "Kiara, go get the other lionesses."
She nodded and started running back to Pride Rock. Kifo started charging at them, Kovu and Simba jumped out of the way. Kovu drilled his claws in Kifo's back. He grabbed on Kovu's mane and threw him off. Simba batted at Kifo's face, hoping to knock him out. All he did was sent him a smirk and did the exact same thing to Simba. It was more effective, but he refused to give up. As soon as he was about to attack again, Kifo pounced at Simba and made him fall onto his back. He was about to end Simba, until Kovu bit down into his back. He grabbed his mane once again and flung him to the ground. He pinned down Kovu as well. He smirked at the two. **_"I told you, you wouldn't win. If only you listened to me."_**
He was about to bite down into both of their necks, but he knocked down by someone. Someone growled, "NO ONE TELLS ME WHAT TO DO!"
Simba questioned, "Nala?"
She smiled at him and went back to fighting Kifo. Sarabi, Vitani, Malkia, and Sarafina came to help. Simba and Kovu got up slowly, trying to ignore the pain coursing through their body. They watched the lioness get beaten by the evil spirit. Simba saw his mother hit the ground hard. He ran over to her and helped her up. She groaned, "He's too strong. I don't know if we can-"
"We have to try." Simba interrupted. She sent him a doubtful look. After a while, the others fell to the ground. Kifo said, **_"You Pridelanders can't defeat me."_** He looked up at the sky; the moon was almost at its peak. He continued, **_"You only have a few minutes until I unleash all of hell onto Africa. There's nothing that can save you"_**
They all started losing their hope. What else could they do? Out of nowhere this blanket of white dust fell in front Kifo and a flame made the dust burst into a bright white fire. They covered their eyes. They heard the blood curdling screams from Kifo as he was getting burned to death. After a while, the fire died down and revealed a burnt up Kifo. Parts of his skin had blood seeping from them, and others were just showing bone. They heard laughing from behind them. They turned around and saw Rafiki. He said, "We won't have to worry about him any longer."
With that, the crazy monkey left. Malkia asked, "Who wants to forget this ever happened?"
They all agreed with her. It turned out to be one crazy night that they **all** want to forget.
* * *
_1 month later_
Everything had been calm for a whole month. Nothing crazy, or spooky, or downright weird, had happened. Simba had left to go patrol the borders and the lionesses left to go hunting. The only one left on Pride Rock was Kovu. He still couldn't believe what happened with Kifo. It was scary and amazing at the same time. He was taking a nap and enjoying his peaceful day. He got tapped on the shoulder and heard someone whisper, "Kovu, I need to tell you something."
He opened his eyes slowly and saw Kiara. He stretched out and yawned, "Oh hey Kiara. What's up?"
She sighed, "I need to tell you something very important."
She motioned him to come into the den. He was very scared but, he followed her anyway. There were a few murmurs in the cave and then silence. After a while, Kovu shouted, "**YOU'RE WHAT!**"
**Bonus Ending**
Kovu sat at the base of Pride Rock, looking very nervous. Nala went up to him and asked, "What's wrong?"
He sighed, "Me and Simba made a prank contest. We want to see who can prank who the best. We haven't really thought of a prize yet, but you know it's a process."
She still didn't understand why he looked scared. He probably knew Simba was gonna win, or he may play a prank that may kill him. But, she rather not get stuck in another one of their adventures. She started walking away from him. After a few steps, she screamed. He ran over to her and saw that she fell down a hole. Out of nowhere, Simba laughed, "HAH! I got y-hold on. If you're here, then who fell?"
"SIMBA!" Nala yelled. He looked down the hole and his face went pale. He shouted, "I love you!"
Somehow, she climbed back up and snarled at Simba. He screamed and started running away. Kovu sighed, "You know what, a friend would go and help him. But, a best friend would get a camera and post it up on YouTube. So, I'm going to be a good best friend. I better go get a camera."
* * *
**That sucks for Kovu. Now he has to deal with this new problem he has. I bet you all know what the problem is. I hope you liked the conclusion and the bonus ending. Please review!**
**Disclaimer: I don't own any TLK characters, settings, yak and yak and yak. I only own Kifo and Malkia.**
End file.
| fanfiction |
courant algebroids were introduced in @xcite as a way to merge the concept of lie bialgebra and the bracket on @xmath4 first discovered by courant @xcite here @xmath5 is a smooth manifold .
roytenberg gave an equivalent definition phrased in terms of the dorfman bracket @xcite , which highlighted the relation of courant algebroids to @xmath6-algebras @xcite observed by roytenberg & weinstein @xcite . despite its importance
, the subject suffered from the lack of examples for a long time .
one important class of courant algebroids , called exact courant algebroids , was discovered by evera @xcite .
a courant algebroid @xmath7 is said to be exact if its underlying vector bundle fits into an exact sequence @xmath8 , where @xmath9 is the anchor map .
evera proved that the isomorphism classes of exact courant algebroids are classified by a degree-@xmath0 class in the de rham cohomology of @xmath5 : the evera class .
furthermore , the structure of transitive courant algebroids courant algebroids with surjective anchors was described independently by vaisman @xcite , evera ( in a private correspondence with weinstein @xcite ) and bressler @xcite .
evera and bressler also classified transitive courant algebroids as extensions of transitive lie algebroids @xcite .
indeed evera also outlined some nice ideas of classification of transitive courant algebroids in @xcite . in @xcite
, the second and third authors introduced the modular class of courant algebroids , a degree 1 characteristic class in the naive cohomology @xmath10 of the courant algebroid @xmath7 .
it is natural to ask whether there is a degree 3 characteristic class for a general courant algebroid resembling the severa class , and if so , what role is played by such a class in the classification of courant algebroids .
the main purpose of this paper is to answer these questions for regular courant algebroids , that is , courant algebroids with a constant rank anchor .
such courant algebroids @xmath7 are particularly easier to handle , for their associated characteristic distributions @xmath11 do not have any singularity .
note that characteristic classes of lie algebroids were studied by evens - lu - weinstein @xcite , crainic and fernandes @xcite .
it would be interesting to explore if there is any intrinsic connection between these constructions . to any regular courant algebroid
, we will construct a degree 3 class , called the characteristic class , in the naive cohomology @xmath12 of the courant algebroid , an analogue of evera s class .
note that when @xmath7 is an exact courant algebroid , @xmath12 is isomorphic to the de rham cohomology @xmath1 .
however , unlike the exact case , @xmath12 does not classify regular courant algebroids .
the classification problem is much subtler in this case . given a regular courant algebroid @xmath7 with anchor @xmath9 , @xmath13 is clearly a regular lie algebroid , i.e. a lie algebroid with a constant rank anchor .
it is called the ample lie algebroid of @xmath7 .
the kernel @xmath14 of the anchor of @xmath15 is a bundle of quadratic lie algebras , which satisfies certain compatibility conditions .
therefore , the lie algebroid @xmath15 is quadratic ( see definition [ def : quad ] ) . the first natural question is whether every quadratic lie algebroid @xmath15 arises in this way .
it turns out that there is an obstruction : the first pontryagin class , an element in @xmath16 naturally associated to any quadratic lie algebroid . here
@xmath17 is the image of the anchor ( an integrable subbundle of @xmath18 ) and @xmath16 stands for the leafwise de rham cohomology of @xmath17 .
this obstruction is similar to the one described by evera and bressler in the transitive case @xcite . to recover a courant algebroid from a given a quadratic lie algebroid @xmath15 with vanishing first pontryagin class
, one needs an extra piece of data : a coherent form @xmath19 .
this is a closed @xmath0-form on the lie algebroid @xmath15 satisfying certain compatibility conditions . in this case
@xmath20 is called a characteristic pair .
an equivalence is introduced on characteristic pairs .
let @xmath21 denote the cohomology groups of the subcomplex @xmath22 of @xmath23 , where @xmath24 is made of the sections of @xmath25 which are annihilated by all sections of @xmath26 .
roughly speaking , two coherent forms @xmath27 and @xmath28 on @xmath15 are equivalent if and only if the class of @xmath29 in @xmath30 is zero .
we prove that there is a one - to - one correspondence between regular courant algebroids up to isomorphisms and equivalence classes of characteristic pairs .
the inclusion @xmath31 is a lie algebroid morphism .
therefore , it induces a morphism @xmath32 .
we denote the class of the well - known cartan @xmath0-form of lie theory in @xmath33 by @xmath34 .
the main result of the paper can be summarized as the following 1 .
there is a natural map from regular courant algebroids to quadratic lie algebroids with vanishing first pontryagin class .
2 . for any quadratic
lie algebroid @xmath15 with vanishing first pontryagin class , the isomorphism classes of courant algebroids whose ample lie algebroids are isomorphic to @xmath15 are parametrized by @xmath35 . here
@xmath36 is a certain abelian subgroup of @xmath37 and @xmath38 denotes the anchor of @xmath15 .
3 . for any regular courant algebroid @xmath7
, there is a degree 3 characteristic class , which is a cohomology class in @xmath39 . here
@xmath15 is the ample lie algebroid of @xmath7 , and @xmath40 is the cartan @xmath0-form .
hence , we have the `` exact sequence '' @xmath41 @xmath42 . to this day
, little is known about courant algebroid cohomology @xcite : roytenberg computed it for @xmath43 and ginot & grtzmann for transitive and some very special regular courant algebroids @xcite .
our result should be useful for computing the courant algebroid cohomology of arbitrary regular courant algebroids .
* acknowledgments * the authors thank camille laurent - gengoux , zhang - ju liu , jim stasheff and alan weinstein for useful discussions and comments . in particular , we are indebted to pavol evera , who provides example [ rmk : severa ] , and called their attention to @xcite , which led to the spotting of an error in an early version of the paper .
a courant algebroid consists of a vector bundle @xmath44 , a fiberwise nondegenerate pseudo - metric @xmath45 , a bundle map @xmath46 called anchor and a @xmath47-bilinear operation @xmath48 on @xmath49 called dorfman bracket , which , for all @xmath50 and @xmath51 satisfy the following relations : @xmath52 } ; \\ \label{algian : caaxioms3 } & { e_1\circ ( fe_2)}=\big(\rho(e_1)f\big)e_2+f({e_1\circ e_2 } ) ; \\ \label{algian : caaxioms4 } & { e_1\circ e_2}+{e_2\circ e_1}=2{\mathcal{d}}{(e_1,e_2 ) } ; \\ \label{algian : caaxioms5 } & { { \mathcal{d}}f\circ e_1}=0 ; \\ \label{algian : caaxioms6 } & \rho(e_1){(e_2,e_3)}={({e_1\circ e_2},e_3)}+{(e_2,{e_1\circ e_3})},\end{aligned}\ ] ] where @xmath53 is the @xmath47-linear map defined by @xmath54 the symmetric part of the dorfman bracket is given by eq . .
the courant bracket is defined as the skew - symmetric part @xmath55 of the dorfman bracket .
thus we have the relation @xmath56 . using the identification
@xmath57 induced by the pseudo - metric @xmath45 : @xmath58 we can rewrite eq . as @xmath59 it is easy to see that @xmath60 , the subbundle of @xmath7 orthogonal to @xmath61 w.r.t .
the pseudo - metric , coincides with @xmath62 , the subbundle of @xmath7 generated by the image of @xmath53 . from eq .
, it follows that @xmath63 for any @xmath50 .
therefore , the kernel of the anchor is coisotropic : @xmath64 the spaces of sections of @xmath61 and @xmath60 are two - sided ideals of @xmath49 w.r.t .
the dorfman bracket .
a courant algebroid @xmath7 is said to be * regular * if @xmath65 has constant rank , in which case @xmath17 is an integrable distribution on the base manifold @xmath5 .
moreover , if @xmath7 is regular , then @xmath61 and @xmath60 are smooth ( constant rank ) subbundles of @xmath7 and the quotients @xmath66 and @xmath67 are lie algebroids . obviously , @xmath66 and @xmath17 are canonically isomorphic .
we call @xmath67 the * ample * lie algebroid associated to @xmath7 .
it will be denoted by the symbol @xmath68 .
the inclusions @xmath69 yield four exact sequences : @xmath70 \ar@(ur , ul)[rr ] & & ( \ker\rho){^{\perp}}\ar[dr ] \ar@(ur , ul)[rr ] & & e \ar[dr]^q \ar@(ur , ul)[rr]^{\rho } & & \frac{e}{\ker\rho } \ar[dr ] \ar@(ur , ul)[rr ] & & 0 \\ & 0 \ar[ur ] \ar[dr ] & & \ker\rho \ar[ur ] \ar[dr]_{\pi } & & \frac{e}{(\ker\rho){^{\perp } } } \ar[ur ] \ar[dr ] & & 0 \ar[ur ] \ar[dr ] & \\ 0 \ar[ur ] \ar@(dr , dl)[rr ] & & 0 \ar[ur ] \ar@(dr , dl)[rr ] & & { \mathcal{g}}\ar[ur ] \ar@(dr , dl)[rr ] & & 0 \ar[ur ] \ar@(dr , dl)[rr ] & & 0 } \ ] ] here @xmath71 .
we use the symbol @xmath72 ( resp .
@xmath73 ) to denote the projection @xmath74 ( resp .
@xmath75 ) . a @xmath76-bilinear and skew - symmetric bracket on @xmath77 determined by the dorfman bracket of @xmath7 through the relation @xmath78}^{{\mathcal{g}}}=\pi({r\circ s } ) , \qquad\forall r , s\in{\gamma(\ker\rho ) } , \ ] ] turns @xmath14 into a bundle of lie algebras .
moreover , the map @xmath79 is a well - defined nondegenerate symmetric and ad - invariant pseudo - metric on @xmath14 , which we will denote by the symbol @xmath80 .
hence @xmath14 is a bundle of quadratic lie algebras .
note that @xmath14 is also a module over @xmath68 ; the representation is given by @xmath81 } , \qquad \forall\ ; x\in{\gamma({\mathcal{a}}_e)},\ ; r\in{\gamma(\ker\rho ) } .\ ] ] this representation is compatible with the pseudo - metric on @xmath14 : @xmath82 let @xmath7 be a regular courant algebroid with characteristic distribution @xmath17 and bundle of quadratic lie algebras @xmath14 .
a * dissection * of @xmath7 is an isomorphism of vector bundles @xmath83 such that @xmath84 for all @xmath85 , @xmath86 and @xmath87 .
such an isomorphism transports the courant algebroid structure of @xmath7 to @xmath88 .
each dissection of @xmath7 induces three canonical maps : 1 .
@xmath89 : @xmath90 2 .
@xmath91 : @xmath92 3 .
@xmath93 : @xmath94 [ prop : courantbracketintermsofdata ] 1 .
the map @xmath95 satisfies @xmath96 for all @xmath97 , @xmath98 and @xmath50 .
the map @xmath99 is skew - symmetric and @xmath76-bilinear .
it can thus be regarded as a bundle map @xmath100 .
3 . the map @xmath101 is skew - symmetric and @xmath76-bilinear .
it can thus be regarded as a section of @xmath102 .
the following lemma shows that dissections always exist .
[ lem : existenceofsplitting ] let @xmath103 be a regular courant algebroid . and set @xmath104 . 1 .
there exists a splitting @xmath105 of the short exact sequence @xmath106 whose image @xmath107 is isotropic in @xmath7 .
given such a splitting @xmath108 , there exists a unique splitting @xmath109 of the short exact sequence @xmath110 with image @xmath111 orthogonal to @xmath107 in @xmath7 .
3 . given a pair of splittings @xmath108 and @xmath112 as above , the map @xmath113 defined by @xmath114 is a dissection of @xmath7 .
\(a ) take any section @xmath115 of @xmath116 .
consider the bundle map @xmath117 defined by @xmath118 where @xmath87 . then @xmath119 is a section of @xmath116 such that @xmath120 ( b ) take any section @xmath121 of @xmath122 .
consider the bundle map @xmath123 defined by @xmath124 where @xmath125 and @xmath126 .
then @xmath127 is the only section of @xmath122 such that @xmath128 ( c ) this is obvious .
let us first recall the notion of @xmath7-connections @xcite .
vaisman s metric connections are a related notion @xcite .
an @xmath7-connection ( or @xmath7-covariant derivative ) on @xmath7 is an @xmath47-bilinear map
@xmath129 such that @xmath130 for all @xmath50 and @xmath131 .
the next lemma shows that each regular courant algebroid @xmath7 admits @xmath7-connections .
if @xmath7 is a regular courant algebroid , there always exists a torsion - free connection @xmath132 on the integrable distribution @xmath133 .
indeed , it suffices to consider the restriction to @xmath17 of the levi - civit connection of some riemanian metric on @xmath5 . in the sequel
, the symbol @xmath132 will be used to denote a chosen torsion - free connection on @xmath17 and the dual connection on @xmath134 as well .
1 . given a dissection @xmath135 of a regular courant algebroid @xmath7 ( identifying @xmath7 with @xmath88 ) and the data @xmath95 , @xmath99 and
@xmath101 it induces , each torsion - free connection @xmath132 on @xmath17 determines an @xmath7-connection @xmath136 on @xmath7 through the defining relation @xmath137^\mathcal{g } } ) + { \nabla^f}_{x}{y},\ ] ] where @xmath87 , @xmath138 and @xmath86 .
this covariant derivative @xmath136 preserves the pseudo - metric : @xmath139 3
. moreover , we have @xmath140 } .\ ] ] we omit the proof as it is straightforward .
let @xmath7 be a courant algebroid .
the nondegenerate pseudo - metric on @xmath7 induces a nondegenerate pseudo - metric on @xmath141 : @xmath142 the isomorphism of vector bundles @xmath143 coming from this nondegenerate pseudo - metric will be denoted by the same symbol @xmath144 . in the sequel , @xmath141 and @xmath145
are sometimes identified with each other when it is clear from the context .
the sections of @xmath146 are called naive @xmath147-cochains . the operator @xmath148 defined by the relation @xmath149 where @xmath150 and @xmath151 , makes @xmath152 a cochain complex .
its cohomology @xmath153 is called the * naive cohomology * of the courant algebroid @xmath7 @xcite . [
rmk : naiveidformsonfat ] if @xmath7 is regular , then @xmath154 is a regular lie algebroid . and
it is easy to see that the cochain complexes @xmath152 and @xmath155 are isomorphic .
indeed , we have @xmath156 and @xmath157 hence the naive cohomology of @xmath7 is isomorphic to the lie algebroid cohomology of @xmath158 .
the map @xmath159 defined by @xmath160 where @xmath51 , is _ not _ a @xmath0-form on @xmath7 as it is not @xmath76-linear .
however , it can be modified using an @xmath7-connection so that the result is @xmath76-linear . if @xmath136 is a covariant derivative on a courant algebroid @xmath7 , then @xmath161 where @xmath162 , defines a @xmath0-form on @xmath7 .
the following is an analogue of the chern - weil construction .
[ thm : main1 ]
let @xmath7 be a regular courant algebroid . 1 .
if @xmath136 is the @xmath7-connection on @xmath7 given by , then the @xmath0-form @xmath163 does not depend on the chosen torsion - free connection @xmath132 .
it only depends on the chosen dissection @xmath135 .
it will henceforth be denoted by the symbol @xmath164 .
2 . the @xmath0-form @xmath164 is a naive @xmath0-cocycle .
3 . the cohomology class of @xmath164 does not depend on the chosen dissection @xmath135 .
the class of @xmath164 is called the * characteristic class * of the courant algebroid @xmath7 .
the proof of this theorem is deferred to section [ sec : proofs ] .
we fix a regular lie algebroid @xmath165_{{\mathcal{a}}}},{a})$ ] over the base manifold @xmath5 and with cohomology differential operator @xmath166 .
we have the short exact sequence of vector bundles @xmath167 where @xmath168 and @xmath169 .
it is clear that @xmath14 is a bundle of lie algebras , called the lie algebra bundle of @xmath15 .
the fiberwise bracket is denoted by @xmath170^\mathcal{g}}$ ] .
[ def : quad ] 1 .
a regular lie algebroid @xmath15 is said to be a * quadratic * lie algebroid if the kernel @xmath14 of its anchor @xmath171 is equipped with a fiberwise nondegenerate @xmath172-invariant symmetric bilinear form @xmath80 satisfying : @xmath173_{{\mathcal{a}}}},{\boldsymbol{s}})^\mathcal{g}}+{({\boldsymbol{r}},{[x,{\boldsymbol{s}}]_{{\mathcal{a}}}})^\mathcal{g } } , \qquad \forall x\in { \gamma({\mathcal{a } } ) } , { \boldsymbol{r}},{\boldsymbol{s}}\in{\gamma({\mathcal{g } } ) } .\ ] ] 2 .
two regular quadratic lie algebroids @xmath174 and @xmath175 are said to be isomorphic if there is a lie algebroid isomorphism @xmath176 , whose restriction @xmath177 to the kernels of the anchors is an isomorphism of quadratic lie algebras .
for example , the ample lie algebroid @xmath154 of any regular courant algebroid @xmath103 is a quadratic lie algebroid .
now a natural question arises as to whether every quadratic lie algebroid can be realized as the ample lie algebroid of a courant algebroid .
it turns out that there is an obstruction . to see this ,
let us introduce some notations .
a * hoist * of the lie algebroid @xmath15 is a section @xmath178 of the anchor @xmath171 .
the bundle map @xmath179 given by @xmath180_{{\mathcal{a}}}}-{\kappa}([x , y ] ) , \qquad\forall x , y\in{\gamma(f)}\ ] ] is its * curvature*. given a quadratic lie algebroid endowed with a hoist , we can consider the @xmath181-form @xmath182 given by @xmath183 for all @xmath184 .
the @xmath181-form @xmath185 is closed and its cohomology class in @xmath16 does not depend on the choice of @xmath186 . following @xcite , this cohomology class is called the * first pontryagin class * of the quadratic lie algebroid @xmath15 .
[ thm : bresslersthm ] a regular quadratic lie algebroid is isomorphic to the ample lie algebroid associated to some regular courant algebroid if and only if its first pontryagin class vanishes . the proof of this theorem is deferred to section [ sec : standard3form ] .
[ defn : good ] 1 .
let @xmath15 be a regular quadratic lie algebroid and let @xmath186 be a hoist of @xmath15 .
a closed @xmath0-form @xmath187 is said to be * @xmath186-coherent * if @xmath188^\mathcal{g}},{\boldsymbol{t}})^\mathcal{g } } ; \\ \label{align : goodformscdt2 } c({\boldsymbol{r}},{\boldsymbol{s}},{\kappa}(x))=0 ; \\ \label{align : goodformscdt3 } c({\boldsymbol{r}},{\kappa}(x),{\kappa}(y))={({\boldsymbol{r}},{r}^{{\kappa}}(x , y))^\mathcal{g}},\end{gathered}\ ] ] for all @xmath189 and @xmath190 .
we also say that @xmath191 is a coherent pair .
a closed @xmath0-form @xmath187 on a regular quadratic lie algebroid is called * coherent * if there exists a hoist @xmath186 such that @xmath19 is @xmath186-coherent .
a * characteristic pair * is a couple @xmath20 made of a regular quadratic lie algebroid @xmath15 and a coherent @xmath0-form @xmath19 on it .
if @xmath192 is a quadratic lie algebra , then the only coherent @xmath0-form is the cartan @xmath0-form defined by eq . .
if @xmath193 is the product lie algebroid with the obvious quadratic lie algebroid structure and @xmath101 is a closed @xmath0-form on @xmath5 , then the @xmath0-form @xmath194 defined by @xmath195^\mathcal{g}},{\boldsymbol{t}})^\mathcal{g}}+{\mathcal{h}}(x , y , z ) , \ ] ] for all @xmath196 and @xmath197 , is coherent .
[ prop : pontryagincoherentextensionallequivalent ] let @xmath15 be a regular quadratic lie algebroid .
the following statements are equivalent . 1 .
the first pontryagin class of @xmath15 vanishes .
2 . there exists a coherent @xmath0-form on @xmath15 .
there exists a courant algebroid whose ample lie algebroid is @xmath15 . consider the subcomplex @xmath22 of @xmath23 , where @xmath24 is made of the sections of @xmath25 which are annihilated by all sections of @xmath26 .
its cohomology groups are denoted @xmath21 . given two coherent @xmath0-forms @xmath27 and @xmath28 on @xmath15 , we have @xmath198 . two characteristic pairs @xmath199 and @xmath200 are said to be * equivalent * if there exists an isomorphism of quadratic lie algebroids @xmath201 such that @xmath202=0\in h^3_{\leftrightarrow}({\mathcal{a}}_1)$ ] .
the equivalence class of a characteristic pair @xmath20 will be denoted @xmath203}$ ] .
our main result is the following : [ thm : onetoone2 ] 1 .
there is a one - to - one correspondence between regular courant algebroids up to isomorphisms and equivalence classes of characteristic pairs .
2 . if @xmath7 is a courant algebroid corresponding to the characteristic pair @xmath204 , then the characteristic class of @xmath7 is equal to @xmath205\in h^3({\mathcal{a}})$ ] .
the proof is postponed to section [ sec : proofs ] .
let @xmath17 be an integrable subbundle of @xmath18 and @xmath14 be a bundle of quadratic lie algebras over @xmath5 .
in this section , we are only interested in those courant algebroid structures on @xmath207 whose anchor map is @xmath208 whose pseudo - metric is @xmath209 and whose dorfman bracket satisfies @xmath210^\mathcal{g } } , \ ] ] where @xmath211 , @xmath212 , and @xmath213 .
we call them * standard * courant algebroid structures on @xmath207 .
given such a standard courant algebroid structure on @xmath207 , we define @xmath95 , @xmath99 , and @xmath101 as in eqs . - .
the following lemma shows that the dorfman bracket on @xmath214 can be recovered from @xmath95 , @xmath99 , and @xmath101 .
[ prop : courantbracketintermsofdata2 ] let @xmath215 and @xmath216 be the maps defined by @xmath217 and @xmath218 then we have @xmath219 } , \\ \label{fsgfg1g2 } & { { \boldsymbol{r}}_1\circ { \boldsymbol{r}}_2}={\mathcal{p}}({\boldsymbol{r}}_1,{\boldsymbol{r}}_2)+{[{\boldsymbol{r}}_1,{\boldsymbol{r}}_2]^\mathcal{g } } , \\ \label{fsgfxi1g2 } & { \xi_1\circ { \boldsymbol{r}}_2}={{\boldsymbol{r}}_1\circ \xi_2}={\xi_1\circ \xi_2}=0 , \\ \label{fsgfx1xi2 } & { { x}_1\circ \xi_2}={l}_{{x}_1}\xi_2 , \\ \label{fsgfxi1x2 } & { \xi_1\circ { x}_2}=-{l}_{{x}_2}\xi_1 + { d^f}{\langle \xi_1| { x}_2\rangle } , \\ \label{fsgfx1g2 } & { { x}_1\circ { \boldsymbol{r}}_2}=-{{\boldsymbol{r}}_2\circ { x}_1}=-2\mathcal{q}({x}_1,{\boldsymbol{r}}_2)+ { \nabla}_{{x}_1}{\boldsymbol{r}}_2,\end{aligned}\ ] ] for all @xmath220 , @xmath221 , @xmath222 . here @xmath223 denotes the leafwise de rham differential . eqs . and are quite obvious . to get eq .
, we observe that , for all @xmath224 , @xmath225 eq .
can be proved similarly . to prove eq . , we only need to show that @xmath226 .
in fact , for all @xmath98 , @xmath227 eq . follows directly from eq . .
[ prop : courantbracketintermsofdata3 ] the following identities hold : @xmath228^\mathcal{g}}={[{\nabla}_x{\boldsymbol{r}},{\boldsymbol{s}}]^\mathcal{g}}+{[{\boldsymbol{r}},{\nabla}_x{\boldsymbol{s}}]^\mathcal{g } } , \\
\label{dcurvautre0 } \big({\nabla}_x{r}(y , z)-{r}({[x , y]},z)\big)+{\text{c.p.}}=0 , \\
\label{curvatureconnectionder } { \nabla}_x{\nabla}_y{\boldsymbol{r}}-{\nabla}_y{\nabla}_x{\boldsymbol{r}}-{\nabla}_{{[x , y]}}{\boldsymbol{r}}={[{r}(x , y),{\boldsymbol{r}}]^\mathcal{g}},\end{gathered}\ ] ] for all @xmath229 and @xmath86 .
moreover , we have @xmath230 where @xmath231 denotes the @xmath181-form on @xmath17 given by @xmath232 where @xmath233 . applying the expressions found for the dorfman bracket in lemma [ prop : courantbracketintermsofdata2 ] , eq .
follows from @xmath234 eq . from @xmath235 eqs . and from @xmath236 and eq .
from @xmath237 in summary , we have proved the following [ thm : standardcourantstructure ] a courant algebroid structure on @xmath207 , with pseudo - metric and anchor map , and satisfying eq . , is completely determined by an @xmath17-connection @xmath95 on @xmath14 , a bundle map @xmath238 , and a @xmath0-form @xmath239 satisfying the compatibility conditions - . the dorfman bracket on @xmath207 is then given by eqs . - .
this courant algebroid structure will be called the standard courant algebroid determined by the quintuple @xmath240 .
we assume again that @xmath17 is an integrable subbundle of @xmath18 and @xmath14 is a bundle of quadratic lie algebras over @xmath5 .
[ prop : standardquadraticliealgebroidstructure ] let @xmath15 be a quadratic lie algebroid with anchor @xmath241 such that @xmath242 and @xmath243 is isomorphic , as a bundle of quadratic lie algebras , to @xmath14 .
then any hoist of @xmath15 determines an isomorphism @xmath244 . the transported lie bracket on @xmath245 is completely determined by an @xmath17-connection @xmath95 on @xmath14 and a bundle map @xmath238 satisfying the conditions - , through the following relations : @xmath246_{{\mathcal{a}}}}={[{\boldsymbol{r}},{\boldsymbol{s}}]^\mathcal{g } } , \qquad { [ x , y]_{{\mathcal{a}}}}={r}({x},{y})+{[x , y ] } , \qquad { [ x,{\boldsymbol{r}}]_{{\mathcal{a}}}}={\nabla}_x{\boldsymbol{r}},\ ] ] for all @xmath247 , @xmath248 , @xmath249 , @xmath250 . this quadratic lie algebroid @xmath251 will be called the standard quadratic lie algebroid determined by the quadruple @xmath252 .
although it is similar to the proof of corollary 3.2 . in @xcite , we now sketch a proof of theorem [ thm : bresslersthm ] for completeness . given a regular courant algebroid @xmath7 , choose a dissection to identify it to @xmath207 .
then , according to eq .
, the pontryagin 4-cocycle of the ample lie algebroid @xmath158 associated to @xmath7 is a coboundary .
conversely , given a quadratic lie algebroid @xmath15 with anchor @xmath253 such that @xmath254 and @xmath243 is isomorphic to @xmath14 as a bundle of quadratic lie algebras , assume there is a hoist @xmath186 of the lie algebroid @xmath15 such that the pontryagin @xmath181-cocycle @xmath185 is a coboundary , say @xmath255 for some @xmath239 .
we define an @xmath17-connection @xmath256 on @xmath14 by setting @xmath257_{{\mathcal{a } } } } , \qquad\forall\;x\in{\gamma(f)},\;{\boldsymbol{r}}\in{\gamma({\mathcal{g}})}.\ ] ] the quintuple @xmath258 satisfies all conditions in theorem [ thm : standardcourantstructure ] and it is clear that @xmath15 is the ample lie algebroid associated to the courant algebroid determined by this quintuple .
let @xmath251 denote the standard quadratic lie algebroid determined by the quadruple @xmath260 .
given any @xmath239 , we define a @xmath0-form @xmath261 by @xmath262^\mathcal{g}},{\boldsymbol{t}})^\mathcal{g } } + { ( { r}({x},{y}),{\boldsymbol{t}})^\mathcal{g}}+{({r}({y},{z}),{\boldsymbol{r}})^\mathcal{g}}+{({r}({z},{x}),{\boldsymbol{s}})^\mathcal{g}},\ ] ] for all @xmath196 and @xmath263 . [ lem : csclosediff ] the following statements are equivalent : 1 .
@xmath101 satisfies eq . ;
@xmath264 is a closed @xmath0-form ; 3 .
@xmath264 is a coherent @xmath0-form .
straightforward calculations lead to @xmath265},z)\big ) + { \text{c.p.}},{\boldsymbol{r}})^\mathcal{g } } , \\
\label{align:3 } ( { \check{d}}c^s)(x , y,{\boldsymbol{r}},{\boldsymbol{s } } ) = & 0 , \\ \label{align:4 } ( { \check{d}}c^s)(x,{\boldsymbol{r}},{\boldsymbol{s}},{\boldsymbol{t } } ) = & -{l}_x{({[{\boldsymbol{r}},{\boldsymbol{s}}]^\mathcal{g}},{\boldsymbol{t}})^\mathcal{g } } + { ( { [ { \nabla}_x{\boldsymbol{r}},{\boldsymbol{s}}]^\mathcal{g } } + { [ { \boldsymbol{r}},{\nabla}_x{\boldsymbol{s}}]^\mathcal{g}},{\boldsymbol{t}})^\mathcal{g } } + { ( { [ { \boldsymbol{r}},{\boldsymbol{s}}]^\mathcal{g}},{\nabla}_x{\boldsymbol{t}})^\mathcal{g } } , \\ \label{align:5 } ( { \check{d}}c^s)({\boldsymbol{q}},{\boldsymbol{r}},{\boldsymbol{s}},{\boldsymbol{t } } ) = & 0,\end{aligned}\ ] ] for all @xmath266 and @xmath267 . the right hand side of eqs . and vanish due to eqs . - .
thus @xmath268 if and only if the right hand side of eq .
the latter is equivalent to eq . .
this proves the equivalence between the first two statements .
the equivalence between the last two statements follows from definition [ defn : good ] and eq . .
let @xmath259 be the standard courant algebroid determined by the quintuple @xmath240
. clearly its associated ample quadratic lie algebroid is the standard quadratic lie algebroid @xmath251 determined by the quadruple @xmath252 .
it follows from proposition [ lem : csclosediff ] and the compatibility conditions satisfied by @xmath269 that the form @xmath264 defined by formula is a closed and thus coherent @xmath0-form on @xmath251 .
since the cocycles of the lie algebroid @xmath251 can be identified to the naive cocycles on @xmath259 , we obtain a naive @xmath0-cocycle on @xmath259 called the * standard @xmath0-form * on @xmath259 . at this point , proposition [ prop : pontryagincoherentextensionallequivalent ] and the following result are quite obvious .
[ pro:3formclass ] let @xmath259 be the standard courant algebroid determined by the quintuple @xmath240 , and @xmath264 the @xmath0-form on @xmath251 defined by .
then the characteristic class of @xmath259 is equal to @xmath270\in h^3 ( { \mathcal{a}}^s)$ ] .
[ generalisomorphism ] given two different standard courant algebroid structures @xmath271 and @xmath272 on @xmath207 , any isomorphism of courant algebroids @xmath273 is of the form @xmath274 for @xmath275 , @xmath125 and @xmath126 . here
@xmath276 is an automorphism of the bundle of quadratic lie algebras @xmath14 and @xmath277 and @xmath278 are bundle maps satisfying the following compatibility conditions : @xmath279^\mathcal{g } } , \\ \label{eqn : iso3 } { r}^2({x},{y})-\tau{r}^1({x},{y } ) = \tau({\nabla}^1_{{y}}{\tau^{-1}}\varphi({x } ) -{\nabla}^1_{{x}}{\tau^{-1}}\varphi({y } ) ) + \varphi{[{x},{y}]}+{[\varphi({x}),\varphi({y})]^\mathcal{g } } , \\ \label{eqn
: iso4 } \begin{split } & \quad { \mathcal{h}}^2({x},{y},{z})-{\mathcal{h}}^1({x},{y},{z } ) + 2{(\varphi({x}),{[\varphi({y}),\varphi({z})]^\mathcal{g}})^\mathcal{g } } \\ & = \big(2{(\varphi({x}),\tau{\nabla}^1_{{y}}{\tau^{-1}}\varphi({z } ) -\tau{r}^1({y},{z}))^\mathcal{g } } + { l}_{{x}}{\langle { y}| \beta({z})\rangle}+{\langle { x}| \beta{[{y},{z}]}\rangle}\big)+{\text{c.p . } } , \end{split}\end{gathered}\ ] ] for all @xmath263 and @xmath98 .
consider the bundle maps @xmath280 where @xmath281 stands for @xmath207 .
it is clear that @xmath282 , for all @xmath126 .
since @xmath283 respects the pseudo - metric , we have @xmath284 , for all @xmath285 and eq . follows .
since @xmath286 for all @xmath125 and @xmath287 , we have @xmath288 .
hence @xmath289 . from eq .
, it is easy to get that @xmath290 , for all @xmath291 . thus @xmath283 must be of the form . since @xmath283 takes the dorfman bracket of @xmath271 to @xmath272 , eqs .
- follow from lemma [ prop : courantbracketintermsofdata2 ] .
the following two technical lemmas follow from direct verifications .
[ lem : dphijj ] given a bundle map @xmath292 , define @xmath293 by @xmath294 for all @xmath285 and @xmath295 .
then the differential of @xmath296 is given by : @xmath297})^\mathcal{g } } \\ -{(j({x}_1),{r}({x}_2,{x}_3)+{[{\boldsymbol{r}}_2,{\boldsymbol{r}}_3]^\mathcal{g}})^\mathcal{g}}+{\text{c.p.}},\end{gathered}\ ] ] for all @xmath298 and @xmath299 .
[ lem : dphijjbis ] given a bundle map @xmath300 , define @xmath301 by @xmath302 for all @xmath285 and @xmath295 .
then the differential of @xmath303 is given by : @xmath304})\rangle } + { \langle { [ x , y]}| k(z)\rangle}\big)+{\text{c.p.}},\ ] ] for all @xmath298 and @xmath299 .
[ lem : ipullbackdiffcoboundary ] the isomorphism @xmath273 of proposition [ generalisomorphism ] yields an isomorphism @xmath305 between the associated ample lie algebroid structures on @xmath306 : @xmath307 if @xmath308 and @xmath309 denote the standard coherent @xmath0-forms ( defined in section [ sec : standard3formabdses ] ) on @xmath310 and @xmath311 , respectively , then @xmath312 .
the proof is a direct but cumbersome calculation using proposition [ generalisomorphism ] , lemmas [ lem : dphijj ] and [ lem : dphijjbis ] , and eq . .
for @xmath163 defined in , it is easy to see the following equivalent formula @xmath313 using the expressions of the dorfman brackets given by proposition [ prop : courantbracketintermsofdata2 ] , one obtains @xmath314^\mathcal{g}},{\boldsymbol{t}})^\mathcal{g}}+{\mathcal{h}}(x , y , z ) , \end{gathered}\ ] ] for all @xmath315 , @xmath196 , @xmath316 .
this shows that @xmath163 coincides with the standard @xmath0-form @xmath264 on @xmath259 ( defined by eq . ) . hence it is naive , closed , does not depend on the choice of @xmath317 and we get statements ( 1 ) , ( 2 ) . finally , we prove statement ( 3 ) . for any two dissections @xmath318 and @xmath319 of @xmath7
, they induce two different courant algebroid structures on @xmath320 , but @xmath271 and @xmath272 are isomorphic . on the other hand ,
the @xmath0-form @xmath321 on @xmath7 is the pull back of a standard naive @xmath0-form @xmath322 on @xmath323 .
therefore , by proposition [ lem : ipullbackdiffcoboundary ] and remark [ rmk : naiveidformsonfat ] , @xmath324 must be a coboundary @xmath325 , for some naive @xmath326-form @xmath327 on @xmath7 .
we first show how to construct a courant algebroid out of a characteristic pair .
let @xmath15 be a regular quadratic lie algebroid and let @xmath328 be a coherent pair .
set @xmath168 and @xmath329 .
together , @xmath15 and @xmath191 induce the @xmath17-connection @xmath330 on @xmath14 ; the bundle map @xmath331 ; and the @xmath0-form @xmath332 defined by @xmath333 , for @xmath229 . by proposition [ lem : csclosediff ] , @xmath19 being a @xmath186-coherent @xmath0-form implies that @xmath334 satisfies eq . and
thus the quintuple @xmath335 satisfies the requirements to construct a standard courant algebroid structure on the bundle @xmath336 described by theorem [ thm : standardcourantstructure ] .
we shall denote such a courant algebroid by @xmath337 .
if @xmath15 is understood , we just write @xmath338 . in the sequel , the isomorphism class of a regular courant algebroid @xmath7 will be denoted by @xmath339}$ ] .
similarly , the equivalence class of a characteristic pair @xmath340 is denoted by @xmath203}$ ] .
define a map @xmath341 from the set of equivalence classes of characteristic pairs to the set of isomorphism classes of regular courant algebroids sending @xmath203}$ ] to @xmath342}$ ] . here
@xmath186 is any hoist of @xmath15 such that @xmath191 is a coherent pair on @xmath15 .
before we can prove it , let us establish some useful facts .
first , we study the change of hoists .
it is obvious that for any two hoists of @xmath15 : @xmath186 and @xmath344 , there exists a unique map @xmath345 such that @xmath346 , @xmath347 .
recall the notation @xmath256 defined by formula .
it is easy to check that @xmath348^\mathcal{g } } , \\
{ r}^{{\kappa}'}(x , y)-{r}^{{\kappa}}(x , y ) = { [ { j}(x),{j}(y)]}-{\nabla}^{{\kappa}}_x { j}(y)+{\nabla}^{{\kappa}}_y { j}(x)+{j}[x , y],\end{gathered}\ ] ] for all @xmath349 , @xmath98 .
write @xmath353 , @xmath354 , @xmath355 , @xmath356 and let @xmath357 .
clearly @xmath358 is determined by the quintuple @xmath359 , where @xmath360 , @xmath361 and @xmath362 .
we have the following equalities : @xmath363^\mathcal{g } } , \\ { r}^2(x , y)-{r}^1(x , y)={[{j}(x),{j}(y)]^\mathcal{g } } -{\nabla}^1_x{j}(y)+{\nabla}^1_y{j}(x)+{j}{[x , y ] } , \\ \begin{split } { \mathcal{h}}^2(x , y , z)-{\mathcal{h}}^1(x , y , z ) & = { ( { j}(x),{\nabla}^1_y{j}(z ) -{\nabla}^1_z{j}(y)-{j}{[y , z]}-2{r}^1(y , z))^\mathcal{g } } \\ & \quad -2{({[{j}(x),{j}(y)]^\mathcal{g}},{j}(z))^\mathcal{g } } + { \text{c.p . } } , \end{split}\end{gathered}\ ] ] for all @xmath316 , @xmath98 .
define a map @xmath364 by @xmath365 where @xmath275 , @xmath125 , @xmath366 , and @xmath278 denotes the map @xmath367 . according to proposition [ generalisomorphism ] and the above equalities
, @xmath368 is a courant algebroid isomorphism .
let @xmath371 , @xmath372 . clearly , @xmath358 is the standard courant algebroid determined by the data @xmath373 , @xmath374 and @xmath375 , where @xmath376 , @xmath377 .
since @xmath191 and @xmath369 are both coherent pairs , we have @xmath378 , for all @xmath125 . by lemma [ lem : dphijj ]
, one can check that this is equivalent to two conditions : @xmath379}=0 , \quad\forall x , y\in{\gamma(f ) } .\ ] ] using these , one has @xmath380 for all @xmath229 . then by proposition [ generalisomorphism ] , the map @xmath364 defined by @xmath381 where @xmath275 ; @xmath125 ; @xmath366 ; @xmath382 ; and @xmath383 , is an isomorphism of courant algebroids .
suppose that @xmath386 , for some bundle map @xmath345 , then according to lemma [ lem : goodpairstandardchange ] , the pair @xmath369 is also coherent . by lemma [ lem : almostidenticalgoodpairsiso ] and
[ lem : cplusdphijproducesameasc ] , we have isomorphisms @xmath387 .
it is clear that @xmath391 , @xmath392 .
thus one can easily check that @xmath388 is a coherent pair .
let @xmath358 be the standard courant algebroid determined by the quintuple @xmath393 , where @xmath376 , @xmath394 .
obviously , @xmath395 . by proposition [ generalisomorphism ]
, we can construct an isomorphism @xmath364 by setting @xmath396 , for @xmath275 , @xmath125 , and @xmath366 . here
@xmath397 is defined by @xmath398 , @xmath399 .
choose @xmath345 so that @xmath406 .
lemma [ lem : almostidenticalgoodpairsiso ] implies that @xmath407 the hoist @xmath408 produces a decomposition @xmath409 .
hence , there exist @xmath410 and @xmath411 such that @xmath412 . by lemmas [ lem : cplusanchorupsdfomega ] and [ lem : cplusdphijproducesameasc ] , we have @xmath413 first we show that @xmath341 is well defined .
suppose that two characteristic pairs @xmath204 and @xmath414 are equivalent , i.e. there is an isomorphism @xmath415 such that @xmath416 , for some @xmath403 .
we need to show that there is an isomorphism of courant algebroids @xmath417 .
it is quite obvious that @xmath418 is also a coherent pair on @xmath15 and @xmath419 since @xmath416 , lemma [ lem : c2c1homologic0producesame ] gives the isomorphism @xmath420 thus we conclude that @xmath417 and @xmath341 is well defined .
\(1 ) let us denote by @xmath421 the set of isomorphism classes of regular courant algebroids , and by @xmath422 the set of equivalence classes of characteristic pairs .
we need to establish a one - to - one correspondence between @xmath421 and @xmath422 . for any regular courant algebroid @xmath7
, one may choose a dissection so as to identify @xmath7 with @xmath423 .
in section [ sec : standard3form ] , we showed that there is a standard naive @xmath0-cocycle @xmath264 on @xmath259 and it corresponds to a coherent @xmath0-form on @xmath424 , also denoted by @xmath264 .
so we can define a map @xmath425 , @xmath339}\mapsto { [ { ( { \mathcal{a}}^s , c^s)}]}$ ] . by proposition [ lem :
ipullbackdiffcoboundary ] , this map is well defined and does not depend on the choice of the dissection . on the other hand
, proposition [ prop : bijectivemapinversewelldefined ] indicates that there is a well defined map @xmath426 .
an easy verification shows that it is indeed the inverse of @xmath427 .
this completes the proof .
[ pro : allcoherentforms ] let @xmath187 be a coherent @xmath0-form
. then any other coherent @xmath0-form is of the form @xmath428 , where @xmath429 is a closed @xmath0-form on @xmath17 and @xmath296 is defined by .
assume that @xmath19 ( resp .
@xmath430 ) is @xmath186 ( resp .
@xmath344)-coherent , for some hoist @xmath186 ( resp .
@xmath344 ) of @xmath15 .
the difference between @xmath186 and @xmath344 determines a bundle map @xmath345 such that @xmath431 .
a direct calculation shows that the @xmath0-form @xmath432 must be the pull back of some @xmath0-form @xmath433 by the anchor map @xmath38 .
conversely , it is easy to verify that @xmath428 is coherent w.r.t .
@xmath431 .
a @xmath0-form @xmath434 of a quadratic lie algebroid @xmath15 is said to be * intrinsic * , if there exists a coherent @xmath0-form @xmath19 and an automorphism @xmath435 over the identity such that @xmath436 .
it is simple to see that every intrinsic @xmath0-form is closed , and therefore defines a class in @xmath30 .
it turns out that this is the obstruction class to lift the automorphism @xmath437 to a courant algebroid automorphism .
[ lem : i ] let @xmath68 be the ample lie algebroid of a regular courant algebroid @xmath7 and @xmath436 an intrinsic form of @xmath68 . then @xmath438}=0 $ ] if and only if @xmath437 can be lifted to an automorphism @xmath439 of the courant algebroid @xmath7 .
let @xmath443 be the natural map from the isomorphism classes of regular courant algebroids to the isomorphism classes of quadratic lie algebroids with vanishing first pontryagin class .
we are now ready to prove the last main theorem of this paper . by theorem [ thm : onetoone2 ] , we understand that every isomorphism class of courant algebroid in @xmath444)$ ] can be characterized by an equivalence class of characteristic pairs @xmath445 , where @xmath19 is a coherent @xmath0-form .
lemma [ pro : allcoherentforms ] implies that @xmath446 acts transitively on @xmath444)$ ] .
now we determine the isotropy group of this action .
assume that @xmath429 is a closed @xmath0-form such that the characteristic pairs @xmath20 and @xmath447 are equivalent . by definition
, there exists an automorphism @xmath437 of @xmath15 such that @xmath448=0 $ ] in @xmath30 .
hence it follows that @xmath449}\in\mathbb{i}$ ] .
conversely , it is simple to see that @xmath36 acts trivially on @xmath444)$ ] .
this concludes the proof of the theorem .
@xmath450 is called the intrinsic group of @xmath15 .
note that the classification problem investigated here differs from that studied by evera and bressler even in the transitive case .
evera and bressler classified the isomorphism classes of transitive courant algebroid extensions of a given lie algebroid @xcite , while we are interested in isomorphism classes of courant algebroids themselves .
let @xmath5 be a contact manifold with @xmath452 being the contact @xmath453-form .
consider the transitive lie algebroid @xmath454 , which is a central extension of lie algebroid @xmath18 by the exact @xmath326-form @xmath455 considered as a 2-cocycle of the lie algebroid @xmath18 .
equip the standard fiberwise metric on @xmath456 .
it is clear that @xmath15 is a quadratic lie algebroid .
it is easy to check that @xmath457=0\in h^3_{\leftrightarrow}({\mathcal{a}})$ ] .
however @xmath458 $ ] is a nontrivial class in @xmath1 . for instance , if @xmath459 with the canonical contact structure , @xmath460 and @xmath461 . as a consequence
, there is a unique courant algebroid ( up to isomorphisms ) whose induced quadratic lie algebroid is isomorphic to @xmath462 . on the other hand , according to @xcite , courant algebroid extensions of @xmath454 are parametrized by @xmath47 . in general
, it is hard to describe explicitly the intrinsic group @xmath450 .
the following example , due to evera @xcite , gives a nice description of the intrinsic group in a special case .
we are grateful to evera , who pointed out this example to us , which led us to find an error in an earlier version of the draft .
[ rmk : severa ] let @xmath463 be a compact lie algebra such that both @xmath464 and @xmath465 are trivial .
assume that @xmath5 is a connected and simply connected manifold .
choose an ad - invariant non - degenerate bilinear form on @xmath463 .
consider the canonical quadratic lie algebroid @xmath466 .
the cartan @xmath0-form induces a coherent @xmath0-form @xmath194 : @xmath467^{{{\mathfrak{g}}}}},{\boldsymbol{t } } ) } , \ ] ] @xmath468 and @xmath197 .
let @xmath469 be a connected and simply connected lie group whose lie algebra is @xmath463 .
then any automorphism @xmath437 of @xmath15 is determined by a smooth map @xmath470 , where @xmath437 can be written as @xmath471 here @xmath472 is the bundle map defined by : @xmath473 to see this , one can consider @xmath15 as the atiyah lie algebroid of the trivial principal bundle @xmath474 .
then @xmath437 is induced by the principal bundle automorphism defined by the gauge group element @xmath470 .
using lemma [ lem : dphijj ] , one obtains @xmath475^{{{\mathfrak{g}}}}},j(z))}.\ ] ] it thus follows that @xmath476}=-(j\circ{a})^ * { [ { \alpha}]}=-{{a}^*}(j^ * { [ { \alpha}]}),\ ] ] where @xmath477 , \cdot ) \in \wedge^3 { { \mathfrak{g}}}^*$ ] .
it is simple to see that @xmath478 , where @xmath479 is the corresponding cartan @xmath0-form on @xmath469 . as a consequence ,
the intrinsic group @xmath450 is generated by elements of the form @xmath480}$ ] , where @xmath481 is any smooth map .
note that @xmath450 is discrete , because when @xmath482 and @xmath483 are homotopic , then @xmath484}=\tau_2^ * { [ { \tilde{\alpha}}]}$ ] .
here is one example .
let @xmath485 .
then @xmath486 and the intrinsic group @xmath450 is isomorphic to @xmath487 with the generator being @xmath488}$ ] .
hence by theorem [ thm : classification ] , the isomorphism classes of courant algebroids with ample lie algebroid isomorphic to the quadratic lie algebroid @xmath489 is parametrized by @xmath490 . | arxiv |
synovial sarcoma is a malignant tumor of pluripotent mesenchymal cells,1
2
3
4 most commonly found in periarticular areas , with few cases occurring in the head and neck.1
2
3
4
5 the first synovial sarcoma was described by jernstrom in 1954.6 in this article , we present a case of synovial sarcoma in the posterolateral wall of the oropharynx .
the patient , a 23-year - old woman , was admitted to the otorhinolaryngology clinic at our hospital with a history of dysphagia and difficulty of breathing for 8 months , resulting in progressive worsening and emergence of snoring , muffled voice , and local pain .
physical examination revealed an oropharyngeal tumor in the left posterolateral wall near the base of the tongue .
1 ) showed a rounded submucosal tumor with intact mucosa , starting at the left posterolateral wall , touching the epiglottis down to the left , narrowing the light of the entire pharynx , preventing full view of the glottis .
cervical magnetic resonance imaging ( figs . 2 , 3 , and 4 ) showed a solid cystic lesion in the submucosal left posterolateral wall of the oropharynx of relatively delimited contour , reducing the airway and rejecting the left piriform sinus .
the mass measured 5.3 3.9 2.2 cm in its greatest axis .
its left lateral region was predominately solid , showing heterogeneous impregnation of paramagnetic contrast , and measured 2.1 2.0 cm , with the cleavage plane delimited by prevertebral muscles .
lymph nodes measured up to 1.3 cm in internal high jugular chains and submandibular ( ib and iia ) on the right .
preoperative laryngoscopy showing the mass at the hypopharynx .
nuclear magnetic resonance , axial view .
nuclear magnetic resonance , coronal view .
nuclear magnetic resonance , sagittal view .
pathologic examination revealed a synovial sarcoma with positive margins , and mohs technique was proposed for edge control .
a full pharyngectomy with ipsilateral modified radical neck dissection was proposed , with the possibility of full laryngeal pharyngectomy depending on surgical margins obtained intraoperatively by freezing anatomy . during surgery , the margins came initially committed , and after expansion , the margins were disease - free .
we also performed the proposed neck dissection , tracheostomy , and passage of a nasogastric tube for nutrition .
postoperatively , the patient 's condition was stable . upon follow - up with an oncologist ,
a gastrostomy was performed for nutrition , as oral feeding was impossible . at swallowing endoscopy
all mobility of the larynx was preserved . within 1 year postoperatively , the patient continues with locoregional control without recurrence and performs pharyngoesophageal dilatations to treat actinic stenosis .
the tracheostomy tube is closed and will be removed as soon as oral feeding is stabilized .
despite its name , synovial sarcoma rarely originates in the synovial membranes.7 it is most commonly found in the vicinity of large joints .
occurrence in the head and neck , a location poor in synovial tissue , is uncommon.8 synovial sarcoma comprises 8 to 10% of all soft tissue sarcoma,1
3
5
7
9 and it is estimated that 3 to 10% of sarcomas occur in the head and neck.4
5
10 these tumors can be located in the prevertebral space from the base of the skull to the hypopharynx , retropharyngeal and parapharyngeal spaces , and anterior neck along the edges of the sternocleidomastoid muscle , as well as sites in the oropharynx and larynx.8
10 synovial sarcomas show a male predominance ( 3:2 ) and predilection for patients between 25 and 36 years of age.4
11
12
this type of tumor usually appears as an asymptomatic mass until it acquires sufficient volume to cause compressive effects on neighboring structures.1 it can be a painless mass or associated with symptoms such as pain , earache , sore throat , and bleeding .
it is important to include laryngoscopy and head , neck , and chest computed tomography to define the local extent of disease and metastasis.4
resection with negative margins remains the foundation of therapy,7
12 which is not so easy to achieve in the head and neck.4
5 local excision is followed by high recurrence rates ( 60 to 90% ) , usually within 2 years.4
5
9 metastasis to regional lymph nodes of synovial sarcomas in the head and neck is not seen often , although there can be clinically enlarged lymph nodes.5 most metastasis originate from hematogenous dissemination , although up to 20% spread through the lymphatics to regional lymph nodes.4
8 cervical lymph node dissection is not routinely performed , except in the presence of enlarged lymph nodes.8
10 hematogenous dissemination is the harbinger of death .
pre- and postoperative radiotherapy , with or without chemotherapy , may be responsible for the increase in survival statistics over the last 2 to 3 decades , but studies are still controversial and inconclusive.4
7
9
despite relatively slow growth , long - term survival for synovial sarcomas from anywhere , including the head and neck , is not good.5 synovial sarcoma in the head and neck has an aggressive nature and a reserved prognosis.3
8 several factors have been evaluated for prognosis , and the most significant were tumor size and deep extension at the time of primary treatment,9 with survival varying inversely with these two factors.5 the age at diagnosis seems to have involvement with prognosis,9 although the relative youth of patients with synovial sarcoma of the head and neck does not seem to give a significantly better prognosis.5
synovial sarcoma is a rare malignant tumor which treatment is essentially surgical resection with high rates of relapse .
although traditional treatment for hypopharynx tumors has been laryngectomy , it can be modified for sarcomas at this area . in these cases ,
radiation therapy with or without chemotherapy appears to be responsible for the increased survival in recent decades .
it is important for the otolaryngologist and head and neck surgeon to be familiar with this aggressive tumor , which carries high mortality and morbidity . | pubmed |
Lozova is a main hub and a railway junction in East Ukraine. It is the second busiest railway station in Kharkiv Oblast after Kharkiv Railway Station. It is located 156.3 km south of Russia and is a subsidy of Southern Railways an administrative branch of Ukrainian Railways.
Building
In 1869 the railway line was opened between Kursk and Azov Sea. The place where the modern building structure is located was named Lozova. Shortly after building a small station it was decided to make it a dividing line railway station.
History
References
External links
Railway Traffic Time Table at Lozova Railway Station
Lozova Railway Traffic within the Oblast
Lozova Railway Station information on Ukraine Railways Website
Aerial View of the Railway Station
Official site of Ukrainian Railways
Category:Railway stations in Kharkiv Oblast
Category:Railway stations opened in 1869 | wikipedia |
Non-pertubative renormalization and correctness of a theory
Even if I start to understand why perturbative renormalization is necessary, I'm not exactly sure why non perturbative renormalization is.
After asking the question to several theorists, what I think I understood is that sometimes (all the time ?) **the theory is just wrong** (ie exact solutions are finite but doesn't correspond to experiments).
So lets take 4 examples : QED, QCD, GR, and Ising model.
For each of these examples :
* Is there some infinite results **without** perturbative development ?
* Is the renormalized theory the same as the non renormalized one ?
* How do we now that non perturbative renormalization is needed ?
For example I was told that QED has some non perturbative finite results, but that they are wrong, and that renormalized QED is a different theory that better match experimental results. On the other hand I think renormalization applied to Ising model is supposed to give the same results as the exact solution.
I also don't understand why lattice QCD need renormalization, or how do we know that non pertubative naively quantized GR gives wrong results.
If a theory contains divergences, there is no need to assume it is plain wrong. It probably won't be the full theory of everything, but that's the only criticism that can be leveled at it. It can still be in perfect agreement with experiments below very-high-energy.
The issue with QED is that QED is not a complete theory. In the real world, QED is just a part of the electroweak theory. This embedding solves all problems of defining QED nonperturbatively (as far as I know).
There is also the issue of renormalization group flow. Lattice QCD needs renormalization because the "fundamental" coupling is not the same as the physical one. If you put QCD on the lattice, your computer code will contain a value for the coupling. If you then measure the effective coupling in the simulations, it will be different, because you will be watching at a different, low-energy scale.
| stackexchange/physics |
doing a research work for a thesis is mandatory for postgraduate ( pg ) medical students in india .
research has been conducted on the medical students using computers nowadays , which has found that most of them are using it for socializing or for other non - academic purposes .
it has also been reported that most of the research done by the pg medical students is quantitative . a seemingly small but a vital component of the process of conducting a research is data entry .
computer - based data entry is the preferred modality nowadays as it paves a smooth transition for data analysis using computer - based statistical softwares .
if data entry is done properly , it can facilitate data analysis to a large extent .
a properly done data entry is referred to as tidy data which is defined as easy to manipulate , model and visualize and has a specific structure : variables are stored in columns and observations in rows and one type of experimental unit per file . if the textual responses are pre - coded into numerical codes during the data entry itself ; carrying out complex statistical analysis like building regression models becomes less time consuming later .
data entry in a format , which can not be handled by the statistical software being used , leads to loss of man - hours and also puts mental stress on the researcher at that stage .
research on computer skills have been done in india , but research on how data entry is being done by the pg students , after collecting the data from the study subjects , has not been found in published literature . though the goal of post - graduation courses is to create specialists , the need of the hour for india is to create physician - researchers who can transition between specialties in order to translate information to best serve the needs of their patients . with the expansion of the horizon of the medical sciences , it has become imperative that even specialist physicians should be fluent as generalist researchers . in this environment
, this study looks at the budding specialists and their ability to conduct clinical research , specifically , at their skills in entering data into structured spread sheets .
this issue assumes particularly important proportions for the primary care physician , who is uniquely positioned at the junction of all the specialties and deals with the whole spectrum of problems that the patient presents with .
thus , primary care physicians in training need to be not only conversant in the jargon of various specialties , but also needs to have a good grasp over the basics of medical research .
this study aims to fulfill the lacunae in the evidence - base regarding the skills of physicians that goes in shaping the scene behind the published research . to assess the data entry skill in a computer based spreadsheet among the 2 year medical pg students
to assess the data entry skill in a computer based spreadsheet among the 2 year medical pg students .
a descriptive , cross - sectional study was carried out among the 2 year medical pg students , who had either completed or were on the verge of completion of data collection at the time of this study .
data was collected during an annual workshop on thesis writing for these students .
the pg students were given four simulated filled case record forms and were asked to do the entry of this data in a blank spread sheet as is the format of microsoft excel that they most commonly used for their data entry .
each simulated case record form was pre - filled with the information related to individuals who were presumed to have been enquired for certain particulars related to socio - demographic characteristics , clinical measurements such as blood pressure , body mass index and some investigation reports such as fasting blood sugar level , etc .
, as entering missing values is also a typical sub - skill , some responses were kept as blank , to see how the pg students enter the missing values in the spread sheet .
there were in all ten sub - skills that were assessed related to the computer - based data entry skill wherein each sub - skill which if found to be correct was given a score of one and a score of zero was given for an improper data entry regarding each specific sub - skill .
thus , the total score ranged from a minimum of zero to a maximum of ten .
data was entered in ms excel and r software was used for preparing one - way tables and data are presented in the form of percentages .
data was entered in ms excel and r software was used for preparing one - way tables and data are presented in the form of percentages .
it was found that most students had scored between 5 and 7 ( 61.3% ) , followed by a score between 0 and 4 ( 21.6% ) and only 17.1% scored above 7 .
table 1 shows the proportion of students who did the data entry in a proper manner with regards to the specific sub - skill of data entry .
the specific sub - skills that were found to be lacking in more than half of the respondents were as follows ; inappropriate coding ( 93.7% ) , long variable names ( 51.4% ) , coding not being done for all the variables ( 76.6% ) , missing values entered in a non - uniform manner ( 84.7% ) and two variables entered in the same column in the case of blood pressure reading ( 80.2% ) .
frequencies of correct responses for the items used for assessing the data entry skill of the postgraduate medical students ( n=111 )
this study assessed the data entry skill in a spread sheet among the medical pg students in a medical college .
a large gap has been identified in computer - based data entry skill using a simulated assessment in this cross - sectional study .
the students were lacking in almost all the sub - skills that are required to do a proper data entry for further data analysis in health research .
rowe et al . , in their study have reported from canada that only 15.0% of the 1 year family medicine residents had performed spread sheet applications .
only 40.3% of 1 year medical students in a study from sri lanka have reported using computers for data base management . a study from south india
has reported that only 23.2% of the medical students surveyed were very confident in using spread sheets . a study from pennsylvania
has assessed the spread sheet and data management skills of students and found that their elementary microsoft excel skills were very limited and they have suggested the need to change their curriculum for teaching them .
it is clear that students belonging to different courses need to possess the relevant course - specific skills regarding the use of a particular computer application .
there could certainly have been many other factors that must have influenced their level of skill , i.e. computer education during their school or college years etc . , but this was just a descriptive assessment to focus on the burden of the problem and provide inputs for future training programs in research methodology .
it is noteworthy that the pg students , especially who would be the primary health care providers and family medicine residents should be capable of being able to find meaningful information from the data that is with them . as they will be usually the initial contact points for patients , the data that will be generated at this level will have the potential to guide the primary and secondary level prevention activities which needs to be put in place for reducing the disease burden . through larger , multi - centric studies ,
we need to examine whether this trend is true across a larger geographical stretch or is a local anomaly .
if it is indeed a trend across multiple , representative centers , then we would need to take a relook at the training curriculum for all pg students , with special emphasis on the curriculum for primary care and family physician training programs to ensure that enduring research skills are inculcated during their pg training program .
the present study did not collect data regarding the specialties of the residents , mainly because the pg students had entered the specialty courses after completing their medical undergraduate course and as this training is uniform , irrespective of which specialty a student 's opt for his / her pg course .
furthermore , they had hardly spent around 2 - 3 months in the respective department after which this assessment was carried out just before their first formal training in
hence , there was no reason to assume that specialty must have made any difference to their data entry skills at this early stage .
the present study did not collect data regarding the specialties of the residents , mainly because the pg students had entered the specialty courses after completing their medical undergraduate course and as this training is uniform , irrespective of which specialty a student 's opt for his / her pg course .
furthermore , they had hardly spent around 2 - 3 months in the respective department after which this assessment was carried out just before their first formal training in thesis protocol writing .
hence , there was no reason to assume that specialty must have made any difference to their data entry skills at this early stage .
a sizeable proportion of the pg students studied did not know of the various basic aspects of doing a proper data entry in a spread sheet .
capacity building with the specific and relevant skill based training is urgently required for the pg medical students , as they are the doctor , academicians and researchers of the future .
inclusion of a session on data entry in a spread sheet in the research methodology training workshops is the need of the hour for the pg students especially belonging to family and primary care physicians and other research intensive pg programs like community medicine . | pubmed |
Need for Speed series 1. Rockport to Palmont
_**Kenji saw Alex's car in the mist of the road, his car comes to her.**_
"Didn't expect you to show your face again. Things have changed around here. This place is a battleground now. Tuners...Muscles...Exotics. Crew's fight for territory in the city, and it all gets settled in the canyon... but you'd never survive it." **Kenji tells Alex of the new stuff in Palmont City.**
_**Alex is driving down the canyon roads, passing a sign for Palmont City in 10 miles. Reminding her about that terrible night that happened. Her old friend, Nikki walks quickly to the car.**_
"Start it up." **Nikki tells Alex to do.**
"Don't disappoint." **Darius reminds Alex as he gives her the car keys. **
_**The race was on between Kenji; Angie; Alex and Wolf. As the race started, the cars roared on into the incoming traffic. Until later, as the cars turned from the corner, Kenji; Angie and Wolf's cars were hit with a blue shining light that missed Alex. Alex turned her car around to see cops capturing the other three racers. Alex panicked and ran out off the scene.**_
"Look, between the heat and the crews you need to walk away. Take my car, go, get out of here!" **Darius reports to Alex ending the flashback.**
_**In the present day, Alex is at Carbon Canyon. What she doesn't know that Cross, from Rockport is back; He bumps into Alex saying to her.
**_
"Hey, guess who's back?"
_**She tries to escape his path before landing in traps that slow her down. Cross gets out of his car and runs towards Alex.**_
"Sit down! How you've been?" **Cross, scares her before finishing his sentence. "**It's time to settle a little score from Rockport, ya' think?"
_**Darius appears from Silverton, sighing about what Cross and Alex have done.**_
"I don't remember asking for your help, Crog. What makes you think you can bounty hunt in Silverton without my approval?" **Darius scolds Cross.**
"It's Cross...and this girl is from out of town." **Cross corrects Darius while pointing to Alex. **
"Been a long time, kid... What's his bounty?" **Darius checks with Cross.**
"$150, 000." **Cross tells Darius.**
"David, take care of this guy." Darius asks one of his goons to check with Cross.
"So that's what you have been up to..." Darius says before a car from the same territory appears. It's Nikki from the flashback.
"Nikki. This should be interesting."
"How dare you show your face here? Let go of me!" **Nikki says while trying to hit Alex.**
"Woah, hey, control yourself!" **Darius tells her to do before one of his cars is stolen by Cross. "** I still don't know what happened that night you took off, but I do know you're into me now for some serious cash. Things have been getting a little too close to comfort around here with all these crews battling for new territory. I think I could use someone with your skills to help me out. The way I see things, I've bailed you out of a serious jam twice now. Time for you to return the favour. Nikki, what do you say you show your old friend the ropes?"
"You got to be joking, right?" **Nikki nearly declines.**
"You got a better idea? Then let's get her started. Right away." **Darius demands Nikki to do. **"Don't disappoint. Not again."
_**Nikki drives Alex to a car park somewhere, where three cars and a man are sighted. The man goes towards Alex, but she recognises him. It's her old cousin Adam.**_
"Thanks for waiting up." **Nikki tells Adam.**
"Yeah, yeah, sure Nikki. Hey uh, why did you bring Alex?" **Adam whines.**
"Doesn't matter. Darius made all these cars available to you. Pick one, whichever one you want." **Nikki asks Alex.
**
"Hey uh, if there's three, do I get one? I mean I don't care which one, although I am partial to the one with the sweet rims." **Adam tells them.**
"Adam, why don't you just shut up and let me pick one."** Alex shouts at him.**
"That's great. I'M THE MONKEY!" **Adam expresses himself.**
"There! That's all you need to get started. I'm done wasting my time on you. Later, Adam." **Nikki scolds him.**
"Well, guess it's just you and me again. Let's go find some trouble." **Adam bribes Alex.**
"To me Adam, you are the trouble." **Alex tells him.
**
"Of course I am." **Adam uses sarcasm.**
_**They drive off into the Silverton to Fortuna motorway.**_
"So you've been gone a while... You got in Rockport, huh? Man, a lot has changed since you took off. There are tons of crews in this town, everywhere man, crazy!" **Adam reminds Alex of **_**Most Wanted (the 2005 version and yes I am getting to that after this)**_
_**Adam and Alex drive so fast that a cop from a hidden passage in the motorway spots them and starts a pursuit.**_
"Look out, cops!" **Adam shouts the obvious.**
"I would have not known that over the sirens?" **Alex scolds him while them two are shaking off more of the cops.**
"Watch this!" **Adam tells Alex before he does two cool tricks to the police car to damage them. He drives to Fortuna while Alex drives down the Downtown way.**
"Who's the coffee grinder, baby?I got your back. I'll lose the heat, stay on the pedal!" **Adam demands Alex to know until they're connection is broken from each other.**
_**After, Alex has evaded the cops; she drives to a house where Adam is located.**_
"Darius gave you this safe house. You can use it to fix your car or chill out when the heat's on. You need a wingman and it looks like I'm in. Let me show you inside." **Adam says the basics to Alex.**
2. Kenji and Yumi
**Recap: **
"Darius gave you this safe house. You can use it to fix your car or chill out when the heat's on. You need a wingman and it looks like I'm in. Let me show you inside." **Adam says the basics to Alex.**
Alex's Need For Speed Carbon Chapter 2
_**Everything Ramped up.**_
_**Alex and Adam laugh as they have appeared from their recent race. **_
"**Did you see that, I completely owned that race!"** Alex boasts.
**"If it wasn't for me, you wouldn't have won." **Adam backs up Alex's boast.
"**Dairus has come by to ask you, Alex on how you're doing." **Nikki tells Alex.
"**I am defiantly allright." **Alex uses sarcasm to let her feelings get to Nikki.
"**Adam, go and get me something to drink." **Nikki orders Adam.
_**He goes to get her a drink whilst talking to him.**_
"**Looks like you cleaned the place up a bit." **Nikki examines the room. **"You've been generating a quite a bit of buzz, but you're not fooling me. I've been trying to figure out that you haven't skipped town yet"**
**"I might be a bit too good to skip town." **Alex responds
_**The door opens to find Sal, Alex's second crewmember.**_
"**Hi" **Sal introduces himself awkwardly as Alex facepalms. **"Umm, Nikki said that you might be looking for a new wingman, you don't know me. But of course I know you. I'm a big fan! I've seen all your races."**
"**And on that note, I'm outta of here." **Nikki exits after Sal's incredibly geeky introduction.
"**See things aren't going to be the same since you've gone. You know there are a lot of posers wanting respect. I know all the back streets; I grew up in these alleys. I can customise anything. I practically built all the kits you see around this place." **Sal explains as Alex actually pays attention.
"**Okay, there wasn't anything good. So there's soda and water. Hey Alex, where the hell did she go?" **Adam tells Alex.
"**I'll even put up with this guy." **Sal says while pointing to Adam.
Alex and Sal see a bunch of green cars go near them and block the road before Alex & Sal put on the brakes.
"**I heard you were back in town, now I want to hear you gone." **The unnamed group leader orders Alex.
_**He drives off leaving the two behind.**_
"**Who the hell was that?" **Alex shouts.
"**Kenji, he runs the Bushido group here in DownTown Palmont." **Sal explains.
_**Sometime, Alex has won every race in DownTown Palmont. Now she must battle Kenji to win his turf.**_
_**Alex drove a little bit before Kenji boosted in front of her with his Nitrous. They stopped to start the race.**_
"You remember me? Right? I don't think you do, because if you did. You would not be sitting there duelling me right now."
_**After 3 hours, 38 minutes and 9 seconds. Alex beat him to the line.**_
**"Now, that is what I am talking about! Hell Yeah!" **Alex shouted as she had won another victory.
"**There's another part to winning and I bet you can't do it." **Kenji reminded her.
_**Then they travelled to the Canyon to race for DownTown Palmont. **_
"**It's your last chance to save reality and BACK OFF!" **Kenji ordered Alex.
"**I would have done that." **Alex murmured before starting her engines. **"Keep my foot on the gas pedal and not on the brake, unless there's a turn." **
Kenji laughed, as Alex got closer to him. She drove past, Kenji knew by his car's clock that more than 10 minutes after she had passed would mean that he is out for the count. He drove as hard as could but Alex stayed on until the race had finished because she knew by default she would win.
But she knew
She was the speed demon.
That time meeting Rachel and going to beat Caleb in Bayview*
"I'm Rachel, I'm Samantha's friend. Finally heard your plane got in, well welcome to Bayview." Rachel introduces herself over the phone.
"Yeah, big deal. It was one race, isn't going to happen again. YOU CAN'T DO THAT! WE HAVE A DEAL! Just give me one more chance and I can sort this thing." Caleb says to his sponsor on the phone.
"YOU! WHAT DO YOU WANT? RIGHT THAT IS IT! YOU AND ME ARE GOING TO DO A RACE! YOU AND ME PUT EVERYTHING ON THE LINE, SO ARE YOU IN?" Caleb orders Alex to race.
"Yeah, it's time to rumble." Alex responds.
She celebrated in the car, cheering on as Kenji banged his head on the wheel of his car. They drove back down to DownTown Palmont.
Kenji drove off, disgusted at his faliure.
A/N: Second chapter finished.
Sorry about the wait, had some YouTube business to take a care of.
So I'm going to read some of the reviews posted.
said. "Can't wait for Chapter 2!"
I reply with. "Chapter 2, being shorter than 1, is well and good, I included a couple of stuff I didn't want to include in 1.
Thebeyblademaster said. "Good story, update soon!"
I reply with. "I agree, the first chapter was good and again sorry for the wait between 1 & 2."
Please Read and Review...
Oh, I almost forgot something.
"I have secret. Thought you would like to know?" Yumi tells Alex.
"I need to know what happened." Alex says.
"I was there the night you left. I was up a fire escape; you can see pretty well up there, you can hear things too. Then the cops came out and hit every car, but the blue one. Yours, That didn't make any sense of that, somebody interfered with you in a big way and you need a good crew to clean up the pieces." Yumi continues.
"Welcome to the crew then." Alex tells Yumi.
They shake hands.
* = Need For Speed: Underground 2 (PlayStation 2; Xbox and GameCube)
End file.
| fanfiction |
Here's a staple jean you'll wear forever and last a lifetime. Our popular and versatile straight leg, Myles, is not too slim, not too relaxed; perfect for the guy wanting a comfortable yet fitted leg. In a classic clean, dark wash, it's the perfect staple jean that works from day to night. | slim_pajama |
import org.junit.Before;
import org.junit.Test;
import static org.junit.Assert.*;
public class TestWhileLoop {
Case mainCase;
Node head;
WhileLoop whileLoop;
@Before
public void SetUpVariables() {
mainCase = new Case(new Variable("i", "int"), new Constant(5), "==");
DelayComponent delay1 = new DelayComponent();
DelayComponent delay2 = new DelayComponent();
delay1.setDelayMilliseconds(3);
delay2.setDelayMilliseconds(5);
Node tail = new Node(delay2);
head = new Node(delay1, tail);
whileLoop = new WhileLoop(mainCase);
}
@Test
public void TestWhileLoop_Constructor_ConditionIsSet() {
assertEquals(whileLoop.getCondition(), mainCase);
}
@Test
public void TestWhileLoop_SetterAndGetterContentHead_ContentHeadIsSet() {
whileLoop.setHeadOfContent(head);
assertEquals(whileLoop.getHeadOfContent(), head);
}
@Test
public void TestWhileLoop_SetterAndGetterContentHead_ConditionIsSet() {
Case newCase = new Case(new Constant(2), new Constant(3), "!=");
whileLoop.setCondition(newCase);
assertEquals(whileLoop.getCondition(), newCase);
}
@Test
public void TestWhileLoop_ToCode_CodeIsFormatted() {
whileLoop.setHeadOfContent(head);
assertEquals(whileLoop.toCode(2), " while ((FV_i) == (5)) {\n" + head.getProgramCode(2 + Settings.getTabDepth()) + "\n }");
}
}
| slim_pajama |
the production of ccn proteins lacking one or more of the four structural modules ( igfbp , vwc , tsp and ct ) that constitute the prototypic ccn protein ( bork 1993 ; holbourn et al .
2008 ) has already been discussed ( perbal 2001 , 2004 ; planque and perbal 2003 ) . aside from the natural ccn5 protein that does not contain a ct domain ( perbal 2001 )
, several other examples of truncated ccn proteins were identified in biological fluids , cell culture lysates , cell culture medium , and normal or tumor tissues ( perbal 2001 , 2006 ; leask and abraham 2006 ; holbourn et al .
, the production of short variants in pig uterine flushings was hypothesized to result from proteolytic digestion of the full length protein ( brigstock et al .
1997 ) . indeed , inter - domain regions that show much less organization than the modules themselves ( holbourn et al .
2008 ) may be the target for proteolytic activity as shown by the cleavage of ccn2 by the mmp2 metalloproteinase at the junction between vwc and tsp1 modules ( dean et al .
2007 ) . a truncated ccn3 variant deprived of both the igfbp domain and the signal peptide that drives secretion of the ccn proteins ( joliot et al . 1992 ; perbal 2001 , 2004 ) was expressed in nephroblastoma tumor cells , because of myeloblastosis associated virus ( mav ) insertional mutagenesis in the genome of the blastemal target chicken cells ( li et al .
ccn3 truncated isoforms that are deprived of the igfbp and vwc modules and contain only the last two c - terminal modules ( tsp1 and ct ) were identified in most cultured cells and tissues which also express the full length protein ( perbal 1999 , 2006 ; su et al .
n - terminal sequencing of the truncated ccn3 protein that is contained in the cell culture medium of insect cells infected with a recombinant ccn3 baculoviral vector ( perbal et al . 1999 ) established that it was generated by a proteolytic cleavage occurring between domain ii ( vwc ) and iii ( tsp1 ) of the full length ccn3 protein . since the cleavage site was found to be identical to that used in the case of ccn2 , we suggested that a common specific protease might be involved in the processing of ccn proteins which generated these variants .
the production of rearranged ccn variants as a result of alternative splicing has also been documented for many times over several years .
indeed , a ccn4 protein lacking the vwc module ii ( wisp1v ) was detected in scirrhous gastric carcinoma cells .
this variant is encoded by a 840 nucleotide alternatively spliced mrna species , missing the 260 nucleotides of exon 3 that encode vwc module sequences in the wild type mrna species ( tanaka et al .
both a similarly spliced message and rearranged variant ccn4 protein were detected in invasive cholangiocarcinoma ( tanaka et al .
2003 ) and in the human chondrosarcoma - derived chondrocytic cells hcs-2/8 ( yanagita et al .
interestingly , another spliced variant expressed in these cells was found to encode a single igfbp module in which eight authentic aminoacids at the c - terminus were replaced by 14 other residues ( yanagita et al .
in addition to the expected full length transcript of wisp1/ccn4 ( 1,204 bp ) , two shorter transcripts of 943 bp and 750 bp were identified in the human hepatoma huh-6 and ha22t / vgh cell lines ( cervello et al .
since the joining of exons 2 and 4 did not result in any reading frame shift , the variant mrna species also encoded a ccn4 protein lacking the vwc module as previously described by tanaka et al .
( 2001 , 2003 ) exons 3 and 4 were not contained in the ccn4 750-bp spliced variant , and the frameshift that was created by the joining of exons 2 and 5 in this rna resulted into a premature translation arrest 38 residues downstream .
as a consequence , the ccn4 variant protein expressed by this spliced message encoded only the igfbp module .
a longer ccn4 transcript containing an insertion of 64 bp between exons 3 and 4 was detected in huh-6 and huh-7 human hepatoma cells .
the insertion of this short stretch caused a frameshift at residue 197 that resulted in a premature translation stop 22 residues downstream .
as a consequence , a half ccn4 protein containing only the two n - proximal igfbp and vwc domains , was encoded by this spliced mrna species .
the first evidence suggesting the existence of ccn1 ( cyr61 ) alternatively spliced messages was obtained in my laboratory in the course of a study aimed at identifying the chromosomal localization and expression of ccn1 in human neuroblastoma and glioblastoma cell lines ( martinerie et al .
1997 ) . because the full length cdna clone mapped only one chromosomal location at 1p22-p31 , we proposed that the additional 3.5 kb ccn1 mrna species that was detected in a few cell lines in addition to the canonical
since the focus of our studies was on the ccn3 gene and protein , we did not pursue the identification of this additional mrna species .
a few years later , another example of an alternatively spliced ccn1 mrnas species was documented in the case of serum - induced normal human fibroblasts , which were shown to express a ccn1 message in which an in frame deletion within exon 4 resulted in the production of a ccn1 protein deprived of the tsp1 module ( leng et al .
interestingly , the new message that is identified in human breast cancer cell lines resulted from retention of the 131 nucleotide intron 3 that separates the exons encoding the vwc and tsp1 domains of ccn proteins .
since this intron contains two stop codons , the authors propose that the alternatively spliced message does not encode a full length protein .
the organization of the various alternatively spliced ccn mrnas identified thus far is depicted in fig . 1 .
the prototypic structure of the ccn proteins ( except fro ccn5 lacking ct ) is represented on the top , with the five exons that encodes , the signal peptide ( sp ) and the von willebrand ( vwc ) , thrombospondin ( tsp1 ) and cterminal ( ct ) domains ( see holbourn et al .
alternative splicing leading to variant proteins has been identified for ccn1 ccn4 , ccn3 . in the case of ccn1 and ccn4 ,
variant proteins resulting from alternative splicing have been identified in scirrhous gastric carcinoma ( a ) , cholangiocarcinoma ( b ) , hcs-28 human chondrosarcoma - derived chondrocytic cells ( c ) , human hepatoma cells ( d ) ewing s tumors ( e ) , human fibroblasts ( f ) , wilm s tumors and normal human embryonic kidneys ( g ) , human breast tumors ( h ) .
see text for details schematic organization of the various ccn spliced variants which have been described thus far .
the prototypic structure of the ccn proteins ( except fro ccn5 lacking ct ) is represented on the top , with the five exons that encodes , the signal peptide ( sp ) and the von willebrand ( vwc ) , thrombospondin ( tsp1 ) and cterminal ( ct ) domains ( see holbourn et al .
alternative splicing leading to variant proteins has been identified for ccn1 ccn4 , ccn3 . in the case of ccn1 and ccn4 ,
variant proteins resulting from alternative splicing have been identified in scirrhous gastric carcinoma ( a ) , cholangiocarcinoma ( b ) , hcs-28 human chondrosarcoma - derived chondrocytic cells ( c ) , human hepatoma cells ( d ) ewing s tumors ( e ) , human fibroblasts ( f ) , wilm s tumors and normal human embryonic kidneys ( g ) , human breast tumors ( h ) .
see text for details in the case of ccn3 , several observations suggested that variant ccn3 proteins might be produced in a regulated way in both normal and pathological conditions .
large amounts of a ccn3 3238 kda doublet were detected in the brain lysates of adult rats in which small amounts of the full length ccn3 protein were detected ( su et al .
2001 ) . since these short variants were detected by the k19 m antibody that was raised against the c - terminal end of ccn3we assumed that they were composed of the two last domains ( tsp1 and ct ) and that they might be generated through alternative splicing . in transfected glioma cells producing exogenous ccn3 , a large amount of a half ccn3 protein was also detected in the cytoplasmic fraction in addition to the truncated form that is usually secreted in the culture medium of cells producing ccn3 (
although we did not investigate the mechanisms leading to the production of the intracellular variant ccn3 species , all these findings suggested the existence of two ccn3 variant species that might result from two different mechanisms : post - translational processing of the secreted full length protein and alternative splicing leading to the intracellular short species . aside from these two pieces of indirect evidence , we recently identified ccn3 variant proteins that most likely result from alternative splicing .
in addition to the full length ccn3 protein , wilm s tumors and normal human embryonic kidneys also expressed a ccn3 variant that was deprived of the tsp1 domain ( subramaniam et al . 2008 ) .
also , 50% of ewing s tumor cells were found to express a truncated ccn3 protein species lacking the vwc module ( perbal et al .
as previously discussed ( perbal 2001 , 2004 ) the multimodular structure of the ccn proteins raises an interesting question as to the contribution of each module to the biological function(s ) of the fully assembled protein .
either the activities of each module sum up or they confer on the whole protein specific functions that might substitute or add to the function of the individual modules .
the present consensus is to view the biological properties of the various ccn proteins as the result of both individual module activities and functional interactions between different modules ( leask and abraham 2006 ; yeger and perbal 2007 ; irvine et al .
2008 ) . in view of the complex array of regulatory factors and receptors that physically interact with ccn proteins ,
the production of variants deprived of one or more elementary module is expected to have profound biological effects . not only can variant ccns titrate receptors and other partners interacting with each individual module , and thereby interfere with biological activity of the full length proteins , but also
, the absence of a single module might induce conformational changes that could potentially modulate , either positively or negatively , the intrisic biochemical functions of the resulting ccn protein .
the amino - proximal half of ccn2 ( which contains only the igfbp and vwc domains ) was reported to be an effective surrogate biomarker for fibrosis ( leask et al .
2009 ) and to mediate both myofibroblast differentiation and collagen synthesis whereas the c - terminal half ( composed of the tsp1 and ct domains ) mediated fibroblast proliferation ( grotendorst and duncan 2005 ) .
more recently , the recombinant igfbp and vwc modules were reported to display stronger binding to aggrecan compared to recombinant tsp1 and ct modules ( aoyama et al .
a mutant lacking the ct domain was unable to promote cell adhesion but had conserved the chemotactic and growth - factor promoting activities of the full ccn1 protein ( grzeszkiewicz et al .
2001 ) the amino - truncated version of ccn3 ( containing the three first modules ) that was cloned from mav - induced nephroblastoma exhibited transforming properties in chicken embryo fibroblasts whereas , the full length ccn3 showed growth inhibitory effect ( joliot et al .
since half proteins show such specific biological properties , it is surprising that neither hirschfeld and colleagues , nor the reviewers who evaluated their manuscript , considered the possibility that the truncated protein likely expressed from the ccn1 mrna species which retain intron3as stated by the authors themselves might play a critical role in the breast cancer cells that contains this spliced variant .
the use of domain specific ccn1 antibodies that are available would have permitted to address this important question .
this is especially critical in the context of this work , since the authors reported exon 3 skipping as a way to produce the full length active ccn1 protein ( hirschfeld et al .
in other words , the strong correlation that was observed between the intron 3 skipping and the invasive breast cancer phenotype might have resulted from the production of a full - length ccn1 in these cells , whereas in non - cancerous tissues , only the amino - proximal half ccn1 was expressed .
these authors also report that the switch from intron retention to intron skipping was induced by hypoxia .
this observation is in line with other results showing that alternative splicing of ccn mrnas is tightly regulated and might affect the tumorigenic potential of cancer cells .
hence , the use of domain - specific antibodies ( lazar et al . 2007 ) allowed us to establish that ccn3 variants lacking the tsp1 domain were expressed in wilm s tumors and that in normal kidneys , the production of ccn3 lacking the tsp1 domain is developmentally regulated ( subramaniam et al .
furthermore , we established that in the case of ewing s tumors , the increased level of variant ccn3 in tumor cells reduces their tumorigenic potential , and results in better outcome .
the existence of alternative splicing leading to the production of variant ccn proteins is well documented and should be regarded as a means to increasing the biological functions of this fascinating family of proteins .
whether the variant forms that were detected in normal and pathological conditions antagonize or synergize the functions of full length ccn proteins remains to be clarified . in some cases ,
the biological activities of variant proteins were associated with particular phenotypes , especially in the tumor cells in which these variants were identified . however , in other cases the origin of the variants is not clearly established even though it is highly probable that alternative splicing is responsible for their production .
when we first established that ccn3 was involved in the development of the human brain ( su et al .
2001 ) , we used the k19 m polyclonal antipeptide that is directed against the c - terminal end of ccn3 ( chevalier et al .
1998 ) . as a consequence , immunocytochemistry experiments performed with this antibody did not permit us to distinguish between a positive staining due to the presence of a full - length or an amino - truncated ccn3 protein .
neither was the k19 m antibody able to identify the variant forms lacking one particular domain .
only the detection of large quantities of a low molecular weight ccn3 variant in rat brain lysates ( su et al .
2001 ) raised the possibility that alternative splicing was involved and that the short amino - truncated ccn3 might play a critical role in this tissue at this particular developmental stage .
the recent results that we have obtained in the course of study performed with ewing s tumors and wilm s tumors , established that domain - specific antibodies such as those we derived for ccn3 are invaluable tools to identify all the ccn isoforms contained in cells and tissues .
the existence of variants generated by both posttranslational processing and alternative splicing can no longer be ignored by the scientific community .
future progress and understanding of the role of ccn proteins in normal and pathological conditions will rely on the thorough characterization of all isoforms that requires the use of appropriate biological tools . | pubmed |
in this paper we study the relation between the bfkl perturbative resummation of leading logarithms @xcite at high energy and the jimwlk / klwmij evolution @xcite,@xcite equations , which take into account the physics of saturation and multiple scatterings @xcite . with a slight abuse of language we call bfkl the second quantized formulation which leads not only to the bfkl equation for two gluon exchange , but also to the whole set of bkp equations for @xmath0-channel exchanges with an arbitrary number of gluons @xcite .
the basic correspondence between the elements of the two approaches was established in @xcite and we will review it briefly below . here
we are interested in the question how to relate the eigenvalues and the eigenfunctions of the bfkl hamiltonian and their counterparts in the jimwlk / klwmij theory .
we will show that the eigenfunctions of the jimwlk / klwmij hamiltonians when expanded in taylor series in the appropriate variable ( @xmath2 for jimwlk and @xmath3 for klwmij ) are eigenfunctions of the bfkl hamiltonian .
however most of the bfkl eigenfunctions when resummed into solutions of jimwlk / klwmij are not normalizable . the question which are , and which are not , can not be settled within the bfkl framework .
we also discuss how to calculate higher corrections to the bfkl eigenfunctions . as an example we concentrate on the reggeized gluon @xcite .
we calculate corrections to the reggeized gluon wave function .
we show that terms with up to two gluons in the @xmath0-channel reggeize due to the bootstrap condition inherent in this approach .
we also point out that in the jimwlk / klwmij framework the bootstrap is a necessary consequence of the hermiticity of the jimwlk / klwmij hamiltonian , and does not require a specific form of the emission kernel .
we calculate corrections to the eigenfunction beyond the two gluon exchange approximation and thereby find the screening correction which appears when at least three gluons are exchanged in the @xmath0-channel .
this is an interesting example of the interrelation between the @xmath0-channel unitarity , which is the origin of reggeons and the @xmath1-channel one which is the inherent feature of the jimwlk / klwmij approach .
let us start by recapitulating the jimwlk / klwmij formalism .
in this approach one considers the scattering of a projectile hadron on a hadronic target .
the projectile is described by a distribution of color charge density in the transverse plane @xmath4 , while the target is viewed as an ensemble of the color fields @xmath5 with probability densities @xmath6 $ ] and @xmath7 $ ] respectively .
the second quantized @xmath8 matrix operator is given by its eikonal expression ( see ) @xmath9 and the forward @xmath8 matrix element at rapidity @xmath10 is given by the functional integral @xmath11\,\,w^t[\alpha_t ] \,\exp\left\{i\int_{0}^{1 } dy^-\int d^2x\,\rho_p^a(x , y^-)\,\alpha_t^a(x , y^-)\right\}\ ] ] the @xmath8 matrix in the jimwkl approach with averaging specified by . ] the rapidity evolution of basic physical observables ( including the @xmath8-matrix ) is determined by the second quantized evolution hamiltonian @xmath12 ( the following pertains to the projectile evolution - we drop the subscript on @xmath2 for brevity ) @xmath13=h_{rft}[\rho , \frac{\delta}{\delta\rho}]w[\rho]\ ] ] the evolution hamiltonian @xmath12 depends on two unitary matrices , @xmath14 here the field @xmath15 is the projectile color field analogous to @xmath16 .
it is related by a nonlinear transformation to the projectile color charge density @xmath2 @xmath17 with @xmath18 $ ] and @xmath19 the @xmath8-matrix at arbitrary rapidity can therefore be represented in terms of the eigenvalues of @xmath12 .
its evolution is given by @xmath20w_y^p[\rho]\,\,w^t[\alpha_t ] \,\exp\left\{i\int_{0}^{1 } dy^-\int d^2x\,\rho^a(x , y^-)\,\alpha_t^a(x , y^-)\right\}\ ] ] given the set of complete eigenfunctionals of @xmath12 @xmath21=\omega_i\psi_i[\rho]\ ] ] one can expand the probability distribution at the initial rapidity @xmath22 as @xmath23=\sum_i\gamma_i\psi_i[\rho]\ ] ] and therefore @xmath24 with @xmath25\,\,w^t[\alpha_t ] \,\exp\left\{i\int_{0}^{1 } dy^-\int d^2x\,\rho^a(x , y^-)\,\alpha_t^a(x , y^-)\right\}\ ] ] given that the hamiltonian @xmath12 is positive definite @xcite , the asymptotic behavior of the @xmath8-matrix is governed by the lowest lying eigenvalues @xmath26 .
the study of the spectrum of @xmath12 is therefore of direct relevance to understanding the high energy behavior of physical amplitudes .
two limits of hamiltonian @xmath12 have been widely discussed in the literature .
one is valid in the limit of dense projectile , but allows only exchange of two gluons with the target @xcite . in the other limit
one assumes that the projectile is dilute , but resumms all possible multiple interactions of the partons of the projectile with the target @xcite .
the two limiting cases are related by the dense - dilute duality transformation @xcite and have therefore identical spectra . in the rest of this paper
we choose to study the klwmij hamiltonian .
@xmath27 with the kernel @xmath28 and the left and right rotation generators @xmath29
\\ j^a_r(x)=-tr\left[r_xt^a\frac{\delta}{\delta r^{\dagger}_x}\right ] \end{aligned}\ ] ] alternatively one can write @xmath30 with @xmath31 the operators @xmath32 are the generators of @xmath33 - the vector subgroup of @xmath34 . as noted above , the jimwlk hamiltonian is obtained from eq.([klwmij ] ) by the dense - dilute duality transformation @xmath35 we note that a generalization of @xmath12 which interpolates between @xmath36 and @xmath37 has recently been derived @xcite .
however due to its complexity we will not deal with it in the present paper . the hamiltonian @xmath36 is the limit of @xmath12 at low color charge density .
the left and right rotation operators @xmath38 and @xmath39 eq.([lr ] ) that appear in eq.([klwmij ] ) are in fact just the color charge density in the hadronic wave function and its conjugate respectively @xcite . some aspects of the structure of the spectrum of @xmath36 were discussed in @xcite . in particular we know that @xmath36 is positive definite since it can be written as @xmath40 with the hermitian amplitude @xmath41j^b_r(x)\ ] ] it has two states with zero eigenvalue : @xmath42 the state @xmath43 corresponds to the physical vacuum , that is to the state which is annihilated by the color charge density @xmath44 while @xmath45 represents the black disk state @xmath46 we will find it convenient to work in the basis of eigefunctions of the operator @xmath47 . written in this basis
the wave functionals of the two states are @xmath48 each one of these states sustains a tower of excitations above it .
the rft states `` close '' to @xmath43 correspond to physical qcd states with small number of particles in the projectile wave function .
this interpretation stems from the fact that , as discussed in detail in @xcite the probability distribution @xmath49 has a convenient representation @xmath50=\sigma[r]\delta[\rho]\ ] ] and thus in the @xmath47 basis @xmath49 is simply a regular function of @xmath47 .
every factor of @xmath47 in @xmath49 corresponds to a gluon in the projectile wave function .
thus expansion of @xmath49 in powers of @xmath51 , is equivalent to expansion in the number of the projectile gluons that scatter on the target .
in this paper we are interested in the eigenstates of @xmath36 which have similar structure , namely in the @xmath47 basis the eigenfunctions are regular functionals of @xmath52 which can be expanded in powers of @xmath51 . since @xmath47 is a regular function of @xmath3 ,
these same states can also be expanded in powers of @xmath3 .
clearly the state @xmath43 is one of those states since the wave function in this case is simply a constant . on the other hand the state @xmath45 does not fall into this category .
its wave function is not expandable in powers of @xmath51 .
the same is true for other states `` close '' to it .
as explained in @xcite those states correspond to `` holes '' in the black disk and their eigenfunctions are expandable in powers of @xmath2 rather than @xmath53 .
the discussion of this paper pertains directly only to the @xmath43 - like states .
the derivation of the hamiltonian @xmath36 @xcite does not assume anything about the strength of the target fields .
if one interested in the situation when the target fields are small , one can expand @xmath36 in powers of @xmath3 .
the expansion in powers of @xmath3 is equivalent to expansion in powers of the target field , since powers of @xmath3 turn into powers of @xmath16 in the calculation of the scattering matrix eq.([smatrix1 ] ) .
the leading order of this expansion gives @xmath54 , which is the second quantized hamiltonian that generates the high energy evolution in the bfkl framework .
the form of @xmath54 is well known ( see for example @xcite ) . for completeness
we present the derivation of @xmath54 in the appendix , carefully keeping track of the path ordering in the definition of @xmath52 .
although this path ordering is not relevant in many cases @xcite , in general it can not be neglected .
the result is @xmath55\left[\frac{\delta}{\delta \rho^d_y}-\frac{\delta}{\delta \rho^d_z}\right]\rho^b_y\ ] ] where @xmath56 in the `` normal ordered form '' this reads @xmath57\left[\frac{\delta}{\delta \rho^d_y}-\frac{\delta}{\delta \rho^d_z}\right]\rho^a_x\rho^b_y+\int_{xz}\beta_{xz}\frac{\delta}{\delta \rho^a_z}\rho^a_x\ ] ] with @xmath58 = \frac{\alpha_sn_c } { 2\pi^2}\left[\delta^2(x - z)\int_u\frac{1}{u^2}-\frac{1}{(x - z)^2}\right]\ ] ] the question we want to address is what is the relation between the eigenvalues and eigenfunctions of @xmath54 and @xmath36 . more importantly , to what extent can we use the results of calculations performed in the framework of bfkl evolution to get information about the spectrum of @xmath36 .
the calculation of the spectrum of @xmath54 is equivalent to solution of the complete set of bkp equations .
the bfkl hamiltonian is a homogeneous function of the coordinates ( @xmath53 ) and momenta ( @xmath2 ) and thus its eigenfunctions are pure powers . taking an eigenfunction in the form @xmath59=\int_{x_1 ... x_n}g_a^{a_1a_2 ... a_n}(x_1 ... x_n)\frac{\delta}{\delta\rho^{a_1}_{x_1}} ... \frac{\delta}{\delta\rho^{a_n}_{x_n}}\ ] ] and acting on it with @xmath54 leads to an eigenvalue equation of the form @xmath60\nonumber\\ & & + \sigma_i\int_x\beta_{xx_i}g_a^{a_1 ... a ... b ... a_n}(x_1 ... x ... x_n)=\omega_ag_a^{a_1 ... a_n}(x_1 ... x_n)\end{aligned}\ ] ] eqs.([bkp ] ) are precisely the bkp equations @xcite for the rapidity evolution of @xmath61 - gluon exchange in @xmath0-channel .
the index @xmath62 denotes various quantum numbers that characterize the eigenfunction @xmath63 , in particular total momentum , color representation , charge conjugation , parity and so on . as mentioned above
, expanding @xmath36 and @xmath64 is powers of @xmath3 is equivalent to expanding the @xmath8 matrix eq.([smatrix ] ) in powers of the target color field @xmath16 .
every factor of @xmath16 represents an exchange of a gluon in @xmath0-channel between the projectile and the target .
thus physically , expansion in powers of @xmath3 is equivalent to expansion in the number of gluons exchanged in the @xmath0 - channel @xcite .
consequently , the quantum numbers denoted by the index @xmath62 in eq.([bkp ] ) are the quantum numbers of the @xmath61 - gluon state exchanged in the @xmath0-channel . for @xmath65 the solution of eq.([bkp ] ) is the reggeized gluon . in this case
the color representation of the exchange is obviously adjoint and the eigenvalues are characterized by the transverse momentum . for the singlet two gluon state , @xmath66 ,
this is the celebrated bfkl equation and the solution is the bfkl pomeron . for arbitrary @xmath61 in the large @xmath67 approximation
these equations have been extensively studied in @xcite where it was shown that the spectrum of the @xmath61 gluon state is described by an integrable spin chain .
although the full spectrum of eq.([bkp ] ) is not known , the salient features are the following .
in the reggeized gluon sector ( @xmath65 ) the eigenvalues are nonnegative . the lowest eigenvalue is vanishing and corresponds to zero transverse momentum exchange @xmath0 .
at nonzero @xmath0 the eigenvalues are logarithmically infrared divergent . for the bfkl pomeron ( singlet @xmath66 exchange )
the lowest eigenvalue is actually negative , corresponding to the growth of the amplitude at high energy with the famous bfkl intercept . at @xmath68
the spectrum is rich .
importantly the lowest eigenvalue for the color singlet exchange is always negative and grows proportionally to @xmath61 , corresponding to the @xmath69 pomeron exchanges this growth is even faster and the absolute value of the most negative eigenvalue is proportional to @xmath70 @xcite . ]
now let us consider @xmath36 .
the eigenvalues and eigenfunctions as noted above are determined by solving @xmath71=\omega_a\psi_a[r]\ ] ] suppose we try to solve this by taylor expanding @xmath72 in powers of @xmath3 .
we thus write @xmath73+\psi^1_a[\frac{\delta}{\delta\rho}]+ ... \ ] ] to find @xmath64 we need to act on it with @xmath36 also expanded in powers of @xmath3 .
it is clear from the mechanics of the expansion of @xmath39 and @xmath38 given in the appendix , that to all orders in @xmath3 , both the charge densities are proportional to the first power of @xmath2 , and only the power of @xmath3 in @xmath36 grow order by order . therefore the hamiltonian @xmath36 can be written as @xmath74 here the first correction to the hamiltonina , @xmath75 schematically has the form @xmath76 the structure of eqs.([expfu],[expeq ] ) is such that in the leading order the wave function @xmath77 $ ] must be an eigenfunction of @xmath54 .
thus the leading order equation determines @xmath78 completely , and the role of the higher order equations is only to determine the higher order taylor series terms in the expansion of the wave function @xmath79 $ ] .
e.g. having found @xmath80 as an eigenfunction of @xmath54 with eigenvalue @xmath78 , to first order one has @xmath81=\frac{1 } { \omega_a - h_{bfkl}}h_1\psi^0_a\ ] ] and so on .
it thus appears that the eigenvalues of @xmath36 can be obtained _ exactly _ from the leading order approximation - the bfkl hamiltonian .
the catch however is that we do not know from the bfkl calculation _ per se _ whether the wave function corresponding to a given `` eigenvalue '' will turn out to be normalizable or not . within the bfkl approximation itself ,
none of the wavefunctions are of course normalizable since they are simple monomials of @xmath3 . however only normalizable eigenfunctions of @xmath36 should be used in the expansion of the @xmath8-matrix eqs.([psii],[psiii ] ) .
a similar situation is encountered in simple quantum mechanics .
take for example a one dimensional harmonic oscillator @xmath82 let us now try to find its ground state wavefunction in taylor expansion .
we take @xmath83 acting on it with the hamiltonian we get @xmath84 and the schroedinger equation @xmath85 thus for arbitrary @xmath86 we simply have @xmath87 so there is a solution for every possible value of @xmath86 ( in fact there are two solutions for each @xmath86 , but the other one is an odd function of @xmath88 and is outside our initial ansatz ) .
this calculation however does not carry a lot of information since we do not know _ a priori _ which of the so found functions are normalizable when the taylor series is summed to all orders .
we know of course that the spectrum in fact is discreet and therefore most of the `` eigenvalues '' do not correspond to normalizable eigenfunctions .
the situation in the klwmij - bfkl system is similar in this respect . as we have noted above
, @xmath36 is hermitian and positive definite , thus its eigenvalues have to be positive .
on the other hand many of the eigenvalues of @xmath54 are negative ( including of course , the pomeron ) .
we are therefore assured that those eigenvalues do not correspond to normalizable eigenfunctions . as for the positive eigenvalues of @xmath54 ,
it is tempting to surmise that they correspond to normalizable eigenfunctions of @xmath36 .
unfortunately , we have no right to do so .
the question whether resummed taylor series is normalizable or not is very complicated and can not be answered in any finite order of taylor expansion .
we note however that the taylor expansion for @xmath36 is in a subtle way different from that for the harmonic oscillator . in the later case
the leading order of the expansion puts no restrictions at all on possible eigenvalues . in the klwmij case
however , the leading order itself leads to an eigenvalue problem , so that not every @xmath78 is allowed .
even though it is not clear whether the eigenfunctions of @xmath54 give rise to normalizable eigenfunctions of @xmath36 , it is still interesting to illustrate the procedure discussed above by some concrete example . in the following section we will therefore consider higher order in @xmath3 corrections to some eigenfunctions .
we will concentrate on the eigenvalues corresponding to the reggeized gluon , which is the simplest eigenfunction of @xmath54 .
let us look for the eigenstate of @xmath36 which corresponds to the quantum numbers of one gluon exchange .
the state must belong to the adjoint representation of @xmath33 and its wave function when taylor expanded should start with the linear term in @xmath3 .
thus we take @xmath89 acting on it with @xmath54 we obtain the eigenvalue equation @xmath90 this is solved by @xmath91 with the eigenvalue @xmath92 this is nothing but the gluon reggeization . to calculate first correction to the reggeized gluon state we have to consider @xmath93 which is quadratic in @xmath53 .
we will perform the calculation in a slightly different way which is technically simpler .
we know that the wave function @xmath64 at the end of the day should depend only on @xmath47 .
therefore it makes sense , rather than taking an arbitrary quadratic function , to choose such a function that itself can be obtained from expansion of @xmath47 .
since @xmath94 is simply represented as expansion of @xmath47 @xmath95=\int d^2x\phi(x)tr \left(t^ar\right)_{\rm first \ order}\ ] ] we will take a simple guess @xmath95+\psi_a^1[\delta/\delta
\rho]=\int d^2x\phi(x)tr \left(t^ar\right)_{\rm first+second \ order}\ ] ] and will show that it indeed satisfies the klwmij eigenvalue equation to second order in @xmath53 .
the matrix @xmath47 is taken here in the adjoint representation .
we now consider the action of @xmath36 in the state @xmath96 the basic elements we need is the action of the left and right rotation generators on the matrix @xmath47 @xmath97=t^ar(y)\delta^2(x - y ) ; \ \ \ \ \ \ [ j^a_r(x),r(y)]=r(y)t^a\delta^2(x - y)\ ] ] with this it is easy to calculate the action of the real and virtual parts of @xmath36 : @xmath98^{cd}j^d_r(y)tr[t^ar_u]=2[r_z-1]^{cd } tr[t^at^cr_xt^d]\delta(x - y)\delta(y - u)\ ] ] and @xmath99[j^c_l(y)-j^c_r(y)]tr[t^ar_u]=tr\left\{t^a[t^c,[t^c , r_x]]\right\}\delta(x - y)\delta(y - u)\ ] ] hence @xmath100^{cd}tr[t^dt^at^cr_u]+tr\left\{t^a[t^c,[t^c , r_u]]\right\}\right\}\ ] ] using @xmath101\right\}=n_ctr[t^ar_u]\ ] ] we write @xmath102^{cd}tr[t^dt^at^cr_u]-n_ctr[t^ar_u]\right\ } \nonumber \\ & = & \frac{\alpha } { \pi^2}\int_{u , z}k_{uuz}\phi_u\left\{-2[r_z-1]^{cd}tr[t^dt^at^c(r_u-1)]+n_c\left(tr[t^ar_u]-tr[t^ar_z]\right)\right\}\end{aligned}\ ] ] we now have to expand this to second order in @xmath3 .
the matrix @xmath47 is expanded as @xmath103
the crucial observation is that the first and second order terms come only from the second term in eq.([1glue ] ) . for first order term
this is obvious .
the second order contribution from the first term in eq.([1glue ] ) is proportional to @xmath104\frac{\delta}{\delta\rho_u^b}\frac{\delta}{\delta\rho_z^e}\ ] ] however , using the properties of the adjoint su(n ) generators @xmath105 one can easily show that @xmath104=0\ ] ] and so this contribution vanishes .
thus to second order the eigenvalue equation is @xmath106\nonumber\\ & & = \omega\int_u\phi(u)\left[\frac{\delta}{\delta\rho_u^a}+\frac{i } { 2}f^{abc } \int_{x^->y^- } \frac{\delta } { \delta\rho^b(u , x^-)}\frac{\delta } { \delta\rho^c(u , y^-)}\right]\end{aligned}\ ] ] obviously , this is satisfied as before by @xmath107 of eq.([eigenf ] ) with the eigenvalue eq.([intercept ] ) .
according to our earlier discussion , the eigenvalue determined in the leading order does not change order by order .
an interesting feature of this calculation is that the second order correction to the eigenfunction is the term which describes the two gluon exchange in the @xmath0-channel such that the two gluons are in the octet .
the fact that this term reggeizes precisely in the same way as the one gluon exchange is the essence of the celebrated bootstrap feature in high energy qcd @xcite .
the two @xmath0-channel gluons in the previous calculation are in the antisymmetric adjoint representation .
it is easy to show that two gluons in the symmetric adjoint also reggeize ( see second paper in @xcite ) . to see this
let us consider a similar calculation but take the matrix @xmath47 to be in the fundamental representation .
as before we take @xmath108\ ] ] where @xmath109 are generators of @xmath110 in the fundamental representation .
the action of @xmath36 on this state is claculated just like before using @xmath111=\tau^ar_f(y)\delta^2(x - y ) ; \ \ \ \ \ \ [ j^a_r(x),r_f(y)]=r_f(y)\tau^a\delta^2(x - y)\ ] ] using of completeness relation of fundamental su(n ) generators @xmath112\ ] ] the properties of fundamental generators @xmath113 and the representation of an adjoint unitary matrix in terms of fundamental matrices @xmath114\ ] ] one can write @xmath115tr[\tau^ar_{f}(z)]+n_ctr\left[\tau^a\left(r_{f}(u)-r_{f}(z)\right)\right]\right\}\ ] ] the first term on the rhs starts in the order @xmath116 .
thus the eigenvalue equation to second order reads @xmath117\nonumber\\ & & = \omega\int_u\phi(u)\left[\frac{\delta}{\delta\rho_u^a}+\frac{1 } { 2 } \left\{if^{abc}+d^{abc}\right\ } \int_{x^->y^- } \frac{\delta } { \delta\rho^b(u , x^-)}\frac{\delta } { \delta\rho^c(u , y^-)}\right]\end{aligned}\ ] ] again the plane wave eq.([eigenf ] ) is the solution of this equation with the eigenvalue eq.([intercept ] ) .
the second order term proportional to the @xmath118 tensor corresponds to exchange of two @xmath0 - channel gluons in the symmetric adjoint representation . as we have seen in the previous subsection , the antisymmetric octet ( the @xmath119 term ) reggeizes .
thus eq.([symreg ] ) tells us that the symmetric adjoint reggeizes by itself .
this is another example of bootstrap at work .
since the bootstrap plays such an important role in the discussions of high energy amplitudes , it is worth while explaining how and why the bootstrap condition in the klwmij approach is satisfied _ by fiat_. first off , we note that the bootstrap condition , which leads to reggeization of the two gluon exchange can be stated as the relation between the real part of the kernel of the bfkl equation and the reggeized gluon trajectory@xcite . @xmath120 here @xmath121 is the real part of the bfkl kernel which evolves the color singlet two @xmath0-channel gluon state .
it arises from the first term in @xmath54 eq.([bfklno ] ) . expressing it in
coordinate space in terms of the kernel @xmath122 we have @xmath123\ ] ] according to eq.([omegabeta ] ) and eq.([eigenf ] ) the fourier transform of @xmath124 into coordinate space is @xmath125 .
fourier transforming the bootstrap condition into the coordinate space we have @xmath126\ ] ] we can derive this condition directly by considering the eigenvalue equation in the symmetric adjoint channel . take the trial function in the form @xmath127 acting on it by @xmath54 we derive the eigenvalue equation @xmath128&+&\big[\beta_{zv}\psi(z , u)+\beta_{zu}\psi(z , v)\big]\nonumber \\ & = & \omega_q\psi(u , v)\end{aligned}\ ] ] assuming that the solution identical to the single gluon exchange @xmath129 exists for all @xmath130 , and taking the integral over @xmath130 we arrive at the configuration space condition eq.([configbootstrap ] ) . ) can not be derived by acting with the bfkl hamiltonian on the color octet antisymmetric two gluon state , even though this state does reggeize .
the reason is that the reggeization of the antisymmetric octet is technically somewhat different form the symmetric one .
the antisymmetric state @xmath131 appears in the wave function @xmath64 in a combination with the one gluon state @xmath132 .
contributions to the two gluon antisymmetric term in the left hand side of the eigenvalue equation eq.([antisreg ] ) arise both from the action of @xmath54 on @xmath131 * and * from the action of @xmath75 on @xmath132 . on the other hand
the action of @xmath75 on @xmath132 does not generate any contributions to the symmetric octet function .
thus the symmetric octet reggeizes by the action of @xmath54 alone , but the antisymmetric state does not . ] with @xmath125 defined in eq.([beta ] ) , this condition is clearly satisfied .
clearly , the bootstrap condition would be satisfied in the klwmij approach for any functional form of kernel @xmath133 , since the relation between @xmath134 and @xmath135 , eq.([beta ] ) is immutable .
it appears simply due to normal ordering of @xmath54 written in the original form eq.([bfkl ] ) .
thus even if @xmath135 is modified in eq.([bfkl ] ) , the bootstrap condition will still be automatically satisfied .
one can contemplate several reasons for such a modification .
first , higher order corrections in @xmath136 certainly lead to modification of @xmath135 @xcite .
another reason to consider a modification of @xmath135 is the unphysical infrared behavior of perturbative gluon emission which leads to violation of froissart bound @xcite . cutting off long distance tails of the weiszacker - williams field in the emission kernel @xmath135 is a possible `` phenomenological '' solution of this problem @xcite .
one could question in principle the starting point of our discussion - eq.([bfkl ] ) .
however the form eq.([bfkl ] ) is dictated by the hermiticity of @xmath54 .
the real emission part is given by the first term in eq.([bfklno ] ) . by itself
this term is not hermitian , and only with the gluon trajectory term , the second term in eq.([bfklno ] ) , the hermiticity of the hamiltonian is restored .
thus we conclude that the bootstrap condition within the klwmij framework is tantamount to the condition of hermiticity of the hamiltonian which generates the rapidity evolution of the scattering amplitude .
the hermiticity of the hamiltonian is related to the unitarity of the high energy evolution , even though the evolution equation is not a schroedinger equation , but rather a diffusion type equation .
the evolution hamiltonian acts on the probability distribution @xmath49 eq.([evoleq ] ) .
since @xmath137 $ ] has the meaning of probability density , it must be positive definite .
the eigenvalues of the evolution thus better be real , otherwise the `` probability density '' will develop an imaginary part even if one starts with a real and positive distribution at initial rapidity .
this is assured if the evolution hamiltonian is hermitian . the origin of reggeization , including the gluon rerggeization , is in the @xmath0-channel unitarity .
on the other hand the jimwlk / klwmij approach is formulated in @xmath1-channel and has the most natural interpretation as the evolution of the @xmath1-channel wave function .
it is therefore interesting to see how @xmath0 and @xmath1 channel pictures are interrelated on the example of the gluon reggeization .
the two pictures lead to the equivalent description , if the evolution in rapidity can be described by a hermitian hamiltonian .
we note that the bootstrap equation was used in @xcite to find the generalization of the gluon reggeization for the running qcd coupling case .
the jimwlk / klwmij hamiltonian is of course modified when the running is taken into account .
the practical conclusion from our discussion in this subsection is the following : if we know how to include the running of the qcd coupling in @xmath134 of , then can be used to generalize the full bfkl hamiltonian to the running coupling case .
this idea has been explored in @xcite and led to the `` triumvirate '' structure @xcite .
the same form of the hamiltonian was derived recently in @xcite by direct summation of the feyman diagrams in the dipole approximation . with @xmath138
gives the correct generalization of the jimwlk / klwmij hamiltotian for running qcd coupling both for linear and non - linear term at any value of @xmath67 .
as we have seen above , expansion in powers of @xmath3 is the expansion in number of gluons exchanged in the @xmath0-channel . for example the linear approximation of eq.([regg ] ) allows only one gluon exchange between the partons of the projectile and the target .
diagrammatically the approximate diagonalization discussed in the previous section corresponds to summing the diagrams of fig.[f1 ] .
the evolution therefore allows for emission of an arbitrary number of gluons in the wave function of the projectile , but only for a single gluon exchange between the evolved projectile and the target .
the terms quadratic in @xmath3 are represented in fig.[f2 ] .
the vanishing of the last diagram on fig.[f2 ] leaves the remaining contributions local in transverse coordinate and thereby ensures the reggeization of the two gluon exchange . the third order terms are not local anymore .
in particular one encounters the diagrams of fig.[f3 ] which give a non vanishing bilocal contribution .
klwmij evolution in the approximation where only one gluon exchange in the @xmath0-channel is allowed . ]
klwmij evolution in the approximation which allows exchanges of up to two gluons in the @xmath0-channel . ] a nonlocal in transverse plain contribution to the eigenfunction with three @xmath0 channel gluon exchanges . ]
reggeization diagramms with arbitrary number of @xmath0-channel gluons that couple to the same parton in the projectile . ]
since the quadratic terms in the expansion of the wave function reggeize in the same way as the linear term , the significant corrections in a sense start form the cubic order .
there is no reggeization of the third order terms in eq.([1glue ] ) nor eq.([regf ] ) , which is another way of stating that three gluon exchange is sensitive to screening corections .
it is thus interesting to calculate the terms of order @xmath116 in the wave function .
although this can be done , the calculation is somewhat tedious . in this section
we will perform a similar calculation , but the one that is easier implemented and has a somewhat more direct meaning in the framework of @xmath36 .
instead of expanding the wave function @xmath139 $ ] in powers of @xmath3 we will expand it in powers of @xmath51 .
this is similar in spirit to @xcite .
since the complete klwmij wave function must depend on @xmath47 , this type of expansion is more direct . to leading order the expansion in @xmath51 and @xmath3
are equivalent . beyond the leading order however they differ both on the calculational and conceptual levels .
expansion in powers of @xmath51 corresponds to the expansion in the number of the projectile partons which participate in scattering . to linear order in @xmath51
our approximation allows only one parton in the projectile wave function to scatter off the target , but it can scatter by exchanging an arbitrary number of @xmath0-channel gluons .
the diagrams which are resummed in this approximation are depicted on fig .
4 . clearly
the leading order expansion in @xmath3 is subsumed in the leading order expansion in @xmath51 , since if we allow only one @xmath0-channel gluon , we also allow only one parton of the projectile to scatter . in higher orders it is
not the case anymore . in this section
we will calculate @xmath140 $ ] correction to the wave function of eq.([quark ] ) .
recall eq.([regf ] ) @xmath141=\frac{\alpha } { 2\pi^2}\int_{u , z}k_{uuz}\phi_u\left\{tr[1-r^{\dagger}_{f}(z)r_{f}(u)]tr[\tau^ar_{f}(z)]+n_ctr\left[\tau^a\left(r_{f}(u)-r_{f}(z)\right)\right]\right\}\nonumber\\ & & = \frac{\alpha } { 2\pi^2}\int_{u , z}k_{uuz}\phi_u\left\{n_ctr\left[\tau^a\left(r_{f}(u)-r_{f}(z)\right)\right]+tr[r_{f}(u)-1]tr[\tau^ar_{f}(z)]-tr[r^{\dagger}_{f}(z)-1]tr[\tau^ar_{f}(z)]+ ... \right\}\end{aligned}\ ] ] the linear term on the rhs is the familiar reggeization term .
we see thus that reggeization is the property of an arbitrary number of gluon exchanges , as long as all the @xmath0-channel gluons couple to * the same parton * ( in this case quark ) in the projectile .
the second term on rhs is second order in @xmath51 .
note that in terms of the expansion in @xmath3 it actually starts with the cubic order .
clearly , to correct the eigenfunction we have to add to our original @xmath142 a term of second order in @xmath51 . guided by the form of the rhs of eq.([hgaf ] )
we take the wave function to second order of the form @xmath143\nonumber\\ g^a_2&=&\frac{1}{n_c}\int_{u , v}\psi(u , v)tr[r^{\dagger}_f(v)-1]tr[\tau^ar_f(u)]+\frac{1}{n_c}\int_{u , v}\tilde{\psi}(u , v)tr[r_f(v)-1]tr[\tau^ar_f(u)]\nonumber\end{aligned}\ ] ] we will see that this ansatz is general enough to satisfy the eigenvalue equation to second order in the large @xmath67 limit . in the rest of this section
all the matrixes @xmath47 are in fundamental representation and we drop the subscript @xmath144 for convenience . the action of @xmath36 on @xmath145 is straightforward to calculate . after some algebra
we find @xmath146tr[\tau^ar_u]= \nonumber \\ & = & \frac{\alpha } { 2\pi^2}\int_{u , v , z}\psi(u , v)\bigg\{k_{uvz}\big\{tr[r^\dagger_z r^\dagger_vr_z\tau^ar_u]+tr[r^\dagger_zr_u\tau^ar_zr^\dagger_v]-tr[r^\dagger_v\{r_u,\tau^a\}]\big\}\nonumber \\ & & -k_{vvz}\big\{tr(r^\dagger_z)tr[(r^\dagger_v-1)(r_z-1)]+tr(r^\dagger_z-1)tr(r^\dagger_v-1)\nonumber\\ & & + tr(r^\dagger_z-1)tr(r^\dagger_z-1)+n_c[tr(r^\dagger_z-1)+tr(r_z-1)]\big\}tr(\tau^ar_u)\nonumber \\ & & -k_{uuz}\big\{tr[r^\dagger_v-1]tr[(r^\dagger_z-1)(r_u-1)]+tr[r^\dagger_v-1]tr[r^\dagger_z-1]\nonumber\\ & & + tr[r^\dagger_v-1]tr[r_u-1]+n_ctr[r^\dagger_v-1]\big\}tr[\tau^ar_u]\nonumber \\ & & + n_ck_{uuz}tr[r^\dagger_v-1]tr[\tau^ar_u]\bigg\}\end{aligned}\ ] ] keeping only @xmath147 $ ] terms and taking large @xmath67 limit for simplicity , we have @xmath148tr[\tau^ar_u]= \\ & & = \frac{\alpha } { 2\pi^2}\int_{uvz}n_c\bigg\{\psi(u , z)k_{vvz}tr[1-r_v]tr[\tau^ar_u]+\big[\psi(u , z)k_{vvz}+\psi(z , v)k_{uuz}-\psi(u , v)k_{uuz}\big]tr[1-r^\dagger_v]tr[\tau^ar_u]\bigg\}\nonumber\end{aligned}\ ] ] similarly to quadratic order in the large @xmath67 limit @xmath149tr[\tau^ar_u]= \\ & = & \frac{\alpha } { 2\pi^2}\int_{uvz}n_c\left\{\tilde{\psi}(u , z)k_{vvz}tr[1-r^\dagger_v]tr[\tau^ar_u]+\left(\tilde{\psi}(u , z)k_{vvz}+\tilde{\psi}(z , v)k_{uuz}-\tilde{\psi}(u , v)k_{uuz}\right)tr[1-r_v]tr[\tau^ar_u]\right\}\nonumber\end{aligned}\ ] ] finally we have @xmath150tr[\tau^ar_u]\nonumber\\ & + & \frac{\alpha } { 2\pi^2}\int_{u , v , z}\left\{\tilde{\psi}(u , z)k_{vvz}+\psi(u , z)k_{vvz}+\tilde{\psi}(z , v)k_{uuz}-\tilde{\psi}(u , v)k_{uuz}\right\}tr[1-r_v]tr[\tau^ar_u]\end{aligned}\ ] ] we determine the functions @xmath151 and @xmath152 by solving the eigenvalue equation @xmath153 with the eigenvalue @xmath154 given by eq.([intercept ] ) . as we have seen in eq([hgaf ] ) the linear terms reggeize and cancel between the left and right hand side .
for the quadratic terms we are then left with the equation @xmath155tr(\tau^ar_z)\nonumber \\ & + & \frac{\alpha } { 2\pi^2}\int_{u , v , z}\left\{\psi(u , z)k_{vvz}+\tilde{\psi}(u , z)k_{vvz}+\psi(z , v)k_{uuz}-\psi(u , v)k_{uuz}\right\}tr[1-r^\dagger_v]tr[\tau^ar_u]\nonumber\\ & + & \frac{\alpha } { 2\pi^2}\int_{u , v , z}\left\{\tilde{\psi}(u , z)k_{vvz}+\psi(u , z)k_{vvz}+\tilde{\psi}(z , v)k_{uuz}-\tilde{\psi}(u , v)k_{uuz}\right\}tr[1-r_v]tr[\tau^ar_u]\nonumber \\ & = & \frac{\omega_q } { n_c}\int_{u , v}[\psi(u , v)tr(r^\dagger_v-1)tr(\tau^ar_u)+\tilde{\psi}(u , v)tr(r_v-1)tr(\tau^ar_u)]\end{aligned}\ ] ] with @xmath156 .
this reduces to the equation for @xmath151 and @xmath157 : @xmath158-\frac{\omega_q } { n_c}\psi(u , v)=\frac{\alpha } { 2\pi^2}\int_zk_{zzu}\phi_z\delta(u - v)\\ \frac{\alpha } { 2\pi^2}&&\int_z\left[\tilde{\psi}(u , v)k_{uuz}-\tilde{\psi}(u , z)k_{vvz}-\tilde{\psi}(z , v)k_{uuz}-\psi(u , z)k_{vvz}\right]-\frac{\omega_q } { n_c}\tilde{\psi}(u , v)=\frac{\alpha } { 2\pi^2}k_{vvu}\phi_v\end{aligned}\ ] ] these equations are easily solved in momentum space .
defining @xmath159 it is starightforward to fourier transform eq.([correction ] ) .
for example @xmath160 the ultraviolet cutoff @xmath161 is needed to regularize the divergence in the fourier transfrom of @xmath162 .
similarly fourier transforming the rest of the terms we get @xmath163 the solution is found straightforwardly as @xmath164 transforming back to the configuration space we find the eigenfunction to second order in @xmath51 and in the large @xmath67 limit @xmath165\big[1-\frac{1 } { n_c}tr[r_f(u)-1]\big]\ ] ]
to summarize we have discussed relationship between the klwmij hamiltonian and its bfkl limit .
eigenfunctions of @xmath36 when expanded to leading order in @xmath3 become eigenfunctions of @xmath54 .
it is however difficult to determine which eigenfunctions of @xmath54 become _ normalizable _ eigenfunctions of @xmath36 when the taylor series is resummed to all orders .
the relation of course pertains only to functions ( functionals ) which are expandable in taylor series in @xmath3 .
we know from the general discussion of @xcite that @xmath36 also has eigenfunctions which do not have such an expansion .
those are states close to the black disk limit . for those states the pertinent expansion is in powers of @xmath2 .
we note that @xmath54 is self dual under the transformation @xmath166 it thus contains eigenstates whose eigenfunctions are monomials in @xmath2 rather than @xmath3 .
the self duality ensures that those have exactly the same spectrum as the eigenfunctions we discussed in the bulk of this paper , even though these states are indeed formally close to the black disk limit the duality transformation eq.([duality ] ) is the linearized version of eq.([densedilute ] ) which transforms @xmath36 to @xmath37 .
thus the same relation as discussed above exists between the second set of the eigenfunctions of @xmath54 and the eigenfunctions of @xmath37 .
we have also discussed the gluon reggeization and the appearance of the bootstrap condition in the kwlmij formalism .
the bootstrap condition is direct consequence of hermiticity of @xmath167 and as such is a necessary attribute of the approach .
any modification of the emission kernel @xmath133 does not ruin the bootstrap property . since the jimwlk picture is a @xmath1-channel one while the reggeization stems from the @xmath0 channel unitarity
, we conclude that the hermiticity of @xmath167 is the property that reconciles these two approaches .
further we have discussed expansion of the eigenfunctions in powers of @xmath51 rather than powers of @xmath3 .
this corresponds to expansion in the number of partons in the projectile wave function which participate in the scattering .
we have calculated @xmath140 $ ] correction to the reggeized gluon wave function and found that is has a very simple form in the large @xmath67 limit .
we note in this respect that while the eigenvalue determines the rapidity dependence of the scattering amplitude , the functional form of the wave function determines the impact factor .
this follows from the expansion eq.([psii ] ) which can be written as the overlap of the `` wave function '' characterizing the projectile hadron at the initial rapidity and the eigenfunction of the evolution hamiltonian @xmath168 thus for example the eigenfunction eq.([1glue ] ) will not have zero overlap with a single quark state , while that of eq.([quark ] ) will not overlap with a gluon projectile , since their incoming color representations can not be combined into a singlet .
thus in order for the amplitudes of both , quark and gluon projectiles to have the same energy dependence , there must be a degeneracy in the spectrum of @xmath36 .
we indeed saw this degeneracy explicitly since both eigenfunctions eq.([1glue ] ) and eq.([quark ] ) correspond to the same eigenvalue . on the formal level
this degeneracy is the consequence of the fact that perturbative vacuum breaks the global symmetry of @xmath36 as @xmath169 , the reggeized gluon being `` the goldstone boson '' associated with this breaking @xcite .
one of us ( e.l . ) thanks physics department of the university of connecticut for hospitality and creative atmosphere during his visit when this work was done .
this work was supported in part by the doe grant de - fg02 - 92er40716.00 and fondecyt ( chile ) grant # 1100648 .
in order to derive the bfkl hamiltonian we have to expand @xmath170 and @xmath171 in powers of @xmath172 .
the expansion of @xmath47 is straightforward . to expand @xmath38 and @xmath39
we will use their commutation relations with @xmath52 .
we start with the klwmij hamiltonian @xmath173 expansion of @xmath47 is straightforward . to
second order we have @xmath174 to expand @xmath39 we use the commutation relation @xmath97=t^ar(y)\delta^2(x - y)\ ] ] it is easy to check that to second order in @xmath3 the following expression satisfies the correct commutation relation @xmath175 now using the fact that @xmath176 we have also @xmath177 now the expansion of the amplitude @xmath178 reads @xmath179j^b_r(x ) \nonumber \\ % & = & \int_x\frac{(x - z)_i}{(x - z)^2}\left[r^{ab}(z)j^b_r(x)-j^a_l(x)\right ] \nonumber \\ & = & \int_x\frac{(x - z)_i}{(x - z)^2}t^{\alpha \beta}_a\left[\int_0 ^ 1dx^{-}_1\int_0 ^ 1dx^{-}_2\rho^\alpha(x , x^{-}_1)\frac{\delta}{\delta \rho^\beta(x , x^{-}_2)}-\int_0 ^ 1dx^{-}_1\int_0 ^ 1dz^{-}_1\rho^\alpha(x , x^{-}_1)\frac{\delta}{\delta \rho^\beta(z , z^{-}_1)}\right]\nonumber\\ & = & \int_x\frac{(x - z)_i}{(x - z)^2}t^{\alpha \beta}_a\left[\rho^\alpha_x\left(\frac{\delta}{\delta \rho^\beta_x}-\frac{\delta}{\delta \rho^\beta_z}\right)\right]\end{aligned}\ ] ] with @xmath180 and @xmath181 . finally we can write the bfkl hamiltonian as in eq([bfkl ] ) .
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graphs and trees , labeled by various kinds of integral data , make numerous appearances across mathematics and its applications , in this note we will discuss instances from algebraic geometry , conformal field theory , representation theory , and mathematical biology . along the way we will see how these instances are related by the same type of geometric structure : a flat family of algebras over the moduli of curves .
a natural example of a family of algebras of labeled trees is the class of deformations of the plcker embedding of the grassmannian of @xmath1-planes @xmath2 parametrized by the tropical grassmannian @xmath3 introduced by speyer and sturmfels in @xcite .
the toric members of this family have a very nice description as the affine semigroup algebras of the cones @xmath4 where @xmath5 is a finite trivalent tree with @xmath6 ordered leaves .
the cone @xmath7 is the set of weightings of the edges of @xmath5 by nonnegative real numbers , such that the triangle inequalities are satisfied for the the three weights incident on any internal vertex of @xmath8 the lattice of integral points in this cone is taken to be integer weightings of @xmath5 such that the sum of the weights about any internal vertex is even .
a similar family of semigroup algebras was constructed by buczynska and wiesniewski in @xcite as an algebraic analogue to the jukes - cantor statistical model of phylogenetics .
these models are parametrized by the same class of trees @xmath9 and aid in the study of ancestral relationships between a set of @xmath6-taxa .
the polytopes @xmath10 ( author s notation ) of buczynska and wiesniewski are defined as the set of weightings of the tree @xmath5 with the same conditions and lattice as @xmath7 , along with the additional condition that the sum of the weights about each internal vertex is equal to @xmath11 this polytope is compact , and so defines a projective toric variety .
buczynska and wiesniewski were able to show that the graded algebras @xmath12 $ ] are deformation equivalent , and therefore share the same hilbert function .
their visually appealing method was to construct pair - wise deformations between algebras associated to topologically similar trees , those related by a so - called flip - move .
buczynksa and wiesniewski conjectured the existence of a global algebra that would have one toric deformation for each tree @xmath5 to @xmath12,$ ] and serve in the same role as the plcker algebra serves for the family @xmath13.$ ] this conjecture was answered by sturmfels and xu in @xcite , where they showed that the cox - nagata ring @xmath14 of the blow - up @xmath15 of @xmath16 at @xmath6 generically positioned points has precisely these properties . in this same paper , sturmfels and
xu drew attention to the work of bauer , @xcite who showed that the moduli space of quasiparabolic rank 2 semistable bundles on the @xmath6-punctured projective line @xmath17 is connected to @xmath15 be a series of flops .
this moduli space caries line bundles @xmath18 where @xmath19 is an @xmath20 tuple of nonnegative integers .
the global sections @xmath21 is known as the space of non - abelian theta functions , and its dimension is computed by the celebrated verlinde formula from mathematical physics , for the case where the symmetries are given by @xmath22 birational flops preserve the picard group and the cox ring , and so ensure that the phylogenetic hilbert functions of buczynska and wiesniewski can also be computed by the verlinde formula .
this intriguing connection was the starting point for this project , it suggests that the combinatorial structures related to the verlinde formula , the `` factorization rules , '' have a geometric underpinning . in this paper
we interpret the factorization rules in terms of deformation relations among graded rings attached to moduli of principal bundles .
we will also extend this structure for all genus and all simple lie algebras @xmath23 over @xmath24 .
the `` geometric factorization rules '' constructed here give a way to recursively study linear series on moduli of principle bundles , in particular for @xmath25 we obtain toric deformations of the moduli of semistable bundles .
this will also allow us to answer a conjecture of millson @xcite on the relationship between linear series on the moduli of bundles for @xmath25 and linear series on weight varieties of the grassmannian variety of @xmath1-planes .
generalizing to arbitrary genus for @xmath25 also extends the result of sturmfels and xu to varieties which define a generalization of the statistical models of buzcynska and wiesniewski to equivalent varieties for `` phylogenetic networks , '' graphs with positive first betti number , studied by buczynska in @xcite
. we will begin by describing the genus @xmath26 @xmath27 variant of our ideas and build up to the general case .
the pairwise deformations of buczynska and wiesniewski along with the global deformation constructed by sturmfels and xu suggest an ambient deformation structured on a stratified space , with the combinatorics of the stratification coming from a `` space '' of trees .
a natural stratified object from algebraic geometry which carries this combinatorial structure is @xmath28 the moduli stack of @xmath6-pointed stable curves of genus @xmath29 naively , we are looking for a flat sheaf of algebras on this stack , with the toric algebras from @xcite showing up as the fibers over the lowest strata .
we would also like to incorporate the mathematical physics of the verlinde formula , which comes ready made with a graph - based combinatorial structure via the factorization rules .
a natural candidate satisfying both conditions comes from the work of tsuchiya , ueno and yamada @xcite on conformal field theory , in the form of the locally free sheaf of conformal blocks @xmath30 on the moduli stack of stable @xmath6-punctured curves of genus @xmath29 here @xmath31 is an @xmath6-vector of dominant @xmath27 weights , and @xmath32 is a positive integer called the level .
let @xmath33 be a smooth genus @xmath34 @xmath6-punctured curve , then there are isomorphisms of vector spaces which establish that the rank of the sheaf of conformal blocks is equal to the dimension of the space of generalized theta functions .
@xmath35 tsuchiya , ueno , and yamada used this identification to prove the factorization rules for the verlinde formula by studying what happens as the curve @xmath33 is allowed to degenerate to a punctured stable curve .
any such curve @xmath36 has a smooth normalization @xmath37 where @xmath38 are the doubled points of the normalization . in @xcite
the following is proved @xmath39 where @xmath40 if the associated puncture points are identified by the normalization .
this is known as the factorization rule for conformal blocks with @xmath27 symmetry .
when @xmath33 is stable of genus @xmath34 , its stable types fall into a finite number of equivalence classes , indexed by labeled trees @xmath8 each term in the sum on the right above then becomes a tensor product over the internal vertices of the tree @xmath8 the above isomorphism gives the following formula for dimensions .
we will simplify to the case of two internal vertices , the reader can generalize the formula to larger trees .
@xmath41 the reader may notice that formula [ fact ] is the counting formula of buczynska and wiesniewski from @xcite when all vertices of @xmath5 are trivalent .
all of the constructions above work for any genus @xmath42 and any simple lie algebra @xmath43 this work was carried out in @xcite , but we refer the reader to the book by shimizu and ueno @xcite , the book by frenkel and ben - zwi @xcite , and the paper by looijenga @xcite for helpful discussion and other points of view . in what follows
objects are fibered over the moduli stack of stable curves with @xmath6 punctures @xmath44 choose once and for all a weyl chamber @xmath45 and for the longest root @xmath46 let @xmath47 where @xmath48 is the corresponding coroot .
let @xmath49 be the moduli stack of parabolic principal @xmath50-bundles on the punctured curve @xmath36 with parabolic structures @xmath51 at the puncture points , for @xmath52 with @xmath50 simply connected .
these stacks carry line bundles @xmath53 where @xmath54 is a vector of dominant @xmath23-weights , and @xmath32 is a non - negative integer . for a punctured curve of genus @xmath42
the verlinde formala calculates the dimension of the space of global sections of these line bundles with the following expression .
@xmath55 here @xmath56 is the dual coxeter number of @xmath57 @xmath58 is the half sum of the positive roots , @xmath59 is a character associated to the tensor product of irreducible representations @xmath60 and @xmath61 is the cardinality of a certain subgroup of a maximal torus of @xmath62 this impressive expression hides the deeper symmetry of the verlinde formula given by the factorization rules , which allow one to calculate the formula for any genus and number of punctures with expressions like equation [ fact ] .
in fact , the above equation can be derived from the factorization rules once one understands the characters of an associated combinatorial structure called the fusion algebra , see the second half of beauville s paper @xcite for details on this beautiful calculation . in their proof of the factorization rules , tsuchiya ,
ueno and yamada constructed , for any tuple @xmath54 of dominant weights , and any non - negative integer @xmath32 ( still called the level ) , a coherent , locally free sheaf @xmath63 with a projectively flat connection on @xmath44 the sheaf of conformal blocks geometrically ties together spaces of partition functions for the wzw model of conformal field theory as the complex curve @xmath36 varies .
a different proof of the factorization rules was obtained by faltings in @xcite .
various authors @xcite , @xcite , have shown that for a point @xmath64 there is an isomorphism of vector spaces @xmath65 conformal blocks have generated much interest , due in part to their relationship with the moduli of principal bundles @xmath66 they have also been useful in the representation theory of kac - moody algebras and quantum groups , and have served as a source of examples for the theory of modular tensor categories , see @xcite .
in addition , conformal blocks have a @xmath67-module structure which have made them objects of interest in the geometric langlands program .
conformal blocks are not unique to nice categories of lie algebras , they can also be constructed from the representation theory of chiral vertex operator algebras , @xcite .
as combinatorial structures associated to conformal blocks have already made appearances in phylogenetic and combinatorial algebraic geometry , it is our hope that the constructions can be suitably generalized to these other cases to provide further sources of interesting combinatorics .
our first order of business is to construct a global algebraic object which ties the algebras of each combinatorial type together .
we do this with sheaves of conformal blocks .
[ t1 ] for any simple lie algebra @xmath23 with associated simple , simply connected reductive group @xmath50 , the direct sum of vector bundles , @xmath68 forms a sheaf of algebras on @xmath44 here the sum is over all tuples @xmath54 with dominant weight entries from @xmath45 and all nonnegative integers @xmath69 fiber - wise , multiplication on this sheaf agrees with multiplication of global sections of the corresponding line bundles on the moduli stacks @xmath66 this is our global object , connecting the algebras over smooth curves with those over stable curves . since each of these sheaves is a sum of vector bundles , the multigraded hilbert functions are independent of base point .
we can calculate the rank of the sheaves @xmath63 with the verlinde formula , @xmath70 there is one catch , we lack a `` factorization '' property on the ring structure .
we desire this property in order to study the more complicated algebras attached to surfaces of higher genus with their smaller genus counterparts .
we remedy this with the following theorem , first a definition . [ cones ] let @xmath33 be a stable curve with punctures at @xmath71 and let @xmath37 be a normalization with new punctures @xmath72 fix a cartan subalgebra @xmath73 of @xmath23 , with dual @xmath74 consider the cone @xmath75 of linear functionals @xmath76 which satisfy @xmath77 for all negative roots .
this is the cone of functionals which respects the ordering on the dominant weights in @xmath78 let @xmath79 be the longest element of the weyl group .
we call @xmath80 such that pairs @xmath81 and @xmath82 are weighted with functionals @xmath83 a @xmath23-weighting of @xmath84 note that the functionals on @xmath85 need not be restricted to @xmath86 the reason for the factor of @xmath87 will be made clear later .
fixing a stable curve type @xmath88 we have a map of stacks @xmath89 which glues the associated points of the normalization .
the image of this map is the stratum of @xmath90 associated to the type @xmath91 we now have enough to state the second theorem .
[ t2 ] for each stability type @xmath88 and a @xmath23-weighting @xmath92 which is strictly negative on negative roots , there is a flat deformation defined by filtration , @xmath93 where the tensor product is over the connected components of the normalization of the type @xmath88 and the symbol @xmath94 denotes fiber - wise torus invariants by the action which identifies weights @xmath95 on a puncture @xmath81 with the dual weight @xmath96 on its partner @xmath97 and forces the levels @xmath32 to be equal . over a point @xmath98
this says that there is a filtration which defines a flat deformation , @xmath99 where @xmath100 is the normalization of @xmath101 this is where the combinatorial data of moduli of curves comes into the picture .
multiplication over the stable locus `` flattens '' to multiplication over each connected component of the normalization .
the algebras over different strata of @xmath102 are then connected by flat families , as in the case @xmath103 @xmath104 in @xcite .
the deformations described in this paper add torus symmetries and so define new polytopes which come with surjections onto the effective cone of @xmath105 if enough torus symmetries are added , one obtains a toric algebra .
let @xmath106 be a finite trivalent graph , and let @xmath107 be the polytope defined by integer weightings of @xmath106 which satisfy the same local conditions which define @xmath108 the algebras associated to these polytopes
@xmath109 $ ] have been studied by buczynska in @xcite , and of course match the phylogenetic algebras of buczynska and wiesniewski when the first betti number of @xmath106 is @xmath29 the next proposition follows from theorems [ t1 ] and [ t2 ] .
[ toric ] for @xmath110 the algebra of conformal blocks @xmath111 for a curve of genus @xmath42 with @xmath6 marked points flatly deforms to @xmath112 $ ] for any graph @xmath106 with first betti number equal to the genus of @xmath33 and number of leaves equal to the number of marked points @xmath85 on @xmath101 for fixed genus and number of punctures , the cones defined in definition [ cones ] fit together into a stratified complex , like a tropical variety .
we will remark later on why we believe this is the case . in the case
@xmath104 these are the moduli of pseudo - tropical curves constructed by brannetti , melo , and viviani in @xcite , for @xmath104 and @xmath113 these are abstractly tropical grassmannians , and can be realized as the tree spaces of billera , holmes and vogtman , @xcite . for genus @xmath34
all graphs @xmath106 are trees with @xmath6 labeled leaves .
there is a natural map relating the space of conformal blocks with labels @xmath54 and an associated space of invariants in @xmath114 an @xmath6-fold tensor product of @xmath23-representations .
@xmath115 we call @xmath116 the space of covariants , and @xmath117 the space of invariants .
when the genus of the curve @xmath33 is @xmath34 this map is injective . in order to make use of this we will study the deformation theory of branching algebras , @xmath118 from the representation theory of @xmath57 these will be defined later .
branching algebras are a way to introduce commutative algebra ( and therefore geometry ) into the study of branching rules along morphisms of reductive groups .
the algebras of conformal blocks are a quantum analogue for representations of kac - moody algebras with respect to the `` fusion '' tensor product structure , and when formulated as morphism of rings , the map @xmath119 allows one to show that the geometry underlying conformal blocks becomes the `` classical '' geometry of the branching rules in the limit @xmath120 .
the branching algebra above has the same relationship to the algebra of conformal blocks as the plcker algebra @xmath121 $ ] does to the cox - nagata ring @xmath122 and in fact for @xmath123 there is an isomorphism @xmath124.$ ] this was shown by howard , manon , and millson as a step in studying the symplectic geometry of polygons in euclidean space , see @xcite for more on this point . to generalize this relationship and make it precise , we define a new algebra @xmath125 using the product from @xmath126 @xmath127 t^l\ ] ] there is then a well - defined injection of rings
@xmath128 for each tree and assignment of functionals , @xmath129 there is a natural filtration of @xmath130 which we will construct from the representation theory of @xmath57 it will then be possible to prove the following theorem .
[ g0 ] let @xmath36 be a punctured stable genus @xmath34 curve of type @xmath8 then the deformations associated to @xmath129 on @xmath111 and @xmath131 agree under the correlation morphism @xmath119 returning now to the moduli @xmath49 , the cox rings of these moduli stacks are in a natural way subrings of @xmath132 they are picked out by the blocks with @xmath54 sitting in the product of faces of the weyl chamber @xmath133 defined by @xmath134 these subrings are respected by the deformations defined by @xmath135 hence we obtain flat families of @xmath24-algebras which connect the cox rings of parabolic moduli stacks to torus invariants of tensor products of the algebras of conformal blocks associated to punctured copies of @xmath136 this can be taken as a `` ringification '' of the factorization rules , and shows that factorization is geometric property of the moduli of bundles as well as a representation theoretic phenomenon . for each @xmath137
there is a stability condition on @xmath49 which picks out a substack of semistable points @xmath138 which has a smooth , projective coarse moduli space @xmath139 which comes with an embedding given by the graded ring @xmath140 the theorems we have described above all descend to this ring by taking torus invariants with respect to the appropriate character . as a consequence of proposition [ toric ] we obtain toric deformations of moduli spaces of quasiparabolic semistable principle bundles @xmath141 in the case @xmath142
let @xmath106 be a finite graph , and let @xmath143 be the subpolytope of @xmath144 defined by setting the leaf - weights to @xmath145 the flat families defined in theorems [ t1 ] and [ t2 ] define a deformation of graded algebras .
@xmath146\\\ ] ] where @xmath106 is any graph with first betti number equal to the genus of @xmath33 with @xmath147 leaves .
letting @xmath148 be the subpolytope of @xmath7 obtained by fixing the weights on the leaf edges to be @xmath31 we see there is an obvious injection of graded rings .
@xmath149 \to \c[p_{\tree}(\vec{r})]\\\ ] ] the algebra @xmath150 $ ] makes an appearance in @xcite and @xcite as a toric deformation of a weight variety of the grassmannian of @xmath1-planes . from theorem [ g0 ]
we get an injection of graded rings , @xmath151 which echoes the injection on toric rings .
for @xmath110 the algebra on the right above is given by a linear series on a weight variety of the grassmannian of @xmath1-planes , where the character of the torus @xmath31 is equivalent to choosing a vector of dominant @xmath27 weights as above .
this led millson to make the following conjecture . for a trivalent tree
@xmath5 with @xmath6-leaves , give the ring @xmath152 the associated term - order filtration from @xcite and @xcite with associated graded isomorphic to @xmath150.$ ] then the associated graded ring corresponding to the induced filtration on @xmath153 $ ] is isomorphic to @xmath154.$ ] we see from theorem [ g0 ] that this is not far from the truth . for a trivalent tree
@xmath5 with @xmath6-leaves , give the ring @xmath152 the associated term - order filtration from @xcite and @xcite with associated graded isomorphic to @xmath150.$ ] then the associated graded ring corresponding to the induced filtration on @xmath155 is isomorphic to @xmath154 $ ] precisely when @xmath33 is the stable curve of genus @xmath34 of stability type @xmath8 we would like to know how to make toric deformations for other simple lie algebras , in order to realize the verlinde formula for these algebras in terms of counting lattice points in polytopes .
this can be carried out for @xmath27 using the factorization rules .
let @xmath110 and let @xmath106 be a trivalent graph with @xmath6 leaves of genus @xmath156 then @xmath157 is equal to the number of lattice points in the polytope and lattice defined by weightings of @xmath106 satisfying 1 .
the three weights about any internal vertex of @xmath106 satisfy the triangle inequalities .
the sum of the three weights about any internal vertex of @xmath106 is even and less than or equal to @xmath158 3 .
the @xmath159-th leaf edge of @xmath106 is weighted @xmath160 a significant step in the understanding of algebras of conformal blocks and obtaining interesting polytope descriptions of the general verlinde formula would be made by obtaining toric deformations of @xmath111 for @xmath33 of genus @xmath34 with @xmath161 punctures , because by theorem [ t2 ] , all algebras of conformal blocks can be `` constructed '' from this case .
one way to approach to this problem is to find toric deformations of @xmath162 and understand them with respect to the map @xmath163 this is our main motivation for using branching algebras . so far , sagbi degenerations of @xmath164 have been constructed in the case @xmath165 and @xmath166 among others by howe , tan , and willenbring in @xcite .
we will also outline an approach using dual canonical basis which applies for large values of @xmath32 .
moduli of bundles also have a well - known symplectic structure , ( for example see @xcite ) , and the effective cones of @xmath49 are deeply related to the geometry of conjugacy classes in the compact lie group @xmath167 where @xmath168 let @xmath169 be the lie algebra of a maximal torus of @xmath167 and let @xmath170 be the conjugacy class of @xmath171 then the rational points of the polytope , @xmath172 are exactly the set of weights @xmath173 such that @xmath174 for some @xmath32 where @xmath175 is chosen so @xmath176 is dominant .
one wonders if factorization can be `` geometrified '' with respect to the symplectic geometry of conjugacy classes in @xmath177 ideas along these lines can be found for the @xmath0 case in the paper of hurtubise and jeffrey on moduli of @xmath178 connections on surfaces , @xcite .
we believe the spectrum of @xmath179 for @xmath0 ought to be deeply related to the `` master space '' of parabolic sheaves constructed in @xcite .
see also @xcite for a similar connection between the symplectic geometry of polygons and deformations of the moduli of points on the projective line .
the paper is organized as follows .
we discuss and prove theorem [ t1 ] in section @xmath180 and construct filtrations of the algebra of conformal blocks to prove theorem [ t2 ] in section @xmath181 in section @xmath182 we introduce branching algebras and their filtrations , we then look at the special case of the diagonal morphism @xmath183 for a reductive group and describe the relationship between this algebra and the algebra of conformal blocks with theorem [ g0 ] . in section
@xmath184 we look at the case @xmath110 where the most is known .
in this section we review the definition of the sheaf of conformal blocks .
we will also construct the multiplication operation , and show that its specialization at stable punctured curve @xmath36 is equal to multiplication of global sections of line bundles on the corresponding moduli stack .
following @xcite , we work with families of curves over complex varieties .
we also refer the reader to @xcite for a more detailed discussion of the conformal block construction .
we thank eduard looijenga for helpful conversations on his construction of the sheaf of conformal blocks . in this subsection
we review the construction of the affine kac - moody algebra associated to a simple lie algebra @xmath43 we also review the construction of some important representations of this algebra , the verma modules and the integrable highest weight modules . for this section
we refer the reader to any of the numerous introductions to this subject as associated with conformal blocks , such as @xcite , @xcite , @xcite , @xcite , @xcite . for each irreducible @xmath185representation @xmath186
we choose a highest weight vector @xmath187 as a vector space the affine lie algebra is @xmath188 the bracket is defined by the following properties . 1 .
@xmath189 is a central element of @xmath190 2 .
@xmath191 = [ x , y ] \otimes fg + ( x , y ) res_0 ( g df ) \mathfrak{c } $ ] where @xmath192 $ ] is the bracket on @xmath23 and @xmath193 is the normalized killing form on @xmath43 this lie algebra has a triangular decomposition defined by the following subalgebras .
@xmath194t\ ] ] @xmath195t^{-1}\ ] ] @xmath196 we have @xmath197 this decomposition implies the existence of various highest weight representations .
we fix a level @xmath69 define an action of @xmath198 on @xmath186 by letting @xmath189 act as multiplication by @xmath32 and @xmath199 act trivially .
the verma module is defined as @xmath200 the subspace @xmath201 can then be identified with @xmath202 the highest weight @xmath203 integrable representation of @xmath190 is defined as @xmath204 for our chosen highest weight vector @xmath205 we also make use of the related lie algebra @xmath206 \oplus \c \mathfrak{c},$ ] with @xmath189 regarded as central and bracket defined by @xmath207 \otimes f_i g_i + \sum res_o(g_i df_i ) \mathfrak{c}\ ] ] this is the lie algebra @xmath208 with the central elements @xmath209 all identified .
the fact that all central elements must therefore act the same on a tensor product of integrable highest weight modules is the reason why we will work with @xmath210 where all the levels are the same .
if we fix a punctured curve @xmath36 , there is an associated lie algebra @xmath211.$ ] there is no map @xmath212 \to \bigoplus_{i = 1}^n \hat{\mathfrak{g}}.$ ] however , there is a map @xmath212 \to \bigoplus_{i = 1}^n \mathfrak{g } \otimes \c((t_i)),$ ] and because of the residue theorem , this map extends to the central extension , so we obtain @xmath213 as a representation of @xmath211 $ ] .
let @xmath214 be a smooth variety over @xmath215 following @xcite we will sheafify the representation theory of @xmath216 over @xmath217 by a stable curve of genus @xmath42 over @xmath214 with @xmath6 puncture points we mean a proper , flat map of varieties @xmath218 where all fibers of @xmath219 are stable curves of genus @xmath220 and @xmath6 pairwise non - intersecting sections @xmath221 which avoid the doubled points
. we will abuse notation slightly , referring to the data @xmath222 as @xmath101 we need a sheafified version of the affine lie algebra attached to a simple complex lie algebra @xmath43 let @xmath223 be the divisor given by the images of the sections @xmath224 the following can be found in @xcite and @xcite , and we refer the reader to @xcite for a more algebraic approach .
we define the following sheaves of lie algebras over @xmath217 let @xmath225 be the formal completion of @xmath226 along @xmath227 @xmath228 \oplus \mathcal{o}_s \mathfrak{c}\ ] ] @xmath229 @xmath230 these are sheaves of lie algebras over @xmath217 the algebra @xmath231 can be realized as a sub lie - algebra object of @xmath232 and the fiber of @xmath233 at @xmath234 is equal to @xmath235.$ ] let @xmath213 be an @xmath6-fold tensor product of integrable highest weight modules of @xmath236 let @xmath237 be an @xmath6-fold tensor product of irreducible highest weight modules of @xmath57 we define @xmath238 @xmath239 by choosing an isomorphism @xmath240 the sheaf @xmath241 is a @xmath242 module , and @xmath243 is a @xmath231 module in a natural way , which is equivariant with respect to its inclusion in @xmath244 in @xcite and @xcite this isomorphsim is shown to be equivalent to selecting tangent vectors at punctures , see also @xcite for discussion of this point . in @xcite
, looijenga gives a construction of this representation that is independent of the choice of isomorphism , see also @xcite .
the algebra @xmath233 can be realized as a sub - lie algebra of @xmath245 to give a representation on @xmath244 for any lie algebra @xmath23 over @xmath24 and representation @xmath246 we have the space of invariants @xmath247^{\mathfrak{g}}\ ] ] the same applies to sheaves of lie algebras and representations over a scheme @xmath248 with @xmath249 the sheaf of morphisms , and @xmath250 as a dualizing object .
the sheaf of covacua @xmath251 is defined to be the sheaf of coinvariants of the action of @xmath233 on @xmath244 the sheaf of vacua or conformal blocks , @xmath252 is defined to be the corresponding sheaf of invariants .
@xmath253 the sheaf of conformal blocks @xmath63 is shown to be coherent and locally free in @xcite , with clarifications in @xcite and @xcite . taking a single fiber @xmath254 of @xmath219 we may define the vector space of conformal blocks , @xmath255 it is not hard to prove @xmath256 moreover
, the definition of conformal blocks commutes with pullbacks of families of @xmath6-punctured curves .
hence there are well - defined coherent , locally free sheaves @xmath63 on @xmath44 now we define the multiplication operation on sheaves of conformal blocks .
recall that we have chosen highest weight vectors @xmath257 for each irreducible highest weight representation of @xmath43 essential to our discussion are the following two commutative diagrams .
@xmath258 @xmath259 the first is obtained by identifying the highest weight vectors @xmath260 the second diagram is obtained from the first diagram by tensoring with @xmath261 it is a commuting square of @xmath231 sheaves over @xmath217 since the level is always fixed across the tensor products ,
the top row is a map of @xmath233 modules .
the first diagram is the localization of the second at a point @xmath262 the following lemma will be used throughout the paper . dualizing :
let the following be a commutative diagram of sheaves .
@xmath263 then the following diagram also commutes .
@xmath264 first , apply the duality functor to the top diagram .
@xmath265 now paste this diagram to the following diagram , which follows from the binaturality property of duality .
@xmath266 [ mainsquare ] the following diagram commutes .
@xmath267 first we consider the bottom row of diagram [ d2 ] . for a sheaf of representations @xmath268
let @xmath269 denote the image of the action map , that is , the sheaf of sections of the form @xmath270 for @xmath271 and @xmath272 this defines the quotient sheaf @xmath273 = w/ \mathfrak{g}(s)w.$ ] since our diagram is equivariant , we get @xmath274 @>v[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\lambda } , l ) \otimes \mathcal{h}_s(\vec{\gamma } , k)]\\ @aaa @aaa\\ v_{\mathfrak{g}(s)}[v_s(\vec{\lambda } + \vec{\gamma } ) ] @>v[c_{\vec{\lambda } + \vec{\gamma } } ] > >
v_{\mathfrak{g}(s)}[v_s(\vec{\lambda})\otimes v_s(\vec{\gamma})]\\ \end{cd}\ ] ] now , consider any tensor product of sheaves of representations @xmath275 and the map @xmath276 \otimes_{\mathcal{o}_s } v[n].\ ] ] given @xmath277 @xmath278 acts as @xmath279 clearly then we have @xmath280 and therefore a natural map
@xmath281 \to v[m ] \otimes_{\mathcal{o}_s } v[n].\ ] ] it is easy then to check that we get a diagram , @xmath274 @>v_{\mathfrak{g}(s)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\lambda }
, l ) ] \otimes v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\gamma } , k)]\\ @a v[i ] aa @a v[i ] aa\\ v_{\mathfrak{g}(s)}[v_s(\vec{\lambda } + \vec{\gamma } ) ] @>v_{\mathfrak{g}(s)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\mathfrak{g}(s)}[v_s(\vec{\lambda})]\otimes v[v_s(\vec{\gamma})]\\ \end{cd}\ ] ] nothing we have said above applies specially to @xmath282 we could have used any sheaf of lie algebras with representations , so we also get a map @xmath283 @>v_{\hat{\mathfrak{g}}(c)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\lambda } , l ) ] \otimes v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\gamma } , k)].\\ \end{cd}\ ] ] consider now the sheaf of representations @xmath244 we have an injection of sheaves of lie algebras , @xmath284 and so by collapsing out by more symmetries we get a map of sheaves @xmath285 \to v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\lambda } , l)].\ ] ] one checks this is a surjection by noting that both are quotient sheaves , and the corresponding map on fibers is surjective - however , this is not important .
this gives us two diagrams , @xmath286 @>v_{\hat{\mathfrak{g}}(c)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\lambda } , l ) \otimes \mathcal{h}_s(\vec{\gamma } , k)]\\ @a\hat{i } aa @a \hat{i \otimes i } aa\\ v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\lambda } + \vec{\gamma } , l + k ) ] @>v_{\mathfrak{g}(s)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\lambda } , l ) \otimes \mathcal{h}_s(\vec{\gamma } , k)]\\ \end{cd}\ ] ] @xmath287 @ >
> > v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}(\vec{\lambda } , l ) ] \otimes v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}(\vec{\gamma } , k)]\\ @a \hat{i \otimes i } aa @a \hat{i } \otimes \hat{i } aa\\ v_{\mathfrak{g}(s)}[\mathcal{h}(\vec{\lambda } ,
l ) \otimes \mathcal{h}(\vec{\gamma } , k ) ] @ > > > v_{\mathfrak{g}(s)}[\mathcal{h}(\vec{\lambda } , l ) ] \otimes v_{\mathfrak{g}(s)}[\mathcal{h}(\vec{\gamma } , k)]\\ \end{cd}\ ] ] a little bit of pasting then gives us the following diagram , @xmath283 @>v_{\hat{\mathfrak{g}}(c)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\lambda } , l ) ] \otimes v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\gamma } , k)]\\ @aaa @aaa\\ v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\lambda } + \vec{\gamma } , l + k ) ] @>v_{\mathfrak{g}(s)}[c_{\vec{\lambda } + \vec{\gamma } } ] > >
v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\lambda } , l ) ] \otimes v_{\mathfrak{g}(s)}[\mathcal{h}_s(\vec{\gamma } , k)]\\ \end{cd}\ ] ] after more pasting we obtain @xmath283 @>v_{\hat{\mathfrak{g}}(c)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\lambda } , l ) ] \otimes v_{\hat{\mathfrak{g}}(c)}[\mathcal{h}_s(\vec{\gamma } , k)]\\ @a \hat{i } aa @a \hat{i } \otimes \hat{i } aa\\ v_{\mathfrak{g}(s)}[v_s(\vec{\lambda } + \vec{\gamma } ) ] @>v_{\mathfrak{g}(s)}[c_{\vec{\lambda } + \vec{\gamma } } ] > > v_{\mathfrak{g}(s)}[v_s(\vec{\lambda } ) ] \otimes v_{\mathfrak{g}(s)}[v_s(\vec{\gamma})]\\ \end{cd}\ ] ] now dualize the above diagram as in the previous lemma .
the space @xmath288 can also be characterized as the subsheaf of @xmath289 of maps which are @xmath34 on the image of the action map of @xmath232 so we have another commutative diagram .
@xmath290 conformal blocks are preserved by pullbacks along maps of families of stable curves , and the top row of the above diagram is obviously preserved by pullbacks , since it is obtained by tensoring a map of representations with the structure sheaf .
this implies that multiplication of conformal blocks is functorial in families of stable curves , and gives the following lemma as a corollary .
the following diagram is obtained from the commutative square in the previous lemma by localizing at a point @xmath262 @xmath291 this lemma will be important when we relate conformal blocks to line bundles on the moduli of principal bundles .
these are our multiplication maps on graded components . because they are defined by identifying our chosen highest weight vectors , and because the tensor product action @xmath292 co - commutes and co - associates , the maps commute and associate .
these diagrams serve the purposes of showing the existence of the multiplication operation , and proving the following theorem .
there is a commuting diagram of sheaves over @xmath293 @xmath294 defining a map of rings of sheaves @xmath295 where @xmath296 when the genus @xmath113 , the map @xmath297 defined in the previous theorem is a monomorphism .
this follows from an observation of tsuchiya , ueno and yamada in @xcite that the corresponding map on individual blocks is a monomorphism of sheaves when @xmath113 .
now fix an @xmath20 punctured curve @xmath298 by identifying highest weight vectors , we get the following diagram of @xmath23 representations . @xmath299 the space on the left is a @xmath300 representation , the middle is a @xmath301 representation , and beauville shows in @xcite that the space on the right is a @xmath302 representation where the action on @xmath303 is by evaluation at @xmath304 .
the following is a ringification of a theorem of beauville , @xcite .
[ reform ] let @xmath33 be a stable curve .
the following are isomorphisms of algebras over @xmath215 @xmath305\\ \end{cd}\ ] ] by a theorem of beauville @xcite the morphism on the right is an isomorphism of vector spaces , and by @xmath306 @xmath307 ( see @xcite , @xcite , @xcite ) the morphism on the left is also an isomorphism of vector spaces .
both maps are defined by identifying highest weight vectors , then dualizing , this gives a diagram of rings , with graded components , @xmath308^ * @ < <
< [ \mathcal{h}(0 , l ) \otimes \mathcal{h}(\vec{\lambda } , l)]^ * @ > > > [ \mathcal{h}(0 , l ) \otimes v(\vec{\lambda})]^*\\ \end{cd}\ ] ] since taking lie algebra invariants picks out subspaces of these spaces which are preserved by multiplication , these are isomorphisms of algebras .
this may be stated as an isomorphism of sheaves of algebras over @xmath309 where the sheaf on the left is the pullback of the sheaf of vacua over @xmath102 be the map which forgets the @xmath20-st punctured point .
also , implicitly we have an identification @xmath310 \cong ( \mathcal{h}(0 , l)^ * \otimes v(\vec{\lambda})^*)^{\hat{\mathfrak{g}}(c \setminus q)}\ ] ] where @xmath311 is the full vector space dual .
the multiplication on the right hand side of this isomorphism of vector spaces is induced by our familiar map given by highest weight vectors .
we will need this in the next subsection .
for this subsection we refer the reader to the work of kumar , kumar - narasimhan - ramanathan , and lazlo - sorger ( @xcite , @xcite , @xcite , @xcite ) . from the last subsection we have that the space of conformal blocks over a punctured curve @xmath36 of level @xmath32 with markings @xmath54 can be identified with the space @xmath312 here @xmath313 is another point of @xmath101 the following
can be found in @xcite and @xcite .
let @xmath50 be a simply connected group with @xmath314 a simple lie algebra over @xmath215 the moduli stack of parabolic @xmath50-bundles on @xmath33 with structure @xmath315 at the puncture points @xmath49 carries a line bundle @xmath316 for @xmath317 a dominant weight in the face of @xmath133 associated to @xmath318 such that @xmath319^{\mathfrak{g}(c \setminus q)}\ ] ] the stack @xmath320 is obtained as a quotient of the @xmath321-variety @xmath322 by an @xmath321-group @xmath88 where @xmath323 is the affine grassmannian .
@xmath324 here @xmath325 is the loop group of @xmath62 for @xmath326 let @xmath327 be the formal completion of the local ring at @xmath328 and let @xmath329 be the quotient field of @xmath330 then @xmath331 and @xmath332 the group @xmath333 is called a maximal parahoric subgroup of @xmath334 the space @xmath335 carries line bundles @xmath336 with global sections equal to @xmath337 multiplication of global sections is given by identifying the highest weight vectors of the representations @xmath338 and @xmath303 and then dualizing .
this is the generalized borel - bott - weil theorem , of kumar @xcite for kac - moody algebras .
moreover , in @xcite lazlo and sorger identified the picard group of @xmath339 @xmath340 where @xmath341 is the character group of @xmath318 equal to the picard group of @xmath342 this result was obtained by analyzing line bundles under the quotient by @xmath91 in fact , the case with markings @xmath49 is a @xmath343 bundle over the case without markings .
the effective cone in @xmath341 is given by the dominant weights associated to @xmath318 in particular if @xmath344 is the borel subgroup @xmath345 then the effective cone is @xmath78 the effective cone in the picard group of @xmath323 is given by the non - negative integers .
for any line bundle @xmath346 on @xmath49 there is an isomorphism between the sections of @xmath346 and the @xmath106-equivariant sections of the pullback bundle on @xmath347 by a standard theorem on quotient stacks , see @xcite .
this proves the following theorem .
[ moduli ] there is a monomorphism of multigraded rings @xmath348 the image of this monomorphism is the direct sum of conformal blocks @xmath252 with @xmath317 a dominant weight in the face of @xmath133 associated to @xmath349 this is an isomorphism when all @xmath344 are borel subgroups .
it seems that much of this story could be reformulated by building the appropriate @xmath102-stack @xmath350 with line bundle @xmath351 the sheaf @xmath352 could then be constructed as a pushforward of this line bundle .
this also suggests a way to axiomatize proofs of our main theorems in terms of line bundles on stacks over moduli of curves .
the general structure of the geometric side of factorization involves a stack @xmath353 over @xmath354 and for each stratum @xmath355 a way to relate the base change of @xmath353 to a torus quotient of a product of components over the lower stratum .
@xmath356 \ \thicksim \
t \ql [ \prod x_{g_i , n_i } ] \\\ ] ] in this paper @xmath353 is the universal torsor of the moduli of parabolic principal bundles , and the relationship is a flat deformation over @xmath215 we wonder if a similar theorem can be proved in the symplectic category , where the relationship is sharing a dense open hamiltonian system .
see @xcite for this type of relationship with moduli of weighted points on the projective line and @xcite for parabolic principal @xmath0 bundles . to a general representation @xmath357 of @xmath190 of level @xmath32
one can associate a sheaf @xmath358 on the moduli of curves @xmath44 taking a direct sum over all @xmath359 then produces a multigraded module for the sheaf of algebras @xmath360
in this section we use the factorization map of tsuchiya - ueno - yamada to define term order deformations of the sheaf of conformal blocks over the locus of stable curves .
taking a punctured stable curve @xmath36 there is a normalization @xmath361 where @xmath38 are the doubled points , which are identified by the map @xmath362 any such @xmath313 has a natural partner @xmath363 the following is the factorization theorem , it was proved in @xcite with refinements in @xcite , @xcite and @xcite . recall that we have selected @xmath364 for each irreducible representation of @xmath23 .
let @xmath365 be the longest root , and recall that @xmath366 there is a canonical isomorphism of vector spaces , @xmath367 where @xmath368 is the number of double points , and @xmath313 is always assigned the weight dual the weight assigned to its partner @xmath363 this isomorphism is constructed as follows .
for each weight @xmath369 and its dual @xmath370 let @xmath371 be the unique equivariant map such that @xmath372 where @xmath373 is the lowest weight vector of @xmath374 this fixes an identification @xmath375 by letting @xmath376 act on @xmath377 as @xmath378 we choose @xmath379 to represent the identity .
we use this element to define a map @xmath380 on @xmath23 representations which sends @xmath381 to @xmath382 another way to construct this map is to find the image of the identity under the isomorphism @xmath383 the map @xmath384 makes sense for integrable highest weight representations of @xmath236 we can define @xmath385 as the map which sends a vector @xmath381 to @xmath386 with @xmath387 taking conformal blocks yields the following map , which is shown to be injective in @xcite .
@xmath388 this map is computed on an element @xmath389 by sending it to the map @xmath390 defined as follows , @xmath391 summing over all @xmath392 gives the factorization theorem .
the nuts and bolts of this construction will be important in what follows .
we will show the existence of a filtration on the ring of conformal blocks , obtained by understanding the multiplication operation with respect to the factorization theorem .
we begin by studying tensor product decompositions @xmath393 taking care that @xmath394 is identified with @xmath395 from our choices in the last section we get the following identification @xmath396 @xmath397 @xmath398 \otimes [ \bigoplus w_{\alpha^ * , \beta^*}^{\eta^ * } \otimes v(\eta^*)],\ ] ] which implies the identity @xmath399 where @xmath400 represents the identity in @xmath401 this is independent of the choice of tensor product decomposition since conjugation by an invertible matrix does not change the identity .
there exists injections @xmath402 which define the direct product decomposition , these give maps @xmath403 where @xmath404 is the @xmath190 verma module for the highest weight @xmath405 the identity [ identity ] above implies that the following diagram commutes .
@xmath406 \otimes [ \mathcal{h}(\vec{\gamma } , k ) \otimes \mathcal{h}(\beta , \beta^ * , l ) ] \\
@a c_{\vec{\lambda } + \vec{\gamma } } aa @a\sum_{\eta } c_{\vec{\lambda } + \vec{\gamma } } \otimes f_{\eta , \eta^ * } aa \\
\mathcal{h}(\vec{\lambda } + \vec{\gamma } , k + l ) @>\sum_{\eta}(i_{\alpha , \beta}^{\eta } \otimes \rho_{\eta } ) > >
\bigoplus_{\eta } \mathcal{h}(\vec{\lambda } + \vec{\gamma } , k + l)\otimes ( w_{\alpha , \beta}^{\eta } \otimes w_{\alpha^ * , \beta^*}^{\eta^ * } \otimes \bar{v}(\eta ) \otimes \bar{v}(\eta^ * ) ) \\ \end{cd}\ ] ] here @xmath407 the bottom map in the diagram sends a vector @xmath408 to @xmath409 so we can go ahead and replace the map @xmath410 with @xmath411 also , for @xmath412 we have by definition @xmath413 [ factor ] the following diagram commutes .
@xmath414^ * vv\\ \mathcal{v}_{c , \vec{p}}^+(\vec{\lambda } + \vec{\gamma } , l + k ) @<\sum_{\eta } \hat{\rho}_{\eta } < < \bigoplus_{\eta } \mathcal{v}_{\tilde{c}}^+(\vec{\lambda } + \vec{\gamma } , \eta , \eta^ * , l + k)\\ \end{cd}\ ] ] we may dualize the diagram above , then it follows from the factorization theorem and the proof of lemma [ mainsquare ] that each morphism connects the appropriate spaces of invariants .
we obtain the following diagram , @xmath415^*vv \\ \mathcal{v}^+_{c , \vec{p}}(\vec{\lambda } + \vec{\gamma } , k + l ) @<\sum_{\eta } \hat{\rho}_{\eta } < <
\bigoplus_{\eta } v^+_{\mathfrak{g}(c \setminus \vec{p } , \vec{q})}(\mathcal{h}(\vec{\lambda } + \vec{\gamma } , l+k ) \otimes \bar{v}(\eta ) \otimes \bar{v}(\eta^*))\\ \end{cd}\ ] ] the picture is completed by applying a theorem of beauville @xcite , also found in @xcite , which asserts the following equality for any smooth curve @xmath416 induced by the map identifying highest weight vectors .
@xmath417 this diagram only represents the case with a single doubled point , but the general case follows by the same methods , albeit with worse notation . taking elements @xmath418 we must have @xmath419 here the @xmath420 are the summands from the `` lower '' components , in order to justify this label note that @xmath421 as dominant weights . choosing a @xmath23-weighting @xmath422 of @xmath423
we get a filtration @xmath424 on @xmath111 defined by letting @xmath425 have filter level @xmath426 note that in the equation above , @xmath427 and @xmath428 always have the same filtration level , whereas the filtration level of @xmath420 is always less or equal to this , and is generically less .
[ filterblocks ] the filtration @xmath424 for @xmath422 respects multiplication on the ring @xmath132 if the components of @xmath429 are strictly positive on all positive roots , then the image of the multiplication map , @xmath430 can be canonically identified with @xmath431 moreover this map is equal to multiplication in the algebra @xmath432 this all follows from the commutative diagram above .
if we choose the functional @xmath433 to be positive on positive roots , and non - negative integral on weights of @xmath57 then we may form the reese algebra @xmath434 \subset \mathcal{v}_{c , \vec{p}}^+[t],$ ] defined as @xmath435 = \bigoplus_{k \geq 0 } f^{\leq k}_{\vec { \theta}}[\mathcal{v}_{c , \vec{p}}^+ ] t^k.\\\ ] ] this algebra is flat over @xmath436,$ ] and is equal to the associated graded algebra over @xmath437 this proves theorem [ t2 ] .
we will now say something about the structure of the functionals @xmath422 which define these filtrations .
the strata of @xmath102 are indexed by graphs , which we will also denote with @xmath88 with numbers @xmath438 -the genus- at each @xmath439 vertex @xmath440 each internal vertex corresponds to a component of the normalization of a representative curve of the stratum .
leaves correspond to punctures and the internal edges of the graph correspond to pairs of points identified by the normalization .
we consider graphs up to homeomorphisms which preserve genus and leaf information .
this fixes the topological type of a stable curve .
the deformations we ve considered here can be interpreted as labellings of the edges of the graph @xmath106 representing the stable type of the curve . each internal edge
is given a functional @xmath441 and its reflection by the longest element of the weyl group , @xmath442 each associated to a different endpoint of the edge .
the stratification poset information of @xmath102 can be recovered by considering weightings which are @xmath34 on some edges .
we imagine these edges as collapsing , bringing the endpoints together .
the resulting vertex is then given the sum of the genus of the endpoints .
if both endpoints are the same , then weighting the edge @xmath34 corresponds to the graph with that edge removed with the endpoint having the previous genus plus @xmath443 we call graphs obtained by these methods the ancestors of @xmath91 for each @xmath106 the set of weightings forms a cone , with boundary components given by the cones associated to ancestors of @xmath106 .
we may glue the cones for distinct @xmath106 together along common ancestors .
this necessitates that we quotient the cone associated to @xmath106 by the action of @xmath444 we say two graphs are related by a flip move if both have a common ancestor obtained by eliminating a single edge . for @xmath104 dual weights
are equal , so we can consider the edges of a graph @xmath106 to be labeled with non - negative real numbers on the internal edges , and general real numbers on the leaf edges . for @xmath445 our definition of conformal blocks
no longer makes sense , we remedy this with `` vacuum propagation '' @xmath446 in this case deformations are technically weightings of @xmath447- pointed , genus @xmath42 graph @xmath88 but we forget the lone leaf . for @xmath104 deformations are then indexed weightings of @xmath34-pointed , genus @xmath42 graphs by non - negative real numbers .
these are the @xmath448 @xmath449 @xmath450 recently studied by brannetti , melo , and viviani in @xcite .
the set of @xmath27-weightings for topological types of stable curves of genus @xmath42 is isomorphic to the moduli space @xmath451 of pseudo - tropical curves introduced in @xcite .
we interpret the set of @xmath27 weightings of @xmath6-pointed stable genus @xmath42 curves as @xmath452 it is not hard to show that the maximal `` cones '' of this space all have the same dimension , and that the `` flip moves '' defined by common ancestors connect each pair of maximal cones via paths through strictly codimension @xmath447 cones . forgetting the cones associated to graphs with non-@xmath34 markings on vertices gives the space of tropical curves described by mikhalkin in @xcite .
if we restrict to the genus @xmath34 case , then all internal vertices @xmath159 are given @xmath453 and no loops are allowed .
the set of weighted trivalent trees with assignments of @xmath454 to the leaves up to label preserving homeomorphism can be identified with the space of phylogenetic trees studied by billera , holmes , and vogtman in @xcite , and is abstractly homeomorphic to the tropical grassmannian of @xmath1 planes .
the tropical grassmannian or rather @xmath455 is the only case known to the author to have an actual tropical structure - as the tropical variety of a homogeneous ideal .
this structure comes from the work of speyer and sturmfels @xcite , where this space is realized as the tropicalization of the variety associated to the plcker ideal , and also from the work of mikhalkin @xcite .
it is possible to produce embeddings of the cone for the graph @xmath106 into the tropical variety associated to any presentation of the algebra @xmath456 where @xmath36 has type @xmath88 we will see more on this in the next section . as we remarked above , the case of general genus with symmetry
@xmath27 has the dimensionality and connectivity properties of a tropical variety , but the presence of automorphisms makes it unclear to the author how to ascribe to it a tropical structure in any known sense , we have been tentatively referring to these spaces as `` tropical stacks , '' or `` tropical orbifolds . '' as a vector space , the algebra of conformal blocks @xmath111 for a punctured stable curve @xmath36 is isomorphic to @xmath457 where taking invariants by the torus @xmath94 ensures that weights assigned to paired puncture points are dual . by choosing a basis for each space of conformal blocks associated to components of @xmath423 we can assemble a basis for @xmath458 each element
of which can be associated to a labeling of the graph @xmath106 which gives the type of @xmath459 in the general case , each internal edge is assigned two @xmath23 dominant weights which are dual to each other , and we remember the endpoint of the edge associated to each weight .
notice that @xmath460 this is why we ve added the factor of @xmath87 to internal functionals , so that the definition agrees with the deformations of the plcker algebra defined by weighted trees .
the filtration level is then computed by applying the @xmath185weighting @xmath422 to the labeling @xmath461 @xmath462 if @xmath422 is chosen so that each component is strictly positive on positive roots , the resulting filtration gives a flat algebra @xmath463 over @xmath436 $ ] called the reese algebra with generic fiber @xmath111 and special fiber the subalgebra @xmath464 of @xmath465 such that the markings on paired points of the normalization are dual .
this proves theorem [ t2 ] .
we may restate this as [ modulideform ] let @xmath36 be a stable punctured curve , and let @xmath37 be its normalization . for @xmath23 labellings of @xmath33 which have each component positive on positive roots , there is a term order deformation , @xmath466 where @xmath467 is a borel subgroup of @xmath62 in the case where @xmath468 the associated graded algebra is isomorphic to a torus invariant subalgebra of the tensor product of the cox rings of the moduli over the component curves .
this means that any algebra of conformal blocks lies in a flat family with a subalgebra of the tensor product of algebras of conformal blocks associated to triple punctured copies of @xmath469 in this case the curve type @xmath106 is a trivalent graph .
[ ex ] we will work out what this means for a curve @xmath33 with @xmath470 and @xmath471 by theorem [ t1 ] there is a flat family connecting the algebra @xmath472 to @xmath473 for @xmath474 a stable curve with genus @xmath34 components .
this curve then has the normalization @xmath475 which is a disjoint union of triple punctured smooth genus @xmath34 curves . by theorem [ t2 ]
there is a term order deformation @xmath476 where @xmath477 explicitly we have , @xmath478.\ ] ] multiplication is computed component - wise over the tensor product . in the case
@xmath104 this ring is the semigroup of weightings on the graph pictured in figure [ fig : ex2 ] , where the middle edge is always weighted even , is less than or equal to twice either of the loop edges , and the sum of twice either loop edge and the middle edge is bounded by the level .
to finish off this section we will say a word about the sense in which the complexes cones given by the functionals @xmath422 are related to tropical geometry .
each such functional can be extended to a function on the algebra of conformal blocks , @xmath479 which satisfies the following properties with respect to the grading of the underlying vector space given by the labellings from the factorization rules , @xmath461 1 .
@xmath480 for @xmath481 + 2 .
@xmath482 when @xmath483 and @xmath484 are homogeneous .
@xmath485 + the functional is already defined on homogeneous elements , we extend it to sums of homogeneous elements @xmath486 by the max convention @xmath487 in general , for an algebra @xmath488 with a grading of the underlying vector space @xmath489 we call a function which satisfies the above properties a graded valuation .
the following is easy to prove using the above properties .
[ utrop ] let @xmath488 be as above , and let @xmath490 be a graded valuation , then for any homogeneous presentation of a subalgebra of @xmath491 @xmath492 @>\phi > > a\\ \end{cd}\ ] ] the point @xmath493 in the grbner fan of @xmath494 lies in the tropical variety @xmath495 so the functionals @xmath422 define a type of `` universal '' tropical point , in the sense that they define a point on each tropical variety associated to ideals which present @xmath458 and nice subalgebras which respect the grading by the factorization labellings , such as @xmath496 the same is true for all of the functionals discussed in this note , including those which give filtrations on branching algebras in the following section .
in this section we define the branching algebra @xmath497 associated to a map of complex connected reductive groups @xmath498 these algebras were also studied by howe , tan , and willenbring in @xcite , for @xmath499 and @xmath50 a symmetric pair .
we define and investigate flat degenerations of these algebras associated to factorizations of @xmath500 we then study the case of the branching algebra associated to the diagonal morphism @xmath501 and show how it is related to our term order deformations of the ring of conformal blocks in the genus @xmath34 case . for more on this construction
see @xcite .
choose maximal unipotent subgroups @xmath502 and @xmath503 for connected reductive groups @xmath50 and @xmath499 over @xmath24 let @xmath504 be a map of reductive groups .
let @xmath505^{u_g},$ ] which carries a left action of @xmath50 , and therefore @xmath499 by the equivariance of @xmath500 we define the branching algebra @xmath497 to be the invariant subalgebra @xmath506 with respect the the left action of @xmath499 on @xmath507 through @xmath500 as a representation of @xmath508 the algebra @xmath507 is equal to @xmath509 with multiplication induced by dualizing the maps @xmath510 given by identifying highest weight vectors .
the vector space @xmath511 is a direct sum over all the highest @xmath499-weight vectors in @xmath512 so it can be canonically identified with @xmath513 multiplication in @xmath497 is given by the following diagrams .
@xmath514 the branching algebra @xmath497 is multigraded by the product of weyl chambers @xmath515 specified by the chosen maximal unipotents .
the grade of the component @xmath516 is @xmath517 we will study a class of filtrations of branching algebras induced by factorizations of morphisms of connected reductive groups over @xmath215 let @xmath518 be a factorization of @xmath519 in the category of reductive groups over @xmath24 .
the vector space @xmath516 has a direct sum decomposition along this factorization .
@xmath520 from now on we denote @xmath521 as @xmath522 when the meaning is clear .
we will use this direct sum decomposition to define filtrations of @xmath497 by proving an analogue of tsuchiya , ueno , and yamada s factorization of conformal blocks for factorizations of maps of complex connected reductive groups , this will be lemma [ f ] , and an analogue of our description of conformal block multiplication [ filterblocks ] , this will be diagram [ d ] .
there is an isomorphic description of branching algebras more amenable to our purposes , we can also take @xmath497 to be @xmath523 the graded pieces of this algebra are the vector spaces @xmath524 let @xmath23 , @xmath525 and @xmath73 be the lie algebras of @xmath50 , @xmath526 , and @xmath499 respectively . recall that @xmath527 we have the following identification .
@xmath528 this is because an element @xmath529 is fixed by @xmath50 if and only if @xmath530 annihilates @xmath531 using our choice of @xmath532 we can identify @xmath533 with @xmath534 by letting @xmath535 act on @xmath186 by @xmath536 this gives us @xmath537 one then checks easily that multiplication on the right is induced by dualizing the maps @xmath538 \otimes [ w(\eta ) \otimes v(\beta)]$ ]
. we may now construct the same structure of a multifiltration on branching algebras as we did for algebras of conformal blocks .
let @xmath539 and @xmath540 be as in the previous section .
let @xmath541 denote the @xmath526-representation @xmath542 @xmath543 as before , let @xmath544 we have the identity @xmath545 define @xmath546 as in proposition [ factor ] .
from these definitions we get a commutative diagram .
@xmath547 here the sum is over all @xmath548 as dominant weights .
[ f ] let @xmath57 @xmath73 and @xmath549 be the lie algebras of @xmath50 , @xmath499 , and @xmath526 respectively .
the map @xmath550 induces an isomorphism @xmath551 we can dualize each component of this map to get @xmath552 viewing each representation as a dual space , this map is calculated by sending @xmath553 to @xmath554(o_{\eta , \eta^*})\otimes f_v.$ ] let @xmath555 then @xmath556x_i ) = f_1(\sum f_{\eta}(f_2 \otimes g_i ) x_i ) = f_1(f_2)$ ] by definition of @xmath557 we may take invariants by lie algebra actions to obtain a map @xmath558^{\mathfrak{h } } @ < < < [ w(\gamma^*)\otimes y(\eta^*)]^{\mathfrak{h}}\otimes [ y(\eta)\otimes v(\lambda^*)]^{\mathfrak{k}}\\ \end{cd}\ ] ] writing this another way we get the following map of homomorphisms .
@xmath559 it is easy to show using the calculation above that this is the composition of morphisms map . by the semisimplicity of the categories involved , this map is injective , and the sum over @xmath560 produces an isomorphism ,
therefore the same is true for the corresponding map on invariants .
after dualizing diagram [ d ] , we can take covariants by @xmath73 on the left and @xmath561 on the right , where the action map @xmath562 is defined by the diagonal morphism and @xmath563 the lemma above and diagram [ d ] imply that @xmath497 has a filtration by dominant weights of @xmath526 in the fashion of proposition [ filterblocks ] , with a similar lower - triangular multiplication property
. we may act on these weights with functionals @xmath564 to produce filtrations .
[ branchingdef ] let @xmath565 @xmath566 be morphisms in the category of reductive groups over @xmath215 then for linear functionals @xmath567 which are positive on positive roots we obtain a filtration which defines a flat deformation , @xmath568^{t_k}\ ] ] where @xmath569 is the maximal torus associated to @xmath570 and the action on @xmath571 is conjugated by the negative of the longest element in the weyl group of @xmath177 the torus action picks out the sub algebra of @xmath572 with conjugate dominant @xmath526 weights .
this follows by the analogue of the argument for proposition [ filterblocks ] .
we define the filtration in the same way , acting on the @xmath526-weights @xmath560 and @xmath573 with @xmath574 and the reflection @xmath575 as in the definition of a @xmath23-weighting of a curve . the associated graded algebra @xmath576^{t_k}$ ]
is then graded by @xmath577 as the deformation seems to add torus symmetries , one asks when it is toric .
this happens when all component branching algebras @xmath497 are toric .
these correspond to morphisms @xmath578 such that every @xmath50 representation factors into @xmath499 representations each with multiplicity one . since the associated graded algebra is obtained by taking torus invariants of a tensor product , we can iterate these deformations , so a chain of morphisms @xmath579 gives a family of flat deformations @xmath580^{t_{g_1 } \times \ldots \times t_{g_{k-1}}}\ ] ] indexed by functionals on @xmath581 for a fixed morphism , different factorizations and functionals yield different deformations , and the sets of functionals form a stratified collection of cones .
the map of reductive groups @xmath582 given as upper left block inclusion has multiplicity one
. we can consider the tower of groups @xmath583 which factors the map @xmath584 and defines the branching deformation of @xmath585 as above .
@xmath586 each piece of this tensor product is toric , so we obtain a toric deformation of @xmath587 to the monoid given by the gelfand - tsetlin basis .
it is possible to show that the filtrations @xmath429 described in this section each satisfy the conditions of proposition [ utrop ] , and also define `` universal '' tropical points .
we study the map @xmath183 sending @xmath42 to @xmath588 let @xmath5 be a tree with @xmath20 labeled leaves . to any such tree we associate a factorization of the diagonal morphism @xmath183 by placing the unique orientation on the edges of @xmath5 which has the @xmath34 leaf as a source and all other leaves as sinks , and for each internal vertex allows exactly one in - flowing edge . to each internal vertex
we assign the morphism @xmath589 where @xmath590 is the valence of the vertex .
we partition the vertices into sets defined by their distance to the @xmath34 leaf , and from this we construct a factorization of @xmath591 by multiplying together all elements of the same partition , adding in identities when necessary . to this data , and a choice of linear functionals as above , we may associate a flat deformation of @xmath592 this amounts to specifying a rooted tree @xmath5 and a labeling of edges @xmath593 by functionals @xmath594 this defines a direct sum decomposition of @xmath595 into components associated to labellings of the tree @xmath9 with a given set of representations at each edge .
a general element of each component is a tree with the labeling of edges by representations and vertices labeled by intertwiners .
the functional @xmath596 acts edge - wise on these elements , in particular for an internal edge @xmath597 the functional @xmath598 acts on @xmath599 if @xmath600 is an element of @xmath601 then @xmath602 for @xmath603 each such deformation is given by a labeling of @xmath5 by nonnegative real numbers , and the resulting structure is a cone of the space of phylogenetic trees .
this is to be expected , since in this case @xmath595 is isomorphic to the plcker algebra of the grassmanian of 2-planes .
also in this case the associated algebra is toric when @xmath5 is trivalent , since @xmath164 is toric for @xmath604 in general , if one exhibits a toric deformation of @xmath164 for a reductive group @xmath50 , then we get toric deformations of any @xmath595 by composing with a branching deformation .
we will outline such a deformation below .
let @xmath79 be the longest root of @xmath43 using the graded multiplication in @xmath595 we can build a new algebra @xmath605t^l]\ ] ] this algebra also comes with a family of filtrations for every labeling of a tree @xmath5 with @xmath20 leaves by functionals .
each graded component has a direct sum decomposition into components indexed by labellings of @xmath9 because they are also components of the branching algebra @xmath592 we let @xmath131 denote the trivial sheaf of algebras on @xmath606 which has @xmath131 as the fiber at each point .
tsuchiya , ueno , and yamada noted in @xcite that the morphism of @xmath607 representations @xmath608 gives a morphism of coherent sheaves @xmath609 recall that there is an isomorphism @xmath610 and the following commutative diagram by lemma [ mainsquare ] .
@xmath611 the maps on the right and left are the multiplication operations on the sheaves @xmath131 and @xmath612 respectively , so there is a morphism of sheaves of rings , @xmath613 which respects the multigrading by @xmath54 and @xmath69 from now on we restrict ourselves to the case @xmath614 we will show that over a stable curve of type @xmath5 the morphism @xmath297 intertwines the factorization property of conformal blocks with the branching decomposition defined by @xmath5 on @xmath615 we will show how this works for trees with one internal edge , the property for more general trees follows by induction .
let @xmath33 be a stable curve of type @xmath9 with @xmath616 we have a commuting square of @xmath23 representations , @xmath617 where @xmath618 morphisms in this diagram above are equivariant with respect the following lie algebra maps .
@xmath619 see @xcite for a description of the top horizontal map of lie algebras .
we may take the coinvariants of the diagram of modules above , then dualize to get a diagram of invariants .
@xmath620 the vertical arrows are the correlation morphism . the top horizontal arrow is the factorization map in genus @xmath26 and the bottom horizontal arrow is the factorization map for the diagonal morphism from the previous section , see specifically lemma [ f ] .
this shows that the the filtrations on the branching algebras and the algebras of conformal blocks agree over the locus of stable curves .
the properties of the tree deformations of both types of algebras only depend on the labels , which have now been shown to agree , so this proves theorem [ g0 ] .
any time @xmath100 is a disjoint union @xmath621 the diagram above commutes .
this implies a version of theorem [ g0 ] is true for general genus , except the correlation @xmath297 is no longer a monomorphism . for a genus @xmath26 triple punctured curve
there is no moduli , @xmath622 so the algebra of conformal blocks is unique . in this case ,
conformal blocks have a nice description as a subspace of the space of invariants in terms of weight spaces by the action of the copy of @xmath0 corresponding to the longest root of @xmath57 see @xcite for the following .
@xmath623 has the following description .
consider the factorization of @xmath533 , @xmath624 and @xmath625 as @xmath27 representations with respect to the longest root @xmath79 of @xmath43 @xmath626 @xmath627 @xmath628 let @xmath629 be the subspace of @xmath630 of components @xmath631 with @xmath632 @xmath633 we are interested in constructing filtrations of @xmath634 with a monoidal associated graded ring , as this would allow the same for general algebras of conformal blocks by theorems [ t1 ] and [ t2 ] .
a sufficient condition for such a filtration would be a basis @xmath635 of each space @xmath636 which has the following properties . 1 .
the bases @xmath635 have a `` lower - triangular multiplication '' property with respect to the multiplication in @xmath637 + 2 .
the intersection @xmath638 is a basis for each @xmath69 + the first property above would mean that there is some natural ordering on the set @xmath639 such that a product of elements @xmath640 when expressed in the basis has a unique highest term with weight equal to the weight of @xmath483 plus the weight of @xmath641 the associated graded ring with respect to the ordering would then be monoidal .
such a basis exists for @xmath642 the dual canonical basis of lusztig @xcite .
this basis was used by alexeev and brion in @xcite to construct toric deformations of spherical varieties .
we will show how to adapt this basis to @xmath637 we include this discussion because dual canonical bases can at least give deformations of @xmath643 when the level is very large , and because the theory of dual canonical bases is tantalizingly close to what we need to construct toric deformations of the cox ring of the moduli of quasiparabolic principal bundles in the general case .
following page 383 of @xcite , the space @xmath636 can be realized as the space @xmath644 of vectors of weight @xmath645 which are annihilated by the raising operators @xmath646 where @xmath647 is a highest weight vector and a basis member of @xmath648.$ ] we summarize these observations with the following proposition , see @xcite .
there is an injection of rings @xmath649,$ ] in particular multiplication on tensor product invariants coincides with cartan multiplication in @xmath650 the subspace of conformal blocks @xmath651^{\mathfrak{g } } \cong v_{\lambda^ * - \mu , \mu}(\gamma)$ ] is defined by the condition @xmath652 where @xmath79 is the longest root of @xmath57 and @xmath653 is the lowering operator in @xmath43 in @xcite , alexeev and brion use the dual canonical basis of @xmath507 to define toric degenerations of @xmath507 and in general the coordinate rings of spherical varieties .
this is possible because the dual canonical basis @xmath654 has a very nice labeling by so - called string parameters @xmath655 , where @xmath656 is the length of the longest word @xmath657 in the weyl group of @xmath62 there is such a parametrization for every decomposition @xmath658 of @xmath659 and the multiplcation operation in @xmath660 is lower - triangular with respect to the lexicographic ordering on the @xmath661 @xmath662\\\ ] ] note that the multiplication described by the main theorem of this work does not satisfy this property , indeed the space of elements with the same multiweight in @xmath111 is not one - dimensional .
dual canonical bases @xmath663 can be shown to be so - called `` good bases '' see e.g. @xcite , this means that the intersection @xmath664 is also a basis , so the subalgebra @xmath665 $ ] inherits a basis from @xmath666 the dual canonical basis members which lie in @xmath164 are parametrized by string parameters which lie in a convex cone @xmath667 see @xcite,@xcite and @xcite for descriptions of this cone and the following proposition .
the dual canonical basis defines a toric degeneration of @xmath668,$ ] one for each string parametrization @xmath669 .
the dual canonical basis defines toric degenerations of @xmath670 $ ] where @xmath671 is the subcone of elements @xmath672 such that the associated dominant weights lie in @xmath673 it is unknown to us whether or not the dual canonical basis restricts to a basis on the subspaces of conformal blocks in general , although this appears to work for @xmath674 see @xcite.it would still be interesting if one could prove that each conformal block , when expanded into its dual canonical components , has a highest term with respect to an ordering of the dual canonical basis which uniquely identifies the conformal block .
it would suffice to find a `` good basis '' which further respects equation [ level ] .
this would then define monoidal deformations of all @xmath111 by composing the above degeneration with those defined by theorem [ t2 ] .
all of our techniques to study algebras of conformal blocks and branching algebras are carried out on graded pieces of these algebras .
because of this , much of what we say can be extended to nice graded subalgebras , in particular for the moduli space @xmath49 and the git quotient @xmath675 of coadjoint orbits , we have a map of projective coordinate rings .
@xmath676 where @xmath677 is the line bundle on @xmath678 with global sections equal to @xmath679 when @xmath103 this map is an injection , in which case can deduce for @xmath113 and @xmath680 the map @xmath681 above is an isomorphism .
this is comparable to remark @xmath682 in @xcite .
the ring @xmath683 is the projective coordinate ring of @xmath684 where the semi - stability condition comes from @xmath685 deformations associated to labeled trees carry over to this case as well .
this implies that for large @xmath686 a toric deformation of @xmath678 gives a toric deformation of the ring of generalized theta functions .
toric deformations of @xmath687 can be constructed from a toric deformation of @xmath595 by taking torus invariants , so these algebras have toric deformations coming from the dual canonical basis .
let @xmath33 be genus @xmath29 for @xmath688 the algebra @xmath683 has a toric deformation for each trivalent tree @xmath5 with @xmath6 leaves and each choice of string parametrization at each internal vertex of @xmath8 see @xcite for a description of the polytopes associated to these toric deformations . for @xmath104 these deformations were studied in @xcite in order to provide commutative algebrainformation about the moduli of points on @xmath469 in @xcite in relation to the symplectic geometry of configuration spaces of euclidean polygons , and in @xcite to construct commutative algebra data for projective coordinate rings of cox - nagata rings and equivalently the moduli of rank @xmath1 semistable vector bundles , @xmath689
in the case of @xmath104 the situation simplifies considerably .
let @xmath36 be stable curve of type @xmath9 a trivalent tree .
an element of @xmath690 is a linear combination of labellings of @xmath691 by nonnegative integers such that 1 .
the weights about each internal vertex satisfy the triangle inequalities .
the sum of the weights about each internal vertex is even .
the leaf edges are all labeled with an integer less than or equal to a level @xmath69 the first two conditions above are the clebsh - gordon rules for @xmath27 which determine when a branching can exist for tensor products of @xmath27 representations .
the kernel of @xmath692 is spanned precisely by those weightings such that the sum of the labels around any internal vertex is less than or equal to @xmath693 this is the @xmath694 clebsch - gordon condition for @xmath123 see @xcite for a discussion of this condition with respect to @xmath27 conformal blocks .
notice that these conditions are identical to the linear conditions which define the toric algebras of speyer - sturmfels and buczynska - wiesniewski , respectively .
each graded piece of @xmath695 is either empty or of dimension @xmath443 so the multiplication operation is given purely by addition on the labels .
the subalgebra of vacua @xmath111 is given by a linear condition on these labels , and is therefore also toric .
the corresponding polytope is discussed in @xcite and @xcite , for @xmath696 it is the simplex defined by the condition that the sum of any two weights be either @xmath34 or @xmath180 and the associated toric variety is @xmath697 since the general case is a torus invariant subalgebra of a tensor product of toric algebras , it is also toric . note that the same observation applies to the genus @xmath698 case . by the same reasoning these algebras of vacua
are the semigroup algebras given by the semigroup of weighted trivalent graphs @xmath88 which obey the above conditions at each internal vertex and leaf .
one can directly verify that the associated toric varieties are those discussed in 4.4 of the paper of hurtubise and jeffrey @xcite .
the operation of taking invariants by the torus is the `` gluing '' construction of hurtubise and jeffrey , used in their study of the complex and symplectic geometry of moduli of framed parabolic bundles .
we note that our work here allows one to obtain the verlinde formula as a count of lattice points in the moment polytope of the hurtubise - jeffrey toric moduli space .
we also mention that buczynksa has constructed pairwise deformations connecting these toric algebras , @xcite .
we do not know the relationship between these flat families and the flat families constructed here .
the commutative algebra of the genus @xmath34 case was extensively studied by buczynska and wiesniewski in @xcite , and also in @xcite , in the former paper it was proved that the deformed algebra of vacua are generated in degree @xmath447 with quadratic relations .
little is known about the general non - trival genus case , although some good results have been obtained by buczynska , @xcite , in particular a generating set for the genus @xmath447 case .
for @xmath699 the algebras @xmath111 are gorenstein .
these algebras are domains , so it suffices to prove they share the same hilbert function with a gorenstein domain . choosing a stable curve with the same genus and puncture information as @xmath700 with genus @xmath34 components , we reduce the problem to showing an affine semigroup algebra is gorenstein . this is the semigroup of lattice points in a cone @xmath701 for some trivalent graph @xmath91 the associated algebra is gorenstein if and only if the module defined by the lattice points in the interior of this cone is principal .
a point is interior if and only if all the of the triangle inequalities and the inequality defining the level condition are strict . over a single trinode ,
one checks that this is the case if and only if the weighting has the element @xmath702 in level @xmath182 as a factor . in general ,
a weighting is interior if and only if the weighting @xmath703 of level @xmath182 is a factor .
this implies that @xmath109 $ ] is a gorenstein algebra , which gives the proposition .
the stack @xmath704 for @xmath0 has cox ring isomorphic to the affine semigroup ring for the semigroup in @xmath705 generated by @xmath706 @xmath707 @xmath708 and @xmath709 this is a polynomial algebra . like the genus @xmath34 case
, the toric algebras of general genus and @xmath27 symmetry are thought to have connections with phylogenetic algebraic geometry .
they are the projective coordinate rings of generalizations of phylogenetic statistical models to networks of evolution which are not contractible .
we thank weronika buczynska , edward frenkel , shrawan kumar , eduard looijenga , diane maclagan , john millson , david swinarski , and fillipo viviani for useful discussions .
this paper was mostly written at the fall 2009 introductory workshop in tropical geometry at msri .
a. beauville , _ conformal blocks , fusion rules , and the verlinde formula _
proceedings of the hirzebruch 65 conference on algebraic geometry , 7596 , israel math .
proc . , 9 , bar - ilan univ . , ramat gan ( 1996 )
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krrillov , p. mathieu , d. senechal , and m.a .
walton , _ crystalizing the depth rule and wznw fusion coefficients _ , proceedings of the xixth international colloquium on group theoretical physics , salamanca , spain , 1992 . | arxiv |
warm dense matter ( wdm ) @xcite , with density @xmath0 to @xmath1 times that of solid and temperature @xmath2 to @xmath3 , is commonly found in astrophysics as well as in high - energy density physics experiments @xcite . until the present , however , the properties of wdm are not well understood and are difficult to predict theoretically .
this is because neither the models of condensed - matter nor from high - temperature plasmas are well suited for describing the intermediate regime of wdm .
detailed information about the thermodynamic states , such as ionization distributions , is of importance in uncovering the involved physical mechanisms .
the widely used models predicting an average ionization degree of atoms are thomas - fermi model @xcite and saha @xcite ionization model , however both of the models assume that plasma conditions are near thermal equilibrium . for laser
produced plasmas and intense beam solid interactions , where many of the involved physical mechanisms take place at the sub - pico - second or pico - second scales @xcite , the equilibrium assumption is no longer correct . to account for the temporal evolution of the plasma ionization ,
an impact model based on electron - ion collisional cross sections has been explored @xcite , which allows to calculate ionization values in much more natural manner .
this model directly describes the inter - particle interactions in the plasmas and thus , accounts for the multi - particle nature of real plasmas .
although this impact ionization model allows improvements in dealing with non - equilibrium plasmas , it is still not complete since it does not account for the inverse process , such as electron - ion recombination @xcite .
besides , the ionization potential depression ( ipd ) should be taken into account when dealing with high density plasmas @xcite , however it is also ignored in the considered model @xcite .
the main challenge to understanding the ionization of wmd is to incorporate self - consistently the non - linear behaviour in such strongly coupled dynamical systems , i.e. , the matter s response to the surrounding plasmas through impact ionization , recombination and ipd , and plasma s response to the material through the dependence of plasma s temperature and density on ionizations and recombinations . to describe the ionization dynamics of wdm more systematically ,
we here propose and analyse a monte - carlo approach that can be configured and embedded into existing particle - in - cell ( pic ) simulation codes . in this approach
, we use a collection of macro - particles to describe a plasma of finite ion or matter density . here , a macro - particle can be regarded as the ensemble of real particles , where a macro - particle can be regarded as a group of particles with `` same '' mass , charge state , position and momentum .
the electrons are classified moreover into bound and free ones , where the former are regarded as part of ions or atoms , and the latter are isolated as part of surrounding plasmas . since we consider a collection of large number of particles and the temporal evolution of the system takes place at pico - second scales , the fine structures , such as sub - shell configurations , excitations and their inverse processes , are ignored in the present model .
only the dominant physical processes are are taken into account , i.e. , impact ionization and recombinations .
furthermore , the idp effects , which are determined by plasma density and temperature , should also be taken into account .
this is because the depression of ionization energy of ions or atoms by the ipd effects will then , in turn , affect both impact ionization and recombination processes .
the paper is organized as follows . the physical model concerning impact ionization , electron - ion recombination and ipd are introduced in sec .
ii . in sec .
iii , the model is embedded into pic simulation code .
the average ionization degree of bulk aluminium varying with temperature is calculated by the pic code , which shows good agreement with the data provied by flychk code .
furthermore , we also explore the ionization dynamics of alloys in this section .
summary and discussion are given in sec .
when temperature of plasma is high with the kinetic energy of free electrons exceeding the ionization potential of ions or atoms , there exists a possibility that the ion or atom will lose a bound electron by the colliding with energetic free electrons , and we call this process as impact ionization .
simultaneously , for cold and dense plasmas , free electrons and charged ions tend to recombine together , and we call this process as electron - ion recombination . different from isolated atom or ion , the debye screening of free electrons would dramatically influence the atomic structure of ions that embedded in dense plasmas , resulting in the lowering of the ionization potential .
the above three processes are usually ignored in high temperature and low density plasmas , such as laser wake field acceleration .
while for dense plasma and warm dense matter regime , they are so important that become the dominant processes of the considered system . in this section , an impact ionization model based on electron - ion collisional cross sections , an electron - ion recombination model based on three - body - recombination and
the ipd effects based on stewart s theory are explored and implemented in pic simulations .
[ [ impact - ionization ] ] impact ionization + + + + + + + + + + + + + + + + + by establishing an electron - ion or atom collisional pair and taking into account the energy of the incoming electron as well as the ionization state of the ion , a cross section of ionization can be derived .
the pioneering work was done by lotz @xcite , with the formula of the total cross section as follows @xmath4,\ ] ] where @xmath5 is the energy of impact electron , @xmath6 is the binding energy of electron in the i - th sub - shell , @xmath7 is the number of equivalent electron in the i - th subshell , and @xmath8 , of unit @xmath9 , @xmath10 and @xmath11 are individual constants which are determined by experiment measurements or theoretical predictions . ref .
@xcite also tabulates these ionization cross sections , and this table is applied in our computations below . following the work of lotz , the ionization cross section among neighbouring levels , such as , al - ii to al - iii , can be formulated as follows , @xmath12,\ ] ] with @xmath13 , where @xmath6 is the ionization potential .
let us note , however , the fine structure levels are ignored in lotz s model , for which the ionization stage is treated as from the ground state to the next ground state .
furthermore , the electron impact ionization cross section can also be calculated using the relativistic multi - configuration flexible atomic code ( fac ) @xcite , where multitude of ionization cross sections can be generated by the fac between the fine structure levels of the initial and final states , and finally combined into a single effective cross section as obtained from a summation over the initial and average over the final states .
the impact ionization rate of ion or atom is @xmath14 where @xmath5 , @xmath15 , and @xmath16 are energy , velocity and density of impact electrons with energy between @xmath5 and @xmath17 . in pic simulations , the integral stands for summarizing over all electrons that reside within the same cell as the given ion of interest .
the expression for @xmath18 in this form can be time - consuming as it requires a double loop over all ions and electrons in the cell .
following the idea presented in ref .
@xcite and taking advantage of the specific scaling of the ionization cross section and electron velocity with energy , i.e. , @xmath19 and @xmath20 , respectively , their product is not sensitive to @xmath5 and can be taken outside the integration . when replaced by their averaged values
, the impact ionization rate takes the form @xmath21 a loop over the electrons updates the average electron energy @xmath22 , velocity @xmath23 and electron density @xmath24 , of unit @xmath25 , in each computational cell once per time step .
then eq .
( [ ci_rate ] ) is applied for each ion keeping track of which cell it belongs to .
the ionization probability of the ion of interest is @xmath26 , where @xmath27 is the simulation time step .
we increase the ionization degree by one unit for each ion and simultaneously put in an electron with the same position , velocity and weight as its host ion randomly when condition @xmath28 is satisfied , where @xmath29 is the computer generated random number . to ensure that the energy remains conserved in the computations , we reduce local kinetic energy by distributing a momentum reduction to all local electrons , which is equivalent to the ionization energy .
[ [ electron - ion - recombination ] ] electron - ion recombination + + + + + + + + + + + + + + + + + + + + + + + + + + the ionization balance of a plasma is determined by the competing processes of impact ionization and recombination , as well as various excitation / de - excitation processes .
in particular , the recombination of electrons and ions takes place mainly by three different reaction modes , the dielectronic ( dr ) , radiative ( rr ) and three - body recombinations ( tbr ) , respectively @xcite .
as we have analysed , in our model only ground state of ions and atoms are concerned , the contributions of dr are averaged out .
note that , rr is the inverse of the direct photo - ionization , while tbr is the inverse process of electron impact ionization .
the rr process is known to predominantly fill the low - lying redberg states , while tbr is mainly responsible in rapidly bringing the high rydberg states into equilibrium @xcite .
thus , the contributions of recombinations mainly come from the tbr process , with @xmath30 , where @xmath31 with @xmath32 of the ion charge state . in the tbr ,
the excess energy released by the recombining electron is carried away by the outgoing electron @xmath33 , so that the tbr does not involve any emission of photons .
a simple expression for tbr rate , which is usually obtained from the relying impact ionization formula by detailed balance , is as follows @xcite , @xmath34 all the tbr formulas exhibit this behaviour @xcite , except for the slightly different numerical factors . in pic simulations ,
the electron temperature @xmath35 , and electron density @xmath24 can be generated by a loop over the electrons in each computational cell once per time step .
then eq .
( [ ir_rate ] ) is applied for each ion after calculating the ion density @xmath36 in the same cell .
the recombination probability is @xmath37 , where @xmath27 is the simulation time step .
we decrease ionization degree by one unit for each ion randomly whenever the random number @xmath29 satisfies @xmath38 . again to ensure that the energy remains conserved , the local kinetic energy , equivalent to the ionization energy , is increased , through a similar way as we have done in impact ionizations , by distributing a momentum modification to all local electrons . to ensure the conservation of remain particles , the local plasma density , equivalent to the ionization recombination ,
is reduced by distributing a weight modification to all local free electrons .
[ cols= " < , < , < , < , < , < , < , < , < , < , < , < , < , < " , ] ( color online ) ( a ) the total plasma energy , by summarizing over all free electrons within a computational cell , as a function of time , where the initial plasma temperature is @xmath3 and pre - defined @xmath39 charge state .
( b ) the same as shown in ( a ) , but with initial temperature @xmath40 and pre - defined charge state of @xmath41 .
the inlet over ( a ) is the final ionization distributions of aluminium after @xmath42 relaxation.,width=321 ] ( color online ) the total plasma energy ( or free electron energy ) within a computational cell as a function of time , where the initial temperature of aluminium carbide is @xmath43 with pre - defined charge states of @xmath44 and @xmath45 and plasma density of @xmath46 .
the inlet is the final ionization distributions of aluminium and carbon after @xmath47 relaxation.,width=321 ] [ [ ipd - by - surrounding - plasmas ] ] ipd by surrounding plasmas + + + + + + + + + + + + + + + + + + + + + + + + + + the calculation of both impact ionization and electron - ion recombination requires values of ionization potentials , which , in principle , can be generated or obtained from data bases of national institute of standard and technology ( nist ) .
the ionization potential of aluminium atom ( al i ) and ions are listed in table [ table1 ] , which are calculated based on the isolated atom or ion model . however in a plasma of finite density and temperature , the ionization potential of a given ion is influenced not only by its own bound electrons but also by the surrounding free electrons , which , in turn , will affect both impact ionization and recombination processes .
therefore , the phenomenon of ionization - potential depression for ions embedded in the plasma are of crucial importance for modelling atomic processes within dense plasmas .
we refer to the theory of ipd introduced by stewart @xcite , which yields ion - sphere and debye - huckel potential models as approximate limiting cases and could provide results over essentially the entire range of temperature and densities of plasmas for which appreciable ionization exists .
let us here consider an atom or ion , @xmath48 , fixed in a sea of free electrons and ions at kinetic temperature @xmath35 .
the free electrons are described by relativistic fermi - dirac statistics and the ions by non - relativistic maxwell - boltzmann statistics .
for such a distribution of plasma electrons , the average electro - static potential near @xmath48 can be evaluated by poisson equations .
it is this potential that cause the idp effects of surrounding plasmas .
the contribution of bound electrons to ipd are excluded , since they are already present in the isolated ions . following stewart s theory @xcite , the lowering of ionization potential
is described by the expressions , @xmath49^{2/3}-1\}t_e/2(z+1),\ ] ] where @xmath35 is temperature of free electrons , @xmath50 with @xmath51 representing the debye length of free electrons . for large @xmath52 , according to eq .
( [ idp_formula ] ) , @xmath53 is reduced to @xmath54 which is the limit of debye - huckel model .
when @xmath52 is small , @xmath53 equals to @xmath55 , which is the limit of ion - sphere model , with @xmath56{3z/4\pi n_e}$ ] representing the radius of ion - sphere . for high density plasmas ,
the idp would have a significant effect on lowing of ionization potential .
for example , @xmath53 of al vii ( with the isolated ionization potential @xmath57 ) can be as large as @xmath3 for bulk aluminium ( @xmath58 ) with temperature @xmath35 below @xmath59 .
apart from such a semi - empirical treatment of ionization potential depressions , the idp effects can also be described from multi - body - quantum - mechanical methods @xcite .
we compared the estimation from stewart s formula with that from references @xcite , and found the calculation methods exhibit similar behaviour , though with slightly different numerical values . in pic simulations ,
the electron temperature @xmath35 and density @xmath24 can be generated by a loop over the electrons in each computational cell , attached to which the debye length @xmath60 is evaluated .
using eq .
( [ idp_formula ] ) and the isolated ionization potential value from nist data bases , the modified ionization potential , i.e. , @xmath61 , is updated for each ion at every computational cell per time step .
the physical model is embedded in a recently extended version of pic code based on lapine @xcite , with which the tunnelling ionization have already been implemented in by one of us @xcite . in pic simulations , we only need to consider a few computational cells , connected by periodic boundaries conditions , with each cell contains @xmath62 ion macro - particles and @xmath62 electron macro - particles initially . in this section ,
we present several case studies of the ionization dynamics of bulk aluminium ( single ) and aluminium carbide ( alloy ) .
the density of bulk aluminium in our case studies is @xmath58 , thus , the aluminium ion density is @xmath63 , with @xmath64 .
[ fig1 ] shows the temporal evolution of the plasma energy , summarizing over all free electrons within one computational cell ( energy density of plasmas ) , where the initial aluminium temperature is @xmath3 [ fig .
[ fig1 ] ( a ) ] and @xmath40 [ fig . [ fig1 ] ( b ) ] with pre - defined charge states of @xmath39 [ fig
. [ fig1 ] ( a ) ] and @xmath41 [ fig . [ fig1 ] ( b ) ] . from fig .
[ fig1 ] ( a ) , we can see that the energy density of plasmas increases with time , after about @xmath42 temporal relaxation , equilibrium is reached , with the final temperature of @xmath65 and average charge degree of @xmath66 .
following the temporal relaxation as shown in fig .
[ fig1 ] ( a ) , the electron - ion recombination rate of aluminium at the very beginning is larger than impact ionization rate , and , therefore , the recombination processes lead to the increase of plasma energy and reduction of average ionization degree , until the arrival of equilibrium .
[ fig1 ] ( b ) indicates that at initial time , the impact ionization rate of aluminium is larger than electron - ion recombination .
similarly , the impact ionization would reduce the plasma energy and increase the average ionization degree .
our model is general and can be applied for both single elements and alloys with quite different compositions .
the aluminium carbide , chemical formula al@xmath67c@xmath68 , is a carbide of aluminium with density @xmath69 . fig .
[ fig2 ] shows the temporal evolution of energy density of plasmas , where the initial aluminium carbide temperature is @xmath43 with pre - defined charge states of @xmath44 and @xmath45 and plasma density of @xmath46 .
as seen from this figure , the equilibrium is reached after @xmath70 ps of temporal relaxation with a plasma temperature of @xmath71 and free electron density of @xmath72 .
the inlet is the final ionization distributions of aluminium and carbon .
( color online ) ( a ) the total plasma energy within one computational cell as a function of simulation time , where the initial aluminium temperature is @xmath3 with pre - defined @xmath39 charge state .
( b ) the corresponding temporal fluctuation of the number of macro - particles in pic simulations.,width=321 ] ( color online ) the average ionization degree of bulk aluminium as a function of plasma temperature .
black square is picked up from the equilibrium states calculated by our pic simulations .
blue , red and green lines are the corresponding average ionization degrees with fixed plasma density of @xmath73 , @xmath74 and @xmath75 calculated by flychk code.,width=321 ] in our model , different strategies were used to ensure that the total number of particles remain conserved .
the reduction of electrons due to recombination is through distributing a weight modification to all local free electrons , which does not change the number of macro - particles . while the increase of electron due to impact ionization is through placing _
new _ macro - particles to the cell of interest .
the major computational effort in the simulation arises from the number of macro - particles . to solve this problem ,
a particle - merging technique is configured and applied .
considering two electrons with position @xmath76 and @xmath77 , momentum @xmath78 and @xmath79 , gamma factor @xmath80 and @xmath81 , as well as weight @xmath82 and @xmath83 , we have the merging weight as @xmath84 , merging position as @xmath85 , merging gamma factor as @xmath86 , and the merging momentum as @xmath87 . in practice , the equation , @xmath88 ,
is not always satisfied for the _ merged _ particles . to solve this problem ,
a coefficient of @xmath89 is multiplied to replace the old merging momentum , with @xmath90 .
the case shown in fig .
[ fig1 ] ( a ) is re - run by including the merging - particle technique .
[ fig3 ] ( a ) shows how the energy density of plasmas evolves in time , while fig .
[ fig3 ] ( b ) displays the corresponding number of macro particles . both the energy evolution and final equilibrium shown in fig .
[ fig3 ] ( a ) is exactly the same as shown in fig .
[ fig1 ] ( a ) . in the simulation
, the merging takes place at pre - defined times .
as we can see , the dropping of the total number of macro particles does not affect the energy evolution or final equilibrium . by using this technique ,
the simulation burden can be dramatically released . following the routine
described above , we plot the variation of average ionization degree of bulk aluminium with temperature .
a collection of data picked from equilibrium represented by black squares is shown in fig .
it is indicated that with the increase of plasma temperature , the average ionization degree also increases accordingly .
we also compare our results with that from flychk @xcite code , in which the ionization calculation is also based on saha ionization model @xcite . in fig .
[ fig4 ] , blue , red and green lines are the corresponding average ionization degrees , calculated from flychk code , as functions of temperature with fixed plasma densities of @xmath73 , @xmath74 and @xmath75 .
note that in our calculations , the aluminium density is fixed , with @xmath91 , but let both the `` plasma '' ( free electrons ) density and ionization charge states free to change with time and temperature .
furthermore , the free electron density and average ionization degree of aluminium are connected by the relationship , @xmath92 .
our calculation method reflects the ionization dynamics of materials in a more natural way , which is quite different from the model used in flychk , where the average ionization degree is calculated with fixed free electron density .
although the calculation configuration is quite different , as we can see , the calculation results on variation of average ionization degree with plasma temperature are in good agreement .
however we still notice some slight difference between our calculation and that from flychk code . at low temperature limit ,
i.e. , temperature below @xmath93 , the average ionization degree from our simulation is close to zero , while that calculated from flychk depends on the plasma density . for plasma of density @xmath75 ,
the average ionization degree is `` @xmath94 '' , while for plasma of density @xmath73 , it is also close to zero . according to the calculations of flychk code , both the calculation results , `` @xmath94 '' and `` @xmath95 '' , make sense . for aluminium of density @xmath58 ,
i.e. , @xmath96 , average charge degree `` @xmath94 '' means the plasma density is @xmath97 .
the average charge degree `` @xmath98 '' corresponds to the plasma of density @xmath73 .
it is hard for us to judge the average ionization degree of a bulk aluminium at low temperature limit , if we follow the calculations of flychk .
for electron temperature between @xmath99 and @xmath100 , it is indicated from our calculation that there exists an `` ionization shelf '' , meaning @xmath101 is a very stable charge state . following the ionization potentials of aluminium listed in table .
[ table1 ] , we can see that the ionization potential abruptly increases from @xmath102 to @xmath103 .
the large ionization potential gap is due to the `` solid '' @xmath104 core . considering the stability of this `` solid '' core
, the existence of `` ionization shelf '' seems reasonable .
in summary , a physical model based on monte - carlo approach is proposed to investigate the ionization dynamics of warm dense matter in pic simulations . in our model ,
both impact ionization and electron - ion recombination are taken into account .
furthermore , the ipd affected by surrounding plasmas are also self - consistently taken into consideration . when compared with other existing models which do not often include the relevant physical mechanisms at the sub - pico second or pico - second scales , our proposed model drops the constrain of thermal equilibrium conditions .
therefore , our model can be applied also for non - equilibrium processes .
the key issue related to impact ionization is the related cross section calculation , which can be calculated or generated either from lotz s formula or from external simulation code , such as multi - configuration flexible atomic code .
the electron - ion recombination model is based on three - body - recombination .
the ipd effect by surrounding plasmas is calculated by the model proposed by stewart .
furthermore , the idp effect can also be calculated by multi - body - quantum - mechanical methods . both the calculation methods exhibit similar behaviour , except for the slightly different numerical values .
the proposed model is implemented into an existing particle - in - cell simulation code .
the temporal relaxation of bulk aluminium and aluminium carbide is calculated . in order to release the calculation burden and
simultaneously ensure the calculation accuracy , a merging particle technique is configured and applied .
the variation of average ionization degree of bulk aluminium with temperature calculated from our model is compared with that from flychk code , showing good consistency .
d. wu wishes to acknowledge the financial support from german academic exchange service ( daad ) and china scholarship council ( csc ) , also thanks b. goswami , j. w. wang and s. z. wu at helmholtz institut - jena for fruitful discussions .
t. g. white , n. j. hartley , b. borm , b. j. b. crowley , j. w. o. harris , d. c. hochhaus , t. kaempfer , k. li , p. neumayer , l. k. pattison , f. pfeifer , s. richardson , a. p. l. robinson , i. uschmann , and g. gregori , phys .
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tauschwitz , and m. roth , phys .
105 , 265701 ( 2010 ) .
m. roth , t. e. cowan , m. h. key , s. p. hatchett , c. brown , w. fountain , j. johnson , d. m. pennington , r. a. snavely , s. c. wilks , k. yasuike , h. ruhl , f. pegoraro , s. v. bulanov , e. m. campbell , m. d. perry , and h. powell , phys .
86 , 436 ( 2001 ) .
o. ciricosta , s. m. vinko , h .- k .
chung , b. i. cho , c. r. d. brown , t. burian , j. chalupsky , k. engelhorn , r. w. falcone , c. graves , v. hajkova , a. higginbotham , l. juha , j. krzywinski , h. j. lee , m. messerschmidt , c. d. murphy , y. ping , d. s. rackstraw , a. scherz , w. schlotter , s. toleikis , j. j. turner , l. vysin , t. wang , b. wu , u. zastrau , d. zhu , r. w. lee , p. heimann , b. nagler , and j. s. wark , phys .
109 , 065002 ( 2012 ) . | arxiv |
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How high could i jump if I weighed only half as much? [closed]
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E.g.
I weigh 150 lbs
I had a thrust device that lifted 75 pounds.
How high could I jump?
What if that thrust lifted 2/3 of my weight (100 lbs)?
Obviously, I cant fly, but I guarantee if I weighed 75 lbs less, I could jump a lot higher than I currently can.
>
> Obviously, I cant fly, but I guarantee if I weighed 75 lbs less, I
> could jump a lot higher than I currently can.
>
>
>
Thank you. I appreciate your guarantee.
>
> How high could i jump if I weighed only half as much?
>
>
>
Under the assumption that you would be able to impart the same amount of energy with your legs, you would be able to jump twice as high. Because
$$
mgh=(\frac{m}{2})g(2h)\;.
$$
...Not sure if this is an appropriate assumption for your case.
I'm assuming that you mean you can use your thrust device *further to* the thrust you can impart with your own legs. Otherwise, something can lift 75 pound weight won't lift you at all.
Also, you need to explain how your thrust device's force changes as you move (a spring, for example, imparts less force the more it relaxes).
So I'll assume your device is something that can impart a *constant* force on you as you jump off the ground and fall back. This, as you imply, is equivalent to having the same thrust capability in your legs when you weigh half your current weight. So now you are solving the DE (here $x$ is the height co-ordinate):
$$F = m\,\ddot{x}= f(x) + T - m\,g \Leftrightarrow \ddot{x} = \frac{1}{m}\,(f(x)+T)-g\Leftrightarrow \frac{1}{2}\mathrm{d}\_x v^2 = \frac{1}{m}\,(f(x)+T)-g$$
where $f(x)$ models the thrust of your legs as you rise of the ground, and it falls to nought after some height $h\_0$ when your feet lose contact with the ground. We also assume $v=0$ when you begin. $T$ models the constant thrust of your thrusting device. So now you explore the above with different values of $T$: $f(x)$ is constant. You reach your maximum height $h\_{max}$ when $v^2 = 0$. So you must solve:
$$\int\_0^{h\_{max}} (f(x)+T)\,\mathrm{d}\,x - m\,g\,h\_{max} = 0$$
Assuming you can jump off the ground without help, you know $h\_{max}>h\_0$ *i.e.* you can at least reach a point where your legs are fully stretched out and you are leaving the ground, so that the first term in your integral must be the constant $E=\int\_0^{h\_0} f(x)\,\mathrm{d}\,x$. $J$ represents your unhelped, "intrinsic" jumping capability. It is the *energy* your legs impart. So now you explore the equation:
$$E+(T-m\,g)\,h\_{max}=0$$
where $m$ is your mass, as a function of $T$ (you can also get this equation from energy considerations). Assuming you know how high you can jump $h\_u$ without help, *i.e.* with $T=0$, you can use this knowledge to solve the above equation for $E$, and thus get the relationship you want.
This answer looks at what happens to your jump height if you actually decrease in mass, while maintaining the same leg jump strength.
So, let us assume that the mechanism by which a person jumps can be modelled as a finite impulse that occurs in an instance (i.e. a very very large force applied in a short frame of time). Let this impulse has a magnitude $I$, and let the original mass of the jumping body be $m\_0$. I'll assume the size of the impulse stays the same regardless of the mass.
So, when you apply this impulse to a body at rest, with mass $m$, you instantly increase the upward momentum by $I$. Therefore, the body will leave the ground with velocity equal to $I/m\_0$.
Now, we can make use of one of the 1D constant-acceleration equations of motion, because the only consider force the body will experience in the air is a constant gravitational force, which causes a constant downward acceleration of $g$. Let's use the equation:
$$v^2 = u^2 + 2as$$
where $v$ is the final velocity, $u$ is initial velocity, $a$ is the constant acceleration, and $s$ is the change in displacement.
Taking our sign convention to be positive upwards, let $a = -g$, $v = 0$ (as max height is reached when the body become instantaneously stationary in mid air), and $s = h$, where $h$ is the max height reached.
$$0 = u^2 - 2gh$$
We already found that $u = I/m$, so:
$$2gh = I^2/m^2$$
$$I^2 = 2ghm^2$$
$I$ is constant, so we can write an equation relating the original mass, $m\_0$ and original jump height, $h\_0$, to the new mass, $m\_{new}$ and new jump height $h\_{new}$:
$$2gh\_0 m^2\_0 = 2gh\_{new}m\_{new}^2$$
$$\therefore h\_{new} = h\_0 \frac{m\_0^2}{m\_{new}^2}$$
So, for example, if you original weight 150lbs, and you could originally jump 1m, reducing you weight to 75lbs would increase your new jump height to 4m. If your weight was now 100lbs, you could jump 2.25m high.
More realistically, if you lose 10lbs, then your new jump height in this example would be 1.15m, a 15cm increase in height!
| stackexchange/physics |
a whole - sky map contains significant amount of foreground emission from astrophysical sources . hence , the ability to clean foreground contamination in cmb data is of the utmost importance for cmb observations . in the wmap observation , foreground
were cleaned by two different methods @xcite .
one is using external templates of the foregrounds , but using external template maps @xcite suffers from dubious extrapolation and template noise of higher level than the wmap @xcite .
the other is using the internal linear combination ( ilc ) method @xcite , where the linear weight for each frequency channel is chosen to minimize the variance of the linear combination of multi - frequency maps , therefore minimizing residual foreground . to take into account the spatial variability , the wmap team defined twelve disjoint regions , where distinct linear weights are assumed for each region . in spite of many merits of the ilc method , it has important limits : first , the definition of disjoint regions requires external information and the use of disjoint regions brings about discontinuities .
second , there exists a cross term between the residual foreground and cmb , which makes the variance minimization proceed as to maximize the cancellation between the residual foreground and cmb @xcite . for the solution of the first problem , we have carried out the variance minimization entirely in spherical harmonic space , where the spatial variability of linear weights can be incorporated in a self - contained and seamless manner . for the solution of the second problem
, we have developed an iterative foreground reduction method , where perturbative correction is made for the cross term .
simulations confirmed that our iterative method reconstructs the cmb with stability and reliability .
we have also applied our method to the wmap data and obtained a foreground - reduced cmb map .
the outline of this paper is as follows . in sec .
[ multifrequency ] , we discuss briefly the foreground reduction method with multi - frequency maps , minimum variance principle and the choice of general form for linear weights . in sec .
[ spherical_space ] , we derive equations in spherical harmonic space , whose solutions correspond to linear weights of minimum foreground .
we present an iterative foreground reduction method in sec .
[ bias ] and simulation results in sec .
[ simulation ] .
the result of application to the wmap three year and five year data are presented in sec . [ wmap ] and [ wmap5yr ] respectively .
we discuss computational issues in sec .
[ computation ] and conclude this investigation in sec .
[ conclusion ] . in appendix
[ matrix_solution ] , the equation for minimum foreground is put in matrix notation and the solution is presented in the form of matrix operations . in appendix
[ supprression ] , we show that the cross term between residual foreground and cmb causes the suppression on the lowest multipole powers of an internal linear combination ( ilc ) map . in appendix
[ comparison ] , we make a brief comparison by summarizing the advantages and disadvantages of ilc variants and the template - fitting method .
with neglect of pixel noise , a thermodynamic temperature map at a frequency @xmath1 and pixel @xmath2 is as follows : @xmath3 where @xmath4 and @xmath5 are cmb signal and the composite foreground signal respectively .
a natural choice for the estimator of the cmb map is a linear combination of multi - frequency maps , which is as follows : @xmath6 to keep the cmb unchanged , a contraint is given such that the sum of linear weights over frequency channels is equal to unity : @xmath7 with eq .
[ t ] and [ nomarlization ] , it is straightforward to show that @xmath8 we can make the foreground signal in eq .
[ ilc_pixel ] vanish , if the linear weights are chosen such that : @xmath9 since we have no information on @xmath5 , we need some function to maximize or minimize , which will lead us toward such linear weights
. one of such powerful methods is variance minimization of the linear combination map @xcite .
it can be shown that the variance of a linear combination map is @xmath10 where the constant term @xmath11 is the variance of cmb and therefore , independent of the choice of linear weight . though the cross term @xmath12 in eq .
[ sigma_ilc ] vanishes , when averaged over a whole ensemble of universes , it is not necessarily zero for our single observable universe .
hence , we assume the cross term to be small but non - zero , and will make perturbative correction for it ( see sec . [ bias ] ) . for
now , we neglect the cross term . the linear weights , which yield a foreground - free map , are functions of the frequency spectrum of foreground components .
since the frequency spectrum varies over sky ( see @xcite for a recent treatment ) , the linear weights should possess spatial variability . to accommodate the spatial variability of linear weights , the wmap team defined twelve disjoint regions in the wmap three year ilc ( wilc3yr ) construction , where distinct values of linear weights are assumed for each region .
the linear weights of wilc3yr have the form @xmath13 , where @xmath14 and @xmath15 denote a frequency channel and a region index . though the wmap team used regions of smoothed boundaries in the final map making , there still exist intrinsic discontinuities from the use of disjoint regions in variance minimization , which may even create artificial peculiarities . to reflect the varying powers of foregrounds on different angular scales , linear weights contrived by tegmark et al .
has multipole dependency as well @xcite , and have the form @xmath16 .
we can easily show that optimal linear weights should possess @xmath17 dependency as well as @xmath18 dependency .
for illustrative purposes , let s consider two frequency channel observation and assume the signal to consist of cmb and one foreground component only . the spherical harmonic coefficient of @xmath14th channel is given by @xmath19 , where @xmath20 denotes the spherical harmonic coefficient of a foreground at @xmath14th channel .
keeping the cmb signal unchanged , we assign a linear weight @xmath21 and @xmath22 to the frequency channel 1 and 2 respectively .
then , the spherical harmonic coefficient of a linear combination map is given by @xmath23 obviously the linear weight @xmath21 yielding a foreground - free linear combination map is @xmath24 as shown in eq .
[ w_rank ] , optimal linear weights should possess @xmath17 dependency as well as @xmath18 dependency .
the linear combination map of minimum foreground formed with multi - frequency maps @xmath25 can be rewritten in the spherical harmonic space , using the clebsch - gordon relation as : @xmath26 where @xmath27 the constraint @xmath28 imposed to preserve the cmb signal is expressed in spherical harmonic space as follows : @xmath29 we can see that linear weights @xmath30 in eq .
[ a_lm ] possess @xmath17 dependency as well as @xmath18 dependency .
[ a_lm ] is equivalent to [ wt ] , physical interpretation on eq .
[ a_lm ] is quite straightforward and we base our approach on eq .
through variance minimization , we are going to derive equations leading toward the linear weights of minimum foreground .
since the function @xmath31 is real - valued , @xmath30 obeys the reality condition @xmath32 .
therefore , only @xmath30 ( @xmath33 ) needs to be determined .
it is computationally convenient to accommodate the reality condition by defining real - valued spherical harmonic coefficients @xmath34 as @xmath35 $ ] , @xmath36 $ ] for @xmath37 , @xmath38 respectively .
the constraints on @xmath34 derived from eq . [ w00 ] and [ wlm ] are as follows : @xmath39 the linear weights of minimum foreground minimize the variance @xmath40 under the constraints eq .
[ w00_constraint ] and [ wlm_constraint ] .
the constrained minimization problem is solved conveniently via lagrange s undetermined multiplier method @xcite . with the introduction of lagrange s multiplier @xmath41
, it can be shown that the variance is minimized under the constraints eq .
[ w00_constraint ] and [ wlm_constraint ] , when @xmath42 by using eq .
[ a_lm ] , it can be shown that eq .
[ variance_minimized ] has the following form : @xmath43+\lambda_{l'm'}=0,\label{minimum_wlm}\end{aligned}\ ] ] where @xmath44 is @xmath45,\label{alpha}\end{aligned}\ ] ] and @xmath46 is @xmath47\end{array}\right.&&\nonumber\end{aligned}\ ] ] for @xmath48 , @xmath49 and @xmath50 respectively , and @xmath51 therefore , the values of linear weights of minimum foreground can be found in terms of lagrange s multiplier @xmath52 by solving the system of simultaneous linear equations given by eq .
[ minimum_wlm ] .
the values of lagrange s multiplier @xmath52 can be easily determined by making the solutions of eq .
[ minimum_wlm ] satisfy the constraints eq .
[ w00_constraint ] and [ wlm_constraint ]
. we can write eq .
[ w00_constraint ] , [ wlm_constraint ] and [ minimum_wlm ] in matrix form and obtain the solution conveniently via matrix operations ( for details on the solution in matrix notation , refer to eq .
[ w_solution ] . ) .
there exists a non - zero correlation between foregrounds and true cmb , so called ` cosmic covariance ' @xcite , which leads to a non - negligible cross term in eq .
[ sigma_ilc ] .
the existence of this non - negligible cross term makes the linear combination of minimum variance differ from that of minimum residual foregrounds @xcite . by noting that the cross term disappears in the absence of cmb signal , we have developed a perturbative method , where the cross term is reduced through iterations .
however , as it was shown in @xcite , this approach is only effective down to the level of ` cosmic covariance ' @xcite .
consider the quantity @xmath53 , where @xmath54 is our best guess cmb map from the @xmath55th iteration with @xmath56 the merit of this quantity is that cmb signal is reduced through iterations , leading to reduction of the cross term .
we obtain linear weights @xmath57 of the @xmath15th iteration through variance minimization of @xmath58 and update our best guess cmb map as follows : @xmath59 using eq .
[ t ] and [ nomarlization ] , we may show that our updated cmb map is @xmath60 where @xmath4 is a true cmb map . using eq .
[ t ] and [ nomarlization ] , we may also show that the variance of @xmath61 is @xmath62 where @xmath11 is a term independent of linear weights @xmath57 .
[ iteration_j ] , the cross term , which is in the last line of eq .
[ variance_iteration ] , may be shown to be @xmath63 therefore , the cross term is getting reduced through iterations , provided that @xmath64 in practice , the cross term converges to some non - zero value , which may be attributed to two causes .
first , foreground are reduced with some error , which arises from the imperfection of the method applied ( e.g. a finite number of assumed @xmath30 , imperfection of twelve disjoint regions of wilc3yr ) .
the residual foreground related to the error are reduced barely through iterations .
second , residual foregrounds of the @xmath15th iteration possesses some level of correlation with that of the @xmath65th iteration .
we have generated simulated data as follows : @xmath66 @xmath67 is the spherical harmonic coefficients of the wmap band maps at @xmath14th channel from the lambda site , and @xmath68 and @xmath69 are those of wilc3yr and a simulated cmb map . @xmath70 is the beam transfer functions of the wmap @xmath14th channel @xcite and @xmath71 is the beam transfer function of a @xmath72 fwhm gaussian beam , which is the smoothing kernel used in wilc3yr .
our procedure for the generation of simulated data is overly conservative , because the presence of instrument noise and residual foreground in the wilc3yr makes some foreground and instrument noise double - counted . using eq .
[ alm_simulation ] , we have generated four hundred simulated data set and carried out foreground reduction on them . ] ] ] ] ] when linear weights are obtained through variance minimization on noisy data , linear weights are chosen as to minimize noise rather than foreground . since
our simulated data are quite noisy on multipoles higher than @xmath73 , we have used only @xmath74 in variance minimization ( i.e. summation over @xmath75 was done up to @xmath73 in eq . [ gamma ] ) .
we have made the assumption that linear weights of minimum foreground will be spatially coherent on small angular scales , and determined only @xmath76 in a finite multipole range @xmath77 .
though ideally the total number of @xmath30 may be as high as the total number of available @xmath78 ( i.e. the number of unknowns may be as many as the number of constraints ) , we found that the number of @xmath30 , which keeps the matrices in eq .
[ w_solution ] numerically non - singular , is much smaller than the ideal case ( i.e. @xmath79 ) ( see section [ computation ] for the discussion on the possible sources of numerical singularity . ) .
we have increased @xmath80 until the numerical instability emerges and found that @xmath81 is optimal for the wmap data .
if more @xmath78 of good snr were available , it would be numerically stable with higher @xmath80 .
we have implemented iterative foreground reduction , which is discussed in sec .
the cross term in the first iteration is quite significant , since the best - guess cmb map of zeroth iteration is set to zero ( see eq .
[ guess_t0 ] ) .
hence , in the implementation of iterative foreground reduction , we have excluded lowest multipoles ( @xmath82 ) in variance minimization of the first iteration for regularization purpose ( see appendix [ supprression ] for details on why exclusion of lowest multipoles reduces the effect of the cross term . ) .
such regularization is not necessary in succeeding iterations ( @xmath83 ) . since it turned out that the improvement after @xmath84 iterations were negligible , we carried out only @xmath84 iterations for each simulated data set .
the power spectra discrepancy between output cmb and input cmb are shown for four hundred cmb realizations in fig .
[ cl2 ] , [ cl3 ] , [ cl4 ] , [ cl5 ] and [ cl20 ] on multipoles ( @xmath85 ) .
the vertical axis denotes @xmath86 , where @xmath87 .
the horizontal axis denotes the enumerating index of four hundred cmb realizations . in fig .
[ sim_22 ] , we show power spectra ( @xmath88 ) of input cmb and output cmb for the realization # 22 , since the realization # 22 among four hundred realizations has the octupole and quadrupole power closest to those of the wmap best - fit @xmath0cdm .
fwhm smoothed maps [ @xmath89 : hilc3yr of the zeroth iteration ( top ) , hilc3yr of the first iteration ( second ) , wilc3yr ( third ) , @xmath90 ( fourth ) , and the difference between the zeroth and the first iteration hilc3yr ( bottom),title="fig : " ] fwhm smoothed maps [ @xmath89 : hilc3yr of the zeroth iteration ( top ) , hilc3yr of the first iteration ( second ) , wilc3yr ( third ) , @xmath90 ( fourth ) , and the difference between the zeroth and the first iteration hilc3yr ( bottom),title="fig : " ] fwhm smoothed maps [ @xmath89 : hilc3yr of the zeroth iteration ( top ) , hilc3yr of the first iteration ( second ) , wilc3yr ( third ) , @xmath90 ( fourth ) , and the difference between the zeroth and the first iteration hilc3yr ( bottom),title="fig : " ] fwhm smoothed maps [ @xmath89 : hilc3yr of the zeroth iteration ( top ) , hilc3yr of the first iteration ( second ) , wilc3yr ( third ) , @xmath90 ( fourth ) , and the difference between the zeroth and the first iteration hilc3yr ( bottom),title="fig : " ] fwhm smoothed maps [ @xmath89 : hilc3yr of the zeroth iteration ( top ) , hilc3yr of the first iteration ( second ) , wilc3yr ( third ) , @xmath90 ( fourth ) , and the difference between the zeroth and the first iteration hilc3yr ( bottom),title="fig : " ] we have applied our foreground reduction method to the wmap three year data from the lambda site @xcite .
spherical harmonic coefficients of the band maps have been obtained as follows : @xmath91 where @xmath67 are the spherical harmonic coefficients of the wmap three year band maps and @xmath70 are the beam transfer functions of the wmap @xmath14th channel @xcite . just as the application to the simulated data in the previous section , the cutoff multipole @xmath80 for linear weights is set to seven , and we have used @xmath78 in the multipole range @xmath92 in variance minimization
( i.e. summation over @xmath75 was done up to @xmath73 in eq .
[ gamma ] ) . in fig .
[ ilc ] , our cmb map , which we call ` harmonic internal linear combination map ' ( hereafter , hilc3yr ) , is shown with the wmap three year ilc map ( wilc3yr ) and the difference map .
the maps in fig .
[ ilc ] are images smoothed with @xmath72 fwhm beam .
cdm model , title="fig : " ] cdm model , title="fig : " ] power spectra estimate on hilc3yr and wilc3yr are made by computing @xmath87 , which are shown with the wmap best - fit @xmath0cdm model in fig .
[ cl_wmap ] . as shown in fig .
[ cl_wmap ] , hilc3yr makes better agreement with the wmap best - fit @xmath0cdm model than wilc3yr ( e.g. the first doppler acoustic peak is visible in the hilc3yr power spectrum around @xmath93 ) .
the huge excess power of wilc3yr and hilc3yr on high multipoles ( @xmath94 ) is attributed to pixel noise . in the multipole range ( @xmath95 ) , where point sources are dominant over other sources @xcite
, hilc3yr makes relatively good agreement with the model , while there is significant discrepancy between wilc3yr and the model .
this may indicates relatively effective reduction of point sources in hilc3yr .
the absolute value of the power spectra difference between wilc3yr and hilc3yr is also shown in fig .
[ cl_wmap ] . through polynomial - fitting in the multipole range ( @xmath96 ) ,
we have investigated the multipole dependency of the the power spectra difference between hilc3yr and wilc3yr .
considering the multipole dependency , we may , with some caution , attribute the power difference to residual point sources and pixel noise .
we have also investigated the linear weights of hilc3yr , and found that hilc3yr gets contribution more from the v band map than the w band map .
hence , the less noise level of hilc3yr does not mean that hilc3yr prefers blindly the least noise channel at the sacrifice of foreground reduction .
the linear weights of hilc3yr , which are continuous over entire sky , are shown in fig .
[ w_hilc ] .
we have computed the variance of our linear weights by @xmath97 to quantify the spatial variation of our linear weights on different angular scales . as shown in fig .
[ wl ] , @xmath98 tends to decrease with increasing multipole , with @xmath99 being the highest .
it is not difficult to see from the tail pattern that there will be some non - zero @xmath30 on multipoles higher than our assumed cutoff multipole @xmath100 .
these unaccounted @xmath30 ( @xmath101 ) may be partially responsible for the residual foregrounds , which is visible around the galactic plane in fig .
however , it is unlikely that low multipole anisotropies are affected significantly by the residual foreground around the galactic plane .
.quadrupole and octupole powers [ cols="^,^,^,^",options="header " , ] [ low_multipole_power2 ] in table [ low_multipole_power2 ] , the quadrupole and octupole powers of hilc5yr are shown with those of the wmap 5 year best - fit @xmath0cdm model and wilc5yr .
the angular separation between the preferred axis of the quadrupole anisotropy and that of the octupole anisotropy is @xmath102 for wilc5yr , while @xmath103 for hilc5yr .
the corresponding probabilities of getting such an alignment is @xmath104 for wilc5yr , while @xmath105 for hilc5yr .
the anisotropy of hilc5yr on low multipoles ( @xmath106 ) are shown in fig .
[ ilc_l2 ] , [ ilc_l3 ] , [ ilc_l4 ] and [ ilc_l5 ] with those of wilc5yr and difference maps . ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] [ @xmath89 : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] [ @xmath89 : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] [ @xmath89 : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] : hilc5yr ( top ) , wilc5yr ( middle ) , wilc5yr - hilc5yr ( bottom),title="fig : " ] the linear weights of hilc5yr are shown in fig .
[ w_hilc5yr2 ] . in fig .
[ wl_5yr ] , we show the variance of the linear weights of hilc5yr , which is computed by @xmath97 .
the computation of linear weights by our harmonic variance minimization can be split as follows : + 1 ) computing @xmath107 by eq .
[ gamma ] + 2 ) computing @xmath44 by eq .
[ alpha ] + 3 ) solving the system of linear equations given by eq .
[ minimum_wlm ] .
let s assume that there are @xmath108 band maps of high snr up to some multipole @xmath109 and the cutoff multipole for linear weights is set to @xmath18 . with the recurrence relation @xcite , we are at present able to compute wigner 3j symbols in eq .
[ gamma ] up to high multipoles ( @xmath110 ) fast enough .
therefore , step 1 ) put relatively little computational load .
+ step 2 ) requires @xmath111 and step 3 ) , which involves @xmath112 by @xmath112 matrix inversion , requires @xmath113 , where @xmath114 and @xmath115 .
@xmath18 is chosen to be much smaller than @xmath109 to keep matrices in eq .
[ w_solution ] numerically non - singular ( e.g. in the application to wmap data , we have set @xmath100 and @xmath116 , with consideration of numerical singularity and the wmap band map s snr . )
since @xmath114 is much smaller than @xmath115 , the total computing time is @xmath117 .
as described previously , we have found @xmath118 phenomenologically by increasing it until numerical singularity in eq .
[ w_solution ] emerges .
while ideally @xmath118 can be as high as @xmath109 , the optimal value of @xmath118 for the wmap data seems to be much smaller than @xmath109 . the numerical singularity for ( @xmath119 )
may be attributed to large bandwidth and relatively small separation of the wmap frequency channels , because in such configurations the frequency spectrum of foregrounds may not be numerically distinct enough over the channels . through simple extrapolation by comparing the beamwidth and snr of the planck surveyor with those of the wmap ,
we may make rough estimate that hilc method with @xmath120 may be numerically stable for the planck temperature data .
in spite of the warning from the wmap team against serious use of the ilc map , the ilc map has been widely used especially for low multipole anisotropy study , since the template - subtraction maps are not suitable for a whole sky map due to heavy foreground contamination within kp2 cut .
we have summarized the advantages and disadvantages of ilc variants and the template - fitting method in appendix [ comparison ] .
for these reason , we have pursued the ilc method and extended it by improving the causes related to the complication in noise properties ( e.g. smoothing on the disjoint regions , monte - carlo ` bias ' correction ) . through our effort toward improved ilc implementation
, we have developed a harmonic variance minimization method , which is derived by converting a general form of pixel - domain approach into spherical harmonic space . in our approach , spatial variability of linear weights
is incorporated in a self - contained manner and linear weights are continuous over whole sky . thanks to full correspondence to a general pixel - domain method , physical interpretation on our method is quite straightforward . in variance minimization , there exists a cross term between residual foreground and cmb , which makes the linear combination of minimum variance differ from that of minimum foreground . we have developed an iterative method , where perturbative correction is made for the cross term . the simulations showed that our method yields reliable and stable reconstruction of the cmb also on lowest multipoles . by applying it to the wmap data , we have obtained a cmb map , whose power spectra makes better agreement with the wmap best - fit @xmath0 cdm model than the wilc5yr . the cmb map and linear weights , which we have obtained , are available from ` http://www.nbi.dk/\simjkim/hilc ` .
capacity of our method to clean foreground , whose spectral indice is a rapidly varying function of position , is limited by the snr of data on high multipoles , since increasing the cutoff multipole of linear weights requires more data to avoid numerical singularity in eq .
[ w_solution ] .
when the data of good snr on high multipoles are available , we will be able to make better reduction of foregrounds by setting the cutoff multipole to higher value .
this is similar to saying that we are able to assume finer disjoint regions in pixel - domain approach , when data of better pixel resolution are available . the foreground reduction method by template fitting is unable to take full advantage of the high resolution low noise planck data , since the available templates do not have such high resolution and low noise over a whole sky .
unlike the template method , the effectiveness of our method scales with frequency channel numbers and angular resolution of the observation data .
hence our method is more suitable for the planck surveyor , which has nine frequency channels with good snr and angular resolution .
our method , which is presented for the application to temperature data , may be easily extended to the polarization data by making the following replacement in eq . [
gamma ] : @xmath121 we believe a blind approach like our method is desirable for the analysis of polarization data from the upcoming planck satellite , since the availability of polarized foreground templates is quite limited . for these reasons , the method presented in this paper will stand out among several foreground reduction methods , when low - noise high resolution data of cmb temperature and polarization are available from the planck surveyor @xcite .
we are grateful to changbom park for helpful discussions .
we acknowledge the use of the legacy archive for microwave background data analysis ( lambda ) .
our simulation and data analysis made the use of healpix@xcite and were performed on the supercomputing facility of the danish center for scientific computing .
this work was supported by fnu grant 272 - 06 - 0417 , 272 - 07 - 0528 and 21 - 04 - 0355 .
we present the solutions of eq .
[ w00_constraint ] , [ wlm_constraint ] and [ minimum_wlm ] through matrix operations .
consider @xmath122 linear weights for maps of @xmath123 frequency channels . in matrix notation , the constraints given by eq .
[ w00_constraint ] and [ wlm_constraint ] are as follows : @xmath124 @xmath125 is a @xmath126 matrix , given by @xmath127 and @xmath128 is a column vector of length @xmath129 , given by @xmath130 in matrix notation , eq .
[ minimum_wlm ] is as follows : @xmath131 where @xmath132 for @xmath133 , @xmath134 , and @xmath135 .
@xmath136 is a @xmath137 matrix , and @xmath138 and @xmath139 are column vectors of length @xmath122 , and length @xmath129 respectively . with eq .
[ awl ] , @xmath138 is solved in terms of @xmath129 undetermined langrange multipliers , provided that @xmath136 is invertible : @xmath140 with eq .
[ constraint ] and [ wal ] , the undetermined @xmath129 langrange multipliers are given by : @xmath141 therefore , linear weights in spherical harmonic space is given as follows : @xmath142 eq .
[ w_solution ] is not reduced to @xmath143 , since @xmath144 and @xmath145 are not square matrices .
to better understand the effect of the cross term , we investigate a simple case of two frequency observation channels and foregrounds of uniform frequency spectra . since the analysis in sec .
[ simulation ] and [ wmap ] are carried out on the multipole of high snr , we neglect instrument noise . we assume linear weights to be constant , because the foreground spectra are assumed to be spatially uniform . keeping the cmb signal unchanged , we assign constant linear weights @xmath21 and @xmath22 for the frequency channel 1 and 2 respectively .
since spherical harmonic coefficients of the linear combination map is @xmath146 the variance of the linear combination map is as follows : @xmath147 where @xmath148 and @xmath149 denote the spherical harmonic coefficients of foregrounds at frequency channel 1 and 2 respectively . since the value of @xmath21 , which minimizes eq .
[ sigma ] , is @xmath150}{\sum\limits_{l'm ' } |a^{\mathrm{fg1}}_{l'm'}-a^{\mathrm{fg2}}_{l'm'}|^2},\end{aligned}\ ] ] the linear combination map of minimum variance has the following spherical harmonic coefficients : @xmath151\right).\nonumber\\\end{aligned}\ ] ] the power spectra of our galactic foregrounds has uneven distribution with high concentration on lowest multipole and azimuthal mode ( i.e. @xmath152 ) .
therefore , the spherical harmonic coefficients of the linear combination map is @xmath153 according to eq .
[ alm_two_channel_approx ] , @xmath154 for ( @xmath155 ) .
this is in agreement with the suppression on lowest multipole powers in an internal linear combination ( ilc ) map , reported by @xcite .
therefore , we attribute the existence of the cross term and highly uneven power spectrum of foregrounds to the suppression on low multipole power in an internal linear combination ( ilc ) map . to test our hypothesis ,
we have carried out simulations with foregrounds of flat power spectrum , which are derived from the wmap maximum - entropy - method(mem ) foregrounds as follows : @xmath156 where @xmath157 is spherical harmonic coefficients of the wmap mem foreground and @xmath158 .
the role of @xmath159 is to match the total power of the flat foreground with that of the mem foregrounds .
the result of simulations show that there is no observable suppression on low multipole powers when foregrounds have flat power spectrum , thereby supporting our hypothesis .
this suppression on low multipole power can be reduced by excluding the multipoles of high foreground concentration ( i.e. low multipoles ) in variance minimization process .
consider minimizing the following variance where low multipoles are excluded : @xmath160 where foreground power in the multipole range ( @xmath161 ) are much bigger than those on higher multipoles .
then , the linear combination map has the following spherical harmonic coefficients : @xmath162\right).\nonumber\end{aligned}\ ] ] with enough number of summation terms , the term inside the big parenthesis of eq .
[ alm_no_bias ] approaches zero because of cancellation .
if we had not excluded low multipoles , the cancellation would be ineffective , due to asymmetric distribution of foreground power ( i.e. high concentration on low multipoles . )
[ alm_no_bias ] is valid for @xmath163 ( @xmath164 ) as well as ( @xmath165 ) . in other words , though the linear weights were determined through variance minimization over ( @xmath166 ) , they are applicable to foreground reduction in @xmath163 ( @xmath164 ) .
we have also investigated the non - uniform frequency spectra case by resorting to a numerical investigation .
we find that there is a tendency of suppression over multipole range ( @xmath167 ) , where @xmath80 is the assumed cutoff multipole of @xmath30 .
we also find that the suppression is reduced by excluding the multipoles of high foreground concentration in variance minimization process , just as in the uniform frequency spectra case .
in this section , we are discussing briefly the advantages and disadvantages of ilc variants and a template fitting method .
the template fitting method is the foreground reduction method most importantly employed by the wmap team .
it has advantage that it has less complicated noise properties and is free from the cosmic covariance problem , while it has the disadvantages that it relies on foreground templates of external sources , hence requiring extrapolation to observation frequencies and currently unable to provide a whole sky map , due to heavy foreground contamination within kp2 cut .
wilc is the ilc implementation by the wmap team .
it has the advantages that it utilizes the boundary shape information of galactic foregrounds and scales with the number of observation frequency channels , while its disadvantages are sharp boundaries of disjoint regions ( smoothing boundaries in the final map making does not solve discontinuity problem completely , since region definition with sharp boundary are used in variance minimization . ) , dubious bias correction of the ` cosmic covariance ' by monte - carlo cmb , its reliance on the pre - defined disjoint regions ( not being a completely blind approach ) .
tcm3yr @xcite is the ilc variant , where the variance of each multipole is minimized separately .
it has the advantages that the dependency of foreground power on angular scales is reflected and scales with the number of frequency channels , while it has the disadvantages of sharp boundaries , ` cosmic covariance ' problem , need for the pre - defined disjoint regions .
@xcite is another ilc variant . instead of using disjoint region definition by the wmap team ,
disjoint regions were derived from the mem reconstructed foregrounds .
it has the advantages that the definition of the disjoint regions may be optimal than those of wilc , and it scales with the number of frequency channels , while it has the disadvantages of sharp boundaries , ` cosmic covariance ' problem , need for the mem foreground ( traces mem foregrounds and hence wilc3yr ) .
hilc , which is our ilc implementation , has the advantages that it does not rely on the definition of disjoint regions ( hence no sharp boundaries ) , scalability with the number of observation frequency channels and angular resolution of data , while it has the disadvantages that it is computationally intensive , and has the ` cosmic covariance ' problem , though reduced . c. bennett , r. s. hill , g. hinshaw , m. r. nolta , n. odegard , l. page , d. n. spergel , j. l. weiland , e. l. wright , m. halpern , n. jarosik , a. kogut , m. limon , s. s. meyer , g. s. tucker , and e. wollack .
first year wilkinson microwave anisotropy probe ( wmap ) observations : foreground emission . ,
148 , 97 , 2003 .
http://lambda.gsfc.nasa.gov .
g. hinshaw , d. n. spergel , l. verde , r. s. hill , s. s. meyer , c. barnes , c. l. bennett , m. halpern , n. jarosik , a. kogut , e. komatsu , m. limon , l. page , g. s. tucker , j. weiland , e. wollack , and e. l. wright .
first year wilkinson microwave anisotropy probe ( wmap ) observations : angular power spectrum .
, 148 , 135 , 2003 . h. k. eriksen , a. j. banday , k. m. gorski , and p. b. lilje . on foreground removal from the wilkinson microwave anisotropy probe data by an internal linear combination method : limitations and implications . , 612 , 633 , 2004 .
g. hinshaw , j. l. weiland , r. s. hill , n. odegard , d. larson , c. l. bennett , j. dunkley , b. gold , m. r. greason , n. jarosik , e. komatsu , m. r. nolta , l. page , d. n. spergel , e. wollack , m. halpern , a. kogut , m. limon , s. s. meyer , g. s. tucker , and e. l. wright .
five - year wilkinson microwave anisotropy probe ( wmap ) observations : data processing , sky maps , and basic results .
k. m. gorski , e. hivon , a. j. banday , b. d. wandelt , f. k. hansen , m. reinecke , and m. bartelman .
a framework for high resolution discretization , and fast analysis of data distributed on the sphere . , 622 , 759 , 2005 | arxiv |
Mastermind is a Charlie Chan spoof feature film. Filmed in 1969, it sat on the shelf for seven years before receiving a limited theatrical release in 1976. It has developed a cult following since its release on home video.
The second of producer Malcolm Stuart's two-picture deal with screenwriter, William Peter Blatty, the project was inspired by the success of the 1964 Peter Sellers comedy A Shot in the Dark which Blatty had co-written with producer/director Blake Edwards. Blatty's script was drastically revised by Ian McLellan Hunter prior to production, and the disgruntled screenwriter chose the pseudonym Terence Clyne for his screen credit. By 1973 it had recorded a loss of $2.9 million. Blatty's original screenplay was published as part of a limited edition collection by Lonely Road Books in 2013 as Five Lost Screenplays by William Peter Blatty.
Plot and setting
Zero Mostel plays an inspector on the trail of criminals who have captured a robot called Schatzi played by Felix Sillas. The inspector has delusions that
he is a great Samurai warrior and the film flashes back and forth between present day and ancient times.
Cast
Zero Mostel as Inspector Hoku Ichihara
Keiko Kishi as Nikki Kono
Gawn Grainger as Nigel Crouchback
Bradford Dillman as Jabez Link
Frankie Sakai as Captain Yamada
Sorrell Booke as Max Engstrom
Felix Silla as Schatzi
Jules Munshin as Israeli Agent
Phil Leeds as Israeli Agent #2
References
External links
Category:1976 films
Category:1970s parody films
Category:1970s mystery films
Category:American parody films
Category:Comedy mystery films
Category:English-language films
Category:Films scored by Fred Karlin | wikipedia |
Does a muon detector on Earth's surface correctly measure the mean lifetime of a muon?
Just a simple question. Does a muon detector on Earth's surface correctly measure the mean lifetime of a muon? I would think the answer is no because most muons detected are created about 15 km above Earth's surface, so on average they will have survived for some amount of time calculated using special relativity before reaching the detector.
The detector I'm talking about is a scintillator, so it detects when the muon enters the detector with a flash, then if the muon decays it detects another flash. The time between flashes is said to be the muon's lifetime.
Is this muon's lifetime the machine giving me the actual lifetime (2.2$\mu s$), or just the lifetime of it on Earth's surface?
here is a plot of my data showing a histogram of decay times
Your worry is not necessary.
In the usual experiment the detector measures the distribution of the time between the muon stopping in the detector and the time of it's decay. Then an exponential curve is fit to the data and the lifetime taken from the fit parameters
Muon decay is a processes analogous to radioactive decay, and (like all exponential processes) it has the special property that the lifetime from the fit *does not depend on the absolute start time*.
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An important thing here is what the "lifetime" means. And what it doesn't mean.
It ***does not*** mean that muons tend to decay $2.2 \,\mathrm{\mu s}$ after they are created (which would imply that you are looking for a peak and that the absolute start time matters).
It ***does*** mean that Given a collection of muons, if you wait $2.2 \,\mathrm{\mu s}$ about 67% of them will have decayed. And if you wait another lifetime about 67% of the one that were left will have decayed. And so on. This means that *anytime* you fit an exponential to the decay time distribution you will always measure the same lifetime.
---
A kind of old school way to see this is to note that $y = A \exp \left( -t/\tau \right)$ implies that (writing $A = \exp \alpha$)
$$ \ln y = \alpha -\frac{1}{\tau} t \,,$$
which is a straight line if you plot $\ln y$ as a function of $t$. The slope of the line is $-1/\tau$ and *does not depend on the range of $t$ over which you measure it*.
"The difference between theory and practice is that, in theory, there's no difference, but in practice, there is."
At Colorado State University over the past several years, students using the Teachspin muon lifetime apparatus have been consistently getting muon lifetimes that are slightly but significantly too short. In late 2012 I spent several months collecting my own data, and re-analyzing the student data from spring 2012. My results are explained in <http://www.riverrock.org/~howard/Teachspin_error.pdf> (Ignore the (relatively small amount of) material about QTD and Van de Graaff generators; they are irrelevant for your purposes.) There are many possible sources of experimental error, some of which I detail in section 4. I also explain how to correctly analyze a truncated exponential (or geometric) distribution, and give source code for all my analysis software.
Section 3.6 explains that "a property unique to the exponential and geometric distributions is that they are *memoryless*; the probability of an event occurring does not depend on how long we have already waited for it to occur. Another way of saying this is that they have a constant failure rate. Because muon decay (like nuclear decay) follows an exponential decay pattern, we do not need to be concerned with the history of the muon before it arrives in our apparatus. Indeed, the entire experiment would not be possible without this property, since we do not measure the entire lifetime of the muon from its creation in a pion decay while still traveling at nearly lightspeed, but only its lifetime after coming to rest in our detector." These distributions are also the maximum-Shannon-entropy distributions given only the constraint of having a particular mean lifetime, which means that assuming *any* other distribution of decays is equivalent to claiming that you know something special about the internal decay process, that allows you to predict it better.
After the above paper, I was able to demonstrate that a part of the error was due to contamination by shorter-lived particles like pions (26 nS) and K\_longs (51 nS). Since CSU is at about 1500 m altitude, a few more of these should be expected than at sea level, but the data indicates even more than that. The best guess at the moment is that the excess were "structural" pions generated by cosmic rays colliding with the steel and concrete of the physics building; these wouldn't have to travel very far. They show up as an increased number of events in the first few decay bins.
However, pion contamination is insufficient to explain the whole discrepancy. Much of the remainder is still a mystery.
| stackexchange/physics |
tinnitus has plagued the human civilization since time immemorial and has been described in the egyptian papyri ( 6000 bc ) .
they all originate , in one way or the other , from inside the head , and they are all known as tinnitus . in some cases , tinnitus exists because there is actually a source of acoustic energy located somewhere in the head and neck area
vascular anomalies , myoclonus , a clicking jaw , respiratory or cochlear otoacoustic emission , etc .
, that can also be heard by a second person , with or without the aid of special devices . however , true tinnitus is a phantom auditory perception arising from a source or trigger in the cochlea , brainstem , or at higher centers and have no detectable acoustic generator .
primary tinnitus is used to describe tinnitus that is idiopathic and may or may not be associated with sensorineural deafness .
secondary tinnitus is tinnitus that is associated with a specific underlying cause ( other than sensorineural deafness ) or an identifiable organic condition .
it is a symptom of a range of auditory and nonauditory system disorders that include simple cerumen impaction of the external auditory canal ; middle ear diseases such as otosclerosis or eustachian tube dysfunction ; cochlear abnormalities such as meniere 's disease ; and auditory nerve pathology such as vestibular schwannoma .
although the exact mechanism of tinnitus still eludes us , the most accepted is the famous neurophysiological model of jastreboff , which stresses that tinnitus , is a subcortical perception and results from the processing of weak neural activity in the periphery .
the tinnitus - related neural activity occurring usually near the periphery of the system undergoes processing in subcortical auditory pathways and finally perceived at a conscious level as sound .
the loudness and pitch of tinnitus depend on the strengths and pattern of electrical activity arriving at the cortex of the temporal lobe after subcortical signal detection , and pattern matching has occurred , the process being the same as for any neural activity generated by the external sounds by the cochlea .
there has been no promising treatment for tinnitus until date mainly because the etiology of tinnitus is still not clear .
the generation of tinnitus has been attributed to the auditory system and neighboring anatomical regions , but at present , no test can identify these regions accurately .
current consensus is that tinnitus results from aberrant neural activity in the auditory system , generally of excitatory nature .
new drugs have been emerging frequently which claim to play a role in managing tinnitus .
shemesh et al . in the year 1993 found vitamin b12 deficiency in tinnitus patients , and its supplementation was found to help these patients .
the aim of this study is to determine the role of vitamin b12 in the treatment of tinnitus .
one of the mechanisms believed to be at play in vitamin b12 deficiency neuropathy is hypomethylation in the central nervous system .
cochlear function is dependent on adequate vascular supply and the normal functioning of nerve tissue .
b12 deficiency is associated with axonal degeneration , demyelination , and subsequent apoptotic neuronal death .
vitamin b12 deficiency may cause the demyelination of neurons in the cochlear nerve , resulting in hearing loss .
in addition , low levels of vitamin b12 and folate are associated with the destruction of the microvasculature of the stria vascularis , which might result in decreased endocochlear potential and in hearing loss and tinnitus .
the objective of the study was to assess the prevalence of vitamin b12 deficiency in chronic subjective tinnitus patients in indian population and therapeutic effect of vitamin b12 injection on tinnitus .
this pilot study was conducted at era 's lucknow medical college from august 2012 to august 2013 .
the study design was a randomized , double blinded , placebo - controlled prospective study .
all the adult patients attending the ent outpatient department aged 18 - 60 years with chronic subjective tinnitus were included in the study .
chronic tinnitus being defined as tinnitus lasting more than 6 month 's duration with frequent occurrence and sufficiently severe that the patients turned to the clinic for treatment .
adult patients aged 18 - 60 years with chronic subjective tinnitus with or without sensorineural hearing loss of more than 6 months duration.no gender bias , normal intelligence level .
adult patients aged 18 - 60 years with chronic subjective tinnitus with or without sensorineural hearing loss of more than 6 months duration .
patients of objective ( pulsatile ) tinnitus.patients suffering with any congenital anomalies which may lead to any otological problem will be excluded from the study.patients suffering from any infective otological problem will be excluded from the study.patients suffering from any psychiatric illness.patients suffering from any otological problem other than tinnitus and sensorineural hearing loss will be excluded from the study.patients with acute acoustic trauma or chronic noise exposure.patients suffering from systemic diseases such as anemia , hypertension , diabetes mellitus , and hypothyroidism which may lead to otological problems will be excluded from the study.patients using any other drugs for last 4 weeks which is known to have an effect on tinnitus such as steroids , cyclendalate , and vasodilators.patients who have undergone ear surgery or having tinnitus after head injury or any other organic illness in head and neck region .
patients suffering with any congenital anomalies which may lead to any otological problem will be excluded from the study .
patients suffering from any psychiatric illness . patients suffering from any otological problem other than tinnitus and sensorineural hearing loss will be excluded from the study .
patients with acute acoustic trauma or chronic noise exposure . patients suffering from systemic diseases such as anemia , hypertension , diabetes mellitus , and hypothyroidism which may lead to otological problems will be excluded from the study .
patients using any other drugs for last 4 weeks which is known to have an effect on tinnitus such as steroids , cyclendalate , and vasodilators . patients who have undergone ear surgery or having tinnitus after head injury or any other organic illness in head and neck region .
this being a randomized , double - blind pilot study , total 40 patients were enrolled , of which 20 were in group a ( cases ) and 20 in group b ( control ) .
group a patients ( 20 ) enrolled randomly received parenteral intramuscular therapy of 1 ml vitamin b12 ( 2500 mcg ) weekly for a period of 6 weeks .
group b ( 20 ) patients were given placebo isotonic saline 1 ml intramuscular in a similar manner for 6 weeks .
patients with chronic subjective tinnitus more than 6 months duration underwent audiometry , tinnitus matching ( pitch and loudness ) , vitamin b12 assay ( premedication and postmedication ) by chemiluminescence method and a self - report by tinnitus severity index questionnaire after detailed history and examination .
the patients were followed for a period of 1 month after 6 weeks of interventional therapy .
they were again subjected to tinnitus severity index testing , vitamin b12 assay , tinnitus matching , vitamin b12 assay , pure tone audiometry , and a self - report on tinnitus questionnaire .
statistical analyses of data were conducted using the spss version 21.0 ( ibm , chicago , il , usa ) and ms excel version 7 .
proportion was calculated for a categorical variable , whereas mean and standard deviation was calculated for continuous variables .
chi - square test was used to check the association between categorical variables and the student t - test was used to check the significance difference for continuous variables .
the statistical model used considered gender ( male , female ) , age group ( group 1 : 17 - 29 , group 2 : 30 - 49 , group 3 : 50 - 66 age ) , tinnitus status ( tinnitus present / no tinnitus , normal ) , response to treatment ( yes / no ) , tinnitus duration , vitamin b12 level ( low / normal ) , and frequency .
adult patients aged 18 - 60 years with chronic subjective tinnitus with or without sensorineural hearing loss of more than 6 months duration.no gender bias , normal intelligence level .
adult patients aged 18 - 60 years with chronic subjective tinnitus with or without sensorineural hearing loss of more than 6 months duration .
patients of objective ( pulsatile ) tinnitus.patients suffering with any congenital anomalies which may lead to any otological problem will be excluded from the study.patients suffering from any infective otological problem will be excluded from the study.patients suffering from any psychiatric illness.patients suffering from any otological problem other than tinnitus and sensorineural hearing loss will be excluded from the study.patients with acute acoustic trauma or chronic noise exposure.patients suffering from systemic diseases such as anemia , hypertension , diabetes mellitus , and hypothyroidism which may lead to otological problems will be excluded from the study.patients using any other drugs for last 4 weeks which is known to have an effect on tinnitus such as steroids , cyclendalate , and vasodilators.patients who have undergone ear surgery or having tinnitus after head injury or any other organic illness in head and neck region .
patients of objective ( pulsatile ) tinnitus . patients suffering with any congenital anomalies which may lead to any otological problem will be excluded from the study .
patients suffering from any psychiatric illness . patients suffering from any otological problem other than tinnitus and sensorineural hearing loss will be excluded from the study .
patients with acute acoustic trauma or chronic noise exposure . patients suffering from systemic diseases such as anemia , hypertension , diabetes mellitus , and hypothyroidism which may lead to otological problems
patients using any other drugs for last 4 weeks which is known to have an effect on tinnitus such as steroids , cyclendalate , and vasodilators . patients who have undergone ear surgery or having tinnitus after head injury or any other organic illness in head and neck region .
this being a randomized , double - blind pilot study , total 40 patients were enrolled , of which 20 were in group a ( cases ) and 20 in group b ( control ) .
group a patients ( 20 ) enrolled randomly received parenteral intramuscular therapy of 1 ml vitamin b12 ( 2500 mcg ) weekly for a period of 6 weeks .
group b ( 20 ) patients were given placebo isotonic saline 1 ml intramuscular in a similar manner for 6 weeks .
patients with chronic subjective tinnitus more than 6 months duration underwent audiometry , tinnitus matching ( pitch and loudness ) , vitamin b12 assay ( premedication and postmedication ) by chemiluminescence method and a self - report by tinnitus severity index questionnaire after detailed history and examination .
the patients were followed for a period of 1 month after 6 weeks of interventional therapy .
they were again subjected to tinnitus severity index testing , vitamin b12 assay , tinnitus matching , vitamin b12 assay , pure tone audiometry , and a self - report on tinnitus questionnaire .
statistical analyses of data were conducted using the spss version 21.0 ( ibm , chicago , il , usa ) and ms excel version 7 .
proportion was calculated for a categorical variable , whereas mean and standard deviation was calculated for continuous variables .
chi - square test was used to check the association between categorical variables and the student t - test was used to check the significance difference for continuous variables .
the statistical model used considered gender ( male , female ) , age group ( group 1 : 17 - 29 , group 2 : 30 - 49 , group 3 : 50 - 66 age ) , tinnitus status ( tinnitus present / no tinnitus , normal ) , response to treatment ( yes / no ) , tinnitus duration , vitamin b12 level ( low / normal ) , and frequency .
the mean age of the patients suffering from tinnitus was 38.37 ( 12.40 ) years and the male to female ratio was 2:3 .
the mean duration of the complaints of tinnitus was 1.36 ( 1.3 ) years [ table 1 ] .
tinnitus presented in both ears in 27.5% and unilaterally in 72.5% ( right ear in 32.5% and left in 40% cases ) . of the total patients of tinnitus ,
17 were vitamin b12 deficient that is 42.5% showed deficiency when the normal levels were considered to be 250 pg / ml . this is significantly high prevalence .
in group a patients , prevalence of vitamin b12 deficiency was 50% , and group b patients , it was 35% [ table 2 ] .
a paired t - test showed that in group a , patients with vitamin b12 deficiency showed improvement in mean tinnitus severity index score after vitamin b12 therapy which was significant ( t = 2.64 , p = 0.016 , df = 18 ) .
however , there was no significant improvement in severity index scores of group a patients without b12 deficiency and group b patients receiving placebo [ table 3 ] .
furthermore , group a patients with vitamin b12 deficiency had a mean visual analog scale ( vas ) of 3.34 0.84 before therapy and 2.89 0.47 posttherapy .
the vas showed a significant improvement with respect to tinnitus loudness ( t = 2.13 , p = 0.04 , df = 18 ) after therapy .
the results show favorable and encouraging outcome of vitamin b12 therapy in vitamin deficient subjects .
subjective improvement was seen in six patients ( 30% ) of group a and four patients ( 20% ) of group b. the subjective improvement in tinnitus between the two groups was not statistically significant .
the mean pitch ( khz ) of tinnitus in patients with vitamin b12 deficiency was 5.9 2.3 ( khz ) and in normal vitamin b12 levels was 5.6 2.7 ( khz ) .
the mean loudness levels of tinnitus in vitamin b12 deficiency patients were 4.2 3.1 ( db sl ) and in normal b12 levels is 5.1 2.9 ( db sl ) [ table 4 ] .
there was no significant difference in the pitch and loudness levels of two groups asserting the insignificant role of vitamin b12 levels on pitch and loudness .
it was also observed that the mean hearing thresholds of group a and group b were almost similar [ table 5 , p > 0.05 ] .
rest of the routine hemogram was normal in all patients . in the tinnitus severity questionnaire , patients reported maximum difficulty due to tinnitus in a quiet room , going to sleep , and difficulty in ignoring tinnitus .
personal characteristics of the study subjects distribution of patients in groups a and b = 0.92 , p = 0.33 and df = 1 , df = degree of freedom , ns = normal saline tinnitus severity scores of patient 's pre- and post - therapy with vitamin b12 injections * significant as p < 0.05 associated with paired t - test , df = degree of freedom , ns = normal saline audiological measures of the tinnitus in patients with and without vitamin b12 deficiency p - value using independent t - test , df = degree of freedom comparison of mean hearing threshold in groups a and b p - value is calculated using independent t - test , ns = normal saline
epidemiologic studies have consistently reported that tinnitus prevalence in adults ranges from about 10% to 15% of the population worldwide . in the beaver dam offspring study of more than 3000 adults between the ages of 21 and 84 years studied between 2005 and 2008 ,
10.6% reported tinnitus of at least moderate severity or causing difficulty falling asleep . in patients with auditory neuropathy spectrum ,
the prevalence of tinnitus was found to be around 67% , mostly bilateral ( 89.5% ) , and seen more often in females ( 70.52% ) .
the subjective pitch was low - pitched in individuals with low frequency hearing loss and the perceived pitch was high with a flat configuration of loss .
the prevalence of frequent tinnitus in the us increased with increasing age , peaking at 14.3% between 60 and 69 years of age .
however , in our study , it was found to be more prevalent in females ( m : f = 2:3 ) approximately , 25% of patients with tinnitus report an increase in severity over time .
though exact data on the prevalence of tinnitus in india is not available , it is estimated that 4.5 millions of patients suffer from tinnitus ( retrieved from www.tinnex.in ) .
it is extrapolated that in india out of 1,065,070,607 people across the country an estimated population of 47,928,177 may have tinnitus .
these prevalence extrapolations for tinnitus are only estimates , based on applying the prevalence rates from the us ( or a similar country ) to the population of india ( retrieved from http://www.rightdiagnosis.com ) .
the observations of our study highlight the high prevalence of serum cobalamin deficiency levels in the north indian population aged 1860 years , i.e. , 42.5% when the threshold value was taken as 250 pg / ml and 15% when the threshold was fixed at 150 pg / ml which are both significantly high . despite poor serum cobalamin levels
1993 found vitamin b12 deficiency in tinnitus patients , and its supplementation was found to help these patients .
the prevalence of cobalamin deficiency was 47% in the tinnitus with noise - induced hearing loss patients , whereas it was 27% in nontinnitus patients with noise - induced hearing loss . in an indian study ,
the published prevalence of subnormal vitamin b12 concentration in elderly varies from 3% to 40.5% depending on the cutoff used for defining deficiency of cobalamin level in serum . using 150 pmol /
l as threshold , 67% men had low vitamin b12-concentration ( 68% rural , 51% slum residents , and 81% urban middle - class ) in india .
pmol / l ) in 16% of the study population in india . in this study ,
the prevalence of cobalamin deficiency in tinnitus patients was significantly high and similar ( 42.5% ) to the result of shemesh et al . and at 15% similar to shobha et al .
when cutoff was taken at 250 pg / ml and 180 pg / ml , respectively .
stouffer and tyler reported that tinnitus was bilateral in 52% of cases , one - sided in 37% of cases , and localized in the cranium instead of the ear in 10% of cases ; in 1% of cases , sounds were perceived as coming from outside the head .
reported 43% of the patients and 57% of the patients had bilateral and single - sided tinnitus , respectively .
however , in this study , tinnitus presented more unilaterally in 72.5% ( right ear in 32.5% and left in 40% cases ) and in both ears in 27.5%.though tinnitus severity was highest in group a with normal cobalamin levels , the improvement in tinnitus severity levels were significant in cobalamin - deficient group .
tinnitus pitch and loudness levels were not found to bear any correlation with serum cobalamin levels .
multiple theories have been put forward to account for tinnitus related to disturbances of the peripheral auditory system , the auditory nerve , and cochlea .
one of the mechanisms believed to be at play in vitamin b12 deficiency neuropathy is hypomethylation in the central nervous system .
inhibition of the b12-dependent enzyme methionine synthase results in a fall in the ratio of s - adenosylmethionine ( sam ) to s - adenosylhomocysteine ; the resultant deficiency in sam impairs methylation reactions in the myelin sheath .
the methylation of homocysteine to methionine requires both methylcobalamin ( an active form of vitamin b12 ) and the active form of folic acid ( 5-methyltetrahydrofolate ) .
deficiency of vitamin b12 leads to accumulation of homocysteine which is a neurotoxin and vascular toxin .
cochlear function is dependent on adequate vascular supply and the normal functioning of nerve tissue .
b12 deficiency is associated with axonal degeneration , demyelination , and subsequent apoptotic neuronal death .
hcy has been implicated as a risk factor for vascular disease as well as brain atrophy .
concentrations of hcy above 11.9 mol / l were associated with approximately 3-fold higher risk for white matter damage when compared to concentrations below 8.6
vitamin b12 deficiency may cause the demyelination of neurons in the cochlear nerve , resulting in hearing loss and tinnitus .
in addition , low levels of vitamin b12 and folate are associated with the destruction of the microvasculature of the stria vascularis , which might result in decreased endocochlear potential and in hearing loss and tinnitus .
martnez - vega et al . in their study , demonstrated , for the first time , that the relationship between hyperhomocysteinemia induced by folate deficiency and premature hearing loss involves impairment of cochlear homocysteine metabolism and associated oxidative stress .
the high prevalence of vitamin b12 deficiency could be attributed to dietary habits such as vegetarianism , poor intake of milk and milk products , socioeconomic factors , and high prevalence of helicobacter pylori .
cobalamin deficiency can manifest as neurological and hematological disorders . in view of the findings of this study , cobalamin deficiency could also present with tinnitus only in the absence of other manifestations and the authors suggest serum cobalamin determination in chronic tinnitus patients . just as myriad
the etiology of tinnitus is equally expansive is the canvas of treatments for tinnitus ranging from different medications such as antipsychotics , vasodilators , herbs , neurotonics , cerebral cognition enhancers to tinnitus retraining therapy , psychophysiology treatment , and low - frequency repetitive transcranial magnetic stimulation . in the ever growing noisy world of fast life and poor dietary habits
, it is imperative to seek the pathophysiology of tinnitus and find means to overcome this annoying malady .
the results suggest role of evaluating serum vitamin b12 levels in patients of chronic tinnitus in view of the significant prevalence of cobalamin deficiency in north indian population .
this pilot study sheds light on the relationship of deficient b12 levels and tinnitus and its supplementation playing a therapeutic role in tinnitus though more studies with larger groups are required to corroborate and establish a direct relationship .
era 's educational trust , era 's lucknow medical college , lucknow , uttar pradesh , india .
era 's educational trust , era 's lucknow medical college , lucknow , uttar pradesh , india . | pubmed |
many of the groups are far too small to allow of any definite opinion being formed at all , having regard to the size of the probable error involved ( karl pearson , 1904 ) .
i use it to refer to the statistical analysis of a large collection of results from individual studies for the purpose of integrating findings .
it connotes a rigorous alternative to the casual , narrative discussions of research studies which typify our attempts to make sense of the rapidly expanding literature ( gene glass , 1976 ) .
karl pearson was probably the first medical researcher to report the use of formal techniques to combine data from different studies when examining the preventive effect of serum inoculations against enteric fever .
all individual estimates were presented for the first time in a table , together with the pooled estimate .
although such techniques would be widely ignored in medicine for many years to come , social sciences , especially psychology and educational research , showed particular interest in them .
indeed , in 1976 the psychologist gene glass coined the term meta - analysis in a paper entitled primary , secondary and meta - analysis of research , to help make sense of the growing amount of data in literature . since the 80s , the amount of information generated by meta - analyses grew constantly , up to the point of becoming overwhelming .
, in the title or in the abstract , yielded 39,840 hints ( update at december 31 , 2012 ) , 7,665 ( 19% ) of them only in the year 2012 ( figure 1 ) .
meta - analysis is a powerful tool to cumulate and summarize the knowledge in a research field through statistical instruments , and to identify the overall measure of a treatment s effect by combining several individual results .
however , it is a controversial tool , because several conditions are critical and even small violations of these can lead to misleading conclusions .
in fact , several decisions made when designing and performing a meta - analysis require personal judgment and expertise , thus creating personal biases or expectations that may influence the result [ 5 , 6 ] . as statistical means of reviewing primary studies , meta - analyses have inherent advantages as well as limitations . pooling data through meta - analysis
can create problems , such as non linear correlations , multifactorial rather than unifactorial effects , limited coverage , or inhomogeneous data that fails to connect with the hypothesis . despite these problems ,
the meta - analysis method is very useful : it establishes whether scientific findings are consistent and if they can be generalized across populations , it identifies patterns among studies , sources of disagreement among results , and other interesting relationships that may emerge in the context of multiple studies .
this short article introduces the basic critical issues in performing meta - analysis with the aim of helping clinicians assess the merits of published results .
meta - analysis protocol registration it is important to write a prospective analysis protocol , which specifies the objectives and methods of the meta - analysis .
having a protocol can help restrict the risk of biased post hoc decisions in methods , such as selective outcome reporting .
the prisma ( preferred reporting items systematic reviews and meta - analysis ) guidelines recommend the prior registration of the protocol of any systematic review and meta - analysis , requiring that this protocol should be made accessible before any hands - on work is done . the prior registration ( i.e. through prospero - international prospective register of systematic reviews - http://www.crd.york.ac.uk/prospero/ )
should prevent the risk of multiple reviews addressing the same question , reduce publication bias , and provide greater transparency when updating systematic reviews .
it is also true that meta - analyses are published only after passing through at least two steps : peer reviews and an editorial decision .
these filters may be sufficient to decide whether a meta - analysis is good and novel enough to deserve publication .
takkouche b et al . stated that an additional committee or register does not increase the quality of what is published but it only increases bureaucracy .
rigorous meta - analyses undertaken according to standard principles ( pre - specified protocol , comparable definitions of key outcomes , quality control of data , and inclusion of all information available ) will ultimately lead to more reliable evidence on the efficacy and safety of interventions than either retrospective meta - analysis .
identification and selection of studies the first reason to criticize the meta - analytic method is that it provides evidence extracted and integrated from a number of primary studies , not from a random sampling ; thus , results can not lead to test relations such as causality .
however , meta - analysis may lead to support or rejection of the generalization of primary evidence , and may contribute to direct future research in a field .
moreover , meta - analysis results can improve understanding , but sometimes they may not be very helpful in clinical practice . in this context , the definition of the scientific start - point ( population and intervention ) is crucial : the clinical question can either be broad or very narrow .
broad inclusion criteria could increase the heterogeneity between studies , making it difficult to apply the results to specific patients ; narrow inclusion criteria make it hard to find pertinent studies and to generalize the results in clinical practice .
hence , the researcher should find the right compromise , focusing on the benefits for the patient .
one of the aims of meta - analysis is to take into account all the available evidence from multiple independent sources to evaluate an hypothesis .
however , meta - analysis usually includes only a small fraction of the published information , often derived from a small range of methodological designs ( i.e. meta - analysis restricted to randomized clinical trials or to english languages ) .
it is also true that with limited resources it is impossible to identify all the evidence available in the literature .
systematic reviews , in contrast to traditional narrative reviews , require an objective and a reproducible search of a series of sources to identify as many relevant studies as possible . the search strategy should be comprehensive and sensitive ; searching more than one computerized database is strongly recommended .
commonly searched databases are : medline ( http://www.nlm.nih.gov/pubs/factsheets/medline.html ) , including pubmed ( http://www.ncbi.nlm.nih.gov/pubmed/ ) , the cochrane central register of controlled trials ( central ) ( http://www.mrw.interscience.wiley.com/cochrane ) , and embase ( http://www.embase.com ) .
these databases are available to individuals free of charge , on a subscription or on a pay - as - you - go basis
. they can also be available free of charge through national provisions , professional organization or site - wide licenses at institutions such as universities or hospitals .
( i.e. scanning of references of retrieved articles and pertinent reviews ) or investigating the grey literature , namely the literature
that is not formally published in sources such as books or journal articles ( i.e. personal communications , conferences , abstracts , etc ) .
authors often provide supplementary data , not included in the original publications or relative to unpublished studies .
decisions regarding what primary evidence to include in a meta - analysis depend on evidence availability .
practical problems , regarding access to primary data , include studies published in languages foreign to the researcher and evidence available only confidentially or in the gray literature of congress and dissertations .
similar issues are faced by analysts who want to perform a meta - analysis with individual patient data ( which has several advantages over analysis on aggregate - level data ) , since patient - level data is often confidential or protected by corporate interests . moreover , many other biases linked to study selection may influence the estimates and the interpretation of findings : citation bias , time - lag bias and multiple publications bias . to overcome these biases , several tools are available .
for example , the sensitivity analysis can spot bias by exploring the robustness of the findings under different assumptions . quality of included studies the conclusions of a meta - analysis depend strongly on the quality of the studies identified to estimate the pooled effect .
the internal validity may be affected by errors and incorrect evaluations during all the phases of a clinical trial ( selection , performance , attrition , detection bias ) , so the assessment of the risk of study bias is a central step when one carries out a meta - analysis .
the quality of randomized clinical trials should be evaluated with regard to randomization , adequate blinding and explanation for dropouts and withdrawals , which addresses the issues of both internal validity ( minimization of bias ) and external validity ( ability to generalize results ) .
the information gained from quality assessment is fundamental to determine the strength of inferences and to assign grades to recommendations generated within a review .
the main problem during the quality assessment process is the inconsistent base for judgment : if the studies were re - examined , the same trained investigator might alter category assignments .
the investigator may also be influenced ( consciously or unconsciously ) by other unstated aspects of the studies , such as the prestige of the journal or the identity of the authors .
the published work can and should explain how the reviewers made these judgments , but the fact remains that these approaches can suffer from substantial subjectivity . indeed , it is strongly recommended that reviewers use a set of specific rules to assign a quality category , aiming for transparency and reproducibility .
the biggest potential source of type i error ( increase of false positive results ) in meta - analysis is probably publication bias .
this occurs when , in clinical literature , statistically significant positive results have either a better chance of being published , are published earlier or in journals with higher impact factors , and are more likely to be cited by others .
the graphical representation to evaluate the presence of publication bias is the funnel plot . in a funnel plot ,
effect size is plotted versus a measure of its precision , such as sample size .
if no publication bias were present , we would expect that the effect size of each included study to be symmetrically distributed around the underlying true effect size , with more random variation of this value in smaller studies .
asymmetry or gaps in the plot are suggestive of bias , most often due to studies which are smaller , non - significant or have an effect in the opposite direction from that expected , having a lower chance of being published .
therefore , it is important to note that conclusions exclusively based on published studies can be misleading .
methods as trim and fill allow estimation of an adjusted meta - analysis in the presence of publication bias .
the small - study effect occurs when small studies have systematically different effects from the large ones .
it has often been suggested that small trials tend to report larger treatment benefits than larger trials [ 19 , 20 ] . such small - study effects can result from a combination of lower methodological quality of small trials or publication bias ( small studies with negative effects are unpublished or less accessible than larger studies ) or other reporting biases .
however , this effect could also reflect clinical heterogeneity , if small trials were more careful in selecting patients , so that a favorable outcome of the experimental treatment might be expected .
researchers that are worried about the influence of small - study effects on the results of a meta - analysis in which there is evidence of between - study heterogeneity ( i>0 ) should compare the fixed- and random - effects estimates of the treatment effect .
if the estimates are similar , then any small - study effect has little effect .
if the random - effects estimate is more beneficial , researchers should consider whether it is reasonable to conclude that the treatment was more effective in smaller studies .
this is because the weight given to each included study through the random effect model is less influenced by the sample size than that given by means of the fixed effects model . in the eventuality
that the small - study effect is present , the researcher should consider analyzing only large studies ( if these tend to be conducted with more methodological stringency ) .
one must note that if there is no evidence of heterogeneity between studies , the fixed- and random - effects estimates will be identical , so there will be an actual difficulty in identifying the small - study effect .
the degree of heterogeneity is another important limitation , and the random effects model should be used during the data analysis phase to incorporate in the treatment effect the identifiable or non - variability between - studies .
it is fundamental to observe that exploring heterogeneity in a meta - analysis should start at the stage of protocol writing , by identifying a priori which factors are likely to influence the treatment effect .
visual inspection of the meta - analysis plots may show whether the results of a subgroup of studies have the same overall direction of the treatment effect .
one should pay attention to meta - analysis in which results have a discordant treatment effect for groups of studies and no explanation of variance has been done .
sources of variation should be identified and their impact on effect size should be quantified using statistical tests and methods , such as analysis of variance ( anova ) or weighted meta - regression . actually , when high heterogeneity is evident , individual data should be not pooled and definitive conclusions should be drawn when more studies become available . moreover , meta - analysis makes it possible to look at events that were too rare in the original studies to show a statistically significant difference .
however , analyzing rare events represents a problem because small changes in data can determine important changes in the results and this instability can be exaggerated by the use of relative measures of effect instead of absolute ones . to overcome this problem
another problem that affects meta - analysis carried out with aggregate data , is the ecological fallacy that arises when the averages of the patient s features fail to properly reflect the individual - level association .
the best scenario is when data at an individual - level is available , but it is equally true that there is resistance from authors to allow ready access to their own dataset containing individual patient data .
very often aggregate data is the only information offered . finally , it is essential to spend a few moments discussing the common problem that occurs when one wants to perform multiple subgroup analysis , according to multiple baseline characteristics , and then examine the significance of effects not set a priori into the protocol .
testing effects suggested by data and not planned a priori considerably increase the risk of false - positive results . to minimize this error it is important to identify the effects to test before data collection and analysis ; otherwise , one may adjust the p - value according to the number of analysis performed .
important decisions in a systematic review are often based on understanding the medical domain and not the underlying methodology
. the clinical question must be relevant to clinicians and the outcomes must be important for patients .
efforts are made to avoid bias by including relevant research , using adequate statistical methodology and interpreting results based on the context and available evidence .
published reports should include quality criteria and should describe the selected tools and their reliability and validity .
the synthesis of the evidence should reflect the a priori analytic plan including quality criteria , regardless of statistical significance or the direction of the effect . published reviews should also include justifications of all post hoc decisions to synthesize evidence .
organizing and carrying out a meta - analysis is hard work , but the findings can be significant . in the best - case scenario , by revealing the magnitude of effect sizes associated with prior research , meta - analysis can suggest how future studies might be best designed to maximize their individual power . on the other hand , low - powered analysis based on a small number of studies can still provide useful insights by revealing publication bias through a funnel plot or highlighting a deficiency in a particular topic that deserves further attention .
meta - analysis represents a powerful way to summarize data and effectively increase sample size to provide a more valid pooled estimate .
however , the results of a meta - analysis should be interpreted in the light of the various checks previously discussed in this work , which can inform the readers of the likely reliability of the conclusions . | pubmed |
the finite size analogs of two - dimensional ( 2d ) wigner crystals have received considerable attention from theoreticians @xcite , and more recently also from experimental groups @xcite .
particles in mutual repulsion can be confined using a variety of methods , most importantly electrostatic traps of the paul or penning types , and simple hard walls , usually of circular shape .
the repulsion between particles depends upon the details of the experiment .
arrays of electrons on the surface of liquid helium @xcite or in quantum dots @xcite can be described by conventional coulomb forces
. however , logarithmic forces are more relevant for vortex clusters in superfluids @xcite or bose - einstein condensates @xcite .
mesoscopic colloidal particles undergo dipolar @xmath0 interactions within an external magnetic field @xcite , or a yukawa ( screened coulomb ) potential when they are charged and placed in a viscous medium .
finite 2d assemblies have also been synthesised on a more macroscopic scale , using metal particles close to 1 mm in size @xcite . in this study , the authors were able to visualise and locate not only stable configurations , but they could also estimate the shape of the transition states , which are here defined as stationary points with hessian index one @xcite .
another example of experimentally accessible wigner crystals occurs for dusty plasmas .
these highly charged particles of micrometer size and charges up to @xmath2 can be stabilised as gaseous plasmas .
the gravitational forces and the electric field balance each other , so that the dust particles form highly regular two - dimensional structures . by changing the electric field , or conversely the pressure , of the plasma , transitions from solid to liquid - like phases
are observed @xcite .
a two - stage melting was proposed , which does not follow the predictions of two - dimensional melting theories , but rather goes through an intermediate phase .
this phase has been described as an oscillating crystal @xcite . finally , by measuring the spectra of dust particles , it has been suggested that the dynamics may be a size - dependent phenomenon , that is the effects of various types of motion such as intershell rotation and breathing may play different roles @xcite .
a major part of our theoretical understanding of the above systems comes from numerical studies .
the static properties of the assemblies were obtained using optimization methods ranging from simulated annealing to genetic algorithms , and a mendeleev - type table was proposed by several authors @xcite to reflect the special stability of certain sizes .
comparisons with the theoretical predictions of the ` thomson atom ' @xcite were also carried out @xcite .
shell effects were more generally investigated semi - analytically by koulakov and shklovskii @xcite .
metastable configurations ( excited states ) and the potential energy barriers between them have been studied in refs .
@xcite , @xcite , @xcite and @xcite .
topological defects were also identified for stable structures @xcite . melting in 2d coulomb clusters has been a subject of debate .
the results of the classical and quantum monte carlo simulations of lozovik and mandelshtam @xcite were interpreted as a two - step melting process , where orientational melting occurs prior to radial melting . in this process
, shells remain quasi - crystalline , but still undergo some concerted rotational motion .
radial melting conversely involves exchanges between particles of adjacent shells .
this two - step process is generally accepted for small assemblies , but it is not clear whether , in large clusters , the external shell may also exhibit orientational melting @xcite or not @xcite .
several factors are likely to influence the stability of 2d coulomb clusters .
first , rotational barriers are strongly dependent on the structure , which in turn depends on the size .
more stable structures are obtained when the core is based on a triangular lattice , thus resembling most observed wigner crystals .
more importantly , the very different nature of orientational and radial melting has led to some confusion about how suitable observables should be defined to probe these processes separately @xcite . in their study of binary 2d clusters ,
drocco _ et al . _
@xcite chose an order parameter based on the polar angles of the particles in order to quantify the extent of orientational motion in langevin molecular dynamics simulations .
however , this measure becomes impractical as soon as a central particle is present , as it then becomes very noisy .
melting in atomic and molecular clusters also displays a very rich phenomenology @xcite .
in particular , surface melting @xcite , plastic transitions @xcite or anomalously high melting temperatures @xcite have been identified from experiments or simulations . for three - dimensional trapped - ion clusters , the structures are sometimes related to those found in atomic clusters @xcite .
the study of atomic clusters also shares with coulomb assemblies the lack of a proper universal order parameter to characterise the melting point .
for instance , the lindemann criterion for melting does not always provide useful information in the case of solid - solid transitions and premelting effects @xcite .
the largest lyapunov exponent @xmath3 , which quantifies chaos and the sensitivity to initial conditions , is a useful tool for probing the complex dynamics of atomic and molecular clusters @xcite , especially at melting . because lyapunov exponents are related to the second derivatives of the potential energy surface ( pes ) @xcite
, we expect them to be sensitive to orientational melting . in this paper
, we revisit the dynamics and thermodynamics of 2d coulomb clusters by focusing on dynamical measures such as @xmath3 or the diffusion coefficient , @xmath4 , and by performing extensive monte carlo simulations employing the parallel tempering strategy @xcite .
we also consider the interplay between the dynamics and the energy landscape of these clusters by constructing disconnectivity graphs @xcite .
finally , we investigate how the thermodynamic behaviour evolves with size .
this article is organised as follows .
after briefly presenting our methods , we choose some specific examples to illustrate the difficulties associated with an unambiguous definition of the melting point in these clusters , and we then discuss the large size variations .
we finally summarise and conclude in section iv .
2d wigner clusters are characterised by the following classical potential energy : @xmath5 in this equation , @xmath6 or 2 are the charges carried by the particles , @xmath7 is the distance between particles @xmath8 and @xmath9 , and @xmath10 is the distance from particle @xmath8 to the cluster centre - of - mass .
the parameter @xmath11 will usually be @xmath12 ( coulomb case ) , but we also specifically studied the case @xmath13 ( dipolar interaction ) for which some results will be selected below .
the range of the electrostatic potential , @xmath14 , was set to 0 ( pure coulomb ) or to a finite value ( shielded coulomb ) . finally , and for comparison with the work reported in ref . on binary clusters ,
we have taken @xmath15 .
it should be noted that , in the absence of the exponential term , the physics of the system is independent of @xmath16 : under the transformation @xmath17 , the energy can be cast in a form that does not depend on @xmath16 . in the following presentation ,
unit masses and charges are used and all properties are explicitly given in dimensionless reduced units .
the global minima of the clusters were investigated using the monte carlo plus minimization algorithm , also known as basin - hopping @xcite .
the 2d clusters can generally be described as multishell systems , and we will use the @xmath18 notation for a homogeneous cluster having @xmath19 particles in its @xmath20 shell .
binary clusters will be referred to as @xmath21 , where @xmath22 and @xmath23 are the respective numbers of singly- and doubly - charged particles . due to the relatively long range of the potential @xcite ,
global optimisation is relatively straightforward for coulomb systems . beyond the stable isomers
, we also investigated higher - index stationary points on the energy landscape . locating the saddle points with hessian index one
enabled us to construct disconnectivity graphs @xcite , in order to relate the observed dynamical and thermodynamical behaviour to the potential energy surface for these clusters .
we refer the reader to ref . for further details of how stationary points are located and disconnectivity graphs are generated .
the dynamics has also been studied by solving hamilton s equations of motion at constant energy .
the coupled equations were integrated by the 4-step runge - kutta method , which keeps the energy constant to at least seven digits .
for the first trajectory , the initial positions of the particles were obtained from the global minimum structure and a random set of momenta were chosen .
the momenta were then scaled to set the linear and angular momentum to zero and the vibrational temperature to around @xmath24 .
the time step was taken to be 0.0025 .
the first @xmath25 steps were used to equilibrate the system and discarded , then @xmath26 steps were used for each simulation .
further trajectories start with the configuration obtained from the previous run , with velocities scaled approximately to give a new temperature increased by a factor 1.25 .
again , the equilibration steps were discarded . for each trajectory the average kinetic temperature , root - mean - square ( rms ) bond length fluctuation index @xmath27 , the maximal lyapunov exponent , @xmath3 ,
( mle ) and diffusion coefficient , @xmath4 , were calculated .
@xmath27 is commonly used to detect melting in bulk or finite ( 3d ) atomic systems , as it is expected to jump from a low value to around 0.10.15 .
both the diffusion coefficient and the lyapunov exponent were calculated from shorter parts of the entire trajectory .
@xmath4 was obtained from the slope of the mean square atomic displacement .
this measure describes the breathing and inter - shell exchanges ( isomerizations ) , but does not identify even qualitative changes in the rotational structure . for homogeneous systems
it is very difficult to define measures of the angular motion .
since the total angular momentum is zero , one can only measure angular velocity and momenta for separate shells ; however , the shell definitions lose their significance once isomerizations start taking place . in addition , the angular properties become ill - defined for clusters having a central particle .
the calculation of the mle was motivated by several studies indicating possible relations between phase changes and this dynamical indicator .
the mle measures the sensitive dependence on initial conditions and is defined from the exponential separation of two trajectories that start infinitesimally close together in the phase space .
a tangent space approach was used in the numerical calculations @xcite .
however , we should mention that semi - analytical theories have also been proposed to quantify the mle from the statistical properties of the potential energy surface @xcite .
the equilibrium thermodynamics of the 2d clusters was also studied by means of parallel tempering monte carlo ( mc ) simulations .
parallel tempering is a particularly efficient method to accelerate convergence in systems whose natural dynamics is affected by broken ergodicity . most often such problems are related to multiple funnels @xcite or ` glassy ' energy landscapes .
the mc simulations were performed in the canonical ensemble , with temperatures in the range @xmath28 .
about 80 runs were carried out in this range , with the temperatures nearly equally spaced on a logarithmic scale . @xmath25
mc cycles were used for equilibration , followed by @xmath26 mc cycles for the actual calculations .
the mc calculations were principally used to compute the thermal properties , such as the heat capacity , @xmath29 . in
both mc and md simulations the relation between the energy and the temperature is quasi linear .
the snapshots obtained from experiments on colloidal particles @xcite or dust plasmas @xcite , as well as the various molecular dynamics ( md ) simulations , exhibit three types of characteristic motion . at low energy or temperature , or for dust plasmas under high pressures ,
only small amplitude motion is observed , in which the particles oscillate around their mean positions . as the energy increases
, these oscillations gain enough momentum to achieve complete rotations in their respective shells .
the directions of these rotations are random , and they may change in time . however , in order to preserve the total angular momentum , different shells must rotate in opposite directions . eventually , actual isomerizations between shells may take place , as previously examined in 3d systems @xcite . in one case
, it has also been reported that isomerizations may occur before the full rotational motion is achieved @xcite .
we expect this observation to be due to rather infrequent sampling of the experimental trajectories @xcite .
it is clear that the angular and the radial motion of particles make different contributions to all the measures aforementioned . in order to study the mechanism of phase transitions in 2d clusters , we have carried out simulations of homogeneous clusters systems in the size range @xmath30 .
we selected several sizes displaying different but typical characteristics . in fig .
[ fig : homogeneous ] , @xmath3 , @xmath4 , @xmath27 and @xmath29 are plotted with respect to the average temperature for sizes 17 , 21 , 22 and 30 .
the global minima for these clusters are found to be ( 1,6,10 ) , ( 1,7,13 ) , ( 2,8,12 ) and ( 5,10,15 ) , respectively , in agreement with ref . .
the mle starts becoming nonzero at very low temperatures , around @xmath31 . in this regime ,
the dynamics are more irregular for @xmath32 and 21 .
similarly , the lindemann index and the diffusion coefficients are also higher for @xmath32 and 21 in the low @xmath33 regime .
both these clusters exhibit an intermediate phase over a broad temperature range ( note the logarithmic temperature scale ) . on the other hand ,
the 30-particle cluster exhibits a single phase transition .
while the three dynamical indicators agree with one another , the heat capacities provide rather little information in comparison .
the general behaviour observed for all sizes is that of harmonic oscillators at very low temperatures @xmath34 or for free , independent particles at high temperatures
( @xmath35 again due to confinement ) . in the intermediate temperature range
, a strong decrease is seen near @xmath36 for all sizes , following an order - disorder peak below @xmath37 .
the curves for a specific cluster are built on the basis of this generic behaviour , which reminds us of the caloric curves computed for lennard - jones polymers @xcite .
for some sizes , such as @xmath38 or 30 , extra bumps or shoulders occur as a consequence of isomerizations . in general
, the strong increase of @xmath3 , @xmath4 or @xmath27 at @xmath39 correlates with a peak in the specific heat .
however , the phenomena responsible for the peculiar dynamical features for the 17- and 21-particle clusters do not have any thermal signature .
the premelting heat capacity peak seen for @xmath38 at @xmath40 does not have any counterpart in the dynamical indices either .
these data can be interpreted using the disconnectivity graphs shown in fig .
[ fig : trees ] . in this figure , saddles connecting two permutations of the same isomers have been included to account for the rotational barriers .
such saddles are manifested by the presence of copies of the corresponding minima on the graph .
the energy barriers , which link the global minimum to itself through an internal rotation , are much lower for @xmath32 ( @xmath41 ) and @xmath38 ( @xmath42 , this is nearly a case of free rotation ) than for larger clusters , where they are closer to @xmath43 .
such degenerate rearrangements @xcite do not play a major role in thermal equilibrium , but can have important dynamical consequences .
this is precisely what we observe in fig .
[ fig : homogeneous ] .
the barriers for rearrangements are much higher in energy than those involved in the rotational motion , but in some cases other stable isomers lie relatively close to the global minimum . for @xmath38 and @xmath44 ,
such isomerizations are indeed seen and correlate with bumps in the canonical heat capacity .
> from the previous results it is clear that one can not draw general conclusions by looking at dynamical indicators alone , or at observables aimed at characterising thermal equilibrium .
we have also looked at two specific cluster sizes , for which the results of the pure coulomb case have been compared to other interaction forms .
the 31-particle cluster was studied with both @xmath45 and @xmath0 interactions , the latter expression being more relevant to colloidal particles , such as the ones involved in the experimental setup of ref . .
the 42-particle cluster has recently been the focus of an experimental report on dust plasmas @xcite . in this situation ,
a screened coulomb or yukawa form @xmath1 is more appropriate than the bare coulomb law .
here we chose @xmath46 , but the results presented hereafter in fig .
[ fig:3142 ] are not significantly different for other values in the range @xmath47 .
we first discuss the 31-particle clusters , which display different behaviour depending on the form of the interaction .
while the coulomb potential leads to a ( 5,11,15 ) 3-shell global minimum , the shorter range dipolar interaction favours a ( 1,5,10,15 ) ground state . because this structure has a central particle , the vibrational motion is more constrained , and the harmonic entropy of ( 5,11,15 ) is actually larger .
this competition between energy and entropy leads to a structural transition , which is seen in the heat capacity of fig .
[ fig:3142](a ) as a significant peak near @xmath48 , while the melting peak is located at @xmath49 .
the coulomb cluster behaves very differently , with a single @xmath29 peak at @xmath48 .
scrutiny of the lindemann index indicates that this cluster undergoes free internal rotation at very low temperatures @xmath50 , before fully melting at @xmath48 . in the case of the dipolar interaction , only a single , but very sharp , increase is seen , at temperatures even higher than the melting peak , @xmath51 . this surprising result has been checked and confirmed by extensive sampling .
after regular quenching of the md trajectories in this temperature range , we found that the sharp increase of @xmath27 was correlated with a sudden isomerization to the ( 5,11,15 ) second - lowest minimum , which is also involved in the preliminary structural transition .
the lowest energy transition state from the global minimum was found to be significantly higher than the energy of the second isomer .
in such a situation , md simulations suffer from broken ergodicity , since they can not sample the available phase space until sufficient energy is added . in cluster
physics , a well - studied example of broken ergodicity is provided by the 38-atom lennard - jones cluster @xcite .
the present sharp jump of the lindemann index should not be interpreted as the onset of melting , but rather as a signature of isomerization .
42-particle clusters were investigated with the aim of finding some thermodynamic confirmation that melting proceeds in multiple steps .
unfortunately , neither the specific heats of fig .
[ fig:3142](b ) nor the lindemann indices of fig .
[ fig:3142](d ) show any multiple - stage behaviour that could be related to the experimental observation @xcite .
we thus conclude that the dust plasma system studied by melzer and coworkers can not be simply modelled as if it were made of a single layer .
comparing the general curves for the coulomb , dipolar and yukawa potentials also provides useful information about the factors influencing the melting point .
yukawa systems exhibit a significant shift of their melting temperature toward lower @xmath33 . since the yukawa potential is an attenuated form of the pure coulomb form , this is the expected trend . at large distances ,
the dipolar interaction is also much smaller than the coulomb interaction .
however , the melting temperature of coulomb clusters is about one order of magnitude _ smaller _ than for the dipolar cluster .
hence the long - range part of the potential plays opposite roles in the dipolar and yukawa forms .
this result suggests that the location of the melting peak is mainly driven by the short - range repulsive part of the potential .
we now turn to small , binary coulomb clusters , such as those recently investigated by drocco and coworkers @xcite .
@xmath22 particles with charge 1 and @xmath23 particles with charge 2 are stabilised in a parabolic trap with @xmath15 .
the structures again consist of concentric shells where the singly charged particles form the inner shells in order to minimize repulsion .
used langevin md simulations for mixed clusters containing @xmath5234 singly charged and @xmath53 , 6 and 7 doubly charged particles , and they also determined the melting points .
these authors concluded that the melting behaviour of these binary trapped particles strongly depends on whether the numbers of particles in the inner and outer shells are commensurate .
they also found that the highest melting points were obtained for @xmath54 , where the corresponding structures all have a single particle at the centre .
we have performed md simulations for these heterogeneous systems under similar conditions to those of the homogeneous clusters . in fig .
[ fig : binary ] , @xmath3 , @xmath4 , @xmath27 and the specific heat @xmath29 are plotted for \{4,5 } , \{5,5 } , \{6,5 } and \{7,5 } , selected as further typical examples , highlighting differences in the stability and dynamics .
the onset of chaos occurs at temperatures close to those seen in the homogeneous systems .
\{6,5 } is the most stable cluster , in the sense that it has the highest melting point in ref . , while \{5,5 } is the most irregular .
both the diffusion and lindemann indices show the same qualitative trends , namely that the melting points , as measured by the strong increase in @xmath27 , follow the order @xmath55 . as for homogeneous clusters , the variation of the heat capacities
does not exactly match the dynamical indices . here
the generic shape again starts at a constant value at low temperature , which corresponds to harmonic behaviour .
the high temperature gas phase is still characterised by the same constant value . in the intermediate temperature range , two main peaks are associated with the melting of successive subclusters made of singly charged , then doubly charged particles .
nearly one order of magnitude separates the two associated melting temperatures .
this interpretation was further confirmed by calculating the heat capacity of the ternary \{7,6,6 } cluster made of 7 singly charged particles , 6 doubly and 6 triply charged particles . for this cluster ,
three clear features are observed in @xmath29 , and only above @xmath36 do the triply charged particles mix with the rest of the cluster . on top of this generic behaviour , a specific isomerization shoulder is seen for the heat capacity of the \{7,5 } cluster in fig .
[ fig : binary](d ) , at the same temperature @xmath56 where the three dynamical parameters increase significantly .
again , the free rotation of some internal shells revealed by @xmath3 , @xmath4 and @xmath27 at low temperature has no thermal signature .
the disconnectivity graphs for these clusters are shown in fig .
[ fig : treesb ] . as is particularly obvious from the graphs for \{5,5 } and \{6,5 } , commensurate
structure between the singly- and doubly - charged shells is not the only factor needed to explain the complicated behaviour exhibited by these finite wigner crystals .
the extremely low barriers for the \{4,5 } and \{5,5 } clusters permit facile rotation , which is correlated with the rapid increase of all dynamical indicators at low temperatures .
the \{6,5 } cluster is especially resistant to isomerization because an extra , central particle hinders the radial motion of the particles in the other shells . only for the \{7,5 } cluster
is the isomerization energy low enough to give rise to an extra peak in the heat capacity .
this case , and the case of the single - isomer \{6,5 } cluster , further show that the multiple - peak structure of the heat capacity is not a consequence of isomerizations . therefore the general , two - peak shape of the heat capacity is not related to isomerization , but is intrinsic to the potential itself and the presence of two types of particles organised in shells .
the variation of the melting temperature with cluster size is shown in fig . [
fig : tmeltb ] for the three \{@xmath57,4 } , \{@xmath57,5 } and \{@xmath57,6 } binary series , with @xmath58 . here
the melting temperature was defined according to the lindemann criterion , as the temperature where @xmath27 sharply increases above 0.1 .
the variation of the computed melting point is qualitatively similar to that reported by drocco and coworkers @xcite . in particular , the high values for \{4,4 } , \{5,5 } , \{6,5 } and \{7,6 } are reproduced .
however , our results quantitatively differ from those of drocco _ et al . _ by a factor of at least 10 . our data , obtained with exactly the same hamiltonian as in ref . ,
are in agreement with the computed melting points for the homogeneous clusters , which are comparable with previous results for the same systems @xcite .
even though the present temperatures result from time averages in our md simulations , their range matches the canonical temperature of our mc runs .
hence we believe that the data of fig . [
fig : tmeltb ] are reliable , and that the differences from the results obtained by drocco and coworkers are the consequence of an unreported alternative choice of @xmath16 in the hamiltonian used in ref .
@xcite .
lastly , we discuss the behaviour of larger clusters and how melting evolves toward bulk . in fig .
[ fig : large](a ) we show the heat capacities calculated from mc simulations for the cluster sizes @xmath59 , 200 , and 500 .
the general trend is that the main peak near @xmath60 becomes narrower and sharper , suggesting that melting is a first - order process rounded by finite size effects @xcite .
however , the main heat capacity peak remains quite broad , so a more detailed study should probably be performed on even larger sizes , including a proper finite - size scaling analysis .
in addition , extra features in the heat capacity are present at low temperatures , even for the largest 500-particle cluster .
regular quenching confirms that these premelting effects are due to isomerizations involving different arrangements of the inner shells . at large sizes , even though the global shape of the cluster is roughly circular , the radial ordering into shells is replaced by a triangular close - packed lattice , possibly with several defects @xcite .
rotation of the various shells then becomes hindered , and the dynamics is reduced to more usual consecutive isomerizations .
[ fig : large](a ) supports the idea that a single , first - order phase transition should occur in the bulk limit , if it could be defined .
since that there is no unified theory of 2d melting @xcite , we should probably be cautious in extrapolating the heat capacities computed from monte carlo simulations . if we choose the peak of the heat capacity as the signature of melting , the melting point thus defined shows very pronounced variations with the cluster radius @xmath61 , as illustrated in fig .
[ fig : large](b ) . the data for all sizes in the range @xmath62 and for larger clusters @xmath63 70 , 80 , 90 , 100 , 120 , 140 , 160 , 180 , 200 , 250 , 300 , 350 , 400 , 450 , 500 ) are included in this graph .
the strong size dependence for small systems is similar to that observed for the binary systems .
however , in the range 50500 the variation of the melting point seems less drastic than in the smaller size range , even though numerous sizes are obviously missing from the reported data .
the bulk limit for the melting point is obtained to be 0.039 .
this observation should not obscure the possibility that even large sizes can exhibit a multiple stage melting .
for example , significant premelting peaks have been reported in large atomic clusters @xcite .
the results obtained for @xmath64 show a similar feature . even though some premelting peaks are present in the caloric curves of large clusters , a major peak seems to dominate above about 100 ions .
this result may suggest that the transition between the finite size regime and bulk @xcite takes place near this size .
in this work , we have investigated some dynamic and thermodynamic properties of finite 2d charged particles confined by a parabolic trap .
our extensive data on homogeneous and heterogeneous clusters were obtained from md and mc simulations .
these data were interpreted by visualising the energy landscape through disconnectivity graphs .
previous experimental and numerical findings suggest that there are three types of motion for a particle : it can oscillate , rotate in a relatively regular orbit , or make jumps between shells , possibly causing isomerizations .
these various phenomena were also observed in the present work , but we found evidence that additional ` premelting ' events due to structural transitions may also occur .
the various stages of melting create ambiguities in defining the melting point , especially in small clusters .
firstly , rotational motion is facile when very small energy barriers separate the global energy minimum from itself , as is apparent from the disconnectivity graphs for the 17- and 21-particle homogeneous clusters , or the \{4,5 } binary cluster .
internal rotation may give rise to significant jumps in the rms bond length fluctuation , sometimes above 0.1 .
radial melting is then seen as yet another increase in @xmath27 or other dynamical indicators at higher energy .
therefore , the lindemann criterion ( @xmath65 ) is not fully reliable for detecting melting .
secondly , rotational melting has no thermodynamic consequence since only a single isomer is involved .
the thermodynamics is sensitive to the presence of different isomers , and also to the intrinsic shape of the potential felt by the particles .
irrespective of the isomers , the heat capacity has a natural drop over a rather broad temperature range , which marks the continuous transition toward the gas phase .
hence , even a single cluster isomer can have heat capacities with complex temperature dependence , as exemplified by the small \{4,5 } binary clusters .
thirdly , several isomers can give rise to preliminary peaks in the heat capacity , which may sometimes obscure the features associated with full radial melting .
we found such a case for the 31-particle cluster interacting through dipolar forces , but very large clusters can also exhibit particularly strong premelting peaks . the structural transition occurring in the 31-particle cluster
has the same origins as the fcc - icosahedral transition in the 3d 38-atom lennard - jones cluster @xcite : the second morphology has a much larger entropy than the global minimum .
this phenomenon has important consequences for the constant energy dynamical behaviour , as this transition is not seen until sufficient energy to surmount the isomerization barrier is present .
thus there is a finite energy range where md simulations starting from the ground state structure are non - ergodic , which is reflected by a strong shift in the estimated melting temperature .
most of our results illustrate how a simple and unique picture of melting is hampered by finite size effects .
both the dynamical parameters and the thermodynamical curves contribute to explaining related but different aspects of melting in these 2d clusters .
in particular , our work does not support a single parameter as a universal measure for the melting point that could be used unambiguously for all clusters .
nevertheless , the landscape approach @xcite that has been followed here was found to provide useful insight for interpreting and understanding the various numerical data .
the data gathered here for a broad range of sizes would seem to prevent a general classification on the phenomenology of melting to be made .
for example , the choice of molecular dynamics or monte carlo method , and the microcanonical or canonical ensemble , can change the observed behavior significantly , particularly at small sizes where the differences between the two statistical ensembles are the largest .
for instance , some structural transitions might not appear with conventional md methods , due to the disconnected character of phase space at low total energies .
however , three main categories of behavior can be inferred from our results . especially in small clusters , a two - step orientational - then - radial melting has been observed , with clear dynamical signatures , but only a weak thermodynamical signature .
clusters exhibiting structural transitions , on the other hand , may not involve any rotational melting but display a strong change in their caloric curve .
finally , a more conventional single - step melting is sometimes seen , as expected in larger clusters , and also for smaller magic sizes .
our calculations indicate that significant finite size effects remain in the thermodynamics of the largest clusters considered .
however , above a few hundred ions , melting seems to be essentially a one - step process .
this result is consistent with the expectation that the dynamics becomes more and more dominated by localised processes , due to the less favourable rotational motion .
this observation seems to justify the use of the lindemann index or other dynamical parameters for larger systems .
additionally , the main heat capacity peak becomes larger , and its maximum value coincides with the onset of disorder in the dynamical indicators .
even though premelting features may remain noticeable , we expect the onset of radial melting to become closer and closer to orientational melting , and eventually similar to a bulk first - order melting process .
we are grateful for a collaborative research grant given by cnrs and tubitak . | arxiv |
antineutrophil cytoplasmic antibodies ( anca ) are directed against primary granules of neutrophils and are associated with neutrophil - mediated inflammation .
anca were first described in 1982 by davies et al . in a series of patients with segmental necrotizing glomerulonephritis ( fngn ) and symptoms of systemic vasculitis . in 1985
van der woude et al . reported the strong association of anca producing a diffuse granular cytoplasmic staining pattern on ethanol - fixed neutrophils ( c - anca ) and granulomatosis with polyangiitis ( gpa ) ( formerly known as wegener 's granulomatosis ( wg ) ) [ 3 , 4 ] ; a few years later , anca producing a perinuclear fluorescent pattern ( p - anca ) on the same cellular substrate were described in patients with idiopathic necrotizing crescentic glomerulonephritis and microscopic polyangiitis ( mpa ) .
initially , the only method available for anca detection was the indirect immunofluorescence ( iif ) test on normal human ethanol - fixed neutrophils .
although currently numerous assay formats such as enzyme linked immunoassays ( elisa ) , chemiluminescent immunoassays ( clia ) , lateral flow assays ( lfa ) , and combinations of iif and microbead assays have been made available , the iif still often remains the method of choice for initial screening .
the classical terms c - anca and p - anca describe iif patterns on granulocyte substrates [ 57 ] .
c - anca ( figure 1(a ) ) is largely due to the presence of autoantibodies targeting the serine protease proteinase-3 ( pr3 ) , while p - anca ( figure 1(b ) ) is caused by antibodies directed mainly against myeloperoxidase ( mpo ) . additionally , antinuclear antibodies ( ana ) and antibodies against the cytoplasmic granule antigens lactoferrin , lysozyme , azurocidin , elastase , cathepsin g , bactericidal / permeability - increasing enzyme ( bpi ) show the so - called atypical anca pattern on ethanol - fixed neutrophils [ 810 ] .
mpo is the most frequently recognized antigen in p - anca and primary systemic vasculitis .
pr3 is a weak cationic protein of 29 - 30 kda molecular weight ( mw ) , belonging to the trypsin family of serine proteases .
pr3 is synthesized as a preproenzyme and subsequently processed in four steps into the mature form .
it is stored in the azurophilic granules of neutrophils but can also be found within the membrane of secretory vesicles .
mpo , which represents about 5% of the total protein content of neutrophils , is a strong cationic molecule ( isoelectric point > 11 ) made up of a heterodimer with a mw of ~140 kda .
the enzyme is characterized by a powerful bactericidal activity , whose peroxidase activity is physiologically inhibited by ceruloplasmin .
anca are the serological hallmark of some idiopathic systemic vasculitides , and the term anca - associated vasculitis ( aav ) has been used to collectively name those primary small vessel vasculitic syndromes in which circulating anca are commonly found : mpa and its renal limited form ( pauci - immune necrotizing glomerulonephritis ) , gpa , and eosinophilic granulomatosis with polyangiitis ( egpa ) [ formerly known as churg - strauss syndrome ( css ) ] [ 14 , 15 ] .
this approach , adopted by the international chapel hill consensus conference ( chcc ) and by the european vasculitis study group ( euvas ) , is supported by the striking clinical and histological similarities between the aav , the widespread use of anca as a diagnostic marker , and the growing evidence of their pathogenetic potential .
an overview of the previous and the new disease nomenclature as proposed by the 2012 chcc for defining small vessel vasculitis is shown in figure 2 .
apart from aav , anca are also useful in the diagnosis and classification of inflammatory bowel disease ( ibd ) [ 19 , 20 ] , autoimmune hepatitis ( aih ) , and primary sclerosing cholangitis ( psc ) . here
, the iif usually produces a perinuclear pattern , with homogeneous or fine speckled cytoplasmic fluorescence on ethanol - fixed slides .
the term atypical anca has been proposed to describe this pattern . since 1995 in vitro , in vivo and clinical studies have been providing increasing evidence in favour of a pathogenetic role for anca ( especially mpo - anca ) in the development of aav . however , to induce severe damage , anca
aav are multifactorial diseases , and the involvement of genetic factors in disease pathogenesis is considered important as are environmental factors such as silica exposure , infections ( in particular with staphylococcus aureus ) and treatment with propylthiouracil and other drugs . discovered by kain et al . in 1995 ,
autoantibodies to lamp-2 , a suggested novel anca subtype , have been reported to be present in almost all patients with active , untreated aav , and renal involvement [ 8 , 25 ] .
the authors also suggested a previous unrecognized molecular explanation for the origin and development of injury in pauci - immune gn ; however , such findings could so far not be confirmed by a subsequent study .
controversy exists about the true prevalence , pathogenicity , and practical utility of anti - lamp-2-autoantibodies for the management of aav patients .
another new aspect of the pathology of anca is the autoantibody stimulation by neutrophil extracellular traps ( nets ) , also known as netosis .
nets are formed from extracellular nuclear dna of neutrophils released by a programmed cell death different to apoptosis , releasing strands of nuclear dna spiked with antibacterial proteins .
bacteria , viruses , and fungi are trapped and killed in these nets , and besides antimicrobial proteins pr3 and mpo are present in the sticky dna fibers [ 2729 ] .
evidence of netosis as a possible trigger of aav is evolving , as it was shown that anca not only induce the neutrophil oxidative burst but also can induce the programmed release of nets in absence of a microbial infection and , even more interesting , that the transfer of activated myeloid dendritic cells enriched with net components into naive mice could cause aav .
also the ineffective clearance of nets from the endothelial vessel wall could give clue to the disease progression in aav .
the sensitive and specific detection of antibodies to pr3 and/or mpo is highly recommended in patients with suspected systemic vasculitis , occurring in about 80% of all aav patients . only fast and adequate treatment can avoid the development of organ failure [ 31 , 32 ] . in 1999 , the international consensus statement on testing and reporting of anca was published , which provided suggestions for anca testing and reporting .
an addendum to this statement was published in 2003 with the quality control guidelines , comments , and recommendations for anca testing in other autoimmune diseases . according to these guidelines , the initial screening method for anca is iif on ethanol - fixed neutrophils of human origin with confirmation by a solid phase assay ( i.e. , elisa ) .
the specificity of the individual tests ( c - anca , p - anca , pr3 , and mpo ) is not satisfactory ; however , combining iif and an elisa for pr3/mpo provides a specificity of 99% versus pathological controls , with only a minor loss of sensitivity . the identification and purification of the pr3 and mpo antigens [ 5 , 35 , 36 ] allowed for the development of several immunoassays for the quantitative detection of antibodies specific for pr3 and mpo , including the conventional elisa and , more recently , line immunoassays ( lia ) , capture [ 38 , 39 ] , and anchor assays [ 40 , 41 ] as well as multiplex assays [ 4244 ] .
as elisas are only moderately fast with assay times between 1.5 and 3 hours , the focus lately shifted towards a decrease in assay time and fully automated technologies .
lateral flow assays ( lfa ) reduce time to result and require limited laboratory equipment . to reduce time to result and minimize hands - on time in the laboratory , new systems combining random access and chemiluminescent immunoassay technology ( clia ) have been developed and offer single patient testing together with assay times of as little as 30 minutes .
the international consensus statement on testing and reporting of anca recommends that the minimum requirements for anca testing are as follows :
iif should be performed on all sera from new patients , since 10% of anca positive sera in patients with gpa or mpa can be demonstrated only by iif [ 23 , 33 ] . in spite of this
, the strategy for the detection of anca varies across laboratories , according to geographical areas , traditions , and local experience .
additionally , the iif method in general , faces many challenges and occupies a special and often not very popular place in the laboratory .
historically both slide preparation and slide reading require considerable manual work , are time consuming , and are prone to technical problems in the hands of less experienced users [ 4648 ] .
furthermore , the handwritten transcription of results in the dark room is a hotbed of transcription errors .
high intra- and interlaboratory variability are also observed in anca testing by iif due to differences in neutrophil sources , preparation , fixation , and subjectivity of laboratory technologists .
unique to anca by iif is the recommendation for two different substrates ( ethanol- and formalin - fixed neutrophils ) and the frequent presence of cross - reactive ana . in recent years
, automated fluorescent microscope systems that acquire , store , and display high resolution digital images obtained on iif slides have been developed ( nova view , inova diagnostics inc .
usa ; aklides , medipan gmbh , germany ; image navigator , immuno concepts ltd .
digital images can be viewed and used any time for follow - up , training , and consultation / second opinion purposes .
software programs provide tools to support the operator 's decision making such as negativity , positivity , and pattern interpretation [ 4650 ] .
an important feature to increase the accuracy of iif interpretation is the possibility of multianalyte screening and computerized display .
such systems can display results of the same sample on different substrates ( i.e. , results obtained on ethanol- and formalin - fixed substrates next to results obtained on hep-2 ana ; see figure 3 ) .
however , these programs should not be used to provide final results as they require competent human confirmation for analysis and reporting .
this process does offer the benefits of reducing hands - on time and transcription errors in addition to eliminating the need for a dark room .
after an initial iif screen , the results should be verified by elisa or an equivalent solid phase assay . in the past
, elisa tests did not reach the sensitivity and specificity of iif on neutrophils [ 51 , 52 ] , but , more recently , new methods offer improved results .
these methods utilize different immobilization strategies resulting in presentation of the antigen in the most native way to enable the best exposure of all relevant epitopes to the antibody .
different immobilization techniques have led to advancement in the generation of immunoassays aimed to improve the sensitivity of the assays .
after the antigens targeted by autoantibodies generating the p - anca and c - anca pattern were described [ 5 , 35 , 36 ] , the first elisas were developed using purified native pr3 and mpo antigens . these test kits used simple adsorption coating methods and the purity of the antigens was quite variable .
the limited sensitivity of these first generation tests was attributed to the adsorption immobilization process resulting in masking and deformation of epitopes . in 1998 , the international consensus statement on testing and reporting of anca by a proposed a combination of iif and elisa test methods .
the low sensitivity of the first generation elisas led to the development of novel approaches to protein modification and different assay methods .
the so - called second generation anca tests used capture molecules , mostly antibodies , to bind the antigens to the surface without causing changes to the structure of the epitopes .
these elisas showed a significant increase in sensitivity and proved superior to the direct binding anca tests .
third generation assays , again , aimed to prevent the antigen from being distorted , due to binding on the elisa plate , utilize anchor techniques to immobilize the antigens .
the antigens are bound to the surface of the elisa plate using anchor molecules which are attached to the surface of the elisa plate .
this method was discussed to provide a better accessibility of epitopes and thus in a further increase in the sensitivity and specificity as compared to iif . a comparative roc analysis of three generations of pr3-anca assays based on the detection of pr3-anca in the sera of 86 gpa patients and 80 healthy control and 450 disease control sera revealed auc values of 0.80 [ 95% ci : 0.760.83 ] ( 1st generation ) , 0.86 [ 95% ci : 0.820.89 ] ( 2nd generation , capture elisa ) , and 0.96 [ 95% ci : 0.940.98 ] ( 3rd generation anchor elisa ) , respectively .
a novel approach using direct coating in elisa uses a mixture of a human native and human recombinant pr3 antigen .
this may offer a significantly higher sensitivity compared to first generation direct coating and second generation capture methods ; however this has not been confirmed in all studies [ 56 , 57 ] .
historically lfas were regarded as fast , but insensitive , reaching only about 80% of the diagnostic performance of elisas [ 5860 ] .
newer developments of lfa made use of liquid antigens and significantly improved the diagnostic performance of these tests .
the antigens are added in solution , to minimize possible masking of epitopes due to surface adhesion .
interpretation of the test result can be done by a hand held reading device and results can be interpreted semi - quantitatively .
preliminary results indicate that this technology might reach the sensitivity of elisas with an assay time of 20 minutes [ 61 , 62 ] . however , clinical use of lfa for the detection of anca is extremely limited at most . a new approach to combine screening for and confirmation of anca
this new technology combines ethanol - fixed neutrophils and the antigens pr3 , mpo , and gbm coupled to different microbeads which are then attached to different compartments of the iif slide .
the different reactivities can be identified by either the size of the respective bead or the position in different compartments of the iif slides .
a first validation of this assay comparing the results against a combination of iif and elisa results showed a positive agreement in 124/129 ( 96.1% ) samples and negative agreement in 540/542 ( 99.6% ) samples .
chemiluminescent assays ( clia ) are significantly different from elisa technology , as the antigen is covalently attached to the surface of the bead particles unlike the passive adsorption used for most elisas . almost at the same time , two different clia assays for the detection of pr3- and mpo - anca have been developed on two systems : zenit ra ( a. menarini diagnostica s.r.l . ,
, san diego , usa ) . in the bio - flash system the epitope conformation of native pr3 and mpo antigens and hence a reliable representation of epitopes
after the beads are incubated with diluted patient serum and washed , antihuman igg isoluminol conjugate antibody tracer is added .
the conjugate is oxidized when sodium hydroxide and peroxide solutions triggers are added and the flash of light produced from this reaction is measured as relative light units ( rlus ) .
the rlus are proportional to the amount of isoluminol conjugate that is bound to the human igg , which is in turn proportional to the amount of autoantibodies bound to the antigen on the beads .
unlike elisa or addressable laser bead immunoassays ( albia ) platforms , the detection system uses a proprietary clia technology that affords a remarkably wider dynamic range , an entirely linear titration curve , and more consistent inter- and intratest reliability .
recently the high sensitivity and specificity of a pr3 clia , for example , could be demonstrated in a large multicenter study covering 11 laboratory sites in 9 different countries .
a total of 1648 samples ( 292 gpa and 1356 disease controls ) were tested using a new pr3 clia assay ( quanta flash pr3 ) , which could discriminate gpa patient samples from various disease controls with a roc auc value of 0.78 and a specificity of 98.0% at a sensitivity of 62.7% ( figure 5 ) . in a smaller part of this multicenter
study a comparison against another assay revealed high percentages of agreement between the new clia assay and another well - established high sensitivity pr3 assay ( elia pr3 thermo scientific , germany ) ( table 1 ) .
both assays could discriminate between samples from gpa patients and controls with similar sensitivities and specificities : 56.1% ( 95% ci 44.767.0%)/98.2% ( 95% ci 93.899.8% ) sensitivity / specificity for quanta flash , and 58.5% ( 95% ci 47.169.3%)/96.5% ( 95% ci 91.399.4% ) sensitivity / specificity for elia pr3 . in another study 95 samples ( 20 p - anca positive by iif versus 75 controls )
were tested with a newly developed mpo clia in comparison to three different commercially available mpo - assays ( wieslab mpo anca elisa , eurodiagnostica ab sweden ; zenit ra mpo elisa , a. menarini diagnostica s.r.l . ,
both the mpo clia and the wieslab mpo - anca elisa revealed highest relative sensitivity / specificity compared to a positive p - anca iif result ( figure 6 ) reflected by auc values of 0.97 ( 95% ci 0.921.00 ) for the wieslab mpo - anca elisa and 0.96 ( 95% ci 0.901.00 ) for the mpo clia . despite several comparative studies ,
it remains debatable as to which methodology for anca detection provides the highest clinical accuracy for the diagnosis of svv [ 53 , 65 , 66 ] .
several studies published over the last decade suggested that the sensitivity of both capture as well as novel anchor assays were superior to classical elisa and even to iif [ 40 , 41 , 53 , 67 , 68 ] . lately
the new emerging technology of clia showed comparable or superior sensitivity compared to established assay types .
anca - associated vasculitides are chronic multisystemic disorders , affecting several organs , and characterized by the occurrence of flares and remissions . because of severe manifestations including alveolar haemorrhage , rapid progressive glomerulonephritis , scleritis , and necrotizing sinusitis , it is of the utmost importance to propose anca results in a timely manner [ 31 , 32 ] .
anca testing at presentation and in the case of suspected disease flares should be requested urgently , in order to rapidly initiate appropriate immunosuppressive therapies and avoid irreversible organ damages [ 68 , 69 ] .
relapses of the diseases occur in 3060% of the patients during 510 years of follow up and increase the risk of end stage renal disease ( esrd ) ; therefore anca testing is also required for the follow - up of the patients [ 70 , 71 ] . according to disease stage and activity ,
follow - up assessments include anca testing at intervals of several months ( three to six months ) .
even if serial anca testing is controversial , anca testing is usually ordered in case of suspicion of relapse , side effect of immunosuppressive therapy or for differential diagnosis with undercurrent infectious diseases [ 72 , 73 ] .
iif is inappropriate in the emergency setting due to its time constraints and inability to quantify results .
although controversially discussed , anca testing at intervals is recommended as anca titres may decline during effective treatment and often rise prior to relapse [ 21 , 74 , 75 ] .
in contrast to iif , tests that give quantitative anca measurements are required to monitor disease activity .
lately it was revealed that the use of native pr3 antigen together with new assay technologies led to results correlating better to the birmingham vasculitis activity score ( bvas ) than assays using a combination of recombinant and native pr3 antigen [ 45 , 56 ] .
atypical p - anca is found in patients with inflammatory bowel disease ( ibd ) , mainly ulcerative colitis ( uc ) . when combined with anti - saccharomyces cerevisiae antibodies ( asca ) , atypical
p - anca has been recommended as a way to help distinguish uc from crohn 's disease ( crd ) [ 22 , 7781 ] .
asca seropositivity is a predominant feature of crd , while atypical p - anca is a marker of uc ( table 2 ) [ 22 , 78 ] .
both asca and anca have been reported to predict the development of ibd . despite several studies ,
the diagnosis of ibd including uc and crd is largely based on endoscopic and histological assessment of the inflamed tissue [ 77 , 84 ] . while several antibody tests can assist in the diagnosis of crd including asca and pancreatic zymogen granule protein 2 ( gp2 ) [ 8587 ] , the only serological biomarker for uc is atypical p - anca detected by iif . however , iif has the limitations described above and is unable to provide information about anca antigen specificity [ 77 , 79 ] .
several studies have attempted to identify the major target antigen of atypical p - anca in ibd [ 83 , 88 ] , but major disease - specific target antigens are still missing .
in contrast to historical data [ 89 , 90 ] , more recent studies reported pr3-anca in a significant percentage of ibd patients . this raises the possibility that akin to aav , pr3-anca may also be a marker for ibd .
however , early studies of pr3-anca in ibd have been based on relatively small cohorts of uc patients [ 44 , 91 , 92 ] . when twelve pr3 anca assays were compared using 22 ibd sera , the reported prevalence of pr3-anca ranged from 4% to 43% , raising concerns as to the reliability of the assays used in these studies [ 44 , 9193 ] . the two assays with the highest sensitivity [ bindazyme ( binding site ltd .
recently it was suggested that pr3-anca measured by a novel chemiluminescent immunoassay ( clia ) on a random access autoanalyzer ( bio - flash ) are useful in the differential diagnosis of uc and crd .
our observation that pr3-anca can be detected in sera from patients with ibd , with higher prevalence in uc versus crd patients suggests that pr3-anca testing could assist in discriminating uc from crd and in discriminating ibd from other gastrointestinal conditions .
ibd unclassified ( ibd - u ) categorize patients in whom the diagnosis of uc or crd is not clear [ 77 , 94 , 95 ] .
the differential diagnosis may be complicated in patients with irritable bowel syndrome , celiac disease , or other gastrointestinal diseases with symptoms indistinguishable from those seen in ibd .
furthermore , our data pointed to a possible role as biomarker for a lesser need of immunomodulatory therapy in uc patients with pr3-anca , although these data should be confirmed in further studies .
the fact that pr3-anca is found in uc could be interpreted as compromising the specificity of pr3-anca for gpa .
however , pr3-anca in patients with gpa are often associated with a c - anca pattern on ethanol - fixed neutrophils , while in uc patients an atypical p - anca is most often observed .
the latter is most likely explained by reactivity to other antigens that have been reported in the past to be associated with uc ; see figure 7 .
consequently , differential diagnosis of gpa and uc in pr3-anca positive individuals can be achieved using the clinical presentation of the patient and the combination of pr3-anca and iif .
interestingly recent studies have described patients with overlapping features of uc and gpa [ 9698 ] . to what extent pr3-anca positive uc patients will develop full - blown aav over the course of their disease
it is widely appreciated that different autoimmune diseases can overlap in certain patients , which was recently described as polyautoimmunity .
therefore , additional studies are required to determine whether there is an overlap between the two chronic inflammatory diseases .
while gpa typically affects the upper respiratory tract and the kidneys , uc is limited to the colon .
although , 10% of patients with svv , can present with ulcerations of the colon , isolated gastrointestinal tract involvement is infrequently seen in anca - positive patients with svv .
the names of the common forms of vasculitis have been recently revised so that the eponyms such as wg and css have been changed to gpa and egpa , respectively .
positive results , or cases of strong clinical suspicion should be run on a solid phase assay for confirmation of the antigenic specificity and quantitation of the results .
automated solutions for autoimmune laboratories performing iif assays simplify and streamline the iif reading / interpretation workflow and increase the reliability of iif testing by sample traceability . despite big improvements in sensitivity and specificity ,
acute disease flares can be confounding , so accurate , rapid diagnosis followed by appropriate therapy is paramount to halting the deleterious effects of anca vasculitic disease , especially in an emergency setting .
pr3-anca are present in a significant percentage of ibd patients and may be a marker of concurrent svv related disease .
pr3-anca measured by clia are promising to aid in the differential diagnosis of uc and crd . | pubmed |
last sunday i saw the new yves saint laurent biopic. what a feast for the eyes. any flaws it might have are easily made up by the visuals. the story was inspiring as well. it made me want to sew, draw, write, shop. it also made me interested in the designer himself, & his (older) work. yves saint laurent is one of those designers i've never really appreciated for some reason. funny, since he introduced pants for women.
the pictures are courtesy of the v&a and met. | slim_pajama |
bacterial infections , especially those caused by staphylococcus aureus , are the most significant complication encountered in the management of wounds.1 furthermore , multidrug - resistant s. aureus strains and their secreted toxins are responsible for interfering with the wound - healing process and creating portals of entry for systemic complications in affected patients.2 with the increasing incidence of staphylococcal resistance to topical antimicrobials , such as mupirocin and fusidic acid,35 there is a pressing need to develop novel antimicrobials and new approaches to circumvent this burgeoning problem .
recently , there has been increased interest in the development of antimicrobial peptides ( amps ) as novel therapeutics , due to their high potency , broad spectrum of activity , and reduced potential for resistance development.6,7 in addition to the potent bactericidal activity of amps , the recognized anti - inflammatory response of certain amps should be an advantage in the treatment of s. aureus skin infections.8 in a recent study , we described two novel short peptides
rr ( wlrrikawlrr ) and rrika ( wlrrikawlrrika ) with potent bactericidal activity in vitro against multiple clinical isolates of methicillin - resistant s. aureus ( mrsa).6 in particular , the peptides were active against the highly virulent mrsa usa 300 - 0114 , a community- associated strain responsible for outbreaks of staphylococcal skin and soft - tissue infections in the us.9 moreover , rr and rrika were superior in reducing adherent biofilms of both s. aureus and staphylococcus epidermidis when compared to conventional antibiotics .
furthermore , both rr and rrika enhanced the antistaphylococcal activity of lysostaphin in vitro more than 1,000-fold.6 although lysostaphin demonstrated potent efficacy against mrsa infections in different animal models,1012 its therapeutic potential was hampered by the emergence of bacterial resistance.10,13 in light of our previous results , showing enhancement of the antimicrobial effectiveness of lysostaphin against mrsa when combined with amps in vitro,6 we moved forward with an in vivo experiment in a mouse model of mrsa skin infection .
we obtained the community - acquired msra strain nrs384 ( mrsa usa 300 - 0114 ) isolated from a wound from a patient in mississippi , usa . the strain is resistant to erythromycin and tetracycline ; positive for mec ( subtype iv ) ; pvl ; multilocus sequence type 8 ; egenomic spa type 1 , egenomic spa repeats yhgfmbqblo ; ridom spa type t008 ; agr grp i. rr and rrika were synthesized by genscript ( piscataway , nj , usa ) .
linezolid and fusidic acid were purchased from chem - impex international ( wood dale , il , usa ) .
female balb / c mice ( 68 weeks old ) were obtained from harlan laboratories ( indianapolis , in , usa ) .
all procedures were approved by the purdue university animal care and use committee ( 1207000676 ) .
the murine model of mrsa skin infection has been described before.14,15 eight groups of mice ( n=5 ) were inoculated with 40 l of mrsa usa 300 ( 3107 cfu ) intradermally .
forty - eight hours after infection and formation of an open wound , six 6 groups were treated topically with either 2% fusidic acid , 2% rr , 2% rrika , 1% rrika , 0.5% lysostaphin , or 1% rrika plus 0.5% lysostaphin formulated in 20 mg petroleum jelly .
one group received vehicle only ( petroleum jelly ) , and the last group was treated orally with linezolid ( 25 mg / kg ) .
twenty - four hours after the last treatment , mice were humanely killed , the area around the wound lightly swabbed with 70% ethanol , and the wound ( around 1 cm2 ) excised for bacterial counting after homogenization in 1 ml tryptic soy broth .
enzyme - linked immunosorbent assay ( elisa ) development kits for detection of cytokines were purchased from r&d systems ( minneapolis , mn , usa ) .
the supernatants were examined for cytokine production : tumor - necrosis factor ( tnf)- , interleukin ( il)-6 , and il-1 using elisa as described before.16 cytokine levels were expressed as percentage change relative to negative control .
statistical analyses were performed using graphpad prism 6.0 ( graphpad software , la jolla , ca , usa ) .
p - values were calculated by the two - tailed student s t - test .
we obtained the community - acquired msra strain nrs384 ( mrsa usa 300 - 0114 ) isolated from a wound from a patient in mississippi , usa . the strain is resistant to erythromycin and tetracycline ; positive for mec ( subtype iv ) ; pvl ; multilocus sequence type 8 ; egenomic spa type 1 , egenomic spa repeats yhgfmbqblo ; ridom spa type t008 ; agr grp i.
linezolid and fusidic acid were purchased from chem - impex international ( wood dale , il , usa ) .
female balb / c mice ( 68 weeks old ) were obtained from harlan laboratories ( indianapolis , in , usa ) . all procedures
the murine model of mrsa skin infection has been described before.14,15 eight groups of mice ( n=5 ) were inoculated with 40 l of mrsa usa 300 ( 3107 cfu ) intradermally .
forty - eight hours after infection and formation of an open wound , six 6 groups were treated topically with either 2% fusidic acid , 2% rr , 2% rrika , 1% rrika , 0.5% lysostaphin , or 1% rrika plus 0.5% lysostaphin formulated in 20 mg petroleum jelly .
one group received vehicle only ( petroleum jelly ) , and the last group was treated orally with linezolid ( 25 mg / kg ) .
twenty - four hours after the last treatment , mice were humanely killed , the area around the wound lightly swabbed with 70% ethanol , and the wound ( around 1 cm2 ) excised for bacterial counting after homogenization in 1 ml tryptic soy broth .
enzyme - linked immunosorbent assay ( elisa ) development kits for detection of cytokines were purchased from r&d systems ( minneapolis , mn , usa ) .
the supernatants were examined for cytokine production : tumor - necrosis factor ( tnf)- , interleukin ( il)-6 , and il-1 using elisa as described before.16 cytokine levels were expressed as percentage change relative to negative control .
statistical analyses were performed using graphpad prism 6.0 ( graphpad software , la jolla , ca , usa ) .
p - values were calculated by the two - tailed student s t - test .
as shown in figure 1 , all treatments significantly reduced the mean bacterial counts compared with the control group ( p0.01 ) . among groups treated with monotherapy , the group treated with
2% rrika had the highest reduction in cfu ( 2.080.20 log10 ) , followed by 2% fusidic acid ( 1.940.36 log10 ) , 2% rr ( 1.830.30 log10 ) , and linezolid ( 1.740.53 log10 ) .
groups treated with 0.5% lysostaphin or 1% rrika achieved a significant reduction of 1.790.56 log10 and 1.080.36 log10 , respectively , when compared with the control group ( p0.01 ) ( figure 1 ) . the combination therapy ( 0.5% lysostaphin with 1% rrika )
was significantly more effective than treatment with rrika or lysostaphin alone , and achieved statistically significant bacterial reduction of 2.650.44 log10 compared to the negative control ( p0.01 ) .
the bacterial reduction in the combined therapy was also statistically significant compared to monotherapy ( p<0.05 ) or control antibiotics ( p<0.05 ) .
previously , rr and rrika showed potent immunomodulatory activities in vitro through inhibition of mitogen - activated protein kinase ( mk2).17,18 in this study , topical treatment with rrika and rr significantly reduced tnf and il-6 production in mrsa skin lesions .
as shown in figure 2a and b , 2% rr and 2% rrika reduced the tnf level by 49% and 56% , respectively , while the il-6 level was reduced by 29% and 60% , respectively .
treatment with 0.5% lysostaphin and 2% fusidic acid caused 39% and 29% reduction of the tnf level , respectively , and 13% and 25% reduction of the il-6 level , respectively , which is in agreement with previous findings.19,20 there was a synergistic anti - inflammatory response observed when 0.5% lysostaphin was combined with 1% rrika .
the combined therapy significantly reduced tnf and il-6 levels by 62% and 67% , respectively . on the other hand ,
none of the treatments interfered with il-1 production , which is necessary for s. aureus clearance in cutaneous infections ( figure 2c).2122 in this study , topical application of rr and rrika was shown to be very effective in reducing the bacterial load in mrsa skin lesions .
moreover , peptides reduced the release of tnf and il-6 , which might benefit the healing of infected wounds.2327 in addition , the combination of rrika with lysostaphin was significantly more effective in the treatment of mrsa skin lesions than treatment with either peptide alone .
this combination therapy is also expected to overcome some of the limitations associated with lysostaphin monotherapy through hindering the emergence of bacterial resistance and lowering the required therapeutic dose . in conclusion
, our findings in mrsa skin lesions should significantly impact and inform efforts to use a combination of anti - inflammatory and amp therapies as novel topical treatment options for multidrug - resistant pathogens . | pubmed |
its incidence worldwide is 10.1 in every 100,000 men and 2.5 in every 100,000 women .
the highest incidence rate of bladder cancer in europe is seen in the western and southern regions , whereas eastern europe has the lowest incidence rate .
the worldwide mortality rate is 4 in every 100,000 men and 1.1 in every 100,000 women .
the mortality rate of bladder cancer in europe in the past decade was 16% in men and 12% in women .
seventy percent of cases of newly diagnosed disease are superficial disease ; roughly 30% of newly diagnosed cases are muscle - invasive metastatic diseases . although local recurrence is significant despite treatment , the natural progression of non - muscle - invasive bladder cancer tends to remain superficial .
about 5% to 20% of superficial tumors will develop into muscle - invasive disease despite treatment .
the most common areas of distant metastases of urothelial carcinomas are typically the liver , lung , mediastinum , bone , and adrenal gland , respectively .
we present a case of non - muscle - invasive bladder cancer that metastasized into the bone , mediastinum , iliac lymph node , and adrenal and thyroid glands .
an 83-year - old male patient visited the urology department with complaints of macroscopic hematuria at intervals over 9 months .
transurethral resection of the bladder ( tur - b ) was performed on the patient when a 17-mm14-mm mass was found in the ultrasound examination .
repeat tur was applied to the patient 4 weeks later and high - grade urothelial carcinoma with lamina propria invasion was found , whereas muscularis propria invasion did not exist .
positron emission tomography ( pet ) was performed during the second month because the patient had chest pain in the postoperative period , and multiple metastatic bone lesions , metastatic lymphadenopathies on the mediastinum and right external iliac area , a hypermetabolic lesion on the left thyroid lobe , and a hypermetabolic lesion on the left adrenal gland were found .
incisional biopsy performed on the fifth rib of the patient was evaluated as urothelial carcinoma metastasis and radiotherapy was applied to the patient for these lesions ( fig .
a fixed , 3-cm mass was palpated on the left lobe of the thyroid . then
, in the neck computed tomography ( ct ) with contrast , a 40 mm34 mm nodular mass was found on the left lobe of the thyroid gland , which caused left - sided destruction of the thyroid cartilage .
malignant tumor cells were observed in the fine - needle aspiration sample taken from the hypermetabolic lesion on the left lobe of the thyroid .
owing to the patient 's clinical history , primary thyroid carcinomas were considered in the differential diagnosis , because metastatic carcinoma and anaplastic and medullar carcinomas are of first priority .
the immunohistochemical panel included thyroid transcription factor-1 ( ttf-1 ) and thyroglobulin in terms of thyroid tumors ; calcitonin , carcinoembryonic antigen ( cea ) , chromogranin a , and synaptophysin in terms of medullar carcinoma ; and cytokeratins ( ck ) 7 and ck 20 antibodies in terms of urothelial carcinoma .
no reaction was observed with neuroendocrine markers ( synaptophysin and chromogranin ) , calcitonin , thyroglobulin , or ttf-1 in tumoral cells .
the tumor was evaluated as a urothelial carcinoma metastasis owing to the clinical history of the patient , the existence of other metastases , the morphological similarity of the tumor cells with the primary tumor , and ck 20 positivity in some cases immunohistochemically ( fig .
because the general condition of the patient worsened while planning chemotherapy , no systematic chemotherapy was applied .
the prognosis and survival of patients with bladder cancer are associated with stage and grade during diagnosis .
survival rates for 5 years were reported as 94% for grade 1 non - muscle - invasive disease , 40% for grade 3 non - muscle - invasive disease , 72% for stage t2 , and 33% for stage t4 muscle - invasive disease .
contrary to muscle - invasive disease , many superficial bladder cancers can be treated by regular monitoring cystoscopy , urinary cytology , and re - tur together or not with protective therapy , transurethral resection , and adjuvant intravesical treatment . despite these measures ,
about 5% to 20% of non - muscle - invasive tumors will progress to muscle - invasive disease .
high - grade non - muscle - invasive tumors are related to a high risk of muscular invasion and metastasis and end up with a worse prognosis .
also , it is known that metastasis can appear without muscular invasion ; these metastases are found in regional lymph nodes during cystectomy .
cases of distant metastasis of low - grade non - muscle - invasive urothelial carcinoma without regional lymph node metastasis have been reported .
errors in clinical staging of bladder tumors are well known . in some pathological staging cases
, it is estimated that low staging was done at a rate as high as 30% to 40% .
the european organisation for research and treatment of cancer ( eortc ) developed a scoring system and a risk table to estimate short- and long - term risks of recurrence and progression separately . in this scoring system ,
clinical and pathological parameters are tumor number , tumor size , previous recurrence rate , t phase , carcinoma in situ presence , and tumor grade . in our patients ,
possible mean progression rates according to the score are reported as 5% in the first year and 17% in the fifth year . in the eortc study ,
no results are reported for new concepts such as re - tur , early single - dose chemotherapy , and maintenance bacillus calmette guerin treatment , and this has been criticized by authors . in our patient ,
early single - dose chemotherapy and re - tur were applied and both pathology reports suggested a high - grade non - muscle - invasive bladder tumor . although the progression rate of our patient for 1 year was estimated as 5% according to the eortc study , progression developed in the patient before initiating induction treatment of intravesical ct and before symptoms associated with bone metastases developed .
there are publications in the current literature that report that low - grade non - muscle - invasive bladder tumors are detected clinically and the distant lung metastasis can appear without regional lymph node involvement .
rare metastases of urothelial carcinoma into the skin , uterus , and orbita and vaginal and omental involvements have also been reported .
. showed a small cell carcinoma that metastasized into the thyroid gland , which is a minor variant of bladder urothelial carcinoma .
small - cell carcinoma is rarely originated from the bladder and comprises of 0.48% to 1% of all bladder tumors .
metastases in the thyroid gland are observed in many patients by physical examination or imaging methods during routine monitoring after primary tumor resection . in these patients
, fine - needle aspiration may be useful for evaluating possibilities and limiting unnecessary operation for diagnostic purposes .
the most significant conflict in cytologic comment is the differentiation between primary thyroid anaplastic carcinoma and high - grade metastatic malignity . in the fine - needle aspiration material of the patient ,
differential thyroid carcinomas and medullar carcinomas can be excluded morphologically and immunohistochemically . in the present case ,
no reaction was observed with neuroendocrine markers ( synaptophysin and chromogranin a ) , calcitonin , thyroglobulin , or ttf-1 in tumoral cells .
although a positive reaction immunohistochemically with thyroglobulin supports a primary thyroid malignancy , only 20% to 30% of anaplastic carcinomas display thyroglobulin positivity and negative results do not have meaning . because 20% to 30% of anaplastic carcinomas display thyroglobulin positivity and negative results do not have meaning
the patient 's clinical history is the most essential part in the differential diagnosis of these lesions , and it is emphasized that a thyroid nodule found in a patient with a known cancer should be accepted as metastasis unless proven otherwise . because our patient had a known urothelial carcinoma history , other metastases , a morphological similarity between the tumor cells and the primary tumor , and ck 20 positivity immunohistochemically in some cells , the tumor was evaluated as a urothelial carcinoma metastasis . in conclusion , non - muscle - invasive bladder tumors may present with multiple distant metastases even without muscle invasion .
this presented case showed that bladder tumors can metastasize into the thyroid gland in addition to known distant metastasis areas .
metastasis of a bladder tumor should also be kept in mind in the differential diagnosis in patients who have a bladder tumor history and are found to have a mass on the thyroid gland . | pubmed |
How does a system interact with environment in quantum mechanics? When would this interaction occur? What is it?
As title says, how does a system interact with environment? I realize that this interaction can lead to interference terms and non-diagonal terms in density matrix being reduced (quantum decoherence). But what exactly is this interaction of system and environment? What would be the example of this interaction and when does this interaction occur?
The quantum evolution in open systems is non-unitary, and is effectively described, usually, by the [Lindblad master equation](http://en.wikipedia.org/wiki/Lindblad_equation). It provides a good description for e.g. modeling cavity loss in a system of atoms interacting with radiation (see this [paper](http://journals.aps.org/pra/abstract/10.1103/PhysRevA.75.013804)).
The interaction between the system and environment is really just any plain old interaction you like. For instance, if you can have electron-EM coupling, or spin-spin interaction or whatever. What is key to decoherence is that once you write the Hamiltonian for the total system+environment you trace over the environment degrees of freedom - this corresponds to ignorance about the microscopic properties of the environment.
@yuggib said that the Lindblad master equation usually describes open quantum systems, which is not quite true. Lindblad is very special and nice (it is defines a completely positive trace preserving map and is Markovian), but decoherence (and thermalization!) is quite a generic process and does not occur only under very special circumstances.
EDIT:
Now I see from your comments that you're confused about locality of interaction. The interaction between the system and the environment can be perfectly local, e.g., you have a spin chain coupled only at one site to the environment. The system need not interact with the all (or even many) degrees of freedom of the whole environment for decoherence What you need is the environment to be very large compared to the system.
| stackexchange/physics |
it is estimated that depression will become the second most common cause of disability , next to heart disease in a few decades .
major depression affects 1 in 20 people during their lifetime . in many cultures , especially in developing eastern countries , talking about emotions
somatic metaphors and complaints are usually expressed as substitutes for emotional discharge . such variability in depression rates , as noted by simon and his colleagues , may represent problems with definition and measurement rather than true differences in prevalence .
it seems that western measures are not reliable sources for the estimation of the prevalence of affective disorders in culturally divergent populations .
as kleinman noted , depression is not a universal psychiatric construct and the ways of understanding the body and the self are so different that this may lead to differences in psychopathology .
neurasthenia refers to a bodily state and for the chinese it is easier to talk about somatic complaints rather than one s emotional status .
one reason for this apparent disregard may be the stigma that is attached to psychiatric symptoms in chinese culture , compared to the relative acceptance of physical complaints .
the who collaborative study assessed 573 patients , and showed that feelings of guilt and self - reproach were commonest in basle and montreal and least in tehran , where suicidal ideation was rare .
in contrast , somatic symptoms were commonest in tehran and least in basle and montreal .
in depressed chinese american patients , researchers found that the most common presenting complains were fatigue , insomnia , headache , cough and pain .
in chinese culture in which psychiatric symptoms are usually stigmatized , somatic symptoms are accepted more than direct presentation of emotional symptoms .
patients exhibited less psychiatric symptoms , when referred to a private physician , than those who were visited by a general primary care physician .
luis caballero and his colleagues studied a population of spanish patients with major depressive disorders .
they observed that 93% of patients had at least one somatic symptom which was fully or partially attributed to depression .
bhui revealed in his study that south asians were more likely to visit their general practitioners ( gps ) , and exhibited somatic manifestations of mental distress more commonly than other groups .
they were less likely to have a recognized mental disorder than white groups , and even with recognizable mental disorder , they were least likely to be referred to specialist care by gps .
on the other hand , some surveys showed no differences in psychological and somatic symptoms between western and other countries . in one study
two thirds of depressed patients in primary care presented with somatic symptoms . in another study , the complaints expressed by the patients as somatic entities , were actually depression symptoms in dsm - iv . in a study of 504 patients in tehran , researchers found a high rate of somatic symptoms in depressed patients . also , a similar study in kerman on 246 depressed patients , with frequent symptoms , showed that 40% of case suffered from somatic symptoms .
according to the above - mentioned studies and our clinical experience , it seems that depression as a disorder has a different picture in eastern cultures compared to the one delineated by western researchers . in regard to the more frequent expression of somatic symptoms in eastern cultures , we assessed the probability of different presentations of depressive signs and symptoms in male and female patients and in cases with different cultural backgrounds and education .
such studies can lead to a better understanding of such disorders and more accurate diagnosis of depression in developing countries .
the definition and differentiation of psychiatric problems presented as somatic symptoms may prevent unnecessary interventions and expenses .
mental health professionals working in such cultural atmosphere have frequently witnessed improvement in patients on antidepressant medications .
these patients often had histories of traveling far and wide in search for a solution to their suffering which eventually has ended in the psychiatrist office . in this study , we have tried to answer some questions about the relationship between cultural background , level of education , age , marital status and gender on the one hand , and presenting symptoms of depressed patients on the other .
this cross - sectional descriptive study assessed the presenting symptoms of 500 patients with major depressive disorder referred to a psychiatric clinic affiliated with shiraz university of medical sciences .
diagnosis of the disorder was made based on the dsm - iv - tr ( diagnostic and statistical manual of mental disorders - iv - text revision ) criteria according to a face to face structured psychiatric interview based on the american psychiatric association criteria for the diagnosis of major depressive disorder .
this is a standard tool for the diagnosis of such disorder in many countries including iran and conducted by a bilingual psychiatrist with more than 15 years of experience .
the criteria for recruiting the patients in the study included no history of current substance abuse or dependency , patient s symptoms could not be justified by a general medical condition or other psychiatric entities such as anxiety or somatoform disorders , receiving no active psychiatric treatment , not visited by a psychiatrist during 3 months before evaluation , and not taking any psychiatric medications during this time .
dsm - iv classifies the signs and symptoms of depression into two groups of vegetative and mental conditions .
since pain is assessed as a frequent vegetative symptom , it was considered as a separate entity and eventually categorized into three groups including mental symptoms , pain , and physical symptoms other than pain . through psychiatric interview , we assessed the presenting complaints of these patients and considered such symptoms as guilt feeling , hypochondriac status , insomnia , and losses of appetite , weight , concentration , and interest , suicidal idea and attempt , hopelessness and crying . also the patients were asked about their chief complaints which were categorized into mental symptoms with pain , and physical symptoms without pain , the duration of the illness , description of the emotional or somatic disorders by the patients , causes of illness expressed by the patients as family problems including interpersonal or intergenerational difficulties , living problems such as occupational or financial difficulties , losses incurred , marital conflicts , and romantic breakups , and the clinician who first visited the patient namely general practitioner , psychiatrist or other specialist .
these variables were compared by proper statistical analysis ( chi - square ) according to sex , age , marital status , cultural background ( rural or urban ) and education level .
logistic regression analysis , backward method , was used to compare the association of different independent variables in patients with or without somatization as a symptom .
of 500 patients studied , 380 ( 76.0% ) were females , 356 ( 71.2% ) married , 246 ( 46.2% ) had elementary school education , and 306 ( 61.2% ) belonged to the urban cultural background .
demographic characteristics of the patients
tables 2 and 3 demonstrate the descriptive features of patients chief complaints and symptoms of which headache ( 15.2% ) was the most frequent complaint , followed by irritability ( 10.6% ) , pain in the other areas of the body ( 10.4% ) , depression ( 8.0% ) and forgetfulness ( 7.2% ) . among physical ( organic ) complaints ,
the gastrointestinal ( 7.0% ) symptoms were more frequent than respiratory ( 3.4% ) and cardiac symptoms ( 3.2%).in this context , pain and physical complaints were more common in persons with lower education ( p<0.001 ) , rural cultural background ( p<0.001 ) , women ( p<0.001 ) and married patients ( p=0.007 ) .
individuals with higher education ( p<0.001 ) and urban cultural background ( p<0.001 ) were more likely to visit a psychiatrist .
there was no significant difference in the referral to psychiatrist between age , sex and marital status .
frequency of chief complaints description of clinical variables hypochondriac obsessions were more common in the married ( p=0.024 ) , elder ( p<0.001 ) and lower educated people ( p<0.001).insomnia was more common in people with rural cultural background ( p=0.009 ) and in individuals with lower education ( p<0.001 ) .
guilt feeling was more common in the older and younger people compared to middle aged patients ( p<0.001 ) .
loss of appetite was more prevalent among older and younger people compared to middle aged patients ( p=0.017 ) and in people with rural cultural background ( p=0.003 ) .
suicidal ideation were present more frequently among married persons ( p<0.001 ) , the lower age group ( p<0.001 ) and people with rural cultural background ( p=0.027 ) .
suicidal attempt was more frequent in the lower age group ( p=0.009 ) and in the married ones ( p=0.047 ) .
our study showed no difference in suicidal ideation and suicidal attempt between men and women .
people with lower education ( p<0.001 ) and with rural cultural background ( p=0.001 ) related their symptoms to physical rather than emotional problems . in response to the question about the cause of illness , people with rural cultural background used more
also , women pointed to marital problems and men to life difficulties as the main causes of their illness ( p<0.001).despair prevailed among the singles ( p=0.012 ) .
in general , this study confirmed our initial assumption about a different profile of depressive symptoms in iranians compared to the western population .
our patients showed a high frequency of somatic symptoms , especially pain , as a manifestation of depression .
contrary to the common findings discussed in the western literature , we could not find a difference between men and women in suicidal ideation and attempt .
however , some of our findings are in accordance with the profile of depressive symptoms in western countries . because of the large number of the variables and to prevent confusion , the depressive symptoms are discussed as separate entities in the following sections .
pain and physical symptoms
this study showed the importance of somatization in a group of depressed patients who seemed to have no word for their emotions .
, men have a dominant role and women often have no knowledge about their rights and their interests .
our finding also confirmed the previous observation in that somatic symptoms played an important role in the manifestation of depressive disorder in iranian patients .
the importance of somatic symptoms in the depressed patients has also been shown in many studies especially those performed in eastern countries .
nieuwsma pointed out that social stigma is the main factor to complain of somatic symptoms instead of depression .
fear of stigmatization and reluctance to appear as psychiatric patients are important factor for expressing their emotional pain via somatic route .
the pattern of somatization , as kleinman noted in his study on chinese patients , may be unfamiliar to western clinicians and may further complicate the concept of depression .
referral to psychiatrist
the general practitioners and other specialists are still primary physicians for persons with lower education and people with rural cultural background .
this can be related to the unavailability of psychiatrists in rural areas . however , the factor of knowledge has to be considered as a contributory parameter for evaluating this condition .
the study conducted by bhui and colleagues revealed that south asians are more likely to visit their general practitioners and less likely to have a recognized mental disorder than white groups , and even if this is recognized , they are least likely to be referred to a specialist by gps .
higher prevalence of guilt feeling in patients with urban cultural background is a finding comparable with the results of who collaborative study which showed the higher prevalence of this symptom in western societies .
one study showed that guilt feelings could be found in patients with both pakistani and austrian cultures , regardless of age and sex .
in fact , guilt feeling was associated with the severity of psychomotor retardation in depression . in some patients ,
, the idea of original sin rooted in the christianity teachings plays a major role in the guilt feeling of depressed patients .
the lesser prevalence of guilt feeling in the middle aged group can be related to the social activity and the functionality of these people compared to the elders and younger people .
hypochondriac ideation
according to the dsm - iv , hypochondriasis is a disorder with relatively similar prevalence in men and women .
accordingly , in this study we could not find a significant difference between men and women in hypochondriac ideations .
hypochondriasisas is an obsession about death and it can be an explanation for the higher prevalence of this symptom in the elderly .
similarity of the prevalence of hypochondriac ideations in rural and urban areas may indicate that this symptom is less affected by the cultural backgrounds of patients than somatization . as a vegetative symptom ,
insomnia is also more frequent in the lower educated people and in rural areas and is associated with somatic symptoms
. logistic regression analysis also showed the interplay of insomnia and somatic symptoms ( table 4 ) .
whether this is representative of sleep disturbance due to somatic problems or vice versa remains to be clarified .
factors associated with the chief complaint of somatization like insomnia , this can be affected by somatic symptoms , especially gastrointestinal manifestations . however , because of the similarity of weight loss in the rural and urban areas , this symptom can be a subjective feeling rather than a true anorexia leading to weight loss .
loss of concentration
this condition has frequently been reported by younger patients who may be more concerned about their memory problems than older people .
however , the elders deny their defects in memory and do not complain about it .
suicidal ideation and attempt
according to the dsm - iv , suicidal ideation is more frequent in women and suicidal attempt is more prevalent in men .
however , our study showed no difference in suicidal ideation and attempt between men and women .
suicidal idea was more frequent among rural inhabitants , but no difference in suicidal attempt was found between them and urban population .
perhaps this may be related to the hesitation of rural people in expressing their emotions .
our findings of higher prevalence of suicidal attempt and ideation in married patients is in contrast with those of other studies .
also , our study showed that both suicidal ideation and attempt are more frequent in the younger age group .
this findings is in conflict with some studies that consider the old age as a risk factor for suicidal attempt .
this difference can be related to the supportive care giving received by the older members of the family in eastern countries like iran .
logistic regression analysis showed the interplay between suicidal ideation and somatic symptoms , but not between suicidal attempt and hopelessness with somatic symptoms .
the higher prevalence of despair in singles is suggestive of the seriousness of the problem in this group .
although a cause and effect relationship can not be derived from a cross - sectional study , the symptoms of hypochondriasis , suicidal idea , crying , irritability and insomnia were significantly associated with the complaint of somatization ( table 4 ) .
one possible explanation is that somatic problems of patients disrupt their sleep and increase their vulnerability to environmental and emotional stimuli .
this in turn , can aggravate the patients affective stability presented by more crying , irritability or thoughts of death . on the other hand , sleeping disorders may also lead to somatic complaints . considering the covariant variables in the regression analysis ,
only gender was associated with the complaint of somatization in patients with major depressive disorder . however , neither of the educational level and patients age are associated with the complaint of somatization .
these results indicated that somatization as a complaint in the patients with major depressive disorder is independent from age and educational level .
one explanation could be that somatization as a complaint in iranian culture is commonly expressed in both higher and lower educated class .
the principal finding of this study is that somatic symptoms especially headache and pain in other areas of the body have a significant weight in the chief complaints of depressed patients .
therapists need to pay attention to the various ways of presentation of this disorder in different cultures in order to understand the symptoms of patients with depression .
hence , more extensive studies in other areas of the country are required to obtain a more reliable profile of depression symptoms in iranian population . | pubmed |
near - infrared ( nir ) observations ( 0.92.5@xmath0 ) are important in practically all areas of astronomy and astrophysics .
for example , low - mass stars and brown dwarfs emit a substantial fraction of their light at these wavelengths and nir spectroscopy is the most efficient way to study these objects .
nir spectroscopy is also one of the best ways to study the early universe because optical and ultraviolet emission lines from distant galaxies are redshifted to nir wavelengths due to hubble expansion .
unfortunately , deep nir observations from the ground are extremely difficult to make due to the presence of a bright atmospheric background .
the background in the range 0.91.8@xmath0 is predominantly from the de - excitation of atmospheric hydroxyl ( oh ) molecules at an altitude of @xmath1 90 km @xcite .
the nir background is @xmath1 1000 times brighter than the optical background and can not be simply subtracted from astronomical observations @xcite because its brightness fluctuates on short timescales @xcite .
solving the nir sky background problem is an important challenge in observational astronomy .
previous attempts at a ground - based solution have not been able to suppress oh emission lines over a broad wavelength range while maintaining high throughput between the lines , which is critical for a wide range of science cases .
for example , observations may be made in a very narrow wavelength range between oh emission lines using ultra - narrow band filters @xcite .
however , this requires a specific unambiguously identifiable feature within the narrow wavelength range from the object . as a result
, the number and nature of objects that may be observed by this technique is severely limited .
more sophisticated approaches attempt to remove oh emission lines by dispersing the light with a diffraction grating at high resolution , selectively masking out the oh lines , and then recombining the light @xcite .
unfortunately , the diffraction grating and the system optics ( which the light must pass through twice ) unavoidably scatters the bright oh light and the scattered portions can not be effectively removed .
thus , oh emission lines are better dealt with before the light reaches any dispersing element .
there have been attempts to use holographic filters for this purpose .
@xcite demonstrated a device with 10 notches 10db deep and 0.1 nm wide with 85% throughput between the notches .
using several of these holographic filters in series would be sufficient to suppress on the order of 100 oh doublets pre - dispersion , but the internotch throughput would be very low in this configuration .
see @xcite for an in - depth comparison of these oh suppression techniques .
oh suppression using aperiodic fiber bragg gratings @xcite overcomes many of the shortcomings of these previous approaches and is the best available solution to the nir sky background problem from the ground @xcite .
fiber bragg gratings ( fbgs ) are common photonic devices widely used in telecommunications .
basic fbgs are single - mode fibers ( smfs ) with a periodic refractive index modulation written into the fiber core by exposing it to ultraviolet light .
the periodic refractive index modulation induces strong reflections at the bragg wavelength , @xmath2 , where @xmath3 is the spatial period of the refractive index modulation , and @xmath4 is the effective index of the core .
reflectivities close to 100% and narrow bandwidths of 0.1 nm are possible with simple periodic fbgs @xcite . however , basic periodic fbgs have limited use for oh suppression .
each periodic index modulation can be thought of as producing a single notch .
a very large number of periodic index modulations would be required to suppress the dense forest of oh lines in the @xmath5 and @xmath6 bands .
writing multiple periodic index modulations in succession in the same fiber results in high loss in the spectral regions between the notches because of the excessive exposure to ultraviolet light @xcite .
aperiodic fbgs are designed with all notches treated simultaneously resulting in a single complex refractive index modulation that encodes @xmath150 irregularly spaced notches over a span of @xmath1100 nm with high internotch throughput .
figure [ fig : afbgresponse ] shows the wavelength response of a single aperiodic fbg with 50 notches between 1.47 and 1.58@xmath0 .
aperiodic fbgs are an attractive means of filtering atmospheric oh lines . however , when used in astronomy , where the wavefront exiting the telescope is distorted by atmospheric turbulence , coupling light into small core diameter smfs is challenging . as a result ,
large core diameter multi - mode fibers ( mmfs ) are more commonly used in astronomy .
unfortunately , mmfs smear out the narrow notches of fbgs into broad , shallow notches because the bragg condition is different for each fiber mode .
oh suppression requires a fiber with the light collecting ability of an mmf and the suppression characteristics of an smf fbg .
the solution to this problem is a device called a photonic lantern @xcite .
the device consists of a multi - mode ( mm ) port connected to an array of smfs by a taper transition .
the photonic lantern converts the modes of the mm port into the supermodes of the smf array and vice versa . by splicing photonic lanterns to an array of fbgs
, we have an `` oh suppression fiber '' that is easy to couple light into and exhibits the exact same transmission characteristics as an fbg in an smf .
the gnosis grating unit is the first oh suppression unit to utilize these oh suppression fibers .
it is independent of telescope and spectrograph but we commissioned the unit at the 3.9 m anglo - australian telescope ( aat ) at siding spring observatory with the existing iris2 infrared imaging spectrograph @xcite to demonstrate the potential of oh suppression fibers .
in addition to the grating unit , gnosis consists of a fore - optics unit and an iris2 interface unit , which connects the grating unit to the telescope and spectrograph , respectively .
the optical light path is shown in figure [ fig : opticalpath ] .
light exiting the back of the aat is collected by a 7 element integral field unit ( ifu ) spanning 1.2@xmath7 mounted inside the fore - optics unit .
the light is transported by a fiber bundle to the grating unit , where oh suppression occurs .
the oh suppressed light is transported by another fiber bundle to the iris2 spectrograph for measurement . in this paper
, we present the design and performance of each gnosis subsystem and as a whole .
we begin by discussing the two components of our oh suppression fibers , the fbgs and the photonic lanterns in sections [ section : fbg ] and [ section : photoniclantern ] .
the oh suppression fibers are housed in the gnosis grating unit , which is described in section [ section : gratingunit ] . in sections [ section : foreoptics ] and [ section : iris2interface ] we discuss the gnosis fore - optics unit and iris2 interface unit , which connects the grating unit to the telescope and iris2 , respectively . section [ section : onsky ] summarizes the on - sky performance of gnosis and section [ section : discussion ] contains a discussion on the future of oh suppression fibers . with the best - fitting butterworth profile ( red line ) .
the notch is deep , narrow , and square , which is ideal for oh suppression.[fig : h1notch],scaledwidth=45.0% ]
the gnosis oh suppression fibers utilize two complex , multi - notch aperiodic fbgs @xcite in series to suppress oh lines over two - thirds of the @xmath6 band ( 1.471.7@xmath0 ) .
the fbgs were manufactured by redfern optical components based on our design to suppress the 103 brightest oh doublets using the line positions and strengths from @xcite .
the h1 fbg has notches in the first portion of the @xmath6 band ( 1.471.58@xmath0 ) and the h2 fbg has notches in the second portion ( 1.581.7@xmath0 ) .
the fbgs are printed in a custom photosensitive smf ( nufern cms8 ) .
fbgs are highly sensitive to both strain and temperature variations , which induce wavelength shifts .
the h1 and h2 fbgs are packaged in 304 stainless steel tubes designed to induce a strain in the fiber that varies with temperature in such a way that it cancels the intrinsic thermal wavelength shift of the fbgs , allowing the notches to remain aligned with the oh lines over the temperature range between -10 and + 25@xmath8c .
, scaledwidth=45.0% ] cccccccc no .
& @xmath9 & @xmath10 & @xmath11 & @xmath12 & @xmath13 & @xmath14 & @xmath15 + & ( nm ) & ( nm ) & ( db ) & ( db ) & ( nm ) & ( nm ) & + 1 & 1466.505 & 0.007 & -30.6 & 4.4 & 0.202 & 0.010 & 8 + 2 & 1469.842 & 0.007 & -32.7 & 4.7 & 0.246 & 0.011 & 8 + 3 & 1470.220 & 0.007 & -18.2 & 4.1 & 0.186 & 0.008 & 8 + 4 & 1471.329 & 0.007 & -13.6 & 3.5 & 0.161 & 0.009 & 8 + 5 & 1474.001 & 0.007 & -25.8 & 3.8 & 0.211 & 0.007 & 8 + 6 & 1475.555 & 0.005 & -23.5 & 3.2 & 0.167 & 0.012 & 8 + 7 & 1477.235 & 0.004 & -28.4 & 3.1 & 0.171 & 0.014 & 8 + 8 & 1478.371 & 0.004 & -31.6 & 3.6 & 0.190 & 0.015 & 9 + 9 & 1479.982 & 0.005 & -31.7 & 3.9 & 0.320 & 0.018 & 9 + 10 & 1480.575 & 0.005 & -28.2 & 3.0 & 0.168 & 0.014 & 7 + 11 & 1483.307 & 0.004 & -33.3 & 4.0 & 0.188 & 0.016 & 7 + 12 & 1486.438 & 0.004 & -29.7 & 2.7 & 0.143 & 0.013 & 7 + 13 & 1488.694 & 0.004 & -28.7 & 3.6 & 0.442 & 0.021 & 7 + 14 & 1490.818 & 0.005 & -21.9 & 3.6 & 0.139 & 0.004 & 6 + 15 & 1490.984 & 0.005 & -22.4 & 1.4 & 0.146 & 0.015 & 6 + 16 & 1493.187 & 0.004 & -30.0 & 2.9 & 0.163 & 0.014 & 9 + 17 & 1500.675 & 0.006 & -11.5 & 1.6 & 0.203 & 0.011 & 7 + 18 & 1502.516 & 0.005 & -14.4 & 3.0 & 0.118 & 0.006 & 5 + 19 & 1502.696 & 0.006 & -14.6 & 1.2 & 0.125 & 0.013 & 5 + 20 & 1505.281 & 0.007 & -28.4 & 2.6 & 0.171 & 0.014 & 7 + 21 & 1505.553 & 0.007 & -34.4 & 4.6 & 0.171 & 0.013 & 9 + 22 & 1506.397 & 0.007 & -22.8 & 2.6 & 0.165 & 0.013 & 7 + 23 & 1506.895 & 0.007 & -32.2 & 3.2 & 0.171 & 0.013 & 8 + 24 & 1508.222 & 0.008 & -17.7 & 2.4 & 0.163 & 0.013 & 6 + 25 & 1508.826 & 0.008 & -28.4 & 2.5 & 0.168 & 0.013 & 8 + 26 & 1510.733 & 0.008 & -9.9 & 1.5 & 0.155 & 0.013 & 5 + 27 & 1511.369 & 0.008 & -21.9 & 2.4 & 0.163 & 0.012 & 8 + 28 & 1514.545 & 0.008 & -13.7 & 1.9 & 0.160 & 0.013 & 6 + 29 & 1518.711 & 0.007 & -32.3 & 3.3 & 0.187 & 0.015 & 8 + 30 & 1524.092 & 0.007 & -36.2 & 5.6 & 0.202 & 0.016 & 9 + 31 & 1528.781 & 0.004 & -34.9 & 4.8 & 0.171 & 0.013 & 9 + 32 & 1533.241 & 0.005 & -38.1 & 7.1 & 0.247 & 0.014 & 11 + 33 & 1539.536 & 0.004 & -34.2 & 4.5 & 0.173 & 0.013 & 9 + 34 & 1543.203 & 0.005 & -38.6 & 8.8 & 0.327 & 0.038 & 8 + 35 & 1543.861 & 0.009 & -8.5 & 1.3 & 0.263 & 0.015 & 7 + 36 & 1546.214 & 0.005 & -21.8 & 2.2 & 0.177 & 0.012 & 8 + 37 & 1547.423 & 0.005 & -16.8 & 1.8 & 0.164 & 0.012 & 8 + 38 & 1550.088 & 0.004 & -30.3 & 2.8 & 0.184 & 0.014 & 8 + 39 & 1550.979 & 0.004 & -32.0 & 3.5 & 0.182 & 0.014 & 9 + 40 & 1551.788 & 0.004 & -25.9 & 2.2 & 0.169 & 0.013 & 8 + 41 & 1554.035 & 0.005 & -34.7 & 4.9 & 0.306 & 0.016 & 11 + 42 & 1554.615 & 0.004 & -33.8 & 3.9 & 0.201 & 0.014 & 9 + 43 & 1557.018 & 0.004 & -30.7 & 2.7 & 0.174 & 0.014 & 8 + 44 & 1559.764 & 0.004 & -34.9 & 4.9 & 0.185 & 0.013 & 9 + 45 & 1563.134 & 0.004 & -35.0 & 4.5 & 0.193 & 0.015 & 7 + 46 & 1565.625 & 0.008 & -32.8 & 3.8 & 0.517 & 0.016 & 12 + 47 & 1570.254 & 0.004 & -29.9 & 2.3 & 0.171 & 0.013 & 8 + 48 & 1576.030 & 0.006 & -15.6 & 1.2 & 0.220 & 0.011 & 9 + 49 & 1578.114 & 0.006 & -17.2 & 2.5 & 0.132 & 0.007 & 7 + 50 & 1578.306 & 0.008 & -18.2 & 1.5 & 0.135 & 0.013 & 6 + cccccccc
& @xmath9 & @xmath10 & @xmath11 & @xmath12 & @xmath13 & @xmath14 & @xmath15 + & ( nm ) & ( nm ) & ( db ) & ( db ) & ( nm ) & ( nm ) & + 1 & 1583.028 & 0.008 & -28.8 & 1.3 & 0.171 & 0.015 & 7 + 2 & 1583.330 & 0.009 & -29.2 & 1.2 & 0.183 & 0.021 & 9 + 3 & 1584.252 & 0.007 & -25.5 & 1.9 & 0.157 & 0.014 & 8 + 4 & 1584.807 & 0.008 & -29.1 & 1.2 & 0.178 & 0.017 & 8 + 5 & 1586.253 & 0.008 & -19.8 & 2.2 & 0.142 & 0.012 & 8 + 6 & 1586.932 & 0.009 & -28.2 & 1.2 & 0.180 & 0.016 & 8 + 7 & 1589.006 & 0.008 & -12.4 & 1.7 & 0.114 & 0.012 & 8 + 8 & 1589.732 & 0.009 & -23.3 & 2.0 & 0.205 & 0.025 & 7 + 9 & 1591.590 & 0.011 & -12.2 & 1.6 & 0.473 & 0.018 & 8 + 10 & 1592.503 & 0.008 & -2.8 & 0.6 & 0.102 & 0.012 & 5 + 11 & 1593.224 & 0.007 & -15.5 & 2.1 & 0.163 & 0.012 & 8 + 12 & 1597.263 & 0.009 & -29.0 & 1.1 & 0.195 & 0.017 & 8 + 13 & 1597.415 & 0.016 & -4.3 & 1.6 & 0.164 & 0.022 & 8 + 14 & 1603.086 & 0.007 & -29.8 & 0.8 & 0.201 & 0.016 & 9 + 15 & 1607.975 & 0.007 & -28.5 & 1.3 & 0.161 & 0.015 & 8 + 16 & 1612.866 & 0.007 & -30.4 & 0.9 & 0.232 & 0.017 & 10 + 17 & 1619.460 & 0.008 & -28.8 & 1.4 & 0.166 & 0.014 & 8 + 18 & 1623.539 & 0.007 & -30.9 & 0.9 & 0.270 & 0.017 & 11 + 19 & 1627.035 & 0.007 & -11.3 & 1.7 & 0.173 & 0.010 & 8 + 20 & 1627.971 & 0.006 & -7.4 & 1.2 & 0.162 & 0.010 & 8 + 21 & 1630.229 & 0.007 & -20.9 & 2.5 & 0.196 & 0.013 & 8 + 22 & 1631.553 & 0.005 & -15.6 & 4.4 & 0.182 & 0.015 & 9 + 23 & 1631.721 & 0.013 & -29.1 & 1.8 & 0.200 & 0.027 & 9 + 24 & 1634.178 & 0.008 & -26.5 & 2.2 & 0.211 & 0.014 & 9 + 25 & 1635.136 & 0.008 & -30.0 & 1.4 & 0.315 & 0.020 & 10 + 26 & 1636.040 & 0.007 & -22.6 & 2.1 & 0.171 & 0.012 & 9 + 27 & 1638.854 & 0.007 & -29.1 & 1.6 & 0.208 & 0.013 & 9 + 28 & 1641.471 & 0.007 & -25.6 & 2.0 & 0.156 & 0.012 & 9 + 29 & 1644.219 & 0.006 & -29.3 & 1.6 & 0.192 & 0.013 & 9 + 30 & 1644.765 & 0.007 & -24.3 & 2.5 & 0.222 & 0.013 & 9 + 31 & 1647.563 & 0.008 & -25.8 & 2.2 & 0.136 & 0.012 & 7 + 32 & 1647.737 & 0.008 & -25.9 & 2.4 & 0.137 & 0.014 & 7 + 33 & 1647.907 & 0.007 & -26.6 & 1.9 & 0.144 & 0.015 & 7 + 34 & 1650.239 & 0.007 & -29.2 & 1.4 & 0.175 & 0.016 & 8 + 35 & 1655.385 & 0.007 & -26.3 & 1.9 & 0.161 & 0.011 & 8 + 36 & 1658.635 & 0.007 & -17.5 & 2.2 & 0.237 & 0.011 & 10 + 37 & 1661.000 & 0.006 & -19.5 & 2.1 & 0.127 & 0.013 & 7 + 38 & 1661.208 & 0.008 & -19.2 & 2.3 & 0.124 & 0.012 & 7 + 39 & 1668.914 & 0.007 & -24.7 & 2.3 & 0.137 & 0.014 & 8 + 40 & 1669.238 & 0.007 & -30.1 & 1.7 & 0.149 & 0.014 & 7 + 41 & 1670.267 & 0.007 & -19.5 & 2.2 & 0.132 & 0.009 & 8 + 42 & 1670.882 & 0.007 & -28.2 & 1.7 & 0.149 & 0.015 & 8 + 43 & 1672.479 & 0.006 & -15.9 & 1.9 & 0.125 & 0.009 & 7 + 44 & 1673.251 & 0.007 & -25.9 & 2.0 & 0.167 & 0.019 & 8 + 45 & 1673.391 & 0.006 & -8.3 & 1.9 & 0.192 & 0.011 & 8 + 46 & 1675.378 & 0.008 & -10.2 & 1.7 & 0.112 & 0.009 & 8 + 47 & 1675.530 & 0.005 & -9.1 & 1.7 & 0.116 & 0.009 & 8 + 48 & 1675.623 & 0.007 & -11.7 & 2.0 & 0.119 & 0.002 & 6 + 49 & 1676.356 & 0.007 & -20.4 & 2.3 & 0.165 & 0.012 & 7 + 50 & 1679.400 & 0.007 & -2.5 & 0.6 & 0.090 & 0.008 & 5 + 51 & 1680.237 & 0.007 & -13.7 & 2.1 & 0.161 & 0.011 & 8 + 52 & 1684.044 & 0.007 & -27.4 & 1.9 & 0.177 & 0.014 & 8 + 53 & 1684.901 & 0.008 & -14.4 & 1.9 & 0.184 & 0.012 & 8 + 54 & 1690.362 & 0.008 & -29.6 & 1.7 & 0.191 & 0.017 & 8 + 55 & 1695.502 & 0.009 & -27.6 & 2.2 & 0.155 & 0.012 & 8 + we measured the position , depth , and width of each notch from the wavelength response of the h1 and h2 fbgs ( @xmath1610,000 ) .
the fbgs were not designed with any particular functional form for the notch profile in mind , but we found that a butterworth profile provided a good fit to the empirical data .
thus , each notch in the wavelength response was fitted with a butterworth profile , @xmath17^{2n}},\ ] ] where @xmath9 is the profile center , @xmath18 is the profile value at the center , @xmath13 is the profile width , @xmath19 is the profile value far away from the profile center , and @xmath15 is the profile index .
the value of @xmath15 affects the steepness of the profile . from the butterworth parameters for each notch
, we take @xmath9 to be the notch position , @xmath11 to be the notch depth , and @xmath13 to be the notch width .
figure [ fig : h1notch ] shows one of the notches in the h1 fbg and the best - fitting butterworth profile ( red line ) .
the h1 fbg notch parameters are listed in table [ table : h1notchtable ] .
the h1 fbg notch parameters are averages measured from the wavelength response of eight separate devices obtained by scanning a narrow tunable laser source across the device bandwidth and comparing with a reference fiber .
a total of 50 notches were measured in the range 14651580 nm in each of the eight h1 devices .
the h2 fbg notch parameters are listed in table [ table : h2notchtable ] .
the h2 fbg notch parameters are averages measured from the wavelength response of 106 separate devices obtained using a broadband source and an optical spectrum analyzer .
a total of 55 notches were measured in the range 15801700 nm in each of the 106 h2 devices .
tables [ table : h1notchtable ] and [ table : h2notchtable ] contain more notches than the original design of 103 . the additional notches may be printing errors from the manufacturing process .
for example , notch 9 in table [ table : h2notchtable ] is not associated with any oh line from @xcite , but we include it here because it is a significant spectral feature of the fbgs . also , some notches are deliberately designed to be wider in order to suppress closely spaced oh lines with a single notch .
, scaledwidth=45.0% ] the throughput of the fbgs between notches is of interest because this is the region where scientific observations are made .
the throughput at several internotch wavelengths was measured using a cutback technique with a photonetics tunics tunable external cavity laser ( 15201640 nm ) and a thorlabs pm100d power meter with an s122c sensor head .
the laser source was calibrated to @xmath200.2 nm before the measurements were carried out .
the internotch measurement wavelengths were chosen to avoid any notches . based on the values listed in tables [ table : h1notchtable ] and [ table : h2notchtable ]
the closest any internotch measurement value comes to the center of a notch is @xmath21 nm .
given that the average notch width is @xmath22 nm , the internotch measurements should have safely avoided all fbg notches .
the internotch throughput of the h1 and h2 fbgs in the range 15201640 nm are shown in figure [ fig : internotch_throughput ] .
the average throughput is 0.954 and 0.896 for the h1 and h2 fbgs , respectively .
a total of nine h1 fbgs were randomly selected and measured .
the points with error bars show the average internotch throughput of all nine h1 fbgs and the 1@xmath23 variation .
the points without error bars are the measured values from one of the nine h1 fbgs .
a total of five h2 fbgs were randomly selected from an initial delivery of 19 devices and measured .
again , the points with error bars show the average and 1@xmath23 variation of all five h2 fbgs and points without error bars are measurements from one of the 5 devices .
the throughput in both devices decreases at longer wavelengths , but this is due mainly to the decrease in the transmission of the cms8 fiber at longer wavelengths ( see figure [ fig : cms8_loss ] ) .
the performance of the h1 and h2 fbgs are highly satisfactory for oh suppression . on average
the notches are deep ( 24db ) , narrow ( 0.19 nm ) , and square and the average throughput between the notches is high ( 0.92 ) .
the gnosis oh suppression fibers use two 1@xmath2419 photonic lanterns ( one for input and one for output ) to provide the fibers with the light collecting ability of an mmf .
the photonic lanterns were manufactured by nkt photonics @xcite and consist of a 50@xmath0 core diameter mm port connected to an array of 19 smfs by a taper transition with a taper ratio of 11 enclosed in a protective metal case .
a 5 m long fc / pc - connectorized delivery fiber is fusion spliced to the mm port to facilitate connecting the photonic lanterns with other components .
the smfs are approximately 3 m in length and not connectorized .
the photonic lanterns are designed to efficiently convert the modes of the mm port into the supermodes of the smf array and vice versa .
the smf array will only support @xmath25 supermodes independent of wavelength , where @xmath25 is equal to the number of smfs .
thus , for maximum efficiency the mm port should be designed to support @xmath26 modes .
however , the number of modes supported by the mm port is wavelength dependent ( @xmath27 ) . for gnosis
the mm port is designed to support @xmath28 modes at @xmath29 with a @xmath30 core diameter , but there will be more ( fewer ) modes at shorter ( longer ) wavelengths .
the mm port parameters determine the numerical aperture ( na ) by @xcite @xmath31 equation ( [ equation : lanternna ] ) gives an na of 0.086 ( @xmath32/5.8 ) for the gnosis photonic lanterns .
we can not measure this value directly because of the delivery fiber fusion spliced to the mm port .
instead , we measured the focal ratio degradation ( frd ) in the delivery fiber and computed the mm port na from the measured output na of the delivery fiber .
we fusion spliced an amplified spontaneous emission ( ase ) source centered at 1.53@xmath0 to a randomly chosen smf .
the na of the light exiting the delivery fiber was taken to be the value that enclosed 95% of the total energy in the far - field image .
the measurement was repeated 10 times for each photonic lantern .
the na of the light exiting the delivery fiber is [email protected] on average for the 14 photonic lanterns .
the laboratory measurement of the delivery fiber frd ratio gave @xmath33/@xmath34 .
thus , the average value of the mm port na is [email protected] , which is in agreement with the estimate from equation [ equation : lanternna ] . the measured mm port na values for each photonic lantern is listed in table [ table : plmeasurements ] . for minimum loss in the mm to sm conversion
, the mm port must be fed at @xmath35 @xmath32/5.8 in order to avoid overfilling . to account for frd in the delivery fiber
the oh suppression fibers should be fed at @xmath35 @xmath32/7 to ensure the light arrives at the mm port at @xmath35 @xmath32/5.8 . at the output end of the oh suppression fibers , it is important to know the f - ratio of the beam exiting our fibers to properly interface them with the subsequent components . based on our measurements of the output photonic lanterns the beam exiting our oh suppression fibers
is @xmath1@xmath32/4.9 . at the design wavelength
, the number of modes supported by the mm port exactly matches the number of supermodes of the smf array resulting in minimum loss in the taper transition .
we determined the sm to mm throughput by splicing the 1.53@xmath0 ase source to a randomly chosen smf and measured the output power of the delivery fiber .
the measurement was repeated 10 times for each photonic lantern .
the average sm to mm throughput of the seven output photonic lanterns is [email protected] with the best throughput at 0.989 .
we measured the mm to sm throughput by injecting a beam with an na of 0.086 ( @xmath32/5.8 ) from an ase source centered at 1.53@xmath0 into the delivery fiber and collecting the power from all 19 smfs .
the average mm to sm throughput of the five measured input photonic lanterns is [email protected] .
recall previously that we found that the delivery fiber must be fed at @xmath35 @xmath32/7 to compensate for frd .
hence , in our measurement scheme we were overfilling the mm port , causing the throughput to be significantly lower than the sm to mm throughput
. however , the gnosis fore - optics unit feeds the oh suppression fibers at @xmath1@xmath32/5 and the measured mm to sm throughput gives a sense of the performance under operating conditions . for reference ,
the throughput of the photonic lanterns near the design wavelength is listed in table [ table : plmeasurements ] .
cccc input & input & output & output + mm to sm & na & sm to mm & na + throughput & & throughput & + 0.857 & 0.081 & 0.996 & 0.084 + 0.849 & 0.082 & 0.975 & 0.089 + 0.838 & 0.078 & 0.962 & 0.088 + not measured & 0.089 & 0.973 & 0.088 + 0.863 & 0.088 & 0.984 & 0.084 + 0.849 & 0.088 & 0.973 & 0.088 + not measured & 0.091 & 0.989 & 0.079 + we have only measured the throughput of the photonic lanterns near the design wavelength . in theory , the throughput of the photonic lantern depends on wavelength because the number of modes supported by the mm port depends on wavelength . in the suppression range of gnosis ( 1.471.7@xmath0 )
, the number of modes varies from 21 to 16 , ignoring dispersion . in the mm to sm conversion , the throughput is lower at the blue end because there are more modes in the mm port than smfs . in the sm to mm conversion ,
the throughput is lower at the red end because there are more smfs or supermodes than can be supported by the mm port .
thus , when two identical photonic lanterns are used back - to - back , the loss at the blue end during the mm to sm conversion and the loss at the red end in the sm to mm conversion should produce a wavelength response that is peaked at the design wavelength .
although this behavior has not been demonstrated for a symmetric photonic lantern system alone , the effect is present in an integrated oh suppression fiber .
the wavelength response of an oh suppression fiber is discussed in section 4.3 and the throughput appears to be peaked at @xmath11.53@xmath0 .
the gnosis grating unit contains seven independent oh suppression fibers .
each oh suppression fiber consists of a 1@xmath2419 input photonic lantern , 19 pairs of h1+h2 fbgs , and an output 19@xmath241 photonic lantern all fusion spliced together and arranged on a plastic tray as shown in figure [ fig : gratingunit01 ] .
the seven trays are mounted within an aluminum enclosure and padded with foam sheets .
the grating unit enclosure is mounted in a standard equipment rack within the cassegrain cage during use . in assembling the oh suppression fibers ,
all splices were carried out using a fitel s175 v.2000 fusion splicer .
cms8 to cms8 fusion splices were carried out using the standard identical smf prescription , which results in an average splice loss of @xmath10.05db .
cms8 to smf-28 fusion splices were carried out using a custom prescription , which results in an average splice loss of @xmath10.15db .
all splices are protected by splice sleeves and excess fiber is spooled into circular drums in each tray .
cms8 fiber is much lossier than smf-28 so we minimized the length of cms8 fiber as much as possible during the assembly of the oh suppression fibers .
we measured the throughputs of all seven oh suppression fibers before installation during the first commissioning run by simulating illumination by the telescope with a thorlabs s5fc1550s(p)-a2 sld source centered at 1.55@xmath0 .
the fibers were fed with a @xmath1@xmath32/5 beam by butt - coupling a mmf to the fiber using a fc - to - fc connector and the output power was measured using a thorlabs pmd100d power meter with an s122c sensor head .
the measured values are listed in table [ table : labthroughputmay2011 ] .
the average throughput of the seven oh suppression fibers is @xmath36 with a maximum and minimum of 0.61 and 0.55 , respectively .
we may compare this measurement to an estimate based on the measurements of individual components . from the cms8 to smf-28 splice loss ( 0.15db ) , cms8 to cms8 splice loss ( 0.05db ) , the average mm to sm throughput ( 0.851 ) of the input photonic lanterns at f/5.8 , the average sm to mm throughput ( 0.974 ) of the output photonic lanterns , and the average internotch throughput of the h1 ( 0.954 ) and h2 ( 0.896 ) fbgs in the range 15201640 nm , the estimated throughput of an oh suppression fiber is @xmath10.61 including fresnel reflections from the fc - to - fc connector .
additionally , we must adjust the mm to sm throughput to an @xmath32/5 input beam .
based on laboratory measurements of a single photonic lantern , the mm to sm throughput for an @xmath32/5 beam is @xmath10.25db lower than an @xmath32/5.8 beam , i.e. , 0.803 . with this adjustment ,
the estimated throughput is 0.575 , which is in agreement with the measured value for the integrated oh suppression fiber .
figure [ fig : gratingthroughputvswavelength ] shows the wavelength response of oh suppression fiber 5 .
the wavelength responses of the oh suppression fibers were measured after installation and alignment of the fore - optics unit ( see section [ section : foreoptics ] ) and iris2 interface unit ( see section [ section : iris2interface ] ) .
iris2 was used to obtain a spectrum of the dome flat lamp through the entire system with and without an oh suppression fiber .
the ratio of the two spectra gives the wavelength response of the oh suppression fiber .
the notches of the fbgs appear as significant dips in the throughput , but they are not as deep or narrow as indicated in tables [ table : h1notchtable ] and [ table : h2notchtable ] because the resolution of iris2 is not high enough to resolve these notches .
the internotch throughput is relatively high near the design wavelength of the photonic lanterns and there is some dependence on wavelength due to the linear loss of the cms8 and the wavelength - dependent loss from a symmetric photonic lantern system .
the grating unit is interfaced with the aat using a fore - optics unit that is mounted at the aat cassegrain focus .
the main function of the fore - optics unit is to re - image the central region of the aat focal plane onto an ifu and feed this light to the grating unit .
the first optical element encountered by the @xmath32/8 beam from the aat is an acquisition mirror .
the acquisition mirror is just a circular mirror with a central aperture .
the central portion of the beam passes through the aperture to the ifu while the rest of the beam is diverted to an acquisition camera . the portion of the beam that passes through the acquisition mirror is then magnified to @xmath32/265 by an optical relay consisting of a magnifying achromatic doublet lens and a doublet field - flattening lens with a pupil stop positioned in the telescope pupil plane between the two lenses .
each lens has an ar coating with a reflectance @xmath37% over the waveband from 1.0 to 1.7@xmath0 .
the beam is then captured by an ifu consisting of an array of seven hexagonal lenslets made of fused silica arranged as shown in figure [ fig : ifuslit ] .
the front face of each lenslet is polished and ar - coated .
the lenslets are glued onto a fused silica substrate , which is fixed in a mount attached to the optical relay assembly . at the ifu surface
the plate scale is 0.2@xmath7mm@xmath38 due to the magnification of the optical relay .
thus , each 2 mm flat - to - flat lenslet spans 0.4@xmath7 on the sky and has a field of view ( fov ) of 0.14arcsec@xmath39 .
the total ifu spans 1.2@xmath7 on - sky , which is about the median seeing in the @xmath6 band at siding spring observatory , and the total ifu fov is 0.97 arcsec@xmath39 .
mm@xmath38 at the ifu surface .
each 2 mm flat - to - flat hexagonal lenslet spans 0.4@xmath7 and the total ifu spans 1.2@xmath7 .
the numbering indicates the iris2 interface unit slit element connected to each ifu element.[fig : ifuslit],scaledwidth=40.0% ] each lenslet feeds an @xmath32/6.5 beam into a 50@xmath0 core diameter mmf positioned at the lenslet focus at the back of the ifu substrate .
the mmfs are approximately 5 m in length and feed a @xmath1@xmath32/5 beam to the oh suppression fibers in the grating unit , based on an frd estimate from @xcite and laboratory measurements .
the fibers are jacketed , reinforced , and bundled together in a limited - bend armoured conduit . at the ifu end
, the fibers are terminated with a glass ferrule and were attached to the substrate using a uv curing adhesive ( norland optical adhesive 61 ) prior to potting with a polyeurethane encapsulant ( opti - tec 4200 ) . during the attachment process
each fiber was individually aligned with the corresponding lenslet by maximizing the power coupled into the fiber from a test source simulating the illumination of the fore - optics by the telescope . at the grating unit end ,
the fibers are terminated in fc / pc connectors the throughput of the fore - optics unit was measured during assembly and installation by illuminating the entrance aperture with an @xmath32/8 beam from a thorlabs s5fc1550s(p)-a2 sld source to simulate illumination by the aat .
before the ifu was installed , the power at the ifu position was measured using a thorlabs pm100d power meter with an s122c sensor head and compared to the power at the entrance aperture yielding a throughput of @xmath40 for the fore - optics relay .
after the ifu was installed , a xenics xeva-1.7 - 640 camera was used to image the front and back surfaces of the ifu .
the fraction of incident power captured by each ifu element was estimated from these images , correcting for aperture losses at the array and non - uniformity in the illumination from the sld source .
comparing the input power at each ifu element , which is the fraction of incident power captured by each ifu element times the output power of the relay , to the power at the end of each fiber gives the ifu ( plus fiber bundle ) throughput of each element .
the average ifu throughput is @xmath41 .
thus , the average total fore - optics unit throughput ( relay+ifu+fiber bundle ) is @xmath10.72 .
the individual throughput of each fore - optics unit element is listed in table [ table : labthroughputmay2011 ] .
the @xmath1@xmath32/4.9 beams from the gnosis oh suppression fibers are fed to the iris2 infrared imaging spectrograph by 50@xmath0 core diameter mmfs 12 m in length . for these observations
, iris2 was positioned below the horseshoe of the telescope mount on the dome floor .
the fibers are jacketed and enclosed together in a steel coil limited bend armored conduit . at the grating unit end ,
the fibers are fc / pc - connectorized and are butt - coupled to the oh suppression fibers using fc - to - fc connectors . at the iris2 end , the fibers are terminated in a linear slit block consisting of a 7-element fused silica v - groove array from ocean optics .
the grooves are designed to hold the fibers , which have a 125@xmath0 diameter cladding , with a center - to - center spacing of 250@xmath0 .
the fibers are glued to the grooves and they are encased in epoxy with a protective casing at the back end for strain relief .
the slit block is mounted to the iris2 interface unit assembly , which sits over the iris2 dewar window .
the interface unit assembly rests on the structure usually used to attach iris2 to the telescope via kinematic mounts and includes various adjustment mechanisms to align the slit block with the slit masks in the iris2 slit wheel .
the interface unit includes an optical relay consisting of two achromatic doublet lenses with a magnification of 3 that images the fibers onto the iris2 slit plane , which is inside the instrument dewar . estimating the frd in the fiber bundle using @xcite
, we expect an @xmath1@xmath32/4 beam from the fiber in the slit block which is magnified to @xmath1@xmath32/12 and the fibers are 150@xmath0 in diameter at the slit plane .
the magnification yields a resolving power of @xmath422350 for iris2 and satisfies the maximum acceptance cone of iris2 ( @xmath32/8 ) .
no modifications were made to iris2 except the addition of custom cold stops and slit masks .
two cold stops ( @xmath32/10 and @xmath32/12 ) are available for use with gnosis .
three slit masks were made by laser drilling with a slit of seven linear 250/200/180@xmath0 diameter holes spaced 750@xmath0 apart in the same position in the spectral axis as for the standard @xmath6-offset slit wheel .
the throughput of the iris2 interface unit was measured before installation by simulating illumination by the aat .
the entire gnosis system was connected and the entrance aperture of the fore - optics unit was illuminated with an @xmath32/8 beam from a thorlabs s5fc1550s(p)-a2 sld source .
we measured the output power of each oh suppression fiber in the grating unit and the power in the slit image when the iris2 interface unit is connected to the grating unit .
the average throughput of the iris2 interface unit is [email protected] and the measured value for each element is listed in table [ table : labthroughputmay2011 ] .
there are additional losses from the alignment of the slit block with the slit mask .
even with perfect alignment , low - level aberrations will result in a loss of a few percent depending on the size of the slit mask holes and the focal ratio out of the fibers in the slit block .
first , focus was adjusted with the dome flat lamp until the central fiber spot image had an fwhm of @xmath43pixels .
next , tip - tilt was adjusted followed by an alignment of the central fiber to within 0.1pixels of the central slit mask hole . then , in - plane rotation was adjusted until the position of the outer fiber images are within 0.1pixels of each other .
the central fiber was again aligned to the central slit mask hole .
lastly , small translational adjustments were then made to maximize the throughput .
the throughput numbers vary from alignment to alignment , but it was typically above 90% and around 97% for the central fiber with the 250@xmath0 slit .
there was a noticeable drop by a few percent in the throughput away from the central fiber , indicating that the magnification of the relay is slightly too large .
this was confirmed by comparing the difference between the spot positions and the slit mask hole positions for all seven fibers . in calculations
we assume an average throughput of 0.95 for slit alignment .
ccccc sky pos & fore - optics & grating unit & iris2 interface & overall + n & 0.790 & 0.612 & 0.91 & 0.38 + wnw & 0.727 & 0.579 & 0.93 & 0.35 + wsw & 0.849 & 0.563 & 0.93 & 0.37 + c & 0.752 & 0.596 & 0.93 & 0.42 + ene & 0.752 & 0.583 & 0.93 & 0.43 + ese & 0.548 & 0.551 & 0.92 & 0.42 + s & 0.605 & 0.551 & 0.93 & 0.31 + average & 0.718 & 0.576 & 0.93 & 0.38 +
we summarize the on - sky performance of gnosis below .
an in - depth analysis of the on - sky performance of gnosis may be found in @xcite .
gnosis was commissioned at the aat over five separate observing runs spread over the months of march , may , july , september , and november of 2011 .
initially , the fore - optics unit was connected to the grating unit by butt - coupling with fc - to - fc connectors . from the may commissioning
run onward , the fore - optics unit was fusion spliced directly to the oh suppression fibers within the grating unit .
the system was configured to maximize the throughput of central sky fiber . with the remaining fibers we maximized the average throughput of the system by connecting the highest throughput fibers with each other . however , this results in greater fiber - to - fiber throughput variation . in most observations
one fiber was configured to bypass the grating unit to serve as a control fiber without oh suppression .
the data reduction procedure is similar to the procedure described in @xcite .
spectroscopic observations were made with the @xmath6 broadband filter , @xmath32/12 coldstop , and the slit mask with 180 or 250@xmath0 diameter holes in multiple - read mode ( mrm ) . in mrm , the detector read noise is minimized ( @xmath18@xmath44 ) because the 1024@xmath241024 rockwell hawaii-1 detector is non - destructively read out during the exposure and the final image is a linear least - squares fit through all the reads .
the detector dark current is @xmath10.0015@xmath44 s@xmath38 .
each image was corrected for detector non - linearities and the spectrum in each fiber was extracted using `` gaussian summation extraction by least squares '' from @xcite .
each spectrum was corrected for fiber - to - fiber throughput variations measured from observations of the dome flat lamp .
the dome flat lamp spectrum in each fiber was extracted and integrated .
the values were normalized to the mean value of all seven fibers to give the fiber - to - fiber throughput variation .
the measured fiber - to - fiber variation is consistent with the laboratory values listed in table [ table : labthroughputmay2011 ] .
the wavelength calibration for each fiber was determined from a xenon arc lamp observation .
the arc lamp spectrum in each fiber was extracted and the pixel position of each xenon line was fit by a cubic polynomial .
the spectra were also corrected for inter - quadrant cross - talk @xcite because the spectra span two quadrants of the iris2 detector . in each spectrum ,
the counts at wavelengths below the @xmath6 filter cutoff ( 1.5@xmath0 ) come from the detector . after correcting for detector dark current ,
the median count rate at @xmath45 was subtracted from the spectrum .
the final correction we applied to all observations was an instrument response correction , which corrects for the variation in throughput with wavelength .
the instrument response was measured from a0v standard star observations .
the spectrum in each fiber was extracted and reduced as discussed above .
then the instrument response for each fiber was taken to be the sky - subtracted spectrum divided by a model spectrum of vega @xcite normalized to the median value in the range 1.51.69@xmath0 .
the average throughput of gnosis ( fore - optics + grating unit + iris2 relay ) was measured to be @xmath10.38 in a laboratory setting at 1.55@xmath0 ( see table [ table : labthroughputmay2011 ] ) . on - sky
, we must include the additional losses from the telescope , the slit block alignment , the iris2 spectrograph , and aperture losses for a point source .
the throughput of the aat is @xmath10.88 including reflections from the two mirrors and extra loss for the accumulation of dirt on the mirrors .
the throughput of iris2 is @xmath10.12 @xcite . for the median seeing of 1.2@xmath7 ,
the aperture loss is approximately 0.30.5 for a point - source offset between 00.6@xmath7 from the center of the hexagonal array @xcite .
thus , the end - to - end throughput of our system was expected to be @xmath10.04 for a diffuse source and @xmath10.018 for a point source with typical aperture losses .
we measured the end - to - end throughput of the system from observations of a0v stars taken during the september commissioning run , which had the best observing conditions .
the spectra were combined by summing each spectral pixel , neglecting the difference in the wavelength calibration of each fiber ( less than 1.5pixels over most of the detector ) .
the combined spectrum of the a0v star was divided by a model vega spectrum scaled to the appropriate brightness and assuming a value for the aperture losses .
the @xmath46-band seeing was measured to be @xmath11.5@xmath7 .
although we are only able to estimate the aperture losses for this seeing , the a0v star observations were consistent with a throughput of @xmath10.020.04 in agreement with the expected value from laboratory measurements . , scaledwidth=45.0% ]
the oh suppression performance of gnosis was measured from observations of blank sky .
a total of 45 blank sky observations were taken during the september run at various locations on the sky .
the exposure time of these observations was either 15 or 30 minutes .
the instrument thermal background is significant in gnosis observations and a separate thermal background subtraction must be applied to blank sky observations .
cold frames , observations where the fore - optics unit was removed and pointed at a container of liquid nitrogen , were obtained with the same exposure time as the blank sky observations .
figure [ fig : cold ] shows the smoothed cold frame spectrum from the central gnosis fiber .
alternatively , we may fit a thermal blackbody spectrum to the continuum points in between the oh lines @xmath47 and subtract the best - fitting model from our spectrum .
figure [ fig : skyspec ] shows the cold - subtracted blank sky spectrum from six suppressed fibers and the control fiber from 8.75hr of observations from 2011
september 1 to 4 .
these 21 blank sky observations were made after moonset and are all @xmath35 60@xmath8 from the moon .
the spectra were flux - calibrated assuming an efficiency of 3.3% .
the strong suppression of the oh lines in the range 1.51.7@xmath0 is evident .
the suppression factor was measured for approximately half the lines and 78% meet or exceed the target specifications .
the other lines that do not meet the target specifications mostly correspond to fbg notches that are too narrow to suppress the entire doublet .
the fbgs are designed based on the doublet separations found in the oh line model of @xcite .
the notches that do not meet the target specification have a much wider doublet separation according to @xcite .
the doublet mean is the same , but the fbg notch is not wide enough to suppress the doublet according to @xcite .
an example is shown in figure [ fig : abrams ] for the 31 q1(4.5 ) transition , which shows the @xcite values in red and the @xcite values in blue .
, scaledwidth=45.0% ] nevertheless , this is a clear demonstration that fbgs can cleanly remove oh lines while maintaining relatively high throughput between the lines .
the integrated background in the range 1.51.7@xmath0 was reduced by a factor of @xmath18 , but there was no significant reduction in the interline background as predicted by @xcite .
this is unexpected given that @xcite recently found that scattered oh dominates the interline background in their @xmath6-band spectrum .
the blank sky observations made with gnosis thus far are detector noise - dominated in the interline regions .
the faintness of the interline background and low system throughput of our current configuration requires 30 minute exposures for an interline background of @xmath110adu per pixel , which corresponds to @xmath145@xmath44 per pixel . of this , approximately 27@xmath44 per pixel are from the detector dark current and the other 18@xmath44 per pixel are from the sky .
thus , the detector s 8@xmath44 per pixel read noise gives @xmath117% uncertainty in the interline background .
thus , it is possible that our oh suppression fibers are reducing the interline background , but we were unable to observe the reduction of the low interline signal among the detector noise .
alternatively , there may be no reduction because of physical sources , but it is impossible to tell without observations that are not detector noise - dominated .
the sensitivity of gnosis was measured from an observation of a low surface brightness galaxy hizoa j0836 - 43 ( @xmath6-band surface brightness of 17.3magarcsec@xmath39 ) .
the galaxy is larger than the gnosis fov and the unknown aperture losses were not an issue .
the sky - subtracted spectrum was divided by the square root of the non - subtracted spectrum to obtain the signal to noise per pixel .
the median signal to noise per pixel was @xmath110 for a 30 minute exposure . the same analysis on the spectrum through the control fiber yields the same result , surprisingly indicating that there was no improvement in signal to noise per pixel when using gnosis oh suppression .
this is because oh suppression mainly improves the signal to noise near the oh lines . in between the lines ( the region that dominates the sensitivity calculation ) the reduction in the background was much smaller than expected
in this paper , we have given a thorough description of each subsystem of gnosis , the first instrument to use fiber bragg grating oh suppression fibers .
these fibers were designed to demonstrate a reduction of the interline background increasing sensitivity by a factor of 40 or more when suppressing the brightest oh doublets in the @xmath6-band .
the line spread function of iris2 shows that the spectrograph s diffraction grating scatters light many pixels from the line center and simulations show that the cumulative contribution from multiple lines leads to a continuum of scattered light that dominates the interline background @xcite .
if the emission lines are suppressed before the light has the opportunity to be scattered by the spectrograph , the continuum of scattered light and therefore the interline background will be reduced . with the oh lines corresponding to @xmath48 transitions from @xcite shown by the dashed blue lines .
these @xmath48 lines were not suppressed by design based on their relative strengths in @xcite but they match up well with the residual features in the spectrum.[fig : abramsr],scaledwidth=45.0% ] to demonstrate this effect , we carried out observations of blank sky with gnosis at the 3.9 m aat with the iris2 spectrograph .
although the oh suppression fibers successfully suppressed most of the brightest oh doublets in the range 1.51.7@xmath0 at the target level or greater and reduced the integrated background by a factor of @xmath110 , the spectra showed no significant reduction in the interline background and thus the same median signal to noise per pixel when compared to a control fiber without oh suppression . a reduction in the interline background and the associated increase in sensitivity would led to oh suppression fibers having an impact on astronomy at the level of adaptive optics or greater . therefore , it is critically important to identify why no reduction was observed in these experiments and determine if improvements can be made to realize the full benefit of oh suppression .
only observations that are detector noise - dominated have been made with oh suppression fibers .
if no interline background reduction is seen in oh - suppressed observations that are not detector noise - dominated it would indicate either oh suppression fibers do not suppress scattered light or the atmosphere is more complex than modeled by @xcite .
specifically , the oh spectrum may be different than the model of @xcite used to design the fbgs , which would result in poor suppression .
we have presented evidence of this above and poorly suppressed lines such as these would scatter more light into the interline regions .
alternatively , there may be unaccounted for atmospheric continuum sources from other molecular species that creates a continuum floor .
it may also be possible that the unsuppressed oh lines are not as weak as indicated by @xcite and they scatter more light into the interline regions . as evidence , we found that the @xmath48 transitions found in @xcite match up well with residual features in our oh - suppressed spectrum of the sky as seen in figure [ fig : abramsr ] .
these doublets according to @xcite are stronger than indicated by @xcite and would contribute more scattered light to the interline region .
the evidence that inaccuracies in the fbg design because of inaccuracies in the oh line model of @xcite , which may result in more scattered light in the interline region than expected , is certainly suggestive . however , this is based on the assumption that oh suppression fibers suppress scattered light , which has yet to be demonstrated .
thus , it is critically important that the next step be a clear demonstration of scattered light suppression with observations that are not detector noise - dominated .
such observations require that the interline signal is greater and/or the detector noise is lower . in general , this may be accomplished by increasing the brightness of the source , increasing the throughput of the system and/or utilizing a low - noise detector
. the system throughput may be increased mostly significantly by optimizing the oh suppression fibers and/or the spectrograph .
presently , without first demonstrating that oh suppression fibers suppress scattered light , fabricating optimized fibers would be difficult to justify .
thus , @xcite suggested that pairing gnosis with a fiber - fed spectrograph with a high efficiency volume phase holographic ( vph ) grating is the best way to go about improving system throughput . if a high - performance detector , a 1.7@xmath0 cutoff hawaii-2rg for example , were included the spectrograph would simultaneously increase throughput and lower detector noise , which would be ideal for oh - suppressed observations of blank sky .
the australian astronomical observatory has plans to build such a spectrograph called praxis for further testing of oh suppression fibers on - sky by early 2014 @xcite .
however , for the purpose of demonstrating scattered light suppression , observations of blank sky are not ideal because the sky spectrum may be considerably more complex than the spectrum the fbgs are designed to suppress .
thus , the ideal source would be an oh line source in the laboratory , such as that created by @xcite .
this would remove any complications from additional atmospheric sources , but the weaker suppressed oh lines are still present .
alternatively , scattered light suppression may also be demonstrated with a single emission line from a bright arc lamp ( xenon has at least one line at 1.6733@xmath0 that coincides with one of the fbg notches ) .
these observations only require gnosis and the iris2 spectrograph without any telescope , which is advantageous because they do not require building a new spectrograph . regardless of whether or not oh suppression fibers can be used to reduce the interline background and increase sensitivity , they provide real benefits for observations at low resolving powers ( 500@xmath493000 ) , which was shown by @xcite using observations of [ ] emission lines in seyfert galaxies and ch@xmath50 absorption in brown dwarfs .
previously , observations at these resolving powers have been too low to resolve out the oh lines , but that is no longer necessary with oh suppression fibers .
the performance of the oh suppression fibers is very good , but there is room for improvement especially the throughput .
the biggest single loss in the oh suppression fibers comes from mm to sm conversion of the input photonic lantern .
the beam feeding the delivery fiber of the input photonic lanterns is @xmath1@xmath32/5 and we argued in section [ section : photoniclantern ] that the oh suppression fibers must be fed at @xmath35 @xmath32/7 to avoid overfilling the mm port ( @xmath32/5.8 ) of the 1@xmath2419 photonic lanterns .
thus , the mm to sm conversion throughput will increase if we slow the beam feeding the oh suppression fiber from @xmath32/5 to @xmath32/7 . for a back - to - back system with 1@xmath2419 photonic lanterns , the total throughput increases by @xmath10.5db ( 11% ) when slowing the input beam from @xmath32/5 to @xmath32/7 @xcite .
however , doing so will decrease the fiber s fov . by conservation of tendue ,
the product of the fiber fov on - sky and the telescope diameter is proportional to the product of the fiber input na and the fiber core diameter .
therefore , it is not possible to underfill the photonic lantern mm port by reducing the core diameter or input na without sacrificing the fiber s fov . as an alternative to slowing the input beam from @xmath32/5 to @xmath32/7 to avoid overfilling the mm port
, we may increase the mm port na to match the input @xmath32/5 beam .
if we keep the core diameter fixed , this corresponds to increasing @xmath25 , the number of smfs in the photonic lantern . based on equation ( [ equation : lanternna ] ) an mm port na of 0.12 ( the @xmath32/5 beam arrives at the mm port at @xmath32/4.2 due to frd ) with @xmath30 corresponds to @xmath51 .
thus , a back - to - back system with 1@xmath2437 photonic lanterns fed at f/5 would be equivalent to a system with 1@xmath2419 photonic lanterns fed at @xmath32/7 and should yield a similar increase in throughput over the current configuration .
the wavelength - dependent loss of a symmetric photonic lantern system may be addressed by designing the mm port of the input and output photonic lanterns to have different nas .
if @xmath25 is the number of smfs then the mm port of the input photonic lantern should be designed to support @xmath52 modes at the blue end of the suppression range .
as @xmath53 there will be @xmath54 modes at the red end of the suppression range and no penalty will be incurred in the mm to sm conversion at any wavelength .
the mm port of the output photonic lantern should be designed to support @xmath55 modes at the red end of the suppression range , which would correspond to @xmath56 modes at the blue end of the suppression range .
thus , in the sm to mm conversion , none of the modes will be lost at any wavelength .
photonic lanterns with large @xmath25 are very cumbersome to handle and the gnosis grating unit is rather bulky and heavy ( 100 kg ) .
a significant reduction in size and weight may be possible with oh suppression fibers consisting of fbgs printed in multi - core fibers ( mcfs ) with each end tapered down into an mmf .
@xcite demonstrated such a device with an mcf containing @xmath1120 cores within a 230@xmath0 cladding and a single notch .
mcfs with 37 cores can be manufactured and it should be a simple matter to taper down each end of the mcf into a 50@xmath0 mmf following a similar process for the manufacturing of the photonic lanterns .
in addition to the reduction in size and weight no splices would be required boosting the throughput by @xmath10.35db ( 8% ) .
assuming complex refractive index modulations can be imprinted into each mcf core with the same level of performance as the current gnosis fbgs and incorporating all the suggestions above would result in a throughput of at least @xmath10.73 .
these next - generation oh suppression fibers are currently under development @xcite . thus far we have discussed improvements to the oh suppression fibers themselves but the other subsystems also require optimization .
retrofitting gnosis to the existing iris2 spectrograph was acceptable for an initial demonstration of oh suppression fibers , but a fiber - fed spectrograph like praxis would be ideal for future science observations . in the current configuration ,
the instrument thermal background is high ( see figure [ fig : cold ] ) and emanates almost entirely from the slit block of the iris2 interface unit reducing the sensitivity of observations .
a spectrograph with a vacuum feed - through would make the iris2 interface unit unnecessary and significantly reduce the thermal background .
also , it would reduce the number of optical surfaces and there would be no slit block alignment errors , which would increase the system throughput by @xmath115% in addition to the increase in throughput due to the high efficiency vph grating and the increase in sensitivity due to the high performance detector .
oh suppression fibers have the potential to significantly expand our window to the universe from the ground if their suppression of scattered light can be confirmed and the atmosphere does not contain bright continuum sources that are un - filterable .
nevertheless , these fibers provide real benefits for spectroscopic observations at low resolving powers and optimized systems utilizing these types of fibers are very feasible .
the gnosis team acknowledges funding by arc lief grant le100100164 .
we thank the referee for providing insightful comments and suggestions which have greatly improved this paper .
c.q.t . gratefully acknowledges support by the national science foundation graduate research fellowship under grant no .
thanks stuart gilchrist , stuart jackson , rene pelton , billy robbins , andrew sheinis , and tim white . | arxiv |
Mechanism of Oxymercuration-Demercuration reaction
I am trying to write a mechanism for OMDM reaction.
I could write the mechanism for oxymercuration part of reaction but I couldn't write the mechanism for remaining part (demercuration) of the reaction. Could anybody help me to proceed forward.
Here is the mechanism I wrote out for you[](https://i.stack.imgur.com/rovnB.png)
Actually, the oxymercuration involves the formation of a cyclic carbocation. This is a non traditional carbocation, but the final reaction becomes non-stereospecific, as you will later find out.
1. First, the mercuric acetate breaks apart into ions, the acetate anion, and the mercuroacetic cation, which you have correctly depicted.
2. In the next step, the mercuroacetic cation gets added on to the double bond, which forms a cyclic cation like this:
(Don't bother about the red arrow for now, we'll come to it in the next step.)
3. Now, water adds on to the carbocation formed from the other side, and this process follows Markownikoff's rule. Now, one $\ce{H+}$ leaves, and a result, we get exactly what you got in your last step. This is, as you called it, the end of the oxymercuration step.
4. Now, for the demercuration part, we can use any reducing agent that will be able to replace the mercuroacetic cation with $\ce{H}$. (E.g. $\ce{NaBH4}$). This essentially demercurates the product, forming an alcohol.
The entire process is shown here:
.
Now, as it is written here, the addition of the mercuroacetic cation followed by water will be anti addition, but when the reducing agent is used, the hydrogen can be added from either side. As a result, we get a non-stereospecific product. In short, this can also be written as addition of just $\ce{H}$ and $\ce{OH}$ without rearrangements, which followed Markownikoff's rule. In fact, the formation of the cyclic carbocation prevents rearrangements, hence enabling chemists to get desired products without worrying about random stabilisations of the carbocations.
| stackexchange/chemistry |
acanthamoeba species may remain viable for many years in environment , even under adverse conditions ( 1 ) .
are reservoirs and vehicles for the spread of bacteria and this may lead to risks to public health ( 3 ) . furthermore , acanthamoeba may act as carriers of cryptosporidium oocysts ( 4 ) .
infection occurs after ingestion of tissue cysts or contact with soil or water contaminated with oocysts ( 5 ) .
several water - borne outbreaks of toxoplasmosis have been documented ( 69 ) and in one instance viable toxoplasma gondii oocysts were found in drinking water ( 9 ) .
further , internalized oocysts were not digested to a significant extent and retained their ability to establish infection in mice ( 10 ) .
several studies for the recovery and detection of t. gondii oocysts in contaminated water have been published by different working groups ( 1114 ) .
worldwide loop mediated isothermal amplification ( lamp ) had been utilized for a broad spectrum of applications in the biomedical field including the detection of viruses , bacteria , fungi and parasites ( 15 , 16 ) .
however , there are few publications about investigating of toxoplasma in water ( 1719 ) .
the advantage of lamp method for the detection of t. gondii have highlighted and demonstrated in some publications ( 14 , 16 , 2025 ) .
lamp method was used successfully for detection of cryptosporidium and giardia in water samples in our previous study ( 26 ) .
determination of these parasites distribution in water resources could assessment the risk of water - borne outbreaks and could be an effective tool for monitoring and preventing of water - borne parasitic outbreaks .
detection of parasites in water is difficult too , so the present study designed to investigate the water - borne parasites , acanthamoeba and toxoplasma in the same aquatic environments .
there is no study about toxoplasma in iranian water sources , therefore in present study , for the first time lamp method was used for detection of toxoplasma in the river water samples from guilan province in iran .
guilan has a humid temperate climate with plenty of annual rainfall and is known for its moderate , mild , and mediterranean - like climate .
the sefidrood is a river approximately 670 kilometers long , rising in guilan and flowing generally northeast to meet the caspian sea .
zarjoob and goharrood rivers are two branches of sefidrood river that across rasht city and finally meet bandar - e anzali lagoon .
many pollutants as rural , urban and animals raw sewage threaten water supplies in cities of guilan ( 27 ) .
all rivers investigated in present study have different uses including agriculture , industry , residential and recreational activities .
thirty four water samples were collected during 2009 to 2010 from the river waters in guilan province ( north of iran ) .
some of the sampling sites chosen for sampling in this study were along the sefidrood river , in different cities of guilan ( fig .
1 ) , and some samples collected from others surface waters including rivers , dams and lagoons in guilan ( table 1 ) .
map of guilan and study area frequency of
acanthamoeba
cysts and
toxoplasma
( oo)cysts in surface water samples of guilan province , iran from each sampling point , one to three water samples were collected in 500 ml sterile bottles for acanthamoeba and 5 liters for toxoplasma .
after sampling , the samples transferred to the laboratory of protozoology , department of parasitology and mycology , school of medicine , shahid beheshti university of medical sciences , tehran , iran for the study of acanthamoeba by pcr .
the lamp method was used for the detection of toxoplasma dna in the laboratory of medical and molecular parasitology at the medical school of the university of cologne , germany . for the isolation of acanthamoeba species ,
approximately 500 ml of the collected water samples were filtered through cellulose nitrate membrane with pore size 0.45 m .
the filters were transferred on non - nutrient agar plates seeded with gram - negative bacteria ( escherichia coli ) as a food source according to our previous study ( 28 ) .
plates were incubated at room temperature and after 3 days they were microscopically examined for the presence of acanthamoeba cysts or trophozoites . in the absence of amoebae , plates were monitored up to 14 days .
acanthamoeba were identified at the genus level , based on morphological characteristics of trophozoites and cysts using light microscopy . for toxoplasma , 5
l environmental water samples were filtrated through membrane filters ( diameter 142 mm ) with a pore size of 1.2 m by means of a vacuum device .
sediment material washed and centrifuged at 1500 g for 15 min . for the removing of particles ,
this process was repeated two times and particles concentrated by centrifugation at 3000 g for 10 min . the sedimented pellet ( 12 ml , depending on water turbidity ) was subjected to sucrose flotation , then the supernatant was subject to dna extraction ( 29 ) .
dna was extracted using the qiaamp dna mini kit ( qiagen gmbh , hilden , germany ) , according to the manufacturer s description , with a modification of lyses solution with 15 freeze
dna was eluted in 100 l elution buffer of the kit used for the lamp analysis ( 25 , 26 ) .
the acanthamoeba specific primer pairs jdp1 ( 5-ggcccagatcgtttaccgtgaa ) and jdp2 ( 5-tctcacaagctgctagggagtca ) as described by schroeder et al .
( 2001 ) ( 30 ) were used for the amplification of the 500 bp of 18s rdna gene ( 31 ) and standard pcrs performed as described in our previously paper ( 28 ) . the emerging method called lamp has not only become common currency for the detection of toxoplasma gondii dna .
the method is highly specific , efficient , simple and rapid and the amplification runs under isothermal conditions .
no specialized heating equipment is required and the amplification of the target is completed within 60 min ( 15 , 16 , 32 ) .
the positive reaction can be visualized either by naked eyes because of the white magnesium pyrophosphate precipitation in the test tube , or by performing the gel electrophoresis ( 33 ) .
a primer set used to detect the toxoplasma b1 gene by lamp method as previously described ( 14 ) .
the results were visualized with uv radiation ( pci - gel - imager , intas , gttingen , germany ) . for each reaction , a positive control [ toxoplasma non virulent strain ( ahc1 ) , national research center protozoan diseases , obihiro university for agriculture and veterinary medicine , japan ] and negative control ( double distilled water ) were included ( 25 ) .
guilan has a humid temperate climate with plenty of annual rainfall and is known for its moderate , mild , and mediterranean - like climate .
the sefidrood is a river approximately 670 kilometers long , rising in guilan and flowing generally northeast to meet the caspian sea .
zarjoob and goharrood rivers are two branches of sefidrood river that across rasht city and finally meet bandar - e anzali lagoon .
many pollutants as rural , urban and animals raw sewage threaten water supplies in cities of guilan ( 27 ) .
all rivers investigated in present study have different uses including agriculture , industry , residential and recreational activities .
thirty four water samples were collected during 2009 to 2010 from the river waters in guilan province ( north of iran ) .
some of the sampling sites chosen for sampling in this study were along the sefidrood river , in different cities of guilan ( fig .
1 ) , and some samples collected from others surface waters including rivers , dams and lagoons in guilan ( table 1 ) .
map of guilan and study area frequency of
acanthamoeba
cysts and
toxoplasma
( oo)cysts in surface water samples of guilan province , iran from each sampling point , one to three water samples were collected in 500 ml sterile bottles for acanthamoeba and 5 liters for toxoplasma .
after sampling , the samples transferred to the laboratory of protozoology , department of parasitology and mycology , school of medicine , shahid beheshti university of medical sciences , tehran , iran for the study of acanthamoeba by pcr .
the lamp method was used for the detection of toxoplasma dna in the laboratory of medical and molecular parasitology at the medical school of the university of cologne , germany .
for the isolation of acanthamoeba species , approximately 500 ml of the collected water samples were filtered through cellulose nitrate membrane with pore size 0.45 m .
the filters were transferred on non - nutrient agar plates seeded with gram - negative bacteria ( escherichia coli ) as a food source according to our previous study ( 28 ) .
plates were incubated at room temperature and after 3 days they were microscopically examined for the presence of acanthamoeba cysts or trophozoites . in the absence of amoebae , plates were monitored up to 14 days .
acanthamoeba were identified at the genus level , based on morphological characteristics of trophozoites and cysts using light microscopy . for toxoplasma , 5
l environmental water samples were filtrated through membrane filters ( diameter 142 mm ) with a pore size of 1.2 m by means of a vacuum device .
sediment material washed and centrifuged at 1500 g for 15 min . for the removing of particles ,
this process was repeated two times and particles concentrated by centrifugation at 3000 g for 10 min .
the sedimented pellet ( 12 ml , depending on water turbidity ) was subjected to sucrose flotation , then the supernatant was subject to dna extraction ( 29 ) .
acanthamoeba dna was extracted by phenol chloroform method according our previously published article(28 ) . for toxoplasma oocysts ,
dna was extracted using the qiaamp dna mini kit ( qiagen gmbh , hilden , germany ) , according to the manufacturer s description , with a modification of lyses solution with 15 freeze
dna was eluted in 100 l elution buffer of the kit used for the lamp analysis ( 25 , 26 ) .
the acanthamoeba specific primer pairs jdp1 ( 5-ggcccagatcgtttaccgtgaa ) and jdp2 ( 5-tctcacaagctgctagggagtca ) as described by schroeder et al .
( 2001 ) ( 30 ) were used for the amplification of the 500 bp of 18s rdna gene ( 31 ) and standard pcrs performed as described in our previously paper ( 28 ) . the emerging method called lamp has not only become common currency for the detection of toxoplasma gondii dna .
the method is highly specific , efficient , simple and rapid and the amplification runs under isothermal conditions .
no specialized heating equipment is required and the amplification of the target is completed within 60 min ( 15 , 16 , 32 ) .
the positive reaction can be visualized either by naked eyes because of the white magnesium pyrophosphate precipitation in the test tube , or by performing the gel electrophoresis ( 33 ) .
a primer set used to detect the toxoplasma b1 gene by lamp method as previously described ( 14 ) .
the results were visualized with uv radiation ( pci - gel - imager , intas , gttingen , germany ) . for each reaction , a positive control [ toxoplasma non virulent strain ( ahc1 ) , national research center protozoan diseases , obihiro university for agriculture and veterinary medicine , japan ] and negative control ( double distilled water ) were included ( 25 ) .
totally 30 ( 88% ) and 2 ( 5.8% ) out of 34 samples were positive for acanthamoeba and toxoplasma respectively .
although waterborne parasites , acanthamoeba and toxoplasma have been reported by some researchers , this is the first study to investigate these two parasites in same samples . because of the predatory activities of different eukaryotic organisms present in aquatic environments
, they may serve as potential vectors and paratenic hosts for the environmental transmission of enteric diseases ( 34 , 35 ) .
therefore establishment of sensitive method for detection of these water - borne parasites are necessary in iran .
t. gondii oocysts have been detected in contaminated water by lamp method in other countries ( 25 ) .
amoebae did not decrease the infectivity and pathogenicity of t. gondii oocysts ( 10 ) .
free - living amoebae are resistant to unfavorable living conditions encountered in nature and to most disinfectants used in the treatment of waters , so they could be resistant ( 3 , 36 ) .
acanthamoeba spp . was the causative agent of an outbreak associated with a contaminated municipal water supply in the usa and free - living amoeba has been commonly found in various environmental water sources throughout the world ( 3741 ) , similar to other studies in iran ( 42 , 43 ) .
acanthamoeba was prevalent in water samples of the study areas and as the results show in the present study acanthamoeba species find more prevalent than another parasite , so could easily uptake toxoplasma oocysts . therefore may have implications for water quality and public health and may have role in transmission of toxoplasma in the study area .
the present study reveals that the investigated water supplies , which are used for agriculture and camping and some time used by animals , are contaminated by toxoplasma and acanthamoeba species .
zarjoob river was the most pollutant river in study area that was contaminated with both parasites ( table 1 ) .
it may because of these surface waters are contaminated more with urban and rural sewages .
free - living amoebae as acanthamoeba may act as carriers of cryptosporidium and toxoplasma oocysts and , thus , may play an important role in the transmission of cryptosporidiosis and toxoplasmosis ( 4 , 10 ) . in other hand
it has also been suggested that the ingestion of oocysts by free - living protozoa and rotifers may have beneficial effects in aquatic ecosystems , such as wastewater treatment systems , as the removal of oocysts would minimize the release of the oocysts into environmental waters from sewage ( 44 ) .
free - living amoebae may be regarded as a potential source of toxoplasma oocycts in the study area .
they may play an important role in the water - borne transmission of toxoplasmasis in iran .
in addition , additional analysis of isolates is needed to confirm the presence of genotypes , which are infectious to humans .
this is the first report of toxoplasma oocysts in water samples of iran detected by lamp method .
the method is effective for detection of these water - borne parasites in treated and untreated water samples . it could be used for prevention and hygienic programs
this study can also serve as a platform for further investigations and researches of water sources in iran . | pubmed |
the response of nanomaterials to alternating electromagnetic fields is of great importance nowadays in the biomedical field , where new approaches to treat diseases are under development
. one of the most innovative and important applications is related to heat delivery through the interaction of nanomaterials with electromagnetic fields .
this heat delivery method can be used to release drugs@xcite , activate biological processes@xcite and even treat tumors@xcite . indeed , using maxwell s equations and
the first law of thermodynamics one finds that the heat loss per unit volume per cycle is given by @xmath0 where @xmath1 is the nanomaterial volume , @xmath2 is the heat loss , @xmath3 the electric field , @xmath4 the free volumetric density current , @xmath5 the electric polarization , @xmath6 the vacuum magnetic permeability , @xmath7 the magnetization and @xmath8 the magnetic field .
the first term in equation correspond to the `` free - current '' loss , whereas the last two describe dielectric and magnetic losses .
moreover the `` free - current '' loss term has an important impact on the biomedical application since it is related to a biological constraint .
this term states that the frequency ( @xmath9 ) and magnitude of the alternating magnetic fields need to be lower than a critical value in order to inhibit possibly harmful ionic currents in the patient s body@xcite .
for instance , for a frequency of 100 khz the maximum field amplitude is in the order of @xmath10 ( @xmath11 ) for a single air - core coil radius of @xmath12 ( expected dimension for breast cancer application@xcite ) .
note that this value is higher than the one usually reported ( order of @xmath13 ) only because the estimation of atkinson used a coil radius of @xmath14 . since the free current loss is proportional to the square of the distance from the coil axis , an estimation of the critical field for a given coil radius ( @xmath15 )
might be obtained from @xmath16 .
figure [ figure1 ] shows the biological critical field as a function of field frequency in the usual therapeutic hyperthermia range using atkinson s criteria@xcite , which indicates that the higher the frequency the lower is this field ( the parameters used to generate the curve are presented in the figure captions ) . on the other hand , the last terms of eq . , which represent hysteretic losses ,
has been the subject of analytical models within the linear response theory ( lrt ) and was used to estimate optimal particle size , understand particle - particle interaction effects and maximum heat generation for hyperthermia@xcite .
curiously , most lrt studies from the literature do not discuss a fundamental limitation of the model , namely , that it is only valid at the low particle size range and low field amplitudes . in fig.[figure1
] we show the range of validity of the lrt , which , as can be seen , is far below the typical fields used for hyperthermia studies .
there are several suggestions for identifying this limit .
for example , carrey et al.@xcite found that the hysteresis area for a longitudinal case ( field applied parallel to the easy axis - see fig .
5(g ) of ref .
@xcite ) deviates from the lrt for @xmath17 ( @xmath18 - where @xmath19 is the saturation magnetization , @xmath20 is the boltzmann constant and @xmath21 is the temperature ) , which suggests that this model can only be applied for particles below a critical size . alternatively ,
verde et al . suggested that deviations occurs for fields @xmath22(@xmath23 is the anisotropy field , that for uniaxial case is @xmath24 with @xmath25 the anisotropy constant)@xcite .
it is important to emphasize that experimentally , it is possible to determine if one is still in the linear regime or not , by verifying if the the heating efficiency ( also known as specific loss power - slp ) scales quadratically with the field . throughout this manuscript , when discussing the theoretical models , low magnetic fields mean values within the lrt range .
in addition , in fig . [ figure1 ] we also include an estimation of the range of validity of the nonlinear response model ( nlrt ) developed in this work , which will be shown later in the manuscript to be @xmath26 .
this corresponds to a 7-fold increase in the range of field validity in comparison to the lrt definition used above .
the result suggests that the model may be useful for biomedical applications , in particular for magnetic hyperthermia . in the subject of heat loss ,
the term `` nonlinear '' has been used in a variety of ways .
for instance , nonlinear dielectric effects have been related to the correlation of distinct relaxation times@xcite . in this case , a superposition of debye processes is used , which predict heat loss scaling with the square of field amplitude .
conversely , for relaxor ferroelectric materials a nonlinear polarization term is included in the dynamic response equation@xcite .
such approach allowed the authors to investigate the third harmonics of the relaxor . on the other hand , in magnetic materials ,
nonlinear response is investigated using the stochastic landau - lifshitz - gilbert ( sllg ) equation@xcite . in this case ,
thermal fluctuations are addressed using the brown s approach@xcite , where the giant spin hypothesis allow one to use the fokker - planck equation to the magnetic moment orientational distribution function .
one can then show that this leads to an infinite hierarchy of equations , which can be solved numerically to find the magnetic moment response of the nanoparticle @xcite .
the method is valid for any field amplitude , but due to its mathematical complexity , it does not yield simple analytical expressions that could be useful in the applied field . indeed , the field and frequency - dependence of heat loss in magnetic materials have been attracting the attention for a long time due to technological applications @xcite . in general
, the loss in magnetic materials can show several contributions , spanning from eddy currents ( that scales with @xmath27 ) , anomalous eddy current con- tributions ( due to complex domain wall dynamics which scales with @xmath28 ) up to multidomain magnetichys- teresis contribution .
the later term can be explained us- ing the rayleigh correction to the magnetic permeability and reveals a power loss scaling with @xmath29 .
curiously , this type of behavior had been reported before in mag- netic nanoparticle hyperthermia experiments @xcite .
the authors suggest that this can be explained by the exis- tence of large particles in the sample @xcite .
so , multi- domain particles could be relevant to heat generation through domain wall motion loss .
however , for most used magnetic fluid samples , multidomain particles are not expected .
for example , in magnetite nanoparticles the single - domain limit is around 80 nm @xcite .
moreover , on the theoretical point of view , carrey et al .
inves- tigated the slp field exponent using numerical simula- tions of the sllg equation ( see fig
. 7 of ref .
the authors found theoretically that this exponent is size de- pendent and showed values below or higher than 2 .
this type of behavior was found experimentally by verde et al .
however , in both works , no simple analytical expression was used to explain this behavior . here
we show that through a modification of bloch s equation , which is linear with respect to the magnetization , one is able to obtain a heat loss expression valid beyond the lrt . indeed , different from other works from the literature
, we demonstrate that even the linear frequency term has higher order field contributions .
also , our model introduces a nonlinear frequency term which adequately describes the magnetic response within the hyperthermia therapeutic window .
the validity of the model is explicitly tested by comparing it with numerical simulations of the sllg approach .
in addition , we included experimental magnetic hyperthermia data that supports our theoretical findings .
twelve powder samples were studied , including cobalt - ferrite , copper - ferrite , nickel - ferrite , maghemite and manganese - ferrite ( doped with zn or co and also undoped ) based nanoparticles .
the analytical nonlinear response model is believed to be useful not only for improving our understanding of magnetic losses , but also may impact other related areas , which could benefit from analytical expressions , as for example , magnetic particle imaging@xcite and magnetic nanothermometry@xcite .
the article is organized as follows : in section ii we discuss several models from the literature . in particular
, we present the linear response theory ( lrt ) , the nonlinear ferguson - krishnan model ( fk ) ( usually applied in magnetic particle imaging ) , the perturbation method developed by raikher and stepanov ( rs model ) , and finally the stochastic landau - lifshitz - gilbert model , which is expected to be the exact solution of the magnetic response of the nanoparticle at alternating field conditions . all the models are critically compared showing the necessity of developing a simple nonlinear analytical model .
the sllg model is than compared with the proposed nonlinear response model ( nlrt ) developed in section iii .
section iv we present the experimental procedure , i.e. the synthesis and characterization of magnetic fluids . in section v we discuss all the theoretical and experimental results .
here we focus on magnetic nanoparticle hyperthermia , but also compare our model with the third - harmonic magnetic particle imaging data from the literature .
finally , in section vi we summarize our findings .
( expected for small tumors in breast @xcite ) , which results in a @xmath30 .
human treatment can only occur below this field .
the lrt limit is calculated assuming @xmath22 for a particle diameter of @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35 and @xmath36 .
the nonlinear response critical field for our model ( nlrt ) corresponds to the solid line . ]
all the models discussed in this manuscript are valid within the single - domain range .
also , they assume the giant - spin hypothesis of brown@xcite , i.e. coherent spin rotation . here
we will consider the case of uniaxial magnetic nanoparticle , where the energy is given by @xmath37 the first term is the uniaxial anisotropy energy , while the other is the zeeman interaction .
@xmath38 represents the angle between the magnetic moment of the nanoparticle and the easy axis direction , while @xmath39 corresponds to the angle between the magnetic dipole and the applied field .
it is common to name the longitudinal case as @xmath40 , which is the case where the field is applied in the anisotropy axis direction .
the simplest quasi - static magnetization model in the literature , named langevin model , neglects the anisotropy term , which can only be done if the ratio of this anisotropy contribution to the thermal energy is very low . in this case
the magnetization can be calculated from @xmath41 @xmath42 is the langevin function , whose series expansion to fifth order gives @xmath43 the first term is the initial ( linear ) susceptibility , the second the cubic , and there on .
the first linear response model to describe heat loss was probably described by debye in the context of rigid electric dipoles@xcite . here
we focus in the magnetic case .
let us first start by assuming that a magnetic particle is subjected to a harmonic field @xmath44 , with the magnetic susceptibility @xmath45 , where @xmath46 and @xmath47 corresponds to the real and imaginary linear susceptibility terms , respectively .
so , the magnetization term can be written as @xmath48 , where @xmath49 with @xmath9 the field frequency . therefore , defining the heating efficiency ( slp ) as the frequency times the hysteresis loss divided by the particle density ( @xmath50 ) one finds @xmath51 this equation represents the heat loss of the magnetic material .
so , one now needs an expression for the imaginary susceptibility term .
if the projection of the magnetization , @xmath52 , in the field direction satisfies the bloch equation , i.e. @xmath53 , where @xmath54 is the magnetization relaxation time , one can show the linear susceptibility term is @xmath55 , revealing that @xmath56 @xmath57 is the equilibrium susceptibility , which within the langevin model is equal to @xmath58 .
however , depending on the model this term would be different
. the relaxation of the magnetization for an uniaxial nanoparticle is @xmath59 with @xmath60 , that is valid when @xmath61 @xcite . here
@xmath1 is the particle volume , @xmath21 is the temperature , @xmath20 in boltzmann s constant and @xmath25 the magnetic anisotropy .
@xmath62 ( about @xmath63s ) , with @xmath64 the electron gyromagnetic ratio and @xmath65 the dimensionless damping factor . for the field applied in the anisotropy direction one finds for the relaxation in the limit of high anisotropy @xmath66^{-1}}{\sigma^{1/2}(1-h^{2})}.\label{taudeh}\ ] ] the field term @xmath67 is given in reduced units , i.e. @xmath68 .
this expression returns to the later in the absence of an applied field .
the first one to describe this heat loss for magnetic fluids was rosensweig@xcite .
the model above predicts a loss proportional to the square of the applied field .
however , this is only true experimentally at low field amplitudes as found in several cases dealing with magnetic nanoparticles @xcite .
note that the same issue occurs in the electric case for dielectrics@xcite or relaxor ferroelectrics@xcite .
in addition , the lrt model predicts elliptical magnetic hysteresis curves , which have been observed at low field amplitudes ( less than @xmath69 ) by eggeman et al .
@xcite and tomitaka et al .
however , this is not consistent with findings at higher field amplitudes , as for instance in magnetic particle imaging where a nonlinear response plays a crucial role @xcite . in an attempt to include nonlinear phenomena in the description ,
ferguson and krishnan@xcite proposed a generalization of linear magnetization , using the langevin function : @xmath70 this approach assumes that the frequency response of higher field order ( quasi - static ) terms are the same as the linear dynamic susceptibility term and neglects the quasi - static contribution from the magnetic anisotropy energy term .
this expression is usually used to obtain the nth - order harmonic magnetization , which represents an important quantity in magnetic particle imaging @xcite .
the harmonic calculation will be discussed in detail in section iii .
using perturbation theory , raikher and stepanov@xcite , included the anisotropy term and showed that the magnetization could be written as @xmath71 .
however , different from the fk model above , the frequency dependence of the cubic term was found to be different from the linear term .
the authors found that the cubic susceptibility could be written as @xmath72 where @xmath73 , @xmath74 is the particle volume fraction of the assembly and @xmath75 .
so , the real and imaginary susceptibility terms are given by @xmath76 @xmath77 using up to the cubic term the magnetization of the nanoparticle in the rs model gives @xmath78 where @xmath79 , @xmath80 , with @xmath81 and @xmath82 and @xmath83 are given by eq .
[ eq : rechi3rs ] and eq .
[ eq : imchi3rs ] .
note that those expressions are valid for an ensemble and low field amplitudes . in order to obtain
the equivalent expressions for the nanoparticle one only need to neglect the particle volume fraction in the equilibrium susceptibilities . because of the perturbation approach this model is expected to be valid only at very low field amplitudes .
the model that is expected to correctly describe the magnetization response of a single - domain nanoparticle at any field amplitude and frequency range is the sllg model . in this case , the magnetic moment of the nanoparticle is assumed to be described by the landau - lifshitz - gilbert equation @xmath84 where @xmath85 the effective field has three contributions : the applied external field , the anisotropy field and the thermal fluctuation field . so the landau - lifshitz - gilbert equation for a magnetic dipole is augmented with a gaussian white noise thermal field @xmath86 whose cartesian coordinates satisfy the statistical properties : @xmath87 and @xmath88 .
the kronecker and dirac deltas indicates that the thermal field is both spatial and temporally uncorrelated . in principle
, one could use the equation above and do numerical simulations .
however , the approach of brown was to connect the sllg equation to the fokker - planck equation of the magnetic moment orientational distribution function @xcite , which can be used to obtain the nanoparticle magnetic moment response . in this work we focus in the longitudinal case .
the first authors to study in detail this problem analytically was dejardin and kamilkov @xcite .
later , others used the same approach to describe dynamic magnetic hysteresis @xcite . here , the magnetic moment orientational distribution function @xmath89 can be shown to obey the fokker - planck equation @xmath90,\ ] ] with @xmath91 the free diffusion time , @xmath92 and @xmath38 the angle between the magnetic dipole and the applied field
. the magnetic anisotropy is assumed uniaxial .
so , the ratio of the particle energy to thermal energy can be written as @xmath93 where the field term @xmath94 .
therefore , the effective field is @xmath95 the fokker - planck equation is then used to obtain the time evolution of the lth - order moment @xmath96 , which is shown to be described by @xmath97 with @xmath98 and @xmath99.\nonumber \end{aligned}\ ] ] this equation shows that each moment depends on others in a nonlinear fashion .
this infinite hierarchy may be solved numerically using fast sparse solvers @xcite and discarding several periods of the external field .
alternatively , one could also expand the @xmath100 in a fourier series as @xmath101 with all @xmath100 real , which implies that @xmath102 , where the asterisks refer to the complex conjugate @xcite .
this will then lead to a hierarchy of algebraic equations for the fourier amplitudes , which also need to be solved numerically@xcite .
, ferguson - krishnan approach , raikher stepanov method and numerical solution of sllg for @xmath103 and @xmath104 .
( b ) longitudinal to langevin susceptibilities ratio for @xmath105 , @xmath106 and @xmath107 . ]
we are now in condition to compare the hysteresis loops of each model , namely the linear response theory using the field - independent relaxation time ( lrt ) and also the field - dependent relaxation time of eq .
( lrt @xmath108 ) , the fk model , the rs model and the exact solution for the sllg model . in fig . [
figure2](a ) we show the magnetization curves of all those models .
it is clear that the lrt model , independent of the relaxation time equation used , shows an elliptical loop .
the rs model showed a similar behavior .
the only model that shows a significant difference from lrt is the fk model .
however , it also shows an elliptical hysteresis , which is distinct from the lrt model because of the langevin equilibrium susceptibility .
so , different from the other models , it does not take into account the anisotropy term .
nevertheless , for the parameters used in this simulation , it is shown that none of the models above represent well the exact solution given by the sllg magnetization hysteresis loop .
although improvements were obtained in each model , in general they are not yet satisfactory .
motivated by this fact , we decided to work out a nonlinear response model , from now on named nlrt model .
this model is able to better represent the magnetization response at higher field conditions , not only in comparison to the lrt , but also far better than the fk or rs models .
in this section we present our nonlinear response model .
firstly , we include the magnetic anisotropy energy term in the longitudinal case , which allow us to obtain any quasi - static ( equilibrium ) susceptibility terms .
those expressions will be named @xmath109 , i.e. the nth - order quasi - static ( qs ) coefficient obtained in the low - frequency limit ( @xmath110 ) . in the next subsection
we introduce our dynamic model , where a new expression for the heat loss and the particle magnetization is obtained . the last subsection is related to the cubic harmonic calculation , which is an important parameter for magnetic particle imaging application . for an uniaxial magnetic nanoparticle in the longitudinal case
, the average magnetization is obtained from @xmath111 for @xmath112 , one can show that the longitudinal magnetization is @xcite @xmath113+\mathrm{erf}\left[i\left(\sqrt{\sigma}-\dfrac{\xi}{2\sqrt{\sigma}}\right)\right]}-\dfrac{\xi}{2\sigma}\right).\ ] ] expanding the longitudinal magnetization in a taylor series : @xmath114\xi+m_{s}\left[\dfrac{\mathrm{e}^{\sigma}\left(6\sigma\mathrm{e}^{\sigma}+i\sqrt{\sigma\pi}(2\sigma+3)\mathrm{erf}(i\sqrt{\sigma})\right)}{12\pi\left(\sigma\mathrm{erf}(i\sqrt{\pi})\right)^{2}}\right]\xi^{3}+ ... \\ & = \chi_{qs,1}h+\chi_{qs,3}h^{3}+ ... ,\nonumber \end{aligned}\ ] ] where @xmath115 and @xmath116 .
note that all @xmath109 are real . in fig .
[ figure2](b ) we show the ratio of the @xmath117 up to the fifth - order ( n=5 ) .
the longitudinal linear susceptibility ( @xmath118 ) calculation demonstrate that in the absence of ( or very low ) magnetic anisotropy the susceptibility approaches the expected langevin result . on the other hand , in the high anisotropy limit
, the linear ratio approaches 3 , which indicates that the longitudinal result tends to the ising result , as expected in this case .
other ratios are also shown in the figure .
therefore , we can conclude that in general it is of great importance to include the anisotropy term when investigating the magnetic response of nanoparticles .
as in lrt model , let us assume that a magnetic particle is subjected to a harmonic field and that the projection of the magnetization , @xmath52 , in the field direction satisfies the bloch equation , i.e. @xmath119 where @xmath54 is the relaxation time and @xmath120 is a function of the alternating field .
hence , it will be periodic , i.e. @xmath121 .
also , in general one might represent @xmath122 , where @xmath123 is the nth - order magnetic susceptibility .
the lrt , discussed before , corresponds to considering just the first term in @xmath120 .
the nonlinear response under bloch s assumption may be computed as follows . in general @xmath120
is a function of @xmath124 so it may be expanded in a cosine series as @xmath125 for certain coefficients @xmath126 , that can be easily identified by expanding @xmath120 in terms of @xmath127 ( another alternative way to obtain those coefficients is using the integrating factor method directly to bloch s equation ) .
the steady - state solution of the bloch equation is therefore @xmath128 in this approach , the corresponding slp is @xmath129 this means that one only needs to worry with the coefficient @xmath130 .
this comes from the fact that in the heat loss integral only the terms obtained from @xmath105 is nonzero .
note that the first term corresponds to the usual debye model , if one assumes that @xmath131 , i.e that @xmath132 is the quasi - static limit linear coefficient .
also , it might be important to mention that the existence of the higher order field dependent terms indicate a correction not reported before in the literature .
as for instance , if one uses the magnetization equation of the rs model , only the the quadratic field term appears .
the same approach can also be used in the dielectric loss case .
for example , the electric field dependence dielectric loss of glycerol ( see inset of fig . 3 of ref @xcite ) .
according to equation , the bloch solution for the magnetization @xmath52 up to cubic terms in the field is @xmath133 where @xmath123 are the nth - order magnetic susceptibility coefficients . in the equation above
is clear that higher - order terms are also relevant to the magnetization dynamics . as for instance
, this nonlinearity effect can be identified even for the first harmonic contribution , which shows higher field order terms .
in addition , if @xmath134 one may write the magnetization ( considering higher - order terms in @xmath120 ) as @xmath135 . for the sake of argument ,
if one assumes that the nth - order susceptibility terms are equal to the quasi - static terms ( @xmath110 ) and that the nanoparticle is at the superparamagnetic regime , than @xmath136 .
note that the first term of this equation has been used systematically in both , magnetic particle imaging ( mpi)@xcite and magnetic nanothermometry ( mnt)@xcite . in mnt the magnetization expression was shown to be useful only at the low frequency range@xcite , which is easily explained by our model due to the range of validity of the later expression .
moreover , in mpi the magnetization is similar , but not identical to our model , and differs mainly due to the term @xmath137 and that the later assumes quasi - static susceptibility terms and superparamagnetic particle . as a consequence ,
our model give different higher - order harmonic magnetization terms and might represent better the experimental mpi data@xcite . curiously , our model gives a similar expression as ref .
@xcite for the heat loss if we assume that @xmath138 .
however , this approximation does not represent correctly the magnetization dynamics .
further , eq . shows that the bloch equation predicts the same frequency dependence as the lrt , which will result in elliptical - like hysteresis curves that are in disagreement with experiment .
the reason for this discrepancy is that bloch s equation is linear , whereas the underlying physical phenomena is not , as discussed before in section ii - d .
one way to circumvent this is to assume that the coefficients @xmath123 depend explicitly on @xmath139 .
the exact form of this dependence is problem specific , but it must be such that when @xmath110 , one recovers the equilibrium nonlinear susceptibilities . the heuristic improvement approach , also used by others@xcite , is able to better represent the magnetization dynamics .
so , to correct for the aforementioned deficiency of the bloch approach , we replace @xmath123 with a frequency dependent function and compare the approximation with exact results , which are obtained for the longitudinal case using the sllg model@xcite . in this strategy
we wrote @xmath140 , where @xmath141 is a function of the frequency .
the quasi - static susceptibility coefficients were obtained from the series expansion of the quasi - static longitudinal solution@xcite . also , from our assumption is obvious that one should have @xmath142 .
moreover , for the first term we should have @xmath143 , which corresponds to the lrt result . for the cubic term we found that @xmath144 similarly as the rs model , the magnetization can be written in the same functional form as eq .
. however , now the real susceptibility terms are @xmath145 @xmath146 while the imaginary terms are @xmath147 and @xmath148 .
those results indicate that the susceptibility terms are distinct from the rs model ( see eqs . 10 and 11 ) , even though the quasi - static susceptibility coefficients give the same result .
also , the linear susceptibility term shows a nonlinear field and frequency contribution , which was absent in other models .
so , returning to the heat loss integral ( eq . ) and using the cubic magnetization ( eq . ) with this correction ( eq . ) , the new expression for slp is now given by @xmath149.\nonumber \end{aligned}\ ] ] moreover , in section v , besides discussing the magnetic nanoparticle hyperthermia , the cubic harmonic magnetic particle imaging ( mpi ) experimental signal data obtained in ref .
@xcite will also be compared with the theoretical calculations using the fk model and the nlrt model ( see section v for details ) .
we will show a better agreement with experimental data using the nonlinear response theoretical model developed in this work .
in addition , because we also investigate soft - magnetic nanomaterials ( low @xmath150 ) , the empirical uniaxial relaxation time expression , valid for any anisotropy value , has been considered @xcite @xmath151^{-1}. \label{taudeh-1}\ ] ]
manganese - ferrite samples were synthesized by hydrothermal route and separated for the hyperthermia analysis after characterization by x - ray diffraction ( xrd ) and vibrating sample magnetometer ( vsm ) .
all chemical reagents ( @xmath152 , @xmath153 , @xmath154 , @xmath155 ) citric acid trisodium salt - @xmath156 , methylamine - @xmath157 , and acetone - @xmath158 ) were purchased with analytical quality and used without any further purification . in a typical approach , @xmath159_{0.25}fe_{2}o_{4}}$ ]
magnetic nanoparticles were prepared as follows : adequate amounts of @xmath160 metal stock solutions were diluted with @xmath161 of distilled water to form a precursor solution containing @xmath162 of @xmath163 , @xmath164 of @xmath165 , and @xmath166 of @xmath167or @xmath168 .
thus , @xmath169 of methylamine at 40% ( w / w ) were quickly poured into the stock solution under vigorous stirring for 10 min and then transferred into a @xmath170 teflon - sealed autoclave and heated up to @xmath171 for 6 h. after cooling to room temperature , the precipitate was separated by magnetic decantation , washed with @xmath172 three times and re - dispersed in @xmath173 of water .
then , @xmath174 of citric acid trisodium salt was added into the solution which was heated up to @xmath175 for 60 min . after adjusting the ph of slurry to 7.0 and washing with acetone three times ,
the precipitate was re - dispersed in @xmath173 of water to form a magnetic sol , after evaporating residual acetone .
thus , a size - sorting process was done by adding @xmath176 of @xmath177 to the as - prepared magnetic sol@xcite .
5 min afterwards under a permanent magnet ( @xmath178 ) , salt adding induced a phase transition and formed an upper ( botton ) sol phase with populations of smaller ( larger ) nanoparticles .
once separated , precipitate of each phase was washed twice with a mixture water / acetone 1:10 ( volume / volume ) and , after evaporating residual acetone , nanoparticles were re - dispersed in water .
this procedure was repeated several times .
powders were obtained from evaporation of sols at @xmath179 for 8 h. details about cobalt - ferrite samples can be found in ref . @xcite and
copper - ferrite and nickel - ferrite samples can be found in ref .
@xcite . after the size - sorting process powder samples were analyzed by xrd ( shimadzu 6000 ) to separate samples with similar sizes .
the previous analysis was performed using the well - known scherrer equation , which is given by @xmath180 , where @xmath181 is the scherrer constant , @xmath182 is the x - ray wavelength , @xmath183 is the line broadening in radians obtained from the square root of the difference between the square of the experimental width of the most intense peak to the square of silicon width ( calibration material ) , and @xmath184 is the bragg angle of the most intense peak ( 311 ) .
this procedure allowed us to select three distinct samples of similar sizes containing @xmath185 , @xmath186 , or @xmath187 nanoparticles .
all the nanoparticles were surface - coated with citric acid , which guarantee stability at phisiological conditions .
the samples were also characterized by vsm ( ade magnetics , model ev9 , room temperature measurements , field up to 2 t ) . table [ table1 ] summarizes the relevant characterization properties of the nanoparticles .
finally , magnetic hyperthermia data was obtained in two systems , one home - made which operates at 500khz , and another one from nanotherics . in particular , the later system operates in a broad frequency range , spanning from 110 up to 980khz . while details about the home - made hyperthermia system has been described elsewhere @xcite .
the calorimetric method used to obtain the experimental slp of the sample used the equation @xmath188_{max},\label{chicomg-1 - 1 - 1}\ ] ] where @xmath189 is the heat capacity of the sample ( here assumed as the heat capacity of the liquid carrier due to the low concentration of particles ) , @xmath190 is the mass of magnetic nanoparticles in unit of grams ( obtained from the analysis of the magnetisation curves of the colloid samples ) , @xmath21 is the temperature of the sample measured with a fibre optic thermometer . note that in the slp calculation we use the value of the maximum rate of temperature increase ( @xmath191_{max}$ ] ) , as discussed previously by others @xcite .
this method is believed to better estimate slp than the most common initial - slope procedure that can underestimate this value @xcite .
and @xmath104 . in ( a ) @xmath192 , ( b ) @xmath103 , ( c ) @xmath193 and ( d ) @xmath194 .
( e ) slp as function of @xmath150 for the lrt and nlrt with distinct field amplitudes .
( f ) slp as function of @xmath150 for the lrt and nlrt with and without the field dependence on the relaxation time .
( g ) real and imaginary susceptibilities as function of temperature for the rs and the nlrt models .
( h ) slp as a function the square of the field for the lrt ( dash ) , nlrt ( solid ) and exact solution using the sllg ( points ) for @xmath150 values of 6 and 10 . ]
several experimental results show the existence of an optimal particle size for hyperthermia @xcite .
this is also contemplated in eq . , which predicts that this optimal size should occur when @xmath195 .
this , however , is only true at low field amplitudes . increasing field amplitude one notice a shift of maximum size towards larger particles in a noninteracting system .
this can be easily modelled within lrt using the field dependent magnetization relaxation time @xcite .
indeed , such drift becomes clear when @xmath196 ( see discussion of fig .
[ figure3](f ) below ) .
further , numerical dynamic hysteresis simulations using the sllg model or kinetic monte carlo method @xcite show that , as the field amplitude increases , the optimal size shifts towards larger particles . it may even disappear , depending ( also ) on the magnetic anisotropy of the nanoparticle @xcite .
most of the results above consider a noninteracting system .
however , in colloids , or real in vivo situation , agglomerate formation plays a key role . in this case , it has been shown within lrt , that the opposite effect occurs , i.e. increasing the strength of particle interaction shift the optimal diameter to lower sizes @xcite . the same was found including particle - particle interaction using a mean field approach to the sllg model at the low field regime @xcite .
anyway , a valuable analytical nonlinear response theoretical model ( nlrt ) should be able to explain at least some of the features discussed above . a comparison between the hysteresis curves obtained from the lrt , our nlrt model and the numerical solution of the sllg model is shown in fig.[figure3](a)-(d ) , for distinct @xmath150 values considering @xmath104 and @xmath197 .
it is found that the inclusion of the corrected cubic term leads to a good agreement with the numerical simulations , adequately describing the deviations from the linear response .
note that the agreement is far better than any other model discussed previously ( see fig .
[ figure2](a ) ) .
the lrt model is shown as a dash line , the exact result using the sllg equation is shown as dash - dot line , while nlrt ( considering eq . ) is shown as solid line .
it is very surprising that , with such a simple assumption , an interesting nonlinear effect is obtained able to represent far better the magnetization dynamics .
indeed , we found that the present model works very well close to this limit of anisotropy value ( @xmath198 ) .
it also has a slight frequency dependence which can be monitored by nonphysical results in the magnetization curve or kinks in the slp versus @xmath150 curves increasing the field . at higher fields we observe deviations from the exact solution that might be only addressed if higher - order terms are determined
nevertheless , as shown in fig .
[ figure1 ] ( see the nlrt line ) , the range of validity of the model is almost completely within the hyperthermia therapeutic window .
this suggests that this model might be applicable for real clinical situations .
figure [ figure3](e ) shows the slp as function of @xmath150 for the lrt ( dashed line ) and the nlrt ( solid line ) for distinct field amplitudes . for simplicity , we are not considering the field dependence on the relaxation time .
one can clearly observe a shift of the maximum of slp towards higher particle sizes in the nonlinear case .
also a decrease of the maximum slp value for the nlrt case .
the phenomenon is strictly related to the nonlinear effect introduced in the model and not due to the field effect from the relaxation .
this result is in accordance with numerical simulations from the literature @xcite . on the other hand , fig .
[ figure3](f ) also shows slp as function of @xmath150 in both cases , but now investigating the field effect on the relaxation time for @xmath199 .
similar behavior as before is observed .
nevertheless , in comparison with the lrt , the nlrt-@xmath200 shows a larger size shift . as for instance , the optimum anisotropy term change from @xmath201 for lrt to @xmath202 for nlrt-@xmath200 , which corresponds to a shift in optimal diameter of the order of 4% . as discussed in section
ii , there are other nonlinear models .
in particular , cubic susceptibility expressions using the rs model had been suggested to represent experimental data of noninteracting magnetic nanoparticles @xcite .
figure [ figure3](g ) shows the cubic susceptibility terms , imaginary and real , for the rs model and the nlrt model as a function of temperature . here
the parameters used were @xmath203 , @xmath32 , @xmath33 , @xmath35 and @xmath36 .
as found in ref .
@xcite the real cubic term in the rs model shows a significant variation as a function of temperature , in particular in the range below @xmath204 , where a quite high positive cubic value is found theoretically .
it is curious to notice that experimentally such effect has not been observed in ref .
@xcite for noninteracting nanoparticle samples .
in fact , discrepancies between the rs model and data of ref .
@xcite had been attributed to polydispersity and particle - particle interaction effects .
note that the inclusion of such effects could be responsible for some of those differences between theory and data .
however , there might be another explanation .
as we have just shown , the nlrt model represents far better the magnetization response . differently from the rs model ,
the real cubic susceptibility from nlrt does not show such strong positive contribution at low temperatures . as a consequence
it might represent better experimental data .
another point that could be commented about the improvement in the nlrt model in comparison to others is the slp calculation .
note that in the rs model the slp calculation , using the magnetization expression of eq .
, provides the same result as the lrt .
so , although the magnetization equations are not the same , the hysteresis area is the same as the lrt case .
again , this is in contradiction with several experimental results . from the experimental point of view , after obtaining the slp data of the samples as a function of the applied alternating field , it is common to try to describe the heating efficiency in terms of a field exponent , i.e. one might try to fit the data with an allometric expression as @xmath205 where @xmath206 is a constant and @xmath207 the field exponent .
if this exponent is equal to 2 one might argue that the sample is within the linear response regime .
figure 3(h ) shows the slp as a function of the quadratic field for distinct @xmath150 values considering the lrt ( dash ) , nlrt ( solid ) and sllg ( points ) .
both situations shows that depending on the particle size or anisotropy , deviations from the expected quadratic field dependence of the lrt are found . at the low barrier regime ( @xmath208 ) , i.e. for particle sizes lower than the optimum value , the field dependence exponent is lower than 2 . while at the high barrier regime , an exponent higher than 2 is observed .
the same behavior is found from sllg , as expected since nlrt model is based on the assumption that sllg is the exact result .
however , because in the nlrt only the cubic term was introduced , deviations between both models are expected for higher fields .
the nonlinear regime has been studied experimentally before on ref .
@xcite , where the transition to the nonlinear regime was explained using the sllg model , though without any analytical expression . the explanation for such behavior may be understood using eq . .
note that @xmath116 , so when @xmath209 the high - order contribution term lowers the linear slp field dependence term .
the consequence of this is an apparent field exponent lower than 2 . on the other hand ,
when @xmath210 the higher order slp term changes sign , which now adds a value to the first order term .
in this case exponents larger than 2 might appear if the field is high enough .
evidence of nonlinear behavior the slp field dependence can be found in distinct ferrite - based powder samples .
table [ table1 ] summarizes the parameters obtained from sample analysis .
four sets of samples were studied .
the first set is composed of three samples : manganese - ferrite based nanoparticles undoped , doped with zinc and doped with cobalt .
since samples were produced using the same method , have ( approximately ) the same magnetization , and the same diameter , this set allow the study of anisotropy influence over slp versus @xmath211 behavior .
the second set is composed by other three samples : cobalt - ferrite , maghemite and copper - ferrite .
these samples have very different magnetization and anisotropy , but the same diameter ( some results published in ref .
the third set is composed by other three samples of cobalt - ferrite , which have a high anisotropy , with different diameters . and
, the last set is composed by three samples of nickel - ferrite , which have a lower anisotropy than cobalt - ferrite , with different diameters .
.characterization parameters of the samples .
@xmath212 crystalline size , @xmath19 saturation magnetization and @xmath213 coercive field .
@xmath207 is the apparent slp field exponent from allometric fit .
[ cols="^,^,^,^,^,^,^,^,^,^,^,^ " , ] magnetic hyperthermia experimental data around @xmath214 is shown in figs .
[ figure4](a ) , [ figure4](c ) , [ figure4](e ) and [ figure4](g ) for powder samples , where we present the slp as a function of the applied field for distinct ferrite - based samples .
most of the applied fields are above the therapeutical values ( see fig.[figure1 ] ) , but are necessary to experimentally observe deviations from lrt .
symbols represent experimental data , while the lines are the fit of the data using the allometric function .
firstly , notice that soft - like materials heat more efficiently at low field amplitudes , in aggreement with what was found before experimentally and theoretically @xcite .
this property , although not discussed in this work , is relevant for in vivo applications @xcite .
table [ table1 ] shows the apparent field exponents obtained from this type of phenomenological approach for all the samples , as well figs .
[ figure4](b ) , [ figure4](d ) , [ figure4](f ) and [ figure4](h ) , compared with 2 ( gray dashed line which represents lrt ) .
the result indicates deviation from linear behavior and the samples shows distinct exponents values , depending ( probably ) on sample anisotropy .
the same behavior has been observed with other ferrites @xcite .
this behavior is in accordance with our previous theoretical analysis .
however , a direct comparison between experimental data and theoretical analysis is compromised by the fact that sample are solid , allows a random anisotropy axis nanoparticle configuration that decreases the equilibrium susceptibility values lowering the slp @xcite .
so , the nanoparticles at this highly packed configuration are at strong interacting conditions , which may affect the magnetic anisotropy @xcite . in this case
, one can not use the longitudinal calculation developed in this work for the powder samples , since the quasi - static susceptibility values are now different .
nevertheless , powder configuration inhibit frictional loss contributions due to the brownian relaxation mechanism @xcite and a similar behavior for slp ( with distinct absolute values ) is also expected . in powder configuration at @xmath215 khz .
( b ) apparent slp field exponent @xmath207 obtained for manganese - ferrite in powder configuration . ( c )
slp as function of the magnetic field for distinct ferrite nanoparticles around @xmath216 in powder configuration at @xmath217 khz .
( d ) apparent slp field exponent @xmath207 obtained for distinct ferrite nanoparticles in powder configuration . ( e ) slp as function of the magnetic field for cobalt - ferrite nanoparticles with distinct sizes in powder configuration at @xmath217 khz .
( f ) apparent slp field exponent @xmath207 obtained for cobalt - ferrite in powder configuration . (
g ) slp as function of the magnetic field for nickel - ferrite nanoparticles with distinct sizes in powder configuration at @xmath217 khz .
( h ) apparent slp field exponent @xmath207 obtained for nickel - ferrite in powder configuration .
symbols are data and lines represent the best fit using the allometric function . ]
the nlrt model developed here is valid for @xmath218 , where magnetization relaxation mechanisms plays a role in the spin reorientation by overcoming the barrier energy .
increasing the field value one need to use directly the sllg model , which due to the complexity of the problem does not reveal any simple analytical equation . nevertheless , a simple approach for qualitative analysis under high field conditions ( @xmath219 might be achieved using the stoner - wohlfarth ( sw ) model @xcite . .
the figure shows the experimental data ( circles ) from ref .
@xcite , calculations using the fk model of ref .
@xcite ( squares ) and the nlrt ( triangles ) calculation . ] besides magnetic hyperthermia , the present model might be useful for magnetic particle imaging ( mpi ) too .
mpi is a nonionizing imaging technique , introduced in 2005 by gleich and weizenecker @xcite , which is capable of imaging magnetic tracers through the nonlinear magnetic response of magnetic nanoparticles . in mpi a dc plus an ac field
are applied to the magnetic material in such a way to create a free field point volume where the nanoparticles can respond to the ac field excitation .
the magnetic response signal can then be measured using detector coils .
the received voltage by the detector coil is @xmath220 @xmath221 is the coil sensitivity ( assumed to be @xmath222 ) and the integration is over the magnetic material .
the mpi third harmonic magnetization signal per unit volume @xmath223 is defined as the module of the discrete fourier transform given by @xmath224\right|,\label{mpiemf-1 - 1}\ ] ] where @xmath225=\sum_{k=0}^{n-1}f\left[k\right]e^{-i\frac{6\pi}{n}k}.\ ] ] the function @xmath226 $ ] is obtained using @xmath227=\frac{\partial m(t)}{\partial t}$ ] and the time discretization as @xmath228 , where @xmath229 is the excitation field frequency and @xmath230 corresponds to the number of intervals discretized within one period . in this work @xmath231 . in nlrt model
the complete magnetization expression is unknown , so we only use the terms up to the third harmonic . on the other hand , for the fk model
, one can expand the langevin expression up to any order .
figure [ figure5 ] we shows the experimental mpi data of the third harmonic magnetization signal of magnetite nanoparticles of distinct sizes performed at @xmath232 ( see ref .
@xcite for details ) .
spheres correspond to experimental data , while squares are related to the fk model of ref .
note the logarithmic scale and that we are presenting the data in terms of @xmath150 .
here we assumed the bulk magnetic anisotropy value , although is well known that the anisotropy is size dependent @xcite .
nevertheless , size dispersity was taken into account .
the calculations used a relaxation time valid for any @xmath150 @xcite and parameters from table 1 of ref .
triangles correspond to our polydisperse calculation taking the discrete fourier transform and using eq . in units of v / g , i.e. taking into account in the calculation of @xmath223 the amount of magnetic material in mass per unit volume .
note that our model represents better the mpi experimental data .
indeed from 10 data points nlrt is in better agreement with 80% of the data .
better theoretical results might be achievable if the anisotropy of each sample is known , or even more if one is able to take into account possible particle - particle interaction effects due to agglomerate formation @xcite .
so , it might be fair to say that , both hyperthermia and mpi experiments seem to be more adequately described by the nlrt model
. finally , it might be relevant to comment that there is a huge interest of not only deliver heat using magnetic nanoparticle hyperthermia , but also , monitor non - invasively heat delivery using magnetic nanoparticles . in order to be successful in such area , analytical expressions , as the ones derived in this work , that better represent the non - linear response of magnetic nanoparticles , are highly needed .
the authors believe that the model developed here might indicate a useful approach towards this important clinical goal .
in conclusion , a nonlinear response model of magnetic nanoparticles valid for single - domain nanoparticles was developed .
the model is valid beyond the linear response theory , and showed good agreement with dynamic hysteresis simulations using the stochastic landau - lifshitz - gilbert approach and experimental hyperthermia data for field amplitudes as high as 10% of the magnetic anisotropy field . in particular ,
a generalized expression for the magnetization and the heat loss efficiency ( slp ) were obtained .
the model showed many features found experimentally in magnetic hyperthermia and mpi studies .
as for example , stoner - wohlfarth - like dynamic hysteresis curves , distinct slp field exponents , optimum hyperthermia nanoparticle size shift , among others .
the magnetization expression was critically compared with the ones used in mpi and mnt , from which we were able to identify when some approximations can be used . moreover ,
the nlrt was found to be valid mostly within the hyperthermia therapeutic window , which suggests strong applicability in the biomedical field .
52ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ]
+ 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1021/nl9018935 [ * * , ( ) ] link:\doibase 10.1038/nnano.2010.125 [ * * , ( ) ] link:\doibase 10.1016/j.nano.2014.01.011 [ * * , ( ) ] link:\doibase 10.2217/nnm.14.106 [ * * , ( ) ] link:\doibase 10.3109/02656736.2013.839056 [ * * , ( ) ] link:\doibase 10.3109/02656736.2013.836758 [ * * , ( ) ] \doibase 10.1049/ip - nbt:20055018 [ * * , ( ) ] link:\doibase 10.1007/s11060 - 010 - 0389 - 0 [ * * , ( ) ] link:\doibase 10.1097/00000658 - 195710000 - 00007 [ * * , ( ) ] link:\doibase 10.1007/s10439 - 012 - 0633 - 1 [ * * , ( ) ] link:\doibase 10.1109/tbme.1984.325372 [ * * , ( ) ] @noop _ _ ( , , ) link:\doibase 10.1109/20.718537 [ * * , ( ) ] link:\doibase 10.1016/s0304 - 8853(02)00706 - 0 [ * * , ( ) ] link:\doibase 10.1038/srep02887 [ * * , ( ) ] link:\doibase 10.1063/1.3551582 [ * * , ( ) ] link:\doibase 10.1063/1.4739533 [ * * , ( ) ] link:\doibase 10.1063/1.4729271 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.97.095703 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.85.2192 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.85.3724 [ * * , ( ) ] link:\doibase 10.1063/1.3676416 [ * * , ( ) ] link:\doibase 10.1103/physrev.130.1677 [ * * , ( ) ] link:\doibase 10.1063/1.3272082 [ * * , ( ) ] link:\doibase 10.1063/1.3684629 [ * * , ( ) ] link:\doibase 10.1103/physrevb.82.174423 [ * * , ( ) ] link:\doibase 10.1103/physrevb.89.014403 [ * * , ( ) ] link:\doibase 10.1109/20.43994 [ * * , ( ) ] link:\doibase 10.1016/s0304 - 8853(99)00145 - 6 [ * * , ( ) ] link:\doibase 10.1109/tmag.2010.2046907 [ * * , ( ) ] link:\doibase 10.1038/nature03808 [ * * , ( ) ] link:\doibase 10.1002/adma.201200221 [ * * , ( ) ] link:\doibase 10.1118/1.3106342 [ * * , ( ) ] link:\doibase 10.1038/srep06338 [ * * , ( ) ] link:\doibase 10.1063/1.4754272 [ * * , ( ) ] link:\doibase 10.1109/tmag.2007.894127 [ * * , ( ) ] link:\doibase 10.1016/j.jmmm.2012.02.060 [ * * , ( ) ] @noop link:\doibase 10.1103/physrevb.55.15005 [ * * , ( ) ] link:\doibase 10.1016/s0304 - 8853(00)00664 - 8 [ * * , ( ) ] link:\doibase 10.1016/j.microc.2010.09.002 [ * * , ( ) ] link:\doibase 10.1063/1.3597820 [ * * , ( ) ] link:\doibase 10.3109/02656736.2013.826825 [ * * , ( ) ] link:\doibase 10.1038/srep09090 [ * * , ( ) ] link:\doibase 10.1016/s0304 - 8853(00)00557 - 6 [ * * , ( ) ] link:\doibase 10.1016/j.jmmm.2008.05.041 [ * * , ( ) ] link:\doibase 10.1103/physreve.83.021401 [ * * , ( ) ] link:\doibase 10.1063/1.4907915 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.72.282 [ * * , ( ) ] link:\doibase 10.1006/jmra.1996.0184 [ * * , ( ) ] link:\doibase 10.1063/1.369383 [ * * , ( ) ] link:\doibase 10.1016/j.cis.2012.12.003 [ * * , ( ) ] | arxiv |
What is the relationship between concentration and voltage in a galvanic cell? How do you calculate the theoretical?
I am a year 12 Chemistry student and I was wondering if you could help me with some questions I have about a Galvanic cell experiment?
I am doing an experimental report in Chemistry. The experiment I decided to do was to change the concentration of the copper sulphate electrolyte in a Daniell cell and measure the voltage produced. The other electrolyte; Zinc nitrate was not changed and kept constant at 0.1M. The copper sulphate concentration increased from 0.25M, 0.5M, 0.75M to 1M. The experiment was performed when the temperature was 24 degrees. The anode was Zinc and the cathode was Copper.
In order to obtain theoretical values - should I use the Nernst equation? Would you be able to tell me how to use the Nernst equation for my experiment?
Also, I understand that voltage increases with concentration, but compared to standard conditions should the voltage produced be higher or lower than the voltage produced at standard conditions and 1M electrolyte?
The potential of the Copper electrode is given by the Nernst equation : $$E(Cu^{2+}/Cu) = + 0.34 V + 0.0295 log[Cu^{2+}]$$ If the concentration $[Cu^{2+}]$ is $0.25 M$ and then $0.50 M$, the potential of these half-cells become respectively $0.32$ V and $0.33 V$.
If you couple this half-cell with a Zinc electrode with $[Zn^{2+}]$ = $0.1 M$, the same sort of calculation gives you a potential $E(Zn^{2+}/Zn)$ =$ -0.76 + 0.0295(-1)$ = $-0.79 V$. If you combine both half-cells, you obtain $1.11 V$ and $1.12 V$ respectively.
This being said, I would like to advise you not to use Zinc nitrate in the zinc half-cell. Please replace Zinc nitrate by Zinc sulfate. The reason is that the ion nitrate attacks the Zinc metal, producing nitrite ions. So the potential of the half-cell made with Zinc metal in a Zinc nitrate solution is not stable.
| stackexchange/chemistry |
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