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Would fog impair echolocation abilities?
I was driving down a major highway today and the fog was thick enough I could barely see 40 ft in front of me.
I then wondered if I had had some other form of perception could I have perceived my environment more clearly. For example, [echolocation](http://en.wikipedia.org/wiki/Echolocation).
How would fog affect the signals echolocators send? Would the distortion be negligible or would the presence of this medium significantly alter the sound waves enough to make information unreliable?
According to [this link](http://wxguys.ssec.wisc.edu/2013/01/06/does-sound-travel-better-in-fog/) sound (especially high frequency sound) is more attenuated in fog, because it is dispersed by the (billions of) air-water interfaces of all the droplets. This is one reason why a fog horn is a very low sound - low frequencies travel further, especially in fog. For echolocation you want to use high frequencies, and fog is more attenuating at those frequencies. Another site confirming this information is [this one](http://www.thenakedscientists.com/HTML/questions/question/2327/) - slightly older than the other one. Of course one might wonder whether one article got its information from the other (it does look similar...).
Finally there is a very thorough (if old - 1953) paper on the attenuation of sound in fog [in the Caltech library](http://authors.library.caltech.edu/9121/1/EPSjasa53.pdf). Interesting diagram from this paper confirms that the attenuation of sound in fog is stronger at higher frequencies (for details of the definition of β see the paper):
Even with the question of attenuation - when visibility is reduced to 40 ft, echolocation will probably beat it handsomely at intermediate distances. There are a couple of other interesting things you can do to improve your ability to see in fog.
1) Yellow "driving glasses". These work because they cut out the blue components of light. When fog droplets are very small, light scattering is in the Rayleigh regime - that is, scatter probability goes as the inverse fourth power of the wavelength, and blue (400 nm) light is 16x more scattered than red (800 nm) [note - using round numbers...]. By cutting out the blue component, you reduce the amount of scatter that reaches the eye and improve the contrast. Skiers also use yellow "fog glasses".
2) Scanning light source. This is one of those magical things that ought not to work but does. With normal (flood) illumination, light scatters "from everywhere to everywhere". If instead you look along the line of (say) a laser shining into the fog, then the only scattered light you see is the light that scatters exactly 180 degrees back at you - which is a small fraction of all the scattered light. If you scan the light source and detection system in sync, and very quickly, you can build up an "almost scatter free" image. This raster scanning technology is used in some underwater search applications and [can penetrate about 6 "attenuation lengths"](http://www.ncbi.nlm.nih.gov/pubmed/20829976). As was discussed in the comments, this method actually works best when the viewing angle is not exactly 180 degrees - not only is the back scatter from the fog weaker (there is a curious doubling of scatter intensity that happens at exactly 180) but also, by looking at a slight angle, you are able to eliminate the back scatter from the closest fog - greatly improving penetration.
More recently [researchers in Israel](http://webhome.weizmann.ac.il/home/feyaron/PDFfiles/ImagingWalls.pdf) have come up with a way to image through thin layers of scattering material - as you can see in the link, they are also able to see "through fog" (although it was not clear to me whether their technique can apply to actual imaging in fog).
From the [Wikipedia article on fog](http://en.m.wikipedia.org/wiki/Fog#Sound_propagation_and_acoustic_effects):
>
> Sound typically travels fastest and farthest through solids, then liquids, then gases such as our atmosphere. The distance the water molecules are from each other, and temperature, are the reasons sound is affected during a fog condition.
> Molecule effect: Though fog is essentially water, the molecules are barely touching each other. High pitched sounds have a high frequency, which in turn means they have a short wavelength (velocity = f x lambda). This means that to transmit a high frequency wave, lots of air has to be moved back and forth, and very quickly; consequently, there can actually be a loss or damping effect of high pitched sounds because they wouldn't travel as far as they might when not being refracted off of separated water molecules which make up the consistency of fog. In contrast, low pitched notes, with a low frequency and a big wavelength, are moving the air less fast and less often, so the losses are reduced. Therefore, low-pitched notes are less affected by fog and will also travel further, thus the low pitched tone of a foghorn.
> Temperature effect: A fog occurs during a temperature inversion where cold air is pooled at the surface helping to create the fog, while warmer air sits aloft. This reversed boundary between cold air and warm air, is able to reflect sound waves back toward the ground, allowing sound that would normally radiate out escaping into the higher atmosphere, to bounce back and travel near the surface. Hence, a temperature inversion increases the distance that lower frequency sounds travel by reflecting the sound between the ground and the inversion layer.
>
>
>
| stackexchange/physics |
Q: realme device app installing take a long time after uninstall in flutter my android phone is realme. one time i delete flutter app, after that i was trying to reinstall that take very long time.(https://i.stack.imgur.com/eGMBW.png)
A: *
*Go to file -> Open -> Select a android -> open in new
window -> connect your device and Run android project.
*After that you try to Run your Flutter project.
*open this image for result
https://i.stack.imgur.com/UgKGJ.png
| slim_pajama |
the rna interference ( rnai ) mechanism uses small rna molecules to control cellular gene expression .
these small molecules are processed from short rna hairpin precursors of which the ends are defined by microprocessor cleavage ( mirnas ) or transcription initiation and termination ( shrnas ) . in the canonical pathway , dicer will cleave the top of the rna hairpin to create a small rna duplex with a 5 ' ( 5p ) and 3 ' ( 3p ) strand ( figure 1a ; left panel ) .
many of the dicer - cleaved mirna duplexes are subject to 3 ' end modification through addition of a few tailing nucleotides , specifically u or a. the addition of 3 ' u is thought to mark the rna for degradation or processing .
addition of 3'a is believed to promote stability , but other reports failed to reproduce this effect .
the processed rna duplex is loaded into the argonaute ( ago)-containing rna - induced silencing complex ( risc ) .
the piwi domain of the ago2 protein has slicing activity that cleaves the passenger strand , thus activating the guide strand .
the selection of guide / passenger is determined by the thermodynamic stability of the duplex ends .
the strand of which the 5 ' end is located at the least stable duplex end is more likely to be selected as guide .
guide - loaded risc will target partially complementary messenger rnas ( mrnas ) for translational suppression or destruction .
recently , additional layers of complexity were added by the description of noncanonical rnai pathways , specifically microprocessor - independent and dicer - independent pathways . in the latter
26,27 ) and the subclass of shrnas termed agoshrnas ( figure 1a ; right panel ) .
the short length of the mirna / shrna stem is a major determinant for entering this pathway .
a stem of 1619 base pair ( bp ) is too small to serve as dicer substrate and will consequently become an ago2 substrate .
ago2 cleaves halfway the 3 ' arm of the duplex between bp 10 - 11 , leaving a single guide strand of which the top remains basepaired ( figure 1a ) .
mir-451 is trimmed by parn to create an unpaired guide ( figure 1a ) , but this modification has no significant effect on the silencing efficiency .
it is important to learn such mechanistic details of agoshrna biogenesis as the property to generate a single guide strand could provide a major therapeutic benefit by avoiding passenger strand mediated off - target effects . in this manuscript
, we present a deep sequencing study on the processing of shrna and agoshrna variants .
we selected the solid method over 454/illumina sequencing because the high yield of small rnas and low error rate are perfectly suited for sequencing of mirnas .
the hairpin variants that we analyzed were previously tested in luciferase knockdown experiments that suggested a shift from shrna to agoshrna activity by stem shortening and a modulatory effect of a top gu bp .
northern blotting confirmed this shift by the appearance of the typical extended agoshrna guide molecule .
we now present further details on dicer - shrna versus ago2-agoshrna processing and 3 ' end modification .
we previously investigated whether replacement of a strong watson - crick bp by a weak gu bp at the top of a shrna stem could force the prototype 21 bp shrt5 hairpin ( figure 1b ) into the agoshrna route .
this shrt5 was chosen as both 5p and 3p arms generated by dicer are active in luc - target silencing and it was shown to be the best inhibitor out of a set of agoshrnas .
several mutations introduced in the top of the hairpin increased agoshrna activity , accompanied by appearance of the typical ago2-cleaved product on northern blot .
rna structures of shrt5 and mutants 6 and 7 and the previous results are summarized in figure 1b . in short , mut 6 produced a modest agoshrna band on northern blot , but the regular dicer cleavage products remained dominant .
mut 7 demonstrated a significant increase in ago2-mediated processing and a concomitant decrease in dicer cleavage .
gene silencing activity was measured with the luc - sense reporter that scores the activity of the 3p strand and the luc - antisense reporter for dicer - cleaved 5p and the ago2-cleaved agoshrna guide .
reduced 3p strand activity was scored for mut 6 and 7 , consistent with decreased dicer cleavage .
we extracted ago2-bound small rnas to determine the relative amount of dicer and ago2 products by deep sequencing .
dominant reads ( > 50 copies in the library ) are listed in supplementary table s1 . for shrt5 and the two mutants , 9699% of the plasmid - matching reads aligned to the expressed shrna ( table 1 ) .
this high coverage permitted us to carefully map the content of the ago2-bound rnas . a major advantage of the agoshrna design over mirna - like designs is that the drosha - processing step is not needed to release the hairpin rna , thus limiting the requirements for processing .
both the 5p and 3p dicer products of shrt5 are equally present in ago2 ( figure 2a ) .
this confirms the symmetric nature of shrt5 and explains the silencing activity measured for both strands ( figure 1b ; luc ) .
the reduced activity of the 3p strand compared to the 5p strand may reflect differential silencing activity of the two strands . a clear shift to 5p / agoshrna products was apparent for mutants 6 and 7 ( figure 2b , c ) .
more ago2-cleaved product was observed for mut 7 ( 9.7% of all reads ) and mut 6 ( 1.3% ) over the wild - type ( wt ) shrt5 ( 0.1% ) .
this correlates with increased agoshrna production by mut 6 and especially mutant 7 on northern blot .
surprisingly , the observed ago2-cleaved product ( ) was 2 nt shorter than the expected agoshrna product ( ) for wt and the two mutants ( figure 1b ) . increased agoshrna loading coincided with decreased 3p - strand loading for both mutants but especially mutant 6 , although 5p loading was maintained ( figure 2b , c ) .
this 3p loading - deficiency correlates with the reported loss of 3p - mediated luc silencing activity , although northern blotting did show normal 3p - strand production .
dicer cleavage is predicted to occur between u and c for 5p and between a and c for 3p ( figure 1b ) .
dicer cleavage does not occur exactly at the predicted site ( figure 2 ) , but rather at multiple sites around this position .
in fact , the major dicer - cleavage event creates a 2-nt staggered cut at u and u , whereas u and c were predicted ( figure 2a ) .
overall , cleavage by dicer is inaccurate and yields multiple products that are loaded in ago2/risc .
the product variation is further increased as the 5p transcripts display various 5 ' ends , likely reflecting differential start site usage by rna polymerase iii at the h1 promoter ( figure 2 ) .
in fact , only 1% of transcripts start at the predicted transcription start site for shrt5 ( mut 6 : 13% and mut 7 : 9% ) , whereas 16% initiate at the -1 position for shrt5 ( mut 6 : 40% and mut 7 : 49% ) . by inspection of the reads
, we observed that the heterogeneity in dicer cleavage site is not linked to this differential start site usage .
lastly , for all three constructs an additional read was observed that starts at a and terminates at a ( figure 2 ) .
next , the shift from dicer to ago2 cleavage was analyzed for a second set of shrnas with decreasing stem length and either a gu or g - c top base pair .
the expected cleavage products of ago2 ( ) and dicer ( ) are indicated on the hairpin templates in figure 3 .
some unexpected details of agoshrna processing were disclosed that will be discussed before we address the general shift from dicer to ago2 cleavage . as observed for mut 6 and 7 , we witnessed a shift in the actual ago2 cleavage site , and an intriguing pattern became apparent . for mutants 17/18/19 ,
cleavage occurred exactly at the predicted position between bp 1011 from the bottom of the stem , but cleavage shifted to bp 1112 and 1213 for mutants 20 and 21 , respectively .
the observed ago2 cleavage sites are marked in figure 3 as arrows ( ) and were used for quantitation of the agoshrna products .
inspection of the reads indicates that the transcripts with a shifted ago2 cleavage site ( mutants 20/21 ) do start at the same -1 position as mutants 17/18/19 .
we observed a small 3 ' a - tail at the ago2 cleavage site that is not encoded by the shrna construct ( table 2 ) .
this tail is not due to sequencing errors as there are no adenines present around the ago2 cleavage site . by use of ligation - based solid deep sequencing
, we also prevent any pcr - based errors that could have added a to the small rna sequence .
the a - tails are short with one to three adenines ( table 3 ) and the modified guide strand is named agosh .
this 3 ' end modification was apparent for all wt and mutant shrnas analyzed in this study , including the previously mentioned mut 7 ( table 2 ) .
of all agoshrna guide strands , 2787% contained a short 3 ' a - tail ( table 2 ) .
no consistent pattern was apparent for 3 ' a - tailing with respect to stem length or gu / gc top .
inspired by recent findings for mir-451 and small nucleolar rna ( snorna ) , we reasoned that 3 ' adenylation may present a signal for parn to trim the agosh into the unpaired agosh molecule ( figure 4a ) .
indeed , a distinct rna population was observed that starts at the tss and terminates just 3 ' of the shrna loop ( figure 4b ) . to determine the relative concentration of each rna product , the shrna - derived reads were defined as dicer - cleaved ( reads ranging from 1922 nt , expected cleavage site 1 nt ) , ago2-cleaved agosh ( reads 27 nt , expected cleavage site 1 nt ) and agosh ( reads between 2328 nt and ending in the loop sequence aagac / uu ( figure 4b ) ) . as expected , the regular 21 bp shrna yields mostly dicer - cleaved products ( ( figure 4c , d ) 55% for 21gc and 94% for 21gu ; black line ) .
the dicer products disappear rapidly with decreasing shrna stem length , concomitant with an increase of the agosh and agosh products .
the agosh product remains a relatively minor product , never increasing above 4% of the total ago2-bound rna population ( figure 4c , d ) .
agosh products constitute more than 50% of the rna population for constructs with a small stem ( 19 bp ) , but are replaced by dicer products for the larger hairpins ( 20 bp ) ( figure 4c , d ) .
no consistent differences were apparent for shrnas with g - c or gu as top bp .
to further investigate the involvement of parn in the generation of agosh products , we performed a parn knockdown experiment with 18gc and 19gc .
the total rna content of transfected cells was separated on a denaturing gel , blotted and probed with a locked nucleic acid probe directed against the 5 ' side of the hairpin ( figure 5a ) .
this probe should thus detect ago2 cleavage products as well as the dicer - cleaved 5p strand .
the knockdown of parn caused the selective disappearance of the agosh product , while leaving the dicer cleaved product intact ( figure 5b ) .
we previously investigated whether replacement of a strong watson - crick bp by a weak gu bp at the top of a shrna stem could force the prototype 21 bp shrt5 hairpin ( figure 1b ) into the agoshrna route .
this shrt5 was chosen as both 5p and 3p arms generated by dicer are active in luc - target silencing and it was shown to be the best inhibitor out of a set of agoshrnas .
several mutations introduced in the top of the hairpin increased agoshrna activity , accompanied by appearance of the typical ago2-cleaved product on northern blot .
rna structures of shrt5 and mutants 6 and 7 and the previous results are summarized in figure 1b . in short , mut 6 produced a modest agoshrna band on northern blot , but the regular dicer cleavage products remained dominant .
mut 7 demonstrated a significant increase in ago2-mediated processing and a concomitant decrease in dicer cleavage .
gene silencing activity was measured with the luc - sense reporter that scores the activity of the 3p strand and the luc - antisense reporter for dicer - cleaved 5p and the ago2-cleaved agoshrna guide .
reduced 3p strand activity was scored for mut 6 and 7 , consistent with decreased dicer cleavage .
we extracted ago2-bound small rnas to determine the relative amount of dicer and ago2 products by deep sequencing .
dominant reads ( > 50 copies in the library ) are listed in supplementary table s1 . for shrt5 and the two mutants , 9699% of the plasmid - matching reads aligned to the expressed shrna ( table 1 ) .
this high coverage permitted us to carefully map the content of the ago2-bound rnas . a major advantage of the agoshrna design over mirna - like designs is that the drosha - processing step is not needed to release the hairpin rna , thus limiting the requirements for processing .
both the 5p and 3p dicer products of shrt5 are equally present in ago2 ( figure 2a ) .
this confirms the symmetric nature of shrt5 and explains the silencing activity measured for both strands ( figure 1b ; luc ) .
the reduced activity of the 3p strand compared to the 5p strand may reflect differential silencing activity of the two strands . a clear shift to 5p / agoshrna products was apparent for mutants 6 and 7 ( figure 2b , c ) .
more ago2-cleaved product was observed for mut 7 ( 9.7% of all reads ) and mut 6 ( 1.3% ) over the wild - type ( wt ) shrt5 ( 0.1% ) .
this correlates with increased agoshrna production by mut 6 and especially mutant 7 on northern blot .
surprisingly , the observed ago2-cleaved product ( ) was 2 nt shorter than the expected agoshrna product ( ) for wt and the two mutants ( figure 1b ) . increased agoshrna loading coincided with decreased 3p - strand loading for both mutants but especially mutant 6 , although 5p loading was maintained ( figure 2b , c ) .
this 3p loading - deficiency correlates with the reported loss of 3p - mediated luc silencing activity , although northern blotting did show normal 3p - strand production .
dicer cleavage is predicted to occur between u and c for 5p and between a and c for 3p ( figure 1b ) .
dicer cleavage does not occur exactly at the predicted site ( figure 2 ) , but rather at multiple sites around this position .
in fact , the major dicer - cleavage event creates a 2-nt staggered cut at u and u , whereas u and c were predicted ( figure 2a ) .
overall , cleavage by dicer is inaccurate and yields multiple products that are loaded in ago2/risc .
the product variation is further increased as the 5p transcripts display various 5 ' ends , likely reflecting differential start site usage by rna polymerase iii at the h1 promoter ( figure 2 ) .
in fact , only 1% of transcripts start at the predicted transcription start site for shrt5 ( mut 6 : 13% and mut 7 : 9% ) , whereas 16% initiate at the -1 position for shrt5 ( mut 6 : 40% and mut 7 : 49% ) . by inspection of the reads
, we observed that the heterogeneity in dicer cleavage site is not linked to this differential start site usage .
lastly , for all three constructs an additional read was observed that starts at a and terminates at a ( figure 2 ) .
next , the shift from dicer to ago2 cleavage was analyzed for a second set of shrnas with decreasing stem length and either a gu or g - c top base pair .
the expected cleavage products of ago2 ( ) and dicer ( ) are indicated on the hairpin templates in figure 3 .
some unexpected details of agoshrna processing were disclosed that will be discussed before we address the general shift from dicer to ago2 cleavage . as observed for mut 6 and 7 , we witnessed a shift in the actual ago2 cleavage site , and an intriguing pattern became apparent . for mutants 17/18/19 ,
cleavage occurred exactly at the predicted position between bp 1011 from the bottom of the stem , but cleavage shifted to bp 1112 and 1213 for mutants 20 and 21 , respectively .
the observed ago2 cleavage sites are marked in figure 3 as arrows ( ) and were used for quantitation of the agoshrna products .
inspection of the reads indicates that the transcripts with a shifted ago2 cleavage site ( mutants 20/21 ) do start at the same -1 position as mutants 17/18/19 .
we observed a small 3 ' a - tail at the ago2 cleavage site that is not encoded by the shrna construct ( table 2 ) .
this tail is not due to sequencing errors as there are no adenines present around the ago2 cleavage site . by use of ligation - based solid deep sequencing
, we also prevent any pcr - based errors that could have added a to the small rna sequence .
the a - tails are short with one to three adenines ( table 3 ) and the modified guide strand is named agosh .
this 3 ' end modification was apparent for all wt and mutant shrnas analyzed in this study , including the previously mentioned mut 7 ( table 2 ) .
of all agoshrna guide strands , 2787% contained a short 3 ' a - tail ( table 2 ) .
no consistent pattern was apparent for 3 ' a - tailing with respect to stem length or gu / gc top .
inspired by recent findings for mir-451 and small nucleolar rna ( snorna ) , we reasoned that 3 ' adenylation may present a signal for parn to trim the agosh into the unpaired agosh molecule ( figure 4a ) .
indeed , a distinct rna population was observed that starts at the tss and terminates just 3 ' of the shrna loop ( figure 4b ) . to determine the relative concentration of each rna product , the shrna - derived reads were defined as dicer - cleaved ( reads ranging from 1922 nt , expected cleavage site 1 nt ) , ago2-cleaved agosh ( reads 27 nt , expected cleavage site 1 nt ) and agosh ( reads between 2328 nt and ending in the loop sequence aagac / uu ( figure 4b ) ) . as expected , the regular 21 bp shrna yields mostly dicer - cleaved products ( ( figure 4c , d ) 55% for 21gc and 94% for 21gu ; black line ) .
the dicer products disappear rapidly with decreasing shrna stem length , concomitant with an increase of the agosh and agosh products .
the agosh product remains a relatively minor product , never increasing above 4% of the total ago2-bound rna population ( figure 4c , d ) .
agosh products constitute more than 50% of the rna population for constructs with a small stem ( 19 bp ) , but are replaced by dicer products for the larger hairpins ( 20 bp ) ( figure 4c , d ) .
no consistent differences were apparent for shrnas with g - c or gu as top bp .
to further investigate the involvement of parn in the generation of agosh products , we performed a parn knockdown experiment with 18gc and 19gc .
the total rna content of transfected cells was separated on a denaturing gel , blotted and probed with a locked nucleic acid probe directed against the 5 ' side of the hairpin ( figure 5a ) .
this probe should thus detect ago2 cleavage products as well as the dicer - cleaved 5p strand .
the knockdown of parn caused the selective disappearance of the agosh product , while leaving the dicer cleaved product intact ( figure 5b ) .
novel agoshrna designs form a promising class of rnai - based therapeutics that avoid dicer cleavage and instead use ago2-slicer activity to create a single guide rna to target a specific mrna for destruction .
agoshrnas thus avoid off - target effects induced by the passenger strand of a regular shrna .
we previously tested the critical elements , in particular the stem length , that cause a shift from regular shrna to agoshrna activity .
the current deep sequencing analysis confirmed these findings by probing for dicer versus ago2 cleavage events .
cleavage at the predicted site confirmed ago2 cleavage for the shorter hairpins , but we noticed an upward shift in cleavage site for the less efficient agoshrnas larger than 19 bp for both mutant sets ( figures 1b and 3 ) .
an intriguing pattern became apparent : cleavage of mutants 17/18/19 occurs exactly at the predicted position in the 3 ' arm between bp 10 and 11 from the bottom of the stem , but was shifted between bp 1112 and 1213 for mutants 20 and 21 , respectively ( figure 6a ) .
mutants 19/20/21 support the new concept of cleavage at 9 bp from the loop instead of the well - established 10 bp from the bottom rule . in search for a mechanistic explanation ,
it is important to realize that the extended hairpins are processed less efficiently by ago2 ( figure 4c , d ) .
we present a mechanistic model in which the 5 ' end of the agoshrna docks in the mid domain and the loop is near the paz domain ( figure 6b ) . we propose a structural realignment in the ago2-containing complex because the extended hairpins sterically clash with the paz and/or mid domains that are in close contact with the hairpin .
a similar steric problem was suggested to occur for ago2-loaded hairpins with a large loop .
structural rearrangement pushes the domains of ago2 out of the optimal position , which can explain the cleavage to shift 1 or 2 bp further up in the stem , albeit at a greatly reduced efficiency .
this mechanistic model also explains the unexpected piwi cleavage sites observed for the initial mutant set with extended stems of 21 bp ( figure 2 ) .
thus , the sequence of an agoshrna does not influence the actual cleavage site , which seems dictated primarily by the duplex length ( and secondarily by the loop size , see liu et al . ) .
cleavage and subsequent trimming by parn may thus be essential to create a free 3 ' end that can dock into the paz domain to reach a stable configuration .
single - stranded agoshtrim products will be accommodated in this stable ago2 complex , thus blocking further parn trimming and explaining the discrete trimming pattern ( figure 4b ) .
another new finding is that a small 3 ' a - tail is added upon agoshrna cleavage to yield the modified agosh guide strand ( figure 4a , b ) .
we present evidence that this agosh guide is a processing intermediate that is subsequently 3'-trimmed to generate a mature agosh rna species ( figure 4c , d ) .
the partially basepaired agosh precursor becomes an unpaired agosh , thus activating its ability to pair with the mrna to cause its inactivation .
further processing may be important as the risc - ago2 complex does not have rna duplex unwinding activity .
parn also plays a role in deadenylation of maternal mrnas during oocyte maturation , mrna degradation , and maturation of mammalian box h / aca small nucleolar rnas .
parn is a poly(a ) specific exonuclease that uses 3 ' a - tails as substrate .
these short 3 ' a - tails could be added by poly(a ) polymerases like papd5 ( ref . ) or papd4 ( ref . ) , but details about what is recognized in agoshrnas and mir-451 remain unknown .
we currently do not know if mir-451 is also 3 ' adenylated before it is trimmed by parn .
we specifically looked for such molecules , but mir-451 was absent from our 293t - based small rna libraries . upon knockdown of parn
, we witnessed a loss of the agosh product on northern blot ( figure 5a ) .
the regular dicer product served as internal control that is not influenced by knockdown of parn .
parn knockdown did not result in accumulation of the agosh precursor , suggesting that it is an unstable intermediate .
many rnai applications use shrna constructs to stably reduce gene expression , but it is becoming increasingly clear that these small rna molecules are less precise than originally thought .
this and other studies indicated that dicer cleavage is rather imprecise , yielding multiple rnas with different silencing efficiency , specificity and/or off - target effects . combined with the multiple transcriptional initiation sites observed for the h1 rna polymerase in this and others studies , a quasispecies of slightly different guide rnas is generated .
the 5 ' end variation also holds for agoshrna reagents , but ago2-mediated processing is more precise than dicer cleavage .
previous northern blot analysis indicated that mut 6 is processed into an equal concentration of 5p and 3p strands , however only the 5p strand showed activity ( figure 1b ) .
these northern blots were performed on total cellular rna , but sequencing of the ago2-bound rna indicated that the 5p strand is exclusively loaded .
this can explain the absence of 3p strand activity . to add to the small rna diversity
, we also describe an alternative transcript that runs from + 6 to + 28 .
we do not understand how this transcript is generated , whether it is alternatively processed or due to a new transcription initiation site .
the generation of a single guide strand instead of two active shrna - derived strands makes the agoshrna design an attractive reagent for biology applications and therapeutic action .
this study and previous results indicate that an active agoshrna should have a stem - length of 19 bp and a small loop .
the introduction of a top gu wobble base pair can push a regular shrna towards the agoshrna route , including subsequent tailing and trimming , as it likely reduces the stem length .
the agoshrna constructs may still be improved by approaches that yield a more precise transcript 5 ' end , either by changing the promoter or the transcription start site .
cell culture , transfection , and constructs . human embryonic kidney ( hek- ) 293 t cells were cultured as monolayer in dulbecco 's modified eagle 's medium ( invitrogen , paisley , uk ) supplemented with 10% fetal bovine serum , penicillin ( 100 u / ml ) , and streptomycin ( 100 g / ml ) at 37 c and 5% co2 . for the rna isolation , cells were cultured in 25 cm flasks and transfected with 4 g shrna plasmid dna and 1 g ago2-flag plasmid using lipofectamine 2000 ( life technologies , carlsbad , ca ) .
the shrna and agoshrna constructs used in this manuscript have been described previously . for parn knockdown , hek-293 t
were reverse transfected in 10 cm wells with a sictrl duplex ( 5-aagcgauaccucgugugugadtdt-3 and 5-ucacacacgagguaucgcuudtdt-3 ) and an sirna mixture against parn consisting of siparn duplex 1 ( 5-ggagaaaacaggaagagaadtdt-3 and 5-uucucuuccuguuuucuccdtdt-3 ) and siparn duplex 2 ( 5-ucaucuccauggccaauuadtdt-3 and
after 48 hours , the siparn - treated cells were reverse transfected with another 50 nmol / l of sirna mixture and 5 g of agoshrna - expressing construct .
post - transfection , the cells were washed several times with cold phosphate - buffered saline and ago2-flag was immunoprecipitated as previously described . in short , the cells were incubated with isob - np40 ( 10 mmol / l tris - hcl ph 7.9 , 150 mmol / l nacl , 1.5 mmol / l mgcl2 , 1% np40 ) for 20 minutes on ice .
the cell - lysates were centrifuged at 12,000 g for 10 minutes at 4 c to clear cell debris .
the supernatant was incubated with 75 l anti - flag m2 agarose bead - suspension ( sigma , st louis , mo ) with constant rotation for 16 hours at 4 c .
the supernatant ( depleted fraction ) was separated from the beads ( enriched fraction ) .
the beads were washed three times with net-1 buffer ( 50 mmol / l tris - hcl ph 7.5 , 150 mmol / l nacl , 2.5% tween-20 ) and resuspended in isob - np40 .
rna was isolated by phenol chloroform extraction followed by dnase treatment using the turbo dna - free kit ( life technologies ) .
the isolated rna was size separated on a 15% denaturing polyacrylamide gel electrophoresis gel next to a size marker ( generuler ultra low range dna ladder ; thermo scientific , waltham , ma ) for size estimation .
the 1555 nt rna fragments were purified from gel using a spin column ( ambion , carlsbad , ca ) . the quality and percentage of mirna
was assayed on a bioanalyzer 2100 ( agilent , santa clara , ca ) using a small rna chip .
the solid small rna library preparation protocol ( applied biosystems , carlsbad , ca ) was used to prepare an rna library that was subsequently analyzed on the solid wildfire system ( applied biosystems ) .
analysis of the solid colorspace reads was performed with lifescope genomic analysis software version 2.5 ( applied biosystems ) using the small rna pipeline .
analysis of the solid deep sequence run yielded 6,796,533 to 14,069,013 reads per sample , with an average of 10,227,999 ( table 1 ) .
the libraries were cleaned for human genome filter sequences ( containing rrna , trna etc ; supplied with lifescope ) and known mirna sequences ( mirbase version 21 ; http://www.mirbase.org/ ) .
subsequently , the filtered reads were aligned against the reference sequences of the shrna - expressing constructs .
we performed two alignments to create read libraries ; one containing perfect reads without mismatch , the other with a perfect seed region ( nt 115 ) but with mismatches in the 3 ' part . for the different constructs , the combined libraries mapped 0.732.4% , with an average of 7.3% of all sequence reads to the reference sequence ( table 1 ) . of
this library without mismatch was used to create the final alignments and to analyze the dicer and ago2 cleavage products ( shrna and agoshrna , respectively ) . the library with 3 ' end mismatches
was used to analyze nontemplated 3 ' end nt addition . supplementary material
table s1 .
abundant plasmid - encoded reads ( n > 50 ) identified by solid deep sequencing .
abundant plasmid - encoded reads ( n > 50 ) identified by solid deep sequencing . click here for additional data file . | pubmed |
Computing $\langle x_ix_{i+1}\rangle$ in a polymer chain
I have a basic question about 1D polymer chains consisting of $N$ rods of length $l$. I have read about ideal chains where we assume that the polymer has zero Hamiltonian. This can be found [here](https://en.wikipedia.org/wiki/Ideal_chain) Now, suppose instead $H(x) = nV$ where $n$ is the number of bends in the polymer $x$ and consider the canonical ensemble of the system. Let $x\_i$ be the individual displacements of the ith link in the chain; i.e. $x\_i = \pm l$. I curious how we determine the average value $\langle x\_ix\_{i+1}\rangle$.
I have that the probability of a state $x$ of a system is given by $\rho(x) = \frac{1}{Z\_\beta}e^{-\beta H(x)}$. That being said, do we have something like
$$\langle x\_i x\_{i+1}\rangle = l^2\Big(\frac{1-e^{-\beta V}}{1+e^{-\beta V}}\Big)$$
from saying that the probability of a bend in $x\_i x\_{i+1}$ is $e^{-\beta V}$?
It looks like your answer is correct. If you need more formal solution, then let's introduce Ising variables $s\_i = x\_{i+1}/x\_i = \pm 1$. Energy has the following expression in terms of this variables
$$
H(x) = nV = \sum\_{i=1}^{N-1}\frac{1-s\_i}2
$$
The variables $x\_1, s\_1,\ldots,s\_{N-1}$ are not subject to any restrictions. Hence the probability factorizes
$$
\rho(x) = C\prod\_{i=1}^{N-1} e^{\beta V s\_i/2}
$$
and gives
$$
\langle s\_i \rangle = \frac{e^{\beta V/2} - e^{-\beta V/2}}{e^{\beta V/2} + e^{-\beta V/2}}
$$
Finally,
$$
\langle x\_i x\_{i+1}\rangle = l^2 \langle s\_i \rangle = l^2 \frac{1 - e^{-\beta V}}{1 + e^{-\beta V}}.
$$
Another method is to introduce Ising variables $\sigma\_i = x\_i/l$. Getting a solution this way takes a little longer, but you can also solve a more general problem about the polymer chain that the force acts on.
| stackexchange/physics |
Glee 1. Chapter 1
**A/N: This isn't my story, it's my friend's, but she doesn't have a FF, so please do favorite, alert and review and I'll pass it on. I loved it! Enjoy. **
**Disclamer: I, nor my friend, own Glee or anything of that sort.**
When Rachel started dating Finn she had this teenager image of love, of them going to prom together, dancing with him, wearing her sparkling dress and high-heeled shoes while he spun her around the dance floor in his arms. Of course as we all know teenager images of love aren't always exactly the way things end up working out. Weeks before prom Finn broke up with Rachel. He found himself still attracted to Quinn, still wanting to date Quinn, still feeling a sort of possessiveness toward her. To Rachel he just said, "Uh, sorry, but I can't see you anymore" and though his face held that puppy dog regretful look, like when you catch your dog chewing on an item that is not his, Rachel could tell Finn was serious.
After Finn broke up with her she started the long walk out of the school to her car, walking through the parking lot she kept her head up, kept her walk purposeful, willing herself not to let one tear slide out of her eye, down her cheek, not until she got in the car, not until her engine was running, not until her car was moving, better yet, not until she was in her room with her door closed and music on so her dad wouldn't come home from work and hear her crying or her other dad for that matter either.
Rachel pulled into the driveway and grabbed her purse and backpack from the passenger seat, she was up the walk and had her key in the lock when she heard his voice behind her.
"Rachel? Did you forget?"
Rachel turned in surprise, she dropped her keys, Puck was standing behind her with his history book and a beat-up notebook and a pencil over his ear. She fumbled picking her keys up, she fumbled opening the door and stuttered as she walked inside, "No, I didn't forget, come on in, the dining room is this way, go ahead and get settled, I'll just be a minute," she left him standing just outside the door as she tried to walk casually up the steps. She'd forgotten, how could she have remembered, what with Finn breaking up with her, how could she have remembered that today she and Puck were studying, studying history.
Puck watched her go up the stairs, he saw her hand tapping along the rail as she walked up, not her fingers, not like she was happily drumming the railing, but the palm of her hand, like she was talking to herself, like she was nervous, like she was reminding herself. Puck closed the door behind himself and looked at the dining room table, clearly this was where Rachel did a lot of her homework, there was a cup of pencils in the center of the table and little eraser shavings on the edge, toward the right of one chair. Puck scratched his head, ran his hand over his Mohawk, then sat down at the table with his book and notebook. He looked around the room, flowers on end tables, framed pictures on the walls, pictures of Rachel and her dads, pictures of her with just one dad or the other, with grandparents, family get together pictures, Puck stood up for a closer look.
"I-I'm sorry about that," Rachel said walking into the room, she was changed from her school clothes of a skirt and top and was wearing shorts and a sweat shirt, and socks, no shoes. Her hair was in a pony tail and she was wearing glasses. "I had to change clothes," she walked over to Puck, stood beside him and looked up at the pictures with him. He looked down at her, in her casual after-school clothes and smiled, he hadn't ever seen Rachel so unwound, so relaxed, it was a welcomed change. He had never seen her with glasses, she looked cute.
"Why don't you dress like this for school?" He asked, motioning from her head to her toes.
"Uh, well, I, it doesn't look nice. Normally I wouldn't dress like this to study, but, I had, such an awful day, I just had to get into comfort clothes. Comfort clothes are like comfort food you know, they can relax you, change your mood, make you feel-" She paused, looking up at Puck's face, at his dark eyes, she took a little uneasy step backward, "-better, all better," she said quietly, finishing her sentence.
Puck didn't know what made her day bad, like any guy he wasn't sure if he should ask or not, but he knew that he was hot and had a smokin' body and a hug from him always made the girls feel good. So, he leaned down, put his arms around the top of Rachel's shoulders and gave her a hug that not only enveloped her arms, but pulled her forward until she was against his chest. Puck smiled to himself, that always helped.
"What was that for?" Rachel asked, a little off balance, Puck hadn't taken his arms off her, but he loosened his grip a little and she could lean back and look at him.
"You looked like you needed a hug and you said you had an awful day," was all he said. Rachel nodded and smiled and gave him a quick squeeze then let go and started for the table. Puck followed her and sat down in the chair closest to the one she was sitting in. He would wait and see if she had anything else to say, she was a girl so he figured she'd share her entire day before he went home for supper.
Rachel sat down and scooted her chair forward, then opened her book and her notebook. When Puck sat down right next to her she was a little surprised, at this point in her life, in her day at least, she was feeling so bad and so rejected from Finn having broken up with her, completely out-of-the blue, in her opinion at least, well, she was just feeling so bad about herself she couldn't believe Puck would choose the chair nearest her when he could have just as easily sat across from her or on one of the table ends.
"Okay, the test is in three days, we need to review chapter 6, have you read it?" She asked him, thumbing through the chapter to the review questions at the end. Puck leaned over her shoulder looking at the pages with her, his arm casually draped over the back of her chair.
"Well, you know, the teacher went over it in class," he scratched the back of his neck, "He had notes and I wrote down what he said, what he wrote on the projector," Puck leaned his head on his hand, his elbow on the table, "I didn't read it at home though, if that's what you're asking." Then he looked at her and smiled, thinking to himself, Charm her, Charm her, or she will scold you.
Rachel sighed, was she the only student who took school seriously? Who read the chapters when the teacher said to read the chapters. But, well, going over the material with Puck would help her learn the information further, and he had to get a B or higher on this test or he was out of Glee. Schools and their grade requirements, didn't administrators know not all students cared about history and science? Some students were artists!
"Well, it is rather dull, I mean, my dad, he taught me a lot about the civil war when I was a kid, so I know it inside out, but-"suddenly as her eyes crossed the room, and looked out of the dining room and down the hall and into the living room, she saw a jacket of Finn's that he'd left at her house just two evenings ago. He'd been over to "study" but had spent the evening sitting on the couch with her, NOT studying. Suddenly Rachel felt angry, embarrassed, furious, she felt her face grow hot, she stood up, forgetting the Civil War, forgetting Puck was sitting next to her, and she stomped from the room.
Stomping with socks isn't as loud as stomping with say, shoes, but she stomped angrily from the dining room, across the hallway, into the living room, ripped the jacket so angrily off the chair that the chair tipped backwards, then without noticing the chair she stomped out the front door and threw the jacket onto the porch. She saw her cell phone on the little table inside the door, and angrily jerked it off the table and began typing so fiercely Puck thought sure she would break something, either the phone or a thumb or something. At that point, he stood up and with a few long strides he was right next to her.
"I thought if we started talking about the Civil War you'd come out of your funk or whatever, but clearly we're not going to get anything accomplished until you get it off your chest," he took the phone from her hand and easily tossed it, sending it sailing across the room, and landing softly on the couch. Rachel looked first after her phone in surprise, then up at Puck's face. He looked so caring and sweet that she couldn't keep it in any longer, and she started to cry.
Puck followed her to the stairs where she sat down on the bottom step, he sat next to her and put his arm around her shoulders and she let her head fall against him and she cried.
2. Chapter 2
Puck liked to maintain the reputation of a player, one of his favorite activities, one that he was most known for, rhymed with his name and that was a coincidence that always made him smile. As he sat on the steps with Rachel leaning against him crying he couldn't help but realize sex was actually the last thing on his mind at the moment. He sort of felt protective of Rachel, only half attracted to her, well, more than half attracted to her, she did have a sort of charm, like, a teacher from the 50s or something. He leaned his cheek on the top of her head and patted her arm, hmm, her hair smelled good.
"I'm so sorry," she sniffled, sitting up straighter, she patted his leg, "Thank you, I'm so sorry, really, I, I hate to cry in front of people like that, and I really am sorry," Rachel stood up, she took her glasses off, wiped them, then set them down on the step and wiped her eyes with the bottom of her shirt. Puck smiled, amused to see this side of Rachel that was so different from her school persona, seeing someone who was always all prim and proper, wipe their tears on their shirt, well, it made her seem real. If only she would wipe her nose on her sleeve, he'd probably have to grab her and kiss her right then.
"No problem, Rachel, I'm sorry you had such a rotten day. What happened anyway?" He hadn't been planning to ask, but, what the hell, she probably wanted to talk about it anyway, she liked to talk, he knew that much about her. Well, that and she had gotten good grades in history all year, which was why he was here in the first place. He hoped she would calm down enough to get back to the studying…
"Finn dumped me," Rachel blurted, she hadn't been planning to get into it, but she hadn't spoken the sentence out loud yet, and it felt good to do so. "Finn," a pause, she frowned, "Broke up," another pause, she looked down at Puck, still sitting on the step, she stifled a sudden giggle, "Finn broke up with me," once she got all the words out she laughed. Puck raised his eyebrows and stood up. What an odd reaction she was having. Rachel stopped laughing and shook her head, she pulled the legs of her shorts down and reach down and pulled her socks up. Once she seemed to feel a little more put together she started for the dining room table, pulling the sides of her sweatshirt down and tucking the ends under about two inches. Puck followed her.
"I'm not really sure what's so funny about that," he said, "But I guess laughing is as good as crying for letting your emotions out," he sat down next to her at the table. He glanced at her book and opened his to the same page, then looked at her expectantly.
"You know, Puck, eh, Noah, I don't know what to call you," her words trailed off.
"Well, what do you feel comfortable with?" He asked her. She smiled and nodded, flipped a page in her book, found the review questions at the end of chapter six and grabbed her pencil.
"Okay, Puck, I'm going to ask you the questions, then you can either write your answers or tell me your answers. Either way works."
"I would rather tell you then have to worry about writing them down," he answered. He felt a little curious and wanted to talk more about Finn, but honestly, what difference did it make, they'd probably end up back together again. He wondered if he should give Finn a little talk tomorrow at school, about breaking up with girls, there had to be a better way to do it. Ah, but screw Finn, he was not exactly competition, but why give him any sort of edge.
The phone rang after about four review questions, it was the home phone, not Rachel's cell, but she pushed her chair back from the table and went to answer it. Puck looked at the notes she'd written down in response to his answers to the questions. She had written that he needed more well-formulated answers, basically, more words to make his answers seem more like he knew what he was doing. He sighed and read ahead the next review questions, preparing the answers in his head.
Rachel stood in the doorway to the kitchen with the phone to her ear. She felt silly talking on a corded phone, surely her dads were the only parents in town to still use a phone with a long spiral cord, though it did give one something to do with their hands while they were on the phone. It was Mercedes on the phone, saying she and Kurt were going to a movie Friday night, well, they had been planning it, but Mercedes had just been asked out for that night by the big hulking hunky quarter back of a foot ball team from their conference, and she really wanted to go, but didn't want to hurt Kurt's feelings. She was asking Rachel what she thought was the best way to change the plans. Rachel said not to worry, she knew there was an exhibit at the museum about an hour away that night that she thought Kurt would enjoy, she would call him right then, ask if he could go, and then call Mercedes back and let her know. Then Rachel glanced up and saw Puck looking at their books and she told Mercedes she would call Kurt later, she was busy.
"Ooo, what kind of busy?" Mercedes teased. Rachel laughed and told her she was just studying with Puck. Mercedes let out a little gasp and asked if Finn knew, then Rachel realized she shouldn't have said anything, because she was dying to spill to her friend all about getting dumped (getting dumped! Still so hard to believe) but she didn't want to get into it and possibly get all weepy again, with Puck right there. Plus she had promised him a good study session.
"Mercedes, I just have to call you later, "she said, then she whispered, "I will explain everything later!"
"I'm sorry Puck, okay, where were we?" Rachel sat down and looked at her notebook. Puck put his hand over her hands and looked at her, waiting for her to look up. He heard her take a breath and look up at him.
"What?" She asked.
"Come on, Rachel; get it off your chest. Why did Finn break up with you? I know it's all in there right now, bouncing around inside that head of yours, and it needs to get out, once you let it out you can really focus on something else, on the ever thrilling Civil War, for example." He smiled, and did a Vanna White gesture toward their school materials. Rachel laughed, then she looked into his eyes, his earnest expression and she put her hands on his wrists and held onto them and leaned forward and kissed him. She kissed him for a long while, and much to her relief he kissed her right back. Finally he shrugged out of her grip and put his hands on her face, kissed her a little more then pulled back and looked at her.
"Uh, Rachel," he began. But she interrupted him by kissing him again, then she moved onto his lap and continued kissing him, he put his arms around her waist.
"Rachel?" her dad's voice came in the back door, startling her back to reality. She jumped off Puck's lap and into her chair, she pulled her sleeve across her mouth and picked up her pencil.
"In the dining room dad!" She called out in the clearest voice she could manage. Puck scooted his chair in closer to the table and wiped his mouth and picked his pencil up.
"We're just in here studying, the Civil War," he called out. Rachel's eyes widened for a moment. She got up hurriedly and went to the kitchen to meet her dad. He came into the dining room with her, she was pleased to see Puck was standing up to greet him by the time they got to the table.
"Ah, the Civil War huh? Yes, brothers fighting brothers, the last great war fought on American soil. Phew, thank goodness for that," her dad put his hand out to shake Puck's hand, "You must be Noah, nice to see another young man around here once in a while," he looked at Puck's Mohawk, "Not that I have anything against Finn, he does give me something to chuckle at now and again." Puck stifled a laugh.
"Nice to meet you Mr. Berry, Rachel is quite the history whiz you know, she's helping me get back on my game in history so I can stay in glee club," he smiled at Rachel, "Not that I ever thought glee club would be my thing, but sir, well, the chicks like a guy with a guitar."
"Yes, so do the guys actually," Rachel's dad teased. Rachel's face grew red and she started pushing her dad out of the room.
"Okay dad, thanks, good to see you, we'll be getting back to our studies now," she pushed him all the way out of the dining room and into the kitchen, he was laughing the whole time and when she came back to the table Puck was laughing too. Men! They could really be annoying!
3. Chapter 3
**A/N: So my friend writes much faster than me, plus she only has one story, and writes when she's bored. Here's chapter three, short, but here (: Enjoy and review! **
When Rachel went to start her car the next morning it wouldn't even turn over, frustrated she glanced at her watch, her parents were already gone for the day and she knew they were too far away to come back for her. She called Mercedes, then Kurt, but neither of them picked up. In a huff she threw her backpack over her shoulder, held her coffee in one hand and wedged her purse under her other arm and started for school as a quick pace. After two blocks she realized if she walked all the way to school at this speed with these shoes she would ruin her feet, so she took her shoes off and carried them in the same hand as her purse. She hurried along.
"Why are you walking?" Came a voice from behind her, she heard a car's rumbling engine slow down. Rachel stopped and turned around, it was Puck, of course.
"My car didn't want to start, I couldn't get a hold of anyone, I have to get to school some how don't I?" Puck noticed some of the normal Rachel-irritation in her voice. Maybe it went with the school clothes, she certainly didn't talk to him that way last night when they were studying.
"Well, you didn't call me, I can give you a ride," he started to unbuckle his seat belt. Rachel watched him walk around and open her door, "I'm not always going to be opening doors for you Miss Berry, but I see you have your hands full," he explained. Rachel slid into the front seat, dropped her purse and back pack to the floor and reached her arm out to shut the door, but Puck was already closing it and walking around the back of the car to the driver's side.
"Thank you, Puck," she tossed her hair over her shoulder and reached down to put her shoes on. He was still sitting there, not driving, she looked at him with surprise, "Um, why aren't we moving?"
"Seat belt. I mean, I know I might sound square or something, but, if you don't buckle up and I get pulled over, which has been known to happen now and again, well, if you don't buckle up then I get the ticket, and I would make you pay me for it, but still-"
"I understand," Rachel laughed. Shoes on, she pulled her seatbelt out from the wall of the car and fastened it. "There, Mr. Safety, I am ready to go to school." She smiled and patted his arm, "Let 'er rip!" She added. Puck laughed and stepped on the gas, the car lurched forward and he gave her a sideways grin as she gripped the side of her door, her body pressing back against the seat from the speed. Puck slowed down in a moment, he didn't want to get a ticket after all, but it was fun to alarm girls with speed, if only for a half a block or so.
"You are crazy!" Rachel said in a shaky voice, "You aren't going to do that again are you?" She looked at him with wide eyes, reaching for her back pack, as if she was preparing herself to get out just in case he sped up again.
"No, relax, jeez," he said turning a corner. Good thing he has slowed down, a police cruiser sat in a driveway watching cars and students, all that morning school traffic. Puck waved to him with a grin as he passed. "That's right, I'm driving the limit, no worries here," he said patronizingly as he drove past. The cop frowned. Rachel shook her head, but she was amused, even impressed, Puck was exciting to be around.
At school Puck pulled his car into a space and got out, Rachel paused a moment, then decided not to give him a chance to get to her door, she opened it and got out, then reached back in for her things. Puck was standing by the hood waiting for her, so she walked over and when he started walking she walked next to him. Our of the corner of her eye she saw Finn walking toward the school, but he must have seen her out of the corner of his eye because he changed direction and walked straight toward her.
"What the hell, Rachel?" He looked from her to Puck and back to her, then back to Puck. Rachel kept walking and Puck stayed right in pace with her.
"Morning Hudson," Puck said, giving Finn a half grin. Finn frowned even harder and reached his hand out to take Rachel's arm.
"What are you doing, Finn?" She asked, jerking her arm away, dropping her back pack, which just then had been slung over that particular shoulder. Finn let go of her arm but stood in front of her.
"What am I doing? What are you doing? Why are you coming to school with this guy? Where's your car? What's going on?" Finn sounded angry, but oddly, he also sounded hurt. Rachel hiked her back pack onto her back and looked at Puck, then looked at Finn. She couldn't understand why he was upset, he was the one who broke up with her, he was the one who wanted to be with someone else, with Quinn for heaven's sake! Why was he upset that she was walking with another guy?
"Finn, YOU broke up with ME!" She stomped her foot and moved toward him a step, "I think that entitles me to do whatever I please and that entitles you to, well, to mind your own business! Well, it doesn't entitle you to mind your own business, it, it, it means you should mind your own business!" Her words stumbled out of her mouth and she stomped her foot again, then started back toward the building. Puck gave Finn a back ward glance, with a smile, and joined her.
"Oh," Finn whispered to himself, "I broke up with you. I broke up with her. Oh yeah," he looked around to see who was watching, to see if anyone heard him remembering out loud, he'd broken up with Rachel, then he sheepishly started walking to the school himself.
"See? I told you," Mercedes said to Kurt, they were a few car lengths down, but had heard the whole incident. The night before after Rachel spilled the whole story to Mercedes, Kurt called, not wanting to have to repeat the entire thing again, Rachel told him to call Mercedes, so she had the job of filling Kurt in. Now, Kurt looked after Rachel and Puck, and Finny trailing behind, his mouth hanging open, Kurt's mouth, not Finn's.
"Wow, just, wow. It's not that shocking that he broke up with her, it's not that shocking that she's coming to school with Puck-although I'd like to get the back story on that! But, did my ears just deceive me or did Finny forget he broke up with Rachel?" Kurt looked from the departing trio to Mercedes. She started to laugh and pulled him along, they had to get in the building and at least on their way to class, before they were too late.
"Kurt, I think he did just that, I think he did forget he broke up with her. Wow."
4. Chapter 4
**Chapter four**
Quinn was waiting for Finn at his locker. She was waiting to see what he had to say, he'd texted her the night before asking her to meet him, so here she was, waiting. When Finn finally strolled in the bell was making the buzz sound that it makes right before it rings. Quinn looked at him with an arched brow, as he cleared his throat to speak.
"I broke up with Rachel," he said it so suddenly, so quickly, so solidly, Quinn actually blinked for a moment. Then she quickly composed herself and switched her books to her other arm.
"And you're telling me this because?" She prompted. Just because he finally broke up with the Annoying One didn't mean much, did he expect her to jump for joy, fall into his arms, profess love for him? Quinn started walking toward class with Finn at her heals for a moment, before he fell in stride next to her.
"I-" he mumbled, but then he suddenly didn't know what to say, so he put his hand in the pocket of his coat and picked up his pace, "Class. I have to get to class." Quinn watched him as he hurried down the hall.
Ever since she could remember there had been something between Finn and herself. When they were kids, in grade school he had always been taller than the other boys, but he used his height to be a guardian of the girls, particularly Quinn, rather than a bully. If another boy bothered a girl, he would take that boy aside at recess and talk to him about the proper way to treat girls. Quinn knew Finn was being raised by his mother alone, and she suspected the reason for his manners was because she was teaching him how to look out for girls.
Then there had been that horrible incident, with Puck… Why did Puck have to have such natural charm, such raw magnetism? Quinn hated herself for sleeping with him, even for kissing him, for getting pregnant by him and lying to Finn. If only she could go back in time, if she could, she would never have spent a moment alone with Puck, then she never would have hurt Finn, then she never would have had to go through a pregnancy and labor and delivery! Ouch! At least she knew her baby had a good mother.
By lunch Quinn was curious if Finn told her he broke up with Rachel because he wanted to date her again or if he was just announcing it. She was just sitting down with a tray with a big salad when Finn's tray dropped next to hers and he sat on the bench right beside her.
"When I found out about you and Puck I was furious," he said quietly. Quinn took a stab of salad and looked at it while she turned her head toward Finn, she wanted him to keep his voice down and figured there was a better chance of that if she listened carefully. "Dating Rachel made me realize, you are the one I want to be with. It's not the whole Cheerios thing, it's not the power couple thing, it's, you. I mean, you can be sort of, well, bossy," Quinn raised an eyebrow at him and took another small bite of salad, "But, somehow it's different. And, I'm used to being bossed anyway, I guess I just like it better from you than other people." Finn picked up his burger for the first time since he'd sat down, and took a bite.
Quinn looked up from her little world, the table and her salad and Finn, and the first person who caught her eye, a few tables across the cafeteria, was of course, Rachel. Rachel was sitting with her usual buddies; Mercedes and Kurt, but Puck was at a table nearby and he was ignoring his jock buddies and looking in Rachel's direction.
"It's like a damn love square," Mercedes said low to Kurt, but not too low, Quinn heard it. She looked back at her salad, avoiding the glances from Rachel's table.
"I don't know Finn," she said quietly, "I haven't minded being a single woman, not to mention I have talked to Sam a little-"
"But do you want to go with him? Has he asked you?" Finn interrupted, around a mouthful of food. Quinn looked to her left, to the jock table where Sam was playfully goofing around with some of the other football players. Puck was sitting next to him and she couldn't help but notice he was still looking at Rachel. Quinn looked at her table and she was leaning over ever so slightly talking to Puck. Puck got up and took his tray to the trash and Rachel followed. Mercedes gave a knowing look to Kurt, who dabbed his mouth with a napkin and shook his head.
"Quinn?" Finn's voice brought her out of her thoughts, she put her fork down and took a drink from a bottle of water.
"I don't know," she said again, "I think you need a little time before you start anything up, with me, or, well, with anyone," she turned her body so she was facing Finn, looking straight at him, she put her hand on his arm without thinking. He looked down at her hand, then scanned her body as he looked up to her face. "You know, the whole rebound thing," Quinn said. She stood up and then picked her tray up, "Talk to you later, Finn," she said and left the table. Finn stared after her, confused as ever. She wasn't with Sam, she obviously wasn't with Puck, he hadn't seen her walking with or riding in a car with any other guys at school, and they already knew each other… Finn gulped down the rest of his food as the lunch bell rang, and hurried off to class.
In her last class of the day Rachel had a hard time keeping her mind on the teacher. Teachers could be dreadfully boring of course, why didn't they try harder to keep a student's interest? All they had to do was bring what they were studying into modern times and one would not only be more attentive to the lesson, but get more out of it. Rachel could see the back of Quinn's blond pony tail, she sat casually toward the front of the class. Puck was in a seat next to her in this class and Rachel for some reason felt her face burn with frustration seeing them sitting near one another, knowing they knew each other in a way she did not know Puck, or any boy for that matter. Finn wasn't in this class, thank goodness for that! Seeing him in a few classes and at lunch and in the hallways today made Rachel glad it was Friday. Suddenly a folded up piece of paper landed on her desk in front of her, Rachel picked it up and opened it right away, the unobservant teacher would never notice.
Is Puck driving you home? If not, I'll take you. Let me know. –Kurt.
Rachel uncapped her pen and wrote on the back of the slip of paper that yes, she suspected Puck was driving her home, because there was no football practice today, but to hang around a few minutes just in case. Then she tossed the note back to Kurt. Suddenly Rachel noticed Quinn's sweater-covered arm reach ballet-like across the space between her seat and Puck's, and drop a paper on his desk top. Rachel's heart doubled time for a minute, she watched the side of Puck's face, hoping to catch a reaction. She saw Quinn glance back at her, and quickly lowered her eyes so Quinn wouldn't know she'd caught the exchange. Oh, how she wanted to know what was in that note! Puck quickly tossed it back, Quinn opened it then pocketed it. Rachel had a hard time keeping her face relaxed.
When the bell rang Rachel tried to stay cool and composed, she gathered her books and stood up serenely and walked to the door. Much to her joy Puck was standing there waiting for her. He stood back and let her go first, then he walked out right behind her and walked next to her.
"Need a ride?" He asked. Rachel nodded. They stopped at their lockers, waiting for each other, then headed out into the parking lot. Rachel didn't want to ask about the note. She was willing herself not to ask, telling herself no she would not ask. Puck put his hand on the small of her back as they turned toward his car. She liked it. He opened her door, waited, closed it, then went around and got behind the driver's wheel. He started the engine and started to pull into the line of cars leaving school.
"Come on now, out with it," Puck said to her. Rachel smiled, then looked at him innocently.
"What?" She asked. Puck laughed, he reached over and gave her upper arm a little rub.
"I know you saw Quinn hand me a note, I know you saw me hand it back. You women are like that, always paying attention, a guy can hardly get away with picking a wedgie what with the way you women keep an eye on everything. So, ask me what was in the note, I know you want to know!" He was grinning from ear-to-ear and Rachel felt annoyed, but she had to laugh.
"Well, I was thinking about it-" she began.
"Of course you were," Puck said, nodding.
"-and I guessed she was asking if you knew why Finn broke up with me, or, if you were seeing me now," Rachel added the last part shyly, feeling a little nervous, she didn't want Puck to think she was asking if he was seeing her, she just wanted things to go on as they were so far, and hopefully lead to something, well, something nice, or something exciting. Puck was so exciting.
"You are wrong, Rachel Berry," Puck said, he stopped at a stop sign and leaned over and kissed her cheek, then turned her face with his finger on her chin and pressed his lips hard and hot onto her mouth. Rachel didn't have time to move before he stopped kissing her and put his foot to the gas pedal, sending the car foreword. "Care to guess again?" He teased.
"No," Rachel answered, a little flustered. Puck chuckled to himself.
"She was asking me if Santana had invited me to a movie night she is having. She is inviting all the football players and all the Cheerios, some big sort of end-of-the-football season shindig." Puck turned onto Rachel's street. He knew she was dying to know if he was going to Santana's party, he decided to torture her a little by not giving her the answer she was waiting for, it was so easy to mess with girls, especially Rachel, though he didn't want to mess with her too much and make her cry or something. Girls were so prone to crying.
"Do you want to come in?" Rachel asked, reaching for her door. Puck nodded and jumped out, by the time he got to her door she had it open, but he held it for her. Once both her feet were on the ground he put his arms around her waist and lifted her up to kiss her, the same kind of pressing, hot kiss he'd given her at the stop light. Rachel dropped her back pack and kissed him back. Neither of them heard the door of her dad's car close. He was already in the drive, looking at Rachel standing outside Puck's car at the curb, in a serious lip lock.
"Eh-um!" Rachel didn't hear that either, as her dad cleared his throat to get her attention. Puck was still kissing her and her arms were at her sides, his were tight around her body, it was the most delicious kiss she'd ever had, better than she'd ever even dreamed of.
When Puck felt someone tap his shoulder, not roughly, but not exactly like a waitress asking if you wanted a refill, he stopped kissing Rachel but kept his arms around her, when he saw it was one of her dads he slowly released her and smiled. It wasn't the first time a dad caught him with his tongue inside a daughter's mouth. Rachel's face was white as a sheet when she realized what her dad just saw her doing! She blushed then and her white face gained two rosy spots. She didn't know what to say. Puck was standing there beside her smiling, not embarrassed at all. She was surprised to see her dad didn't even look mad, just mildly amused. He picked up her back pack and started for the house. Rachel looked at Puck, then glanced after her dad, he was walking slowly up the front walk.
"I don't know what to do," she confessed to Puck. He only laughed, kissed her cheek, then planted one on her mouth, and started around the front of his car.
"I will call you later," he opened his door, but looked at her over the top of his car, "Okay?"
"Sure. Yes. Okay, talk to you later," Rachel answered, her response sounding all jumbled up, she took a deep breath, and could still smell Puck's scent on her clothes, "Talk to you later," she said, smiled, and walked after her dad, who was still poking his way up the sidewalk. She glanced over her shoulder one last time to see Puck smile and wave, then pull away from the curb like a driver's ed student, slow and easy. She caught up with her dad who put his arm over her shoulder and kissed the side of her head.
"Boys," he said, kind of like he missed that youthful time of life, "Being a teenager can be so exciting, I hope you remember everything we've taught you," Rachel sighed, she felt a sex talk coming. It didn't even embarrass her anymore when her dads talked to her about sex, she knew they only wanted to make sure she was informed and safe. Though getting caught making out on the boulevard in front of the house wasn't her favorite moment. Although, she was making out with Noah Puckerman, and she could not imagine anytime she'd be embarrassed caught in his arms.
5. Chapter 5
Mercedes and Kurt flopped down on his dad's living room couch after school. He dropped his back pack on the floor next to the couch and Mercedes dropped her's in front of her feet. Kurt's dad was still at work and so was Finn's mom, the plan was to study, but Kurt and Mercedes usually got so busy talking they didn't even open their back packs.
"Sometimes I just don't want to even give other people's relationships another thought," Kurt said, putting his feet up on the foot stool in front of him. Mercedes rubbed her temples and sighed.
"I know what you mean. Sometimes I just want to talk about MY relationships!" She winked and Kurt and he burst out laughing. They heard the door opened, craned their necks, and saw Finn walk in.
"Hey Kurt, Mercedes," he said when he saw them on the couch. He sat down in the recliner his mom brought when they moved in. "What are you up to?" He propped his own feet up on the coffee table.
"Homework," Kurt said at the same time Mercedes answered, "Gossip." They both started laughing. Finn could tell this conversation would keep erupting into giggles and he wasn't in the mood. He nodded absently, went to the kitchen, grabbed a snack and went upstairs. Mercedes and Kurt looked at each other and started laughing.
Finn sat on the edge of his bed for a moment, not really staring at anything, not really seeing anything. He thought about Rachel, he thought about Quinn, he thought about Brittany, he couldn't remember the last time he was in his room that he didn't think about Brittany, it was just a natural thing for a guy to do. He tried to think about his thoughts about each girl. Rachel made him feel, tired, she was pretty and she could be sweet, but he felt she was always pushing him in some direction or another. Thinking about Quinn made him feel, made him feel… so many things. He felt betrayed and hurt, always when her name and face popped into his head, knowing what she'd done with Puck, what she tried to pin on him. But then he felt a certain familiarity when he thought of her. With Brittany, he just thought of how she flung her hair around when she danced. And her legs, her long legs. Finn laid back on his bed and sighed, he had homework to get to.
"It sure is quiet up there," Mercedes commented, gesturing toward the stairs with her head. Kurt actually had his math book out, and a notebook, and was rummaging for a pencil.
"Yeah, you know, he has a lot of things to think about, he usually spends some time up there after school, processing, or, something," He got the pencil and sat back, and straightened up at the same time, "Let's get some work done, Mercedes, I'd love to be done with school work so I can talk to Blaine later." Mercedes obligingly got her math stuff out and flipped to the page they were on. She was good at math, Kurt was good at math, their study sessions were more of a race to see who could Finnish first, the loser had to check the answers to make sure they didn't make any mistakes.
As Mercedes worked a problem she thought about Finn upstairs, he was in his bedroom, she wondered how many girls he'd made out with up there on his bed. She hadn't been in his room, so she couldn't picture it. Kurt was the only boy's room she'd been in, and they only talked, of course. Suddenly Mercedes found herself putting her book and paper on the coffee table, she headed for the stairs. Kurt was so immersed in his work he didn't notice she was gone.
Mercedes came to the top of the stairs, she knew Kurt's room was downstairs because she'd helped him with some of his interior design, she looked at the doors, they were all open but one. Bathroom-check, master bedroom-check, a small den-nice! She stopped at the closed door, it smelled like teenage boy, or teenage man? No, teenage boy. She put her hand up to knock but then thought better of it and slowly turned the knob.
Finn was laying on his back on one side of his bed, he had his arm over his eyes, his other arm hanging off the bed. Mercedes pushed the door shut all the way. Finn lifted his head to see who was in his room.
"Mercedes?" He frowned. She sat down on the bed next to him.
"You had a big day today, Finn," she said quietly, "And you are ending your day as a single man," she settled down on her side next to him. Finn didn't move a muscle. Mercedes put a hand on his chest and propped her head up with her other arm, her elbow leaning on the bed.
"I-" Finn started. Mercedes put her Finnger on his lips, bent down and kissed him. Much to her surprise he kissed her back, he put his hand up on the back of her neck and held her so she couldn't back up, and kissed her back!
Downstairs Kurt zoomed through his last problem and looked up expectantly at Mercedes' empty spot. He frowned and looked at her paper, she only did three problems. That was odd. Kurt walked to the kitchen, she wasn't there, he checked the hall bathroom, the door was open, the light was off, the room was empty. He glanced out the front window, she wasn't outside, sometimes she stepped out to take a call or a juicy text so Kurt wouldn't tease her and make her type something ridiculous or if she was talking say something crazy.
Suddenly Kurt heard a noise. He walked to the bottom of the steps and listened carefully. He took three steps up and froze, listening.
"Oh. My. God." Kurt whispered to himself. He dashed up the stairs noiselessly and stopped at the top of the stairs. "Ohmygod," he gasped all in one breath. He tiptoed closer to Finn's door, he could hear the bed rattling, he could hear breathing, he could hear other noises.
"Finn!" he heard the unmistakable sound of Mercedes' voice, but he'd never heard her sound like that. Then he heard a groan, the kind of noise Finn made when he got sacked on the football field. Kurt put his hand out to take the door knob, but then he came to his senses and hurried back downstairs. He picked his phone up, then set it down. He picked his math up, then set it down.
"Blaine, oh do I need to talk to you!" he said quietly. Then he felt uncomfortable, what should he do? Should he keep his math in front of him and pretend he was doing work when Mercedes came down? Should he fix something to eat in the kitchen? Should he go outside and call Blaine? He didn't want Mercedes and Finn to know he'd heard them. What the hell was going on? Did he just think to himself, "Mercedes and Finn?" Mercedes and Finn! MERCEDES AND Finn! A thump against the wall upstairs caught his attention. "Ohmygod!" Kurt said to himself once again, and he grabbed his cell and ran outside.
Blaine, I need to talk. He texted. His phone vibrated in his hands immediately. What is it Kurt? Kurt was about to text, but his thumbs were frozen. He looked around, there were kids playing across the street. He looked into the open garage, there was a car in there his dad had been working on, he jumped into the front seat and called Blaine.
"Blaine, it's me, Kurt!" He breathed.
"What's wrong? You sound sort of out-of-breath," Blaine answered.
"You wouldn't believe it if I told you! But, I have to say something to someone, I just, can't believe I'm saying this!" Kurt gasped. He was so shocked he was shaking, he tried to calm his voice so he could speak. "Mercedes and Finn are upstairs, in Finn's room, right now," He began.
"Yes? So?" Blaine couldn't imagine what the big deal could be.
"Having sex! They are doing it, Blaine! Mercedes," Kurt lowered his voice to an even lower whisper, "And Finn!" Kurt winced when he heard the sound of Blaine's phone hit the floor.
6. Chapter 6
"I've never done it before," Mercedes whispered. Finn lay on his back with his arm under her neck. He smiled, felt a little cool and a lot studly, then smiled again even bigger.
"Yeah, I, wow," he started at the ceiling, "I uh, I was with Santana, but that's all. I mean, Quinn and Rachel-" he broke off. [Soft Break]"Yeah, I know," Mercedes answered, "I haven't even come close until now," she swallowed, cleared her throat, "I liked it," she giggled to herself, "I liked it, Finn." She felt his arm tighten around her shoulder and his fingers rubbed her arm.
"Yeah, me too."
When Mercedes walked into school the next morning Kurt was waiting inside the door for her. He looked at her with raised eyebrows and hooked his arm through her's.
"Miss Mercedes, Miss Mercedes, what am I going to do with you woman!" He steered her down the hallway toward his locker.
"What are you talking about?" She asked innocently, but she was wondering, what did Kurt know? Had he noticed her absence and come upstairs unbeknownst to her? Had he heard anything?
She noticed when she came downstairs, finally, that Kurt was in the kitchen munching on a snack. She figured he has finished his math and gotten a snack, thinking maybe she was in the bathroom.
They had finished checking their math and then talked a while before she told him she had to get home and he told her Blaine was coming over anyway.
"What am I talking about? Come on, Mercedes, you can't just disappear for half an hour during Math Time and not expect me to notice? I'm not one of those unobservant guys, am I? No! I noticed you were gone, I checked around downstairs, I looked outside, Hmm, no Mercedes I thought, I heard a noise coming from upstairs." When he said upstairs Mercedes blushed, she pressed her lips together and pulled him into an empty classroom.
"Shh!" She looked around nervously, "You can't say anything, you can't say a word. Rachel would, she would flip out! She's my friend!"
"I know she's your friend! That's part of why this is so, so, shocking!" Kurt choked out.
"I know," Mercedes shook her head, "I don't even know, I have no idea what possessed me, or him," she shook her head again, but she was smiling and blushing.
"Well, I guess you need to talk to him then, don't you?" Kurt saw Finn go by in the hall and he grabbed Mercedes and gave her a shove right out the door. Mercedes was surprised by Kurt's strength when she found herself bumping right into the back of Finn. He looked at her in surprise and smiled quickly.
"Good morning Miss Jones," he gave her his lopsided smile and she blushed, her cheeks pinking and warming.
"Finn," she glanced around to see if anyone was paying attention, she felt certain anyone seeing them in the hallway would know, would just know! They rounded a corner and came face-to-face with Quinn! She was standing right in the middle of the hallway, she was wearing one of her school marm slash church lady dresses, complete with the three quarter length sleeve sweater.
"Why Finn, Mercedes, how are you two this morning?" Quinn spoke in her usual quiet, reserved voice. The one that scared Finn because he knew a lecture was coming, the same voice that annoyed Mercedes and made her want to slap Quinn so she would raise her voice a little.
"We didn't have sex," Finn blurted out. Mercedes' mouth dropped open and her eyes flew open wide as she gaped from Finn to Quinn and back to Finn again. Something inside her said to run down the hall, or at least walk quickly so as not to create suspicion, but she was rooted to her spot. Quinn's smile vanished. She dropped her books. Her eyes narrowed as she looked from Finn to Mercedes. She knew it was true, she knew they had done it, she knew, she could tell by the way they stood there, by the way they looked at her, by the way Finn's eyes had dropped to the floor.
"Which of you is the biggest whore is beyond me," she said in such a low voice Finn almost didn't hear what she said, but Mercedes did, and so did Santana who was coming up behind them.
"Who's a whore?" Santana asked stepping between Finn and Mercedes. "Well, other than the little mother here," she looked Quinn straight in the eye. Quinn whisked up her books in a fluid motion and spun on her heel and not only marched down the hall, but kept going and went out the door to the parking lot. Santana looked at Finn, then she slowly turned her head and looked at Mercedes, a slow smile played about her lips then she laughed.
"Wow!" she laughed again and hooked her arms through their arms, throwing her head back and laughing again, "Oh, Finn and Mercedes, we have so much to talk about!"
Mercedes had never ditched school, neither had Finn, but somehow sitting in the back of Santana's car driving away from the school during the school day didn't seem like that big of a deal. Mercedes felt her face warm when Santana made a turn too fast and she and Finn slid into one another. Finn smiled at her and slipped his hand around hers. Mercedes had no idea what to think of him. At first she thought yesterday was just one of those moments you hear about, where two people come together unexpectedly, but it is actually quite meaningless. Then she thought, last night while she was falling asleep, that maybe it was going to end up being one of those Friends with Benefits things, but that was so unlike her and so unlike Finn, which, maybe is what made it make sense. But now that he was looking out his window with his hand casually wrapped around her hand she was not sure what to think.
"-and that is how it has been with Brittany and me." Mercedes blinked back into reality to hear the last few words of Santana's sentence.
"I don't know yet, Santana, but at least neither of us is seeing anyone. For Brittany to be seeing Artie and mess around with you, that is cheating, even if you are not a guy," Finn stated with amazing clarity.
"But she is my best friend, we're not lovers, we are just friends who sometimes practice kissing together, it's been that way for a long time. All I'm saying is maybe you two are going to end up, you know, blowing off steam together. There is no harm in it." Santana said with finality, she pulled her car into the parking lot of a coffee shop.
The three of them walked in and ordered drinks and sat down. Mercedes had a brownie, Santana had a muffin, Finn had some sort of big sandwich. It was early in the day, but teenagers can always eat, the waitress thought as she put their tray in front of them. She gave the group one last glance and went back to her work.
"Okay, so, you had sex," Santana began, "Now what? I can counsel you right through this or right into this, whatev." She took a bite of her muffin and rested her chin on her fist, the point of her elbow on the table. Sex was easy to figure out, relationships were too, just because she didn't have things straightened out yet for herself, well, that didn't mean she couldn't help these two, they had so little experience, it would be easy to get them on the right track. "So, first question, do you want to have sex with each other again?" She watched their faces to catch the reaction they may not speak.
"Yes." They said at the same time. Mercedes followed with a giggle and Finn blushed. Santana nodded.
"Okay then, Finn, Mercedes, do you want to date, do you want this to be public? I assume Kurt knows, so if Kurt knows I would assume Blaine knows, and Rachel will know within 24 hours, if Rachel knows then Miss Pillsbury will know, if she knows Schuester will find out, I would guess Puck will know the next time you are in class together…" Santana trailed off, her eyes to the ceiling as she calculated.
"Quinn figured it out," Mercedes reminded. Finn choked on a bite of sandwich and for some reason started laughing. "What exactly is so funny about that?" Mercedes asked. She'd seen Quinn in action, Quinn could really make a person miserable if she wanted, that condescending tone, oh, it was the worst. Mercedes gulped down a slurp of her iced coffee.
"I totally forgot about the prom queen wanna be!" Santana burst out laughing. She took a few moments to compose herself, "Well, then instead of spending our time thinking about who knows I guess we can think about who does not know, but honestly, at this point, you may as well go public. Let's face it, enough of us know."
Finn looked at Mercedes. It wasn't that he didn't want people to know he was dating her, she was beautiful and she did have a rockin' dancing body and she could really sing. He just wasn't sure what people would think of him, going from one girl to another in such a short time. But, who did he care about caring?
Mercedes returned Finn's look, she managed a half-smile. Finn? She just wasn't sure she wanted that much responsibility. Really, look how much work and time and energy Rachel and Quinn had spent on him, trying to make sure things didn't get mucked up. All the time Rachel was with Finn she typed longer and longer texts every day talking about him, about his blunders, about her expectations of him. Mercedes looked at Finn, he was taking a drink of his coffee, his sandwich was gone, he was looking at the tv which was displaying a sports event, looked like golf. Just because he'd had two bossy girlfriends didn't mean it had to be that way if she was his- well, if she was with him. And they were having sex, well, they'd had sex, if they continued, that was a whole different dynamic.
"Do you want to like, go out, or be boyfriend and girlfriend, or whatever?" she asked him. He turned around in his chair to be totally facing her and that Finn grin came over his face.
"Yes," he said.
"This is a blast," Santana said, she stood up, threw her purse over her shoulder and headed for the door. Finn took Mercedes' hand and they followed her, smiling.
End file.
| fanfiction |
in this paper we report the discovery of a new planetary nebula ( pn ) in cassiopeia .
the pn appears nearly perfectly elliptical , and its central star is a late - type star with enhanced abundances of carbon and _ s_-processelements .
the system thus appears to represent the immediate aftermath of the formation of a barium star . in the following sections we present the serendipitous discovery of the nebula , the classification of the nucleus as a star , a study of the star s photometric properties and variability , estimates of the distance to the system , and an evolutionary scenario for the origin of this remarkable object .
we conclude with suggestions for follow - up studies .
in 1995 , one of us ( r.f.w . ) discovered an unusual nebulous object while verifying the coordinates of ls i + 61@xmath0303 , a well - known stellar x - ray source . the digitized sky survey ( dss )
was used to generate an image of ls i + 61@xmath0303 . during examination of the source and its surrounding field , r.f.w . noticed a faint , elliptical nebula surrounding a 14th - mag star , lying @xmath1 to the southwest of ( and unrelated to ) ls i + 61@xmath0303 .
subsequently obtained narrow - band ccd images of the object , with the 0.9-m telescope at kitt peak national observatory ( kpno ) in autumn 1996 , and later with the kpno mayall 4-m telescope as described below .
filters isolating [ ] 5007 and h@xmath2 + [ ] 6584 showed the object to be a previously unrecognized303 , and confirmed it optically using the dss ; they suggested that it is a small region . ]
the name webo 1 was proposed by bond , ciardullo , & webbink ( 1996 ) , and will be used here . in the nomenclature of the _ strasbourg - eso catalogue of galactic planetary nebulae _ ( acker et al .
1992 ) , which is based on galactic coordinates , the object s designation would be pn g135.6 + 01.0 . the central star is listed in the usno - a2.0 catalog at the j2000 coordinates given below in table 1 .
unusually for a pn nucleus , the star appears to be quite red : the usno - a2.0 approximate photographic @xmath3 and @xmath4 magnitudes are 16.0 and 14.4 , respectively .
our best narrow - band images of webo 1 were obtained by h.e.b . on 1999 january 16 with the kpno 4-m telescope and its mosaic ccd camera .
the [ ] and h@xmath2 + [ ] images are shown in figs .
1a and 1b , respectively .
the frames were taken through cirrus clouds , but under good seeing conditions : the fwhm of stellar images in [ ] and in h@xmath2 + [ ] was @xmath5 and @xmath6 , respectively . in h@xmath2 + [ ] , webo 1 has a striking morphology , appearing as a nearly perfect ellipse with major and minor axes of about @xmath7 .
the shape strongly suggests that the pn is a thin circular ring with a very low ratio of height to radius , viewed at an inclination of @xmath8@xmath9 .
such a morphology is nearly unique among pne , matched only by the southern - hemisphere pn suwt 2 , which has a nearly identical appearance ( schuster & west 1976 ; bond , exter , & pollacco 2001 ) .
the h@xmath2 + [ ] ring has a generally clumpy appearance , a bright , sharp inner rim , and is brightest at the two ends of its major axis ( perhaps simply a path - length effect ) .
the interior of the ring is almost hollow , although the brightness level is brighter than the surroundings ( which are overlain with diffuse h@xmath2 emission at this low galactic latitude ) . in [ ]
the pn appears more diffuse , but the ring is still apparent . unlike the h@xmath2 + [ ] image ,
the interior of the ring is not hollow .
the images suggest a gradient in ionization level , with the interior of the pn filled with high - ionization material radiating in [ ] , surrounded by cooler material around the periphery of the ring emitting strongly in ( presumably ) [ ] .
images through filters that separate h@xmath2 and [ ] would shed further light on the morphology of webo 1 .
a ccd spectrogram of the central star of webo1 was obtained by d.l.p . at the 2.5-m isaac newton telescope at la palma , canary islands , on 1997
january 12 .
the intermediate dispersion spectrograph was used at a dispersion of 35.3 mm@xmath10 .
the spectral coverage was 980 , at a resolution of 1.6 , and the exposure was 1800s .
2 shows the spectrum . to our surprise , the star is cool and chemically peculiar .
molecular bands of c@xmath11 , ch , and cn are prominent , and the lines of at 4077 and at 4554 are extremely strong . remarkably , the core of the h line is filled by very strong emission .
( k is , unfortunately , just outside the spectral range that we covered . )
the star thus has all of the properties of a classical barium star ( or `` star '' ) .
stars were first identified as a spectroscopic class by bidelman & keenan ( 1951 ) .
they show enhanced abundances of carbon and of heavy elements produced by _
s_-process neutron - capture reactions .
the modern view of stars ( see mcclure 1984 ; jorissen et al .
1998 ; bond & sion 2001 ) is that they are the binary companions of more massive stars that became asymptotic - giant - branch ( agb ) stars , dredged up c and _
s_-process elements from their interiors , and transferred them to the companions .
the agb stars have now become optically invisible white dwarfs , leaving the contaminated companions as the visible stars .
we classified the spectrum of webo 1 by displaying it as a `` photographic '' spectrogram , and comparing it visually with the atlas of keenan & mcneil ( 1976 ) . to estimate the strength , which classically ( warner 1965 ) is on a scale from 1 ( slightly enhanced over normal ) to 5 ( extremely strong ) , we compared our spectrum with the sequence illustrated by l et al.(1983 , their fig . 2 ) .
the resulting classification is k0 iii : p ba5 .
the luminosity class is essentially indeterminate from our material ( due to the abnormal strength of all of the luminosity indicators at this resolution ) , and the `` p '' refers to the presence of c@xmath11 bands , which are generally seen only in a subset of the stars , as well as to the emission .
ccd _ bvi _ photometry of the nucleus was obtained by h.e.b . on six occasions on four different photometric nights in 1996 and 1997 september .
the kpno 0.9-m reflector was used with a tektronix ccd , and the photometry was reduced to the johnson - kron - cousins _ bvi _ system through observations of landolt ( 1992 ) standard stars .
two nearby stars were chosen as comparison stars for a variability study ( see below ) and were also calibrated to the _ bvi _ system .
results are given in table 1 .
the errors , determined from the internal scatter among the six different measurements , are @xmath120.01 mag in @xmath13 and @xmath14 , and @xmath120.02 mag in @xmath15 .
the central star of webo 1 , at @xmath16 and @xmath17 , is very red for its spectral type ; a normal k0 iii star has @xmath18 and @xmath19 ( bessell 1979 ) .
the star thus appears to have an interstellar reddening of @xmath20 , corresponding to @xmath21 ( using the formula of dean , warren , & cousins 1978 ) .
the intrinsic color is @xmath22 , suggesting that the star is somewhat redder in @xmath14 than a normal k0 giant because of its strong carbon bands as well as the influence of the broad bond - neff ( 1969 ) flux depression around 4000 that is seen in barium stars . given that the optically visible star in webo 1 is very cool , we can speculate that it is a member of a binary system with a much hotter , but optically inconspicuous , companion that is responsible for the ionization of the pn . in order to search for variability , h.e.b .
obtained ccd images in _ bvi _ on 40 occasions spread over 6 nights each in 1996 and 1997
september , 4 in 1998 march , and 2 in 1999 january .
the 0.9-m kpno telescope was used , as described above . since several of these nights were non - photometric , we calculated differential magnitudes between webo 1 and the sum of the intensities of the two comparison stars .
the central star is definitely variable , but at a low level .
we searched the data for periodic variations , using the lafler - kinman ( 1965 ) algorithm .
the smoothest light curves are obtained for a period of 4.686 days .
however , the nearby alias periods at 4.347 and 5.074 days also give plausible light curves , so we can not make a definitive claim that 4.686 days is the correct period .
it is even possible to fit the data with a sub - day alias near 0.82 days , but with significantly larger photometric scatter . in fig .
3 we plot the differential magnitude and color curves for the adopted ephemeris @xmath23 . to estimate the uncertainties , we calculated the standard deviations of the comparison star 1 minus comparison star 2 magnitudes , which are 0.011 , 0.007 , and 0.008 mag in @xmath3 , @xmath13 , and @xmath24 respectively .
the radii of the plotted points in fig . 3
were then set to these values ( with the errors combined in quadrature for @xmath14 and @xmath15 ) .
the webo 1 nucleus shows a nearly sinusoidal variation in all three filters , with a peak - to - peak amplitude of about 0.03 mag .
there are no significant changes in color .
we can identify four mechanisms that could produce this variation : ( 1 ) pulsation , ( 2 ) heating ( reflection ) effects in a close binary , ( 3 ) ellipsoidal variations ( at a period of @xmath25 days ) , and ( 4 ) starspots on a rotating star .
pulsation appears unlikely because of the lack of any color variations .
for a planetary - nucleus cooling age comparable to the estimated expansion age of the nebula ( see below ) , we estimate its luminosity should exceed @xmath26 , in which case heating of the facing hemisphere of the ba star in a 4.7-day binary would produce a reflection effect nearly two orders of magnitude larger than the observed photometric amplitude ( unless the binary is seen nearly pole - on ) , with colors decidedly bluer than observed .
the reflection effect should also dominate ellipsoidal variability at all inclinations , unless the barium companion is not the ionization source for the pn .
we consider starspots the most likely explanation , in which case 4.7 days is the stellar rotation period .
the strong emission indicates that the star is very chromospherically active , supporting the starspot interpretation and suggesting that the activity is dynamo - driven by the relatively rapid rotation .
we can constrain the distance to webo 1 using three different methods . the first one uses the estimated interstellar reddening of @xmath27 and the three - dimensional extinction model of arenou , grenon , & gmez ( 1992 ) . the observed reddening is close to the asymptotic limit at large distances in this region of the sky , but the arenou et al .
model allows us to set a 1@xmath28 lower limit on the distance of 0.75 kpc , a result which is in excellent accord with the extinction maps of neckel & klare ( 1980 ) . an upper limit to the distance of webo 1 follows from equating the 4.7-day photometric period with the rotational breakup period of the barium star . assuming a mass of @xmath29 for that star ( jorissen et al .
1998 ) , we find that its radius can not exceed @xmath30 . the observed magnitude and reddening
then imply that a k0 iii star of this radius must be no farther than 2.4 kpc .
a third method uses a statistical distance scale for pne .
there are several of these in the literature , but we have chosen that of cahn , kaler , & stanghellini ( 1992 , hereafter cks ) .
ciardullo et al .
( 1999 ) have shown the cks formalism to produce reasonably good agreement with pne of known distance , albeit with the factor - of - two scatter typical of all statistical pn distance scales . adopting the 6 cm flux density of 4.4 mjy given by martet al .
( 1998 ) , and an angular radius of @xmath31 , we use the cks method to yield a distance estimate of 2.2 kpc .
we adopt a nominal distance of @xmath32 kpc ( the approximate mean and range defined by the lower and upper limits ) . at this distance ,
the absolute visual magnitude of the central star is @xmath33 .
thus it has roughly the luminosity of a normal red giant ( in agreement with most of the classical stars , e.g. , mennessier et al .
1997 ) . at this distance ,
the major axis of the pn is @xmath34 pc , and the radius of the central star is @xmath35 . on the assumption of a nominal @xmath36 expansion velocity ,
the age of the pn is 12,000 @xmath12 6,000 yr . if 4.7 days is the rotation period of the star , then with a radius of @xmath37 and an inclination @xmath38 ( the apparent inclination of the pn ) , it would have a projected rotational velocity @xmath39 .
since this is less than the @xmath8@xmath40 resolution of our spectra , we would not expect to see an obvious spectroscopic signature , even though this would be about 2/3 of the rotational breakup velocity .
webo 1 has several properties in common with the class of `` abell 35''-type planetary nuclei .
this class was defined by bond , ciardullo , & meakes ( 1993 ) , and has been discussed by bond ( 1994 ) , jasniewicz et al .
( 1996 ) , jeffries & stevens ( 1996 ) , and gatti et al .
( 1997 ) . in the three known a 35-type nuclei ( a 35 , lotr 1 , and lotr 5 ) , a rapidly rotating late - type giant or subgiant is seen optically , while a hot companion is detected at uv wavelengths .
the cool components vary photometrically with periods of a few days , corresponding to their rotation periods .
a definitive orbital period has not been found for any of these three objects from radial - velocity studies , suggesting that the orbital periods may be long .
this suspicion is confirmed in the case of the field star hd 128220 , which lacks a pn but is otherwise similar in all respects to the a 35-type nuclei : its orbital period is 872 days ( howarth & heber 1990 ) .
these systems , then , have almost certainly not undergone common - envelope interactions , which would have decreased their orbital periods by substantial amounts .
as discussed by jeffries & stevens ( 1996 ) , there is a closely related class of wide binaries containing hot white dwarfs and cool , rapidly rotating , magnetically active _
dwarfs_. these authors propose a mechanism in which an agb star in a wide binary develops a dense stellar wind , part of which is accreted by the companion star .
their calculations suggest that significant spin - up of the companion may occur , along with accretion of chemically enriched material from the agb star .
although jeffries & stevens considered their suggestion somewhat speculative ( in the absence of actual 3-d hydrodynamical simulations of the accretion and spin - up ) , observational support has arisen in the past several years .
this includes the finding of mild ba enhancements in the rapidly rotating dk component of 2re j0357 + 283 ( jeffries & smalley 1996 ) , and in the nuclei of a 35 and lotr 5 ( thevenin & jasniewicz 1997 ) .
webo 1 , with its pronounced ba and c overabundances , now provides further support .
a scenario that emerges to explain the properties of webo 1 is thus as follows .
the progenitor system was a fairly wide binary whose components had nearly equal masses ( initial mass ratio @xmath80.98 ) .
the more massive star evolved to the agb stage , at which point the less massive component had also begun to ascend the red - giant branch .
the agb star was constrained to rotate with the orbital period , so that , as it developed a dense wind , the wind was ejected preferentially in the orbital plane , leading to the ring - like nebular morphology .
the wind was enriched in ba and other _
s_-process elements , and had @xmath41 .
a portion of the wind was accreted by the companion giant , spinning it up to the observed 4.7-day rotation period , and contaminating its photosphere with ba , c , and other pollutants . at present
, the agb star has completely shed its envelope , exposing its hot core whose uv radiation ionizes the ejected ring .
several follow - up studies are clearly warranted .
( 1 ) ultraviolet spectra would confirm the expected presence of a hot companion ; a determination of its surface gravity from its ly@xmath2 profile would provide a mass determination , and thus an estimate of the progenitor s initial mass and constraints on evolutionary scenarios .
( 2 ) radial velocities from ground - based spectra would allow a search for the orbital period , or set a lower limit if , as we suspect , the orbital period is long .
( 3 ) high - dispersion spectra of the barium star should be obtained , to determine its rotational velocity and atmospheric elemental abundances .
in particular , it would be of great interest to search for lines of technetium , which should be present if the star is really a very recently created barium star .
( 4 ) an abundance analysis of the nebula would also be of interest , since it may be possible to detect lines of heavy _
s_-process elements .
the discovery of webo 1 would not have been made without the dss , and we acknowledge the roles of the late b.m .
lasker and the many other persons involved in creating this valuable resource .
kpno is operated by aura inc .
, under contract with the national science foundation .
we made use of the simbad database , operated at the cds , strasbourg , france .
thanks b.d .
fields for useful discussions , and acknowledges support from nsf grants ast 92 - 18074 and ast 96 - 18462
thanks r. gallino and d. d. clayton for useful suggestions , and w. p. bidelman for introducing him to stars more than three decades ago .
lcccccc webo 1 central star & 1500 - 02588384 & 02:40:14.35 & + 61:09:17.0 & 14.45 & 1.72 & 1.77 + comparison 1 & 1500 - 02586253 & 02:40:05.78 & + 61:09:17.9 & 14.67 & 1.64 & 1.93 + comparison 2 & 1500 - 02584109 & 02:39:56.80 & + 61:10:03.8 & 13.86 & 1.92 & 2.19 + | arxiv |
Gornal is a railway station on the LlobregatAnoia Line. It is located in the neighborhood of the same name, in the L'Hospitalet de Llobregat municipality, to the south-west of Barcelona, in Catalonia, Spain. It was opened in 1987, when the line's section between Ildefons Cerdà and Sant Josep stations was put underground. It is served by Barcelona Metro line 8, Baix Llobregat Metro lines , and , and commuter rail lines , , and .
Bellvitge railway station, served by Rodalies de Catalunya commuter and regional rail services, is located adjacent to Gornal station, on the west side of it, allowing for street-level transfers between the two stations.
Rail services
External links
Information and photos of the station at trenscat.cat
Video on train operations at the station on YouTube
Category:Barcelona Metro line 8 stations
Category:Stations on the LlobregatAnoia Line
Category:Railway stations in L'Hospitalet de Llobregat
Category:Railway stations opened in 1987
Category:Railway stations located underground in Spain | wikipedia |
day 1 adult neuronally gfp - labeled worms ( punc119::gfp or pmec-4::gfp ) were prepared for cell isolation as previously described with modifications ( extended data fig .
the pellet ( ~250 l ) was washed with 500 l lysis buffer ( 200 mm dtt , 0.25% sds , 20 mm hepes ph 8.0 , 3% sucrose ) and resuspended in 1000 l lysis buffer .
worms were incubated in lysis buffer with gentle rocking for 6.5 minutes at room temperature .
the pellet was washed 6 with m9 and resuspended in 20 mg / ml pronase from streptomyces griseus ( sigma - aldrich ) .
worms were incubated at room temperature ( < 20 minutes ) with periodic mechanical disruption by pipetting every 2 min . when most worm bodies were dissociated , leaving only small debris and eggs , ice - cold pbs buffer containing 2% fetal bovine serum ( gibco ) was added .
rna from facs - sorted neurons was prepared for rna - seq and subsequent analysis ( see extended data for details ) .
day 1 adult neuronally gfp - labeled worms ( punc119::gfp or pmec-4::gfp ) were prepared for cell isolation as previously described with modifications ( extended data fig .
the pellet ( ~250 l ) was washed with 500 l lysis buffer ( 200 mm dtt , 0.25% sds , 20 mm hepes ph 8.0 , 3% sucrose ) and resuspended in 1000 l lysis buffer .
worms were incubated in lysis buffer with gentle rocking for 6.5 minutes at room temperature .
the pellet was washed 6 with m9 and resuspended in 20 mg / ml pronase from streptomyces griseus ( sigma - aldrich ) .
worms were incubated at room temperature ( < 20 minutes ) with periodic mechanical disruption by pipetting every 2 min . when most worm bodies were dissociated , leaving only small debris and eggs , ice - cold pbs buffer containing 2% fetal bovine serum ( gibco ) was added .
rna from facs - sorted neurons was prepared for rna - seq and subsequent analysis ( see extended data for details ) .
a ) daf-16 tissue - specific transgenics ; heat map of all genes with expression differences 1.5-fold in 3 arrays .
b ) significant gene ontology ( go ) cluster terms from punc-119::daf-16-regulated up- and down - regulated genes ( enrichment score > 1 ) .
c ) pairwise pearson correlations between arrays of daf-16-up - regulated or down - regulated targets . the red box highlights the negative correlation between neuronal daf-16 rescued targets ( punc-119::daf-16::gfp;daf-16;daf-2 vs daf-16;daf-2 ) and intestinal daf-16 targets ( pges-1::daf-16::gfp;daf-16;daf-2 vs daf-16;daf-2 ) , while the blue box shows the positive correlation between intestinal daf-16 targets ( pges-1::daf-16::gfp;daf-16;daf-2 vs daf-16;daf-2 ) and whole worm daf-16 targets ( pdaf-16::daf-16::gfp ; daf-16;daf-2 vs daf-16;daf-2 ) .
the green box shows the weak correlation between neuronal rescued and whole worm daf-16 targets .
d ) tissue enrichment analysis ( mean sem ) of significant daf-16-rescued up- and down - regulated genes ( supplementary table 1 ) ( fdr < 0.5 ) .
e ) significant gene ontology ( go ) terms ( adjusted p - value < 0.05 ) for daf-16 up - regulated and down - regulated genes from whole worm , intestine- , neuron- , and muscle - rescued daf-16 strains . genes used for
go analysis ( supplementary table 2 ) were derived from sam analysis of the microarrays in ( a ) and supplementary table 1 .
c ) heat map of wild type neuron - expressed relative to whole worm - expressed genes .
d ) actinomycin d ( transcription inhibitor ) treatment ( 100 g / ml ) during the cell isolation process demonstrates that the neuron isolation technique induces minimal transcriptional changes in wild type animals .
gene ontology ( go ) terms represent genes up - regulated in the absence of actinomycin d ( fig 1b , supplementary table 4 ) .
f ) c. elegans tissue gene expression prediction confirms neuronal character of adult wild - type neuron - enriched genes .
bin 1 : fdr<0.003% ; bin 2 : 0.003%0.03% ; bin 3 : 0.03%1.3% ; bin 4 : 1.3%4% ; bin 5 : 410% .
g ) principal component analysis ( pca ) shows a clear separation between wild - type adult neuronal and whole - worm samples .
h ) down - sampling of wild - type neuron sequencing reads demonstrates sufficient sampling depth . the number of genes detected at the 3 counts per million threshold ( for expressed genes ) with different proportions of total sequencing depth analyzed .
a ) promoter::gfp transcriptional fusions of candidate uncharacterized neuronal genes ( day 1 of adulthood ) .
non - overlapping go terms suggest a transition from development - related processes in embryonic and larval animals to neuronal processes involved in behavior in adults ( supplementary table 5 ) .
c ) venn diagram depicting the overlap between genes classified as expressed among embryonic and larval neurons and adult neurons from our rna - seq analysis ( supplementary table 5 ) .
a ) principal components analysis of the whole worm and isolated adult neuron samples obtained for this study .
b ) venn diagram depicting the overlap of daf-2- and daf-16;daf-2-expressed genes with those expressed in wild - type adult neurons .
d ) the daf-16 cell - autonomous and cell non - autonomous targets are distinct .
the number of genes that overlap between neuronal daf-16-rescued whole - worm targets ( punc-119::daf-16::gfp;daf-16;daf-2 vs daf-16;daf-2 ) and isolated neuron iis targets ( daf-2 vs daf-16;daf-2 ) is shown ( supplementary table 8) .
hypergeometric distribution analysis ( p - values ) shows that the extent of overlap between the gene categories is not significant .
a ) the different classes of neuronal iis / foxo genes shown in figure 2b were analyzed for dbe and dae sequences in the 1 kb upstream promoter regions .
the genome - wide % of dbe and dae occurrences across the 1 kb promoters of all gene - encoding regions is reported .
comparison of whole - worm ( class i ) vs neuronal - iis / foxo - regulated targets .
b ) go terms of class i whole worm vs. neuronal - iis up - regulated genes ( left ) and class ii whole worm vs neuronal - iis down - regulated genes ( right ) ( supplementary table 5 ) .
daf-2 mutants are defective for salt chemotaxis learning , and daf-16 is not involved in salt chemotaxis learning .
furthermore , salt learning utilizes a unique daf-2c isoform in a daf-16-independent manner , suggesting a learning mechanism distinct from the associative memory paradigms studied here .
we are specifically interested in understanding how activation of daf-16 results in the improved and extended abilities of daf-2 mutants to carry out olfactory associative learning , short - term associative memory , and long - term associative memory , all of which require daf-16 .
a ) chemotaxis index profile of wild type ( n2 ) and daf-2 animals at time points following memory training .
b ) rnai knockdown of sod-3 , a non - neuronal daf-16-regulated target that influences lifespan , has no effect on the extended short - term associative memory ( stam ) of daf-2 mutants when treated with rnai - feeding bacteria throughout the whole life ( b ) or only the post - developmental ( adult - only ) period ( c , d ) of the animal .
e ) knockdown of the neuronal iis candidate genes zip-5 and best-23 does not affect stam .
time - courses showing the chemotaxis index for each time point are shown in d and e. learning indices are shown in b , c , f , and g. b e ) two - way repeated measures anova , bonferroni post hoc tests .
f ) treatment of daf-2 worms with neuronal daf-16 target rnai does not affect short - term associative learning .
g ) neuronal - rnai sensitive worms ( punc-119::sid-1 ) in a wild - type background were treated only during adulthood with rnai targeted against the neuronal daf-16 target genes .
( 0h ) learning and 1 h short - term associative memory time points are shown .
g ) mean sem , * p < 0.05 , * * p < 0.01 , * * * p < 0.001 , * * * * p < 0.0001 .
a ) six adult mechanosensory neurons labeled by mec-4p::gfp were isolated for rna - seq .
b ) axon length from the cell body to the site of injury was measured in m immediately after axotomy and 24 hours later .
regenerative capacity of wild - type plm axons declines from day 1 to day 5 of adulthood .
c ) day 5 wild - type animals regrow axons that are significantly shorter than in day 1 animals .
d ) axotomies of daf-2 mutants grown on vector control , sod-3 , or daf-16 rnai demonstrate that sod-3 , a lifespan - regulating daf-16 target , does not influence the axon regeneration capacity of daf-2 worms at day 5 of adulthood .
e ) fkh-9 does not affect the regenerative capacity of daf-2 axons on day 1 of adulthood .
f ) mean sem , fisher s exact test , * p < 0.05 .
g ) overexpression of the a and b isoforms of fkh-9 in wild - type animals causes axonal structural defects . rescuing fkh-9 activity in the mechanosensory neurons of daf-2;fkh-9 mutants results in severe beading and degeneration of axons .
wormbase ( www.wormbase.org ) gene models for ( a ) fkh-9 and ( b ) sod-3 are shown with modencode data for daf-16 chip - seq experiments .
c ) posterior intestinal fkh-9::gfp expression is only modestly increased in daf-2 compared to wild - type animals expressing fkh-9p::fkh-9::gfp .
c ) rnai knockdown of fkh-9 exclusively during adulthood results in reduced daf-2 stam comparable to daf-16 rnai - treatment .
d , e ) daf-2;fkh-9 mutants have reduced learning ( tested immediately following stam training ) and stam compared to daf-2 .
mean sem , * p < 0.05 , * * p < 0.01 , * * * p < 0.001 , * * * * p < 0.0001 .
mean sem , * p < 0.05 , * * p < 0.01 , * * * p < 0.001 , * * * * p
time - courses showing the chemotaxis index for each time point are shown in b and e. learning indices are shown in a , c , and d. adult - only ( a ) or whole - life ( b ) fkh-9 rnai treatment increases matricide in daf-2 worms .
the cumulative % of animals dead as a result of bagging and/or exploding was recorded every other day .
c ) neuronal rescue of fkh-9 in daf-2;fkh-9 animals does not diminish the rate of vulval protrusions with age .
d ) neuronal rescue of fkh-9 does not restore longevity of the daf-2;fkh-9 double mutant . | pubmed |
in the standard model ( sm ) of electro - weak and strong interactions , there are four types of gauge vector bosons ( gluon , photon , @xmath8 and @xmath9 ) and twelve types of fermions ( six quarks and six leptons ) @xcite .
these particles have been observed experimentally . at present , all the data obtained from the many experiments in particle physics are in agreement with the standard model . in the standard model
there is one particle , the higgs boson , that is responsible for giving masses to all of the other particles @xcite . in this sense ,
the higgs particle occupies a unique position . before the startup of the large hadron collider ( lhc ) the tevatron remains the high energy frontier .
higgs searches at the tevatron are a priority for high energy physics .
the standard model ( sm ) higgs may be produced at the tevatron via several mechanisms .
the higgs is expected to be produced predominantly via gluon - gluon fusion @xcite and higgs strahlung off a @xmath9 or @xmath8 boson .
the third dominant process at the tevatron is vector boson fusion ( vbf ) for @xmath10 @xcite .
a significant fraction of the higgs produced via these mechanisms will be associated with at least one high transverse momentum ( @xmath2 ) hadronic jet .
the kinematics of higgs signals in association with jets differ significantly from that of known sm backgrounds .
these properties can be exploited to select corners of the phase space where the expected signal - to - background ratios are larger than in a purely inclusive approach . searching for a sm higgs boson at the tevatron via its decay @xmath11
was first considered in @xcite .
the relevance of observing a low mass sm higgs in association with one or two jets of high @xmath2 at the lhc has been pointed out by a number of authors @xcite .
the atlas and cms experiments have confirmed these expectations with detailed detector simulations @xcite . the feasibility of the higgs searches using the decay @xmath12 in association with one high @xmath2 jet is not discussed in the literature and is investigated here .
in this paper we study the sensitivity of the tevatron experiments to a sm higgs with a mass @xmath0 using the decay @xmath12 in association with hadronic jets .
we evaluate the feasibility of three event selection schemes involving events with one or two tagging jets and the impact of these selections on the sensitivity to sm higgs searches for the d0 and cdf experiments .
in addition to the potential enhancement of the sensitivity , a study at the tevatron of the final states discussed here will bring significant benefit to future searches at the lhc in terms of understanding qcd effects on the production of known sm particles in these corners of the phase space .
the final state under study consists of the following signatures * two high @xmath2 leptons ( @xmath13 ) of opposite sign . * missing transverse momentum ( @xmath14 ) inconsistent with detector fluctuations . * one or two high @xmath2 hadronic jets . for the generation of the higgs signal processes specified in section [ sec : introduction ] , leading order ( lo ) matrix elements ( me )
were interfaced with the pythia @xcite and herwig @xcite packages to provide parton showers and hadronization effects .
the cross - section computation and the event generation were performed using the parameterization of the parton density functions provided by cteq6 @xcite .
qcd next - to - leading - order ( nlo ) effects are known to be sizeable for the @xmath15 process .
however , qcd nlo effects are not known for all of the backgrounds . therefore , the potential improvement in sensitivity due to these effects were not considered here .
.cross - sections ( in fb ) of the sm higgs signal ( @xmath5 ) and the main background processes considered in this paper ( see text ) . [ cols="^,^,^,^,^,^",options="header " , ] the cuts used in the event selections presented in sections [ sec : selection1]-[sec : selection3 ] are the result of the optimization of the @xmath3 confidence level limit for each channel individually .
the event selections have not been optimized here to achieve the best limit for the three channels combined .
the expected exclusion limit was calculated using a likelihood technique @xcite .
table [ tab : results ] shows the expected @xmath3 confidence level limit as a function of the higgs mass with 5fb@xmath7 and @xmath16fb@xmath7 of integrated luminosity ( for two experiments combined ) . in conclusion , the searches of a higgs boson using @xmath17 with the event selections presented in this paper
could further enhance the sensitivity of the tevatron experiments reported in @xcite .. ] it is important to note that we use lo cross - sections for the @xmath15 process .
the nlo k - factors for this process are expected to be large , thus significantly enhancing the sensitivity of analysis i. in addition , no multivariate techniques have been implemented . with tagging hadronic jets the complexity of the final state increases and with it the relative sensitivity of a multivariate analysis with respect to the simple cut - based approach used here .
in particular , variables like the transverse mass of the higgs - leading jet system , the invariant mass of the two leading jets can be used as additional discriminating variables when appropriate .
the analysis strategy presented here is conservative and leaves room for significant improvement in the sensitivity .
the authors are most grateful to y. fang , l. flores - castillo , t. han , m. herndon , f. petriello and t. vickey for most valuable comments and suggestions .
this work was supported in part by the united states department of energy through grant no .
de - fg0295-er40896 .
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let @xmath1 be a field of characteristic zero with an embedding @xmath3 into the field of complex numbers .
[ [ paraabv ] ] let @xmath4 be a field or a dedekind ring and @xmath5 be a representation of a quiver @xmath6 with values in the category @xmath7 of finitely generated projective @xmath4-modules . in the unpublished work @xcite ( see also @xcite for surveys ) , m. nori has constructed an @xmath4-coalgebra @xmath8 such that the representation @xmath9 has a universal factorization ( see ) @xmath10 where @xmath11 is the category of left @xmath8-comodules that are finitely generated over @xmath4 , @xmath12 is a representation and @xmath13 is the forgetful functor .
then , m. nori applies this tannakian formalism to betti homology to obtain the abelian category @xmath14 of effective homological motives over @xmath1 ( see e.g. @xcite ) . by construction , given a @xmath1-variety @xmath15 , a closed ( reduced ) subscheme @xmath16 and an integer @xmath17 , there is a motive @xmath18 in @xmath14 which realizes to the usual betti homology .
[ [ section ] ] j. ayoub and l. barbieri - viale have shown in ( * ? ? ?
* theorem 5.2 , theorem 6.1 ) that the thick abelian subcategory of nori s category of effective homological motives generated by the @xmath19 and @xmath20 of pairs is equivalent to : the abelian category @xmath21 associated with the representation @xmath22 where @xmath23 is the category of pairs @xmath24 where @xmath25 is a smooth affine @xmath1-curve , @xmath26 is a closed subset consisting of finitely many closed points and @xmath27 is the first betti homology group of the pair @xmath28 ; the abelian category @xmath29 of deligne s 1-motives with torsion @xcite .
note that by ( * ? ? ?
* thorme 3.4.1 ) the derived category of deligne s abelian category of 1-isomotives @xmath30 is known to be equivalent to the thick triangulated subcategory of voevodsky s category of geometrical effective motives with rational coefficients generated by motives of smooth @xmath1-curves .
[ [ section-1 ] ] such a description is not possible integrally for the extension of the theory of 1-motives introduced by g. laumon in @xcite and studied in @xcite .
indeed the category of laumon 1-motives with torsion @xmath31 of @xcite contains the category of infinitesimal formal @xmath1-groups as a full subcategory - groups is equivalent via the lie algebra with the category of finite dimensional @xmath1-vector spaces . ] .
in particular not all hom groups in @xmath31 are finitely generated abelian groups and therefore there can not exist a quiver @xmath6 and a representation @xmath32 such that @xmath31 is equivalent to @xmath33 .
if the field @xmath1 is too big ( e.g. @xmath34 ) , the same obstruction applies with rational coefficients . the abelian category @xmath35 of laumon @xmath36-isomotives still contains the category of infinitesimal formal @xmath1-groups as a full subcategory and therefore not all its hom groups are finite dimensional @xmath37-vector spaces .
again this prevents the existence of a quiver @xmath6 and a representation @xmath38 such that @xmath35 is equivalent to @xmath33 .
[ [ section-2 ] ] if @xmath0 , one may still hope for describing the abelian category @xmath35 of laumon @xmath36-isomotives over @xmath1 via nori s tannakian formalism .
the main result of this work is such a description in that case .
more precisely , let a @xmath1-curve with modulus be a triplet @xmath39 where @xmath15 is a smooth proper @xmath1-curve and @xmath40 are effective divisors on @xmath15 with disjoint supports .
define the de rham cohomology of a such a @xmath1-curve with modulus as the finite dimensional @xmath1-vector space @xmath41)\ ] ] where @xmath42 and @xmath43 are the ideals in @xmath44 that define @xmath45 and @xmath46 .
the @xmath1-curves with modulus define a category @xmath47 for which a morphism @xmath48 is a morphism @xmath49 of @xmath1-varieties such that @xmath50 and @xmath51 .
the de rham cohomology of curves with modulus define a functor @xmath52 and our main theorem is the following ( see theorem [ maintheo2 ] ) .
[ maintheo ] let @xmath0 . the @xmath37-linear abelian category associated with the representation of quiver @xmath53)\end{aligned}\ ] ]
is equivalent to the category @xmath54 of laumon 1-isomotives over @xmath1 .
generalizes the equivalence between ( a ) and ( b ) recalled in and proved by j. ayoub and l. barbieri - viale in ( * ? ? ?
* theorem 5.2 ) . note that we do not provide any definition for a non homotopy invariant analog of the full category of nori s motives of varieties with modulus .
moreover in @xcite the main theorems are valid over any field of characteristic zero embedded into the complex numbers and admit also integral variants . here
we are not able to provide such generality .
we leave these issues as future problems . throughout the paper we work over a base field @xmath1 with a fixed embedding @xmath55 . from [
sect : start - assuming - k - is - q ] onward , we further assume @xmath0 . for a @xmath1-scheme @xmath15 ,
we denote by @xmath56 the sheaf of khler differentials on @xmath15 relative to @xmath1 . if @xmath46 is a closed subscheme of @xmath15 , we write @xmath57 for the ideal sheaf of @xmath46 . for a vector space @xmath58 over @xmath1 , we write @xmath59 for the @xmath1-linear dual of @xmath58 .
let @xmath4 be a ring and let @xmath60 be an @xmath4-algebra .
for an @xmath4-linear abelian category @xmath61 , we denote by @xmath62 its scalar extension .
this is a @xmath60-linear abelian category having the same objects as @xmath61 and @xmath63
[ [ section-3 ] ] let @xmath64 be a field . following ( * ? ? ?
* chapitre ii , 4 ) , recall that a @xmath64-linear abelian category @xmath65 is said to be finite if it is noetherian and artinian i.e. @xmath65 is essentially small and any object in @xmath65 has finite length .
we shall say that @xmath65 is hom finite if for any objects @xmath66 in @xmath65 the @xmath64-vector space @xmath67 is finite dimensional . by ( * ? ? ?
* theorem 2.1 ) , we have the following theorem . [ norilength ]
let @xmath65 be a @xmath64-linear abelian category which is finite and hom finite , @xmath6 be a quiver and @xmath68 be a representation of the quiver @xmath6 with values in @xmath65 .
then , there exist a @xmath64-linear abelian category @xmath61 , a representation @xmath69 , a @xmath64-linear faithful exact functor @xmath70 and an invertible 2-morphism @xmath71 such that for every @xmath64-linear abelian category @xmath72 , every representation @xmath73 , every @xmath64-linear exact faithful functor @xmath74 , and every invertible 2-morphism @xmath75 the following conditions are satisfied .
* there exist a @xmath76-linear functor @xmath77 and two invertible @xmath78-morphisms @xmath79 such that @xmath80 ^ -{g{\star}\gamma}\ar[d]^-{\delta{\star}r } & { g\circ s}\ar[d]^-{\beta}\\ { f\circ r}\ar[r]^-{\alpha } & { t}}\ ] ] is commutative . *
if @xmath81 is a @xmath76-linear functor and @xmath82 are two invertible @xmath78-morphisms such that the square @xmath83 ^ -{g{\star}\gamma'}\ar[d]^-{\delta'{\star}r } & { g\circ s}\ar[d]^-{\beta}\\ { f\circ r}\ar[r]^-{\alpha } & { t}}\ ] ] is commutative , then there exists a unique @xmath78-morphism @xmath84 such that @xmath85 and @xmath86
. it will be useful to keep in mind the following remark .
[ remanoricat ] when @xmath87 the previous theorem is due to m. nori .
more precisely , let @xmath88 be a full subquiver of @xmath6 with finitely many objects and @xmath89 be the subring of @xmath90 formed by the elements @xmath91 such that @xmath92 for every object @xmath93 and every morphism @xmath94 in @xmath6 .
then , its linear dual @xmath95 is a coassociative , counitary @xmath64-coalgebra which is finite dimensional over @xmath64 .
we may then consider the @xmath64-linear abelian category @xmath96 of finite dimensional left comodules over the coassociative and counitary @xmath64-coalgebra @xmath97 where the colimit is taken over full subquivers of @xmath6 with finitely many objects .
for every object @xmath98 the finite dimensional @xmath76-vector space @xmath99 inherits a structure of left @xmath100-comodule .
this provides a representation @xmath101 such that @xmath102 where @xmath103 is the forgetful functor .
the main result proved by m. nori is that the uplet @xmath104 satisfies the universal property of when @xmath87 .
the general case is deduced from nori s result .
indeed , let @xmath105 be a finite and hom finite @xmath64-linear abelian category and @xmath106 be a representation .
a result ( see ( * ? ? ?
* corollary 4.3 ) ) that can be easily deduced from ( * ? ? ?
* theorem , 5.8 ) assures the existence of a @xmath64-linear exact faithful functor @xmath107 .
let @xmath108 and consider the associated representation @xmath109 the universal property of @xmath110 applied to the uplet @xmath111 provides a @xmath64-linear exact faithful functor @xmath112 and an invertible natural transformation @xmath113 .
one checks then that the uplet @xmath114 satisfies the universal property stated in ( see @xcite for details ) .
[ [ section-4 ] ] let @xmath6 be a quiver and @xmath115 be a representation .
let @xmath116 be an uplet where @xmath72 is a @xmath64-linear abelian category , @xmath73 is a representation , @xmath74 is a @xmath64-linear exact faithful functor , and @xmath75 is an invertible natural transformation . by the universal property of ,
there exist a @xmath76-linear functor @xmath117 and two invertible natural transformations @xmath118 such that the square @xmath119 ^ -{g{\star}\gamma}\ar[d]^-{\delta{\star}r } & { g\circ s}\ar[d]^-{\beta}\\ { f_t\circ \overline{t}}\ar@{=}[r ] & { t}}\ ] ] is commutative ( here we use the notations from ) . in (
* proposition 2.1 ) , j. ayoub and l. barbieri - viale have given a criterion for the functor @xmath120 to be an equivalence .
the proof of our main result relies on this criterion .
[ ayoubbv ] assume the following conditions
[ conda ] for every vertices @xmath121 , there exist @xmath122 in @xmath6 and edges @xmath123 , @xmath124 such that the map @xmath125 is an isomorphism in @xmath72 ; 2 . [ condb ] every object in @xmath72 is a quotient of an object of the form @xmath126 for some vertex @xmath98 .
[ condc ] for every map @xmath127 in @xmath72 there exists a finite sub - quiver @xmath128 containing @xmath129 such that @xmath130 is a sub-@xmath131-module of @xmath99 .
then the functor @xmath117 is an equivalence of categories .
[ [ section-5 ] ] let @xmath132 and @xmath133 be two finite and hom finite @xmath64-linear abelian categories .
let @xmath134 , @xmath135 be quivers , @xmath136 be a morphism of quivers and @xmath137 be two representations .
let @xmath138 and @xmath139 be uplets obtained by applying to the representations @xmath140 and @xmath141 respectively .
the next proposition shows that certain exact functors can be lifted to universal categories ( for a proof , see ( * ? ? ?
* proposition 6.6 ) ) .
[ fonc3 ] let @xmath142 be a pair where @xmath143 is an _
@xmath64-linear functor and @xmath144 is an isomorphism of representations .
there exist an exact functor @xmath145 , an invertible natural transformation @xmath146 , and an isomorphism of representations @xmath147 such that @xmath148 ^ -{\phi\star\alpha_1}\ar[dd]_-{\rho\star r_1 } & { \phi\circ t_1}\ar[rd]^-{\phi } & { } \\ { } & { } & { t_2\circ d}\\ { f_2\circ\psi\circ r_1}\ar[r]_-{f_2\star\varrho } & { f_2\circ r_2\circ d}\ar[ru]_-{\alpha_2\star d } & { } } \ ] ] is commutative .
[ [ section-6 ] ] in this work we will need to lift natural transformations as well .
let @xmath149 be morphism of quivers .
let @xmath150 , @xmath151 be a pairs where @xmath152 are _ exact _ @xmath64-linear functor and @xmath153 , @xmath154 are isomorphisms of representations . by ,
there exist exact functors @xmath155 , invertible natural transformations @xmath156 , @xmath157 , and isomorphisms of representations @xmath158 , @xmath159 such that the corresponding diagrams as in are commutative .
[ nattransf ] let @xmath160 be a pair where @xmath161 and @xmath162 are natural transformations such that the square @xmath163 ^ -{\phi_1}\ar[d]^-{\theta{\star}t_1 } & { t_2\circ d_1}\ar[d]^{t_2{\star}\theta_d}\\ { \phi_2\circ t_1}\ar[r]^-{\phi_2 } & { t_2\circ d_2}}\ ] ] is commutative .
then there exists one and only one natural transformation @xmath164 that makes the squares @xmath165 ^ -{\varrho_1}\ar[d]^-{\overline{\theta}{\star}r_1 } & { r_2\circ d_1}\ar[d]^{r_2{\star}\theta_d}\\ { \psi_2\circ r_1}\ar[r]^-{\varrho_2 } & { r_2\circ d_2 } } \qquad \xymatrix{{\phi_1\circ f_1}\ar[r]^-{\rho_1}\ar[d]^-{\theta{\star}f_1 } & { f_2\circ \psi_1}\ar[d]^{f_2{\star}\overline{\theta}}\\ { \phi_2\circ f_1}\ar[r]^-{\rho_2 } & { f_2\circ \psi_2}}\ ] ] commutative . let @xmath15 be an object in @xmath166 . let us sketch the construction of a morphism @xmath167 in @xmath168 which makes the square @xmath169 ^ -{\rho_{1,x}}\ar[d]^-{\theta_{f_1(x ) } } & { f_2(\psi_1(x))}\ar[d]^-{f_2(\overline{\theta}_x)}\\ { \phi_2(f_1(x))}\ar[r]^-{\rho_{2,x } } & { f_2(\psi_2(x))}}\ ] ] commutative . since @xmath170 is faithful , such a morphism is necessarily unique .
when @xmath171 for @xmath172 , we define @xmath173 to be the unique morphism that makes the square @xmath174 ^ -{\varrho_{1,p}}\ar[d]^-{\overline{\theta}_x } & { r_2(d_1(p))}\ar[d]^-{r_2(\theta_{d , p})}\\ { \psi_2(x)}\ar[r]^-{\varrho_{2,p } } & { r_2(d_2(p))}}\ ] ] commutative .
this defines also @xmath175 when @xmath15 is a finite direct sum of such objects .
assume now the existence of an epimorphism @xmath176 in @xmath166 where @xmath45 is an object for which @xmath177 has been constructed .
it is then enough to check the existence of a factorization @xmath178 ^ -{\psi_1(s)}\ar[d]^-{\overline{\theta}_y } & { \psi_1(x)}\ar@{.>}[d]\ar[r ] & { 0}\\ { \psi_2(y)}\ar[r]^-{\psi_2(s ) } & { \psi_2(x)}\ar[r ] & { 0.}}\ ] ] as the rows are exact , this amounts to checking that @xmath179 vanishes on the kernel of @xmath180 . but this is true since it is after applying @xmath170 and @xmath170 is faithful .
similarly , one shows the existence of @xmath173 when @xmath15 is any subobject of an object @xmath45 in @xmath166 for which @xmath177 has already been constructed .
this concludes the proof since by ( * ? ? ?
* proposition 7.1.16 ) every object in @xmath166 is a subquotient of a finite direct sum of objects of the form @xmath171 for @xmath172 .
[ remamono ] note that since @xmath170 is a @xmath64-linear exact and faithful functor , if @xmath181 is a monomorphism ( resp .
epimorphism ) then @xmath182 is a monomorphism ( resp .
epimorphism ) .
[ [ section-7 ] ] let us denote by @xmath183 the following category .
an object in @xmath183 is a triplet @xmath39 where @xmath15 is smooth proper @xmath1-curve and @xmath40 are effective divisors on @xmath15 such that @xmath184 .
a morphism @xmath185 in @xmath183 , is a morphism @xmath49 of @xmath1-varieties such that @xmath186 and @xmath187
. it will be useful to consider also the following variant : @xmath188 is the category with the same objects as @xmath183 but this times a morphism @xmath185 in @xmath189 is a morphism @xmath49 of @xmath1-varieties such that @xmath50 and @xmath190 .
[ defidr ] let @xmath39 be an object in the category @xmath183 .
we define @xmath41)\ ] ] to be the first hypercohomology group of the complex of @xmath44-modules @xmath191 $ ] , where @xmath42 is placed in degree zero .
( recall that by our convention @xmath56 is the sheaf of khler differentials on @xmath15 relative to @xmath1 , and that @xmath42 and @xmath192 are the sheaves of ideals defining @xmath45 and @xmath46 respectively . )
this is a finite dimensional @xmath1-vector space .
let @xmath193 be a morphism in the category @xmath183 .
it defines a morphism of @xmath1-vector spaces @xmath194 and so we have a functor @xmath195 where @xmath196 is the category of finite dimensional @xmath1-vector spaces .
[ prop : uv ] let @xmath25 be a smooth proper curve over @xmath1 and let @xmath197 be an effective divisor on @xmath25 .
we set @xmath198 then the differential map induces isomorphisms @xmath199 write @xmath200 .
then we have @xmath201 where @xmath202 denotes the maximal ideal of the local ring @xmath203 of @xmath25 at @xmath204 .
thus the first statement follows from the bijectivity of @xmath205 which is readily seen .
similarly , we have @xmath206 thus the second statement follows from the bijectivity of @xmath207 which is readily seen .
[ cor : dual - uv ] two @xmath1-vector spaces @xmath208 and @xmath209 are canonically dual to each other .
we may suppose @xmath197 is ( effective and ) non - trivial .
then we get @xmath210\ ] ] from an exact sequence @xmath211 . on the other hand , another exact sequence @xmath212 and the above proposition yield @xmath213.\ ] ]
now the corollary follows from the serre duality .
[ prop : pull - push - uv ] let @xmath214 and @xmath215 be pairs of a smooth proper @xmath1-curves and an effective divisor .
let @xmath216 be a @xmath1-morphism .
the canonical maps @xmath217 and the trace maps @xmath218 for each @xmath219 induce the following functoriality : 1 . if @xmath220 , then we have @xmath221 2 . if @xmath222 , then we have @xmath223 this is elementary and left to the reader .
[ [ section-8 ] ] [ candec ] for any @xmath224 , there is a canonical decomposition @xmath225 moreover , the decomposition is functorial with respect to maps in @xmath183 . since @xmath226 for a pair of a smooth proper @xmath1-curve @xmath25 and an effective divisor @xmath197 ,
we are reduced to showing @xmath227 to show the first isomorphism , we construct canonical maps @xmath228 such that @xmath229 and @xmath230 . for this
we first note that the map @xmath231 \to [ { \matheusm{i}}_{y_{\mathrm{red } } } { \rightarrow}{\matheusm{i}}_{z}^{-1}\omega^1_x]\ ] ] ( induced by the inclusions @xmath232 and @xmath233 ) is a quasi - isomorphism by proposition [ prop : uv ] . using this ,
we define @xmath234 to be the composition @xmath235 ) \\ & \overset{\cong}{\leftarrow } { \mathbf{h}}^1(x , [ { \matheusm{i}}_{y } { \rightarrow}{\matheusm{i}}_{y}{\matheusm{i}}_{y_{\mathrm{red}}}^{-1 } { \matheusm{i}}_{z}^{-1}\omega^1_x ] ) \\ & \to { \mathbf{h}}^1(x , [ { \matheusm{i}}_{y } { \rightarrow}{\matheusm{i}}_{z}^{-1}\omega^1_x ] ) = { \mathbf{h}}^1_{\mathrm{dr}}(x , y , z),\end{aligned}\ ] ] where the second map is induced by the inclusion @xmath236 .
next , @xmath237 is given by @xmath238 ) \\ & \to { \mathbf{h}}^1(x , [ { \matheusm{i}}_{y_{\mathrm{red } } } { \rightarrow}{\matheusm{i}}_{z}^{-1}\omega^1_x ] ) = { \mathbf{h}}^1_{\mathrm{dr}}(x , y_{\mathrm{red}},z)\end{aligned}\ ] ] which is induced by the inclusion @xmath232 .
it is obvious that the composition @xmath239 is the identity .
it is also clear from this construction that @xmath230 .
note also that proposition [ prop : uv ] tells us that @xmath240 , as it should be .
the second isomorphism @xmath241 is constructed in a similar way .
we omit it .
[ prop : dual - hdr ] for any @xmath224 , two @xmath1-vector spaces @xmath242 and @xmath243 are canonically dual to each other .
apply lemma [ lem : dual - curve ] with @xmath244 $ ] and @xmath245 $ ] .
[ lem : dual - curve ] let @xmath246 and @xmath247 be two complexes of sheaves of @xmath1-vector spaces on @xmath15 such that @xmath248 and @xmath249 are locally free @xmath44-modules for all @xmath250 and that @xmath251 unless @xmath252 .
let @xmath253 be a map of complexes and suppose that it induces @xmath254 and @xmath255 .
then @xmath256 induces a perfect duality between @xmath257 and @xmath258 for all @xmath250 .
this is reduced to the serre duality by an exact sequence @xmath259 and a similar sequence for @xmath247 .
[ rem : cov - hdr ] recall that @xmath260 is contravariant functorial for morphisms in @xmath183 .
the proposition implies that it also has covariant functoriality for morphisms in @xmath188 .
[ [ section-9 ] ] the following definition introduces our main object of studies .
the category @xmath261 of effective cohomological isomotives of curves with modulus is the @xmath1-linear category associated with the representation @xmath262 by construction the representation @xmath260 has a factorization @xmath263 into a representation @xmath264 and a @xmath1-linear faithful exact functor @xmath265 .
[ [ sect : ehm - ecm ] ] let @xmath266 be the category defined as follows ( see @xcite ) .
an object is a pair @xmath24 where @xmath25 is a smooth affine curve and @xmath26 is a closed subset consisting of finitely many closed points .
let @xmath64 be a field of characteristic zero .
recall that by definition ( see @xcite ) the @xmath64-linear abelian category @xmath267 of effective homological isomotives of curves is denoted by @xmath268 while @xmath267 stands for the the thick abelian subcategory of nori s category of effective cohomological isomotives generated by the first cohomology motive of pairs .
both categories are equivalent by ( * ? ? ?
* theorem 5.2 , theorem 6.1 ) . ] is the universal category associated with the representation @xmath269 where @xmath270 is the betti homology of the pair @xmath28 ( with integral coefficients ) .
let us denote by @xmath271 the universal category associated with the representation @xmath272 where @xmath273 is the betti cohomology of the pair @xmath28 .
the @xmath64-linear dual functor @xmath274 induces an equivalence @xmath275 in this work , it will be convenient to define effective cohomological motives of curves using algebraic de rham cohomology instead of betti cohomology .
for this we consider the representation @xmath276 where @xmath277 is the smooth compactification of @xmath25 , @xmath278 is the set of points at infinity and @xmath279 is defined as in with both @xmath45 , @xmath280 viewed as closed reduced subschemes of @xmath277 .
let us denote by @xmath281 the @xmath1-linear abelian category associated with the representation @xmath2 in .
by construction the representation @xmath2 has a factorization @xmath282 into a representation @xmath283 and a @xmath1-linear faithful exact functor @xmath284 .
[ isoper ] there is a canonical isomorphism of functors @xmath285 on the category @xmath266 .
for a @xmath1-variety @xmath58 we write @xmath286 for the complex analytic variety associated with @xmath58 .
let @xmath28 in @xmath266 and let @xmath287 , @xmath288 be the ideals of @xmath289 and @xmath290 in @xmath291 .
the canonical map @xmath292)\ ] ] is an isomorphism of @xmath293-vector spaces by gaga . on the other hand , we have canonical quasi - isomorphisms @xmath294 , \qquad i _ * { \mathbb{c}}_{y^{\mathrm{an } } } \cong [ { \mathscr{o}}_{\overline{c}^{\raisebox{-2pt}{{\tiny an}}}}/{\matheusm{i}}{\rightarrow}0],\ ] ] where @xmath295 and @xmath296 are immersions and @xmath297 ( resp .
@xmath298 ) denotes the constant sheaf on @xmath299 ( resp .
@xmath289 ) . there is an exact sequence of complexes @xmath300 \to [ { \mathscr{o}}_{\overline{c}^{\raisebox{-2pt}{{\tiny an}}}}{\rightarrow}{\matheusm{j}}^{-1}\omega^1_{\overline{c}^{\raisebox{-2pt}{{\tiny an } } } } ] \to [ { \mathscr{o}}_{\overline{c}^{\raisebox{-2pt}{{\tiny an}}}}/{\matheusm{i}}{\rightarrow}0 ] \to 0.\ ] ] hence the lemma follows from the fact that @xmath301 is computed as the hypercohomology of the cone of @xmath302 with degree shifted by one . [ prop : equiv - betti - dr ] the categories @xmath303 and @xmath281 are equivalent .
consider the 2-fiber product @xmath61 of two copies of the category @xmath196 over @xmath304 .
an object of @xmath61 is thus a triplet @xmath305 where @xmath306 are finite dimensional @xmath1-vector spaces and @xmath307 is an isomorphism of @xmath293-vector spaces .
the category @xmath308 is a @xmath1-linear abelian category with two @xmath1-linear exact faithful functors @xmath309 given by the projection on the first and second factors . we may then consider the representation @xmath310 where the isomorphism @xmath311 is the one of .
we have the commutative diagram @xmath312\ar[r]\ar@{.>}[d]^-{\overline{\pi}_1 } & { { \mathop{\mathsf{mod}}\nolimits}(k)}\\ { { \mathrm{crv}}^{\mathrm{op}}}\ar[r]^{h^1_{{\mathrm{dr}},{\mathrm{b}}}}\ar@/_2em/[rd]_-{\overline{h}^1_{{\mathrm{b}}}}\ar@/^2em/[ru]^-{\overline{h}^1_{\mathrm{dr } } } & { { \mathscr}a}\ar[rd]^-{\pi_2}\ar[ru]_-{\pi_1 } & { } \\ { } & { { \mathrm{ecm}}_1^k}\ar[r]\ar@{.>}[u]_-{\overline{\pi}_2 } & { { \mathop{\mathsf{mod}}\nolimits}(k)}}\ ] ] where @xmath313 and @xmath314 are the functors provided by the universal properties . the subdiagram @xmath315 ^ -{\pi_2\circ\overline{\pi}_1 } & { } \\ { { \mathrm{crv}}^{\mathrm{op}}}\ar[ru]^-{\overline{h}^1_{{\mathrm{dr}}}}\ar[rd]_-{\overline{h}^1_{{\mathrm{b } } } } & { } & { { \mathop{\mathsf{mod}}\nolimits}(k)}\\ { } & { { \mathrm{ecm}}_1^k}\ar[ru]\ar@{.>}[uu ] & { } } \ ] ] provides then a @xmath1-linear functor @xmath316 .
similarly we get a @xmath1-linear functor @xmath317 and it is easy to check that they are quasi - inverse to one another
. let @xmath25 be any smooth affine @xmath1-curve .
we denote by @xmath277 its smooth compactification and set @xmath278 viewed as a reduced subscheme of @xmath277 .
this induces a morphism of quivers @xmath318 since by definition @xmath319 as representations of the quiver @xmath320 , the universal property of nori s construction ( see e.g. ( * ? ? ?
* theorem 2 ) ) ensures the existence of a @xmath1-linear exact faithful functor @xmath321 and isomorphisms of functors @xmath322 that makes the square @xmath323\ar[d ] & { f^a_{\mathrm{dr}}\circ \overline{{\mathbf{h}}}^1_{\mathrm{dr}}\circ \overline{(-)}}\ar[d]^-{=}\\ { f_{\mathrm{dr}}\circ \overline{h}^1_{\mathrm{dr}}}\ar[r]^-{= } & { h^1_{\mathrm{dr}}}}\ ] ] commutative .
let us consider now the @xmath1-linear abelian category @xmath72 defined as follows .
an object in @xmath324 is a tuplet @xmath325 where @xmath306 are finite dimensional @xmath1-vector spaces and @xmath326 and @xmath327 are morphisms of @xmath1-vector spaces such that @xmath328 .
a morphism @xmath329 in @xmath324 is simply a pair of @xmath1-linear morphisms @xmath330 such that @xmath331 and @xmath332 .
note that by construction , we have two @xmath1-linear exact functors obtained by projection on the first and second factor . @xmath333 and that moreover @xmath334 is faithful .
let @xmath15 be a smooth proper @xmath1-curve and @xmath40 be closed subschemes of @xmath15 .
recall from that there are two morphisms @xmath335 and @xmath336 such that @xmath337 .
we may therefore consider the representation @xmath338 where @xmath234 and @xmath237 are the morphisms and . by construction @xmath339 and from we have @xmath340 where @xmath341 is the morphism of quivers @xmath342 by ( * ? ? ?
* theorem 2 ) , there exists a faithful exact @xmath1-linear functor @xmath343 and two isomorphisms of functors @xmath344 , @xmath345 such that @xmath346 ^ -{\pi_2{\star}\gamma}\ar[d]^-{\delta{\star}\overline{{\mathbf{h}}}^1_{\mathrm{dr } } } & { \pi_2\circ { \mathbf{h}}^1_{{\mathrm{dr}},{\mathscr}b}}\ar[d]^-{=}\\ { f^a_{\mathrm{dr}}\circ \overline{{\mathbf{h}}}^1_{\mathrm{dr}}}\ar[r]^-{= } & { { \mathbf{h}}^1_{\mathrm{dr}}}}\ ] ] is commutative
. we may apply ( * ? ? ?
* proposition 6.6 ) to @xmath347 to obtain the existence of a @xmath1-linear exact and faithful functor @xmath348 and isomorphisms of functors @xmath349 such that the diagram @xmath350 \ar[d]^-{\pi_1{\star}\gamma } & f_{\mathrm{dr}}\circ \pi_{{\mathrm{ecm } } } \circ \overline{{\mathbf{h}}}^1_{\mathrm{dr}}\ar[r ] & f_{\mathrm{dr}}\circ \overline{h}^1_{\mathrm{dr}}\circ ( -)_{\mathrm{\'et}}\ar[ld]^-{= } \\
\pi_1 \circ { \mathbf{h}}^1_{{\mathrm{dr}},{\mathscr}b } \ar[r]_= & h^1_{{\mathrm{dr } } } \circ ( -)_{\mathrm{\'et}}}\ ] ] commutes .
( see ( * ? ? ?
* proposition 6.7 ) for uniqueness . )
let @xmath351 be the functor that maps @xmath58 to @xmath352 . the diagram @xmath353 ^ -{f_{\mathrm{dr}}}\ar[d]^-{i_{\mathrm{ecm } } } & { { \mathop{\mathsf{mod}}\nolimits}(k)}\ar[d]^-{i_{\mathscr}b}\ar@{=}[rd]\\ { { \mathrm{ecmm}}_1}\ar[r]^-{f^a_{\mathscr}b}\ar@/_2em/[rr]_-{f^a_{\mathrm{dr } } } & { { \mathscr}b}\ar[r]^-{\pi_2 } & { { \mathop{\mathsf{mod}}\nolimits}(k)}}\ ] ] is commutative up to isomorphisms of functors . [ embeddingmotives ] the composition @xmath354 is isomorphic to the identity .
moreover the functor @xmath355 is fully faithful .
since @xmath356 is the identity on the quiver @xmath266 the first assertion is an immediate consequence of the uniqueness statement ( * ? ? ?
* proposition 6.7 ) .
let @xmath357 be objects in @xmath281 and @xmath358 be a morphism in @xmath359 .
note that for such an @xmath360 , we have @xmath361 let @xmath362 .
it is enough to show that @xmath363 and since @xmath265 is faithful , it is enough to show this equality after applying @xmath265 .
we have @xmath364 this concludes the proof .
in this section , we recall necessary material from @xcite , @xcite , introducing notations .
[ [ section-10 ] ] recall that we are working over a field @xmath1 of characteristic zero .
let @xmath365 be the category of affine schemes over @xmath1 , and let @xmath366 be the category of sheaves of abelian groups on the fppf site on @xmath365 . for @xmath367
, we abbreviate @xmath368 for a @xmath1-algebra @xmath4 , and we put @xmath369/(\epsilon^2 ) ) \to f(k)]$ ] .
[ [ section-11 ] ] we shall consider full subcategories of @xmath366 . let @xmath370 be the full subcategory of @xmath366 consisting of objects that are represented by connected commutative algebraic groups @xmath371 over @xmath1 ( see ( * ? ? ?
* ( 4.1 ) ) ) .
we identify such a @xmath371 with the object in @xmath366 represented by @xmath371 .
let @xmath372 be the full subcategory of @xmath370 consisting of linear commutative algebraic groups over @xmath1 , we write @xmath373 ( resp .
@xmath374 ) for the full subcategory of @xmath372 consisting unipotent ( resp .
multiplicative ) groups . for any @xmath375
, there is a canonical decomposition @xmath376 , where @xmath377 and @xmath378 .
the functor @xmath379 is an equivalence , by which we often identify them .
let @xmath380 be the full subcategory of @xmath370 consisting of abelian varieties . recall that any @xmath381 canonically fits in an extension @xmath382 , where @xmath383 and @xmath384 .
we ease the notation by putting @xmath385 and @xmath386 .
we call @xmath387 the _ semi - abelian part _ of @xmath371
. let @xmath388 be the full subcategory of @xmath366 consisting of formal groups over @xmath1 without torsion in the sense of ( * ? ? ?
* ( 4.2 ) ) .
we write @xmath389 ( resp .
@xmath390 ) for the full subcategory of @xmath388 consisting of connected ( resp . tale ) formal groups . for any @xmath391
, there is a canonical decomposition @xmath392 , where @xmath393 and @xmath394 .
the functor @xmath395 is an equivalence , with a quasi - inverse @xmath396 , where @xmath397 denotes the formal completion of @xmath398 .
[ [ section-12 ] ] following ( * ? ? ?
* ( 5.1.1 ) ) , define a _
laumon @xmath36-motive _ to be a complex @xmath399 $ ] in @xmath366 such that @xmath391 ( placed at degree @xmath400 ) and @xmath381 ( placed at degree @xmath401 ) .
we denote the category of laumon @xmath36-motives over @xmath1 by @xmath402 ( or by @xmath403 if we with to stress the dependency on @xmath1 ) .
there is an equivalence @xmath404 , called _
cartier duality_. [ [ sect : deligne-1-motives ] ] a laumon @xmath36-motive @xmath399 $ ] is called a _
deligne @xmath36-motive _ if @xmath405 and @xmath406 .
denote by @xmath407 the full subcategory of @xmath402 consisting of deligne @xmath36-motives .
along with this , we denote by @xmath408 ( resp .
@xmath409 ) the essential image of an obvious full faithful functor @xmath410:=[0 \to u ] , \\
( \text{resp.}~ & { \mathscr s}_{\inf } \to { \mathscr{m}}^a_1 , \quad f
\mapsto f[1]:=[f \to 0]).\end{aligned}\ ] ] [ [ sect : def - grm ] ] let @xmath411 \in { \mathscr{m}}^a_1 $ ] .
we define a filtration on @xmath412 by @xmath413 \supset { \mathrm{fil}}^2_{\mathscr{m}}m=[0 \to g_{\mathrm{uni } } ] \supset { \mathrm{fil}}^3_{\mathscr{m}}m=0.\ ] ] we put @xmath414 so that @xmath415,~ { \mathrm{gr}}^1_{\mathscr{m}}m \cong [ f_{{\mathrm{\'et } } } \to g_{\mathrm{sa } } ] = : m_{\mathrm{del}},~ { \mathrm{gr}}^2_{\mathscr{m}}m = { \mathrm{fil}}^2_{\mathscr{m}}m = g_{\mathrm{uni}}[0].\ ] ] we have defined functors @xmath416 note that all these functors are exact , and that @xmath417 ( resp .
@xmath418 ) is a left ( resp .
right ) adjoint to the inclusion @xmath419 ( resp .
@xmath420 ) . following @xcite
, we also define ( recall that @xmath421 ) @xmath422.\ ] ] the functor @xmath423 is a left adjoint of the inclusion @xmath424 .
[ [ section-13 ] ] we call @xmath411 \in { \mathscr{m}}^a_1 $ ] _ unipotent free _ if @xmath406 . for such @xmath412 , it is shown in ( * ? ? ?
* ( 2.2.3 ) ) that there is an extension @xmath425 \in { \mathscr{m}}^a_1
$ ] of @xmath412 by @xmath426 such that it is universal among extensions of @xmath412 by an object of @xmath427 .
( here @xmath428 denotes @xmath1-linear dual .
recall that by convention we identify a @xmath1-vector space with an object of @xmath373 . )
[ [ section-14 ] ] now take any @xmath429 \in { \mathscr{m}}^a_1 $ ] .
note that @xmath430 and @xmath431 ( introduced in [ sect : def - grm ] ) are unipotent free . by (
* ( 2.3.2 ) ) , an exact sequence @xmath432 \to 0\ ] ] induces an exact sequence @xmath433 where @xmath434 \in { \mathscr{m}}^a_1 $ ] .
let us write @xmath435 $ ] and @xmath436 $ ] .
then we get an exact sequence @xmath437 which admits a canonical splitting given by @xmath438 .
we also need the following remark .
the universality of @xmath439 induces maps @xmath440 and @xmath441 in the following commutative diagram with exact rows @xmath442 & { \mathrm{ext}}(m_\times , { \mathbf{g}}_a)^ * \ar[r ] \ar[d]^{v_m } & ( m_\times)^\natural \ar[r ] \ar[d]^{v_m^\natural } & m_\times \ar[r ] \ar[d]^{= } & 0 \\ 0 \ar[r ] & g_{\mathrm{uni}}\ar[r ] & m \ar[r ] & m_\times \ar[r ] & 0 } \ ] ] [ [ section-15 ] ] the _ sharp extension _ @xmath443
$ ] of @xmath411 \in { \mathscr{m}}_1^a$ ] is defined to be the pull - back of @xmath439 by the canonical surjection @xmath444 .
( if @xmath412 is unipotent free , then @xmath445 . )
there is a commutative diagram with exact rows and coloums @xmath446 & 0 \ar[d ] & \\ & & g_{\mathrm{uni}}\ar[r]^{= } \ar[d ] & g_{\mathrm{uni}}\ar[d]_{i } & \\ 0 \ar[r ] & { \mathrm{ext}}(m_\times , { \mathbf{g}}_a)^ * \ar[r ] \ar[d]_{= } & m^\sharp \ar[r]_{p } \ar[d]_q & m \ar[r ] \ar[d ] & 0 \\ 0 \ar[r ] & { \mathrm{ext}}(m_\times , { \mathbf{g}}_a)^ * \ar[r ] & ( m_\times)^\natural \ar[r ] \ar@{-->}[ur]_{v_m^\natural } \ar[d ] & m_\times \ar[r ] \ar[d ] & 0 \\ & & 0 & 0 . & } \ ] ] note that the dotted arrow @xmath441 makes the lower right triangle commutative by , but it is _ not _ necessarily the case for the upper left triangle .
the middle vertical exact sequence in admits a canonical splitting @xmath447 characterized by @xmath448 .
hence there also is an exact sequence @xmath449 equipped with a canonical splitting . combined with
, we obtain a canonical decomposition @xmath450 [ [ section-16 ] ] following ( * ? ? ?
* ( 3.2.1 ) ) , we call an exact functor @xmath451 ) : = { \mathop{\mathrm{lie}}\nolimits}(g^\sharp).\ ] ] the _ sharp de rham realization_. by , we have a canonical decomposition @xmath452 for any @xmath411 \in { \mathscr{m}}^a_1 $ ] .
[ [ section-17 ] ] let @xmath453 be the @xmath37-linear abelian category of deligne @xmath36-isomotives ( see )
. recall from
[ sect : ehm - ecm ] that @xmath454 is the universal @xmath37-linear category associated with the betti homology functor ( with @xmath455 ) . in @xcite , l. barbieri - viale and j. ayoub
show the following important result which will be a key ingredient in the proof of our main result .
[ equivdel ] we have an equivalence of @xmath37-linear abelian categories @xmath456 this functor is induced by a functor @xmath457 via universality ( see remark [ rem : a - bv - functor ] ) .
we will construct its modulus version in the next section .
in this section , to a smooth proper @xmath1-curve @xmath15 and two effective divisors @xmath458 on @xmath15 with disjoint support , we associate a laumon @xmath36-motive @xmath459 .
we shall see functorial properties that yield two functors @xmath460 and @xmath461 .
[ [ sect : gen - jac ] ] let @xmath15 be a smooth proper @xmath1-curve and @xmath45 an effective divisors on @xmath15 .
we denote by @xmath462 the _ generalized jacobian _ of @xmath15 with modulus @xmath45 in the sense of rosenlicht - serre @xcite .
recall that @xmath463 is the connected component of the picard variety @xmath464 of a proper @xmath1-curve @xmath465 that is obtained by collapsing @xmath45 into a single ( usually singular ) point ( see ( * ? ? ?
* chapter iv ,
it can also be defined as the albanese variety attached to a pair @xmath466 @xcite .
let @xmath467 be another smooth proper @xmath1-curve and @xmath468 an effective divisor on it .
let @xmath469 be a @xmath1-morphism .
when @xmath470 , we have a pull - back @xmath471 deduced by the functoriality of the picard variety .
when @xmath472 , we have a push - forward @xmath473 deduced by the functoriality of the albanese variety .
there exists a canonical isomorphism ( cf .
proposition [ prop : uv ] ) @xmath474 if @xmath475 , then @xmath463 is an abelian variety so that @xmath476 , and hence the lemma holds .
we suppose @xmath477 in what follows .
consider an exact sequence of sheaves on @xmath15 : @xmath478 we have @xmath479 since @xmath45 is a non - empty effective divisor .
it follows that @xmath480 by ( * ? ? ?
* chapter v , 10 , proposition 5 ) , there are canonical isomorphisms @xmath481 now the lemma follows from an exact sequence @xmath482 and a canonical isomorphism @xmath483 .
[ [ section-18 ] ] let @xmath15 be a smooth proper @xmath1-curve and @xmath46 an effective divisors on @xmath15 .
we construct an object @xmath484 as follows .
first , we define @xmath485,\ ] ] where the map is the one induced by the closed immersion @xmath486 . here for any @xmath1-variety @xmath58 , we define @xmath487 by declaring @xmath488 is the free abelian group on the set of connected components of @xmath489 for @xmath490 .
this depends only on the reduced part of @xmath58 .
next , we define ( cf . proposition [ prop : uv ] , see also @xcite ) @xmath491 let @xmath467 be another smooth proper @xmath1-curve and @xmath468 an effective divisor on it .
let @xmath469 be a @xmath1-morphism .
there is a pull - back @xmath492 ( resp .
a push - forward @xmath493 ) when @xmath472 ( resp .
@xmath470 ) . on the infinitesimal ( resp .
tale ) part , they are defined by proposition [ prop : pull - push - uv ] ( resp .
pull - back and push - forward of cycles ) .
[ [ section-19 ] ] we recall from @xcite russell s results that we will use .
let @xmath58 be a noetherian reduced scheme .
define @xmath494 to be the sheaf that associates to @xmath495 the group of all cartier divisors on @xmath496 generated locally on @xmath497 by effective cartier divisors which are flat over @xmath4 .
there is a canonical `` class '' map @xmath498 to the picard variety @xmath499 of @xmath58 .
denote by @xmath500 the inverse image of the connected component @xmath501 of @xmath502 by @xmath503 .
we have @xmath504 ( the group of cartier divisors on @xmath58 ) and @xmath505 , where @xmath506 is the sheaf of total ring of fractions of @xmath507 . in (
* proposition 2.13 ) it is shown that for any @xmath391 and a pair of maps @xmath508 there exists a unique map @xmath509 that induces a map @xmath510 ( resp .
@xmath511 ) via @xmath512 ( resp . by taking sections over @xmath513 ) .
let @xmath15 be a smooth proper @xmath1-curve and let @xmath458 be two effective divisors on @xmath15 with disjoint support .
we apply the above argument to @xmath514 , where @xmath465 is the curve we discussed in
[ sect : gen - jac ] .
since @xmath45 and @xmath46 are disjoint , we may identify @xmath46 as a closed subscheme of @xmath465 .
we define @xmath515 to be the map induced by the inclusion @xmath516 . also , we define @xmath517 by sending @xmath518 to @xmath519 .
it restricts to @xmath520 \to \underline{{\mathrm{div}}}_{x_y}^0(k).\ ] ] using them , we define @xmath521 where we used the notations from and .
we then define a laumon @xmath36-motive attached to @xmath522 by @xmath523 \in { \mathscr{m}}^a_1.\ ] ] from this definition it is evident that @xmath524 [ [ fonclm ] ] let @xmath467 be another smooth proper @xmath1-curve and let @xmath525 be two effective divisors on @xmath467 with disjoint support .
let @xmath526 be a @xmath1-morphism .
if @xmath470 and @xmath527 , then the square @xmath528 ^ -{\tau(x',y',z')}\ar[d]^-{f^ * } & { j(x',y')}\ar[d]^-{f^*}\\ { f(x , z)}\ar[r]^-{\tau(x , y , z ) } & { j(x , y)}}\ ] ] commutes . similarly if @xmath470 and @xmath527 then the square @xmath529 ^ -{\tau(x , y , z)}\ar[d]^-{f _ * } & { j(x , y)}\ar[d]^-{f_*}\\ { f(x',z')}\ar[r]^-{\tau(x',y',z ' ) } & { j(x',y')}}\ ] ] commutes
this enables us to make the following definition .
we define a functor @xmath530 by setting @xmath531 and @xmath532 ( resp .
@xmath533 ) for a morphism @xmath534 in @xmath183 ( resp . in @xmath188 ) .
[ rem : a - bv - functor ] the composition of @xmath535 with @xmath536 from factors through @xmath537 ( see [ sect : deligne-1-motives ] ) .
this induces the functor in theorem [ equivdel ] via universality .
[ prop : compati ] there is an isomorphism of functors @xmath538 .
let @xmath224 . by , , and , we have @xmath539 moreover , by ( * ? ? ?
* corollary 2.6.4 ) there is a canonical isomorphism @xmath540 .
now the proposition follows from .
there is also an isomorphism of functors @xmath541 , considered as functors @xmath542 , see remark [ rem : cov - hdr ] .
( this remark will not be used in the sequel . ) for any @xmath224 , we find that @xmath543 and @xmath544 are cartier dual to each other .
in other words , using a functor @xmath545 defined by @xmath546 , we get a commutative diagram @xmath547_{{\mathrm{sw } } } \ar[r]^{{\overline{\mathsf{l}}\mathsf{m}}^{\mathrm{op } } } & ( { \mathscr{m}}_{1}^a)^{{\mathrm{op } } } \ar[d]^{\text{cartier dual } } \\
{ \underline{\mathrm{m}}{\mathrm{crv}}}\ar[r]_{{\underline{\mathsf{l}}\mathsf{m } } } & { \mathscr{m}}_{1}^a . } \ ] ] [ [ section-20 ] ] let @xmath548 be the @xmath37-linear abelian category of laumon @xmath36-isomotives ( see ) .
[ quotprop ] any laumon @xmath36-motive @xmath549 $ ] is a quotient in @xmath550 of @xmath551 for some object @xmath522 of @xmath183 . if @xmath412 is such that @xmath552 , then @xmath522 can be choosen as @xmath553 similarly , if @xmath412 is such that @xmath554 , then @xmath522 can be choosen as @xmath475
this will be apparent from the proof given below .
we divide the proof into three steps .
_ step 1 . _
( compare ( * ? ? ? * chap .
vii , 2 , no .
we first prove the proposition assuming that @xmath1 is algebraically closed , and that both @xmath555 and @xmath556 are injective .
choose a @xmath557-basis @xmath558 of @xmath559 , and put @xmath560 .
let @xmath561 be the identity element .
we take a one - dimensional closed integral subscheme @xmath562 on @xmath371 that contains @xmath563 as regular points .
also , choose a @xmath1-basis @xmath564 of @xmath565 , and put @xmath566 .
we extend @xmath567 to a @xmath1-basis @xmath568 of @xmath569 . for each @xmath570 , we take a one - dimensional closed integral subscheme @xmath571 on @xmath371 that passes @xmath572 regularly and that has tangent @xmath573 at @xmath572 . for @xmath574 , we let @xmath575 be the normalization . we denote the preimage of @xmath576 in @xmath577 by the same letter @xmath576 .
( here @xmath578 for @xmath579 , and @xmath580 for @xmath570 . )
let @xmath581 be the smooth completion of @xmath577 .
let @xmath582 be a modulus for the morphism @xmath583 .
this means that @xmath582 is an effective divisor supported on @xmath584 and that @xmath585 factors as @xmath586 .
we also define effective divisors @xmath587 , @xmath588 , and @xmath589 .
let @xmath15 be the disjoint union of @xmath590 , and let @xmath591 . by definition , we have @xmath592
, hence we can define an isomorphism @xmath593 by @xmath594 . also , by definition
, we have @xmath595 , hence we can define an isomorphism @xmath596 by @xmath597 .
we have defined an isomorphism @xmath598 .
finally , we define @xmath599 as the sum of @xmath600 over @xmath601 .
since the image of @xmath602 contains @xmath573 , we find @xmath603 is surjective , hence @xmath604 itself is also surjective .
it is straightforward to see that @xmath534 and @xmath605 define an epimorphism @xmath606 in @xmath402 .
( here we do not need to tensor with @xmath37 . )
_ we drop the assumption that @xmath1 is algebraically closed , but keep the assumption that both @xmath607 and @xmath608 are injective . by step 1
, we can find a finite extension @xmath609 such that the base change of @xmath412 to @xmath610 satisfies the conclusion of the proposition .
the weil restriction functor @xmath611 ) = [ r_{k'/k}(f ) \to r_{k'/k}(g)]\ ] ] is exact .
( here we denote by @xmath612 and @xmath613 for the category of laumon @xmath36-isomotives over @xmath1 and over @xmath610 . )
moreover , for any @xmath614 we have @xmath615 , where for an @xmath610-scheme @xmath616 we write @xmath617 for the @xmath1-scheme @xmath616 with structure morphism @xmath618 .
( this follows from a general fact that the picard functor commutes with base change . )
this proves the proposition in this case .
_ we prove the proposition in general case .
let @xmath619 , ~m_2:=[f_2 \to 0]$ ] .
then there is a non - canonical isomorphism @xmath620 in @xmath550 .
now we apply the result from step 2 , and we are done .
[ [ sect : start - assuming - k - is - q ] ] from now on until the end of the paper , we suppose @xmath0 .
note that @xmath35 is a @xmath37-linear abelian category . by and , we obtain a @xmath37-linear exact faithful functor @xmath621 and two invertible natural transformations @xmath622 , @xmath623 .
the main result of this article is the following : [ maintheo2 ] suppose @xmath0 .
the functor @xmath624 in is an equivalence .
we keep assuming @xmath0 . in this section , we construct on every object of @xmath261 a two steps filtration that mirrors the one on laumon @xmath36-motives defined in .
[ [ fil1 ] ] consider the morphism of quivers @xmath625 if @xmath39 is a @xmath37-curve with modulus , let us observe that by construction @xmath626 .
hence the square @xmath627 ^ -{{\mathsf{lm}}}\ar[d]_-{(-,-,-_{\mathrm{red } } ) } & { { \mathscr{m}}^a_{1,{\mathbb{q}}}}\ar[d]^{{\mathrm{fil}}_{\mathscr{m}}^1}\\ { { \overline{\mathrm{m}}{\mathrm{crv}}}^{\mathrm{op}}}\ar[r]^-{{\mathsf{lm } } } & { { \mathscr{m}}^a_{1,{\mathbb{q}}}}}\ ] ] commutes and shows the existence of a @xmath37-linear exact functor @xmath628 and two invertible natural transformations @xmath629 such that the corresponding diagram as in is commutative .
let us now show that there exists a natural transformation @xmath630 which is a monomorphism for every object in @xmath261 .
let @xmath39 be a @xmath37-curve with modulus .
since @xmath631 , the identity of @xmath15 defines an edge @xmath632 that provides a natural transformation @xmath633 of functors from @xmath634 with values in @xmath634 . note that this transformation induces the monomorphism @xmath635 in @xmath54 and that the square @xmath636\ar[d]_-{\iota_{\mathscr{m}}{\star}{\mathsf{lm } } } & { { \mathsf{lm}}\circ ( -,-,-_{\mathrm{red}})}\ar[d]^-{{\mathsf{lm}}{\star}\iota}\\ { { \mathsf{lm}}}\ar@{=}[r ] & { { \mathsf{lm}}}}\ ] ] is commutative . we may therefore apply to obtain a natural tranformation @xmath637 that makes the squares @xmath638 ^ -{\varrho}\ar[d]^-{\overline{\iota}{\star}\overline{{\mathbf{h}}}^1_{\mathrm{dr } } } & { \overline{{\mathbf{h}}}^1_{\mathrm{dr}}\circ ( -,-,-_{\mathrm{red}})}\ar[d]^-{\overline{{\mathbf{h}}}^1_{\mathrm{dr}}{\star}\iota}\\ { \overline{{\mathbf{h}}}^1_{\mathrm{dr}}}\ar@{=}[r ] & { \overline{{\mathbf{h}}}^1_{\mathrm{dr } } } } \qquad \xymatrix{{{\mathrm{fil}}^1_{\mathscr{m}}\circ{\mathbf{lm}}}\ar[r]^-{\rho}\ar[d]^-{\iota{\star}{\mathbf{lm } } } & { { \mathbf{lm}}\circ{\mathrm{fil}}^1}\ar[d]^-{{\mathbf{lm}}{\star}\overline{\iota}}\\ { { \mathbf{lm}}}\ar@{=}[r ] & { { \mathbf{lm}}}}\ ] ] commutative .
note that by , for every object @xmath639 in @xmath261 the morphism @xmath640 is a monomorphism .
[ [ fil2 ] ] so far we have constructed the first step of the filtration .
let us now construct the second one . let @xmath6 be the full subquiver of @xmath183 with vertices the @xmath37-curves with modulus @xmath39 such that @xmath46 is _
reduced_. we denote by @xmath641 the kernel of the exact functor @xmath642 .
this is the category of laumon 1-isomotives without infinitesimal part and by definition it is the full subcategory of @xmath54 of objects @xmath412 such that @xmath643 that is such that @xmath644 is an isomorphism .
similarly we denote by @xmath645 the kernel of the exact functor @xmath646 constructed in . the compatibility given in ensures that the functor induces an exact functor @xmath647 [ univinf=0 ] the universal @xmath37-linear abelian category associated with the representation
@xmath648 is equivalent to @xmath645 .
let us denote by @xmath649 the associated category and by @xmath650 the canonical factorization of the restriction of @xmath651 to @xmath652 . since the restriction of @xmath264 to @xmath652 takes its values in the abelian subcategory @xmath645 , the universal property of nori s category ensures the existence of a @xmath37-linear exact faithful functor @xmath653 and two invertible natural transformations @xmath654 and @xmath655 such that the square @xmath656 ^ -{f^a_{\mathrm{dr}}{\star}\gamma}\ar[d]^-{\delta{\star}\overline{{\mathbf{h}}}^1_{\mathscr}c } & { f^a_{\mathrm{dr}}\circ \overline{{\mathbf{h}}}^1_{\mathrm{dr}}}\ar@{=}[d]\\ { f_{{\mathscr}c}\circ\overline{{\mathbf{h}}}^1_{\mathscr}c}\ar@{=}[r ] & { { \mathbf{h}}^1_{\mathrm{dr}}}}\ ] ] is commutative . to construct a quasi - inverse to the functor @xmath657
let us go back to the construction of @xmath658 in .
observe that takes its values in @xmath6 and that the square can be refined in a square @xmath659 ^ -{{\mathsf{lm}}}\ar[d]_-{(-,-,-_{\mathrm{red } } ) } & { { \mathscr{m}}^a_{1,{\mathbb{q}}}}\ar[d]^{{\mathrm{fil}}_{\mathscr{m}}^1}\\ { { \mathscr}d^{\mathrm{op}}}\ar[r]^-{{\mathsf{lm}}|_{\mathscr}d } & { { \mathscr{m}}^{\inf=0}_{1,{\mathbb{q}}}}}\ ] ] by and , this shows the existence of a @xmath37-linear exact functor @xmath660 and an invertible natural tranformation @xmath661 .
let us denote by @xmath662 the inclusion functor of @xmath663 into @xmath261 .
since @xmath664 is isomorphic to the identity , the composition @xmath665 is isomorphic to the identity .
this shows that the faithful functor @xmath657 is an equivalence and that @xmath665 is a quasi - inverse .
now consider the morphism of quivers @xmath666 since the square @xmath667 ^ -{{\mathsf{lm}}}\ar[d]_-{(-,-_{\mathrm{red}},- ) } & { { \mathscr{m}}^{\inf=0}_{1,{\mathbb{q}}}}\ar[d]^-{{\mathrm{gr}}^1_{\mathscr{m}}}\\ { { \mathscr}d^{\mathrm{op}}}\ar[r]^-{{\mathsf{lm } } } & { { \mathscr{m}}^{\inf=0}_{1,{\mathbb{q}}}}}\ ] ] is commutative , and show the existence of a @xmath37-linear exact functor is not yet the graded pieces associated to a filtration . ] @xmath668 and two invertible natural transformations @xmath669 such that the corresponding diagram as in is commutative .
note that , for every laumon 1-isomotives @xmath412 , there is a canonical epimorphism @xmath670 .
in particular , if @xmath412 is without infinitesimal part , there is a canonical epimorphism @xmath671 since @xmath672 , the identity of @xmath15 induces an edge from @xmath673 to @xmath39 in @xmath6 .
note that if @xmath45 is not reduced , then the identity of @xmath15 does not define an edge from @xmath39 to @xmath674 in @xmath183 .
this is the main reason for introducing the subquiver @xmath6 .
this provides a natural transformation @xmath675 of functors from @xmath652 with values in @xmath652 .
note that the square @xmath676\ar[d]_-{\pi_{\mathscr{m}}{\star}{\mathsf{lm}}|_{\mathscr}d } & { { \mathsf{lm}}|_{\mathscr}d}\ar[d]^-{{\mathsf{lm}}|_{\mathscr}d{\star}\pi_{{\mathscr}d}}\\ { { \mathrm{gr}}^1_{\mathscr{m}}\circ{\mathsf{lm}}|_{\mathscr}d}\ar@{=}[r ] & { { \mathsf{lm}}|_{\mathscr}d\circ ( -,-_{\mathrm{red}},-)}}\ ] ] commutes .
we may therefore apply to obtain a natural tranformation @xmath677 that makes the squares @xmath678\ar[d]^-{\overline{\pi}{\star}\overline{{\mathbf{h}}}^1_{\mathrm{dr } } } & { \overline{{\mathbf{h}}}^1_{\mathrm{dr}}}\ar[d]^-{\overline{{\mathbf{h}}}^1_{\mathrm{dr}}{\star}\pi_{\mathscr}d}\\ { { \mathrm{gr}}^1\circ\overline{{\mathbf{h}}}^1_{\mathrm{dr}}}\ar[r]^-{\varrho } & { \overline{{\mathbf{h}}}^1_{\mathrm{dr}}\circ ( -,-_{\mathrm{red}},- ) } } \qquad \xymatrix{{{\mathbf{lm}}}\ar@{=}[r]\ar[d]^-{\pi_{\mathscr{m}}{\star}{\mathbf{lm } } } & { { \mathbf{lm}}}\ar[d]^-{{\mathbf{lm}}{\star}\overline{\pi}}\\ { { \mathrm{gr}}^1_{\mathscr{m}}\circ{\mathbf{lm}}}\ar[r]^-{\rho } & { { \mathbf{lm}}\circ { \mathrm{gr}}^1}}\ ] ] commutative . note that in the above squares , all natural transformations are between functors on @xmath652 or @xmath663 . by , for every object @xmath639 in @xmath645 the morphism @xmath679 is an epimorphism .
let @xmath639 be an object in @xmath261 .
then @xmath680 belongs to @xmath663 and we set @xmath681.\ ] ] note that by definition @xmath682 .
in this section , we take @xmath0 .
we complete the proof of theorem [ maintheo2 ] .
recall from proposition [ embeddingmotives ] that we have a fully faithful functor @xmath683 .
the composition of @xmath355 with @xmath684 factors through the category @xmath30 of deligne @xmath36-isomotives .
this induces a functor @xmath685 by universality .
let @xmath686 be the intersection of the kernel of the exact functors @xmath687 and @xmath688 constructed in and .
an object @xmath639 in @xmath689 belongs to the full subcategory @xmath690 if and only if the canonical monomorphism @xmath691 is an isomorphism .
since the functor @xmath692 is compatible with the filtration , it induces a @xmath37-linear exact faithful functor ( see [ sect : deligne-1-motives ] ) @xmath693 note that @xmath694 is simply the category of unipotent commutative algebraic groups over @xmath37 and that the restriction of the de rham realization @xmath695 to @xmath694 is nothing but the functor that associates with a unipotent commutative algebraic @xmath37-group its lie algebra and is therefore an equivalence .
we define a subquiver @xmath697 of @xmath183 as follows .
the vertices are given by @xmath698 , \emptyset ) \in { \mathrm{mcrv}}$ ] .
for any integer @xmath699 . the edges from @xmath700 to @xmath701
consists of two types : @xmath702 consider the representation @xmath703 and its canonical factorization @xmath704 where @xmath705 is nori s universal category ( see ) .
note that the restriction of the representation @xmath264 to the subquiver @xmath697 takes its values in @xmath706 .
hence , by the universal property of nori s construction ( see ) , there exist a @xmath37-linear exact faithful functor @xmath707 , two invertible natural transformations @xmath708 and @xmath709 such that the diagram @xmath710_-{\overline{t}}\ar[r]^-{\overline{{\mathbf{h}}}^1_{\mathrm{dr } } } & { { \mathrm{ecmm}}_{1}^{\mathrm{uni}}}\ar[r]^-{{\mathbf{lm } } } & { { \mathscr{m}}_{1,{\mathbb{q}}}^{{\mathrm{uni}}}}\ar[r]^-{r_{\mathrm{dr } } } & { { \mathop{\mathsf{mod}}\nolimits}({\mathbb{q}})}\\ { } & { { \mathscr}u}\ar@/_2em/[rru]_-{f_t}\ar[u]_-{u } & { } & { } } \ ] ] is commutative .
since the functor @xmath711 is faithful , to show the proposition it is enough to show that @xmath13 is an equivalence of categories ( note that the functor @xmath712 will then also be an equivalence ) .
it suffices to see that @xmath8 is the @xmath37-linear dual of the algebra @xmath37 . and
this amounts to check that for every full subquiver @xmath88 of @xmath697 with finitely many objects @xmath713 we may assume @xmath88 of the form @xmath714 for some integer @xmath715 . write @xmath716)$ ] and put @xmath717 , @xmath718 so that @xmath719 is defined by @xmath720 . by and ,
the representation @xmath9 maps @xmath721 to the @xmath37-vector space @xmath722/(s^n)$ ] .
we compute the action of morphisms on this space in three instances : 1 .
let @xmath723 and consider the edge @xmath724 of type given by @xmath725 where @xmath234 is a fixed element in @xmath726 .
then @xmath727 is the linear map represented by a diagonal matrix @xmath728 with respect to the basis @xmath729 , 2 .
let @xmath723 and consider the edge @xmath724 of type given by @xmath730 .
then @xmath727 maps @xmath731 to @xmath732 .
3 . let @xmath733 and consider the edge of type .
then @xmath727 is the canonical surjection @xmath734 ( the one induced by the identity on @xmath722 $ ] ) .
let @xmath360 be an element in @xmath735 .
then @xmath360 is a family @xmath736 such that for every edge @xmath737 in @xmath697 @xmath738 the condition for all edges of the form ( a ) implies that all @xmath739 are represented by a diagonal matrix in the canonical basis .
then , the condition , for all edges of the form ( b ) implies that all @xmath739 are given by multiplication by some scalar .
using now of all edges of type ( c ) we find that all these scalars are the equal .
this completes the proof . to prove it is enough to show that we are in a situation where the criterion of applies .
the first condition is obviously satisfied and the second one follows from .
it remains to prove that the third condition is also satisfied .
let @xmath639 be an object in @xmath261 , @xmath412 be an object in @xmath54 and @xmath744 be a morphism in @xmath54 . by applying the functor @xmath695
we get a morphism @xmath745 of @xmath37-vector spaces .
note that @xmath746 induces a commutative diagram in @xmath54 @xmath747 & { { \mathbf{lm}}({\mathrm{fil}}^1(a))}\ar[r]\ar[d ] & { { \mathbf{lm}}(a)}\ar[d]\\ & { { \mathbf{lm}}({\mathrm{gr}}^1(a ) ) } & { { \mathbf{lm}}({\mathrm{gr}}^0(a ) ) } } \pos(25,-25 ) \xymatrix@c=1.5cm{{{\mathrm{fil}}^2_{\mathscr{m}}(m)}\ar[r]\ar@{<- } [ " * " ] & { { \mathrm{fil}}^1_{\mathscr{m}}(m))}\ar[r]\ar[d]\ar@{<- } [ " * " ] & { m}\ar[d]\ar@{<- } [ " * " ] \\ & { { \mathrm{gr}}^1_{\mathscr{m}}(m)}\ar@{<-}["*"]|(.58)\hole & { { \mathrm{gr}}^0_{\mathscr{m}}(m)}\ar@{<-}["*"]|(.58)\hole } \endxy\ ] ] applying the functor @xmath695 yields a commutative diagram @xmath748 & { f^a_{\mathrm{dr}}({\mathrm{fil}}^1(a))}\ar[r]\ar[d ] & { f^a_{\mathrm{dr}}(a)}\ar[d]\\ & { f^a_{\mathrm{dr}}({\mathrm{gr}}^1(a ) ) } & { f^a_{\mathrm{dr}}({\mathrm{gr}}^0(a ) ) } } \pos(25,-25 ) \xymatrix{{r_{\mathrm{dr}}({\mathrm{fil}}^2_{\mathscr{m}}(m))}\ar[r]\ar@{<-}["*"]^-{v_2 } & { r_{\mathrm{dr}}({\mathrm{fil}}^1_{\mathscr{m}}(m)))}\ar[r]\ar[d]\ar@{<- } [ " * " ] & { r_{\mathrm{dr}}(m)}\ar[d]\ar@{<-}["*"]_-{v } \\ & { r_{\mathrm{dr}}({\mathrm{gr}}^1_{\mathscr{m}}(m))}\ar@{<-}["*"]|(.58)\hole^(.4){v_1 } & { r_{\mathrm{dr}}({\mathrm{gr}}^0_{\mathscr{m}}(m))}\ar@{<-}["*"]|(.58)\hole_(.7){v_0 } } \endxy\ ] ] where we set @xmath749 , @xmath750 , @xmath751 and @xmath752 to simplify notations . by construction of the category @xmath261
( see ) , there exists a finite subquiver @xmath88 of @xmath183 such that in the diagram @xmath753 & { f^a_{\mathrm{dr}}({\mathrm{fil}}^1(a))}\ar[r]\ar[d ] & { f^a_{\mathrm{dr}}(a)}\ar[d]\\ & { f^a_{\mathrm{dr}}({\mathrm{gr}}^1(a ) ) } & { f^a_{\mathrm{dr}}({\mathrm{gr}}^0(a))}}\ ] ] all objects are canonically endowed with a @xmath754-module structure and all morphisms are @xmath754-linear .
using , and , by allowing @xmath88 to be bigger , we may assume that the kernels of the maps @xmath755 are sub-@xmath131-modules .
an easy diagram chase in shows that the kernel of @xmath756 is a sub-@xmath131-module of @xmath757 as well .
this concludes the proof .
serre , _ groupes algbriques et corps de classes _ , second ed . ,
publications de linstitut mathmatique de luniversit de nancago , 7 , hermann , paris , 1984 , actualits scientifiques et industrielles , 1264 . | arxiv |
Why does the focus point of the eye does not burn the retina?
To see an object, its light rays have to meet on the retina in the focal point. But the focal point is a small white dot. Basically nothing would be distinguishable and the retina would burn because all energy is concentrated at a single point? Obviously, this is not happening. But why?
The following diagrams show how the eye focuses:
There may be people with vision problems such that the focal point is a single point on the retina, but this can be corrected with glasses.
In ordinary life, only a point object will focus to a point image. Otherwise the light is spread out, just as the object is spread out. But a very intense object *can* injure your retina: don't stare at the sun!
With lasers, collimated light simulates a point object at large distance. Lasers can be seriously hazardous to your vision.
Even with ideal vision, all the light from an extended object is not focused onto a single point in the retina. Instead each *point* on the object is brought to a focus at a different point on the retina - the image of the whole object is spread out. So only very bright objects (such as the sun) can cause damage to the retina.
Part direct answer, part reply to your follow-up question on Gandalf's answer, "Doesn't [light from an extended object not focusing on a single point] imply that the focal point must be slightly in front of the retina and not directly on it?"
Concentration of rays on a single point in geometric optics is an approximation. A target and a light source are in thermal contact. If we could make energy go from the source to the target such that the target was hotter than the radiation temperature of the place where the light was originally emitted, we would be transporting heat from a cold region to a hot region without doing extra Work, which violates the 2nd Law. In optics this limitation is expressed as the conservation of optical [etendue](https://en.wikipedia.org/wiki/Etendue). The light from a given source can't be more squished together than the the light emanating from the surface of that source. This is why very bright (the sun) and very squished (a laser) light sources are both hazardous.
(Note as regards the temperature of sources and targets that the light from a laser is emitted from deep inside the tube where the extremely hot lasing medium is, not the comparatively cool tip where the light comes out of the tube.)
>
> To see an object, its light rays have to meet on the retina in the focal point.
>
>
>
That's not what focus is. Not that the light rays from A and B don't meet up at the same point on the retina.
[](https://i.stack.imgur.com/Hnp2m.png)
If all the light from an object was brought together at a single point, there would be no image formed. Lenses don't do that. Instead they bring light from different points on the object together at different points on the retina.
It is impossible for any lens to bring the light from different points together at single point. To see this just imagine the lens in reverse.
This is true of any lens. Even if you have used a "burning glass" to focus the sun, you don't bring the sun's rays to a single point; you create a small image of the sun, small enough to be very hot.
There might be a confusion about what you call focal point.
The focal point of an ideal lens is a single given point. Only the light rays **parallel to the optical axis** will pass through the focal point. Parallel rays at an another angle will be collected at different points in the so-called *focal plane*.
Light rays coming from (not too distant) point sources will be collected at other points again, behind the focal plane. (However the lens in our eyes can adapt and reduce its focal distance, so that the image formed *behind the focal plane* falls on the retina.)
| stackexchange/physics |
the use of biomass as a source of energy used in heating systems , power and cogeneration plants or vehicle motors is forecast to grow considerably in the next decades ( nakicenovic and swart , 2000 ) .
bioenergy is promoted for several reasons , e.g. reducing the dependency on exhaustible fossil energy , greenhouse gas ( ghg ) emissions and import dependency as well as creation of jobs and income in rural areas .
however , in recent years the awareness has been growing that energy crop production could have far - reaching adverse consequences if natural and socioeconomic constraints are not respected .
examples include the discussion on possible impacts of bioenergy on food prices ( world bank , 2008 ) , ecological consequences of agricultural intensification ( tilman , 1999 ; tilman et al . , 2002 ) , deforestation and high ghg emissions from land - use change ( fargione et al
. , 2008 ; searchinger et al . , 2008 ) , soil degradation ( lal , 2006 ; van vuuren et al . , 2009 ) , water demand of energy crops ( gerbens - leenes et al . , 2009a ) and pressures on biodiversity ( gibbs et al . , 2008 ) .
some of these potential adverse impacts might even annihilate the environmental benefits of bioenergy ( tilman et al .
forging bioenergy strategies that maximize benefits and minimize adverse effects is a formidable challenge , aggravated by a limited understanding of the magnitude and geographic distribution of future potentials , and their large uncertainties ( haberl et al . , 2010 ) .
biomass currently contributes approximately 46 ej / yr of technical energy in the form of solid , liquid and gaseous fuels from primary ( harvest ) as well as secondary and tertiary ( waste and residue utilization ) sources ( iea , 2006 ) .
recent estimates of additional future bioenergy potentials range from approximately 30 to over 1000 ej / yr for 2050 ( beringer et al . , 2011 ; berndes et al . , 2003 ; campbell et al .
, 2008 ; field et al . , 2008 ; haberl et al . , 2010c ; haberl et al . ,
, 2003 ; hoogwijk , 2004 ; smeets et al . , 2007 ; van vuuren et al . , 2009 )
. the enormous differences between these studies largely result from differing assumptions regarding the large number of factors that influence the availability of biomass for energy and material use , such as the availability and suitability of land , achievable yield levels of energy crops , technological progress in agriculture and livestock breeding , and on the impact of competing land uses such as the demand for food and feed , biodiversity and forest conservation and soil protection . in this context , we here study the following factors that influence global primary energy crop potentials in 2050 .
first , we analyze possible constraints on the area available to grow energy crops resulting from ( 1 ) future changes in food systems , i.e. food demand ( diets ) , food and feed crop yields , feed demand of livestock ( fodder crops and roughage ) depending on livestock feeding efficiency , ( 2 ) political factors , i.e. sufficient stability of nations to allow investments required for establishing bioenergy plantations ( exclusion of failed states ) and ( 3 ) competing area demands for biodiversity conservation ( e.g. nature reserves ) .
our study is based on the conservative assumption that additional deforestation is excluded for both food and energy crop production in order to avoid long carbon payback times from direct and indirect land - use change ( fargione et al . , 2008 ; searchinger et al . , 2008 ;
second , we evaluate the influence of energy crop yields on future bioenergy potentials by assuming different plausible levels of energy crop yields .
bioenergy potentials from forestry as well as from agricultural residues , manures and other wastes , which are substantial ( haberl et al . ,
food first approach , i.e. only areas not required to feed the world population forecast to exist in 2050 according to the specified diet are assumed to be available for bioenergy .
we use a simple and transparent biophysical biomass - balance model ( erb et al . , 2009a ; haberl et al . , 2010
; haberl et al . , 2012a ) that is based on material flow accounting ( mfa ) principles and large , consistent land - use socioeconomic and ecological biomass - flow databases ( including net primary production ; erb et al .
we aim at analyzing the effect of various constraints on future primary bioenergy potentials , but it is neither our objective to forecast bioenergy supply in 2050 , nor to assess its social implications , e.g. economic and social effects of land competition ( e.g. land rents , food and bioenergy prices or expulsion of peasants ) .
thus , we here aim at exploring the biophysical option space for primary bioenergy production in 2050 , using food - first and zero - deforestation assumptions as framework condition of our analysis .
we do not aim at assessing economic bioenergy potentials , e.g. modeling energy demand and supply in dependency of price developments , nor technical bioenergy potentials , i.e. maximum potentials related to technological capabilities .
the biomass - balance model is based on the thermodynamic principles underlying material and energy flow accounting ( mefa ) methods , basically the conservation of mass and energy and the entropy law ( ayres and simonis , 1994 ; fischer - kowalski , 1998 ; fischer - kowalski and httler , 1998 ; haberl , 2001 ; haberl et al . ,
the model calculates the global primary energy crop potential based on assumptions on diets , agricultural technology and cropland area assumed for the year 2050 ( fig .
the model was constructed using a comprehensive land use , npp and biomass - flow database for the year 2000 ( erb et al .
the database integrates global land use and socioeconomic data with npp data across a range of spatial scales , from the grid level ( 5 min resolution , 1010 km at the equator ) to the country level ( 160 countries ) .
it fulfills multiple consistency criteria across scales and domains : biomass flows are traced from the net primary production ( npp ) of each of the five land - use classes ( built - up and infrastructure , cropland , forestry , unused and unproductive , all other land ) to national - level data on primary and final biomass consumption .
the database was used to derive factors and multipliers to match the demand for final products of biomass ( food , fibers ) with gross agricultural production and land use for eleven world regions ( for reference see haberl et al . , 2012a and http://www.uni-klu.ac.at/socec/downloads/wp116_web.pdf ) .
that is , in a first step , the model was calibrated for the year 2000 using the above - described databases . in a second step ,
several critical factors and input parameters were modified in order to reflect assumed changes from 2000 to 2050 ( see below ) .
the biomass - balance model uses a spatially explicit land - use dataset ( erb et al .
, 2007 ; see table 1 ) that distinguishes five land - use classes ( 1 ) infrastructure and urban areas , ( 2 ) cropland , ( 3 ) forestry , ( 4 ) unused areas ( wilderness , including unproductive areas ) , and ( 5 ) all other land ( denoted as grazing land in the original paper ) at a resolution of 5 arc minutes ( approximately 10 per 10 km at the equator ) . the area of class 5 all other land was calculated by subtracting from each gridcell 's total area the area covered by all other four land - use classes .
forests were either subsumed in class 3 ( forestry ) or class 4 ( unused land ) , depending on presence or absence of human artefacts as identified in the underlying
the land - use dataset was extensively cross - checked against independent datasets ( erb et al . , 2007 ) .
land - use class 5 includes only non - forested land used by humans , ranging from high quality meadows and grazing land to shrub - dominated or otherwise marginally productive areas that allow only extensive grazing , including also savannahs , abandoned farmland , as well as degraded and extensively used areas and semi - deserts .
furthermore , this land use class is classified according to its suitability for livestock grazing , discerning four quality classes , from 1 ( best ) to 4 ( poorest ) , based on land - cover information from the glc-2000 map ( mayaux et al . , 2006 ) and npp data ( for reference see erb et al . , 2007 ) .
wilderness , occupies approximately one quarter of the global ice - free land surface ( i.e. excluding greenland and antarctica ) but holds little promise for energy crops because most of this land is extremely unproductive ( e.g. , arctic or alpine tundra or extreme deserts ) .
wilderness class also includes pristine forests which were excluded from the here presented analysis due to very long carbon payback times associated with their use and biodiversity conservation considerations .
areas potentially available in the year 2050 for growing energy crops are estimated as the sum of ( a ) cropland not required for food , feed and fiber production and infrastructure and ( b ) land potentials existing in the all other land category .
infrastructure and urban areas in the year 2050 ( table 1 ) were extrapolated from values for 2000 based on the medium un population forecast and urbanization trends ( un , 2007 ) . with respect to
the all other land category , area can only be assumed to be available for energy crops if roughage demand for livestock is satisfied , according to the food first principle ( see fig .
1 ) . in order to estimate the area that could be made available for energy crops in 2050 on such lands , depending on roughage demand
, we assumed that all other land of the highest grazing suitability ( grazing class 1 ) could be intensified to an extent currently observed in countries with high grazing intensity , i.e. a harvest level of up to 67% ( developing countries ) and 75% ( industrialized countries ) of aboveground npp .
we then assumed that the area set free through this assumed intensification would be available for energy crops in 2050 ( additional constraints
the trend scenario for 2050 was derived based on the un medium population forecast ( un , 2007 ) and fao agricultural projections .
the fao study world agriculture towards 2030/2050 , which was used here , assumes a global growth in cropland area of 9% ( table 1 ) and a growth of cropland yields of 54% ( weighted average of all crops and regions ) from the year 2000 to 2050 ( bruinsma , 2003 ; fao , 2006 ) .
the trend diet ( table 2 ) was constructed by assuming that each region would attain the food supply enjoyed in the country within each region that currently has the
this procedure yielded results that were very similar to the fao forecast ( fao , 2006 ) , despite the different methodology ( erb et al . , 2009a ) .
2 ) were extrapolated to 2050 separately for grazers ( cattle , sheep , goats , etc . ) and monogastric species ( pigs , poultry , etc . ) based on region - specific trends derived from fao statistics for the year 19612000 ( erb et al . , 2009a ; krausmann et al . , 2008
this estimates were complemented by a second variant in which lower feeding efficiencies , i.e. those currently achieved in organic farming , were assumed to prevail in 2050 ( see erb et al .
in addition to the cropland scenario displayed in table 1 we also considered a massive cropland expansion variant in which fao assumptions on cropland expansion in each region were doubled ( and held constant in regions where the fao forecasts a declining cropland area ) . this variant assumes a global growth of cropland area of 19% until 2050 .
this massive cropland expansion variant is still lower than the cropland expansion assumed to occur in some other global scenario studies ( iaastd , 2009 ) .
the largest expansion of cropland areas is assumed to occur in sub - saharan africa and latin america , as these are the regions generally thought to have the largest cropland potentials ( iiasa and fao , 2000 ; ramankutty et al . , 2002 ) .
it was assumed that the additional cropland has a 10% lower productivity than the cropland of the trend expansion because it would be located on less productive lands .
we assumed that the area expansion of cropland and infrastructure would consume the areas with the highest suitability for grazing in the other land class .
this assumption seems justified as regions with much land best suited for grazing according to our land - use dataset are also those in which gaez ( iiasa and fao , 2000 ) and other studies ( ramankutty et al . ,
in contrast , regions with little cropland expansion potential according to iiasa and fao ( 2000 ) and ramankutty et al .
( 2002 ) also have small areas of high - quality grazing land according to the erb et al .
land in grazing class 1 was found to be large enough to account for this change with the exception of the region
north africa and western sahara. in this region , cropland and infrastructure area expansion is assumed to consume land of grazing quality class 2 as well . reduced roughage production in 2050 as a result of the consumption of grazing areas by cropland was explicitly accounted for in the biomass - balance model in the respective regions . grazing land expansion through forest clearance was not considered . despite this restrictive assumption ,
grazing area was not found to limit roughage supply in any of the scenarios . in order to assess the possible effect of changes in diet on the area available for energy crops , three alternative diet variants were defined ( table 2 ) . in the
rich variant we assumed global convergence towards diets currently enjoyed in western europe and the usa , although these levels are not fully reached in 2050 . in the
less meat variant we assumed the same level of calorie and protein supply as in the trend scenario but with a lower level of animal - based products ( milk , meat and eggs ) .
the fair and frugal variant results in a convergence towards a global daily per - capita calorie intake of 2 800 kcal / cap / day ( 11.72 mj / cap / d ) , paired with a relatively low level of animal product supply .
this latter diet is nutritionally sufficient ( also in terms of protein supply , which is assumed to be based to a large extent on pulses and other protein - rich vegetables ) but requires globally equal distribution of food in order to avoid malnutrition in parts of the global population .
conversely , even at the highest supply level malnutrition can not be entirely ruled out if inequality in per - capita supply is assumed to remain at its current level ( erb et al . , 2009a ) .
in order to reflect changes in cropland yields , we defined three alternative variants regarding future cropland yields ( table 3 ) . the maximum yield level ( max )
was defined based on the global orchestration scenario in mea ( millennium ecosystem assessment , 2005 ) which assumes yields that exceed the level forecast by the fao in 2050 by 9% .
a minimum yield level was defined by calculating crop yields in 2050 under wholly organic conditions ( org ) , i.e. by assuming that 100% of the cropland area would be cultivated according to standards of organic agriculture . according to a literature review ( erb et al .
, 2009a ) , yields in organic agriculture are approximately 40% lower than those of industrialized agriculture if calculated over the whole crop rotation cycle , i.e. taking fallow cycles or the cultivation of n - fixating leguminous plants into account ( halberg et al . , 2006 ; connor , 2008 ; von fragstein und niemsdorff and kristiansen , 2006 ) .
this yield reduction was only applied to high - input cropland systems that mainly prevail in industrialized countries , and not to low - input agriculture . in developing countries ,
organic agriculture would allow further yield growth because the nutrient status of croplands is often very poor and can be improved with organic techniques ( halberg et al .
thus , the deviation of the organic yield scenario from the baseline was based on the regional mix between high - input and low - input agriculture ( table 3 ) .
the intermediate ( int ) yield scenario was calculated as the arithmetic mean between fao and org .
it may be interpreted as a scenario in which cropland agro - ecosystems are not pushed to their very limits due to environmental considerations , or as a trajectory in which yield levels forecast by the fao are not achieved for economic ( lack of investment ) or biophysical ( physiological limits , soil degradation , etc . ) reasons .
the biomass - balance model was used to determine the feasibility of combinations of assumptions on diets ( 4 variants ) , food and fodder crop yields ( 4 variants ) , cropland expansion ( 2 variants ) and livestock feeding efficiency ( 2 variants ) .
scenarios in which global cropland area demand exceeded global cropland availability by more than 5% were labeled as non - feasible and not further considered .
we considered a difference of supply and demand smaller than 5% not to be significant given the uncertainties in the biomass balance model .
the matching between supply and demand was performed on the global level ; regional imbalances were assumed to be equalized by trade .
roughage supply was not found to be a limiting factor , as a consequence of the large extent of global grazing areas ( erb et al . , 2007 ) and low average grazing intensities in most regions .
feasible we calculated the area available for energy crops as the sum of ( a ) cropland area not required for food , feed and fiber and ( b ) area available for energy crops on all other land while covering roughage supply for livestock on smaller , but more intensively used areas ( see above ) .
feasible scenarios as follows . in the trend scenario we assumed that aboveground biomass yields of energy crops are related to natural productivity ; that is , net primary production or npp ( field et al . , 2008 ; campbell et al . ,
as we were interested only in primary energy potentials , we did not differentiate between energy crop plants or bioenergy utilization pathways ( first / second generation ) . on croplands , we assumed biomass yields equal to the aboveground npp of potential vegetation ( i.e. the vegetation assumed to exist in the absence of land use ) . on all other land areas we used data on the aboveground npp of the currently prevailing vegetation .
all npp data were taken from prior work ( haberl et al . , 2007 ) .
( 2008 ) , who used the same approach , argued that this assumption may be regarded as optimistic because cropland npp is currently 35% lower than the potential npp of the respective areas .
this assumption implies that energy crops will achieve substantially higher yields in 2050 than those currently achieved by food crops in the global average , compared to the natural potential of the areas on which they are grown .
first generation biofuels are based on food crops , therefore our energy crop yield assumptions may be regarded as optimistic for most first - generation crops with the exception of sugarcane ( wbgu , 2009 ) .
low yield variant based on the conservative assumption that energy crop yields in 2050 would only achieve a level of 65% of the potential aboveground npp of the area on which they are planted .
however , much previous work on energy crop potentials was based on much higher yield expectations .
( 2009 ) assumed second generation energy crop yields of 13 kg dry matter per m and year which is approximately 1.54.5 times larger than the potential aboveground npp of the cropped area .
calculations with the dynamic global vegetation model lpjml suggest that the biological productivity of second generation biofuel crops such as c4 grasses and short - rotation coppice ranges from 0.8 to 1.2 kg / m / yr of dry matter biomass , i.e. slightly higher than potential npp , largely depending on the level of irrigation ( wbgu , 2009 ; beringer et al . , 2011 ) .
in line with a recent study ( johnston et al . , 2009 ) suggesting that yield assumptions for first generation biofuels had been largely overestimated , we did not assume high energy crop yield estimates as implemented in image ( van vuuren et al . , 2009 ) but rather those resulting from lpml ( beringer et al .
, 2011 ; wbgu , 2009 ) by assuming a high yield variant in which energy crops yields were 1.3 times higher than potential aboveground npp .
we assumed that dry - matter biomass has a gross calorific value of 18.5 mj / kg to derive primary energy supply potentials from the biomass flow data .
the conversion from primary biomass to final or useful energy can entail significant losses , in particular for first generation bioenergy , depending on the respective technology ( campbell et al .
, 2008 ; field et al . , 2008 ; wbgu , 2009 ) , which are not deducted here .
we also do not deduct direct or indirect energy inputs ; e.g. energy used for cultivation , fertilizer production or processing in other words , we report gross biomass production potentials of energy crops . in order to consider potential constraints from biodiversity conservation , we followed an approach used in recent studies ( beringer et al . , 2011 ; brooks et al . , 2006 ; wbgu , 2009 ) based on ( a ) biodiversity hotspots , ( b ) wilderness areas and ( c ) protected areas . for ( a )
biodiversity , we used data on biodiversity hotspots ( myers et al . , 2000 ) , endemic bird areas ( stattersfeld et al . , 1998 ) , centers of plant diversity ( wwf and iucn , 1994 ) and the global 200 dataset ( olson and dinerstein , 2002 ) . in order to consider ( b ) wilderness areas , we used biodiversity wilderness areas ( mittermeier et al . , 2003 ) , frontier forests ( bryant et al . , 1997 ) and the last of the wild wilderness area map ( sanderson et al . , 2002 ) .
in addition , we ( c ) superimposed the protected areas with iucn levels i and ii provided by the world database on protected areas ( unep - wcmc , 2010 ) .
we used the number of conservation data sets for a given area as a proxy for calculating a per - cent reduction in the area availability for energy crops .
less restrictive , variant 100% of the area of each pixel was excluded only if more than one wilderness layer was present , 50% of the area if two biodiversity hotspots were present , and 80% if there were three or more .
each of these rules was applied separately , and the most restrictive result was implemented . for the second , more restrictive , variant we decreased the area available for energy crops by 100% if a pixel was classified as
all land areas , regardless of the presence of any biodiversity hotspot or protected area , suffer a 10% decrease in available energy crop area . with the presence of one ( two , three , four ) biodiversity hotspot(s ) , the share of area assumed to be available for energy crops was reduced by 20% ( 30% , 50% , 80% ) .
again , the three calculations were performed separately and the most restrictive result was used . in order to exclude areas
where investment in energy crop plantations is highly unlikely due to lack of stable legal and political framework conditions , we excluded failed states ( newman , 2009 ) based on the list published by the fund for peace for the year 2010 ( www.fundforpeace.org )
. this list ranks 177 countries by analyzing 12 primary social , economic and political indicators , each of which split into a set of sub - indicators , which are summed up to a failed - state index .
the 30 countries with the highest index were treated as areas without any energy crop potential due to lack of stability required for investments into energy crop plantations .
in the trend scenario which assumes cropland expansion and yields as forecast by the fao , livestock efficiencies as well as diets in line with the fao projections and ignores constraints from biodiversity conservation and unstable political framework conditions , we find a global primary energy crop potential of 77 ej / yr .
this result is based on the trend variant of energy crop yields ( the notion of
scenario here stands for a unique combination of variants , i.e. assumptions on the different factors discussed in the
3 shows a map displaying the spatial distribution of the bioenergy production in this scenario which underlines that a considerable proportion of the total potential is located in sub - saharan africa and latin america .
4 displays the bioenergy potential in the 43 ( of a total of 64 ) scenarios which were classified as
feasible , showing a large range from 26 to 141 ej / yr from dedicated energy crops .
4 vary according to changes in diets , cropland expansion , food and feed crop yields and feed conversion efficiencies of livestock as discussed above .
they do not consider constraints from biodiversity conservation or lacking political stability and are based on the trend assumption on energy crop yields .
4a ) : richer diets result in lower energy crop potentials , while more frugal diets , especially those with less animal products , leave more space to plant energy crops .
the interrelation between food crop yields and energy crop potentials is less straightforward , however . while there is a general tendency that energy crop potentials increase with food crop yields ( fig .
4b ) , variability between the highest and lowest values also increases the highest and lowest scenario in terms of energy crop potential are both based on the max yield variant .
5a shows how constraints resulting from political instability ( failed states ) and exclusion of areas for biodiversity conservation affect the energy crop potential in 2050 .
these calculations were all based on the trend scenario with respect to food system and energy crop yields .
the exclusion of failed states reduces the global energy crop potential by 18% ; a large part of this reduction results from exclusion of areas in sub - saharan africa .
the exclusion of areas for biodiversity conservation reduces the global bioenergy potential by 932% , depending on the ambition of conservation efforts .
the combined effect of constraints from conservation and political stability reduces the global energy crop potential by 2545% .
the low assumption a relation between energy crop yields and the npp of potential vegetation on the areas planted with energy crops equal to that currently found on the world 's average croplands reduces the energy crop potential in 2050 by 26% compared to the trend scenario , while high energy crop yields could boost the potential by up to 48% to 114 ej / yr . under such optimistic assumptions , yield growth could approximately compensate the losses resulting from exclusion of areas in failed states and high - biodiversity areas .
in interpreting the results , it is important to bear in mind that we here calculated primary biomass supply potentials .
some conversion pathways , e.g. production of liquid biofuels , can only use parts of the plants and entail considerable conversion losses , e.g. in liquefaction .
moreover , biomass production as well as conversion to fuels requires energy inputs ( pimentel et al . , 1973 ; wbgu , 2009 ) .
hence , the net energy ( cleveland , 2007 ) delivered to society is considerably lower than the primary energy crop potentials calculated here ( e.g. , blottnitz and curran , 2007 ; cleveland et al .
the optimization of biomass utilization pathways in order to maximize the amount of useful energy delivered per unit of primary biomass harvested is beyond the scope of this paper , but is of course highly important in designing sustainable bioenergy strategies ( e.g. , see haberl and geissler , 2000 ; wbgu , 2009 ) .
the primary energy crop potentials calculated in this study on basis of a biophysical analysis , is 77 ej / yr in the trend scenario , with wide ranges resulting from different assumptions on the food and agricultural system , political stability required for investment security , and biodiversity conservation , are similar to those identified with the dynamic global vegetation model lpjml ( beringer et al . , 2011 ; wbgu , 2009 ) , higher than those assumed to exist on abandoned land , i.e. 2741 ej / yr ( campbell et al . , 2008 ; field et al . , 2008 ) , and considerably lower those identified in earlier studies ( hoogwijk et al . , 2003 ; hoogwijk , 2004 ; smeets et al . , 2007 ) .
our result is similar to a recent model - based assessment ( popp et al .
2011a ) which reported a global economic bioenergy potential in 2050 of approximately 70 ej / yr if deforestation was excluded ( 100 ej / yr if not ) based on a combination of a plant growth model ( lpjml ) with a land allocation model ( magpie ) and an energy model ( remind ) .
another study of global bioenergy trajectories under different carbon tax systems using the minicam integrated assessment model ( wise et al . , 2009 ) found that bioenergy supply might grow to over 100 ej / yr if only fossil - fuel based c emissions were limited , which would , however , trigger considerable deforestation . when all c emissions were limited , including those from land - use change , bioenergy supply in 2050 was much lower ( below 40 ej / yr ) .
assumptions on the energy crop yields that can be achieved in 2050 are among the most important reasons for the discrepancies in estimates of global bioenergy potentials .
previous modeling studies may have been overly optimistic in their assumptions on future energy crop yields .
( 2007 ) suggested that in 2050 up to 1272 ej / yr of bioenergy could be produced from energy crops grown on up to 36 million km ( 27% of the global land surface excluding antarctica and greenland ) .
however , this result was based on a yield assumption that was 3.8 times higher than current npp of these areas ( haberl et al . ,
2010 ) as discussed above , yield assumptions in past studies of energy crop potentials may have been too high ( johnston et al . ,
2009 ) , although vegetation models suggest that high - yielding energy crops such as c4 grasses or short - rotation coppice can achieve yields that exceed natural productivity by perhaps 2040% ( beringer et al . , 2011 ; wbgu , 2009 ) .
water supply may become an issue here , as high - yields can only be achieved if sufficient water is available ( fader et al .
, 2010 ; gerbens - leenes et al . , 2009b ; rost et al . , 2008 ) .
on the other hand , while it may be technically possible to achieve high yield levels or improve livestock feeding efficiencies to an extent that would allow to plant more area with energy crops than assumed here , the environmental and economic costs of such strategies could be substantial and need to be considered .
our results suggest that the future global energy crop potential strongly depends on changes in the food system .
assumptions on diet have a strong effect on the area demand for food production ( stehfest et al . , 2009 ) , and thus on the energy crop potential .
rich diet leaves little space for bioenergy plantations , irrespective of food and feed crop yields , while the fair & frugal diet allows for large bioenergy crop potentials .
as one moves from rich to poorer diets , the range between the lowest and highest potential also increases ( fig .
this is a result of the fact that the fair & frugal diet leaves a lot of area available for bioenergy if the most intensive technologies with respect to food and feed crop yields and feeding efficiency are adopted .
however , while such a combination would allow a high level of energy crop production , it may also be perceived as being particularly unlikely . in the case of
the fair & frugal diet , substantial energy crop potentials exist even if organic yields and low feeding efficiency are assumed .
changes in the assumptions on food and feed crop yields also have a substantial effect on the energy crop potential : higher yield levels leave more space for energy crop plantations if everything else remains constant . however , it does not seem likely that future diets are independent on food crop yields and vice versa .
higher yields are likely to be linked with richer diets , for example because food consumption and agricultural technology are both linked to affluence : rich societies can afford to eat better , but they also acquire the means to increase their agricultural yields ( godfray et al .
4b ) , the lowest bioenergy potential estimate found in any of the scenarios was based on high food and feed crop yields .
the reason is that the rich diet can only be provided with high yields .
this diet variant combined with lower yields were all classified as not feasible and consequently excluded .
a rich diet leaves little space for energy crop plantations due to the high roughage demand for livestock , irrespective of yield levels of food crops . in other words ,
pushing yields to their limits also allows richer diets , which then in turn may reduce the energy crop potential if people adopt diets that include more animal products .
it is beyond the scope of this article to assess whether , and under which conditions , it is more favorable in terms of ghg emissions / uptake to use the area that becomes available due to high yields and/or more vegetarian diets for bioenergy provision instead of using it for c sequestration ( stehfest et al . , 2009 ;
our study , however , reveals that this is not the only trade - off related to bioenergy production that requires systematic attention .
our analysis clearly illustrates trade - offs between maximizing energy crop supply and adopting environmentally less burdensome agricultural technologies . at present , agricultural intensification results in higher yields but is often associated with substantial environmental pressures resulting from fertilizers , pesticides , machinery use , etc
. impacts of intensive agriculture include soil degradation , nitrogen leaching , risks from pesticides , among others ( iaastd , 2009 ; popp et al . , 2011b ; smeets et al . , 2009 )
everything else being equal , lower food and feed crop yields leave less space for energy crop plantations , and lower energy crop yields also result in a lower bioenergy potential .
many technologies proposed to reduce environmental pressures from agriculture , e.g. organic farming , tend to reduce yields , which mean that more area is needed to produce the same amount of food . to what extent these trade - offs can be mitigated through
sustainable intensification ( godfray et al . , 2010a ; tilman , 1999 ) remains to be seen .
an additional trade - off exists between biodiversity conservation and maximization of energy crop production .
our results suggest that the exclusion of wilderness areas , protected areas and biodiversity hotspots could lower the global energy crop potential by 932% , depending on the ambition of conservation efforts .
this calculation does not include the possibility that conservation targets could also constrain food crop production , which might indirectly result in additional restrictions for planting more energy crops . a focus on biomass residues and wastes instead of purpose - grown bioenergy plants would allow to tap into a substantial energy potential of up to 100 ej / yr ( haberl et al . , 2010 ) and would deliver energy without increased pressures on ecosystems resulting from additional land demand .
however , use of some residues may pose a risk for the maintenance of soil fertility ( blanco - canqui and lal , 2009 ; lal , 2006 ) , hence secure upper limits to extraction of agricultural residues need to be respected .
where these limits are depends on soil characteristics , climate and many other region - specific factors ; this is an area where more research is needed .
about one quarter of the global energy crop potential calculated for 2050 in the trend scenario is located in countries currently classified as failed states. no projection is available to what extent lacking political stability might affect global energy crop potentials in 40 years , so the share of the global potential that is inaccessible due to political constraints is at present unknown .
however , our calculations support the conclusions of previous assessments ( beringer et al . , 2011 ; wbgu , 2009 ) that such constraints might be substantial .
the design of sustainable bioenergy crop production policies needs to resolve intricate trade - offs between food and energy supply , renewable energy and biodiversity conservation or yield growth and reduction of environmental pressures from intensive agriculture .
our assessment indicates that policy strategies are needed that succeed in simultaneously optimizing production and consumption systems and considering the many potential conflicting uses of biomass , land and water .
increasing crop yields seems to be essential , given the growing world population , the growing energy demand in the light of global environmental changes .
but such strategies will only be successful if not overcompensated by consumption surges and if sustainable methods for intensification can be developed .
our analysis also reveals that successful policies will have to optimize the increasingly globalized , i.e. spatially separated , land use and biomass utilization chains in integrative ways ( erb et al .
in this context , our analysis reveals one particular intricacy : whereas the largest bioenergy demands are expected in regions where energy potentials are low such as europe and parts of asia , the largest energy potentials are found in regions such as sub - saharan africa .
expanding agricultural land use in these regions will require massive investments , which might not be affordable for local governments or land users and are not attractive for international investors if political stability is low .
moreover , sensitive legislation will be required to avoid land - use changes with negative social effects , e.g. see the current land grab discussions ( friis and reenberg , 2010 ; zoomers , 2010 ) . by necessity , growing energy crops requires land .
if substantial amounts of bioenergy should be derived from purpose - grown energy crops , the land area required needs to be significant as well .
the gross energy content of all biomass harvested by humans globally for food , feed , fiber and bioenergy was approximately 230 ej / yr in the year 2000 ( krausmann et al . , 2008 ) .
this biomass was harvested on almost three quarters of the global land surface ( excluding antarctica and greenland ) through cropping , grazing and forestry ( erb et al .
ej / yr of energy crops in 2050 , in addition to the growth of biomass required to adequately feed a world population of perhaps 9.1 billion , is therefore an endeavor that should not be underestimated . | pubmed |
several recent works have been contributed to our understanding of the dynamical evolutionary processes related to stellar bars in galaxies ( see @xcite for a review ) .
much of these works point to the possibility that these processes may be related to the formation and/or building of galactic bulges , as opposed to a pure monolithic scenario ( @xcite ) and the hierarchical scenario ( e.g. , @xcite ) . we know that bars are very easy to form in stellar disks due to non
circular orbits of the stars in the disk , or due to instabilities generated by the presence of a companion . in the rc3 ( @xcite ) , for instance , 30% of the spiral galaxies are strongly barred .
recent theoretical studies based on n body simulations ( e.g. , @xcite and references therein ) show that , once formed , the stellar bar induces a series of dynamical processes in the host galaxy .
basically , these studies show two routes for the formation and/or building of galactic bulges . in the first one
, stellar bars could collect gas from the outer disk , generating bursts of star formation and a chemical enrichment in the central regions .
another possibility is that the stars themselves might be transported from the disk to the bulge , through , for instance , the hose mechanism ( @xcite ) , orbital resonances ( @xcite ) and the onset of irregular stellar orbits ( e.g. , @xcite ) .
moreover , @xcite , among other theoretical works , showed that the central concentration of mass , induced by the bar , could destroy its orbital structure and eventually the bar itself .
these authors suggest that the formation of the bar , its dissolution and consequent formation and/or building of the bulge , may be a fast recurrent process ( i.e. , @xmath1 years ) .
@xcite suggest that the continuous building of the bulge in a galaxy could actually change its overall morphology .
one sc galaxy , for instance , might become in a first step a sbb , and then a sb , giving an evolutionary meaning to the late type spiral scheme along the hubble sequence . from the observational point of view , comparative studies related to the general properties of barred and non barred galaxies seem to give some support to the formation and/or building of galactic bulges through this secular evolutionary scenario .
@xcite found that triaxial bulges , which are normally associated with bars , rotate faster than bulges of non barred galaxies .
@xcite showed that bulges of barred galaxies have a central velocity dispersion smaller than the one presented by bulges in non barred galaxies . @xcite and @xcite
show that barred galaxies have less pronounced o / h gradients than non barred galaxies .
@xcite show that barred galaxies present a higher degree of central concentration of co molecular gas than non barred galaxies .
moreover , box shaped bulges , representing at least 2030% of edge on s0 s ( @xcite ) , seem to show this morphology as a consequence of steps in the secular dynamical evolutionary processes in bars , as indicated by a series of recent results ( @xcite ) .
studies related to general properties of spirals ( e.g. , @xcite ) revealed similar broadband colors of the inner disk and bulge ; @xcite and @xcite found a correlation between the scale lengths of disks and bulges .
these results indicate the existence of an evolutionary connection between these two components ( see @xcite for a review ) , and have been interpreted as a consequence of the dynamical secular evolutionary scenario .
another way to obtain clues related to the formation and evolution processes in galaxies is through the study of radial color distribution .
however , surprisingly , there are few statistical works in the literature exploring the broadband colors to study the bulge and the disk components separately .
the study of the integrated broadband colors in galaxies have been done to obtain information concerning the stellar population ( e.g. , @xcite ) , as well as the internal extinction caused by the interstellar dust ( e.g. , @xcite ) .
exceptions are the works of @xcite and @xcite , for instance .
such studies certainly bring clues about the bulge formation scenarios . the main goal of this paper is to compare the color gradients behaviour in barred and non barred late type galaxies and verify if these results are in agreement with the predictions from evolutionary processes
. a very fast way to verify alternative scenarios for the formation and/or building of bulges , exploring the radial color distribution in a statistical point of view , is to use the available data in the literature . with this objective ,
we have selected a sample of 257 sbc galaxies with broadband colors available in the literature and observed through photoelectric aperture photometry ( sect .
2 ) . using robust statistical methods , we estimated , for each galaxy , the color gradient as well as the mean total and bulge characteristic color indices ( sect .
3 ) . moreover , we have also acquired ccd images for 14 galaxies in the sample ( sect .
4 ) in order to test the accuracy of our results . in sect .
5 we present the main results of our analysis and , finally , in sect .
6 we present a general discussion and our main conclusions .
the photoelectric data used in this analysis were extracted from the compilation by @xcite and its supplement ( @xcite ) .
both compilations will hereafter be referred to as ldv83,85 , respectively . among other information
, the catalogue presents for different galaxies the ( u@xmath0b ) and ( b@xmath0v ) aperture color indices extracted from the literature .
we have selected galaxies with hubble stage index t = 3 , 4 or 5 , corresponding to morphological types sb , sbc and sc , barred and non barred , and having b@xmath2 brighter than 14 , according to the third reference catalogue ( @xcite ; hereafter rc3 ) .
this criterion assures that the morphological classification is more reliable , since fainter objects are , in general , more difficult to be classified .
nevertheless , it is worth notice that several galaxies were distinctly classified in the ldv83,85 and in the rc3 .
since the rms uncertainty associated with the morphological type is of order 2 units ( @xcite ) , we will consider all galaxies in our sample as belonging to one unique mean morphological class ( t = 4 @xmath3 1 ) .
we remark that our choice for galaxies in this specific type range was motivated by the fact that these are the most luminous objects in the b broadband along the hubble sequence ( @xcite ) .
this is possibly indicating that these systems have the highest rate of star formation among spirals .
another reason for this choice comes from the observation that it is possible that the dynamical evolutionary processes occur mainly in late
type spirals rather than in early type ones ( @xcite ) . a first selection of the data was partially done with the electronic version of the catalogue , available at the cds ( _ centre de donnes astronomiques de strasbourg _ ) , and resulted in a sample containing 531 objects .
in order to have an equally representative set of data , we have removed from the sample those objects with less than 5 different color aperture data .
thus , we selected only those objects for which a more careful study of the distribution of the color indices could be done .
we know that extinction by dust can strongly affect studies of the radial color distribution in the u , b and v bands , in particular for late type galaxies .
however , these bands are well suited for the study proposed here , since in these bands we can detect recent star formation , which is a possible consequence of the dynamical secular evolutionary scenario . in order to minimize the effects of dust
, we have also performed a visual inspection of all galaxies , using images of the dss ( digitized sky survey ) , eliminating those peculiar systems , ( e.g. , ngc 891 ) , presenting clear perturbations , such as strong dustlanes or close companions in strong interaction , that could disturb the analysis .
after this last step we ended with a final sample having 257 galaxies , used in the present analysis .
as mentioned before , we have used the ldv83,85 data to estimate the ( u@xmath0b ) and ( b@xmath0v ) color gradients of the galaxies in our sample .
since this is a compilation of data acquired by different observers , telescopes , instruments and in different atmospheric conditions , it is natural that , for any given galaxy , some data will not appear consistent , due to larger internal errors .
for instance , different authors could assign quite distinct values for the color index of the same galaxy at the same aperture . indeed ,
this is the case , for example , of ngc 2377 in the aperture of 2.6 arcminutes , where three different sources gave to the ( u@xmath0b ) color index the values 0.11 , 0.20 and 0.38 !
therefore , trying to fit a straight line to the color data , using these discrepant values and the classical least squares regression ( ls ) , will result in a quite uncertain estimative for the color gradient . since we do not know a priori how to identify the bad data , it is mandatory to use some robust statistical technique more insensitive to the presence of these uncertainties . in our analysis
, we choose to apply the least median of squares ( lms ) method ( @xcite ) .
contrary to the classical ls regression , this method minimizes the _ median _ of the squared residuals .
the results obtained are more resistant to the effects of contamination in the data .
more specifically , the estimation of the color gradient was done with the program progress ( @xcite ) , available at the statlib ( http://www.lib.stat.cmu.edu/ ) .
this program performs a robust regression analysis by means of the lms method , yielding more reliable estimates of the regression parameters , and allowing to identify outliers in the data .
progress first calculates the regression parameters by ls , then by lms , and finally by a reweighted ls ( in which the outliers have weight zero ) . through this algorithm
, the estimated gradient has , in most cases , the same value obtained through the lms method alone .
however , the reweighted ls method works better than the lms method when the number of data points is small ( @xcite ) .
the color gradient was estimated following the same definition of @xcite , i.e. , @xmath4 where @xmath5 represents the integrated color index in magnitudes within an aperture @xmath6 in units of 0.1 arcminute .
the estimation of each gradient was also accompanied by a graphical visual inspection , since , in some cases , the results from the non reweighted ls were more representative than those by lms or by the reweighted ls .
this could happen because , when trying to minimize the errors , the lms method can be fooled by a small group of data points that fits very well a straight line .
thus , in these cases , we defined the gradient by the parameters obtained by the classical ls regression . from our sample of 257 galaxies , we obtained 239 ( b@xmath0v ) and 202 ( u@xmath0b ) color gradients .
the other estimations were rejected either because the number of data points were too small and/or the points were too inconsistent to result in a reliable value .
figure 1 shows four examples of the radial color distribution in galaxies .
ngc 1425 and ngc 2613 are examples of objects having the more typical negative color gradient .
an example of object with a clear null gradient is ngc 1672 .
the more rare case of objects with a positive gradient is represented here by ugc 3973 . in this figure
, we can also compare the fits using the three different methods discussed above .
the dashed lines refer to the standard ls method , while dotted lines refer to the lms method and the solid lines refer to the progress algorithm .
note the importance of using a robust statistical method to determine color gradients in such cases as for ngc 2613 and ugc 3973 .
the ldv83,85 data is not corrected for either galactic reddening or internal reddening . in determining the color gradients ,
the correction for galactic reddening is not necessary , since it only introduces a constant vertical shift of the points , not affecting the gradient evaluation .
however , the correction for internal reddening is quite difficult to predict correctly , due to the still unsolved problems related to the optical thickness and the inclination of galaxies ( e.g. , @xcite ) .
however , although such a correction could be important for any particular object , it will only produce minor changes compared to the uncertainties involved in the measurement and determination of the color gradients . on the other hand , in models of the dust distribution in disk dominated galaxies , it was shown ( @xcite ) that only a small fraction of the color gradients could be due to dust reddening , i.e. , dust reddening plays a minor role in color gradients .
furthermore , color gradients induced by dust are small from u to r broadbands , because the absorption properties do not change very much among these bands . in fig .
2 we show the color gradients plotted against both the galactic reddening and the inclination of the galaxies .
we can see from this figure that the two corrections mentioned above do not interfere with the distribution of color gradients obtained in our sample .
the top panels show that there is no correlation between color gradients and galactic reddening , represented by the color excess @xmath7 , determined through the recently obtained maps of @xcite . on the other hand , since the internal reddening varies with the inclination of the galaxy along the line of sight , which can be represented by the @xmath8 parameter of the rc3 , the bottom panels of fig . 2
show that there is no clear correlation between color gradients and internal reddening . since no correlation was found , we opt to neglect the internal reddening when estimating the color gradients .
we remark , however , that both effects are still obviously relevant when dealing with the integrated color , as we present in the next subsection .
we have used two different procedures to determine the total and the bulge characteristic color indices . in the first one , we adopt the bulge color as the one observed through the smallest aperture , and the total color as the one observed through the aperture that reaches the 25 mag arcsec@xmath9 b isophotal level , as presented in the rc3 . in some cases ,
when the data do not reach the dimensions required , an extrapolation was done using the estimated gradient . on the other hand ,
an average was done for apertures with several data points .
no reddening corrections were made in this method .
we stress that this method is completely unbiased , in the sense that we use the original data , and therefore it is useful to verify if the total colors and the colors of bulges are correlated .
such correlation should in fact exist , since the colors of bulges and disks are correlated ( @xcite ) .
they have used the ( u@xmath0r ) , ( b@xmath0r ) , ( r@xmath0k ) and ( j@xmath0k ) colors in a sample of 30 early type spirals ( earlier than sbc ) . as shown in sect .
5.5 , we also found a good correlation , consistent with the findings of these authors .
since galaxies have different angular sizes and were observed through different sets of apertures , the method described above is only an approximated procedure , since , in many cases , the measurements were made at different galactocentric distances . in order to compare the data of galaxies at the same physical dimension
, we have defined a characteristic bulge color index as the one measured within 1/5 of the galaxy effective radius .
even if there is some disk contamination at this aperture , the major contribution comes from the bulge , and therefore we made no attempt to correct for this contamination . using the definition of gradient ( eq .
( 1 ) ) , this bulge color was derived from our fits as @xmath10 where @xmath11 is the effective color index , measured within the effective aperture in the b band .
we have also define a characteristic total color as the one measured within 2 effective radius , corresponding therefore to @xmath12 equations ( 2 ) and ( 3 ) , and the effective color indices given by the rc3 , were used to determine these characteristic colors .
as we have already mentioned , this second method is more suitable to compare the values from different galaxies .
however , we could not use this method to verify the correlation between the total colors and the colors of bulges , since eq(s ) .
( 2 ) and ( 3 ) already imposes such a correlation , as one can see by subtracting them .
therefore , this justifies our first rough method used only to verify the existence of a real correlation , since that method do not suffer from this kind of bias .
we have corrected these characteristic color indices for galactic reddening using the maps of @xcite to obtain the ( b@xmath0v ) color excess , and used the relation @xmath13 which can be found in @xcite .
we did not correct these values for any differential internal reddening between bulge and disk .
instead , we have applied an integrated correction to account for the effects of inclination .
according to @xcite , the internal extinction as a function of the inclination of the galaxy , derived from i band images of sc galaxies , is @xmath14 where @xmath15 and @xmath16 are , respectively , the major and minor axis of the galaxy . for the u , b and v bands , @xcite shows that the extinction coefficients are , respectively , 3.81 , 3.17 and 2.38 times the extinction coefficient in the i band , according to observations done in the galaxy . since the galaxy is likely a sbc galaxy we used these same relations for the objects in our sample . using the definition of the color excess and the fact that @xmath17 is approximately equivalent to the @xmath8 parameter of the rc3
, we finally arrive to the relations used in our work : @xmath18 and @xmath19 it is interesting to observe that the corrections we have applied are actually @xmath20 23 times larger than the ones adopted in the rc3 ! indeed , earlier works ( see , e.g. ,
@xcite ) argued that spiral galaxies were nearly transparent .
but more recent studies ( e.g. , @xcite ) show that the optical thickness of spiral galaxies is higher .
the adopted corrections in eq(s ) .
( 6 ) and ( 7 ) assume that spiral galaxies have a large optical thickness , and thus are much more realistic .
although the galaxies in our sample can be considered as local ( -295 km / s ( ngc 224 ) @xmath21 8720 km / s ( ugc 4013 ) ) , with a typical value of @xmath22 2000 km / s ) , we have also applied the k correction , using the equations of the rc3 .
the galaxies analyzed in this work , as well as the results from the determination of the ( b@xmath0v ) and ( u@xmath0b ) gradients , and of the total and bulge color indices , can be seen in table 1 .
the ideal set of data to study the radial color distribution in the disk and bulge components is obtained by using ccd photometry , which permits a differential evaluation of the color along the galaxies . however , as mentioned before , we have choose a more fast way in order to have a statistically significant set of data .
this was the main reason which lead us to use the available data from ldv83,85 .
it is interesting , therefore , to compare the color distribution obtained from ccd and aperture photoelectric photometry . in this subsection
, we present a comparison with the ccd data of 14 galaxies observed at the pico dos dias observatory ( pdo / lna cnpq , brazil ) .
the ccd observations were done with a 24 inch telescope having a focal ratio f/13.5 , and using a thin back illuminated ccd site si003ab , with 1024 @xmath23 1024 pixels .
the plate scale is 0.57 arcsec / pixel , resulting in a field of view of approximately 10 @xmath23 10 arcmin .
the ccd gain was fixed on 5 electrons / adu and the read out noise on 5.5 electrons .
all objects were observed in the b , v , r and i passbands of the cousins system . for each object , we have done 6 exposures in the b band , 5 in the v , and 3 in the r and i bands , typically , with an exposure of 300 seconds .
the multiple exposures aim to ease cosmic ray removal .
the data was calibrated with a set of standard stars of @xcite and corrected for atmosphere and galactic extinction .
the later correction was done using the maps of @xcite .
the standard processing of the ccd data includes bias subtraction , flatfielding and cosmetics .
the first step in the sky subtraction was done by editing the combined images in each filter , removing the galaxy and stars .
after that step we determined the mean sky background and its standard deviation ( @xmath24 ) .
then , we removed all pixels whose values were discrepant by more than 3 @xmath24 from the mean background .
an sky model was obtained by fitting a linear surface to the image , and this model was subtracted from the combined image .
we finally removed objects such as stars and hii regions .
all these procedures were done using the iraf package .
we then used the ellipse task to calculate the surface brightness profiles of each galaxy in each band . subtracting the profiles we obtained color gradients , constructing tables in the same units of the ones in ldv83,85 .
these tables were used in the progress algorithm to provide values for the gradients in the same way it was done for our whole sample . in fig .
3 , we show a plot of the ccd gradients and those obtained with the photoelectric aperture data , showing that both estimations are essentially the same .
the good correlation between these two set of values ( pearson correlation coefficient r = 0.93 ) gives support to the results obtained with the ldv83,85 data .
the mean difference is g@xmath25 @xmath0 g@xmath26 .
we have also done a comparison with the ccd observations made by @xcite to study color profiles in a sample of 86 face on disk galaxies .
we have applied for the 8 galaxies our samples have in common , the same method we have used in this work , using the b and v ccd images kindly provided by de jong .
we have simulated photometric apertures on these images using the imexamine task from iraf .
the comparison of the ( b@xmath0v ) gradients obtained using the photoelectric data by ldv83,85 and de jong s ccd images revealed a pearson correlation coefficient of @xmath27 . if we do not consider two outliers the pearson coefficient is @xmath28 .
@xcite , hereafter ph98 , have also estimated the ( u@xmath0b ) and ( b@xmath0v ) gradients , using both ccd and photoelectric aperture photometry , for a large fraction of the galaxies in our sample . to avoid the uncertainties due to inconsistent measures these authors have attributed different statistical weights to each source of data . in fig .
4 we present a comparison between the gradients determined in the present work and those estimated by ph98 .
the correlation coefficient r is 0.85 for ( b@xmath0v ) and 0.81 for ( u@xmath0b ) .
moreover , we can see that there are no systematic differences between the two works .
the mean value of the differences is 0.004 in ( b@xmath0v ) and 0.011 in ( u@xmath0b ) .
in this section , we will analyse the results obtained from sect .
3 , regarding the color gradients , as well as those relating to the total and bulge color indices .
we have separated our sample into barred ( sab+sb ) and non barred ( s+sa ) galaxies , in order to test the bulge formation in the evolutionary and monolithic scenarios . since the identification of bars is much more difficult in edge on systems , and the effects of dust extinction are minimized in face on galaxies , we took the special care of analysing the face on and the edge on galaxies separately .
we use the same criterion as @xcite , defining as face on those galaxies with @xmath29 , corresponding to @xmath30 .
galaxies which do not obey this criterion we regard as edge on .
the following galaxies , ic 983 , ngc 253 , ngc 1169 , ngc 1625 , ngc 1964 , ngc 2276 , ngc 2377 , ngc 2525 , ngc 3344 , ngc 3646 , ngc 4394 , ngc 4402 , ngc 5054 , ngc 6215 , ngc 6300 , ngc 6878a , ngc 7307 and ugc 11555 , whose gradients were too uncertain to be used , were removed from our sample .
table 1 shows the color gradients and its errors for all galaxies in our sample , as well as the bulge and total characteristic color indices .
the errors of the gradients are the ones obtained through the progress algorithm and thus are fit errors , which are larger than the photometric errors alone .
one can see that the mean error on the ( b@xmath0v ) gradient is 0.03 , and on the ( u@xmath0b ) is 0.05 .
the mean errors for the bulge and total color indices are , respectively , 0.04 and 0.03 for ( b@xmath0v ) and 0.05 and 0.04 for ( u@xmath0b ) .
the distribution of the color gradients for barred and non barred galaxies , considered separately , both face and edge on projections , can be seen in fig .
5 . the statistical data from this figure are presented in table 2 , where column ( 1 ) contains the description of each subsample , while columns ( 2 ) and ( 5 ) contain the total number of objects in each subsample in each color index . columns ( 3 ) and ( 6 ) show the mean values and their respective standard errors .
finally , columns ( 4 ) and ( 7 ) contain the standard deviations of these distributions .
these values were obtained through a gaussian fit to the observed distribution .
we can observe from fig .
5 that the ( u@xmath0b ) distribution for barred galaxies , for both the face and edge on projections , is wider than the distribution for non barred galaxies .
the results in table 2 also show that barred galaxies have wider distributions . from this table
, we can see that the differences in the standard deviations are larger than the expected photometric errors , indicating that this is indeed a real effect . with a smaller amplitude , the same effect is also present in the ( b@xmath0v ) gradients
. even considering that the photometric errors are larger in the u band , this can hardly explain this effect since such errors affect both kinds of objects , barred and non barred , in the same way .
therefore , this is a real characteristic of barred galaxies , namely , to present a larger interval of ( u@xmath0b ) color gradients , probably associated with recents episodes of star formation .
we note that the larger distributions are caused by a larger fraction of barred galaxies having zero or positive gradients . in ( u@xmath0b ) , for instance , 55% @xmath3 8% of the face on barred galaxies have zero or positive gradients , whereas for the face on non barred galaxies this fraction is reduced to 32% @xmath3 12% .
however , considering the ( b@xmath0v ) index , these fractions are more similar , being 41% @xmath3 6% among barred galaxies and 31% @xmath3 11% among non barred galaxies . at this point
we might suspect that this difference between the two color indices may be caused by a larger age / metallicity sensibility of the ( u@xmath0b ) color index .
we remark that this effect is present even when we do not separate the edge and face on galaxies .
moreover , one can see in fig .
5 that the majority of barred galaxies have less pronounced ( u@xmath0b ) gradients than the non barred galaxies , as can be also verified through the mean values presented in table 2 . but , interestingly , this behaviour does not occur in the ( b@xmath0v ) color .
this is probably an effect that any enhancement in the star formation rate affects more the ( u@xmath0b ) than the ( b@xmath0v ) color .
another interesting effect is that the edge on galaxies show a tendency of having more pronounced negative gradients compared to the face on systems , specially in ( u@xmath0b ) .
this effect may well be related to the fact that the internal reddening is more expressive in edge on galaxies , and points to the presence of a small differential internal correction that affects the bulge and the disk in different ways .
indeed , one can conclude that the light emitted by the central regions shall be more affected by reddening , a result that agrees with the ones presented by @xcite .
we present in fig .
6 the ( u@xmath0b ) versus the ( b@xmath0v ) gradients for the non barred galaxies ( a ) , barred galaxies ( b ) and for the total sample ( c ) .
we can see from this figure that the gradients in both colors are well correlated , and that there is no difference in the correlation for barred and non barred galaxies .
in fact , the pearson correlation coefficient r is 0.71 for non barred , 0.80 for barred , and 0.78 for the whole sample .
the same correlation was observed separating face and edge on galaxies without noticeable differences .
again , we can see that barred galaxies have a more extended color gradient amplitude in these plots .
these correlations are indeed expected , since the same physical reason rules the gradients in both colors , namely , variations between the stellar populations of the inner and outer regions of the galaxies .
the models of @xcite , for instance , show that , for a population formed in a single burst , the variation in ( b@xmath0v ) for populations with a difference in age of 10 giga years is 1.1 , while for ( u@xmath0b ) it is 1.5 .
thus , in these conditions , we shall expect @xmath31 .
since the color gradients are @xmath32 and @xmath33 , then we shall have @xmath34 .
surprisingly , the correlations in fig . 6
give us @xmath35 , which is very close to what is predicted from these simple models .
this difference might indicate that we are seeing stellar populations mixed with dust , since larson and tinsley s models do not take dust into account .
thus we interpret that the reason for this agreement , as will be seen in sect .
5.5 , is that the total color index is relatively stable among galaxies in our sample , but the color of the bulge varies noticeably between the barred and non barred populations .
therefore , the amplitude of variation in the color gradients shown in fig(s ) . 5 and 6 is related to variations in the stellar population of the bulges .
it is interesting to ask what would happen if the weakly barred galaxies ( sab s ) would have been analysed separately .
the answer to this question is the analysis would remain the same .
indeed , barred and weakly barred galaxies show essentially the same mean color gradient in both the ( b@xmath0v ) and ( u@xmath0b ) . the values for barred galaxies alone are @xmath36 and @xmath37 , respectively , while for the weakly barred galaxies these values turn to @xmath38 and @xmath39 .
the vast majority of the galaxies in our sample have negative gradients , as one can see from fig .
5 , implying therefore that the bulge is redder than the disk .
this result , in principle , is consistent with the monolithic scenario , where the older and redder population is located in the central parts , whereas the younger and bluer populations are more predominant in the outer regions of spiral galaxies . in order to get some further insight ,
we have considered three arbitrary categories for the color gradients , according to their values . the first category is constituted by objects having negative gradients , with @xmath40 ; the second have galaxies with almost zero gradient , defined by @xmath41 , and finally the third category have those galaxies with positive gradients , @xmath42 . in table 3
we show for the face on galaxies in our sample , where the distinction between barred and non barred is more reliable , the distribution among these three classes of objects , in both colors .
there are a total of 124 face on galaxies with the ( b@xmath0v ) gradient , and 104 with the ( u@xmath0b ) . in column
( 1 ) we present the total number of galaxies in each class of color gradient , while column ( 2 ) gives their fraction of the total sample .
column ( 3 ) , ( 4 ) and ( 5 ) show , respectively , the fractions of non barred , weakly barred and barred galaxies in each gradient interval . column ( 6 ) shows the total fraction of barred ( sab+sb ) galaxies and , finally , column ( 7 ) shows the number of galaxies hosting agn s .
galaxies with agn were identified through the catalog of @xcite .
the reason to investigate this class of galaxies in this study comes from the suggestions presented by other authors ( e.g. , @xcite ) that bars can fuel agn through processes similar to the ones of the secular evolution .
we can verify that , with small variations in each color index , we have approximately 59% of the galaxies presenting negative gradients , 27% with zero gradients , and 14% with positive gradients .
we remark that this result does not change considerably when we consider a more restrictive definition of the zero gradient class , as @xmath43 .
moreover , essentially the same result is also obtained when we consider the whole sample , including together face and edge on galaxies .
the total fraction of face on barred galaxies in our sample is 79% .
we can see in table 3 that there exists an excess of barred galaxies among the ones with null or positive gradients . in ( b@xmath0v ) , the fraction of barred galaxies with negative gradient is 75% , while it raises to 91% among the ones with zero gradient . in ( u@xmath0b ) , 73% of the galaxies with negative gradient are barred , while 83% of the ones with null gradient are barred , and 90% of the positive gradient galaxies are barred .
if we consider the more restrictive criterion for null gradient ( @xmath43 ) , this excess is substantially emphasized .
the fraction of barred galaxies with null ( b@xmath0v ) gradient then raises to 94% and the fraction of barred galaxies with null ( u@xmath0b ) gradient raises to 88% .
this result indicates that barred galaxies are over represented among the objects having null or positive gradients .
therefore , bars seem to act as a mechanism of homogenization of the color indices , and thus , of the stellar population , along galaxies . as a consequence , we are forced to conclude that a classical monolithic scenario would have difficulties to explain this result .
another interesting feature of table 3 is that the fraction of galaxies with agn increase from @xmath20 8% for systems with negative gradients to @xmath20 36% for objects with positive gradients . even considering the low number statistics
, this might be an indication that the homogenization of the stellar population , induced by bars , is related to the agn phenomenon .
recent theoretical studies ( e.g. , @xcite ) related to the dynamical secular evolution show that a stellar bar is able to collect gas from the outer to the inner regions of the disk , through shocks and gravitational torques that remove angular momentum from the gas .
thus , a large scale mixing of the gas must occur along the galaxy , which could be , in principle , observed in the radial abundance profiles of certain chemical elements .
@xcite , hereafter mr94 , and @xcite , hereafter zkh94 , present o / h abundance gradients in spiral galaxies determined through the observation of hii regions .
both studies show that barred galaxies tend to have less pronounced gradients . moreover ,
mr94 conclude that the gradients become less pronounced as the normalized length of the bar , or its apparent ellipticity , increases . on the other hand , studies from @xcite
show that barred galaxies have a higher central concentration of molecular gas ( co ) than non barred galaxies .
both results are in agreement with the prediction from the theoretical studies of dynamical secular evolution .
then , if the abundance is affected by this mechanism we also should expect it affected the color gradients . in order to verify this possibility ,
we have compared 12 galaxies in common with mr94 , and 18 with zkh94 . in fig .
7 , we plot our color gradients versus the abundance gradients of mr94 ( top panel ) and zkh94 ( bottom panel ) .
we can see that there is no clear correlation between the photometric and the abundance gradients .
hardly this absence of correlation could be a consequence of errors in the photometric gradients , which typically range from 0.02 to 0.05 .
on the other hand , the errors in the abundance gradients are more difficult to determine , as we can see by looking at the quite different values of the ngc 2997 gradient as estimated by mr94 and zkh94 .
however , these errors are also hardly larger than 0.02 dex @xmath23 kpc@xmath44 ( zkh94 ) .
one can interpret that the absence of such correlation is a real feature , and thus it is interesting to explore its consequences .
since the color indices are sensible to both age and metallicity , this result could indicate that the excess of barred galaxies with zero color gradients , as we found in sect .
5.2 , reflects a difference in the behaviour of the mean _ age _ of the stellar population along barred and unbarred galaxies , and not of its metallicity .
however , in principle , this absence of correlation could be attributed to the effects of dust extinction .
we have argued in sect .
3.1 that these effects shall be small , but in sect . 5.6 below we will show a quantitative analysis of these effects , and we conclude that it is possible that the lack of this correlation may be caused by dust extinction .
we would expect to find such correlation in the dynamical secular evolutionary scenario . however , if we consider that bars are a relatively fast recurrent phenomenon , this absence of correlation would be natural .
indeed , we can imagine the following picture .
if we consider a galaxy formed through the monolithic scenario , we shall expect it to show both the abundance and color gradients negative . in that case
the galaxy would be placed in the lower left region of fig .
7 . this galaxy can develop a bar and then have its abundance gradient shallower , while its color gradient shall remain the same , because the time scale to mix the gas in the disk shall be smaller than the time required to form new stars in the central region .
galaxies in that stage would occupy the lower right part of fig . 7 .
after the gas accumulates in the central region it will form new stars and then the color gradient will become shallower and the galaxy would be in the upper right part of fig . 7 .
instabilities generated by the mass accumulated in the central region will destroy the bar interrupting the transfer of gas along it and steepening the abundance gradient , while keeping the color gradient unchanged . in this case
, we will see the galaxy in the upper left part of fig .
. the lack of new star formation in the central region and the aging of the stars will then turn negative the color gradient and the galaxy will again occupy the lower left part of fig . 7 . if a new bar is developed then the changes in the abundance and color gradients can occur again . in an attempt to perform a quantitative morphology of bars in galaxies , @xcite , hereafter m95 , made visual estimates of the axial ratio , @xmath45 , the major axis length ( normalized by the 25 mag arcsec@xmath9 isophote ) , @xmath46 , and the apparent ellipticity of bars in spiral galaxies . in that work
, it is found a relation between the length of the bar and the diameter of the bulge , in the sense that galaxies with large bulges also have large bars .
moreover , he found an apparent correlation between the presence of intense nuclear star formation and the axial ratio of the bar , in the sense that strong bars , those with @xmath47 , are present in galaxies with nuclear bursts of star formation .
a total of 45 galaxies in our sample were studied in m95 , allowing us to verify correlations between our color gradients and the parameters of the bar morphology .
figure 8 shows for these objects our color gradients plotted against the bar parameters axial ratio , @xmath45 , length , @xmath46 , and apparent ellipticity , @xmath48 .
we detect no correlation of these morphological bar parameters with the color gradients , meaning that the color gradient does not depend on the morphology of the bar .
thus , there are galaxies with the same gradient and bars with quite distinct morphologies . and , on the other hand , there are systems with the same bar morphology and quite different color gradients .
it is worth notice that mr94 found that the o / h abundance gradients in barred galaxies turn less pronounced as the ellipticity or the length of the bar increases , i.e. , galaxies with stronger bars have less pronounced o / h abundance gradients .
again , it is not unlikely that extinction by dust is masking a correlation .
however , these results may be explained by different time scales in the homogenization of abundance gradients , measured in gas , and color gradients , measured in stars .
we remark that our total color indices are obviously affected by the contributions of both the bulge and the disk .
the relative importance of these two components can be measured by the factor @xmath49 , representing the bulge to disk luminosity ratio in the b band . on the other hand ,
both components have intrinsic colors ( b@xmath0v)@xmath50 , ( b@xmath0v)@xmath51 and ( u@xmath0b)@xmath50 , ( u@xmath0b)@xmath51 . the total color is related to these component colors through the relations @xmath52 and @xmath53 where @xmath54 and @xmath55 .
table 4 shows the median values of the characteristic total and bulge color indices for the galaxies in our sample , separated by the gradient class , together with their standard errors . for those objects with null color gradient
we show a single color value . in the right part of this table
, we present the data relative only to the face on objects .
we can see that the same trend is present in both samples . considering both the face on galaxies and the total sample , one can observe that the total colors remain almost with the same value for the three classes of gradients .
the differences are small in both the ( u@xmath0b ) and ( b@xmath0v ) colors , within the errors .
however , bulges of zero or positive gradient objects are systematically bluer than the ones found in negative gradient objects .
the differences are much larger than the errors , indicating that it is a real effect .
indeed , there is a difference of order 0.40 magnitudes between the colors of bulges in negative and positive gradient objects , while the estimated errors are within @xmath20 0.03 magnitudes .
therefore , one major factor determining the value of the gradient is the bulge color .
moreover , the disk colors should also be redder , for objects with null or positive gradients , in order to keep the total colors almost unchanged , as it is observed .
this is an effect which is not compatible with the monolithic scenario , since it indicates that , in the process of homogenization of the stellar population , induced by bars , bursts of star formation occur in the bulge , in complete agreement with the secular evolutionary scenario . another way of looking to this effect is shown in fig .
9 , where we plot the relation of the total and bulge color indices for different classes of gradients , considering only face on galaxies .
although we have the total color instead of the disk color , these correlations have the same meaning as the ones found by other authors ( @xcite ) , showing that the formations of bulge and disk are parts of the same process .
however , this figure also shows that the zero point scale of the correlation is quite different for objects having negative and positive color gradients .
while the correlations are in the same sense , we can see again that the bulge is much bluer in objects with positive gradients , while the mean total color is the same , irrespective of the gradient category .
these results do not change when we consider also the edge on galaxies . once again , it is interesting to verify if there are any differences in the properties of barred and weakly barred galaxies .
like the color gradients , the characteristic total and bulge mean color indices for sb s and sab s are essentially the same .
the bulge colors for sb s are @xmath56 and @xmath57 in ( b@xmath0v ) and ( u@xmath0b ) , respectively , while for sab s they are @xmath58 and @xmath59 . on the other hand ,
the total colors for sb s are @xmath60 and @xmath61 in ( b@xmath0v ) and ( u@xmath0b ) , and they are @xmath62 and @xmath63 for sab s . a fundamental point to be considered in this study
are the effects of dust extinction and reddening . in principle
, dust can disturb the analysis of color distribution in galaxies . to minimize its effects
we have made a careful sample selection excluding galaxies presenting strong dust lanes .
moreover , we have made our analysis considering also a sub sample containing only the face on galaxies of our total sample , in which it is well known that the effects of dust are minimized .
we also consider the results from the models of dust distribution in disk dominated galaxies by @xcite which show that the dust reddening plays a minor role in color gradients .
this author also argues that color gradients produced by dust are small from the u to the r bands because the absorption properties do not change very much in these bands .
furthermore , we have shown that there is an excess of barred galaxies with blue bulges in comparison with non barred galaxies , and we conclude that this is related to recent bursts of star formation . since the effects of dust do not depend on whether or not the galaxy hosts a bar , this main conclusion remains unaltered , even if the extinction is considerable . nevertheless ,
although the extinction in face on galaxies is smaller than in edge on galaxies , it might be considerable in the central regions ( see @xcite ) .
moreover , extinction and reddening depend on the geometry of the system and on the distribution of dust and stars ( see , e.g. , @xcite ) , so that it is prudent to verify empirically the role of dust in color gradients . with this aim ,
we have used hst archival data ( nicmos and wfpc2 ) , and some ccd images obtained at pico dos dias , in order to determine the optical ( b , v , i ) and near ir ( h , k ) color gradients for some galaxies , which are useful to evaluate the role of dust .
these galaxies were chosen to have an inclination representative of our sample . as we have no photometry data in all selected passbands for all galaxies used in this analysis ( see table 5 )
, we will assume that such gradients like ( @xmath64 ) indicate variations in the old stellar population , while those like ( @xmath65 ) or ( @xmath66 ) are specially sensitive to recent star formation .
color gradients like ( @xmath67 ) or ( @xmath68 ) will primarily show the extinction caused by dust , as well as old stellar population gradients ( see @xcite ) .
all galaxies belong to our main sample ( sect .
as the hst data were measured only in the central region of the galaxies ( inner @xmath20 2 kpc ) , these central gradients shall not be compared with the global ones obtained in sect .
since it is in the central region where most of the dust is accumulated , its role in color gradients evaluated here may be considered as an upper limit .
let us evaluate firstly the hst data .
as the dust and gas contribution are not the same for all galaxies , we will discuss the results for each one individually , and summarize them in table 5 .
ngc 3310 shows a very small old population gradient ( @xmath69 ) and a small old population / dust gradient ( @xmath70 ) , while the color gradient produced by recent star formation is large ( @xmath71 ) .
thus one can conclude that , for this galaxy , dust may be responsible for @xmath72 of the observed central color gradient .
ngc 5033 have also a very small old population gradient ( @xmath73 ) but a _ positive _ and large star formation gradient ( @xmath74 ) .
this means that , even with the dust present in the centre of this galaxy ( as can be seen in the hst images ) , the blue light emitted by the young population are strong enough to produce positive color gradients .
another possibility to explain this behaviour is the presence of a strong dust lane off centered , but this lane was not found in the images .
ngc 5194 also have a very small old population gradient ( @xmath75 ) and a considerable old population / dust gradient ( @xmath76 ) . with the star formation gradient values
one can conclude that , in this galaxy , dust may cause nearly half of the observed central color gradient .
finally , ngc 5248 have a considerable old population / dust gradient ( @xmath77 ) , but a _ positive _ star formation gradient .
conclusions are the same as for ngc 5033 .
another way to study the role of dust in color gradients is to determine the reddening it causes . using the hst data again we can estimate an upper limit , considering that there is no dust reddening beyond 1 @xmath78 and that there are no stellar population gradients .
thus , the difference in color from the center to 1 @xmath78 can be assumed to be all done by dust extinction .
when the data does not reach 1 @xmath78 we used the farthest available radius .
we thus estimated such color excesses in ( @xmath79 ) for ngc 3310 , ( @xmath80 ) for ngc 5194 , and ( @xmath68 ) and ( @xmath67 ) for ngc 5248 .
results are in table 5 . with the galactic extinction law
@xcite we have determined the extinction @xmath81 in the centre of these galaxies .
its average value is @xmath82 .
@xcite applied the same analysis to a sample of early type spirals , obtaining @xmath83 .
the same procedure we have used to the hst data we applied for 5 galaxies observed by us at the pico dos dias observatory in the b , v and i bands ( see table 5 ) . assuming that ( @xmath65 ) gradients are sensitive to recent star formation , while ( @xmath84 ) gradients are old population / dust gradients
, we can infer the dust contribution to the observed color gradients to be of up to 45% in the central region .
as one can see , there are 2 galaxies with a negative old population / dust gradients but with positive star formation gradients .
this result is in agreement with the one obtained using the hst data .
we have also estimated an average value for @xmath81 using the ( @xmath84 ) color excesses .
its value is @xmath85 .
this value is lower than the one obtained with the hst data simply because it was not obtained with optical near infrared colors .
now , assuming that the color excesses obtained truly represent an effect of dust extinction , we can `` correct '' the colors inside 1 @xmath78 and re calculate the ( @xmath65 ) and ( @xmath86 ) color gradients , using the galactic extinction law .
table 6 shows the results and compares them with the gradients determined in sect .
it can be seen that , with the hst data , dust effects can , in some cases , alter significantly the color gradients determined .
but in other cases , even the high values of the upper limit for @xmath81 do not change the results .
table 6 also shows that using the color excesses obtained through our b , v and i ccd imaging make no significant changes in the color gradients .
this study has led us to conclude that indeed extinction in the center ( inner @xmath20 2 kpc ) of late type spirals is high , with a typical value for @xmath87 magnitudes
. however , the results shown here seems to indicate that dust is very much concentrated in the center , so that _ global _ color gradients are not much disturbed by dust , in general .
the fact that , even with dust present in the center , some galaxies have positive gradients , shows that the excess of barred galaxies with blue bulges , found in this work , is a result which is not affected by our ignorance on the dust effects .
it means also that , in these blue bulges , one can have an underlying old stellar population beneath a recent burst of star formation . on the other hand , it seems that the absence of correlations between color gradients and abundance gradients ( sect .
5.3 ) , and color gradients and the bar morphology ( sect .
5.4 ) , could possibly be explained by dust extinction .
in the previous section we noticed that barred galaxies have less pronounced ( u@xmath0b ) mean color gradients . moreover , both at ( u@xmath0b ) and ( b@xmath0v ) the amplitude of variation of the gradient , as measured by the standard deviation of its distribution , is larger in barred , as opposed to non barred galaxies .
these results imply that there is an excess of barred galaxies among the objects with null or positive gradients , as can be seen from table 3 . as a consequence ,
we conclude that bars act in the sense of promoting a more homogeneous stellar population in late type spirals . besides an underlying old and red stellar population , disks of late type spirals have ubiquitous young and blue stars .
bulges in general have an old stellar population , but we have shown here that bulges of late type barred galaxies have also an important young stellar component .
therefore , the stellar population of barred galaxies tend to show a degree of mixing not compatible with the pure monolithic scenario .
we found no correlation between the color and abundance gradients .
we must consider here the results of sect .
5.6 , i.e. , dust extinction is considerable in the central region of late type spirals , but does not strongly disturb global color gradients , in general . in spite of the caveat that this lack of correlation may be caused by the effects of dust , judging from the estimated photometric and abundance errors , we believe that this could be a real effect , indicating that color gradients may be not associated with metallicities ( but see @xcite ) . therefore , the presence of color variations inside a given galaxy is quite probably related to an age effect caused by bursts of star formation .
the absence of this correlation could also be explained if we consider that bars are a fast recurrent phenomenon .
another conclusion from this study is that the mean total color indices remain remarkably constant independently of the galaxy s color gradient . from the sample of face on objects we can verify in table 4 that the total mean colors are ( b@xmath0v)@xmath88 and ( u@xmath0b)@xmath89 . on the other hand , bulges behave quite differently .
the mean colors of bulges in null gradient galaxies are @xmath20 0.20 bluer than the colors of bulges in negative gradient systems .
bulges of positive gradient galaxies are even bluer , @xmath20 0.50 bluer than bulges in negative gradient objects .
we see also in table 4 that this difference is quite too large to be explained by photometric errors . in order to keep the total color unchanged
it is necessary that the disks of the null or positive gradient galaxies become redder , i.e. , evolve passively .
this same effect can be clearly seen from fig .
9 , where we present the correlation between total and bulge colors . in both the negative and positive gradient regimes
there is a correlation between these two colors .
these correlations are in agreement with the ones found by other authors ( @xcite ) for the colors of bulges and disks .
however , we can also see from fig .
9 that the correlation of the positive gradient objects is shifted in the blue direction by @xmath20 0.50 magnitudes in their bulges . according to these authors , assuming similar metallicities for bulges and disks , their correlations imply in a difference of the order of less than 30% between the ages of the stellar populations in these two components . again
, the presence of a correlation between the total and bulge colors , as well as the bluer colors of bulges in galaxies with null or positive gradients , are not consistent with the pure monolithic scenario .
a more difficult task is to identify the correct evolutionary scenario responsible for these observable properties .
the capture of nearby dwarfs in the accretion process of the hierarchical scenario seems to be incompatible with the constancy of the mean total colors of galaxies presenting different classes of color gradients , since this process do not predict a passive evolution for the disk .
moreover , the hierarchical scenario also does not predict an excess of barred galaxies showing null or positive color gradients . on the other hand , the secular evolution induced by a bar can result in an enhancement of the star formation rate in the central regions of galaxies .
this effect can be responsible for the bluer colors observed in bulges of galaxies showing null or positive color gradients . at this point
we can not say , however , whether this enhancement is occurring in the bulge or in the internal region of the disk .
it is a pleasure to thank ronaldo e. de souza and rob kennicutt for fruitful discussions and suggestions , and for a careful reading of a preliminary version of the paper , and tim beers for presenting us the lms method .
special thanks go to roelof de jong for providing us his ccd observations .
we also thank g. longo for helpful answers to our questions .
we thank the anonymous referee for helping to improve the article , specially the discussion on dust effects .
we acknowledge the conselho nacional de pesquisa e desenvolvimento ( cnpq ) , the nexgal pronex and the fundao de amparo pesquisa do estado de so paulo ( fapesp ) for the financial support .
we would also like to thank the staff at the pico dos dias observatory ( opd / lna cnpq ) for helping during the observational runs .
sakamoto , k. , okumura , s.k .
, ishizuki , s. , and scoville , n.z .
1999 , in when and how do bulges form and evolve ?
, ed . by c.m .
carollo , h.c .
ferguson & r.f.g .
wyse , cambridge university press , astro - ph/9902005 cccccccccc eso271 - 010 & sabcd(s ) & -0,02 & 0,03 & 0,04 & 0,06 & 0,39 & 0,39 & -0,22 & -0,22 + ic0342 & sabcd(rs ) & 0,43 & 0,08 & 0,57 & 0,09 & 0,23 & 0,66 & -0,51 & 0,06 + ic1954 & sbb(s ) & -0,06 & 0,03 & 0,15 & 0,10 & 0,24 & 0,24 & -0,40 & -0,25 + ic1993 & sabb(rs ) & -0,05 & 0,03 & -0,01 & 0,10 & 0,73 & 0,73 & 0,24 & 0,24 + ic2554 & sbbc(s ) & -0,06 & 0,03 & 0,08 & 0,04 & 0,19 & 0,19 & -0,45 & -0,45 + ic4444 & sabbc(rs ) & 0,00 & 0,03 & & & 0,40 & 0,40 & &
+ ic4839 & sabc(s ) & -0,28 & 0,03 & -0,44 & 0,06 & 0,88 & 0,60 & 0,41 & -0,03 + ic4845 & sb(rs ) & 0,13 & 0,00 & -0,01 & 0,07 & 0,45 & 0,58 & 0,05 & 0,05 + ic4852 & sbbc(s ) & -0,13 & 0,05 & 0,03 & 0,07 & 0,67 & 0,54 & -0,07 & -0,07 + ic5092 & sbc(rs ) & -0,01 & 0,03 & -0,02 & 0,09 & 0,69 & 0,69 & 0,09 & 0,09 + ic5179 & sbc(rs ) & -0,17 & 0,04 & -0,11 & 0,03 & 0,46 & 0,29 & -0,12 & -0,23 + ic5186 & sabb(rs ) & -0,11 & 0,01 & -0,11 & 0,04 & 0,53 & 0,42 & -0,06 & -0,17 + ic5325 & sabbc(rs ) & -0,18 & 0,03 & -0,05 & 0,05 & 0,69 & 0,51 & -0,07 & -0,07 + mcg-2 - 14 - 4 & sabcd(rs ) & -0,33 & 0,11 & 0,07 & 0,01 & 0,64 & 0,31 & -0,11 & -0,11 + ngc0001 & sb & -0,14 & 0,01 & -0,19 & 0,05 & 0,76 & 0,62 & 0,19 & 0,00 + ngc0024 & sc(s ) & -0,20 & 0,06 & -0,14 & 0,06 & 0,29 & 0,09 & -0,33 & -0,47 + ngc0134 & sabbc(s ) & -0,18 & 0,01 & -0,35 & 0,03 & 0,49 & 0,31 & 0,12 & -0,23 + ngc0150 & sbb(rs ) & -0,22 & 0,00 & -0,21 & 0,04 & 0,54 & 0,32 & -0,05 & -0,26 + ngc0151 & sbbc(r ) & -0,36 & 0,03 & -0,46 & 0,06 & 0,73 & 0,37 & 0,33 & -0,13 + ngc0157 & sabbc(rs ) & -0,23 & 0,03 & -0,27 & 0,04 & 0,60 & 0,37 & 0,07 & -0,20 + ngc0210 & sabb(s ) & -0,17 & 0,02 & -0,32 & 0,00 & 0,78 & 0,61 & 0,30 & -0,02 + ngc0224 & sb(s ) & -0,03 & 0,00 & -0,08 & 0,01 & -0,10 & -0,10 & -0,26 & -0,26 + ngc0278 & sabb(rs ) & -0,03 & 0,04 & & & 0,51 & 0,51 & &
+ ngc0289 & sbbc(rs ) & -0,19 & 0,02 & -0,34 & 0,02 & 0,78 & 0,59 & 0,32 & -0,02 + ngc0309 & sabc(r ) & -0,63 & 0,04 & -0,47 & 0,10 & 0,91 & 0,28 & 0,26 & -0,21 + ngc0440 & sbc(s ) & -0,16 & 0,02 & -0,24 & 0,06 & 0,51 & 0,35 & -0,03 & -0,27 + ngc0470 & sb(rs ) & -0,13 & 0,03 & 0,01 & 0,06 & 0,63 & 0,50 & -0,06 & -0,06 + ngc0488 & sb(r ) & -0,13 & 0,02 & -0,28 & 0,04 & 0,90 & 0,77 & 0,58 & 0,30 + ngc0578 & sabc(rs ) & -0,21 & 0,03 & -0,10 & 0,01 & 0,50 & 0,29 & -0,15 & -0,25 + ngc0613 & sbbc(rs ) & 0,01 & 0,02 & 0,03 & 0,04 & 0,63 & 0,63 & 0,06 & 0,06 + ngc0615 & sb(rs ) & -0,12 & 0,01 & -0,27 & 0,02 & 0,55 & 0,43 & 0,29 & 0,02 + ngc0628 & sc(s ) & -0,14 & 0,01 & -0,23 & 0,02 & 0,64 & 0,50 & 0,09 & -0,14 + ngc0685 & sabc(r ) & -0,22 & 0,03 & -0,15 & 0,04 & 0,62 & 0,40 & -0,04 & -0,19 + ngc0779 & sabb(r ) & -0,11 & 0,02 & -0,25 & 0,03 & 0,45 & 0,34 & 0,10 & -0,16 + ngc0782 & sbb(r ) & -0,31 & 0,00 & -0,53 & 0,06 & 0,82 & 0,51 & 0,44 & -0,09 + ngc0864 & sabc(rs ) & -0,11 & 0,03 & & & 0,55 & 0,44 & & + ngc0908 & sc(s ) & -0,22 & 0,02 & -0,50 & 0,04 & 0,54 & 0,32 & 0,17 & -0,33 + ngc0958 & sbc(rs ) & -0,13 & 0,04 & & & 0,48 & 0,35 & &
+ ngc1055 & sbb & -0,10 & 0,02 & -0,26 & 0,04 & 0,53 & 0,43 & 0,13 & -0,13 + ngc1068 & sb(rs ) & -0,10 & 0,01 & 0,01 & 0,01 & 0,74 & 0,64 & 0,00 & 0,00 + ngc1073 & sbc(rs ) & -0,17 & 0,03 & -0,47 & 0,04 & 0,62 & 0,45 & 0,22 & -0,25 + ngc1084 & sc(s ) & -0,14 & 0,04 & -0,26 & 0,01 & 0,50 & 0,36 & 0,03 & -0,23 + ngc1087 & sabc(rs ) & -0,01 & 0,04 & 0,11 & 0,04 & 0,31 & 0,31 & -0,36 & -0,25 + ngc1097 & sbb(s ) & 0,08 & 0,03 & 0,12 & 0,02 & 0,64 & 0,64 & 0,03 & 0,15 + ngc1187 & sbc(r ) & -0,15 & 0,02 & -0,10 & 0,04 & 0,60 & 0,45 & -0,01 & -0,11 + ngc1232 & sabc(rs ) & -0,24 & 0,01 & -0,60 & 0,04 & 0,79 & 0,55 & 0,45 & -0,15 + ngc1255 & sabbc(rs ) & -0,36 & 0,02 & -0,14 & 0,04 & 0,62 & 0,26 & -0,10 & -0,24 + ngc1288 & sabc(rs ) & -0,30 & 0,02 & & & 0,88 & 0,58 & &
+ ngc1300 & sbbc(rs ) & -0,18 & 0,03 & -0,22 & 0,03 & 0,71 & 0,53 & 0,21 & -0,01 + ngc1365 & sbb(s ) & 0,11 & 0,02 & 0,13 & 0,04 & 0,43 & 0,54 & -0,16 & -0,03 + ngc1421 & sabbc(rs ) & -0,30 & 0,02 & -0,22 & 0,03 & 0,24 & -0,06 & -0,28 & -0,50 + ngc1425 & sb(s ) & -0,13 & 0,02 & -0,25 & 0,02 & 0,51 & 0,38 & 0,13 & -0,12 + ngc1483 & sbbc(s ) & -0,09 & 0,04 & -0,04 & 0,04 & 0,39 & 0,39 & -0,26 & -0,26 + ngc1515 & sabbc(s ) & -0,09 & 0,02 & -0,12 & 0,01 & 0,33 & 0,33 & -0,05 & -0,17 + ngc1530 & sbb(rs ) & -0,12 & 0,04 & -0,02 & 0,01 & 0,55 & 0,43 & -0,11 & -0,11 + ngc1536 & sbc(s ) & -0,03 & 0,10 & & & 0,51 & 0,51 & & + ngc1566 & sabbc(s ) & -0,06 & 0,03 & -0,06 & 0,05 & 0,57 & 0,57 & -0,04 & -0,04 + ngc1614 & sbc(s ) & 0,02 & 0,03 & 0,16 & 0,04 & 0,44 & 0,44 & -0,34 & -0,18 + ngc1620 & sabbc(rs ) & -0,24 & 0,01 & & & 0,56 & 0,32 & & + ngc1637 & sabc(rs ) & -0,22 & 0,04 & -0,26 & 0,06 & 0,76 & 0,54 & 0,18 & -0,08 + ngc1672 & sbb(s ) & 0,00 & 0,01 & 0,04 & 0,01 & 0,57 & 0,57 & -0,05 & -0,05 + ngc1688 & sbd(rs ) & 0,15 & 0,04 & 0,42 & 0,12 & 0,30 & 0,45 & -0,44 & -0,02 + ngc1703 & sbb(r ) & -0,18 & 0,00 & -0,64 & 0,00 & 0,69 & 0,51 & 0,36 & -0,28 + ngc1784 & sbc(r ) & -0,30 & 0,00 & -0,22 & 0,05 & 0,81 & 0,51 & 0,24 & 0,02 + ngc1792 & sbc(rs ) & -0,19 & 0,03 & -0,22 & 0,04 & 0,51 & 0,32 & -0,06 & -0,28 + ngc1796 & sbc(rs ) & -0,08 & 0,01 & -0,09 & 0,04 & 0,31 & 0,31 & -0,26 & -0,26 + ngc1832 & sbbc(r ) & -0,43 & 0,02 & -0,42 & 0,06 & 0,77 & 0,34 & 0,19 & -0,23 + ngc1888 & sbc(s ) & -0,14 & 0,05 & -0,26 & 0,05 & 0,43 & 0,29 & 0,11 & -0,15 + ngc1961 & sabc(rs ) & -0,33 & 0,09 & & & 0,73 & 0,40 & &
+ ngc2082 & sbb(r ) & -0,18 & 0,03 & -0,13 & 0,06 & 0,67 & 0,49 & -0,08 & -0,21 + ngc2090 & sc(rs ) & -0,10 & 0,02 & -0,20 & 0,03 & 0,61 & 0,51 & 0,17 & -0,03 + ngc2206 & sabbc(rs ) & -0,25 & 0,05 & & & 0,66 & 0,41 & & + ngc2207 & sabbc(rs ) & -0,32 & 0,03 & & & 0,64 & 0,32 & & + ngc2223 & sabb(r ) & -0,25 & 0,02 & -0,57 & 0,08 & 0,88 & 0,63 & 0,54 & -0,03 + ngc2268 & sabbc(r ) & -0,08 & 0,02 & & & 0,53 & 0,53 & & + ngc2336 & sabbc(r ) & -0,21 & 0,03 & -0,61 & 0,05 & 0,60 & 0,39 & 0,37 & -0,24 + ngc2339 & sabbc(rs ) & -0,12 & 0,02 & & & 0,75 & 0,63 & & + ngc2347 & sb(r ) & -0,19 & 0,03 & & & 0,76 & 0,57 & & + ngc2389 & sabc(rs ) & -0,21 & 0,08 & & & 0,55 & 0,34 & &
+ ngc2417 & sbc(rs ) & -0,12 & 0,03 & -0,09 & 0,08 & 0,62 & 0,50 & 0,00 & 0,00 + ngc2442 & sabbc(s ) & -0,30 & 0,02 & -0,30 & 0,01 & 0,86 & 0,56 & 0,34 & 0,04 + ngc2487 & sbb & -0,38 & 0,03 & -0,42 & 0,08 & 0,93 & 0,55 & 0,41 & -0,01 + ngc2512 & sbb & -0,08 & 0,01 & 0,02 & 0,05 & 0,54 & 0,54 & -0,05 & -0,05 + ngc2565 & sbbc & 0,02 & 0,01 & -0,08 & 0,12 & 0,52 & 0,52 & 0,07 & 0,07 + ngc2595 & sabc(rs ) & -0,06 & 0,02 & -0,01 & 0,02 & 0,60 & 0,60 & 0,07 & 0,07 + ngc2608 & sbb(s ) & -0,09 & 0,06 & -0,08 & 0,07 & 0,53 & 0,53 & -0,06 & -0,06 + ngc2613 & sb(s ) & -0,16 & 0,01 & -0,42 & 0,04 & 0,47 & 0,31 & 0,28 & -0,14 + ngc2683 & sb(rs ) & -0,08 & 0,01 & -0,23 & 0,02 & 0,34 & 0,34 & 0,07 & -0,16 + ngc2712 & sbb(r ) & -0,19 & 0,03 & & & 0,63 & 0,44 & & + ngc2715 & sabc(rs ) & -0,11 & 0,06 & & & 0,27 & 0,16 & & + ngc2776 & sabc(rs ) & 0,04 & 0,05 & 0,04 & 0,05 & 0,52 & 0,52 & -0,11 & -0,11 + ngc2815 & sbb(r ) & -0,24 & 0,02 & -0,34 & 0,07 & 0,60 & 0,36 & 0,37 & 0,03 + ngc2841 & sb(r ) & -0,12 & 0,01 & -0,24 & 0,03 & 0,68 & 0,56 & 0,36 & 0,12 + ngc2874 & sbbc(r ) & -0,26 & 0,04 & -0,40 & 0,04 & 0,62 & 0,36 & 0,23 & -0,17 + ngc2889 & sabc(rs ) & -0,26 & 0,02 & -0,39 & 0,10 & 0,87 & 0,61 & 0,37 & -0,02 + ngc2903 & sabbc(rs ) & 0,03 & 0,02 & 0,16 & 0,03 & 0,40 & 0,40 & -0,24 & -0,08 + ngc2935 & sabb(s ) & -0,12 & 0,05 & -0,07 & 0,10 & 0,76 & 0,64 & 0,13 & 0,13 + ngc2955 & sb(r ) & 0,19 & 0,07 & & & 0,21 & 0,40 & &
+ ngc2964 & sabbc(r ) & -0,08 & 0,04 & -0,06 & 0,01 & 0,49 & 0,49 & -0,18 & -0,18 + ngc2989 & sabbc(s ) & -0,17 & 0,03 & -0,12 & 0,00 & 0,42 & 0,25 & -0,16 & -0,28 + ngc2997 & sabc(rs ) & 0,08 & 0,02 & 0,19 & 0,03 & 0,68 & 0,68 & 0,01 & 0,20 + ngc3001 & sabbc(rs ) & -0,09 & 0,06 & -0,12 & 0,06 & 0,58 & 0,58 & 0,02 & -0,10 + ngc3054 & sabb(r ) & -0,14 & 0,02 & -0,23 & 0,03 & 0,74 & 0,60 & 0,26 & 0,03 + ngc3079 & sbc(s ) & -0,25 & 0,01 & -0,50 & 0,07 & 0,31 & 0,06 & 0,02 & -0,48 + ngc3095 & sabc(rs ) & -0,39 & 0,03 & -0,44 & 0,05 & 0,67 & 0,38 & 0,19 & -0,25 + ngc3124 & sabbc(rs ) & -0,19 & 0,03 & & & 0,80 & 0,61 & & + ngc3145 & sbbc(rs ) & -0,25 & 0,01 & -0,12 & 0,12 & 0,72 & 0,47 & 0,18 & 0,06 + ngc3177 & sb(rs ) & 0,04 & 0,02 & -0,21 & 0,05 & 0,54 & 0,54 & 0,51 & 0,30 + ngc3223 & sb(s ) & -0,25 & 0,00 & -0,34 & 0,04 & 0,76 & 0,50 & 0,36 & 0,02 + ngc3281 & sab(s ) & -0,10 & 0,01 & -0,19 & 0,06 & 0,74 & 0,64 & 0,31 & 0,12 + ngc3289 & sb0+(rs ) & -0,04 & 0,03 & -0,03 & 0,02 & 0,31 & 0,31 & -0,01 & -0,01 + ngc3310 & sabbc(r ) & 0,00 & 0,01 & 0,05 & 0,04 & 0,19 & 0,19 & -0,54 & -0,54 + ngc3318 & sabb(rs ) & -0,34 & 0,02 & -0,50 & 0,04 & 0,58 & 0,24 & 0,13 & -0,37 + ngc3333 & sabbc & -0,19 & 0,04 & 0,13 & 0,15 & 0,20 & 0,01 & -0,55 & -0,42 + ngc3347 & sbb(rs ) & 0,03 & 0,01 & -0,07 & 0,02 & 0,61 & 0,61 & 0,16 & 0,16 + ngc3351 & sbb(r ) & 0,03 & 0,02 & 0,19 & 0,05 & 0,66 & 0,66 & -0,03 & 0,16 + ngc3353 & sb & 0,13 & 0,06 & 0,13 & 0,05 & 0,17 & 0,30 & -0,57 & -0,44 + ngc3390 & sb & -0,13 & 0,02 & -0,16 & 0,08 & 0,32 & 0,19 & -0,06 & -0,22 + ngc3521 & sabbc(rs ) & -0,07 & 0,03 & & & 0,52 & 0,52 & & + ngc3627 & sabb(s ) & -0,20 & 0,02 & -0,21 & 0,02 & 0,62 & 0,42 & 0,18 & -0,03 + ngc3628 & sb & -0,11 & 0,04 & & & 0,28 & 0,17 & &
+ ngc3689 & sabc(rs ) & 0,13 & 0,10 & & & 0,37 & 0,50 & & + ngc3810 & sc(rs ) & -0,21 & 0,06 & -0,27 & 0,07 & 0,64 & 0,43 & 0,08 & -0,19 + ngc4051 & sabbc(rs ) & 0,28 & 0,04 & 0,50 & 0,05 & 0,37 & 0,65 & -0,44 & 0,06 + ngc4088 & sabbc(rs ) & -0,36 & 0,01 & & & 0,55 & 0,19 & & + ngc4096 & sabc(rs ) & -0,20 & 0,05 & -0,22 & 0,03 & 0,32 & 0,12 & -0,15 & -0,37 + ngc4156 & sbb(rs ) & -0,01 & 0,08 & 0,32 & 0,17 & 0,72 & 0,72 & -0,31 & 0,01 + ngc4216 & sabb(s ) & -0,20 & 0,02 & -0,29 & 0,03 & 0,59 & 0,39 & 0,35 & 0,06 + ngc4254 & sc(s ) & -0,15 & 0,01 & -0,14 & 0,00 & 0,64 & 0,49 & 0,06 & -0,08 + ngc4258 & sabbc(s ) & -0,06 & 0,03 & 0,03 & 0,06 & 0,39 & 0,39 & -0,04 & -0,04 + ngc4273 & sbc(s ) & -0,03 & 0,09 & & & 0,33 & 0,33 & & + ngc4303 & sabbc(rs ) & -0,13 & 0,03 & 0,04 & 0,07 & 0,65 & 0,52 & -0,01 & -0,01 + ngc4321 & sabbc(s ) & 0,04 & 0,01 & 0,06 & 0,06 & 0,61 & 0,61 & -0,04 & -0,04 + ngc4388 & sb(s ) & -0,03 & 0,01 & 0,09 & 0,01 & 0,17 & 0,17 & -0,34 & -0,34 + ngc4414 & sc(rs ) & -0,17 & 0,01 & -0,37 & 0,15 & 0,75 & 0,58 & 0,38 & 0,01 + ngc4501 & sb(rs ) & -0,24 & 0,01 & -0,34 & 0,03 & 0,76 & 0,52 & 0,36 & 0,02 + ngc4527 & sabbc(s ) & -0,24 & 0,03 & -0,14 & 0,05 & 0,68 & 0,44 & 0,08 & -0,06 + ngc4535 & sabc(s ) & 0,09 & 0,02 & 0,07 & 0,09 & 0,53 & 0,53 & -0,06 & -0,06 + ngc4536 & sabbc(rs ) & -0,29 & 0,02 & -0,17 & 0,06 & 0,54 & 0,25 & -0,08 & -0,25 + ngc4548 & sbb(rs ) & -0,16 & 0,03 & -0,28 & 0,01 & 0,87 & 0,71 & 0,49 & 0,21 + ngc4565 & sb & -0,19 & 0,02 & -0,20 & 0,07 & 0,32 & 0,13 & 0,06 & -0,14 + ngc4579 & sabb(rs ) & -0,12 & 0,01 & -0,16 & 0,02 & 0,84 & 0,72 & 0,41 & 0,25 + ngc4593 & sbb(rs ) & 0,28 & 0,11 & 0,62 & 0,03 & 0,65 & 0,93 & -0,40 & 0,22 + ngc4647 & sabc(rs ) & -0,32 & 0,12 & & & 0,83 & 0,51 & &
+ ngc4651 & sc(rs ) & -0,26 & 0,00 & -0,52 & 0,00 & 0,73 & 0,47 & 0,34 & -0,18 + ngc4666 & sabc & -0,15 & 0,00 & & & 0,42 & 0,27 & & + ngc4699 & sabb(rs ) & -0,05 & 0,01 & -0,14 & 0,02 & 0,75 & 0,75 & 0,41 & 0,27 + ngc4900 & sbc(rs ) & 0,12 & 0,01 & 0,12 & 0,09 & 0,42 & 0,54 & -0,27 & -0,15 + ngc4902 & sbb(r ) & -0,39 & 0,09 & & & 0,94 & 0,56 & & + ngc4911 & sabbc(r ) & -0,17 & 0,06 & -0,34 & 0,01 & 0,86 & 0,69 & 0,41 & 0,07 + ngc4939 & sbc(s ) & -0,29 & 0,02 & -0,36 & 0,06 & 0,70 & 0,41 & 0,24 & -0,12 + ngc5005 & sabbc(rs ) & -0,16 & 0,03 & -0,18 & 0,02 & 0,69 & 0,53 & 0,29 & 0,11 + ngc5033 & sc(s ) & -0,30 & 0,03 & -0,11 & 0,06 & 0,65 & 0,35 & 0,15 & 0,04 + ngc5055 & sbc(rs ) & -0,16 & 0,01 & -0,37 & 0,06 & 0,68 & 0,52 & 0,19 & -0,18 + ngc5188 & sabb(s ) & -0,21 & 0,10 & -0,34 & 0,06 & 0,62 & 0,41 & 0,19 & -0,15 + ngc5194 & sbc(s ) & -0,14 & 0,01 & -0,24 & 0,02 & 0,58 & 0,44 & 0,04 & -0,20 + ngc5236 & sabc(s ) & 0,32 & 0,01 & 0,25 & 0,04 & 0,47 & 0,79 & -0,20 & 0,05 + ngc5248 & sabbc(rs ) & -0,07 & 0,02 & -0,10 & 0,03 & 0,58 & 0,58 & 0,06 & -0,04 + ngc5364 & sbc(rs ) & -0,18 & 0,02 & -0,36 & 0,03 & 0,67 & 0,49 & 0,24 & -0,12 + ngc5371 & sabbc(rs ) & -0,35 & 0,03 & -0,55 & 0,04 & 0,91 & 0,56 & 0,51 & -0,04 + ngc5426 & sc(s ) & -0,22 & 0,04 & -0,33 & 0,10 & 0,53 & 0,31 & 0,00 & -0,33 + ngc5427 & sc(s ) & -0,09 & 0,00 & & & 0,52 & 0,52 & &
+ ngc5483 & sc(s ) & -0,14 & 0,03 & & & 0,63 & 0,49 & & + ngc5530 & sbc(rs ) & -0,29 & 0,04 & -0,50 & 0,02 & 0,74 & 0,45 & 0,50 & 0,00 + ngc5592 & sbbc(s ) & -0,08 & 0,01 & -0,05 & 0,05 & 0,52 & 0,52 & -0,04 & -0,04 + ngc5633 & sb(rs ) & -0,32 & 0,15 & & & 0,70 & 0,38 & & + ngc5643 & sabc(rs ) & 0,07 & 0,14 & 0,21 & 0,08 & 0,58 & 0,58 & -0,10 & 0,11 + ngc5653 & sb(rs ) & 0,31 & 0,10 & -0,09 & 0,07 & 0,24 & 0,55 & -0,12 & -0,12 + ngc5676 & sbc(rs ) & -0,22 & 0,02 & -0,40 & 0,02 & 0,59 & 0,37 & 0,20 & -0,20 + ngc5746 & sabb(rs ) & -0,17 & 0,04 & -0,45 & 0,10 & 0,46 & 0,29 & 0,29 & -0,16 + ngc5792 & sbb(rs ) & -0,21 & 0,02 & -0,20 & 0,00 & 0,47 & 0,26 & 0,01 & -0,19 + ngc5850 & sbb(r ) & -0,23 & 0,04 & -0,26 & 0,05 & 0,90 & 0,67 & 0,45 & 0,19 + ngc5859 & sbbc(s ) & -0,05 & 0,06 & & & 0,40 & 0,40 & &
+ ngc5861 & sabc(rs ) & -0,26 & 0,06 & & & 0,68 & 0,42 & & + ngc5879 & sbc(rs ) & -0,14 & 0,02 & & & 0,36 & 0,22 & &
+ ngc5899 & sabc(rs ) & -0,18 & 0,06 & & & 0,59 & 0,41 & & + ngc5907 & sc(s ) & -0,23 & 0,01 & -0,30 & 0,04 & 0,17 & -0,06 & -0,21 & -0,51 + ngc5921 & sbbc(r ) & -0,15 & 0,02 & -0,27 & 0,02 & 0,73 & 0,58 & 0,23 & -0,04 + ngc5962 & sc(r ) & -0,19 & 0,04 & -0,16 & 0,06 & 0,66 & 0,47 & 0,11 & -0,05 + ngc5970 & sbc(r ) & -0,17 & 0,00 & & & 0,71 & 0,54 & &
+ ngc5985 & sabb(r ) & -0,13 & 0,02 & -0,31 & 0,03 & 0,67 & 0,54 & 0,27 & -0,04 + ngc5987 & sb & -0,10 & 0,04 & & & 0,63 & 0,53 & & + ngc6052 & sc & 0,08 & 0,03 & -0,16 & 0,03 & 0,18 & 0,18 & 0,20 & -0,54 + ngc6181 & sabc(rs ) & -0,18 & 0,02 & -0,17 & 0,03 & 0,49 & 0,31 & -0,12 & -0,29 + ngc6207 & sc(s ) & 0,06 & 0,02 & -0,04 & 0,02 & 0,20 & 0,20 & -0,39 & -0,39 + ngc6217 & sbbc(rs ) & 0,12 & 0,04 & 0,17 & 0,03 & 0,40 & 0,52 & -0,31 & -0,14 + ngc6221 & sbc(s ) & -0,18 & 0,02 & 0,03 & 0,03 & 0,62 & 0,44 & -0,06 & -0,06 + ngc6239 & sbb(s ) & -0,05 & 0,02 & 0,06 & 0,03 & 0,18 & 0,18 & -0,39 & -0,39 + ngc6384 & sabbc(r ) & -0,26 & 0,03 & -0,26 & 0,04 & 0,70 & 0,44 & 0,28 & 0,02 + ngc6412 & sc(s ) & -0,12 & 0,03 & & & 0,57 & 0,45 & & + ngc6574 & sabbc(rs ) & -0,12 & 0,03 & -0,12 & 0,06 & 0,67 & 0,55 & 0,10 & -0,02 + ngc6643 & sc(rs ) & -0,14 & 0,01 & -0,17 & 0,05 & 0,49 & 0,35 & -0,10 & -0,27 + ngc6699 & sabbc(rs ) & -0,22 & 0,02 & -0,24 & 0,04 & 0,76 & 0,54 & 0,14 & -0,10 + ngc6744 & sabbc(r ) & -0,10 & 0,03 & 0,20 & 0,09 & 0,71 & 0,61 & 0,40 & 0,60 + ngc6753 & sb(r ) & -0,13 & 0,02 & -0,17 & 0,03 & 0,86 & 0,73 & 0,24 & 0,07 + ngc6764 & sbbc(s ) & 0,13 & 0,06 & 0,26 & 0,06 & 0,32 & 0,45 & -0,35 & -0,09 + ngc6769 & sabb(r ) & -0,20 & 0,03 & -0,49 & 0,13 & 0,76 & 0,56 & 0,42 & -0,07 + ngc6780 & sabc(rs ) & -0,28 & 0,10 & -0,04 & 0,07 & 0,76 & 0,48 & 0,01 & 0,01 + ngc6814 & sabbc(rs ) & -0,11 & 0,05 & 0,28 & 0,13 & 0,82 & 0,71 & -0,06 & 0,22 + ngc6872 & sbb(s ) & -0,11 & 0,02 & -0,24 & 0,03 & 0,52 & 0,39 & 0,31 & 0,07 + ngc6887 & sbc & -0,20 & 0,07 & -0,37 & 0,09 & 0,52 & 0,32 & 0,16 & -0,21 + ngc6890 & sb(rs ) & -0,21 & 0,02 & -0,24 & 0,04 & 0,82 & 0,61 & 0,24 & 0,00 + ngc6923 & sbb(rs ) & -0,38 & 0,04 & -0,33 & 0,04 & 0,76 & 0,38 & 0,23 & -0,10 + ngc6925 & sbc(s ) & -0,35 & 0,02 & -0,52 & 0,12 & 0,55 & 0,20 & 0,23 & -0,29 + ngc6951 & sabbc(rs ) & 0,00 & 0,05 & 0,07 & 0,07 & 0,62 & 0,62 & 0,10 & 0,10 + ngc6984 & sbc(r ) & -0,35 & 0,03 & -0,36 & 0,01 & 0,62 & 0,27 & 0,06 & -0,30 + ngc7038 & sabc(s ) & -0,13 & 0,03 & -0,27 & 0,03 & 0,63 & 0,50 & 0,25 & -0,02 + ngc7083 & sbc(s ) & -0,20 & 0,02 & -0,27 & 0,02 & 0,63 & 0,43 & 0,13 & -0,14 + ngc7090 & sbc & -0,01 & 0,06 & -0,05 & 0,01 & -0,11 & -0,11 & -0,59 & -0,59 + ngc7125 & sabc(rs ) & -0,14 & 0,01 & 0,09 & 0,09 & 0,36 & 0,22 & -0,20 & -0,20 + ngc7126 & sc(rs ) & -0,17 & 0,02 & -0,30 & 0,05 & 0,49 & 0,32 & 0,01 & -0,29 + ngc7137 & sabc(rs ) & 0,02 & 0,01 & 0,07 & 0,02 & 0,51 & 0,51 & -0,12 & -0,12 + ngc7171 & sbb(rs ) & -0,20 & 0,01 & -0,35 & 0,05 & 0,67 & 0,47 & 0,15 & -0,20 + ngc7177 & sabb(r ) & -0,16 & 0,02 & -0,17 & 0,02 & 0,76 & 0,60 & 0,33 & 0,16 + ngc7184 & sbc(r ) & -0,28 & 0,01 & -0,33 & 0,09 & 0,50 & 0,22 & 0,11 & -0,22 + ngc7205 & sbc(s ) & -0,29 & 0,01 & -0,44 & 0,02 & 0,60 & 0,31 & 0,11 & -0,33 + ngc7314 & sabbc(rs ) & -0,21 & 0,02 & -0,32 & 0,05 & 0,54 & 0,33 & 0,01 & -0,31 + ngc7329 & sbb(r ) & -0,20 & 0,04 & -0,35 & 0,01 & 0,78 & 0,58 & 0,38 & 0,03 + ngc7331 & sb(s ) & -0,13 & 0,01 & -0,33 & 0,04 & 0,57 & 0,44 & 0,25 & -0,08 + ngc7339 & sabbc(s ) & 0,08 & 0,11 & 0,17 & 0,03 & 0,32 & 0,32 & -0,37 & -0,20 + ngc7412 & sbb(s ) & -0,23 & 0,01 & -0,50 & 0,03 & 0,64 & 0,41 & 0,29 & -0,21 + ngc7448 & sbc(rs ) & -0,14 & 0,02 & -0,22 & 0,00 & 0,30 & 0,16 & -0,17 & -0,39 + ngc7479 & sbc(s ) & -0,25 & 0,02 & -0,27 & 0,02 & 0,78 & 0,53 & 0,30 & 0,03 + ngc7496 & sbb(s ) & 0,23 & 0,03 & 0,33 & 0,06 & 0,35 & 0,58 & -0,42 & -0,09 + ngc7531 & sabbc(r ) & -0,23 & 0,01 & -0,38 & 0,02 & 0,60 & 0,37 & 0,19 & -0,19 + ngc7537 & sbc & -0,22 & 0,03 & -0,08 & 0,04 & 0,30 & 0,08 & -0,42 & -0,42 + ngc7541 & sbbc(rs ) & -0,21 & 0,04 & -0,22 & 0,05 & 0,45 & 0,24 & -0,10 & -0,32 + ngc7590 & sbc(rs ) & -0,36 & 0,03 & -0,37 & 0,10 & 0,55 & 0,19 & 0,05 & -0,32 + ngc7606 & sb(s ) & -0,18 & 0,04 & -0,29 & 0,08 & 0,57 & 0,39 & 0,11 & -0,18 + ngc7640 & sbc(s ) & -0,20 & 0,02 & -0,01 & 0,02 & 0,02 & -0,18 & -0,59 & -0,59 + ngc7673 & sc & 0,12 & 0,04 & 0,23 & 0,14 & 0,19 & 0,31 & -0,58 & -0,35 + ngc7716 & sabb(r ) & -0,22 & 0,03 & & & 0,81 & 0,59 & & + ngc7723 & sbb(r ) & -0,09 & 0,04 & 0,00 & 0,05 & 0,58 & 0,58 & 0,00 & 0,00 + ngc7742 & sb(r ) & -0,15 & 0,05 & -0,37 & 0,20 & 0,79 & 0,63 & 0,32 & -0,05 + ngc7755 & sbc(rs ) & -0,13 & 0,03 & -0,07 & 0,04 & 0,74 & 0,61 & 0,05 & 0,05 + ngc7757 & sc(rs ) & -0,24 & 0,07 & -0,29 & 0,12 & 0,51 & 0,27 & -0,07 & -0,36 + ngc7782 & sb(s ) & -0,25 & 0,06 & -0,59 & 0,19 & 0,82 & 0,56 & 0,51 & -0,08 + ugc03973 & sbb & 0,13 & 0,10 & 0,30 & 0,07 & 0,30 & 0,43 & -1,02 & -0,72 + ugc04013 & sb & 0,13 & 0,05 & 0,44 & 0,12 & 0,13 & 0,26 & -1,08 & -0,64 + ccccccc ( a ) non barred face on galaxies & 26 & -0.14 @xmath3 0.01 & 0.06 & 22 & -0.19 @xmath3 0.03 & 0.14(b ) barred face on galaxies & 98 & -0.14 @xmath3 0.02 & 0.15 & 82 & -0.08 @xmath3 0.03 & 0.27(c ) non barred edge on galaxies & 46 & -0.16 @xmath3 0.01 & 0.07 & 41 & -0.26 @xmath3 0.02 & 0.12(d ) barred edge on galaxies & 68 & -0.16 @xmath3 0.01 & 0.10 & 56 & -0.19 @xmath3 0.03 & 0.20 ccccccccc g @xmath90 0.1 & ( b - v ) & 14 & 11% & 28% & 29% & 43% & 0.4cm72% & 5(36% ) + -0.1 @xmath91 g @xmath91 0.1 & & 32 & 26% & 9% & 53% & 38% & 0.4cm91% & 4(12% ) + g @xmath92 -0.1 & & 78 & 63% & 25% & 47% & 28% & 0.4cm75% & 8(10% )
+ g @xmath90 0.1 & ( u - b ) & 19 & 18% & 10% & 37% & 53% & 0.4cm90% & 7(37% ) + -0.1 @xmath91 g @xmath91 0.1 & & 30 & 29% & 17% & 53% & 30% & 0.4cm83% & 2(7% ) + g @xmath92 -0.1 & & 55 & 53% & 27% & 42% & 31% & 0.4cm73% & 4(7% ) + ccccccc g @xmath90 0.1 & ( b@xmath0v ) & [email protected] & [email protected] & ( b@xmath0v ) & [email protected] & [email protected] + -0.1 @xmath91 g @xmath91 0.1 & & [email protected] & [email protected] & & [email protected] & [email protected] + g @xmath92 -0.1 & & [email protected] & [email protected] & & [email protected] & [email protected] + g @xmath90 0.1 & ( u@xmath0b ) & [email protected] & [email protected] & ( u@xmath0b ) & [email protected] & [email protected] + -0.1 @xmath91 g @xmath91 0.1 & & [email protected] & [email protected] & & [email protected] & [email protected] + g @xmath92 -0.1 & & [email protected] & [email protected] & & [email protected] & [email protected] + cccccccccccccccc * ngc 3310 & & -0.41 & & & & & + -0.11 & -0.11 & -0.04 & & & & & 0.42 + * ngc 5033 & + 0.01 & & + 0.39 & & & + 0.01 & + & & & & & & & + * ngc 5194 & -0.40 & & -0.50 & -0.47 & & & -0.21 + & & -0.02 & & & 1.41 & & + * ngc 5248 & & & & & + 0.20 & -0.24 & + -0.38 & & & & 0.68 & & 0.75 & + * ngc 782 & -0.36 & & & & -0.10 & & + & & & 0.11 & & & & + * ngc 6769 & + 0.16 & & & & -0.18 & & + & & & 0.25 & & & & + * ngc 6890 & -0.19 & & & & -0.06 & & + & & & 0.04 & & & & + * ngc 6923 & -0.37 & & & & -0.28 & & + & & & 0.31 & & & & + * ngc 7496 & + 0.31 & & & & -0.30 & & + & & & 0.22 & & & & + * * * * * * * * * ccccc ngc 3310 & 0.00 & + 0.26 & + 0.05 & 0.35 + ngc 5194 & -0.14 & -0.12 & -0.24 & + 0.09 + ngc 5248 & -0.07 & + 0.11 & -0.10 & -0.05 + ngc 782 & -0.31 & -0.28 & -0.53 & -0.47 + ngc 6769 & -0.20 & -0.19 & -0.49 & -0.42 + ngc 6890 & -0.21 & -0.18 & -0.24 & -0.09 + ngc 6923 & -0.38 & -0.38 & -0.33 & -0.22 + ngc 7496 & + 0.23 & + 0.23 & + 0.33 & + 0.40 + | arxiv |
Why radioactive elements emit alpha beta and gamma rays
I am confused about this that why radioactive elements emits alpha beta and gamma rays WHILE other elements can't do so.
The stability of nuclei is really a sophisticated topic in theoretical quantum mechanics. But there is a simple way to think about what is happening that doesn't get too intense with the quantum mechanical theory.
Nuclei are made from two particles: protons and neutrons. But protons are positively charged and repel each other. The electromagnetic force is very strong and therefore this force is very large. So the first mystery is why all nuclei don't just fly apart.
The reason they don't is that there are two very short-range but very strong forces that bind the nucleus together: the strong and weak nuclear forces. Without getting into mind-bending topics in theoretical physics we can understand something about their net effect like this.
The interaction of the electromagnetic force and the two nuclear forces has some structure (it's quantum stuff, just accept it). Some combinations of protons and neutrons are more stable than others. Each combination has an energy level and some combinations have lower energy than others. Nuclei with even numbers of protons and neutrons are more stable than odd-odd combinations and nuclei with wildly unbalanced neutron to proton ratios are less stable. Neutrons act a little like a glue, helping protons stick together (this is an oversimplification as too many neutrons is also a source of instability: this is a consequence of a complicated interplay of several forces). But bigger nuclei are less stable and need a higher ratio of neutrons. And some large nuclei are just too large for the forces to keep them together so beyond a certain point all nuclei are unstable.
Some nuclei can be transformed into a more stable (lower energy) nucleus by various forms of radioactive decay. Nuclei with too many neutrons can emit a beta particle (this decay mode converts a neutron into a proton); elements with too many protons can emit a positron (converting a proton into a neutron). Bigger nuclei can become more stable by kicking out an alpha particle (which makes the nucleus significantly smaller, moving it towards the stable zone). Gamma radiation is associated with some of these modes: the high energy photons "mop up" the excess energy (I'm simplifying a lot).
This picture (more detail on [wikipedia](http://www.wikiwand.com/en/Stable_nuclide)) sums up what we know about nuclear stability:
[](https://i.stack.imgur.com/wWyXx.png)
To sum up: nuclei are held together by the interaction of several forces but the forces not equally effective for all possible combinations of protons and neutrons. Some nuclei have so much energy that they are unstable and can decay into more stable nuclei in various ways depending on the mix on neutrons and protons they have. In some cases the forces hiding the nuclei together are strong enough that they never decay.
| stackexchange/chemistry |
antineutrophil cytoplasmic antibodies ( ancas ) are generated mostly against myeloperoxidase ( mpo ) and proteinase 3 , and are associated with systemic small - vessel vasculitis .
anca - associated vasculitis ( aav ) is an autoimmune disease . in renal tissue ,
fibrinoid necrosis mainly occurs as a segmental lesion , representative of vasculitis of the glomerular capillaries and interlobular arteries . in vitro and animal studies
have given compelling evidence that anca interacts with and activates cytokine - primed neutrophils to cause endothelial damage .
recently , netosis , a unique type of cell death of neutrophils , has been discovered .
it is characterized by the active release of chromatin fibers , so - called neutrophil extracellular traps ( nets ) that trap and kill invading microbes .
kessenbrock et al . noted anca - dependent net formation and deposition of nets in the small - vessel vasculitis - inflamed kidney . for net formation , nuclear localizing peptidylarginine deiminase 4 ( pad4)-mediated histone citrullination is associated with chromatin decondensation and release [ 58 ] .
we investigated the association of net occurrence with the foci of mpo - aav . here , we describe concurrent presentations of the net components of citrullinated histone , pad4 and mpo around fibrinoid necrotic foci in a glomerulus and along an interlobular arterial wall with the focal class of mpo - anca - associated glomerulonephritis .
a 70-year - old man who had a low - grade fever was treated with antibiotics and a nonsteroidal anti - inflammatory drug .
he was admitted to our renal department and his condition was diagnosed as rapidly progressive glomerulonephritis . he had no family history of kidney disease .
physical examination findings included the following : height 160 cm ; weight 45 kg ; body temperature 37.2c ; blood pressure 137/72 mmhg ; edema present in both of the lower legs .
a further clinical workup indicated kidney failure with mpo - anca - positive vasculitis , supported by the following laboratory data : serum creatinine 2.19 mg / dl ( 200 mol / l ) , egfr 23.7 ( ml / min/1.73 m ) ; egfr ( ml / min/1.73 m ) = 194 serum creatinine age ) urea nitrogen 48.0 mg / dl ( 19 mmol / l ) , c - reactive protein 7.39 mg / dl , mpo - anca 276 eu ( reference < 20 eu ) , negative serologic tests for pr-3-anca and anti - glomerular basement membrane antibodies , and urinalysis showed protein ( + ) and blood ( 3 + ) .
a percutaneous kidney biopsy was performed 1 day after the admission . in light microscopy ,
the renal specimen shows a fibrinoid necrosis with cellular crescent and apoptosis - like appearance of neutrophils ( figure 1a ) .
then , the serial sections were immunostained for citrullinated histone using anti - citrullinated histone h3 peptide antibodies , for mpo using an antiserum against mpo and for pad4 using anti - pad4 antibodies in a coupled reaction with peroxidase - conjugated goat anti - rabbit igg antibodies ( figure 1b d ) .
the three antibodies were recognized to be distributed in cytoplasmic and extracellular sites , as well as the nuclei of the cells of the foci .
more exactly , double immunofluorescence staining of the section revealed the codistribution of significant signals of mpo and citrullinated histone in the fibrinoid necrosis of the cellular crescent in the lesion ( supplementary figure s1 ) .
the three other glomeruli with fibrocellular crescents showed no immunostaining for citrullinated histione , mpo and pad4 ( figure 2 ) . in the 11 glomeruli showing only minor abnormalities ,
the other view field of the sections exhibited a typical fibrinoid necrosis of the interlobular artery ( figure 3a ) .
some immunostains for citrullinated histone , mpo and pad4 were distributed in the extracellular and cytoplasmic sites , as well as in the nuclei , of the cells throughout the lesion ( figure 3b d ) . more directly , double immunofluorescence staining of the section indicated the codistribution of mpo and pad4 in the fibrinoid necrosis of the interlobular artery ( supplementary figure s2 ) .
mpo - aav was recognized as belonging to the focal class , according to the histopathologic classification .
immunostaining of renal biopsy sections from a patient with anti - glomerular basement membrane glomerulonephritis revealed no signals of pad4 , citrullinated histone and mpo in the cellular crescent of glomerulus in the lesion ( supplementary figure s3 ) .
the occurrence of net components is likely to be specific for a type of renal disease .
1.immunomicrograph of fibrinoid necrosis of the cellular crescent with the early focal phase of mpo - anca - associated glomerulonephritis .
consecutive sections of a renal biopsy from a patient with mpo - aav were stained with periodic acid - schiff , and immunostained with anti - pad4 igg , anti - citrullinated histone igg and antiserum against mpo .
( a ) periodic acid - schiff stain ; ( b ) pad4 stain ; ( c ) citrullinated histone stain ; ( d ) mpo stain . note that the signals appear concurrently with pad4 , citrullinated histones and mpo , distributed in fibrinoid necrosis of the cellular crescent .
2.immunomicrograph of a fibrocellular crescent with the early focal class of mpo - anca - associated glomerulonephritis .
the view field of fibrocellular crescent for the sections described in figure 1 is shown .
( a ) periodic acid - schiff stain ; ( b ) pad4 stain ; ( c ) citrullinated histone stain ; ( d ) mpo stain .
3.immunomicrograph of fibrinoid necrosis of the interlobular artery with the early focal class of mpo - anca - associated glomerulonephritis .
the view field of necrotizing interlobular artery is shown for the sections described in figure 1 .
( a ) periodic acid - schiff stain ; ( b ) pad4 stain ; ( c ) citrullinated histone stain ; ( d ) mpo stain .
the signals appear concurrently with pad4 , citrullinated histones and mpo , distributed in fibrinoid necrosis of the interlobular artery .
immunomicrograph of fibrinoid necrosis of the cellular crescent with the early focal phase of mpo - anca - associated glomerulonephritis .
consecutive sections of a renal biopsy from a patient with mpo - aav were stained with periodic acid - schiff , and immunostained with anti - pad4 igg , anti - citrullinated histone igg and antiserum against mpo .
( a ) periodic acid - schiff stain ; ( b ) pad4 stain ; ( c ) citrullinated histone stain ; ( d ) mpo stain .
note that the signals appear concurrently with pad4 , citrullinated histones and mpo , distributed in fibrinoid necrosis of the cellular crescent .
immunomicrograph of a fibrocellular crescent with the early focal class of mpo - anca - associated glomerulonephritis .
the view field of fibrocellular crescent for the sections described in figure 1 is shown .
( a ) periodic acid - schiff stain ; ( b ) pad4 stain ; ( c ) citrullinated histone stain ; ( d ) mpo stain .
immunomicrograph of fibrinoid necrosis of the interlobular artery with the early focal class of mpo - anca - associated glomerulonephritis .
the view field of necrotizing interlobular artery is shown for the sections described in figure 1 .
( a ) periodic acid - schiff stain ; ( b ) pad4 stain ; ( c ) citrullinated histone stain ; ( d ) mpo stain .
the signals appear concurrently with pad4 , citrullinated histones and mpo , distributed in fibrinoid necrosis of the interlobular artery .
first , the patient received steroid pulse therapy consisting of a series of three intravenous infusions of 1 g methylprednisolone plus 40 mg / day oral prednisolone for 30 days , and then ( for induction therapy ) 50 mg / day oral cyclophosphamide .
after 60 days , the patient successfully entered into complete remission , as evidenced by the following laboratory findings : serum creatinine 0.62 mg / dl ( 60 mol / l ) ; egfr 80.5 ( ml / min/1.73 m ) ; c - reactive protein 0.2 mg / dl , mpo - anca 20 eu ( reference < 20 eu ) and urine protein ( ) and blood ( ) .
sections ( 2 m thick ) of paraffin - embedded tissue from the renal biopsy were prepared . for antigen retrieval ,
the sections were microwaved in boiling 10 mm citrate buffer ( ph 6.5 ) for 3 min three times at 1-min intervals and then cooled to room temperature .
endogenous peroxidase was blocked with 3% h2o2 in water for 5 min at room temperature .
the sections were immunostained with the following antibodies : 1 g / ml rabbit anti - human pad4 igg in phosphate - buffered saline ( pbs ) including 0.1% tween 20 and 1% bovine serum albumin ( bsa ) and incubated overnight at 4c , rabbit antiserum against human mpo diluted 1:8000 in pbs including 0.1% tween 20 and 1% bsa and incubated for 2 h at room temperature , 0.2 g / ml rabbit anti - citrullinated histone ( abcam , rabbit polyclonal cit h3 to histone h3 : citrulline 2 + 8 + 17 , -chlp grade ) in pbs including 0.1% tween 20 and 1% bsa and incubated overnight at 4c .
the bound rabbit antibody was detected using a peroxidase - labeled polymer conjugated to goat anti - rabbit and goat anti - mouse igg ( envision kit / hrp ; dako ) for 30 min at room temperature and a diaminobenzidine substrate for 10 min at room temperature .
for counterstaining , specimens were immersed in a solution of mayer 's hematoxylin for 1 min at room temperature , and then mounted with malinol medium ( muto pure chemicals co. , ltd . ) . for double immunofluorescence staining
, the sections were prepared in the same way as described above and were treated with the solution containing 5% donkey serum and 1% bsa in pbs-0.01% tween 20 for 1 h at room temperature .
they were immunostained with the mixture of 25 l of 1 g / ml rabbit anti - human pad4 igg in pbs including 1% bsa , and 25 l of 1 g / ml mouse anti - human mpo monoclonal antibody 3 - 2h3 [ 11 , 13 ] in pbs including 1% bsa overnight at 4c or with the mixture of 25 l of 0.2 g / ml rabbit anti - human citrullinated histone in pbs including 1% bsa and 25 l of 1 g / ml mouse anti - human mpo monoclonal antibody overnight at 4c and then the bound antibodies were detected by incubation with the mixture of 25 l of 10 g / ml alex fluor 594-labeled donkey anti - rabbit igg ( invitrogen ) , and 25 l of 10 g / ml alex fluor 488-labeled donkey anti - mouse igg ( invitrogen ) for 60 min at room temperature .
dna was stained with 0.17 g / ml hoechst 33342 for 5 min at room temperature .
the sections were mounted by coverslips using a prolong gold antifade reagent ( life technologies ) .
on the basis of the immunostaining results , this work provided convincing evidence for the concurrent appearance of net components of citrullinated histone , mpo and pad4 in necrotizing lesions of the early focal phase of anca - associated polyangiitis . in net ,
neutrophil elastase and mpo cooperatively enhance chromatin decondensation , leading to cell rupture and net release .
mpo component acts cell - autonomously and in part contributes to host defense for innate immunity .
kessenbrock et al . noted netting neutrophils and the deposition of nets in small - vessel vasculitis - inflamed kidney .
these findings together give further evidence for the hypothesis that netting neutrophils [ 5 , 14 , 15 ] are responsible for vessel wall damage in aav syndromes , characterized by fibrinoid necrotic lesions .
as shown in figures 1 and 3 , immunostaining of sections of kidney biopsy highlighted the spontaneous deposition of the net components of citrullinated histone , pad4 and mpo in fibrinoid necrotic lesions consisting of cellular crescents with many apoptosis - like neutrophils and fibrinoid necrotic lesions of interlobular arterial walls .
however , some signals of citrullinated histones , mpo and pad4 are not always simultaneously found in both the glomerular capillary tuft and the interlobular artery , suggesting that degradation of net components in the lesion may occur in a different way and at a different rate .
the net components sustained in the lesions might be involved in developing further immunogenic responses . in particular
, mpo could act as an autoantigen in acquired immune response and in innate immunity . to date , no measurable immune complex of mpo has been observed in the kidney tissue in cases of mpo - aav .
this means that net components should be rapidly cleared . as for substantial net involvement in systemic lupus erythematosus , delayed clearance of net
is associated with development of lupus nephritis and with the onset of the disease early in childhood [ 16 , 17 ] .
in addition , mpo - ancas of individuals have recognition properties with several epitopes of mpo and also different affinities for mpo [ 18 , 19 ] .
recently , nakazawa et al . reported that nets are involved in the pathogenesis of thrombosis , in a patient with microscopic polyangiitis . determining whether net occurrence in lesions of aav is associated with mpo - ancas or not will require further research
. in summary , we report that the net components of citrullinated histone , pad4 and mpo appear concurrently in fibroid necrosis of both the glomerular capillary tuft and the interlobular artery from a kidney biopsy classified as a focal class from patients with mpo - anca - associated glomerulonephritis .
this study was supported in part by a grant - in - aid for intractable vasculitis disease research and progressive renal diseases research , research on intractable diseases , from the ministry of labor and welfare of japan . | pubmed |
numbers of penguins and is one of Australia's major shearwater breeding site.
Montague Island is home to over 1000 fur seals. Viewed from the boat on the northern edge of the island, these animals peak in number around late winter and spring, Numbers drop off to around 200 individuals after December.
Narooma is the closest access to Montague Island, 6kms east and 22kms north of Bermagui.
The island has an abundance of fish, including yellowfish kingfish, tuna, marlin, wahoo, and snapper. The Aughinish Rocks just south of the island is great for snapper.
Montague island is ideal for diving, both scuba and snorkelling. There are dangerous hazards and sharks are known to feed in the waters. So be careful!
Manta Rays, Wobbegongs, Bull Rays, turtles, Port Jackson and Grey Nurse sharks as well as schools of tropical fish, octopus, cuttlefish and nautilus. Various dive sites have hard or soft corals, sea tulips and exquisite fans. | slim_pajama |
Tension in the simple pendulum (polar coordinates)
Let's consider the simple pendulum as is displayed [here](http://www.aeromech.usyd.edu.au/AMME1550/Resources/pendulum_motion.pdf) or [over there](http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec05.pdf) (page 10). The analysis of the second Newton's law in polar coordinates goes as follows:
$$
\vec{F} = m\frac{d^2\vec{r}}{dt^2}, \\
F\_r \hat{r} + F\_\theta \hat{\theta} = m\frac{d^2 (r\hat{r})}{dt^2} , \\
F\_r \hat{r} + F\_\theta \hat{\theta} = m(\ddot{r} - r\dot{\theta}^2) \hat{r} + m(r\ddot{\theta} + 2\dot{r}\dot{\theta}) \hat{\theta} , \\
F\_r \hat{r} + F\_\theta \hat{\theta} = ma\_r \hat{r} + m a\_\theta \hat{\theta} .
$$
Substituing the forces we get,
$$
-T + mg\cos(\theta) = ma\_r = m(\ddot{r} - r\dot{\theta}^2) , \\
-mg\sin(\theta) = ma\_\theta = m(r\ddot{\theta} + 2\dot{r}\dot{\theta})
$$
Considering the restrictions $r = L$ and $\dot{r} = \ddot{r} = 0$ we get
$$
-T + mg\cos(\theta) = m(- L \dot{\theta}^2) , \\
-mg\sin(\theta) = m(L\ddot{\theta})
$$
The second one is the known pendulum equation
$$
\ddot{\theta} + \frac{g}{L}\sin(\theta) = 0 ,
$$
while the first one is a much less used equation
$$
T = mL \dot{\theta}^2 + mg\cos(\theta)
$$
¿Is it the correct equation to calculate the tension? Note that this implies that $a\_r \neq 0$; which in words means that the radial acceleration is different from zero which looks unphysical, ¿where is the trick? ¿Has it something to do with noninertial forces?
Yes this is the correct equation for $T$ and yes $a\_r \neq 0$. In fact $$ a\_r = -L \dot{\theta}^2$$
The particle must accelerate in the normal direction in order to track a radial path. If $a\_r=0$ then the path would be a straight line.
| stackexchange/physics |
successful endodontic therapy depends on thorough chemo - mechanical preparation as well as three - dimensional obturation that provides a complete sealing of the root canal system . during cleaning and shaping procedure instrumentation with various root canal instruments leaves an amorphous , granular , and irregular layer covering root dentin known as smear layer that contains inorganic and organic material .
the first researchers to describe the smear layer on the surface of instrumented root canals were mccomb and smith .
the smear layer may adversely affect the disinfection of dentin walls while blocking irrigants and sealants from entering dentinal tubules .
in addition , it may increase post obturation microleakage , and may serve as a source of nutrients for some species of intra - canal microbiota .
removal of smear layer after root canal instrumentation and before canal obturation improves the adaptation of root filling materials to the canal walls , resulting in a superior seal .
so far the most commonly used method of smear layer removal has been the chemical method using chelating agents , with ethylenediaminetetraacetic acid ( edta ) being the most common agent used . the most advocated combination of 17% edta plus 5.25% naocl
removes the smear layer completely in the coronal and middle thirds but is less effective in the apical third . for effective removal of smear layer
apart from edta new irrigating agents such as qmix 2 in 1 , mtad , have been introduced as final irrigants .
the aim of the present study is to evaluate the smear layer removal efficacy of different final irrigating solutions .
they were decoronated to get the stable reference point and to standardize the root canal length of 14 mm .
all specimen teeth were randomly divided into four groups as follows :
group 1 : saline.group 2 : edta.group 3 : biopure mtad.group 4 : qmix 2 in 1 .
patency of the root canal is established by passing a stainless steel number 15 k - file ( kendo , germany ) just beyond the apex of all canals .
canals were prepared using protaper rotary system ( dentsply maillefer , ballaigues , switzerland ) .
india ) irrigant was used between each subsequent file size in all experimental groups while saline was the sole irrigant in group 1 . to determine the effects of final irrigating solutions on the surface of root canals after instrumentation ,
the irrigating solution was delivered using a 30-gauge side - vented needle ( dentsply tulsa dental , tulsa , ok , usa ) passively placed to within the apical third of the root canals .
nonpenetrating grooves were made in all specimen teeth at the cement - enamel junction ( cej ) and longitudinally on the buccal and lingual aspects .
the teeth were then longitudinally split into two halves using chisel and mallet and the half containing the greater part of the apex was selected as the representative sample for each group and they were evaluated under scanning electronic microscope .
coded samples were mounted on metallic stubs , gold sputtered and viewed under a scanning electron microscope ( sem ) .
photographs at magnifications of 1000 were taken for each specimen in the apical third ( 4 mm from root apex ) .
the images at 1000 magnification were then analyzed for the amount of smear layer present [ figures 1a , b and 2a , b ] .
the amount of smear layer remaining on the surface of the root canal and dentinal tubules was scored according to a three score system developed by torabinejad et al .
( a ) scanning electron microscope picture of saline , ( b ) scanning electron microscope picture of ethylenediaminetetraacetic acid ( a ) scanning electron microscope picture of mtad , ( b ) scanning electron microscope picture of qmix 2 in 1
score 1 : no smear layer no smear layer was detected on the surface of the root canal , and all tubules were open.score 2 : moderate smear layer no smear layer on root canal walls but tubules contained debris.score 3 : heavy smear layer smear layer covered the root canal wall surface and the tubules .
score 1 : no smear layer no smear layer was detected on the surface of the root canal , and all tubules were open .
score 2 : moderate smear layer no smear layer on root canal walls but tubules contained debris .
score 3 : heavy smear layer smear layer covered the root canal wall surface and the tubules .
coded samples were mounted on metallic stubs , gold sputtered and viewed under a scanning electron microscope ( sem ) .
photographs at magnifications of 1000 were taken for each specimen in the apical third ( 4 mm from root apex ) .
the images at 1000 magnification were then analyzed for the amount of smear layer present [ figures 1a , b and 2a , b ] .
the amount of smear layer remaining on the surface of the root canal and dentinal tubules was scored according to a three score system developed by torabinejad et al .
( a ) scanning electron microscope picture of saline , ( b ) scanning electron microscope picture of ethylenediaminetetraacetic acid ( a ) scanning electron microscope picture of mtad , ( b ) scanning electron microscope picture of qmix 2 in 1
score 1 : no smear layer no smear layer was detected on the surface of the root canal , and all tubules were open.score 2 : moderate smear layer no smear layer on root canal walls but tubules contained debris.score 3 : heavy smear layer smear layer covered the root canal wall surface and the tubules .
score 1 : no smear layer no smear layer was detected on the surface of the root canal , and all tubules were open .
score 2 : moderate smear layer no smear layer on root canal walls but tubules contained debris .
score 3 : heavy smear layer smear layer covered the root canal wall surface and the tubules .
statistical analysis was done using kruskal - wallis h test and mann - whitney u - test using software version spss 17.0 version ( spss inc . ,
the results showed that qmix 2 in 1 ( group 4 ) showed least smear layer scores ( 1.30 0.48 ) when compared to others .
this was followed by mtad ( 2.00 0.00 ) , edta ( 2.40 0.52 ) , and saline showed highest smear layer scores ( 3.00 0.00 ) .
during mechanical instrumentation smear layer formation occurs on the root canal dentinal wall occluding dentinal tubules , for efficient disinfection and sealing of the root canal system its removal is necessary .
irrigation is an important step during and after instrumentation for effective removal of smear layer and also for lubrication of root canal system .
naocl is the traditional irrigant which is used most commonly , however due to its inability to remove inorganic part of smear layer other irrigants were introduced .
there are different final irrigating solutions which are used after instrumentation for effective smear layer removal .
qmix 2 in 1 is a new root canal irrigating solution , and it contains a mixture of a bisbiguanide an antimicrobial agent , a polyaminocarboxylic acid , a calcium - chelating agent , saline , and a surfactant .
eliot et al . evaluated the effectiveness of the three different formulations of qmix on the removal of canal wall smear layer and compared to a standard solution of 17% edta .
sem analysis showed the effectiveness of all three qmix formulations were superior to edta in smear layer removal and exposure of dentinal tubules in the root canal system in single - rooted teeth .
analyzed the precipitate formation on the surface and in the tubules of dentin irrigated with sodium hypochlorite and a final rinse of chlorhexidine or qmix and concluded no precipitates or pca were detected with qmix and naocl in dentinal tubules .
evaluated efficacy of a novel root canal irrigant , qmix , against enterococcus faecalis and its ability to remove smear layer was examined , using sem .
it was concluded that qmix and naocl were superior to chx and mtad under laboratory conditions in killing e. faecalis and ability to remove smear layer by qmix was comparable to edta .
this was also supported by studies done by ballal et al . , who showed that wetting of root canal dentin was better with qmix 2 in 1 due to its low surface tension .
these studies correlate with our study ; qmix 2 in 1 showing better smear layer removal compared with other final irrigating solutions and there is a significant difference among all the groups .
dai et al . , evaluated the smear and debris scores of qmix in the coronal third , middle third , and apical third of root canals using two versions of qmix 2 in 1 ( qmix i [ ph = 8 ] , qmix ii [ ph = 7.5 ] ) using sem .
it was concluded that the two versions of the experimental antimicrobial ( qmix ) are as effective as 17% edta in removing canal wall smear layers from the entire root canal space in straight root canals after the initial use of naocl as the initial rinse .
biopure mtad is a mixture of tetracycline isomer ( 3% doxycycline ) , 4.25% citric acid , detergent ( 0.5% polysorbate 80 ) .
is used instead of its free - base doxycycline monohydrate , to increase the water solubility .
it is considered to be clinically effective and a biocompatible endodontic irrigant . in this study
mtad shown to be next to qmix 2 in 1 in removing smear layer , this may be because of its low surface tension ( 34.5 mj / m ) , these results correlate with the study conducted by paul et al .
, who showed that mtad is better irrigating solution removing smear layer even in apical third .
shenoy et al . , compared the smear layer removal efficacy of tublicid plus , mtad , edta and found that tublicid plus and mtad are better when compared to edta .
within the limitations of this study , it was observed that among the final irrigating solutions used qmix 2 in 1 displayed effective smear layer removal when compared to edta , mtad and saline . | pubmed |
Glee 1. I Wish I Could Save You
This story holds dark themes so you've been warned.
Disclaimer: yep, still don't own Glee. Evidence? Note the lack of Puckleberry smut on my TV screen.
* * *
"Hey, Puckerman, coming to my party tonight?" Puck looked up from his duffel bag, raising an eyebrow at Azimio. Normally, the boy wouldn't even look at him without saying some smartass comment about Glee club or Puck's relationship with Lauren. Then Puck would get into his face and say something equally badass and scary and Azimio would back off, grumbling about how Puck's all bark and no bite.
Right. That's why Puck was two minutes away from bashing the asshole's head in with his guitar.
Puck stood up straight, throwing the strap of the bag onto his broad shoulder. "There gonna be beer? I need some alcohol," Puck replied, shutting his gym locker and grinning at the dark-skinned boy. Azimio nodded wordlessly and shut his own locker, pulling on his bag then started towards the locker room door, opening it.
"Yeah, see ya there." Puck nodded and walked out after him, advancing in the opposite direction. Suddenly, Sam had caught up with him, his own bag in his hands. The usually talkative blond just nodded at Puck and continued to walk beside him, singing a rap song under his breath.
"What are you singing, Evans?" Sam looked up in surprise then grinned, evidently glad that Puck had asked.
"No Hands by W-" The tall, lean boy was suddenly cut off by a heart-breaking scream. Both looked at each other, confused when yet another screamed echoed through the empty halls. Puck's chest clenched because suddenly, he knew the only person who hit a high note like that. Panic filled his lungs and he couldn't breathe. Sam looked towards him, shock covering his usually bright sky-colored eyes."Dude, what the hell was that?"
Puck started to run towards where he heard the scream, shaking his head and dropping his duffel bag on the cool tile floors. "That's just it. Not what, _who_, Evans," He stated, clenching his jaw. Sam quickly matched his pace, dropping his bag as well. Another scream pierced the air. All that was going through Puck's head was what could happen if he didn't get to her in time. He turned a corner and a sob almost crawled out of his throat at the sight before him.
Three unidentifiable boys were crowding a form on the floor, making Puck clench his fists. One was getting up off the floor, zipping up his jeans. Another was kicking the bloody body on the floor and the last was looking around suspiciously. The third caught sight of Puck and Sam and signaled to the other two that they had company. The first one smirked and grabbed his two friends by their sleeves sprinting down another hallway. Sam took off down the hallway and down the other, chasing the three boys who were loudly cackling throughout the empty building.
Puck, however, lingered behind, walking slowly to the body. With all his air, he murmured the prayer they used in Temple under his breath, praying that she was alive, that she wasn't just _raped_. He knew the latter was in vain because he could see her skirt lying behind her, completely soaked in her blood. He held his breath until he was inches away from the sobbing girl who had already sat up and had her face in her hands. "R... R-Rachel?" The sobbing had slowly faded and she looked up, her beautiful chocolate brown eyes filled with fear and it _broke_ him. It made him wish he had gotten here sooner, that he had actually saved her.
"No, no, no! Get away,_ get away from me_!" She shrieked and swatted at him briefly before scooting away, sobbing uncontrollably, hands covering her head. "Don't.. please, I'm-I'm begging you," She pleaded, tears dropping onto the bloody tiles around her.
"Rachel, please. It-It's me, _Noah_," He desperately murmured, dropping to his knees. His hand tentatively touched her bare shoulder where they had ripped at her shirt and she didn't shrink away. A sigh of relief came from him and he felt like maybe everything was going to be okay as her heartbeat and breathing had steadied. His heart then broke when her body visibly flinched as a result to his hand moving to her arm to see the scratches inflicted. They had done it. They had done what Quinn and himself and Finn and Santana and Jesse had failed to do.
They had broken her. They had broken Rachel Berry, the star. They had taken her innocence, left her with an experience she'd never forget or possibly move on from. She would never get that romantic first time she had always desired and she would most likely never fully trust another human being again.
"N-N-Noah?" He broke away from his thoughts and looked at the petite girl sitting in front of him. "Noah?" He touched her in response and although she whimpered and shrugged it off, he was relieved to know that she at least somewhat trusted him. "I.. I wanna go home. I wanna go to bed." Her voice was soft and cracking and she sniffled at the end, hands moving from her head to wipe away tears.
"You can't, Rachel. You need to go to the hospital. I-I think Mr. Schuester is still here. Wait here, okay? Just stay right here." He went to stand up and she started to sob and shaking her head, grabbing his hand.
She sniffled loudly, tears running down her red cheeks. "Don't! Noah, please don't leave me. What if they-they come back for more?" Sighing, he realized she was right. If they did come back, she could be even more damaged than before. He nodded at her then picked her up bridal style, trying desperately to ignore the way she squeezed her eyes shut or avoided any unnecessary contact.
He started to walk away, towards the Spanish classroom which he knew was down the right hallway. She squirmed in his arms, obviously uncomfortable since her blouse and skirt was torn to shreds by those bastards. When he got to the room, he kicked open the door, successfully getting his Spanish teacher's attention.
"Puck? Why did you just-" He stopped getting up when he saw Rachel with her hair matted with blood and her clothes barely there. "What happened?" He got up, walking over to Rachel. Puck was sure she was going to freak out but from the journey over here, she had managed to fall unconscious. Thankfully.
"I.. Me and Sam, we were walking down the halls from football practice and we heard her screaming and she was down the left wing hallway, three boys beating her and Sam ran after them and I stayed back to help her and please, Mr. S, please help me." His voice broke with desperation as he finished his long sentence. His teacher rubbed his face, tears building up. Nodding, he grabbed his keys and walked out with Puck, glancing at the deep scratches on the poor girl's arms with shock.
Sam suddenly rushed up to them as soon as they were out in the hallway, panting and a bruise forming on his cheek. "They ran away, sorry, Puck." His normally bright blue eyes had darkened and they lowered to the tiny, broken girl in his arms. His face turned serious and he looked up at the two other males in the area. "You guys do know that her life will never be the same?"
Mr. Schuester nodded and lowered his head to look at his shoes. "Boys, this is deadly serious. I think you should come with her to the hospital, to describe the situation to the police." Puck couldn't even imagine why his teacher would think he would do anything else. Sam just nodded. Then they all walked out the school, save Rachel, deadly serious expressions on. When they got to the beat-up car of their choir director, Sam opened the backseat door for Puck to put the unconscious girl in and he obeyed the silent demand, making sure she didn't bump into anything because he wasn't sure how serious her injuries are. But then again, from this angle, it looked as though her ankle was twisted. Shaking that from his mind, he clambered in after, letting Sam shut the door. The blond boy then sat in the passenger seat, beside their Glee Club coach. With a turn of his keys, they were peeling out of the parking lot and driving fast towards the hospital.
All Puck could think was that he was going to make sure with all his might that she was alright.
2. A Beautiful Disaster
I don't really like this. Yes, I'm not sure where I'm going with this. I'd absolutely LOVE suggestions on what to do. Obstacles and people to help Rachel out and the like. So yeah, review and leave in what you think would be good.
Disclaimer: if i did own Glee, Finn wouldn't be here.
* * *
Puck never did like hospitals, you know. they're full of people who smell of rubbing alcohol and wear all white as though it's not the most disgusting place in town, full of infections and shot wounds and the like. Lima General Hospital sucked most of all. The doctors were all male and seemed to never show up on time. The nurses were all young and snooty except for one, Puck's mom. She seemed to be the only qualified person to be treating people there. And yet, she barely made enough money to keep Puck full(which, he admits, is a hard job in itself) and his sister entertained and happy. She worked hard, she gave life her all and yet she was single, a mother of two rowdy kids, and basically working herself to death. He hated the hospital with all his might and if he could, he would never set foot in it.
But yet again, a certain Broadway-loving, immensely talented midget changed his opinion about it.
A sigh escapes his lips before he can help it and Sam glares tiredly at him. "Puck, come off it. They're doing their best." A snort almost comes out but Puck holds back, smirking. Sam has obviously never been in Lima General.
"You've never been to the hospital here, have you?" Warily, Sam shakes his head no and Puck nods as to say, 'There you go then' and shifts uncomfortably in the plastic waiting room chairs. Mr. Schuester was already gone, saying something about telling her fathers about the incident. Puck had almost snickered at his glee club coach. Like her fathers cared. But the curly-haired Spanish teacher was probably trying to reach them in, what, Rome? Ireland? England? Who the fuck knows where they are.
Well, except for their unconscious daughter.
The magazines on the wooden table in front of him and Sam are from like, 2009 and Puck is tired of reading about Kanye West and that blonde chick again and again. He sighs yet again, more frustration poured in and Sam doesn't say anything, just mumbles under his breath about the stench of hydrogen peroxide. Then, fin-fucking-ally, a doctor with gray streaks in his brown, kind of shaggy hair, walks over, eyes scanning his clipboard.
"Yes, uh, the family of Rachel Berry?" He says and looks up, taking one look at Sam and furrowing his brow. It's pretty obvious that Sam's not related to her(the kid's pale as Casper and blond as Brittany) and so Puck speaks up before the doctor can question about it.
"We're not family," Puck mumbles, not looking at the doctor. It was weirdly embarrassing to admit it. Sam turns pink.
"Oh. Then friends?"
A pause comes over them and then Sam's the one to speak up, staring at the floor in shame. "No. We're... we found her, I guess." Puck closes his eyes, sighing in defeat. They found her. _Found_ her. They should have saved her from all this. The guilt drenched knife plunges down his throat and he swallows thickly, ignoring the stinging behind his eyes. The doctor doesn't speak for a few moments and Puck opens his eyes hesitantly before seeing that the man in the white cotton outfit is gazing at him with strong sympathy.
Sam clears his throat and the middle-aged man looks quickly down at his clipboard, coughing. "Well.. She's fine. Not completely, mind you. There's her broken wrist so that's in a cast. And she's got some bruising along her collarbone and ribs which means she'd need to rest for at least a week. The cast is gonna need five weeks. But other than that, fine."
Yeah, if you exclude the rape. Puck stares at the hallway in which her door is located. Sam gazes at it too. "Oh yes, she should be waking up soon. You can see her. Just try not to upset her. Upsetting her can.. can do some drastic things." Whatever the fuck _that_ meant.
Getting up, he and Sam lock eyes and nod at each other. They both know what they're going to face. Puck knows how much he will want to cry and Sam knows how much guilt he will feel. But they have to be strong for her, for Rachel Berry, the strongest person in Ohio.
Following the doctor down the hallway, they pass by plenty of rooms, rooms with lots of family in it and rooms with no one but the victim. Something that tastes horrible crawls up his throat but then again, he thinks determinedly to himself, they're visiting her. She's not alone.
"Ah, here she is. Room 789." With a nod and a vague 'good luck', they're in the room and shutting the door quietly. Turning to the bed, Puck's stomach lurches in his throat and Sam's whispering a prayer that the other boy is _sure_ came from Quinn.
The doctor said she was fine! He fucking lied, obviously. Her face was contorted into a face that one would make when experiencing a nightmare. The skin across her eyebrow is split but threaded back together with stitches. Most of the skin on her cheekbones is purple and slightly yellow, surely going to turn uglier shades later on. And the slight bruising along her collarbone? Yeah, right. There's nothing slight about it. It was dark purple, an angry violet, creeping up a little along her neck. And her wrist is laying on her stomach, wrapped in a white cast, starting from the middle of her forearm to the middle of her palm. It is also wrapped around her thumb. Puck suddenly remembers that this is her left arm, the arm she writes with. And they were only a month away from Regionals. She was hellbent on writing a song for them to perform. But how would she do that now, with her wrist broken? She would be upset, heartbroken even, to see that some of the simplest things in life to do, she could not.
She is anything but fine and it's evident. Sam stares at her, horror reflected on his face. Puck turns away, hands itching to grab the boys responsible and stop their breathing for a few moments and make them look at her right now. He wants them to see the destruction they had caused.
Sam chokes on a sob and Puck snaps out of his thoughts, shoving the bleached-haired boy in anger. "Shut the hell up, Trout Mouth. What if she wakes up and hears you whining like a bitch?" Sam glares back, eyes shining.
"What's with the mouth jokes, man? It's not even relevant anymore. It's not even that big!" Sam practically shouts. Puck glares harder. He really doesn't have the patience for this shit. Not right now anyway.
"Okay, fine! No more mouth jokes. God, when did you become such a little bitch? After Hudson stole your girl out from under you?" Puck hisses, raising an eyebrow in satisfaction when Sam's face screws up in fury.
"He didn't steal her!" Puck snorts. "Don't you fucking snort! He didn't! I broke up with her. She was crying! She still loves me. She just.. She's only with him because.. because.." Puck at first thinks he's trailing off because he doesn't even know why Quinn and Finn are fooling around. But the other boy's eyes widen comically and Puck whips around in a hurry, watching with shock as the tiny girl in the hospital bed sits up and rubs at her eyes with one hand, obviously knowing that her other is rendered useless. She yawns and runs her fingers through her brown hair, not noticing the boys frozen in shock. Opening her eyes, she stares down at her cast, analyzing it with a horror-stricken expression. When she was done with that, she stares at the tiny cuts Puck and Sam failed to notice along her other arm. Then, as though they only just came into the room, she slowly looks at Puck and Sam.
Then she screams. She screams louder than any high note she ever sang in a song. She screams like they were the one who did this to her. She scream so brokenly that Sam starts to sob, loudly, and he runs out of the room, looking green. She's still screaming when Puck tries to walk towards her. "Rachel! Rachel, it's me, Noah!" She falters, tears falling endlessly on her bruised cheeks. She's coiled up on the bed, as far away as she can be from him. It breaks his heart more than he thought it would.
"N-Noah?" It's not Rachel. It can't be. Rachel Berry wouldn't sound so broken. Rachel Berry wouldn't be so scared of him. Rachel Berry was gone, it seems. She locks eyes with him and then he thinks that maybe, just maybe, everything will be fine. Maybe she'll move on eventually and then they'll get together and they'll live happily ever after and those three boys would go to jail for the rest of their lives. However, life just didn't like him very much.
He knows that because right after she calmed down, three male doctors came in and everything just went to shit.
3. Middle Of The Ride
It had been a week since that fateful incident. A week packed with questions from the police(with no answers given) and poking and prodding from men in white lab coats. A week full of nurses begging her to speak, to utter 'yes' or 'no'. A week interrupted daily with biological mothers, sympathetic Spanish teachers and OCD guidance counselors. A week that was much too long for a girl named Rachel Berry.
She was reading at the time, nose buried in a book named The Cure(A/N: sorry. my Spanish teacher has recommended it to me and I just had to put it in. Fantastic book.). It seemed very good when Shelby came around with a box full of a books for her to choose from. Apparently, their new connection was not Broadway or sewing but books.
Gemm, a teenage boy living in the future, had just chosen the cure(hence the name of the book) and was being strapped down when the door beeped then swung open with a bang on the wall behind it. A nurse rushed in, a heavy white paper bag with twisted paper handles in her left hand.
"Well, Ms. Berry," Said the young blond, eyes twinkling with excitement. Rachel stared in momentary shock before closing her book, allowing the older woman to continue. "You're being checked out! Your father has come to get you." Well, this was a big shock to the mute brunette in the stark white bed. For eight days, her fathers had took their sweet old time to come home from England and now her father, most likely Leroy, just randomly arrived and was ready to pick her up?
Silence passed for a few seconds, surely full of the nurse waiting for a response. She was new, evident by her expectant expression. It was now known to every nurse and doctor dealing with the young girl that she never talked anymore. She did, however, tap imaginary piano notes onto any stable surface whenever she could. "Okay, well, uh, this bag is for your cast," At this, the young singer looked at her wrist which was blocked as a large, thick, white cast generating from about the forearm, maybe longer than that, and to the start of her palm but wrapping around her thumb, just enough to expose the top. "To put on when you're showering and such. In about three weeks, you can come back to get it taken off. Oh, and your outfit is right here." And with a pat of her hands on the pants sitting on one of the chairs, she walked out, humming a tune.
With careful delicateness, Rachel unwrapped the blanket around her to not brush across her extremely sensitive bruises. Then she stood up on slightly wobbly legs, ignoring that sick feeling in her stomach as she grabbed the outfit, minus the shoes, and walked to the bathroom, shutting the door behind her. It seemed almost impossible to undo the tight knot that held her hospital gown together. When it fell to the floor, she felt exposed, so exposed that tears brimmed her amber eyes and she felt the air hastily go out of her lungs. Visions of boys with perverse grins filled her mind and she hyperventilated to herself, trying not to scream.
Her lungs felt like they were shrinking and her throat seemed to be blocked by something invisible. No air could get through and her mouth was clenched, trying not to let out her screams. She thought she felt hands rubbing her exposed skin and the bright lit room seemed to get dimmer and dimmer by the minute. She was sure that she was going to die from the pain.
However, as quickly as the panic attack(she would find out later by searching it up) had invaded her, it left without a warning, leaving waves of air flowing freely to her pained lungs.
She took a minute or two to calm herself down and wipe away the tears before pulling on the black long-sleeved blouse and white sweatpants with elastic around the ankles. She loved her father for thinking of how she'd feel in her old clothing. With a nostalgic sigh, she pulled her hair into a ponytail, eying the ugly bruises decorating her cheeks. They were faded and could have easily passed for a bad makeup job. The cut above her head was covered with a thin white bandage to avoid blood trickling down her head. Overall, though, she looked fine. Well, from the neck up. From the neck down, she was covered with cuts and bruises and a _cast_, for God's sake.
"Baby? Are you ready?" She jumped out of her deep, trapping thoughts at the deep, low voice in the main room. She warily rolled up her sleeves, trying to avoid bumping her arm into anything. Picking up the gown, she looked around before walking out and setting it on the bed. Her father, Leroy, was big and buff, his dark brown skin standing out against his white and black striped polo shirt. His deep green eyes stared at her bruises and cast and they softened immediately as well as glistened with tears. He rushed to her and enveloped her with a hug. She felt uncomfortable at first, he never was very affectionate, but eventually she sighed into it, feeling a warm emotion she could only label as love flow from his skin to hers. She just really needed a hug.
"I'm so sorry," He mumbled into her hair, voice cracking with guilt. She tightened her arm's hold around his waist and tried to will her tears away but to no avail. They flowed from her eyes and onto her cheeks, stinging the bruises slightly. With a sigh, he rubbed her back in comfort, humming a tune. It took a few moments but eventually Rachel pulled away, wiping at her eyes with an embarrassed smile on. "I'll never leave you again, Rachel. I'll.. no one will ever hurt you again. I promise," He declared with a steely sort of tone. Rachel stared up at him before sniffling and pulling on her socks and shoes. She wanted to believe him, she really truly did.
However, she wasn't a little girl and he wasn't a bodyguard. He couldn't ensure that she wouldn't be hurt ever again and obviously, he couldn't just stay by her side forever. She wanted to believe he could but the incident had made her a realist. The Oscars, and the Tonys and the Broadway dreams? That's just it. They were dreams. She couldn't possibly think she was the best thing ever and there was probably a million other small town girls with big voices. She shook her head, banishing the depressing but dishearteningly true thoughts. He grabbed her book and bag and off they went, both mentally praying for normality to come.
It didn't.
She didn't know what she had expected but she expected to come home to silence and emptiness yet again and to frozen TV dinners and just something other than the warmness that enveloped her as soon as she stepped in. Hiram, her second father, smothered her with kisses and though she flinched visibly in terror, he continued to hug her and murmur promises that did nothing to shake her realist beliefs. The loving feeling was slowly fleeting. It was fading in her chest, leaving the hopelessness and depression she was now used to.
She nodded towards the stairs and although her fathers were notified of her lack of speech, they stared at her mouth with a look of pure disappointment. Guilt was swimming in her stomach and she turned away, walking up the stairs and stopping in front of her door. It made her sick, the brightness that seemed be the mood of her bedroom. She gulped and then, with no thinking at all, she tore it all off, not caring that her wrist was throbbing with pain from being tried so hard so early into its process of healing.
All of it was on the floor now. The smiley faces, the large plastic gold star hanging, the stickers surrounding it, everything. She wasn't a star, she wasn't amazing. She wasn't anything anymore. She was a girl who was foolish enough to think that life was easy and that same life came and bite her in the ass. She had to live with this now. She clenched her jaw and stared at the destroyed decoration on her wooden floor in the empty hallway, ignoring the hot tears racing down her bruised cheeks. She rushed into the room and sat down on the bed, drawing her knees to her chest. She pushed her palms into her eyes, trying to block out the world. Her teeth dug into her bottom lip so hard that she could taste the metallic liquid.
She stayed like that for a while, rocking back and forth, mind blissfully blank and breathing steady and calming. Then her phone buzzed and she jumped, her position forgotten. She stared in horror at the bedazzled Blackberry before sighing and picking it up.
There were 10 missed calls, 3 voice messages, and 14 texts. She went through the texts first, scrolling past with a frown.
_'Berry, where r u? NATIONALS SETLIST MEETING, MEMBER?'_ from Santana.
_'i thought we had a starbuckz run? nvm then. thx.'_ from Kurt.
_'r u rlly dis upset ovr what i said? sorry for speakin da truth.'_ from Quinn.
_'we need u at glee. don't be a drama queen, diva.'_ from Mercedes.
That was all from the day after the incident. The rest were scattered throughout the week.
_'dont worry, its not my job to tell any1.'_ from Noah. Her chest tightened.
_'did u like die, or somethin? come back pls.'_ from Finn.
_'Ms. Pillz told the club. They no what hpned.'_ from Sam. Her eyes grew wide and the brunette pursed her lips to keep from crying.
_'oh god. i'm so so so so so sorry.'_ from Santana. She stared at the message, shocked.
_'i'm heree forr youu, Rachh.'_ from Tina.
_'if you want, i can beat up every guy in Lima until i get to those boys! (:'_ from Mike.
_'r u ever coming back? i need to apologize, rach.'_ from Quinn.
_'If you need anything, I'm sure my cat will help you out. Sorry Broadway.'_ From Brittany. Or she could assume it was Brittany. She didn't think that was her type of texting but then again, the adorably naive blond always amazed her.
_'we need to talk if ur gonna be ignoring me. thought we were friends? w/e then.'_ from Kurt.
'shelby told me. can we talk?' from, surprisingly, an unknown number in Los Angeles. Somehow, she had a feeling it was Jesse.
Sighing, she deleted them all with no hesitation. She didn't want to think about how upset they were. She deleted all the missed calls and then dialed her voicemail, putting it on speaker. "Please enter your passcode and then press pound," The monotonous woman spoke and Rachel obliged before listening closer. "Monday, March 28th, 2011, at 3:50 PM from the number -." Then it beeped and a whimper immediately echoed through the phone.
_"Oh my god, Rachel!"_ She could hear Quinn weeping and Tina's fearful tone made her close her eyes to calm down. _"I'm-I'm so sorry. I thought you were just being a drama queen... oh god. you were r-r-"_ Tina didn't finish and started sobbing. The sound jostled as though the phone was being handled over.
_"I'm sorry. I'm so fucking sorry. I always bullied you and I was just jealous. You were so strong and determined and you weren't side-tracked by anything and now you got hurt and I swear to god, if they find those boys I will fucking tear out their throats and shoot their di-"_
_"Santana!"_ Mr. Schuester shouted, apparently having had attempted to calm down the Latina. Rachel almost smiled.
_"Whatever! I-I can't-"_ Santana's words became garbled and no one was able to calm her down, it seemed. Someone else took the phone and she could hear the crying more louder than normal. She flinched at the raise in volume.
_"I'm such a jerk!"_ Finn shouted and Rachel found herself nodding along. _"I didn't forgive you for making one little mistake and you might have died and god, if you did and I never got to accept your apology, I wouldn't be able to live with myself. I hope you're doing okay."_ Another person snatched the phone and they walked away because the noises of crying and comforting words faded slightly.
_"I didn't tell them. I swear. God, I just... I wish I could save you from all this. I know you're hurting and I know that those boys, they broke you but I promise, I fucking promise, me and Sam will put you back together. You don't deserve this."_ She immediately turned off her phone after the message ended with a beep. She took out the battery and set it in her sock drawer. Then she did what she had been wanting to do since she woke up. She pulled off her shoes and socks and crawled under her blanket, wiping away falling tears. She fell asleep, dreaming of tear-filled eyes and about fourteen arms reaching out to hug someone just one inch away. They couldn't get her, even if they stepped closer.
She was just too faraway for anyone to reach.
4. It Consumes You
**Ooh. You guys probably hate me. Sorry. My fault. Serious Writer's Block, guys. So I've been thinking about the storyline and I think that the day Quinn told Rachel she didn't belong was the day after Regionals, am I wrong? So let's pretend that Regionals was after school. Rachel missed Regionals and because they were all sure they'd win, they had a Nationals Setlist Meeting the day after. I suppose that makes sense. So okay, I'm good now. Review please. I love reviews. (:**
* * *
"So how are you today, Rachel?" How was she? She was annoyed, she was sick and tired, she was sick and tired of being sick and tired-
_She was screaming in pain and they all just laughed at her attempts to shout through the tape, their alcohol-stained breaths invading her nose and mouth, she tried, really, to crawl away but-_
She shrugged, nails picking at the leather chair and eyes on the bookshelf behind the professional looking woman sitting in front of her. It was filled with books, thousands of them it seemed. She remembered a book she once read called It's Kind Of A Funny Story, that was maybe a movie, she wasn't sure, and the boy had said all the good 'shrinks' had a book of diseases. Her eyes scanned the titles but she quickly realized that the woman was talking. She could look at it at another time.
"-your fathers told me something, Rachel." Rachel kind of liked her. She had this kind of trusting, sweet-faced look to her. Her hair was down though and a lovely shade of blond. The kind of blond that you could argue was either a really light red or a dirty blond. Her eyes are narrow and cat-like in a way and a normal shade of brown. She wasn't skinny like most women her age(about 22) but she wasn't overweight either. She was a very nice weight of what Rachel guessed to be about 135. The woman, her name was Miss Savory-Felton, always smiled at her. Not a smile that says, 'Hey, come talk to me because your fathers are paying 160 bucks an hour' but a smile that makes you open up. Or maybe they were the same.
Rachel nodded, looking at her with an arched eyebrow, something she picked up from Noah. Ms. Savory-Felton cleared her throat, clearly uncomfortable with her not speaking. Nodding, she stared at her notepad. "You like to sing, don't you?"
Used to.
Rachel nodded, not bothering to correct her. "Oh, that's lovely. I like to sing as well. I'm in my church choir, you know. Are you? In a choir, I mean." Rachel nodded again and Ms. Savory-Felton wrote something down.
"I heard what happened, you know."
Well, obviously.
Rachel didn't react.
"Do you blame yourself?"
_"Hey, doll, I'm lost, can you help me?" She stared at the three guys in a flaming red car, leering at her. Glee Club was almost starting and she should really be getting back into the school and out of the parking lot. "Come on, darling, just for a minute. I need to get to a phone."_
_"I have a phone," She answered, looking quite nervous. She had this feeling that they didn't need a phone but she ignored it, pulling out her Blackberry and checking her messages, seeing one from Santana but she didn't look at it. They grinned at each other and all got out of the car, stepping towards her in a clumsy way. It now apparent they were drunk._
_"Why are you backing up, baby? I just want to use your phone," He stated, slurring his words and smirking in a creepy way, not like Noah. Oh, she wished Noah was here. She backed up again, putting her phone away and looking around for anyone. She had stupidly forgotten her rape whistle. Damn._
_One's hand grabbed her wrist and she panicked, shaking him off and whimpering in fear. "Help!"_
_ His face easily turned menacing. "You shouldn't have done that."
_
_She turned around, quickly walking to her school, opening the doors and sprinting in, panting. Her mistake, she ran in the one farthest from anyone in the school. She could hear their angry calls and she turned a corner, seeing the end of the hallway was the doors to the boys gym locker room. Noah was probably getting out now, planning on skipping Glee to shower, he told her earlier. _
_Before she could get closer, a hand snapped closed around her waist and another over her mouth, silencing her scream. Silencing her completely. _
She didn't answer, mind in a painful memory. "Rachel. Do you blame yourself?"
A nod escaped her and her therapist stared at her with an unreadable expression before writing something down on her notepad. "I've read your medical report, Rachel." She flinched. "They really hurt you."
_He tore at her shirt and she squirmed under his weight on her waist, tears streaming down her face and onto the waterproof duct trap on her mouth. She felt the cool air nip at her chest and he grinned at her then began to tear her shirt more, the fabric's rips cutting through the air. _
_\Her arm escaped his friend's grasp and she punched him in the face, her fist burning with the contact of his hard nose. Their laughs silenced, her shirt stopped ripping and she stared in horror as the man's hand touched his bloody nose and his flaming eyes looked at her. "You bitch."_
_Before she could even blink, he stood up and stomped on her chest, making it erupt in pain. She cried out but the duct tape muffled it. He kicked her chest and stomach and face and from the red filter-like vision she was seeing through, she knew he cut into her. He stopped after a while, panting and kneeling down. "Ain't so tough now, are you, slut?" Then he proceeded to pull her now bloody skirt down and she kicked and screamed loud through her tape, praying that someone save her. _
_No one did._
Her tears raced down her still bruised cheeks and she nodded, looking out the window. Silence overtook them for a few minutes before Ms. Savory-Felton spoke softly. "Rachel, this isn't going to consume you. I won't let that happen. Your dads won't. Mr. Puckerman and Mr. Evans surely won't. You shouldn't." Then a buzzer went off and the older woman sighed. "That's all for now, I'll see you next Tuesday."
Rachel stood up, shook hands with the blonde and then proceeded to step out into the waiting room, waiting for her father to get ready. She glanced at the other people in curiosity. She wondered if one of them doesn't speak either. Stepping outside of the building and getting into the backseat of her father's car, she noticed the pink bookbag on the floor of the vehicle. Her eyes narrowed. He got in minutes later and she glared at him. He sighed, his gaze lowering to his shoes. "You need to go back to school, Rachel." She didn't want to though. Why did no one ask her what she wanted?
A small part of her answered in a voice eerily sassy like Santana, "Because you don't even speak. What, do you want a pen and a piece of paper and everyone to wait on you hand and foot? Life isn't fair. You should know that by now."
"If it gets to be too much, you can go to the office and call me to pick you up." She stared at him, unsure. "Please... for me." Leaning back into her seat and buckling up, he took that as a yes and drove off toward her high school.
Her breath hitched and she wanted to to go into another panic attack, anything to stop from going back there. Anything to stop from reliving those memories. Anything to stop from seeing people who cared about her. She didn't want anyone to care.
Knowing that she had support just made her fall even more. She couldn't help but hate herself a little because for some reason, for some weird reason, their caring wasn't enough. She was still alone and she was still falling into this depression.
Her father parked right outside of the school and she stared out at the window at the empty parking lot but full building.
He turned halfway, looking at her through the rear view mirror. "It's okay, Rachel. We care." She nodded and got out out of the car with a note in her hand, shutting the door with her other, the other with the broken arm attached. She walked inside the school, mind racing with one question only.
So why did she feel so alone?
End file.
| fanfiction |
John George Weld Weld-Forester, 2nd Baron Forester PC 9 August 1801 10 October 1874, was a British Tory politician. He served as Captain of the Honourable Corps of Gentlemen-at-Arms under Sir Robert Peel from 1841 to 1846.
Background
Forester, born in Sackville Street, London, was the eldest son of Cecil Weld-Forester, 1st Baron Forester, and Lady Katherine Mary Manners, daughter of Charles Manners, 4th Duke of Rutland. The Prince of Wales, later King George IV, a friend of his father, was godfather.,
Political career
Forester was elected to the House of Commons for Wenlock in 1826, a seat he held until 1828, when he succeeded his father as second Baron Forester and entered the House of Lords. In 1841 he was appointed Captain of the Honourable Corps of Gentlemen-at-Arms in the Tory administration of Sir Robert Peel, which he remained until the government fell in 1846. He was admitted to the Privy Council in 1841.
Associations with Disraeli
He was a friend of Benjamin Disraeli. Through Lord Forester's mother, another friend of Disraeli, Lord John Manners later Duke of Rutland, a figure in Disraeli's Young England movement, was his own second cousin.
Lord Forester secured Disraeli's nomination as Tory parliamentary candidate for Shrewsbury for the 1841 General Election. Disraeli was subsequently returned as M.P., despite bitter opposition at the election, and held the seat until the 1847 General Election, when he contested and was subsequently elected for Buckinghamshire.
Later in life Disraeli, then a widower, had a simultaneous correspondence with two of Forester's sisters, the then-married Selina, Countess of Bradford and widowed Anne Elizabeth, Countess of Chesterfield. A collection of over 1,100 letters he wrote to the former between 1875 and his death in 1881, during most of which period he was Prime Minister, are preserved at Weston Park, Staffordshire.
Other interests
Lord Forester served in the South Salopian Yeomanry Cavalry, being promoted from Lieutenant to Captain in May 1826 and as late as 1852 was in command of a troop of theirs at Wellington, Shropshire. He took part with his troop when the yeomanry were deployed to suppress the 'Chartist' riots in Montgomeryshire in 1839.
A keen fox hunter from university days, Lord Forester was Master of Fox Hounds of the Belvoir Hunt in Leicestershire, of which the Duke of Rutland's family were also members, from 1830 to 1858, and was credited with bringing competitive athletics into Shropshire by his patronage of the Wenlock Olympian Games, where he normally presented the prize cups for the tilting matches.
In 1833 Lord Forester served as treasurer of the Salop Infirmary in Shrewsbury.
Personal life
Lord Forester married on 10 June 1856, at St John's, Paddington, London, a German, Alexandrine Julie Theresa Wilhelmina Sophie, Countess von Maltzan, daughter of Joachim Carl Ludwig, Count von Maltzan of Prussia, and widow of Frederick Lamb, 3rd Viscount Melbourne, from whom she had been separated in the last years of Melbourne's life. After Lord Forester's death it was stated the couple had one son who died an infant, although this does not appear stated in standard reference works on the peerage.
Lord Forester died childless at Willey Hall in October 1874, aged 73, and was buried at Willey parish church. His widow died in 1894. He was succeeded in the barony by his younger brother George, who was also a Tory politician.
References
External links
Category:1801 births
Category:1874 deaths
Category:Barons in the Peerage of the United Kingdom
Category:Honourable Corps of Gentlemen at Arms
Category:Masters of foxhounds
Category:Members of the Parliament of the United Kingdom for English constituencies
Category:Members of the Privy Council of the United Kingdom
Category:Shropshire Yeomanry officers
Category:Eldest sons of barons
Category:UK MPs 18261830 | wikipedia |
Jane Griffiths may refer to:
Jane Griffiths actress 19291975, British actress
Jane Griffiths poet born 1970, British poet
Jane Griffiths politician born 1954, British Labour party MP 19972005 | wikipedia |
rna interference ( rnai ) is now widely used to knockdown gene expression in a sequence - specific manner , making it a powerful tool for studying gene function ( 13 ) .
the process of rnai is mediated by double - stranded rna ( dsrna ) that contains a sequence homologous to the target mrna .
long dsrna introduced into the cell is cleaved by the enzyme dicer into short - interfering rna ( sirna ) followed by incorporation into the rna - induced silencing complex ( risc ) , which is responsible for target mrna degradation ( 4 ) .
one of the most serious problems in rnai is off - target silencing effects ( 5 ) .
off - target silencing effects are caused by sirna ( introduced directly into cells , or produced in vivo from long dsrna ) that has sequence similarities with unrelated genes . in caenorhabditis elegans , drosophila or plants , rnai experiments
are usually performed using long dsrnas . in these cases , there is a high risk of cross - suppression or co - suppression between closely related genes that share a highly conserved region . to minimize the possibility of off - target effects ,
it is necessary to perform an off - target search to design dsrna or sirna that has limited sequence similarities with unrelated genes .
recently , fast and sensitive off - target search software for sirna design has been reported ( 6,7 ) , but commonly used sirna design servers are not useful in performing off - target searches for long dsrnas .
deqor server uses blast to perform off - target searches for endoribonuclease - prepared sirnas ( 8) , although blast frequently fails to identify off - targets ( 6 ) .
therefore , we have developed a new web - based online software system , dscheck , to provide fast and accurate off - target searches for long dsrna sequences .
dices the input sequence into an sirna cocktail and performs an exhaustive scan for each sirna to find off - target gene candidates , simulating the biochemical process of dsrna - mediated rnai in vivo .
dscheck also provides efficient design of off - target minimized dsrna by avoiding regions that share a considerable number of diced sirnas with a specific off - target gene , and monitoring the total number of off - target hits .
the software should be especially useful for checking whether previously designed dsrnas have off - target gene candidates , as well as for designing target - specific dsrna when off - target effects are suspected .
the key idea of the program follows the biochemical process of dsrna - mediated rnai shown in figure 1a .
the input dsrna sequence is diced into 19 nt substrings of an sirna cocktail , and an exhaustive off - target search is performed for all individual sirnas using the sidirect engine , which makes it possible to enumerate the complete set of off - targets in a reasonable amount of time ( 7 ) . in dscheck ,
the in silico dicing size is set to 19 , as a complete match at the 19 nt double - stranded region of an sirna is sufficient for the target mrna degradation .
for example , an input 500 bp dsrna sequence is processed into 482 substrings each 19 nt in length , which are subjected to the off - target search individually . in the next step ,
all the hits with a complete match ( i.e. 19/19 matches ) , one mismatch ( 18/19 matches ) or two mismatches ( 17/19 matches ) are counted individually for every off - target gene candidate and sorted in descending lexicographic order for the output .
figure 1b shows a typical output for a 1497 bp query sequence of the drosophila pou domain protein , pdm2 ( nm_078834 , coding region ) .
the result shows significant hits against pdm2 ( two splicing variants : nm_078834 and nm_165017 ) , and two unrelated genes , nub ( nm_057311 ) and vvl ( nm_079224 ) .
these proteins share the highly conserved pou domain shown in figure 1c , indicating a high risk of cross - suppression by dsrna targeting this region . to design off - target minimized dsrna sequences ,
one approach would be to suppose that the off - target effects are caused by a considerable number of collaborative hits by diced sirnas on the same gene , and to select a region that minimizes the maximum number of collaborative off - target hits , which are defined as complete or partial matches of multiple 19 nt substrings against the same off - target gene . according to this criterion ,
if multiple regions are optimal , it also examines the maximum number of partial match collaborative off - target hits to select the best one .
if the complete match , collaborative hits on a sequence exceed 80% of the total number of diced 19 nt substrings , dscheck regards the sequence as the intended target gene .
some dsrna sequences include 19 nt substrings that may react with a large number of off - target genes , which differs from the collaborative silencing effects acting on a single off - target gene .
an additional criterion is necessary to evaluate the silencing effect of one sirna sequence on many off - targets , although the effect may not be as serious as the collaborative silencing effect , as the concentration of single sirna is low in diced sirna cocktails .
one reasonable measure would be the total number of off - target hits for each 19 nt substring of designed dsrna . to attract attention to this risk
, dscheck displays a warning if the total number of off - target hits exceeds a specified threshold .
figure 2 illustrates how dscheck designs target - specific dsrna for the drosophila pdm2 gene ( nm_078834 , coding region ) .
given that the length of dsrna is 100 bp , dscheck returns the positions 424523 for the target - specific region that successfully avoids the collaborative silencing effects on the major off - target genes nub ( nm_057311 ) and vvl ( nm_079224 ) . in mammalian rnai ,
the efficacy of each sirna varies widely depending on its sequence ; hence , several groups have reported guidelines for the selection of sirnas ( 912 ) . however , in drosophila cells , it is reported that most , if not all , sirna sequences may act as effective silencers ( 9 ) .
incorporation of sirna efficacy prediction may run the risk of underestimating off - target effects in non - mammalian rnai .
currently , off - target searches can be performed against the drosophila , c.elegans , arabidopsis and oryza sativa mrna sequences stored in the ncbi refseq database ( 13 ) . since off - target searches demand a substantial number of mrna sequences that are likely to cover the entire set of transcripts , we plan to incorporate additional species when ample cdna collections are available .
the key idea of the program follows the biochemical process of dsrna - mediated rnai shown in figure 1a .
the input dsrna sequence is diced into 19 nt substrings of an sirna cocktail , and an exhaustive off - target search is performed for all individual sirnas using the sidirect engine , which makes it possible to enumerate the complete set of off - targets in a reasonable amount of time ( 7 ) . in dscheck ,
the in silico dicing size is set to 19 , as a complete match at the 19 nt double - stranded region of an sirna is sufficient for the target mrna degradation .
for example , an input 500 bp dsrna sequence is processed into 482 substrings each 19 nt in length , which are subjected to the off - target search individually . in the next step ,
all the hits with a complete match ( i.e. 19/19 matches ) , one mismatch ( 18/19 matches ) or two mismatches ( 17/19 matches ) are counted individually for every off - target gene candidate and sorted in descending lexicographic order for the output .
figure 1b shows a typical output for a 1497 bp query sequence of the drosophila pou domain protein , pdm2 ( nm_078834 , coding region ) .
the result shows significant hits against pdm2 ( two splicing variants : nm_078834 and nm_165017 ) , and two unrelated genes , nub ( nm_057311 ) and vvl ( nm_079224 ) .
these proteins share the highly conserved pou domain shown in figure 1c , indicating a high risk of cross - suppression by dsrna targeting this region .
to design off - target minimized dsrna sequences , one approach would be to suppose that the off - target effects are caused by a considerable number of collaborative hits by diced sirnas on the same gene , and to select a region that minimizes the maximum number of collaborative off - target hits , which are defined as complete or partial matches of multiple 19 nt substrings against the same off - target gene . according to this criterion ,
if multiple regions are optimal , it also examines the maximum number of partial match collaborative off - target hits to select the best one .
if the complete match , collaborative hits on a sequence exceed 80% of the total number of diced 19 nt substrings , dscheck regards the sequence as the intended target gene .
some dsrna sequences include 19 nt substrings that may react with a large number of off - target genes , which differs from the collaborative silencing effects acting on a single off - target gene .
an additional criterion is necessary to evaluate the silencing effect of one sirna sequence on many off - targets , although the effect may not be as serious as the collaborative silencing effect , as the concentration of single sirna is low in diced sirna cocktails .
one reasonable measure would be the total number of off - target hits for each 19 nt substring of designed dsrna . to attract attention to this risk
, dscheck displays a warning if the total number of off - target hits exceeds a specified threshold .
figure 2 illustrates how dscheck designs target - specific dsrna for the drosophila pdm2 gene ( nm_078834 , coding region ) .
given that the length of dsrna is 100 bp , dscheck returns the positions 424523 for the target - specific region that successfully avoids the collaborative silencing effects on the major off - target genes nub ( nm_057311 ) and vvl ( nm_079224 ) .
in mammalian rnai , the efficacy of each sirna varies widely depending on its sequence ; hence , several groups have reported guidelines for the selection of sirnas ( 912 ) .
however , in drosophila cells , it is reported that most , if not all , sirna sequences may act as effective silencers ( 9 ) .
incorporation of sirna efficacy prediction may run the risk of underestimating off - target effects in non - mammalian rnai .
currently , off - target searches can be performed against the drosophila , c.elegans , arabidopsis and oryza sativa mrna sequences stored in the ncbi refseq database ( 13 ) . since off - target searches demand a substantial number of mrna sequences that are likely to cover the entire set of transcripts , we plan to incorporate additional species when ample cdna collections are available .
( b ) the output for the 1497 bp query sequence of the drosophila pdm2 gene ( nm_078834 , coding region ) .
significant hits against two off - target genes , nub ( nm_057311 ) and vvl ( nm_079224 ) were detected .
off - target minimized dsrna for the drosophila pdm2 gene ( nm_078834 , coding region ) .
( a ) the maximum number of collaborative off - target hits by 82 adjacent 19 nt substrings in 100 bp dsrnas .
the arrowhead indicates the recommended region for designing an off - target minimized dsrna of 100 bp in length .
the 19 nt substrings in the shaded area may react with a large number of off - target genes . | pubmed |
Cartoon X-overs Nicktoons: The Combining Factor
**Here I am with my first Nicktoon story, I am really thinking that us was too well. If you like it good and if you don't well don't read. On with the story.**
* * *
At a secret base in Danny Phantom's world. Four villains wear sitting around a table. Ember, Plankton, Gary, and Evil Jimmy.
"Why am I here?" Ember asked the three others villains around here.
"Who knows, I just got a letter staying I was invited to a party." Plankton says.
"Same with me," Gary says, "Lying about awesome parties is totally not cool."
"I was invited to do some damage." Evil Jimmy says.
"Who were all invited for the same reason." A figure said from the middle chair in between them. The chair turned to show that the figure was hooded.
"Who are you?" Plankton asked.
The figured only smirked and answered, "I am the guy that is going to help you simply take down those Nicktoons."
"Really? Tell me more." Plankton said.
"You guys will be glad to know that I have been watching those Nicktoons for quite so,e time now." The Figure said.
"And?" Ember asked
"And I know what their weaknesses are." The Figure replied.
"What?" Gary asked curiously.
The figure throws a folder to the villains and they look at four pictures in there. The pictures are of Sam Mason, Sandy Cheeks, Cindy Vortex, and Missy.
"These are the Nicktoons little love puppies." The figure says.
"So what you're saying is we capture them." Plankton says. The figure nods.
"Then we capture those nick toons as the try to rescue their worthless love creatures." The figure says.
* * *
Danny Phantom was on a date with his girlfriend, Sam. They were at the nasty burger and they were sharing a meal together.
"This has been great Danny." Sam says eating a burger.
"No problem same." Danny said.
"Anything going on with the Nicktoons yet?" Sam asked him.
"Nah that all busy." Danny says.
Danny's ghost sense goes on and Ember burst into the building.
"I'm going ghost!" Danny yells changing into ghost mode.
Ember then uses her guitar to blast Danny.
"Sorry dipstick but I'm gonna have to borrow you're girlfriend." Ember says and grabs Sam by the hand and flys out of the restaurant as Danny lies on the floor knocked out.
* * *
Meanwhile in Dimmsdale, Timmy and Missy are sitting on the park bench taking.
"I love you're pink hat Timmy." Missy says.
"Thank you Missy." Timmy says and without her looking winks to his fairies who are looking as flys. They poof up some flowers and Timmy hands them to Missy. "For you."
"Thanks Timmy." Missy says and Crocker pops out of the bushes.
"Turner I'm giving you a K," Crocker says, "FOR KNOCKED OUT!'
Crocker then holds out a device that punches Timmy.
"Missy I'm also giving you a K," Crocker says, "FOR KIDNAPPED!"
Crocker traps Missy in a net and runs off with her.
* * *
Meanwhile in Bikini Bottom. Sandy was walking to the Chum Bucket. She knocked on the door and Plankton answered.
"Sandy," Plankton says, "I've been expecting you."
"What's this all about Plankton?" Sandy asked narrowing her eyes.
"We seeing as we're the only two scientist in Bikini Bottom," Plankton says, "So I have came up with an idea for a project."
"Really? What?" Sandy asked interested.
"We come up with the most tasty sandwich ever," Plankton says, "One that's better than the krabby patty."
"I will not help you in your quest to take over the world." Sandy replied.
Plankton smirked, "That's okay because this was all a trick."
"What do you mean a..." Sandy is cut off when something grabs her mouth.
* * *
In Retroville Jimmy was working in his lab when something came up his screen.
"Hello Jimbo." Evil Jimmy says.
"What?! How did you get back?!" Jimmy asked.
"That doesn't matter," Evil Jimmy says, "What does matter is that I have your girlfriend."
Evil Jimmy says Cindy tied up.
"What the..." Jimmy asked when Danny, Timmy, and Spongebob came to the lab.
"Jimmy! Sandy, Missy, and Sam are gone!" Spongebob said.
"That's right." Evil Jimmy says and then Ember, Crocker, and Plankton appear next to him.
"You're all working together?!" Danny asked.
"Duh." Plankton said.
"Why do you have our girlfriends?!" Spongebob asked.
"Cindy isn't my girlfriend." Jimmy says.
"Enough talk," Evil Jimmy says, "This wasn't our idea, It was our leaders."
"Your leader?" Timmy asked.
The four villains moved and a hooded figure appeared on the screen.
"Who are you?' Jimmy asked.
"Call me Lord Z." The figure says.
"Why are you doing this?" Danny asked.
"You wanna know why?" Lord Z asked, "You're just going to have to come to our hideout and find out."
"We will be there!" Timmy says, "And we're going kick your bad guys butts!"
"We'll see about that," Lord Z says, "But I must inform you is that the only butts that will be kicked our yours."
"Where are you?!" Spongebob asked.
"If you must know we're in Ghost Boy's world." Lord Z says and the villains disappear grim then screen.
"Let's get to Amity Park." Danny says.
"Alright I've let's take the portal." Jimmy opens the portal and they leave.
* * *
Meanwhile a the villain hideout, Lord Z was getting ready.
"Soon those Nicktoons powers will be mine." Lord Z says.
"What do you mean?" Plankton asked.
Lord Z paused to see the four staring at him.
"I mean...we will destroy the nick toons." Lord Z says.
"We will beat them and capture Timmy Turner's FAIRIES!" Crocker yells.
"And the formula." Plankton says.
"And I will control minds with my music." Ember says.
Lord Z and the other villains laugh evilly.
* * *
**So who is this Lord Z in the hood? Will the nick toons stop him? We'll just have to wait and find out.**
End file.
| fanfiction |
Iowa Highway 22 Iowa 22 is a westeast state highway that traverses primarily rural areas in east-central Iowa. The highway begins near Thornburg at an intersection with Iowa Highway 21 and ends in southwestern Davenport, at U.S. Highway 61 Business.
Route description
Iowa Highway 22 begins west of Thornburg at Iowa Highway 21. It continues east through Keswick and Webster. Between Webster and South English, Iowa 22 is overlapped with Iowa Highway 149. It continues east from South English through Kinross and Wellman before intersecting Iowa Highway 1 at Kalona. It proceeds east from Kalona to go through Riverside and then intersects U.S. Highway 218 and Iowa Highway 27. After crossing the Iowa River, it goes through Nichols, where a short overlap with Iowa Highway 70 begins. It then continues eastward and intersects U.S. Highway 61 at Muscatine. It goes around the west and north city limits of Muscatine before intersecting Iowa Highway 38 and Business US 61 and turns south into Muscatine. It then turns east along a route next to the Mississippi River and passes through Buffalo before intersecting Interstate 280 at Davenport. It then turns north to end at U.S. 61.
To locals, Iowa Highway 22 is most notable as one of two main highways connecting Muscatine and Davenport U.S. Highway 61 being the other. This eastern section of highway follows the Mississippi River.
The segment of the highway between Muscatine and Davenport is part of the Great River Road.
History
Iowa Highway 22 was designated in 1926, and followed what is now U.S. Highway 61 between Muscatine and Davenport, passing through Blue Grass; U.S. 61 followed the Mississippi River route at the time. The highway was extended to Thornburg in 1931.
For years, several sections of Iowa Highway 22 was either gravel or had a bituminous surface. One of these sections the section between Muscatine and Blue Grass was paved in 1957, the same year U.S. 61 and Iowa Highway 22 switched routes; U.S. 61 now went through Blue Grass, while Iowa Highway 22 now followed the Mississippi River through Buffalo.
The last segment between U.S. Highway 218 east of Riverside to Iowa Highway 405 north of Lone Tree, was upgraded from bituminous to paved in 1988.
Major intersections
References
022
022
22 | wikipedia |
imipramine was found to improve mood while being used in a protocol to search for an antipsychotic : ' iproniazid , a drug used in the treatment of tuberculosis , was likewise found to have beneficial effects on mood .
the former , a tricyclic antidepressant ( tca ) , and the latter , a monoamine oxidase inhibitor ( maoi ) , belong to two classes of drugs still in use today .
depressive mood appears to be attributable to diminished activity of the dopaminergic , noradrenergic , and serotonergic neurotransmitter systems .
antidepressants restore the activity of these transmitters by inhibiting reuptake in the presynaptic neurons . additionally , the classic antidepressants have effects on other neurons ( eg , histamine , acetylcholine ) , resulting in major side effects limiting their broader use .
depressive symptoms have been described in as many as 40 different disorders , which would imply that they could be used in all of them .
although the efficacy of tcas has been well established , the high incidence of side effects and the high number of nonresponders or treatment - resistant patients represent drawbacks that have made it necessary to search for new drugs .
the development of selective serotonin reuptake inhibitors ( ssris ) was the first attempt based on a pathophysiological approach .
these drugs , which have similar efficacy , but less side effects than the tcas , have become the preferred pharmacological treatment for depression . however , the high number of nonresponders and the delay in onset of response have limited their value .
today , up to seven different classes of antidepressants are available , which mainly differ in their selectivity for the respective monoamines and their receptors .
these discoveries have intensively stimulated biochemical - pharmacological research into the mechanism of action of antidepressants .
findings from these investigations suggest that enhanced activity of the central noradrenergic and/or serotonergic transmitter system is essential for the clinical antidepressant action .
such enhancement could be achieved either presynaptically by blocking 2-adrenergic receptors , or in the synaptic cleft by inhibiting the transmitter reuptake or the main metabolic enzyme monoamine oxidase ( mao ) . the increased transmitter concentration in the synaptic cleft after chronic treatment leads to a downregulation of postsynaptic -receptors , sometimes modulated by interaction with neuropeptides and hormones .
in addition , depending on the antidepressant used , the sensitivity of 5-ht2a , somatodendritic 5-ht1a , or noradrenergic 1 receptors may be reduced , leading to an overall increase in serotonin transmission .
such receptor alterations appear to provide the best explanation for the delay in clinical antidepressant response .
the introduction of new classes of antidepressants has led to renewed thinking about their mechanism of action .
recent investigations of second messenger systems such as the adenylate cyclase system and the phosphatidylinositol system are very promising .
antidepressant drugs , including the mood stabilizers lithium and carbamazepine , modulate both of these second messenger systems , which in turn modulate the phosphorylation status of neuronal proteins via protein kinase .
the outcome is a positive alteration of the gene expression of the relevant biochemical structures ( enzymes , transporters , receptors ) , thus restoring the normal function of the respective neuronal systems .
thanks to clearer understanding of the function of this complex serotonergic system we now know that a great number of normal and abnormal behaviors can be attributed to dysfunction of the serotonergic neurons , in addition to their role in depression .
the limited number of serotonin neurons in the brain ( approximately 300 000 ) suggests that their role is mainly a modulating one .
this implies that they act to either dampen or accelerate a given type of behavior .
drugs targeting the serotonergic system are therefore able to influence many kinds of behavior abnormalities ( figure 1 ) .
concerning the norepinephrine system
as already mentioned , some forms of depression are assumed to be accompanied by reduced noradrenergic activity .
however , this is a matter for discussion , and some forms of depression may even be accompanied by increased noradrenergic function .
it is hypothesized that noradrenergic neurons in the locus ceruleus are activated or increased in anxiety and panic disorders .
conversely , a norepinephrine deficit is invoked to explain disturbances of attention , psychomotor retardation , and impaired vigilance .
some antidepressants also increase dopaminergic neuron activity , either directly or indirectly , by acting on serotonergic and noradrenergic pathways .
dopamine , a major transmitter of the reward system also plays a role in depressive states .
dopaminergic antidepressants could be of interest in some subgroups of depression , but so far no such drugs are available in europe
. however , in some patients with refractory depression , dopaminergic drugs like amphetamine have some beneficial effects .
neuronal circuits establish functional relationships between serotonergic , noradrenergic , and dopaminergic systems , which explains why deficiency in one system impairs the other systems as well , and why even specific drugs like the ssris arc also able to modulate the other systems .
the variety of the clinical uses for the newer antidepressants may necessitate a reexamination of traditional diagnostic categories and of theories on the way antidepressants work .
antidepressant drugs are used in a wide range of psychiatric disorders . empirical evidence in the 70s suggested that the nonselective serotonin antidepressant clomipramine improved symptoms of ocd .
newer generations of antidepressants with fewer side effects have proved to be even more active in ocd . furthermore , 5-ht1a serotonin agonists are being investigated in general anxiety disorders .
other potential indications for ssris and the new generation of antidepressants are panic disorders , premenstrual dysphoric disorder , eating disorders , substance abuse disorder , chronic pain , dementia , and personality disorders with aggression or impulse disturbances , and general anxiety disorders .
depressive symptoms arc frequently diagnosed in patients with schizophrenia and have been described in schizoaffective disorders .
. this may be the reason why such patients are frequently ( 50% of cases ) treated simultaneously with antipsychotics and antidepressants .
antidepressants are also useful in the treatment of a group of disorders that may be phenomenologically and genetically related to major depression , such as fibromyalgia , chronic fatigue syndrome , migraine , irritable bowel syndrome , atypical facial pain , and premenstrual dysphoric disorder .
it is likely that the etiology of depression ( as a symptom ) in these disorders is similar to that of major depression as an entity , and therefore would explain the efficacy of ssris .
although not impossible , it would be contrary to expectation if the mechanism of antidepressant effect was independent of the mechanism of depression in migraine , premenstrual dysphoric disorder , and other conditions . and it would be even more difficult to believe that different , chemically unrelated antidepressant drugs , share the same pharmacological properties while having different mechanisms of action .
disturbances in neurodevelopment and/or abnormal immune function may be responsible for schizophrenic symptoms . additionally , abnormal
dopamine , norepinephrine , and serotonin transmitter activities in some areas of the brain may be pathophysiological relevant to some schizophrenic syndromes . other theories put forward disturbances in the glutamatergic and gabaergic circuits .
because of this heterogeneity and the impossibility of characterizing clinical subgroups of schizophrenic patients , none of these theories has been conclusively proved so far .
the discovery of chlorpromazine for the treatment of schizophrenia opened new perspectives for the care of psychiatric patients .
unfortunately , chlorpromazine and the other classic neuroleptics produce side effects that limit their widespread use . for many years
, the dopamine hypothesis , based on the assumed mechanism of action of these compounds , was the predominant theory .
the introduction of new atypical neuroleptics such as clozapine , which was the first one , paved the way for revisiting the dopamine hypothesis of schizophrenia and related theories on the mechanism of action of neuroleptics . to explain the unique features of clozapine , new theories have been put forward , partly in relation to interference with dopamine receptor subtypes and partly in relation to interference with other neurotransmitters such as norepinephrine and serotonin .
the nonspecificity of second - generation atypical neuroleptics for the dopaminergic system , the therapeutic ineffectiveness of some selective dopaminergic drugs , the lack of success of genetic studies targeted to the dopaminergic system , and the disappointing biochemical findings in schizophrenic patients have resulted in alternative theories of pathogenic causes of schizophrenia being proposed , opening up new perspectives for the development of future drugs . based on neuropath ological and neuroanatomical findings and in concordance with the revised dopamine hypothesis ,
new models have been postulated focusing attention on the excitatory amino acid y - aminobutyric acid ( gaba ) and the most ubiquitous amino acid transmitter in the brain , glutamate .
psychotic symptoms of schizophrenia have been divided into negative symptoms ( blunted affect , anhedonia , asociality , inability to initiate and carry out complex tasks to completion ) , which seem to be related to cortical hypofunction , and which , in turn , may be associated with decreased mesocortical dopaminergic activity and positive symptoms ( hallucinations , delusions , and thought disorders ) .
they also appear in disorders other than schizophrenia as well as many nonpsychotic disorders , and are related to increased activity of the subcortical striatal dopaminergic neurons .
was considered as the standard treatment for bipolar depressive and manic patients , the pharmacological strategies for bipolar disorder included neuroleptics and antidepressants .
they are now mainly used to treat the psychotic symptoms present during one of the poles of the disorder , or as an adjunctive treatment when other alternatives have failed .
there have been several reports that clozapine may be more effective in patients with mania and schizoaffective disorder than in patients with schizophrenia .
preliminary reports suggest that the newer atypical antipsychotics olanzapine and sertindole may also be effective in stabilizing mood or in the management of affective symptoms .
the occurrence of psychotic symptoms is frequent during the evolution of idiopathic parkinson 's disease and other parkinsonian syndromes .
they seem to be related to interactions between the underlying neuropathologies manifestations of the syndromes and the adverse effects associated with chronic antiparkinsonian drug administration . in patients with advanced parkinson 's disease
olanzapine has been reported to be effective in the suppression of psychotic symptoms in these patients , but the currently available dose increments may result in an exacerbation of motor disability .
as mentioned above , since no solid alternatives have emerged from biological research to replace the current hypothesis regarding the pathogenesis of psychiatric disorders , the development of new psychotropic drugs remains based on the restoration of the imbalance in the monoamincrgic system .
this is exemplified by the development of the new antidepressants . the postulate that depression results from a dysfunction in the noradrenergic , serotonergic , and dopaminergic systems leads logically to the attempt to design antidepressants that act mainly on one of the neurotransmitter systems .
the idea is to increase selectivity without compromising efficacy , while at the same time reducing the side effects that result of interactions with these and other neurotransmitter systems .
thus , blockade of serotonin reuptake gave rise to the now well - known ssris . a new class of drugs , which selectively inhibit the reuptake of norepinephrine , was recently introduced onto the market
however , experience with psychotropic drugs acting on either the noradrenergic or the serotonergic systems suggest how important it is ( at least in certain situations ) to act on both systems at once .
research was therefore undertaken to develop new antidepressants with a dual action on these systems .
although drug development tries to focus on specific mechanisms involved in depression and its symptoms , clinical research is not nosologically but transnosologically oriented .
the tools used to monitor therapeutic response in clinical trials are usually rating scales that evaluate the depressive or psychotic state rather than treatment efficacy on a specific entity .
efficacy , nosology , and duration of treatment are based on the antidepressant effect , and , therefore , in many of the specific entities where they are presently used , these variables have not been confirmed .
similarly , in most trials focusing on therapeutic outcome , there are no differences between different drugs belonging to the same therapeutic group .
the current situation is therefore characterized by disharmony prevailing between psychotropic drug development , nosological classification of diseases , clinical research , and therapeutic uses of psychotropic drugs . | pubmed |
A peanut butter cookie is a type of cookie that is distinguished for having peanut butter as a principal ingredient. The cookie originated in the United States, its development dating back to the 1910s. If crunchy peanut butter is used, the resulting cookie may contain peanut fragments.
History
George Washington Carver 1864-1943, an American agricultural extension educator, from Alabama's Tuskegee Institute, was the most well known promoter of the peanut as a replacement for the cotton crop, which had been heavily damaged by the boll weevil. He compiled 105 peanut recipes from various cookbooks, agricultural bulletins and other sources. In his 1925 research bulletin called How to Grow the Peanut and 105 Ways of Preparing it for Human Consumption, he included three recipes for peanut cookies calling for crushed or chopped peanuts.
It was not until the early 1920s that peanut butter was listed as an ingredient in the cookies.
Fork pressing and patterning
Early peanut butter cookies were either rolled thin and cut into shapes, or else they were dropped and made into balls; they did not have fork marks. The first reference to the famous criss-cross marks created with fork tines was published in the Schenectady Gazette on July 1, 1932. The Peanut Butter Cookies recipe said: [s]hape into balls and after placing them on the cookie sheet, press each one down with a fork, first one way and then the other, so they look like squares on waffles.
Pillsbury, one of the large flour producers, popularized the use of a fork in the 1930s. The Peanut Butter Balls recipe in the 1933 edition of Pillsbury's Balanced Recipes instructed the cook to press the cookies using fork tines. These early recipes do not explain why the advice is given to use a fork, though. The reason is that peanut butter cookie dough is dense, and unpressed, each cookie will not cook evenly. Using a fork to press the dough is a convenience of tool; bakers can also use a cookie shovel spatula.
See also
List of cookies
List of peanut dishes
References
Cooks.com's Peanut Butter Cookie Recipes - A wide assortment of recipes
George Washington Carver. How to Grow the Peanut and 105 Ways of Preparing it for Human Consumption, Tuskegee Institute Experimental Station Bulletin 31, 1916.
Andrew F. Smith, Peanuts: The Illustrious History of the Goober Pea Chicago, University of Illinois Press, 2002.
Easiest Flourless Peanut Butter Cookie Recipe
Category:Cookies
Category:Peanut butter
Category:American desserts | wikipedia |
the inflammasomes are signaling platforms , which are assembled in response to pathogen - associated and damage - associated molecular pattern molecules and environmental irritants .
currently , inflammasomes are distinguished into two families : the nod - like receptor ( nlr ) family and the pyrin and hin200 ( haematopoietic interferon - inducible nuclear antigens with 200 amino - acid repeats ) domain - containing protein ( pyhin ) family .
the nlr family consists of nlrp1 , nlrp2 , nlrp3 , nlrp6 , nlrc4 , and nlrp12 .
the nlrp3 inflammasome is a multiprotein , large cytoplasmic complex ( > 700 kda ) , composed of a specific member of the nod - like receptor protein ( nlrp ) subfamily , the adaptor protein named apoptosis - associated speck - like protein containing a card ( asc ) , and procaspase-1 , which are preferentially expressed in adipose tissue macrophages ( atms ) . unlike the typical signaling cascades downstream of many innate receptors such as other nlrp members ,
nlrp3 contains an n - terminal pyrin domain ( pyd ) , which is used to physically interact with the pyd domain of asc , thus facilitating the subsequent recruitment and activation of procaspase-1 .
, once activated , caspase-1 , as far as we are currently aware , cleaves the proforms of two potent proinflammatory cytokines interleukin- ( il- ) 1 and il-18 in the cytoplasm .
this has two main effects ; firstly it activates the two cytokines and secondly in this mature form these cytokines can be released from the cell .
the active form of caspase-1 also has the ability to induce the release of il-1 and hmgb-1 ( high mobility group box 1 ) , as well as initiate a lytic form of cell death called pyroptosis [ 24 ] ( figure 1 ) .
the primary role of the inflammasome and its products seems to be as part of the body 's innate immune system , in that they can be triggered to assist in the defense against invading pathogens .
indeed much of the data published on the inflammasome / caspase 1 is on its role in the body 's response to microbial molecules ( bacterial , fungal , or viral ) with conserved molecular structures known as pathogen associated molecular patterns ( pamps ) [ 5 , 6 ] .
in addition to pamps , the nlrp3 inflammasome is also proficient in sensing stress to endogenous ( nonmicrobial ) danger signals ( danger associated molecular patterns , damps ) from damaged cells .
damps can include molecules such as reactive oxygen species ( ros ) , adenosine triphosphate ( atp ) , hypotonic stress , uric acid crystals , or noxious exogenous factors such as environmental insults , asbestos , and uv radiation .
there are a number of potential mechanisms for the assembly of the nlrp3 inflammasome , as described earlier . according to one hypothesis ,
mitochondria are the principal source of reactive oxygen species ( ros ) required for inflammasome activation ; several recent studies have implicated ros produced by mitochondria , rather than phagosomes , in nlrp3 activation exerting an indirect effect on pathways of metabolism [ 8 , 9 ] .
a second mechanism involves the disruption of lysosomal membrane integrity by crystalline materials and peptide aggregates [ 10 , 11 ] . upon uptake of such substances
, lysosomal rupture leads to the leakage of lysosomal proteases , specifically cathepsins b and l , into the cytosol where they could possibly mediate nlrp3 inflammasome activation by an as - yet - undefined cleavage event .
in addition , type-2 diabetic patients and mice fed a high - fat diet demonstrate il-1 production following inflammasome activation from obesity - induced danger signals .
mice have also been shown to become glucose intolerant following activation of the inflammasome in hematopoietic cells by the saturated fatty acid palmitate . very recently ,
vajjhala and colleagues have shed light on the molecular details of the complex mechanisms of nlrp3 inflammasome assembly and activation , identifying multiple binding sites on the pyd domain of the adaptor protein asc which allow self - association and interaction with binding partners .
several in vitro , in vivo studies and clinical trials provide evidence that supports a causative role of il-1 in the pathogenesis of type 2 diabetes , and elevation in circulating levels of il-1 predicts type 2 diabetes when combined with serum il-6 levels .
prolonged il-1 treatment has been demonstrated to reduce the insulin - induced glucose uptake in murine adipocytes .
in contrast , addition of the il-1 receptor antagonist to adipocytes resulted in increased insulin sensitivity as reflected by increased levels of phosphorylated akt in response to insulin .
these results were confirmed by showing that il-1 knockout mice were more insulin sensitive as compared to wild - type control animals . in humans ,
elevated plasma levels of il-1 have been found to be predictive of type 2 diabetes , and clinical studies have suggested that treatment with the il-1 receptor antagonist anakinra has beneficial effects in type 2 diabetic patients .
a number of recent landmark studies have pointed out a key role for an excessive nlrp3 inflammasome activation in the il-1-related development of type 2 diabetes .
the association between the nlrp3 inflammasome and both insulin resistance and obesity has been suggested by animal studies showing that genetic ablation of nlrp3 improved insulin sensitivity and glucose homeostasis .
specifically , adipocytes isolated from nlrp3-deficient mice showed an increase in insulin sensitivity as determined by phosphorylation of akt . in line with the rise in insulin sensitivity , il-1 production of adipose tissue isolated from nlrp3 knockout mice
other studies [ 12 , 13 ] have shown that improvement in insulin sensitivity ( increased phosphorylation of the insulin receptor subtrate-1 and akt ) can also be detected in liver and muscle of nlrp3 knockout mice on a high - fat diet for 12 weeks .
this effect was associated with a significant reduction in the tissue mrna expression of inflammatory cytokines compared to wild - type control .
ablation of the nlrp3 in mice has been also reported to protect from obesity - associated macrophage activation in adipose tissue , reducing m1-like macrophage gene expression ( tumor necrosis factor- , chemokine ligand 20 , and chemokine ligand 11 ) and increasing the expression of m2-like cytokines ( interleukin-10 ) .
this effect was associated with an increase in the number of m2 macrophages in nlrp3-deficient obese mice , without affecting the m1 macrophage frequency . to confirm the clinical relevance of these data generated from mouse models ,
the same authors have demonstrated that weight loss reduced nlrp3 expression in abdominal subcutaneous adipose tissue in obese patients with type 2 diabetes , which was accompanied by improved glucose homeostasis .
furthermore , strong correlations between the expression of nlrp3 inflammasome - related genes and insulin resistance have been recently reported in obese male subjects with impaired glucose tolerance .
additionally , type 2 diabetic patients showed elevated levels of nlrp3 , asc , il-1 , and il-18 mrna and protein expression in monocyte - derived macrophages , compared with those in healthy control subjects . besides , the cleavage of caspase-1 and release of mature il-1 were significantly elevated in monocyte - derived macrophages from type 2 diabetic patients compared with controls .
inflammatory cytokines are known to contribute crucially to the development of insulin resistance by activating different kinases that disrupt insulin signaling .
the endoplasmatic reticulum ( er ) is an extensive membrane network which has been recently demonstrated to be involved in the transduction of cytokines effects into activation of different kinases .
the early steps of insulin biosynthesis occur in the er of pancreatic cells , thus further suggesting the key role of er load and folding activity in the insulin biosynthesis
. a major role of the er is to ensure the synthesis and folding of membrane and secreted proteins , and any disturbance in this function ( e.g. , excessive protein synthesis or accumulation of unfolded or misfolded proteins in the er lumen ) leads to an er stress
the recent literature suggests that er stress may act directly as a negative modulator of the insulin biosynthesis and insulin signaling pathways but also indirectly by promoting lipid accumulation [ 25 , 26 ] .
er stress also plays a role in the dysregulation of adipokine secretion by adipose tissue , frequently observed in obesity and insulin resistance [ 27 , 28 ] , and cd14 + monocytes isolated from diabetic patients showed evidence of er stress , which may underlie the functional defects in these cells .
interestingly , er stress has been recently demonstrated to activate the nlrp3 inflammasome , resulting in the subsequent release of il-1 by human macrophages , with an activation mechanism similar to that of other known nlrp3 activators , requiring ros generation and potassium efflux .
the thioredoxin - interacting protein ( txnip ) , a critical node in the development of er stress leading to programmed cell death of pancreatic cells , activates the nlrp3 inflammasome , causing procaspase-1 cleavage and il-1 secretion in human monocytic cells .
the role of er stress in promoting nlrp3 inflammasome activation is consistent with the subcellular localization of nlrp3 . in resting cells ,
nlrp3 is associated with er membranes , and then upon activation nlrp3 is redistribute to the perinuclear space where it colocalizes with endoplasmic reticulum and mitochondria organelle clusters .
nlrp3 inflammasome plays a substantial role in sensing obesity - associated inducers of caspase-1 activation and therefore regulates the magnitude of the inflammation and its downstream effects on insulin signaling in different organs , as reported here later .
nlrp3 expression is detected mainly in the cytosol of granulocytes , monocytes , dendritic cells , t and b cells , and osteoblasts .
thus , most of the first studies characterizing the role of nlrp3 signaling have been conducted in cells of the immune system .
several studies on innate immune cells have demonstrated that the myeloid - derived nlrp3 inflammasome complex may contribute to promote inflammatory cytokine production and insulin resistance through reduction of insulin signaling . in vitro experiments have shown that elevated concentration of saturated fatty acids ( sfas ) , caused by a high - fat diet , may activate the nlrp3 inflammasome in macrophages through a newly identified amp - activated protein kinase and unc-51-like kinase-1 autophagy signaling cascade . besides , both ex vivo and in vivo exposure of bone marrow derived dendritic cells to dietary sfa resulted in increased nlrp3 inflammasome activation and reduced adipocyte insulin sensitivity .
more specifically , dietary sfa may act as a primer of the nlrp3 inflammasome protein complex enhancing nlrp3 , caspase-1 , and pro - il-1 mrna expression .
a second signal is then required to induce maturation of il-1 from inactive pro - il-1. this second step can be triggered by exposure to atp , ros , or ceramide .
overall , these data suggest that exposure to dietary sfa represents the key metabolic stressor relevant to both priming and processing of il-1 in both adipocytes and innate immune cells .
however , it must be stressed that the high expression of nlrp3 in primary adipocyte fractions of enzymatically digested adipose tissue may be attributable in large part to lipid - laden macrophages that contaminate enriched adipocyte fractions , as also suggested by immunofluorescence and qrt - pcr data , showing that nlrp3 is highly expressed in adipose tissue macrophages with low expression in adipocytes .
besides , standard isolation procedures for isolating primary adipose cells often involve collagenase digestion , which have been shown to be a potent inducer of cytokine gene transcription and protein secretion .
these findings highlight a new model of organ crosstalk , in which leukocyte and macrophage recruitment in key insulin target tissues , such as liver , adipose , and muscle , may promote insulin resistance by enhancing inflammasome activation .
this is in keeping with recent studies showing that il-1 's role in regulating the endocrine function of adipose tissue is mediated by its own ability to evoke local macrophage recruitment and lipid accumulation in an autocrine / paracrine manner . as in diabetic patients pancreas , adipose tissue , liver , and kidney , with infiltrated macrophages ,
are major sites of origin of inflammation , it might be intriguing to investigate the specific contribution of nlrp3 inflammasome activation in these different insulin target tissues and to identify the specific inducers that selectivity participate in the mechanism of tissue nlrp3 inflammasome activation .
pancreatic islets of type 2 diabetic patients have amyloid deposition and increased production of proinflammatory cytokines and chemokines .
the unique , primary component of islet amyloid deposits is the islet amyloid polypeptide ( iapp ; also known as amylin ) .
mice overexpressing iapp produce higher amounts of il-1 , and exposure to high levels of il-1 has been demonstrated to induce beta cell death in cell culture , interfering with signaling to nf-b through ikk or the ib super - repressor . in keeping with these results , neutralizing il-1 on isolated beta cells using il-1 receptor antagonist
however , the precise mechanism(s ) by which il-1 affects pancreatic -cell failure is still debated .
were the first to identify a possible signaling pathway involved in nlrp3 inflammasome activation under conditions of metabolic stress .
they showed that thioredoxin - interacting protein ( txnip ) , also known as vitamin d3 upregulated protein 1 ( vdup1 ) , is an upstream and highly selective activating ligand for nlrp3 , with no effect on the activity of other inflammasomes ( e.g. , nlrc4 and aim2 ) .
txnip - dependent nlrp3 inflammasome activation drives il-1 secretion from pancreatic islets in response to chronic elevated glucose , thus suggesting , for the first time , that nlrp3 , activated under conditions of metabolic stress , mediates il-1-driven islet failure .
other authors have identified oligomers of iapp , as a key trigger for nlrp3 inflammasome activation and the following processing of il-1 .
obesity - induced pancreatic -cell death is regulated , at least in part , by the nlrp3 inflammasome , as demonstrated in nlrp3-deficient mice in late - stage obesity , where the ablation of nlrp3 is associated with reduced cell death and increase in pancreatic islet size and local insulin levels . as noted by vandanmagsar et al .
, the nlrp3 inflammasome is activated in adipose tissue in mouse models of obesity and attenuated by calorie restriction .
nlrp3 inflammasome levels also correlate with glycaemia in type 2 diabetes patients after weight loss interventions . besides
, mice deficient in inflammasome components are protected from body - weight gain and adipocyte hypertrophy , induced by chronic exposure to a high - fat diet .
nlrp3 inflammasome components have been reported to be abundantly represented in adipocytes of patients with metabolic syndrome , mainly in adipocytes from samples of visceral adipose tissue .
in contrast , the inflammasome in subcutaneous adipose tissue adipocytes did not seem to be grossly influenced by the presence of the metabolic syndrome .
interestingly , caspase-1 activation in adipose tissue of obese animals takes place partly independent of macrophage infiltration .
partial depletion of macrophages from adipose tissue of obese animals decreased the expression of the macrophage marker cd68 , with no significant alteration in the expression of caspase-1 , thus suggesting that the effects of the nlrp3-asc - caspase-1 protein complex on adipose tissue are not only exerted though infiltrating macrophages .
this observation was also confirmed in in vitro experiments showing caspase-1 activation in adipocytes in settings free of inflammatory cells and increased insulin sensitivity in adipocytes lacking of caspase-1 or the inflammasome component nlrp3 .
in addition , adipocyte upregulation of il-1 expression and secretion in response to inflammatory stimuli has been shown to induce hepatic insulin resistance , thus suggesting a further intriguing role for nlrp3 inflammasome activation in the dysfunctional communication between adipocytes and hepatocytes [ 35 , 43 ] .
overall these data reveal a novel metabolic function of the nlrp3 inflammasome in adipose tissue , suggesting that its pharmacological modulation in obese and/or patients with type 2 diabetes may restore the metabolic function of adipose tissue and subsequently improve insulin sensitivity .
the involvement of the inflammasome in nonalcoholic fatty liver disease ( nafld ) and non - alcoholic steatohepatitis ( nash ) is slowly being elucidated .
the presence of nlrp3 inflammasome and/or inflammasome activation has been shown in sinusoidal endothelial cells , stellate cells , and hepatocytes . recently , inflammasome activation has been associated with nash , and long - term high - fat diet administration resulted in reduced hepatic steatosis in nlrp3 knockout mice .
selective deficiency in il-1 in liver parenchymal cells , but not in bone - marrow - derived cells , protected mice from diet - induced steatohepatitis and fibrosis .
increased mrna expression of nlrp3 inflammasome components was found in human livers of nash patients where nlrp3 levels were decreased after weight loss .
these observations suggest that inflammasome activation by different cell types may contribute to different aspects of steatohepatitis .
in contrast , to date , there are no data suggesting a potential role of nlrp3 inflammasome activation on impaired glycogen synthesis and/or augmented glycogenolysis .
there is evidence that the inflammasome components are important in the maintenance of the integrity of the intestinal epithelium and the defense against pathogenic organisms that can invade the gastrointestinal tract .
for instance , mice lacking the inflammasome components nlrp3 and caspase-1 are hypersusceptible to gastrointestinal inflammation induced by citrobacter rodentium , an enteric bacterial pathogen of the mouse intestinal tract that triggers inflammatory responses resembling those of humans infected with enteropathogenic and enterohemorrhagic escherichia coli .
the increased host susceptibility to c. rodentium is due to the failure to produce normal levels of il-1 and il-18 in the presence of nlrp3 and caspase-1 deficiency .
nlrp3-deficient mice had been reported to show increased susceptibility to dextran - sulfate - sodium- ( dss- ) induced colitis with increased mortality and weight loss in three different studies [ 4951 ] .
however , other authors did not show a negative regulatory effect of nlrp3 on colitis , showing that nlrp3-null mice or mice pretreated with the caspase-1 inhibitor pralnacasan had less severe colitis when treated with dss , which was related to decreased il-1 secretion of dss - exposed nlrp3-deficient macrophages in vitro [ 52 , 53 ] .
this discrepancy could be due not only to differences in protocols but also to baseline differences in the gut microbiota that might account for the dissimilar phenotypes .
the crucial role of inflammasome components in the impairments of the gut microbiota composition is also suggested by recent studies demonstrating that nlrp3 inflammasome regulates the gastrointestinal microbiome and can thereby affect host susceptibility to diseases beyond the gastrointestinal tract , including obesity and diabetes .
in particular , modulation of the intestinal microbiota through multiple inflammasome components has been recently demonstrated to be a critical determinant of nafld / nash progression as well as multiple other aspects of metabolic syndrome such as weight gain and glucose homeostasis .
inflammasome - deficiency - associated changes in the configuration of the gut microbiota are associated with exacerbated hepatic steatosis and inflammation through influx of tlr4 and tlr9 agonists into the portal circulation , leading to enhanced hepatic tumour - necrosis factor- ( tnf- ) expression that drives nash progression .
little is known of the role of the nlrp3 inflammasome complex in the development of renal metabolic damage . in humans , il-18 and caspase-1
are expressed in renal tubular epithelium , and patients with chronic kidney disease or the nephrotic syndrome exhibit elevated levels of il-18 [ 5557 ] . in a cohort of renal biopsies from patients with nondiabetic kidney disease , levels of mrna encoding nlrp3
correlate with renal function , strongly suggesting that nlrp3 contributes to the pathogenesis of chronic kidney disease .
this is supported by experimental data showing that inflammasome - regulated cytokines such as il-1 and il-18 are implicated in animal models of chronic kidney disease , including glomerulonephritis and renal ischemic injury . in an animal study aimed to evaluate the renal consequences of the chronic administration of high - fructose corn syrup ( hfcs-55 ) , the major sweetener in foods and soft - drinks
, we have recently demonstrated that hfcs-55 feeding caused a significant increase in body weight and more importantly dyslipidemia , hyperinsulinemia , and an increase in insulin resistance due to impaired insulin signaling .
most notably , the hfcs-55 diet evoked upregulation of renal nlrp3 expression , resulting in activation of caspase-1 and the subsequent cleavage of pro - il1 to the biologically active secreted form il-1. these effects were due , at least in part , to the marked hyperuricemia afforded by the dietary manipulation , as also confirmed by a previous study demonstrating that increased levels of uric acid directly activate the nlrp3 inflammasome .
similarly , rats fed with fructose , which is known to raise uric acid levels , showed a significant increase in renal protein levels of nlrp3 .
however , one important question that remains to be answered regards the specific cell types involved in renal nlrp3 activation .
as several studies have shown that monocyte / macrophage recruitment to the kidney significantly contributes to the renal injury , we can not rule out that the increased nlrp3 activation in the kidney is due to an increase in the infiltrating macrophages or , more likely , to a crosstalk between macrophages and tubular / glomerular cells .
although it has been recently proposed that sarcopenia ( loss of muscle mass ) and myosteatosis ( fat infiltration in skeletal muscle ) exert a key role in triggering insulin resistance in obese patients , so far the potential role of nlrp3 complex activation in muscle activity and muscle production of inflammatory mediators has not yet been investigated .
however , there is evidence that components of the inflammasome complex are upregulated in dysferlin - deficient human muscle , thus suggesting that skeletal muscle cells can actively participate in inflammasome activation .
this is a crucial point as recent studies have demonstrated that skeletal muscle cells produce and release cytokines ( myokines ) that act in an autocrine , paracrine , and/or endocrine manner to modulate metabolic and inflammatory process .
for example , it has been demonstrated very recently that muscular expression of pgc-1 alpha stimulates the secretion of a newly identified myokine , irisin , which improves glucose homeostasis and causes weight loss .
however , the interactions between local nlrp3 expression / activity and myokines production as well as the effects of these interactions on muscle structure , function , and insulin - sensitivity in animals and humans have never been investigated .
interestingly , both il-1 and il-18 seem to exert a crucial role also in the initiation and progression of the idiopathic inflammatory myopathies , a heterogeneous group of chronic disorders with predominant inflammation in muscle tissue , including dermatomyositis , polymyositis , and myositis [ 6567 ] .
studies elucidating the detailed involvement of muscular inflammasome protein complex may thus provide promising targets for new therapies for this heterogeneous group of inflammatory muscle diseases .
individuals with obesity and insulin resistance have an increased burden of cardiovascular disease ( cvd ) . in the kuopio ischemic heart disease study , lakka et al . reported a 4.26-fold relative risk for mortality due to heart disease and a 1.77 relative risk for all - cause mortality in obese , insulin - resistant patients .
similarly , in the botnia study the risk for coronary heart disease ( chd ) and stroke was shown to be increased threefold and the risk for cardiovascular mortality was increased six fold .
the hoorn study examined 615 men and 749 women aged 50 to 75 years without diabetes or a history of cvd at baseline and reported that the development of insulin resistance and/or obesity was associated with about a twofold increase in age - adjusted risk of fatal cvd in men and nonfatal cvd in women .
studies published during the past decade have convincingly demonstrated a pathophysiological role for the inflammatory response in the development of both insulin resistance and related cvd . the finding a little over a decade ago that the secretion of il-1 and il-18 was increased in an ischemia / reperfusion ( i / r ) model of suprafused human atrial myocardium provided the first clear link between inflammasome activation and cvd development .
experimental studies in mice with genetic deletion of caspase-1 have identified caspase-1 inhibition as a potential target for pharmacological intervention in the setting of cvd [ 7274 ] .
a recent report described formation of the inflammasome in a mouse model of myocardial i / r , mainly in cardiac fibroblasts and infiltrating cells , and reported that asc knockout mice were protected , with a significant decline in cardiac infiltration of phagocytes , inflammatory cytokine levels , infarct size , and myocardial fibrosis and dysfunction .
the inflammasome was also detected in cardiomyocytes bordering the infarct zone during the infarct process , and prevention of inflammasome activation limited infarct size and cardiac enlargement after acute myocardial i / r injury in the mouse .
nlrp3 deficiency protects mice also from renal i / r injury [ 77 , 78 ] .
both studies showed that the absence of nlrp3 protected kidneys against renal i / r injury to a greater extent than the absence of asc , suggesting that nlrp3 may play an additional role in renal i / r injury independently of asc and caspase-1 .
overall , the ability of members of the nlrp3 inflammasome protein complex to target molecular and cellular pathways involved in both metabolic and cardiovascular diseases suggest that selective pharmacological modulation of nlrp3 inflammasome has the potential to exert synergistic effects in the control of metabolic disorders and its cardiovascular complications .
thus , this unique therapeutic strategy could decrease the burden of cardiovascular morbidity and mortality in the presence of obesity and insulin resistance , although , to date , there are no clinical data to support this concept .
in conclusion , nlrp3 inflammasome is a novel protein complex that integrates multiple exogenous and endogenous danger signals into the immediate secretion of il-1 and il-18 .
most recent data suggest that activation of the nlrp3 inflammasome complex contributes to the pathophysiological mechanisms that explain the development of visceral obesity and insulin resistance .
thanks to its wide distribution in different tissues and organs , the nlrp3 inflammasome protein complex may represent a crucial signaling pathway that facilitates organ crosstalk and local injury in tissues target of metabolic damage . a better understanding of this novel pathway could help to clarify the crucial role of the molecular mechanisms of interorgan crosstalk during obesity and insulin resistance development .
studies using animal models and human biopsies will be useful to determine the spatial and temporal expression of inflammasome components inside the organs and to correlate these findings with disease activity or prognosis .
gene polymorphism studies on suitable patient cohorts could help to determine the functional significance of the protein expression data .
finally , the identification of selective pharmacological tools able to affect expression and/or activity of this novel pathway could represent the ultimate proof of significance of the inflammasome - caspase-1-il-1/18 axis in the development of metabolic inflammation .
the effects evoked by these novel pharmacological tools should be compared with effects obtained by targeting selective cytokine receptor activities in order to better elucidate the potential crucial role of nlrp3 inflammasome protein complex in mediating inflammatory diseases .
this approach may not only offer a potentially fruitful area of research , but it will also hopefully lead to novel and specific therapies for obesity - related conditions such as insulin resistance and its associated cardiovascular complications . | pubmed |
Relation between antiparticle and the Dirac conjugate? bar symbol
The Dirac conjugate is defined as
$$
\bar{\psi} = \psi^{\dagger}\gamma^0
$$
where $\psi$ is a spinor (4 dim for spin 1/2) that can describe a mixture (direct sum?) of fermion and anti-fermion states. And $\bar\psi$ is just another form of $\psi$ that can form an Lorentz invariant bilinear.
In other places, however, the bar notation is used for antiparticles, notably, $\bar{u}u$ $\bar{d}d$ to mark antiparticle particle pairs.
These two different ideas can be mixed sometimes, for example in Peskin's QFT Sec. 19.3, the lagrangian and currents used bar symbols to represent the Dirac conjugate,
>
> $$\begin{aligned}j\_L^\mu=\bar Q\_L\gamma^\mu Q\_L, \qquad &j\_R^\mu=\bar Q\_R\gamma^\mu Q\_R, \qquad
> \\j\_L^{\mu a}=\bar Q\_L\gamma^\mu\tau^a Q\_L, \qquad &j\_R^{\mu a}=\bar Q\_R\gamma^\mu\tau^a Q\_R,\end{aligned}\tag{19.84}$$
>
>
>
while immediately after, it represents antiparticles:
>
> as Fig. 19.5 shows, they must contain net chiral charge, pairing **left-handed quarks with the antiparticles of right-handed quarks**. The vacuum state with a quark pair condensate is characterized by a nonzero vacuum expectation value for the scalar operator
> $$
> \langle 0|\bar QQ|0\rangle=\langle 0|\bar Q\_LQ\_R+\bar Q\_rQ\_L|0\rangle\ne 0,\tag{19.87}
> $$
> *[bold mine]*
>
>
>
So, is there a connection in the concept of antiparticle and Dirac conjugate, and that the bar notation is an intentional choice? If so, how should I distinguish when spinor represents only particle or a superposition of both?
The bar notation is necessary in order to make all of the quantities above Lorentz invariant. In short the relationship between the bar'ed quantitites and charge conjugates of fermions have to do with taking the hermitian conjugate of the creation / annihilation opeartors.
Let us focus for now on a free theory of Fermions. A Dirac Fermion can be written down as the following solution to the Dirac equation
$$
\psi(x) = \sum\_{s \pm}\int\tilde{dp}\big[ a\_s(\textbf{p})u\_s(p)e^{ip\cdot x}
+ b\_s^{\dagger}(\textbf{p})\nu\_s(p)e^{-ip\cdot x}\big] \\
\bar{\psi}(x) = \sum\_{s \pm}\int\tilde{dp}\big[ a^{\dagger}\_s(\textbf{p})\bar{u}\_s(p)e^{ip\cdot x}
+ b\_s(\textbf{p})\bar{\nu}\_s(p)e^{-ip\cdot x}\big]
$$
where $\tilde{dp}$ is a Lorentz invariant measure and $u\_s(p)$ and $\nu\_s(p)$ are four-component spinors
$$
u\_s(p) = \begin{pmatrix}
\sqrt{p\cdot \sigma} \;\xi^s \\ \sqrt{p\cdot \bar{\sigma}} \;\xi^s \end{pmatrix};\; \nu\_s(p) =\begin{pmatrix}
\sqrt{p\cdot \sigma} \;\eta^s \\ -\sqrt{p\cdot \bar{\sigma}} \;\eta^s \end{pmatrix};\; \overset{(-)}{\sigma\_{\mu}} = (\mathbb{1}, \pm \vec{\sigma})
$$
corresponding to fermion and anti-fermion spinors. $a^{(\dagger)}\_s(\textbf{p})$ and $b^{(\dagger)}\_s(\textbf{p})$ are annihilation (creation) operators that can act on the Vacuum
$$
a\_s(\textbf{p})|0\rangle = b\_s(\textbf{p})|0\rangle = 0 \\
a^{\dagger}\_s(\textbf{p})|0\rangle = \frac{1}{\sqrt{2E\_{\textbf{p}}}}|\textbf{p},s\rangle\_{\text{ferm}};\;
b^{\dagger}\_s(\textbf{p})|0\rangle = \frac{1}{\sqrt{2E\_{\textbf{p}}}}|\textbf{p},s\rangle\_{\text{anti-ferm}};
$$
Charge conjugation is a symmetry that is manifest in some theories of phenomenalogical interest (and some that are not). Therefore Charge conjugation is an operator that commutes with that Hamiltonion and thus, is a quantum number for states in the Hilbert Space.
For a general state one has
$\mathcal{C}|\phi\rangle = \eta\_C|\phi^c\rangle$ for some field $\phi(x)$. Therefore, if we want to do a charge conjugation on some state, based off of how the creation operators act on the vacuum, what we want is
$$
\mathcal{C}^{-1}a\_s(\textbf{p})\mathcal{C} = b\_s(\textbf{p})
$$
and vice-versa. As it turns out, the charge conjugate of the Dirac fermion field operator is
$$
\mathcal{C}^{-1}\psi(x)\mathcal{C} = \psi^c(x) = \eta\_cC\bar{\psi}^T(x).
$$
Noting the following from Srednickie pg 245
$$
C\bar{u}\_s(p)^T = \nu\_s(p);\; C\bar{\nu}\_s(p)^T = u\_s(p)
$$
one obtains
$$
\psi^c(x) = \sum\_{\pm}\int\tilde{dp}\big[ b\_s(\textbf{p})u\_s(p)e^{ip\cdot x}
+ a\_s^{\dagger}(\textbf{p})\nu\_s(p)e^{-ip\cdot x}\big].
$$
Now both $\bar{\psi}$ and $\psi^c$ are different field operators. But think about how both operators act on the vacuum for this free Fermion theory.
To me at least this is how I see it. When people talk about *anti-quarks* or something in expressions that look like $\bar{u}(x)\gamma^{\mu}u(x)$, I just thing of it as an "abuse of notation" to make physical sense about the quantity we are looking at. In a way they are speaking about the "bar'ed" quantities with respect to how the corresponding free Fermion operator acts on the vacuum.
The reliability of this physical reasoning lies on the reliability of a perturbative expansion of some interacting theory over free fields. Strictly speaking, in strongly coupled theories (or even in something like low-energy QED if you are purist), this kind of physical argument has no rigorous basis.
I hope I answered your question. Hell I hope I am understanding this right. This is just the way I have always understood it.
| stackexchange/physics |
k.h . would like to thank g.c .
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this research was supported in part by the u.s .
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de - fg03 - 93er40757 and de - fg02 - 95er40896 and in part by the university of wisconsin research committee with funds granted by the wisconsin alumni research foundation . the h1 collaboration , c. adloff et al . ,
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1 . event distributions at @xmath18 in @xmath9 from the h1 ( solid points ) and zeus ( open points ) experiments
. 2 . integrated cross sections versus a minimum @xmath2 for @xmath9 for the sm ( solid curve ) and the contact interactions of ( [ contrib - a ] ) ( dashed curve ) and ( [ contrib - b ] ) ( dotted curve ) .
the data points are combined h1 and zeus measurements .
3 . predicted @xmath13 and @xmath14 distributions for @xmath10 and @xmath142 for the sm ( solid curves ) and with two choices of the contact interactions of ( [ contrib - a ] ) ( dashed curves ) and ( [ contrib - b ] ) ( dotted curves ) .
the drell - yan cross section @xmath143 at the tevatron ( @xmath144 tev ) for the sm with the contact interactions of ( [ contrib - a ] ) ( dashed curve ) and ( [ contrib - b ] ) ( dotted curve ) .
preliminary cdf data from ref .
@xcite are compared .
a constant @xmath20-factor is determined from the data in the region of the @xmath45-resonance . | arxiv |
automatic object recognition and image classification are important and challenging tasks .
this paper is inspired by the remarkable recent work of poggio , serre , and their colleagues @xcite , on rapid object categorization using a feedforward architecture closely modeled on the human visual system .
the main directions it departs from that work are twofold .
first , trading - off biological accuracy for computational efficiency , our results exploit more engineering - motivated mathematical tools such as wavelet and grouplet transforms @xcite , allowing faster computation and limiting ad - hoc parameters .
second , the approach is generalized by adding a degree of _ feedback _ ( another known component of human perception ) , yielding significant performance and robustness improvement in multiple - object scenes . in experiments ,
the resulting scale- and translation - invariant algorithm achieves or exceeds state - of - the - art performance in object recognition , but also in texture and satellite image classification , and in language identification .
as in @xcite , the algorithm is hierarchical . in addition , motivated in part by the relative uniformity of cortical anatomy @xcite , the two layers of the hierarchy are made to be computationally similar , as shown in fig .
[ fig : algo ] .
layer one performs a wavelet transform @xcite in the @xmath0 unit followed by a local maximum operation in the @xmath1 unit .
the transform in the @xmath2 unit in layer two is similar to the grouplet transform @xcite , and is followed by a global maximum operation in the @xmath3 unit .
+ @xmath4 * wavelet transform*. the frequency and orientation tuning of cells in visual cortex v1 can be interpreted as performing a wavelet transform of the retinal image @xcite .
let us denote @xmath5 a gray - level image of size @xmath6 .
a translation - invariant wavelet transform is performed on the ] where @xmath7 denotes the orientation ( horizontal , vertical , diagonal ) , @xmath8 is a wavelet function and @xmath9 are the wavelet coefficients .
scale invariance is achieved by a normalization @xmath10 where @xmath11 is the image energy within the support of the wavelet @xmath12 .
one can verify that @xmath13 where @xmath14 and @xmath15 are the coefficients of @xmath5 and of its @xmath16-time zoomed version @xmath17 .
the normalization also makes the recognition invariant to global linear illumination change .
+ @xmath18 * local maximum * limited translation invariance is achieved at this stage by keeping the local maximum of @xmath14 coefficients in a subsampling procedure : @xmath19 the maximum being taken at each scale @xmath20 and orientation @xmath21 within a spatial neighborhood of size proportional to @xmath22 .
the resulting @xmath23 map at scale @xmath20 and orientation @xmath21 is thus of size @xmath24 .
@xmath25 * grouplet - like transform*. cells in visual cortex v2 and v4 have larger receptive fields comparing to those in v1 and are tuned to geometrically more complex stimuli such as contours and corners @xcite .
the geometrical grouplets recently proposed by mallat @xcite imitate this mechanism by grouping and re - transforming the wavelet coefficients .
the procedure in @xmath2 is similar to the grouplet transform . instead of grouping the wavelet coefficients with a multi - scale geometrically adaptive association field and then re - transforming them with haar - like functions as in @xcite ,
responses of @xmath2 are obtained via inner products between @xmath23 coefficients and sliding patch functions of different sizes : @xmath26 where @xmath27 of support size @xmath28 are patch functions that group the 3 wavelet orientations in a square of size @xmath29 .
while the grouplet functions are adaptively chosen to fit the geometry in the image @xcite , the patch functions @xmath27 , @xmath30 are learned with a simple random sampling as in @xcite : each patch is extracted at a random scale and a random position from the @xmath23 coefficients of a randomly selected training image , the rationale being that patterns that appear with high probability are likely to be learned .
+ @xmath31 * global maximum*. a global maximum operation in space and in scale is applied on @xmath32 and the resulting @xmath33 coefficients @xmath34 are thus invariant to image translation and scale change . + * classification * the classification uses @xmath33 coefficients as features and thus inherits the translation and scale invariance .
while various classifiers such as svms can be used , a simple but robust nearest neighbor classifier will be applied in the experiments .
structures that appear with a high probability are likely to be learned as patch functions through random sampling .
however , they are not necessarily salient and neither are the resulting @xmath33 features .
this suggests active selection of the learned patches .
for example , lowe and mutch have constructed sparse patches by retaining one salient direction at each position @xcite .
a simple patch selection is proposed here by sorting the variances of the @xmath33 coefficients of the _ training _ images .
a small @xmath35 variance implies that the corresponding patch @xmath27 is not salient .
[ fig : c2:variance]-a plots the variance of the @xmath33 coefficients of the motorcycle and the background images in the caltech5 database ( see fig .
[ fig : caltech5 ] ) , the @xmath32 patches being learned from the same images . out of the 1000 patches , 200 salient ones whose resulting @xmath33 have non - negligible variance are selected .
other patches usually correspond to nonsalient structures such as a common background and are therefore excluded .
[ fig : c2:variance]-b and c show that after patch selection the 200 @xmath33 coefficients are mainly positioned around the object , as opposed to the 1000 @xmath33 coefficients spreading over all the image prior to patch selection .
the recognition using these salient patches is not only more robust but also 5 times faster .
[ cols="^,^,^ " , ]
inspired by the biologically motivated work of @xcite , we have described a wavelet - based algorithm which can compete with the state - of - the - art methods for fast and robust object recognition , texture and satellite image classification , language recognition and sound classification .
a feedback procedure has been introduced to improve recognition performance in multiple - object scenes .
potential applications also include video archiving ( semantic video analysis ) , video surveillance , high - throughput drug development , texture retrieval , and robotic learning by imitation . to further improve and extend the algorithm , a key aspect will be a more refined use of feedback between different levels .
such feedback will naturally involve stability and convergence questions , which will in turn both guide the design of the algorithm and shape its performance .
in addition , contrary to the nervous system , the algorithm need not be constrained by information transmission delays between different levels .
preliminary ideas in this direction are briefly discussed in the appendix .
+ * appendix *
the first step towards introducing a dynamic systems perspective aimed at further development of feedback mechanisms is simply to rewrite the algorithm in terms of differential equations , which puts it in a form more suitable to subsequent analysis of stability and convergence . with spike amplitude equal to @xmath46 @xmath47
the function @xmath48 is discussed later in this section and in a companion paper .
the dynamics of @xmath49 can be modified in turn so that states corresponding to each object appear in sequence according to the state @xmath50 where , componentwise , @xmath53 where @xmath54 is active and and @xmath55 otherwise .
note that @xmath50 smoothly transitions between @xmath56 and @xmath46 according to the attended object .
the positive gain @xmath57 is chosen such that @xmath58 , where @xmath59 is the spike duration , itself a fraction of the interspike period .
techniques for globally stable spike - based clustering are described in a companion paper , based on modified fitzhugh - nagumo neural oscillators @xcite , similar to @xcite , @xmath60\nonumber\end{aligned}\ ] ] where @xmath61 is the membrane potential of the oscillator , @xmath62 is an internal state variable representing gate voltage , @xmath63 represents the external current input , and @xmath64 , @xmath65 and @xmath66 are strictly positive constants . using a diagonal metric transformation @xmath67
, one easily shows , similarly to @xcite , that one of the most immediate additional feedback mechanisms to be explored is that of generalized diffusive connections ( @xcite , section 3.1.2 ) . in a feedback hierarchy , these correspond to achieving consensus between multiple processes of different dimensions .
similarly to @xcite , composite variables for dynamic tracking can be used at every level , based on both top - down an bottom - up information .
this allows one to implicitly introduce time - derivatives of signals in the differential equations , without having to measure or compute these terms explicitly .
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, pp.18 - 32 , 2000 . | arxiv |
it has been argued ( jore , haynes & broeils 1997 ) that some of the massive bulges of sa type galaxies have not been formed during the collapse of the protogalaxy or by secular evolution of the galactic disk ( pfenniger , combes & martinet 1994 ) , but by capture of satellite galaxies .
jore , haynes & broeils ( 1997 ) present a sample of sa galaxies with kinematically distinct components in their inner parts such as counter - rotating disks .
these might be well interpreted as debris of satellite galaxies which disintegrated while they merged with their parent galaxies . on the other hand , ostriker ( 1990 )
has pointed to the fact that the disks of sa galaxies are dynamically cool enough to develop spiral structure . since
galactic disks are dynamically heated during the merging process , this sets severe constraints on the accretion rate of satellites ( tth & ostriker 1992 ) .
recently gerssen , kuijken & merrifield ( 1997 ; hereafter referred to as gkm ) have observed the kinematics of the stellar disk of ngc488 .
ngc488 is a typical sa galaxy which is actually surrounded by dwarf satellites ( zaritsky et al . 1993 ) , so that there might have been indeed minor merger events in the past .
gkm discuss implications of their observations , in particular the shape of the velocity ellipsoid , for dynamical disk heating by molecular clouds and transient spiral density waves .
but their data allow also to state ostriker s ( 1990 ) objections to the scenario of steady accretion of small satellites in a quantitative way .
for this purpose i construct in sections 2 and 3 dynamical models of the bulge and disk of ngc488 using the photometric and kinematical data presented by gkm . in the final section
i discuss the dynamical state of the disk and implications for the merging history of ngc488 .
i adopt the decomposition of the major - axis surface brightness profile into bulge and exponential disk contributions , respectively , given by gkm . in fig .
1 the surface brightness profile of the bulge is shown either as a de vaucouleurs profile ( left panel ) or the surface brightness profile of a spherical bulge model with a density distribution of the form @xmath0 the surface brightness profile follows a similar law with the exponent lowered by one and is shown in the right panel of fig . 1 fitted to the data of gkm .
the core radius which i find this way is @xmath1 = 63 or 920 pc if a distance of 30 mpc to ngc488 is assumed .
gkm have determined the rotation curve of ngc488 using absorption line spectra of the stars and give a parametrization in the form @xmath2 where the fiducial radius @xmath3 corresponds to a galactocentric distance of 40or 5.8 kpc .
this is equal to the radial exponential scale length of the disk in the b - band .
the rotation curve determined by gkm fits well to the rotation curve derived by peterson ( 1980 ) using emission line spectra .
peterson ( 1980 ) has also determined circular velocities in the region dominated by the bulge , which i have combined to a single data point in figs .
unfortunately , no hi rotation curve is available . to the observed rotation curve
i fit a model rotation curve of the form @xmath4 where @xmath5 , @xmath6 , and @xmath7 denote the contributions due to the bulge , disk , and dark halo , respectively .
the bulge contribution is given according to equation ( 1 ) by @xmath8 where g denotes the constant of gravitation .
the rotation curve of an infinitesimally thin exponential disk is given by @xmath9 where @xmath10 is the central face - on surface density of the disk .
@xmath11 is the radial exponential scale length , @xmath12 is an abbreviation for @xmath13 , and @xmath14 and @xmath15 are bessel functions ( cf . binney & tremaine 1987 ) .
finally , i consider a dark halo component , which i approximate as a quasi - isothermal sphere , @xmath16 with a rotation curve @xmath17 the free parameters to be determined by a fit of equation ( 3 ) to the observed rotation curve are the central densities of bulge , disk , and dark halo , respectively , and the core radius of the dark halo . as is well known ( see van albada 1997 for a comprehensive discussion ) , the decomposition of rotation curves is by no means unique , but allows for a large variation of the parameters .
the bulge parameters , however , are well constrained , because they rely mainly on the inner most data point in figs . 2 to 5 , where the disk and dark halo contributions are negligible .
the central density of the bulge is determined as @xmath18 which implies a total mass of the bulge of @xmath19 .
first , i consider the ` maximum disk ' case , where the disk contribution to the rotation curve is maximised . as can be seen from fig . 2 only a very minor dark halo , if any at all , is required to fit the observed rotation curve .
next , i illustrate a ` medium disk ' decomposition which requires a dark halo in fig . 3 .
de jong ( 1995 ) has shown that the radial exponential scale lengths of galactic disks are usually smaller in the infrared than at optical wavelengths . since the infrared scale may be more appropriate to describe the distribution of mass in the disk , i consider also cases where the scale length of ngc488 has been reduced following de jong ( 1995 ) by a factor of 2/3 . in figs . 4 and 5 the corresponding ` maximum disk ' and a ` medium disk ' decomposition of the rotation curve are shown .
the parameters derived from the various fits are summarized in table 1 .
as can be seen from table 1 the dark matter contributes in most cases considerably to the mass budget .
.disk and dark halo parameters [ cols="^,^,^,^,^,^,^,^ " , ] total mass within a radius of @xmath20 .
in order to discuss the viability of the dynamical disk models derived in the previous section i consider two diagnostics .
first , i estimate the expected _ vertical _ scale height of the disk , even though finite scale heights have been neglected in the decompositions of the rotation curve .
an isothermal self - gravitating stellar sheet follows a vertical @xmath21 density profile ( cf . binney & tremaine 1987 ) , with the vertical scale height given by @xmath22 where @xmath23 is the dispersion of the vertical velocity components of the stars and @xmath24 denotes again the surface density of the disk .
since the bulge is so massive its gravitational force field has to be taken into account . in regions @xmath25 and @xmath26 , which are of interest here , the vertical gravitational force field due to the bulge is approximately given by @xmath27 fuchs & thielheim ( 1979 ) have considered the case of an isothermal sheet imbedded in a linear force field .
they show that the density profile of such a disk follows still approximately a @xmath28 law with a modified scale height which can be expressed using equation ( 9 ) as @xmath29 this can be solved explicetely for @xmath30 .
next , i consider the toomre stability parameter @xmath31 ( cf . binney & tremaine 1987 ) , @xmath32 where @xmath33 denotes the epicyclic frequency , @xmath34 , and @xmath35 is the radial velocity dispersion of the stars .
the velocity dispersions have been directly observed in ngc488 by gkm and in equations ( 8) and ( 10 ) i use the analytical fitting formulae given by the authors . in the maximum disk case
the derived vertical scale height is rather small , @xmath36 = 0.07 at @xmath37 = 5 kpc .
the ratio of vertical - to - radial scale lengths is related to the flattening parameter of the disk by @xmath38 ( fuchs et al .
guthrie ( 1992 ) finds for the disks of sa galaxies typical values of @xmath39 , implying @xmath40 .
an even more severe argument against this disk model is a @xmath31 parameter less than one .
such a disk will undergo violent gravitational instabilities ( hockney & hohl 1969 ) , whereas the very smooth optical appearance of the disk ( elmegreen 1981 ) gives no indications for such processes .
the medium disk model is much more acceptable in this respect .
its vertical scale height is about twice that of the maximum disk , but still smaller than the values found by guthrie ( 1992 ) . the maximum disk model assuming a shorter radial scale length is very similar to the medium disk model with the optical radial scale length ; @xmath36 is 0.21 in this case .
in the medium disk model with the shorter radial scale length the ratio of vertical - to - radial scale lengths is @xmath41 0.31 , which would be consistent with the upper value given by guthrie ( 1992 ) .
however , the stability parameter is @xmath42 3 which would make the disk dynamically too hot to develop spiral structure , as can be seen , for instance , in the numerical disk simulations by sellwood & carlberg ( 1984 ) , whereas the optical image of ngc488 ( elmegreen 1981 ) shows clear regular spiral arms . thus i conclude that only models of the second or third type give a reasonable description of the dynamics of the disk of ngc488 .
this discussion shows that the disk of ngc488 must be dynamically cool .
obviously this fact sets severe constraints on the merging history of ngc488 .
the details of energy transfer from a satellite galaxy merging with its parent galaxy to the disk of the parent galaxy are fairly complicated .
they have been studied by tth & ostriker ( 1992 ) and , in particular , by quinn & goodman ( 1986 ) , quinn , hernquist & fullagar ( 1993 ) , walker , mihos & hernquist ( 1996 ) , and huang & carlberg ( 1997 ) in extensive numerical simulations .
these simulations have shown that a satellite galaxy looses its orbital energy due to a number of effects .
it induces coherent distortions of the disk of the parent galaxy such as tilts , warps , and non axisymmetric structures like bars and spiral arms , which are not very effective in heating the disk dynamically .
some of the energy of the satellite is carried away by its debris .
quinn , hearnquist & fullagar ( 1993 ) estimate that only about one half of the energy of the satellite is converted to random kinetic energy of the disk of the parent galaxy .
huang & carlberg ( 1997 ) have shown that the energy transfer depends also on the structure of the satellite .
low density satellites , for instance , do not reach the inner parts of the disk before they are disrupted .
they heat only the outer part of the disk or the inner halo , but do not contribute to the bulge .
observational evidence for such merging events in nearby spiral galaxies is discussed by zaritzky ( 1995 ) .
gkm have observed the kinematics of the inner part of the disk of ngc488 .
the numerical simulations show that satellites which reach these parts of the disk will be on orbits which are lowly inclined with respect to the plane of the parent galaxy .
the energy which the satellites loose while they spiral inwards will be then deposited mainly into the disk until they have reached the bulge , because the disk density is dominating as can be shown using the parameters given in table 1 . in order to illustrate the disk heating effect i consider the strip of the disk ranging from galactocentric radii 5 to 10 kpc .
it is straightforward to calculate from the centrifugal forces modelled in equations ( 4 ) to ( 7 ) the loss of potential energy @xmath43 of a satellite spiralling from radius 10 kpc to 5 kpc . using the parameters given in table 1 i find for all disk models about the same value of @xmath44 , where @xmath45 denotes the mass of the satellite .
this energy loss will lead to an increase of the peculiar velocities of the disk stars , which is approximately given by ( ostriker 1990 ) , @xmath46 where @xmath47 is the disk mass contained in the strip from 5 to 10 kpc radius .
equation ( 12 ) may be cast into the form @xmath48 averaging the observed velocity dispersion @xmath49 radially and assuming a pre - merger stability parameter of @xmath50 , i obtain for disk models 2 and 3 mass estimates of @xmath51 , meaning that the present dynamical state of the disk of ngc488 is consistent with _
one _ merging event in the past with a satellite galaxy of such a mass .
the build - up of the entire bulge of ngc488 , on the other hand , would have required about 100 of such mergers .
reshetnikov & combes ( 1997 ) have argued that stellar disks will be cooled dynamically after a merging event by newly born stars on low - velocity - dispersion orbits .
fresh interstellar gas maintaining a high star formation rate is supposed to be replenished in the inner parts of the disks by radial gas inflow which is induced by non - axisymmetric tidal perturbations during the merging event .
the gas consumption rate required to cool the disk can be estimated in the following way . if , for instance , the surface density of the disk has grown after a certain time interval to @xmath52 , the stability parameter is roughly given by @xmath53 where i approximate the velocity dispersion of the disk by a mass weighted average of the velocity dispersion of the heated stellar component and the velocity dispersion @xmath54 of the cooling stars .
the stability parameter ( 14 ) can be expressed in terms of the stability parameter of the heated disk , @xmath55 , as @xmath56 where i have neglected the velocity dispersion of the newly born stars .
thus , if a cooling of the stability parameter by an amount of @xmath57 is necessary , this requires a relative increase of the disk mass of @xmath58 in the form of newly born stars .
if , for instance , @xmath59 this implies @xmath60 .
this is of the order of what is available in ngc488 in the form of interstellar gas .
the total mass of hydrogen in atomic and molecular form in ngc488 is estimated as @xmath61 ( young et al .
1996 ) , which after multiplication with a factor of 1.4 in order to account for heavier elements has to be compared with the stellar disk mass estimates given in table 1 .
the gas content of dwarf spirals is typically of the order of @xmath62 ( broeils 1992 ) , i.e. only about one tenth of the mass needed to cool the disk after a merging event . from this discussion
i conclude that the disk of a sa galaxy may in principle ` recover ' from a minor merger and flatten its disk again and develop again spiral structure , although this has still to be studied in detail .
the build - up of the bulge of ngc488 , however , would require about 100 mergers implying a merger rate of 10 mergers per gyr if a steady merger rate is assumed .
this would mean that in ngc488 at present about five times the stellar disk mass must be converted per gyr from interstellar gas into stars in order to keep the stellar disk in its present dynamical state .
the actually observed star formatiom rate ( young et al . 1996 ) , on the other hand , is only @xmath63 .
so it seems unlikely that the bulge of ngc488 has been build up entirely by accretion of satellite galaxies . | arxiv |
the inherent complexities of science and technology in recent years have caused most countries , universities , and research institutions to face difficulties in finding the right human resources and enough budgets for their research projects .
one of the results of these complexities is that solo , individual researches are being replaced by collective research attempts in many disciplines such that scientific collaboration has become one of the most important social mechanisms in recent research projects .
newman believes that useful and effective sharing of viewpoints , specialization of scientific disciplines , multi - discipline studies , increasing of research costs , and political factors all played important roles in increasing the level of collaboration between researchers .
the result of this collaboration is that in order to complete their research , many scientists collaborate with their peers in other organization , disciplines , and even other countries .
one of the most tangible forms of this collaboration is co - authorship , which can be seen in articles published in any technical and scientific journal nowadays . during recent years
, the discipline of library and information science in iran had grown in both educational and research dimensions .
continuity in publication of research journals and emergence of new ones are among the most important happenings regarding its research dimension . due to these changes
, many researchers tried to investigate the research structure of this discipline in different national and international levels , aiming to identify its strengths and weaknesses in order to improve the studies conducted in this discipline . in his study , farajpahlou investigated the collective articles of iranian authors in library and information science in four specialized farsi journals between years 2001 and 2003 .
his findings showed that among 168 investigated articles , only 23 articles ( 14% ) were the results of collaboration of several authors and the average collaboration was 2.04 authors per paper .
an investigation of pakistan library and information science journal ( plisj ) by naseer and mahmood between years 1998 and 2007 showed that 88.6% of the articles published in this journal had one author .
indexed in emerald between years 2003 and 2008 showed that the collaboration coefficient of researchers in library and information science discipline is 0.08 .
yousefy and malekahmadi also investigated the collaboration between authors of library and information science discipline in isi , scopus , and pubmed databases between years 2001 and 2010 .
their findings showed that 60.45% of the articles had a one author pattern and 30.46% of them had multi - author pattern .
also , the collaboration coefficient of the researchers during the investigated time period was 0.25 .
a review of the previous studies shows a low collaboration rate between researchers in library and information science discipline where many articles follow a single author pattern .
this is in contrast with the scientific collaboration between researchers in physics , biology , and astronomy .
the aim of current study is an assessment of scientific collaboration and co - authorship patterns in library and information science researches conducted in iran . for this end
, the published articles related to this discipline in iranian journals between years 2005 and 2009 were investigated .
this research aims to reach the following goals :
investigating the frequency of individual and collective scientific productions in library and information science in iran.investigating the growth of individual and collective scientific studies in library and information science during the investigated time period.investigation of co - authorship patterns of iranian library and information science researchers andinvestigation of collaboration coefficient , collaboration index ( ci ) , and degree of collaboration ( dc ) in iranian library and information science researchers .
investigating the frequency of individual and collective scientific productions in library and information science in iran . investigating the growth of individual and collective scientific studies in library and information science during the investigated time period .
investigation of co - authorship patterns of iranian library and information science researchers and investigation of collaboration coefficient , collaboration index ( ci ) , and degree of collaboration ( dc ) in iranian library and information science researchers .
the statistical population consisted of 942 documents published in iranian journals regarding library and information science between years 2005 and 2009 [ table 1 ] . in order to gather the research data ,
first , the articles were downloaded onto a personal computer from the main website of each journal . then
, the necessary information such as journal title , number of articles , and number of authors were extracted using a checklist and then analyzed .
ms - excel software was used for data analysis . also , collaboration coefficient , collaboration index ( ci ) , and degree of collaboration ( dc ) were calculated using the following equation : number of published librarianship and information science articles based on publication year and journal where fi the total number of articles with j authors published during a certain period of time , n is the total number of articles published during the same time period , k is the number of authors per article in each discipline , and f1 is the number of articles with a single author published during a certain period of time .
the findings show that in the five year period investigated , a total number of 942 articles were published by researchers in the librarianship and information science field in related journals iran . among those ,
506 documents ( 53.70% ) were written individually and 436 ( 46.30% ) documents were the result of collaboration between two or more authors .
this shows that the researchers in librarianship and information science prefer to work individually [ table 2 ] .
individual and collective scientific productions in librarianship and information science in iran as can be seen in figure 1 , the collective articles have increased over time , and the most number of collective articles were published in year 2009 . on the other hand , despite some fluctuations , individual articles show a decreasing trend with the least number of individual articles being published in year 2009 [ figure 1 ] .
the growth rate of individual and collective articles in librarianship and information science investigating the co - authorship patterns of researchers in librarianship and information science in iran shows the individual authorship pattern to be the most common pattern with 506 ( 53.70% ) of the documents being published individually and without help from other authors .
the second place belongs to two authorship pattern with 341 ( 36.20% ) of the documents [ table 3 ] .
frequency of scientific productions following different co - authorship patterns during the investigated period figure 2 shows scientific productions with individual co - authorship pattern have been declining overtime reaching its lowest point in year 2009 ( with 81 documents ) . on the other hand , all of the other co - authorship patterns ( those with two , three , four , and more than four authors ) show an increasing trend .
growth rate of different co - authorship patterns in librarianship and information science articles in iran analysis of co - authorship patterns of librarianship and information science in different journals shows that highest rank in all co - authorship patterns belongs to national journal of librarianship and information organization ( code h ) , except three authors co - authorship pattern , which belongs to library and information science ( code f ) [ table 4 ] .
the frequency of scientific productions of different journals following different co - authorship patterns during the investigated time period collaboration index is the average number of authors per article .
data in table 5 shows that the collaboration index of librarianship and information science has relatively grown during the investigated time period , and the highest collaboration index ( 1.92 ) was seen in year 2009 . also , the five year collaboration index of librarianship and information science was 1.58 .
degree of collaboration of authors in the investigated articles was 0.46 , which means that there is a moderate trend for co - authorship .
however , the desire for co - authorship had grown during the investigated period , reaching its apex in year 2009 .
the collaboration coefficient of the researchers also shows significant growth between years 2005 and 2009 .
the closer this coefficient is to one , there is more desire for collaboration , and a coefficient near zero means a trend toward individual works .
however , total collaboration coefficient of 0.23 shows low collaboration between librarianship and information science researchers .
analysis of collaboration coefficient ( cc ) , collaboration index ( ci ) , and degree of collaboration ( dc ) of different journals showed that library and information science research ( b ) had the highest collaboration coefficient ( 0.45 ) , collaboration index ( 2.14 ) , and degree of collaboration ( 0.79 ) [ table 6 ] .
collaboration coefficient , collaboration index and degree of collaboration of the researchers in librarianship and information science collaboration coefficient , collaboration index and degree of collaboration of different iranian journals in librarianship and information science
investigating the co - authorship patterns of researchers in librarianship and information science in iran shows the individual authorship pattern to be the most common pattern with 506 ( 53.70% ) of the documents being published individually and without help from other authors .
the second place belongs to two authorship pattern with 341 ( 36.20% ) of the documents [ table 3 ] .
frequency of scientific productions following different co - authorship patterns during the investigated period figure 2 shows scientific productions with individual co - authorship pattern have been declining overtime reaching its lowest point in year 2009 ( with 81 documents ) . on the other hand , all of the other co - authorship patterns ( those with two , three , four , and more than four authors ) show an increasing trend .
growth rate of different co - authorship patterns in librarianship and information science articles in iran analysis of co - authorship patterns of librarianship and information science in different journals shows that highest rank in all co - authorship patterns belongs to national journal of librarianship and information organization ( code h ) , except three authors co - authorship pattern , which belongs to library and information science ( code f ) [ table 4 ] . the frequency of scientific productions of different journals following different co - authorship patterns during the investigated time period
data in table 5 shows that the collaboration index of librarianship and information science has relatively grown during the investigated time period , and the highest collaboration index ( 1.92 ) was seen in year 2009 . also , the five year collaboration index of librarianship and information science was 1.58 .
degree of collaboration of authors in the investigated articles was 0.46 , which means that there is a moderate trend for co - authorship .
however , the desire for co - authorship had grown during the investigated period , reaching its apex in year 2009 .
the collaboration coefficient of the researchers also shows significant growth between years 2005 and 2009 .
the closer this coefficient is to one , there is more desire for collaboration , and a coefficient near zero means a trend toward individual works
. however , total collaboration coefficient of 0.23 shows low collaboration between librarianship and information science researchers .
analysis of collaboration coefficient ( cc ) , collaboration index ( ci ) , and degree of collaboration ( dc ) of different journals showed that library and information science research ( b ) had the highest collaboration coefficient ( 0.45 ) , collaboration index ( 2.14 ) , and degree of collaboration ( 0.79 ) [ table 6 ] .
collaboration coefficient , collaboration index and degree of collaboration of the researchers in librarianship and information science collaboration coefficient , collaboration index and degree of collaboration of different iranian journals in librarianship and information science
the study of scientific collaboration , which is one of the subcategories of scientometrics , has gained increased popularity in recent years , and many researchers attempted to discover the scientific collaboration patterns of different disciplines . the current study aimed to investigate the scientific collaboration patterns of librarianship and information science in iran between years 2005 and 2009 .
the findings showed that in the investigated time period , a total of 942 documents were published in this discipline , 506 ( 53.70% ) of which were created individually and 436 ( 46.30% ) of them had two or more authors .
this is in agreement with the findings of farajpahlou , naseer and mahmood and yousefy and malekahmadi .
study of evolution of scientific products in librarianship and information science shows that the number of individual articles has decreased while the number of collaborative articles has increased , reaching its apex in year 2009 .
this can be due to the increase in the number of graduate students in librarianship and information science in recent years .
most of articles published by these graduate students are results of dissertations or class works and , therefore , it 's necessary to add the name of the supervisor and advisor as collaborative authors leading to the amount of scientific collaboration . on the other hand , another reason for this increase in scientific collaboration can be due to the needs of the researchers because the multi - discipline nature of librarianship and information science and new research trends in masters , doctorate , and post - doctorate levels increases the necessity of collaboration between researchers of multiply disciplines . investigating
the co - authorship patterns of librarianship and information science in iran shows that single author pattern is the most common pattern among the researchers in this area .
more than half of the researchers ( 53.72% ) used individual pattern for their works and had no collaboration with other researchers , and 36.20% of the researchers collaborated with only one other individual ( two author pattern ) .
therefore , research individualism and a preference for creating groups of two are the dominant co - authorship patterns .
also , investigating the co - authorship pattern of different journals shows that the first rank of all co - authorship patterns except three author pattern belongs to national journal of librarianship and information organization ( code h ) . relative increase of collaboration coefficient ( cc ) , collaboration index ( ci ) , and degree of collaboration ( dc ) shows an increase in the desire of researchers in librarianship and information science for working in groups of two and three . investigating the collaboration index shows that in average , each article was the result of collaboration between 1.58 researches .
this collaboration index was lower than the collaboration index reported by osareh for astronomy in 2006 .
on the other hand , a degree of collaboration of 0.46 showed a relative tendency towards collaborative works .
the collaboration coefficient also had an increasing trend with the total of 0.23 , which is in agreement with findings of yousefy and malekahmadi who reported a collaboration coefficient of 0.25 for researchers of librarianship and medical information science .
also , investigating the journals for these three indicators showed that journal of library and information science research ( b ) had the first place in all three indicators . | pubmed |
Is there a quick way to approximate a logarithm in Nernst equation?
The problem is as follows:
>
> In a galvanic cell the cathode is an $Ag^{+}(1.00\,M)/Ag\_{(s)}$
> half-cell. The anode is a standard hydrogen electrode immersed in a
> buffer solution containing $0.10\,M$ benzoic acid $(C\_6H\_5COOH)$ and
> $0.050\,M$ of sodium benzoate $(C\_6H\_5COO^{-}Na^{+})$. The measured
> cell voltage is $1.030\,V$. What is the $pK\_a$ of benzoic acid?.
>
>
>
What I did to solve this problem was to find the potential for the cell involving the standard hydrogen electrode. At first I was confused because there are three "elements" featured in the problem. One being the silver electrode, the other the standard hydrogen electrode and the other a buffer solution, so I didn't know how to proceed from there.
Then I noticed that to get the constant of equilibrium I only require the concentration of $[H^{+}]$ ions as,
$K\_a=\frac{[C\_6H\_5COO^{-}][H^{+}]}{[C\_6H\_5COOH]}$
Therefore to obtain those protons I did this:
The half equations in the cell are:
$\begin{array}{cc}
Ag^{+}+1e^{-}\rightarrow Ag\_{(s)}&E^{0}=0.7999\,V\\
H^{+}+1e^{-}\rightarrow \frac{1}{2}H\_{2(g)}&E^{0}=0.0000\,V\\
\end{array}$
Hence the overall reaction for this process would be:
$E^{0}\_{cell}=E\_{cathode}-E\_{anode}=0.7999-0.0000=0.7999\,V$
Which is for:
$Ag^{+}+\frac{1}{2}H\_{2}+\rightarrow Ag\_{(s)} + H^{+}$
Hence:
$E\_{cell}=E^{0}-\frac{0.0592}{n}\log\frac{[H^{+}]}{[Ag^{+}]p^{\frac{1}{2}}\_{H\_{2(g)}}}$
Since it indicates that the cell potential is $1.030\,V$ then:
$1.030=0.7999-\frac{0.0592}{1}\log\frac{[H^{+}]}{[1](1)^{\frac{1}{2}}}$
Solving this I'm getting:
$[H^{+}]=0.000125306\,M$
Now all that's left is to plug in this value in the equation to get the equilibrium constant:
$K\_a=\frac{[C\_6H\_5COO^{-}][H^{+}]}{[C\_6H\_5COOH]}$
$[C\_6H\_5COO^{-}]=0.05\,M$ and $[C\_6H\_5COOH]=0.1\,M$
Hence:
$K\_a=\frac{(0.05)(1.25306\times 10^{-4})}{(0.1)}=6.2653\times 10^{-5}$
Therefore the $pKa$ of benzoic acid would be:
$pKa=-\log Ka=-\log\left(6.2653\times 10^{-5}\right)=4.20306$
Which does seem to be within the value of benzoic acid which I have on different references. But the problem with this method it is that it required the use of logarithm.
Given this situation, does it exist an approximation or anything that can be done right of the bat to get an idea where that value would be?. Does it exist another method which I could use?.
From your comments it seems that you are looking for an approximation of a log. I wish you clarified that in the main question without mentioning calculators. It seemed you just wanted to avoid a calculator for some unknown reasons. As Poutnik states, anyone who can post here, will certainly have access to computers and hence the ability to calculate logs.
A first-hand approximation is $ln (1+x)$= $x-x^2/2+x^3/3-x^4/4+...$
Also see <https://www.quora.com/How-can-I-calculate-ln-x-without-using-a-calculator>
Use you use a simple ln to log conversion factor in the Nernst equation.
So whatever number you get after dividing the concentrations, subtract "one" from it. This is your $x$. Since you are assuming that a calculator or computer is not available, all you need is a paper an pencil to evaluate the right hand side.
No need to memorize anything for logs.
If you can afford a slide rule, <https://en.wikipedia.org/wiki/Slide_rule>, it can also help as a mechanical calculator. I never used them but Youtube has videos on it.
[Padé Approximation for ln(1+x)](http://www.nezumi.demon.co.uk/consult/logx.htm) provides very interesting trade off between simplicity and accuracy ( See also [Wikipedia - Padé approximant](https://en.wikipedia.org/wiki/Pad%C3%A9_approximant) ):
>
> $$P\{ \ln( 1+x ) \} = \frac{x(6+x)}{6+4x}$$
>
>
> $\ln(1) = 0$, $\ln(2) = 0.7$, $e\_\mathrm{max} = 0.00685$, $e\_\mathrm{max, rel} \lt 1\% $, $e\_\mathrm{RMS} = 0.00258$
>
>
> This is already a good and fast approximation to $\ln(1+x)$ and in many applications like realtime displays can be used as a basis for logarithmic scaling with a few minor modifications for integer arithmetic.
>
>
> Where greater accuracy is required the expression can be optimised by least squares fitting of the coefficients over the range 0-1. This yields:
>
>
> $$p'\{ \ln( 1+x ) \} = \frac{x \cdot (6 + 0.7662\cdot x)}{5.9897 + 3.7658 \cdot x}$$
>
>
> $\ln(1) = 0$, $\ln(2) = 0.69358$, $e\_\mathrm{max} = 4.3E-4$, $e\_\mathrm{max, rel} \lt 0.1\% $, $e\_\mathrm{RMS} = 1.5E-4$
>
>
> This is about as good as you can get with this simple formula, and these coefficients may be scaled up to suitable integers for use.
>
>
> Much higher accuracy is possible by starting from a better series:
>
>
> Define: $y = x/(2+x)$, then $\ln{ \frac{1+y}{1-y} } = 2y + 2y^3/3 + 2y^5/5 + ... $
>
>
> $\ln(1) = 0$, $\ln(2) = 0.69300$, $e\_\mathrm{max} = -0.00014$
>
>
> From which the Pade approximation yields:
>
>
> $$P\{ \ln \frac{1+y}{1-y} \} = \frac{2y\*(15 - 4y^2 )}{15 - 9y^2}$$
>
>
> $\ln(1) = 0$, $\ln(2) = 0.693122 $, $e\_\mathrm{max} = -0.000025$
>
>
> Again this expression can also have its coefficients tweaked to improve accuracy over a narrow range still further.
>
>
>
| stackexchange/chemistry |
thirty years ago virtually nothing was known of the genetics of the retina , and none of the genes responsible for any of the various inherited pathologies of the retina in man had been identified .
but since 1980 a veritable zoo of more than 200 genes causing human retinal pathologies ( retnet , http://www.sph.uth.tmc.edu/retnet/ ) have been identified and with the possible exception of the erythrocyte , the genetics of the photoreceptors have been more intensively studied than any other body cell .
these disease genes cause a vast diversity of abnormalities affecting every aspect of photoreceptor cell form and function .
many of these mutations effect photo transduction function and lead to secondary degenerative changes in the forms of the cells . in many cases of retinitis pigmentosa , for example , the degenerative changes in the photoreceptors may lead to a secondary loss of outer segments and a rounding up of the cells .
other mutations cause primary morphological defects in the photoreceptors , particularly in the cilium and outer segments .
for example , mutations in the rds gene ( peripherin ) cause disorganized outer segment lamellae .
similarly mutations in the rp1 gene lead to incorrectly oriented outer segment discs that fail to stack properly .
mutations in genes specifying proteins associated the connecting cilium such as retinitis pigmentosa gtpase regulator ( rpgr)-interacting protein and rpgr also cause grossly oversized discs . another gene causing retinal degenerative disease mak ( male germ cell associated kinase ) regulates retinal photoreceptor ciliary length and sub compartmentalization .
mak is localized both in the connecting cilia and outer - segment axonemes of photoreceptor cells . in the mak - null retina , photoreceptors exhibit elongated cilia and progressive degeneration .
remarkably among these 200 or so genes known to cause retinal pathologies very few ( if any ) have been identified which might be construed to be anything more than ordinary structural or functional components of the mature photoreceptor .
there is no genetic evidence that any of the genes expressed in the photoreceptors causing dysmorphologies are morphogenes in franklin harold 's sense that is , genes whose primary function is directing or supervising the deployment of the constituents of the photoreceptors into their complex three - dimensional native cellular architectures . as in the case of the red cell ( see accompanying paper ) , all mutations identified to date , which cause dysmorphologies appear to cause defects in ordinary or mundane structural and functional components of the mature photoreceptor !
given the complexity of these remarkable cells and the fact as mentioned above that the genetics of the photoreceptors have been the subject of intensive study , this is an important finding , which has not been reported before and which provides significant support for the growing consensus among cell biologists that cell forms arise mainly from the self - organization of their constituents rather than by instruction from a detailed blueprint in the genome .
we conclude that the native cytoarchitecture of the photoreceptors is essentially epigenetic structures arising from the spontaneous self - organization of the material constituents of the cells themselves , a conclusion consistent with the developing epigenetic self - organizational paradigm in cell biology . while in the case of the far simpler red cell some of the emergent biophysical causal factors
have now been identified , many additional studies will need to be carried out before the emergent biophysical and biomechanical forces responsible for the morphogenesis of more complex cells are understood . | pubmed |
Degrassi, Total Drama series 1. Pilot
My friend Pokémon Ranger Is Amazing 123 actually owns the rights to the Battle Challenge series, but he gave me permission to write a spin off to High School.
Disclaimer: I do not own Battle Challenge, by friend does
* * *
Hunter was in the living room of his house, he lived with his wife, Jennifer and they had 2 kids, Thomas and Brooke.
Hunter was a child actor but now he was 21 and hadn't gotten an acting job in 3 years, he recently auditioned for a new detective show called 'Riley'. He hadn't found out if he got the part yet.
Jennifer walked through the living room to go out.
"Hey sweetie, you still haven't gotten the phone call yet?" asked Jennifer
"Not yet, I'm getting worried" said Hunter
"Well, don't worry, I'm sure they'll call soon" said Jennifer
"Thanks" said Hunter
Hunter gave Jennifer a kiss on the cheek before she left.
==Later==
Jennifer still hadn't returned home. Hunter's phone rang.
"Hello?" asked Hunter
"_Is this Hunter Blakesfield, who auditioned to play detective Jack Riley on the new detective show, Riley?_" asked the man on the other end
"Yes" said Hunter
"_Congratulations, I'm Peter Walron, the creator of Riley, the job is yours if you want it_" said Peter
"Yes, I would love the part" said Hunter
"_Great, I'll see you in Hollywood, California in a week_" said Peter
"Wait, what?" asked Hunter
"_The show is being produced in Hollywood, California, that's not a problem, is it?_" asked Peter
"Um, a little bit, it's just that my wife and my kids live in New York, I'm not sure how they would feel about moving to California" said Hunter
"_Tell you what, talk to your wife about it and call me back, but I need your answer in a week or the offer is off the table_" said Peter before hanging up
==1 Hour Later==
Jennifer was back.
"Hey Hunter, did you get the call?" asked Jennifer
"As a matter of fact, yes, I did" said Hunter
"And?" asked Jennifer
"I got the role" said Hunter
"That's great" said Jennifer
"There's just one thing, if I want it, we would have to move to Hollywood, California" said Hunter
"Oh, well, what did you tell them?" asked Jennifer
"I told them I would get back to them, I'm not sure if we should because our lives are here" said Hunter
"Well, Hunter, this what you've been waiting for" said Jennifer
"But do you even want to move to Hollywood?" asked Hunter
"Well, why not? It could be fun" said Jennifer
"Really? So, should we move to Hollywood?" asked Hunter
"I guess we should" said Jennifer
Hunter and Jennifer seal the deal with a hug.
==The Next Day==
Hunter and Jennifer were at the airport with their kids. When they were there they noticed 2 people that they knew, it was Rodger and Sally.
"Rodger? Sally?" asked Hunter
"Hunter? Jennifer? It's nice to see you, what are you doing?" asked Rodger
"We're moving to Hollywood, Hunter got a part in a new Crime Show" said Jennifer
"That's great, actually, we're moving to Hollywood too" said Sally
"Really? Well, maybe we'll see eachother" said Rodger
Hunter and Jennifer wandered around the airport more and found another one of their old friends, Brandon Baxter.
"Hey Brandon, long time no see" said Hunter
"Hey you guys, what are you doing here?" asked Brandon
"We are moving to Hollywood because Hunter got a part in a new crime show" said Jennifer
"That's great, I'm moving to Hollywood too" said Brandon
"Why?" asked Hunter
"By boyfriend broke up with me, I just want to start over" said Brandon
"That makes sense" said Jennifer
==Later==
After, the 5 arrived in Hollywood, they took a taxi cab.
"Alright, my agent said he took care of the first month's rent at this place" said Hunter to Jennifer, showing her the address
"Where to?" asked the driver
"To Ashton Drive" said Hunter
The driver laughed
"Why did you laugh?" asked Jennifer
"Ashton DRIVE" said the driver
The driver took the 5 to Ashton Drive, only Hunter, Jennifer and Brandon got out.
"Brandon, why did you get out?" asked Hunter
"Um, I don't have a place to stay, so do you mind if I stay at your place until I do?" asked Brandon
"Um, why not? Sure" said Hunter
The three enter their apartment.
"Wow, this is a nice place" said Brandon
"Yeah, it is, I have a feeling that we're gonna like it here.
Meanwhile, with Rodger and Sally, the 2 arrived at their new apartment.
"Well, we're here, what do you think?" asked Rodger
"It's brilliant" said Sally
==The Next Day==
Hunter, Jennifer and Brandon woke up at their apartment.
"Morning Brandon" said Hunter
"Morning you 2, what's the plans for today?" asked Brandon
"Well, I gotta get to the set for the show" said Hunter
"And I'm gonna stay here to take care of Thomas and Brooke" said Jennifer
"Alright, well, I'll see you later" said Brandon
"Where you going?" asked Hunter
"I'm going out to get some breakfast" said Brandon
Brandon went to a coffee shop not far from the apartment, he ordered a coffee and a muffin and sat at a table, when a man walked over to him.
"Excuse me, is this seat taken?" asked the man
"Um, no" said Brandon
"Thanks, it's just that the whole place is packed in the mornings" said the man
Brandon looked at the man, he noticed he looked familiar.
"Hey, aren't you the cab driver from yesterday?" asked Brandon
"Well, I am a cab driver, but you may be thinking of someone else" said the man
"You drove me and my 4 friends to Ashton Drive from the airport" said Brandon
"Then, yeah, that's me, I'm Wyatt" said the man
"I'm Brandon" said Brandon
"Nice to meet you Brandon, what brings you to Hollywood?" asked Wyatt
"Bad breakup, I came to start over" said Brandon
"Ah, makes sense" said Wyatt
Meanwhile, Hunter arrived at the set for his show.
"Ah, Hunter, you're here, nice to see you" said the producer
"Thank you, same goes to you too" said Hunter
"Now, before we start, I wanna introduce your co-star, Trevor Shane" said the producer
"Trevor Shane?" asked Hunter
"Yep, that's me" said Trevor
Trevor Shane had short, black hair, pale skin and no facial hair, he was average height and skinny.
"Nice to meet you, Trevor, I'm Rory, but my friends call me Hunter" said Hunter
"Why do they call you Hunter?" asked Trevor
"Get me a knife and a crossbow and I'll show you" joked Hunter, the truth is, he didn't really know why people called him Hunter, but he was glad hardly anyone knew his real name
"Alright, well, let's get started" said Trevor
"Alright" said Hunter
Meanwhile, Brandon and Wyatt were walking down the street.
"So, what do you do for a living?" asked Wyatt
"I actually haven't found a job yet, I plan to start looking for one in about a week, shouldn't be too hard since I went to Law school" said Brandon
That's when Wyatt saw something.
"Oh god" said Wyatt
"What is it?" asked Brandon
Wyatt pointed to what he saw, it was 2 men, they were holding hands
"A gay couple, so what?" asked Brandon
"It doesn't bother you?" asked Wyatt
"Nah, why should it?" asked Brandon
"Homosexuality is just wrong, love should only be between a man and a woman" said Wyatt
Brandon was definitely shocked, Wyatt hated homosexuality, so he doesn't know that Brandon is gay. Wyatt's phone started ringing.
"Hang on, hello? Oh hi Charlene, what? What was it for this time? Seriously? Alright, I'll be right over" said Wyatt, before hanging up.
"Who was that?" asked Brandon
"It was my wife, apparently, my son got suspended from school again" said Wyatt
"You have a son?" asked Brandon
"I have 2, hey, I'll catch you later, I gotta get home" said Wyatt before leaving
"Alright, see you around" said Brandon
==Meanwhile==
Hunter and Trevor just finished the episode of the show.
"Not bad, wouldn't you say?" asked Hunter
"No, not bad, awful" said Trevor
"Excuse me?" asked Hunter
"You have got to be the worst co star I have ever worked with" said Trevor
An intern walked over to the two.
"Mr Shane, I have your muffin" said the intern
"I asked for blueberry, not chocolate chip" said Trevor, before swatting away the plate with the muffin and walking away
"My god, what a jerk" said Hunter
Later, Hunter and Brandon returned to the apartment.
"How are you two?" asked Jennifer
"My day could have been better" said Brandon
"What's wrong?" asked Jennifer
"Well, I thought I met the perfect guy, but turns out he's straight, married, has 2 kids and hates homosexuality" said Brandon
"Oh, I'm sorry to hear that" said Jennifer
"My day was alright, I had fun on set shooting the first episode of Riley, even though my co star is a complete Asshole" said Hunter
"Who's your co-star?" asked Brandon
"Trevor Shane" said Hunter
"That loser?" asked Jennifer
"Yep" said Hunter
"Well, it's only our first day in Hollywood, I'm sure things will get better" said Jennifer
"Yeah, you're right" said Brandon
"You know, I wonder what Rodger and Sally are doing right now?" asked Hunter
Rodger and Sally were in the coffee shop, just relaxing.
"Hey, it's getting late, we should head back" said Rodger
"Alright" said Sally
* * *
**That ends the pilot of Battle Challenge: Hollywood**
**READ AND REVIEW**
2. Waitress on Hand and Foot
Here is the newest edition of Hollywood
Disclaimer: I do not own Battle Challenge, by friend does
* * *
Jennifer was in the living room of the apartment, when Hunter, Brandon, Rodger and Sally entered
"...I'm telling you, no one beats me in Hockey" said Hunter
"You got lucky, you're going down next time" said Rodger
"Yeah right, hey Jennifer" said Hunter
"Hey Hunter" said Jennifer
"Hey, where are the kids?" asked Rodger
"Thomas is at kindergarten and Brooke is at Pre School" said Hunter
"Oh" said Rodger
"Hey, I'll see you guys later" said Brandon
"Where are you going?" asked Rodger
"I'm going to hang out with Wyatt" said Brandon
"You mean the Wyatt who doesn't like gay people?" asked Hunter
"Yep, he still doesn't know that I'm gay" said Brandon before leaving
"How long before that guy finds out that he's gay?" asked Hunter
"I give it a week" said Sally
"Next Friday" said Jennifer
"Before he comes back" said Rodger
"Hey, we're gonna leave too" said Sally
"Where are you going?" asked Hunter
"We're going home, we haven't finished unpacking yet" said Rodger
They both left.
"So Jennifer, what did you do today?" asked Hunter
"Nothing" said Jennifer
"What do you mean 'Nothing'?" asked Hunter
"I mean, I didn't do anything, I haven't had anything to do ever since we arrived in California" said Jennifer
"That can't be true" said Hunter
"Oh really? One of the most common things I did in New York was spending time with my friends, here, I have 3 friends and all of them are busy" said Jennifer
"Well, there's still gotta be something you can do" said Hunter
"Nope, absolutely nothing" said Jennifer
"Well, why don't you get a job? Bring in some extra money and it gives you something to do all day" said Hunter
"You know, that's not a bad idea" said Jennifer
"Great" said Hunter
Jennifer got up to leave
"Where you going?" asked Hunter
"To pick up the kids, can I take your car, mine's low on gas" said Jennifer
"Sure" said Hunter
Hunter threw Jennifer the keys to his car and she left.
Later, Brandon and Hunter arrived at the coffee shop that Brandon went to on his first day, where he met Wyatt
"So this is the place?" asked Hunter
"Yeah, nice isn't it?" asked Brandon
"Yeah, it is" said Hunter
They both sat down at a coffee table, when a waitress walked up to them.
"Hello, what'll you be having?" she asked
"I'll have a..." said Hunter
Hunter looked up at the waitress, it was Jennifer.
"Jen? What are you doing here?" asked Hunter
"I'm asking what you'd like" said Jennifer
"I'll have a diet cola" said Hunter
"I'll have a latte" said Brandon
"Alright" said Jennifer before walking away
Meanwhile, with Rodger and Sally, the 2 just finished unpacking.
"Alright, that's everything" said Rodger
"Finally, god my back really hurts after this" said Sally
"Well, you just sit back and relax, I'll fix us something to eat" said Rodger
Later, back at Hunter and Jennifer's apartment, the trio had just returned.
"Okay, so mind explaining the thing at the Coffee shop?" asked Hunter
"Yeah, I thought about what you said about getting a job, and you were right, so that's what I did" said Jennifer
"Well, good for you, do you enjoy it?" asked Hunter
"Yeah, it's a relaxing job, I get to be nice to people, and apparently, I get to see you sometimes" said Jennifer
Hunter gave Jennifer a kiss on the cheek.
The next day, Hunter and Trevor had finished shooting the newest episode of their crime show.
"God, not a bad episode, even I was surprised" said Hunter
"That's because you only have an 4th grade education" said Trevor
"Okay, I am really getting tired of you" said Hunter
"Whatever Rory" said Trevor
Jennifer arrived.
"Hey Hunter" said Jennifer
"Hey Jen" said Hunter
Trevor pushed Hunter away.
"Hi there, Trevor Shane, but you already knew that" said Trevor
"I did" said Jennifer
"So Jennifer, what are you doing here?" asked Hunter
"I came to surprise you" said Jennifer
"Well, we just finished shooting the episode, we should get home" said Hunter
"Alright, I'll wait for you in the car" said Jennifer
Jennifer left.
"Wow, she's one hot piece of..." said Trevor, before being cut off by Hunter
"Don't you dare say the next word" said Hunter
"But she is" said Trevor
"That's my wife" said Hunter
"Do you think that's ever stopped any of the ladies that I've been with?" asked Trevor
"Listen you, if I ever see you near Jennifer, I will tear you to shreds and drown you in a canal, do I make myself clear?" asked Hunter
"Crystal" said Trevor, clearly scared
Meanwhile, Brandon was talking to Wyatt
"Um Wyatt, there's something that I've been meaning to tell you" said Brandon
"What is it?" asked Wyatt
"Well, I know that you don't like homosexuality, but..." said Brandon
"What? You're not gay, are you?" asked Wyatt
"Um, no, but I have friends who are" said Brandon, panicked.
Later that day, everyone met in the Coffee shop, of course, Jennifer was there working.
"So, how were your days?" asked Jennifer
"I finally stood up to Trevor, granted he had to cross the line in order for it to happen" said Hunter
"Well, me and Sally finished unpacking and were able to get settled into our new apartment" said Rodger
"What about you Brandon? How was your day?" asked Hunter
"Um, I'll tell you about it another time" said Brandon
"Um, alright, overall, seems like a great day for all of us" said Hunter
"Yeah" said Jennifer
End file.
| fanfiction |
quantum spin chains are one - dimensional models of interacting quantum systems .
they have been used to model magnetic properties of materials , in particular when strongly anisotropic behaviour suggests a one - dimensional modelling .
they also arise as limits of two - dimensional lattice models of classical statistical mechanics , in an anisotropic limit where the lattice spacing in one space direction vanishes . in particular ,
the ising quantum chain discussed below is related to the classical ising model in this way ; and the parameter in the hamiltonian corresponds to the temperature variable of the two - dimensional classical model . at criticality , quantum spin chains as well as two - dimensional lattice models
possess scaling limits that correspond to @xmath0-dimensional conformal field theories .
the critical exponents describing the non - analytic behaviour of thermodynamic quantities are given by conformal dimensions of certain conformal operators .
for translationally invariant quantum chains , the scaling limit corresponds to a conformal field theory on the torus , and the partition function is a quadratic expression in terms of virasoro characters , distinguishing left and right moving excitations . for free or fixed boundary conditions
, we have a conformal field theory on the half plane , with a partition function which is linear in virasoro characters .
if the spin chain possesses global symmetries , we can define toroidal boundary conditions , i.e. , specific twists at the boundary that do not destroy translational invariance .
however , this does not seem to yield all possible boundary conditions one might expect from the conformal field theory .
recently , such `` conformal twisted boundary conditions '' have attracted growing attention @xcite , and were realised in solvable lattice models @xcite . here , we consider the simplest possible example of such an exotic boundary condition . at least in this case , it is once more related to a symmetry of the model , which turns out to be duality @xcite .
furthermore , the complete spectrum of the hamiltonian is obtained exactly @xcite , even for finite chains of length @xmath1 .
the scaling limit partition function is computed , verifying the result expected from a mapping to the xxz heisenberg quantum spin chain which originally led to the discovery of these duality twisted boundary conditions in the ising model @xcite .
before we come to the particular example of the ising quantum chain , we first discuss the construction of toroidal boundary conditions in more generality .
for simplicity , we consider quantum spin chains with nearest neighbour couplings only . in this case , the hamiltonian for a system of @xmath1 spins has the form @xmath2 where @xmath3 and @xmath4 are arbitrary constants which are independent of @xmath5 .
the hamiltonian is expressed in terms of local spin operators @xmath6 acting on a tensor product space @xmath7 , @xmath8 where @xmath9 denotes the identity operator on the vector space @xmath10 .
let us assume periodic boundary conditions for the moment , i.e. , @xmath11 , so the last spin couples to the first in the same way as the neighbouring spins along the chain .
we define a unitary translation operator @xmath12 by its action on the local spin operators @xmath13 which obviously commutes with the hamiltonian @xmath14 , so @xmath15 . as @xmath16 , the identity operator on @xmath7 , the eigenvalues of @xmath12 are of the form @xmath17 , with @xmath18 , and define the lattice momenta of the one - dimensional chain .
consider now the case where the hamiltonian has a global symmetry , i.e. , it commutes with an operator @xmath19 , where @xmath20 belongs to a representation of some group .
we can then define a modified hamilton operator @xmath21 by setting @xmath22 so @xmath21 differs from @xmath14 only in the coupling term at the boundary , which is twisted by the local transformation @xmath20 . on first view , this may appear to be no longer translationally invariant , due to the different coupling between the first and the last spin .
however , the transformation @xmath23 is a symmetry of the model , which means that the nearest neighbour coupling @xmath24 commutes with the product @xmath25 .
we thus can define a modified translation operator @xmath26 which commutes with @xmath21 , @xmath27 the corresponding boundary conditions are known as toroidal boundary conditions .
the hamiltonian of the ising quantum chain is given by @xmath28 where @xmath29 and @xmath30 are pauli matrices , so @xmath31 .
it has global spin reversal symmetry , i.e. , @xmath14 commutes with the operator @xmath32 .
corresponding to this @xmath33 symmetry we have periodic ( @xmath34 with @xmath35 ) and antiperiodic ( @xmath36 with @xmath37 ) boundary conditions , the latter yielding a change in sign of the @xmath38 coupling term , because @xmath39 .
it turns out that it is useful to consider the mixed - sector hamiltonians @xcite @xmath40 and @xmath41 instead , where @xmath42 are projectors .
duality is a symmetry that relates the ordered and disordered phases of the classical ising model .
it provides an equality between the partition functions at two different temperatures , the critical temperature being mapped onto itself . in the quantum chain language , duality relates the hamiltonians @xmath14 with parameters @xmath43 and @xmath44 ; the critical point corresponds to @xmath45 . in order to understand the duality transformation ,
it is advantageous to rewrite the mixed - sector hamiltonians @xmath46 as follows @xmath47 - [ ( e_{2n-1}^{}-{\textstyle\frac{1}{2 } } ) -\lambda(e_{2n}^{\pm}-{\textstyle\frac{1}{2}})],\ ] ] where the temperley - lieb operators @xmath48 are given by @xmath49 defining invertible operators @xmath50 , with @xmath51 and @xmath52 , the appropriate duality transformations are @xmath53 and @xmath54 @xcite .
the corresponding duality maps are @xmath55 .
evidently , @xmath56 act on the operators @xmath48 like a translation , i.e. , @xmath57 for @xmath58 , and at the boundary @xmath59 and @xmath60 .
thus the squares of the duality transformations @xmath56 commute with the corresponding hamiltonians @xmath46 and are nothing but the appropriate translation operators @xmath61 of the mixed - sector hamiltonians @xcite . at criticality , when @xmath45 , duality itself becomes a symmetry , as @xmath62 .
thus we can define corresponding twisted boundary conditions .
this works in a slightly different way as for the periodic and antiperiodic boundary conditions discussed above , as we have to consider an odd number of generators @xmath48 .
the corresponding mixed - sector hamiltonians are given by @xcite @xmath63 where the operators @xmath48 , for @xmath58 , are defined as in equation ( [ eq : ej ] ) above , and where @xmath64 .
so the duality - twisted ising hamiltonian contains coupling terms of the type @xmath65 at the boundary , and , in particular , does _ not _ contain a term @xmath66 .
the hamiltonians @xmath67 are translationally invariant @xcite , the corresponding translation operators @xmath68 can be constructed as above as the squares of the appropriate duality transformations @xmath69 and @xmath70 , which commute with the critical hamiltonians @xmath71 and @xmath72 , respectively , of equation ( [ eq : ht ] ) .
the spectrum of the duality - twisted ising quantum chain can be calculated by a modified version @xcite of the standard approach .
essentially , the hamiltonians @xmath67 ( [ eq : ht ] ) are rewritten in terms of fermionic operators by means of a jordan - wigner transformation , and the resulting bilinear expressions in fermionic operators are subsequently diagonalised by a bogoliubov - valatin transformation , see @xcite for details .
the diagonal form of the hamiltonian is @xmath73 where @xmath74 and @xmath75 are fermionic creation and annihilation operators , respectively .
the energies of the elementary fermionic excitations are given by @xmath76 the ground - state energy @xmath77 is @xmath78\ ] ] which shows the expected finite - size corrections of a translational invariant critical quantum chain with an effective number of sites of @xmath79 , reminiscent of the fact that it is related to the xxz heisenberg quantum chain with an odd number @xmath80 of sites @xcite . with the appropriate finite - size scaling ,
the linearised low - energy spectrum in the infinite system is @xmath81+\frac{1}{16}\ ] ] where the fermionic operators @xmath82 and @xmath83 follow from the @xmath75 by suitable renumbering , and where @xmath84 denotes the ground - state energy of the @xmath1-site ising quantum chain with periodic boundary conditions .
the conformal partition functions are given by the combinations @xmath85 and @xmath86 , respectively , of characters @xmath87 of irreducible representations with highest weight @xmath88 of the @xmath89 virasoro algebra , corresponding to operators with conformal spin @xmath90 and @xmath91 .
for the ising and potts quantum chains @xcite , `` exotic '' conformal twisted boundary conditions can be realised by means of twists related to duality , which is a symmetry of the model at criticality .
it would be interesting to know whether this is a more general feature .
if this is the case , this observation might help to identify non - trivial symmetries in quantum chains or two - dimensional solvable lattice models of statistical mechanics . | arxiv |
Sookie Stackhouse/Southern Vampire Mysteries 1. Chapter 1
**Disclaimer: I do not own these characters, they belong to the wonderful Charlaine Harris.**
Chapter 1
Another day at high school.
It was the first day back after Christmas vacation and I couldn't wait until I was finished and could go to college. I was a senior, and 13 years of school was most definitely enough. However, this was the home stretch and there were only a few months and finals to endure, then I would be free for the whole summer.
I parked my car and made my way to my first class of the day, maths, just as the bell was ringing. My friend Tara waved me over and I went and took my seat next to her. We'd been friends ever since elementary school and she was one of the few people who had stuck by me through the aftermath of my parents' death when I was seven. They were killed in a car accident and I was quiet and withdrawn for a long time afterwards, most of my friends at the time started avoiding me. But not Tara, oh no, she sat with me at lunch and if ever I needed a partner for anything she was there. Soon we were inseparable and she was at my house all the time. When my parents died, my brother and I moved in with my Gran and Tara became a part of the family.
"Glad to be back, Sook?" Tara asked me with a wicked glint in her eye.
"Tara you know I can't wait to be finished with school", I replied.
"I know", she grinned back, "me neither."
"Are you swimming tonight?" she asked.
"Yup, sure am. Our coach has retired, and I hear they've got someone new in to replace him. I hope they're nice. I like Alec and I don't really want anything drastic to change."
Just then, Mrs Wood, my maths teacher walked in and immediately started today's lesson. We were starting integration today, apparently. I copied down the notes and examples and then started on the questions in the textbook.
As I was working, I started worrying about the new coach we were getting tonight. Shreveport Amateur Swimming Club wasn't very big and most of the members weren't really into the whole competition scene. I mean we attended the local galas and other events, but anyone who wanted to swim seriously moved on to other clubs. I had joined the club just before the death of my parents. My mom had had both, my brother Jason and I on the waiting list since we were old enough to join at the age of five. There wasn't a pool in Bon Temps and that's how we ended up in Shreveport. It was a bit of a drive but mom didn't seem to mind. She was really enthusiastic about us joining, and that carried down to me. I got so excited the first time we all went. Mom sat up in the balcony and watched us for the hour, waving down at me smiling every time I looked up.
After our parents died Jason gave it up, but I kept going. I loved it. It became my sanctuary. It is a very quiet sport and when you are swimming it's just you and your thoughts. I've used my time swimming many times throughout the years to sort through my thoughts and feelings on different things in my life. If you _don't _want to think, you can do that to, you just focus on moving your body through the water, and pushing yourself to do the training with your best times. Although I'm not a bad swimmer I'm not great either, I would say I'm one of the best in our club at breaststroke, but that's about it. Alec, our old coach, liked us making good times and encouraged us to enter into competitions but also understood that I really just liked swimming for swimming's sake and wasn't too fussed with all of the competitive stuff that goes with it. I got along well with him. Many of the younger swimmers didn't like him much as he didn't like it when they were lazy and just stood at the bottom of the lane talking to their friends, but I for one would really miss him as our coach.
***
The rest of the morning passed without incident. Tara and I went over and joined Sam and JB at our table for lunch. Tara had recently started seeing JB, and although she was trying to convince me that it was nothing serious, I'd seen how happy they had both been lately. Sam was the son of my bosses Peter and Susan, I worked weekends waitressing at their bar Merlottes. We'd all been friends for a while now and although I got the impression Sam had a soft spot for me, I didn't see him as anything more than a good friend. I think he knew that, as he had never said anything to me about it.
We were eating our lunch and telling each other all about our Christmases. Sam had just been with his parents for Christmas. I'd seen quite a bit of him as we were both working quite a bit throughout the holidays; I'd taken on a few extra shifts so that I could replenish my savings after Christmas, and he was helping his parents out behind the bar. Tara had come to ours for Christmas dinner like normal as her mum was not doing too well. She is an alcoholic and although she sometimes cleans herself up for periods, so far she has always reverted back to her old self. JB had been away visiting relatives over the holidays.
Just then, Bill walked into the cafe with Lorena. The SOB had the audacity to walk right past our table and smirk at us. I hold my head high and try not to let him get to me. The rest of my table all glare back up at him. I don't know what I ever saw in that guy. Tara never liked him and I should have listened to her, but he seemed like such a gentleman, at least in the beginning. In the beginning, he was kind and sweet to me. We dated for six months, and one night at a party, I walked in on him with his pants around his ankles, pounding into Lorena from behind. I was devastated. I've not spoken to him since then. He called constantly for a week, then I heard nothing more from him and I was grateful he had given up. I'm pretty sure Tara had something to do with that, but I never asked and she never mentioned it. Even almost a year later, he still sometimes got to me.
"Just ignore him Sookie, he's an idiot." Sam said under his breath to me.
I smiled at him in thanks and we all continued with our lunch, ignoring Bill and Lorena.
***
After handing in my essay for English Lit that I did over the holidays I headed on out to my car. My car wasn't anything special, it was yellow and rather run down looking, but it had character and it got me where I wanted to go. I jumped in and turned on the radio looking around for Tara, I spotted her making her way towards the car. I was giving her a ride home as her mother had once again decided to take the car out whilst under the influence and managed to drive it into a tree. She was fine, but the car wasn't. Tara got in and I dropped her off on my way home.
As I walked into the house, I caught a whiff of something that smelt delicious coming from the kitchen. I walked in and there was Gran, standing over the stove stirring the wonderful concoction that was causing my mouth to water. Gran loves cooking and is always on the lookout for new recipes to try.
"Hi Gran, I'm home. Do you need any help?" I ask.
"Oh hello dear. No, no, I'm fine. You go on up, I'm sure you have plenty to do. Dinner will be ready in an hour. Did you have a good day?"
"Ok Gran. Yeah it was good to see everyone; I did get given quite a lot of homework today so I suppose I should start some of that." I replied.
I headed upstairs and got my bag ready for swimming. I sat down at my desk trying to decide what to start first. I figured I would start with what was due in first, which happened to be maths.
After I'd attempted a few questions and only managed to complete two, I gave up and headed downstairs for dinner. It was delicious and I was gutted that I was unable to have seconds as I had swimming and so didn't want to eat too much before hand. I thanked Gran for the wonderful meal and quickly did the dishes for her, before running up and grabbing my bag for swimming. I gave my Gran a kiss on the cheek and told her that was me away.
Gran was incredible and I loved her deeply. When our parents died she took both my brother and I in even though she had already raised her own children. She ferried me to swimming and Jason to football without complaint, and was there for us whenever we needed her. She held me when I woke up in the middle of the night crying and helped me start to live my life again.
I got in my car and drove the 45 minutes to Shreveport. Swimming started at seven and I was there in plenty of time. I went down the stairs and found an empty cubicle to change in. I changed into my suit - I was quite exited to wear it, as it was a new. It was a Speedo endurance one, black with a red design at the top and an open back. It fitted great, I sometimes had a bit of trouble as my breasts were quite large and I hated not feeling secure in my swimsuit. I grabbed my water bottle, cap, floats and my goggles and threw the rest of my stuff into a locker. I didn't bother locking it as it was just the swimming club that was in tonight and no one really bothered. There was nothing valuable in there anyway and the key just got in the way.
The pool was quite a new one with flumes and a wave machine. Of course we didn't get to use them when we where there with the club but the staff sometimes put them on for the younger ones at the end of their session. That was what was currently going on, so of course the kids were going nuts over them. I remember that being the best part when I was little. You would swim for 45 minutes and the remaining time was spent running up the stairs trying to have as many goes on the flumes before they were closed again. The less able swimmers had their training before ours and we went in once they had finished.
I headed over past the showers to the poolside to wait until the last of the lanes empty out. I spotted my friend Amelia sitting over on the steps. The steps were on the bridge, which connected the baby pool to the big pool. Amelia had joined the club when she was 15. Her dad had been pushing her to enter all the competitions and do the whole training seven times a week thing but she eventually put her foot down, quit her old club, and joined here instead. I've known her for two years now and we have become good friends. She is a year younger than me but was planning to leave school after this year and go to college. She had met Tara a few times and we all got on well together and we were thinking about getting a flat together next year when we all went to college. I was looking forward to it immensely.
"Hi Ames," I called as I made my way over to her.
"Sookie!" Amelia cried as she jumped up to give me a hug. We hadn't seen each other since before the holidays as Christmas was two of the four weeks out of the year that swimming wasn't on. The other two being sometime throughout the summer holidays.
"How was your Christmas?" She asked me.
"It was good", I replied. "Tara and Jason came round for presents and Christmas dinner. How was yours, did your dad make it back?"
"Yes he did, and he got me a new car!"
"Oh wow, Ames. That's great."
Amelia's Dad was some big business man and was rarely around. He seemed to think that was fine as long as he lavished her with expensive gifts. Amelia really hated it but had decided a couple years back that it wasn't worth getting worked up over anymore.
As we were chatting, everyone else had arrived and were putting their stuff next to their lanes ready for training.
"Oh. My. God. Sookie, look behind you." Ames whispered to me.
_What?_ I slowly turned around. I think my jaw hit the floor. He was breathtaking. There, standing in front of me was the embodiment of Adonis himself. He was gorgeous. He had striking blue eyes the colour of the sea on a clear summer's day. His hair was tied back and was an almost identical shade of blonde as mine. He was wearing a black tank top, which showed off his well-defined torso and muscled arms...
Ugghhh, yuummm.
A/N: Please be nice as this is my first ever story and I've not written anything fictional since standard grade English. I don't have a Beta so all mistakes are mine. I've read over it a couple of times so it shouldn't be too bad, but if there's anything I'm consistently doing wrong please let me know.
2. Chapter 2
**Disclaimer: I do not own these characters, they belong to the wonderful Charlaine Harris.**
Chapter 2
My brain had turned to mush and I was just standing there drooling over this hunk of a man standing in front of me. My eyes made their way back up his tall frame to his face and saw that he was watching me, his lips curving up into a knowing smirk.
_Shit! Get it together Sookie!_ I thought as I quickly closed my mouth and tried to pull myself back to reality. _Who is this guy, and what is he doing down at the poolside when it's club time? _He looked slightly too old to be a new member, but I could dream right._ Oh shit!_ Just then, a thought popped into my head. _No, no, no, no, no..._
"Hi everyone. I am Eric Northman and I am going to be your new coach." He said, grinning at us all. I felt my stomach drop. _Why did this have to happen to me?_ Was it just me or did his eyes linger on mine slightly while he was looking everyone over. I shook that thought right out of my head, that was just wishful thinking.
The girls standing around me were all just staring at him with sappy grins on their faces, while the guys were looking at each other warily.
"Well what are you all waiting for? Into the water with you. Start warming up." He slowly raised his eyebrow and challenged, "Show me what you can do."
This was going to be a long two hours.
Most of the girls all jumped into action and were ready and swimming in seconds – most definitely a new record – while the guys all rolled their eyes and slid in behind them. Trying not to look as ridiculous as some of the girls, I slowly slid into my lane gasping as the cold water surrounded me and quickly ducked under the water to wet my hair leaning back to pull it up into a bobble as I did so. I pulled on my cap, making sure that all my hair was safely tucked away, and put on my goggles. I kicked off from the side ignoring the other people in my lane. I decided that since Eric had neither told us what to do nor put up a schedule yet, that I would just do the normal 1000m warm up. As this is a 25m pool that's 40 lengths, I figured that would give me some greatly needed time to calm down.
You know when you're running on a treadmill, how you're running as fast as you can, but you're not really going anywhere. Well I really dislike treadmills for that exact reason; I feel that if you're going to run it's much better if you are running to somewhere. For the first time ever, that was how I was feeling about swimming. I wanted to swim far away from here, but I was stuck just swimming back and forward, confined to my lane.
_Why did he have to be our new coach? Why, why, why?_ I new this would happen the moment that I realised he was taking over as our coach. I could feel myself doing it already. I was swimming considerably faster than I normally would for a warm up and I was hyperaware of every move my body was making as it was gliding through the water. I was purposely putting in the effort required to kick my legs from my hips and not my knees (Alec had been trying to get me to do just that for years and never managed it, and now I was doing it of my own accord). I was also making sure that my arms were moving elegantly, both inside the water, and when I brought them back up and round through the air. Last year I was awarded the prize for most graceful swimmer in the club and I was seriously trying to utilize that skill now.
This is so frustrating. I love swimming. The pool is my sanctuary, my place away from real life, where it is just me and the water. It is my Valhalla, the place where I could completely relax and be myself. That is, it _was_. Until Eric Northman crash landed, smack bang in the middle of it. Completely devastating it in the process. I was certainly no longer even remotely relaxed. In fact I was now just the opposite, I was on edge and self-conscious. Knowing that he was standing right there on the poolside but not knowing if he was watching me or not. It was driving me crazy.
Before I knew what was happening I was the only one still swimming. I quickly realised that I had forgotten to keep track of the number of lengths I had done. _Oops!_
I swiftly made my way to the shallow end of the pool and stood up. Everyone was looking at me strangely. I wondered just how long I had been going until I finally realised I had forgotten to keep count. From the way everyone was looking at me it must have been quite a while.
I made my way over to my water bottle grabbing it and taking a drink, trying to act like nothing was amiss. Ames was looking at me with a small smile on her face. She knows that when I get distracted by my thoughts I sometimes zone out. I would bet everything I owned that she had correctly guessed the reason for my lack of concentration this time.
"Nice of you to join us…" Eric stated, he looked down at the clip board in his hand, "…Sookie?"
Yes, emm…, sorry, I lost track of how many lengths I'd done." I reluctantly admitted, blushing a bright shade of scarlet.
Now that I was looking up at him from the pool I could seriously appreciate just how tall he actually was. He must have been at least 6 4", which was huge in normal terms but when looking up at him the effect was magnified ten fold.
He eyed me up and down critically, "Of course you did."
_Ugh, what an ass! As if I could get any more embarrassed._
"Well now that everyone is here, we can get on with the sub set. I figured we could start of with IM 50s so that I can see what your like at all of the strokes and it will also give me an indication of how your turns are."
Well that didn't sound too bad. It was just 2 lengths of each stroke, but in between each two you did another two, one of the first stroke you did, followed by the one you were moving onto next. So it went; 2 fly, 1 fly, 1 back, 2 back, 1 back, 1 breast, 2 breast, 1 breast, 1 free, 2 free. Apart from having to do a few lengths butterfly and my fun but pathetically slow back to breast turn it should be fine. And I couldn't possibly miscount 2 lengths (thank God).
At least you started off with the butterfly so that you weren't already tired, then had to swim it. Everyone was pushing off from the side and I decided to go near the end as I wasn't the fastest at fly and back. I kicked off from the side and went for it. That was the only way to really do butterfly. There was no such thing as a half-assed attempt as it ended up taking more energy in the long run. I did the turn at the end, butterfly turns were pretty much the exact same as breast stroke ones so I was fine at those.
Butterfly had the added obstacle of ta k i n g up a l ot of s p a c e , and I only just managed to avoid cra s h i n g arm s w i t h Debbie as she was swimming up the other side of her lane.
I finished up the fly and went onto the backstroke lengths.
As I was on my back I could see Eric making his way down the pool out of the corner of my eye. I realised he was wanting to see our back to breast turn and started to feel slightly nauseous. My back to breast turn was completely useless and I knew it.
I mean I wasn't the only one. The newer ones in lanes one and two probably didn't even know about the turn as we really didn't do it much at all. However everyone in my lane and above would do it properly. Everyone, eventually me included, found it hilarious that when we were shown it for the first time and I was trying to copy what I had seen Claudine do, I had somehow managed to hit my head on the bottom of the pool. I had been at the shallow end and it really hurt. Ever since then I had refused to attempt it anywhere but in the deeper part of the pool.
_I could just not do the turn._
_No_.
It had never bothered me before and if he wasn't here I wouldn't think twice about it. I actually liked the turn and I most definitely was not going to back out just because he was watching.
I saw the flags above me and counted my strokes to the wall. My hand touched the wall and I flipped myself over backwards. Although I couldn't see myself I knew that it was certainly not the most graceful thing in the world. And I may have actually been quicker just not bothering, but I'd never get any better if I didn't try it.
I twisted in the water and pushed off from the side. I surfaced from the water and spotted Eric walking back up the length of the pool with a huge grin on his face. He was laughing at me!
Ugh! He had some nerve! At least I tried it.
Well, I'd show him. It was breast stroke now and that, I could do. I was further behind the others as I wasn't as fast at fly and back but I knew I could more than catch up the distance on the rest of the people in my lane on breast stroke. Claudine was the only other girl that could match me on breast stroke and Claude, Claudine's twin brother was the only one who was faster in the club. As they were both in the top lane and I was in the middle lane three I was good to go.
I started powering through the water and quickly caught up with everyone. Ames let me go in front of her as we were turning as she knew I was faster, her stroke is back.
We finished off the subset, repeating the series once more. However, Eric did not watch the turns again, for which I was grateful.
Once everyone was finished and guzzling down their water – I wasn't the only one swimming significantly faster than normal tonight – Eric stood up from where he'd been sitting on the bridge steps.
"Good work guys, all in all that was nice swimming. A few of you need to work on your turns and a lot of you need to pick up your stamina but you are all pretty competent swimmers."
_Competent?_ No shit Sherlock. The fact that we were in the top session kind of makes you hope that we could all swim _competently._
"Anyway, everyone take five then we'll start the main set."
Everyone made their way over to the steps and started climbing out to go and either fill up their water bottles or nip to the toilet. When I realised I was going to be left alone in the pool area with Eric I quickly decided going to the toilet was a very good idea indeed.
I walked into the girls bathroom and it was a hive of activity in there. Everyone exclaiming over just how hot Eric is. Amelia bounced over to me saying,
"He is a God!"
She put her hand up to her forehead pretending to faint. I frowned at her and replied, trying to keep myself grounded,
"Amelia Broadway, he's our coach!"
"I know. But that doesn't stop us from looking and admiring. Anyway, you can't talk; you were so distracted by the gorgeous hunk of man meat that you completely forgot to stop swimming!"
She snorted and burst into hysterical giggles. I went bright red and tried to keep a straight face but it was futile. I gave in and laughed with her, it was pretty funny. Once we got a hold on ourselves she continued,
"And he's not that much older than us. He looks about what, mid twenties maybe. You could so get away with that." She grinned at me with a dangerous glint in her eyes.
Uh oh, I thought to myself. This cannot be good.
"No, I'm pretty sure he thinks I'm a complete idiot", I quickly tried to head her off.
"Oh, you didn't see what I saw", she announced confidently.
I cut her off. "What, first, me forgetting to stop and looking like a scatter brained little girl, and then him laughing at my turn." I replied indignantly.
"No…" She grinned at me. "When you were no doubt rather preoccupied with what I assume was you checking out that mouth watering figure of a man, he was doing the exact same thing back to you."
I shook my head at her. "Your wrong Amelia, I'm sure you just misinterpreted what you saw."
"I know what I saw Sook. But I'll drop it if that's what you want."
I nodded my head and smiled slightly in thanks.
I turned around and rolled my eyes at what I saw happening behind me. Both Arlene and Debbie, who were both in the lane below Ames and I, were frantically trying to adjust their costumes so that their cleavage was shown off to its best advantage.
I'd had enough. I made my way back out to the pool and saw that all the guys were already back in the water. I slid back into my lane and Lafayette turned and winked conspiratorially at me, glancing Eric's way as he did so. Eric was just making his way back over, carrying one of those ridiculous cone shaped disposable cups of water (you know the ones, where it's impossible to put the thing down and they always seem to get in the way). It looked tiny encompassed in his large hand.
Once again I was completely drawn into some kind of a trance just looking at him until Lafayette nudged me whispering,
"Drool worthy, huh?"
"Oh yeah." I replied absently. Lafayette had officially came out last year and although it was slightly awkward with the guys in their suits at first they soon got used to it. Him chuckling to himself broke though my daydreaming and I smiled back at him.
All of the girls had made their way back into the pool. That is all except two, they must be hoping to make some kind of big entrance. Sure enough two seconds later out came Arlene and Debbie. Both of them were slowly walking towards the pool, and consequently Eric, seductively swaying their hips as they came. It was ridiculous to watch. I turned my attention to Eric wondering what he would do.
I saw the moment he noticed what they were doing, they were about half way over when he glanced up and caught sight of them, his eyes widened ever so slightly in what could only be described as complete shock with a hint of panic mixed through. He quickly recovered though and clamped down his face, leaving it completely emotionless. He then frowned disapprovingly at them,
"Come on girls. We want to get started."
They looked a bit disappointed that they didn't get more of a reaction for their efforts, but gave it up for now, sliding back into their lane.
"What are we doing?" I asked.
"Oh, I put a schedule up in each of your lanes, we're doing split hundreds." Eric answered my question.
Yes! Split hundreds were one of my favourites. They were really quite easy. Swim one length, rest 5seconds, another length, rest 5, two lengths then go again when the red hand of the minute timer on the wall was at quarter to. You could swim any stroke you wanted but it was on too fast a time to do all breast stroke so I tended to do mostly front crawl with the occasional length of breast. Also the faster you finished the hundred the more rest time you got.
I made my way over to the side and sure enough there was a schedule inside a polly wallet stuck to the wall. I groaned as I read it, and the noise was quickly being repeated by other people as well as they realised that our rest time had been cut by 15seconds!
Looking up at Eric I asked, "Eric, have you made a mistake with these times, we usually get another 15seconds?"
"No, no mistake." Eric looked down at me with an amused expression. "I'm sure you can all manage these times just fine."
He was right, I knew I could make those times if I wanted to, but I also knew that if I did I would be completely exhausted by the end of it. Well I sure as hell wouldn't be the only one not managing it. It looked like everyone else had come to the same conclusion as I had as they were all looking both resigned and determined at the same time.
"Right everyone, you're leaving at the next red top." Eric informed us.
Well here goes nothing, I thought to myself as I pushed off the side of the pool after Lafayette. I started off fast. Not too fast, but the kind of fast I could hopefully keep up for a while, we did have to do 16 of these.
After the first half I was boiling, even in the cold water. Luckily my face didn't go any farther than a dark pink shade when I was pushing myself. Some people weren't so lucky. Arlene was slowly turning a deep shade of red and I knew from experience that it would end up having a slightly purple tinge by the time we had finished.
By the time I got to the last three hundreds I was only just making it back in time before I had to go again
I finished and collapsed at the side. Eventually I managed to make my way to get my water bottle and slowly sipped from it until I got my breath back. No one in my lane was talking, everyone was completely drained. The lanes above had already started on their swim down and the ones below us were yet to finish their split hundreds.
"Well done! You all did great." Eric congratulated us on completing it within our time. "Now eight lengths swim down, nice and slow."
I floated off with my water bottle in hand and slowly glided the 8 lengths, using as little energy as possible. As I knew I would be before I started the main set, I was completely exhausted. But I was also quite proud of myself.
I gathered up my things and ducked under the lane ropes on my way to the steps to climb out. Eric was at the side of the pool collecting together his things and I caught him watching me. I blushed and looked away suddenly very self conscious of the fact that I was in only my swimsuit. I made my way around to the showers and had the quickest shower imaginable as I didn't want to run into Eric again and further embarrass myself.
I then took a long while getting dressed hoping that by the time I emerged he would have left. But of course it was not to be.
I'd just decided that it was safe to make a run for it, as it had gotten quiet and I was sure everyone else had already left. I opened the door and rushed out only to smack straight into none other than Eric himself.
I currently found myself pressed right up against his body, his hands on my hips steadying me, and my hands resting on his chest. Oh and what a chest it was too, I think I let out a small moan of appreciation. I was so close I could smell him, a wonderful concoction of masculinity mixed with something that was just Eric. I looked up and saw him watching me.
"Sookie," Eric breathed. I jumped back away from him.
"Oh, I'm so sorry Eric, I wasn't looking where I was going." I quickly apologised.
"Don't mention it." Eric replied nonchalantly.
I picked up my bag from where it had fallen when I'd collided with Eric. We made our way up the stairs to the exit in awkward silence.
"So..." Eric began as we got to the door, "I'll see you Thursday then." It wasn't really a question.
"Erm, yup. Bye." I walked over to my car, climbed in and started the engine, letting out a sigh as I drove away.
The journey seemed to take forever. I was more tired than usual and that probably didn't help. I also couldn't get Eric out of my head.
I went round in circles. Yes he was the living embodiment of a Norse god and probably the most gorgeous man on the planet. But he was also my coach and nothing was ever going to happen. Not to mention the fact that he probably thinks I'm some silly little girl. I'd lost count of the number of times I'd managed to embarrass myself tonight. It was ridiculous.
By the time I made in back onto Hummingbird Lane I'd decided that I wasn't going to let him affect me. He was not going to take swimming away from me. I was here first and I refuse to let him being there affect what I usually took so much pleasure in. I would pretend he wasn't there at all.
I pulled up to the house and went on in. Gran was already in bed. I emptied out my bag putting my towel into the washing machine and turned on the cold water to fill the basin to put my swimsuit in to soak.
Once that was taken care of I switched of the lights and made my way to bed. I was absolutely spent, and fell asleep as soon as my head hit the pillow.
A/N: Hey, sorry about the long wait on this chapter. I was hoping to get it out before my exams but my laptop died and I had to bring up the desktop from home. Anyway just had my last exam this morning so hopefully I'll have more time to spend writing. Thanks for all the reviews and alerts/favourites, I realise what other authors mean when they say it gets addictive now, and I really appreciate them.
End file.
| fanfiction |
the formation of cooper pairs in a superconductor is essential for superconductivity @xcite@xcite .
cooper pairs are of bosonic nature , and it is believed that they generate a supercurrent in the same mechanism as helium atoms generate a superflow .
it is clear that , once the cooper pairs in a superconductor are broken , superconductivity will be lost .
an intersting question is that , can the system become dissipative without the breaking of cooper pairs ? from the view point of many - body physics , one can see there is a rather striking difference between the origin of cooper pairs and the origin of superconductivity .
cooper pairs is due to some _ attractive _ interactions between fermions , while superconductivity , like superfluidity , has something to do with _ repulsive _ interactions between its composing bosons , _
i.e. _ , the cooper pairs @xcite@xcite .
this difference implies that the physical regime of cooper pairs is not exactly the same as that of superconductivity .
we suggest that , under some circumstances , cooper pairs are not broken when one increases a supercurrent to above critical current .
we shall also show that , at the above - critical current region , the electrical resistance , caused by the scattering of cooper pair , has a different temperature dependence from the case where the charge carriers of the current are fermions ( electrons or holes ) .
thus the existence of cooper pairs can be signified by the temperature behavior of the resistance .
is the superconducting region where there are metastable current - carrying states corresponding to the local minima of the curve ; region @xmath0 is dissipative without metastable states .
the many - body eigen energy states at region @xmath1 can be mapped to the states at region @xmath0 by galileo transformation .
, width=288 ] like the case of superfluidity @xcite@xcite@xcite , the dissipative behavior of a superconductor above a critical current @xmath2 , can be explained naturally in terms of the many - body dispersion spectrum @xmath3 of the charge carrier system ( @xmath3 is the lowest eigen energy at given current @xmath4 ) . beyond @xmath2 ,
@xmath3 is a monotonically increasing function of @xmath4 ( see fig .
[ dispersion ] ) , thus a current can continuously lose its energy and momentum to the environment , corresponding to a dissipative decay process .
this is contrast to the case in the @xmath5 regime where the supercurrents are metastable states , corresponding to the local minima of the @xmath3 curve , whose decay is prevented by the energy barriers among the minima .
the dissipation mechanism illustrated above does not involves breaking of cooper pairs .
moreover , the low - lying eigen energy states below @xmath2 can be galileo boosted to generate the low - lying states above @xmath2 @xcite@xcite @xcite .
the galileo boost , also could being viewed as center - of - mass - mention transformation , does not modify the inner structure of the states such as pair correlations .
thus , the cooper pairs , present in states below @xmath2 , survive the boost and exist in the states above @xmath2 @xcite . in literature , landau s criterion of a superconductor
is generally used for the analysis of transitional regime , which determines a critical velocity to be @xmath6 , where @xmath7 is the pairing gap and @xmath8 is the fermi momentum .
landau s criterion requires an exchange of a quantum , with a large momentum ( the order of @xmath8 ) and with a certain energy , between the superconducting charges and its environment .
however , this exchange process could be inhibited for that the spectrum of the environment may generally be incompatible to absorb such an unusual quantum . in a superconductor ,
the self - induced magnetic field of the supercurrent could lead to loss of superconductivity by breaking cooper pairs , ( _ i.e. _ , silsbee effect @xcite ) . in this case
, there is an external critical current determined by the critical magentic field , and the cooper pairs do not exist above critical current . however , silsbee effect can be largely reduced by alignment of the currents and their geometries ( see fig . [ currentalignment ] ) , thus one might be able to obtain an intrinsic critical supercurrent , like the case of superfluid @xmath9he , and reach a dissipative regime without breaking cooper pairs
. we shall assume the existence of cooper pairs above critical current in follows . to weaken the silsbee effect ,
four thin superconducting films are used to carry the current .
film i is on top of film ii , and film iii on top of film iv .
film i is in the same plane of film iii , and film ii in the same plane of film iv .
current in the film i ( blue arrow ) points to the same direction as to the current in film iv ( red arrow ) , while the currents in the film ii ( red arrow ) and film iv ( blue arrow ) point to the opposite direction .
, width=288 ]
the eletrical resistance in a superconductor above @xmath2 and below @xmath10 is mainly caused by the scattering properties of cooper pairs with phonons .
we shall discuss the temperature behavior of the resistance .
for simplicity , we assume physical properties of the superconductor are isotropic .
first , we consider the dispersion relation of a cooper pair .
the dispersion is linear at small momentum @xmath11 , _ i.e. _ , @xmath12 ( we approximate @xmath13 by the critical velocity of the supercurrent @xmath14 ) . at large @xmath15 ,
the energy of a cooper pair is approximately @xmath16 where @xmath17 is the mass of a cooper pair assumed to be @xmath18 ( @xmath19 is the mass of an electron ) . a general form of dispersion @xmath20 can be used for approximation for all @xmath15 values @xcite .
we consider the leading scattering process in which one phonon is adsorbed or emitted by a cooper pair ( see fig [ onephonon ] ) .
the total energy and momentum should be conserved ,
@xmath21 @xmath22 where @xmath23 ( @xmath24 ) is the momentum of a cooper pair before ( after ) the scattering , @xmath25 is the momentum of the phonon , @xmath26 is the sound velocity , and @xmath27 ( @xmath28 ) corresponds to the emission ( absorption ) of the phonon . combining eq .
1 , eq . 2 and eq . 3 , one gets , latexmath:[\[\sqrt{v_c^2 q_1 ^ 2 + ( q_1 ^ 2/4 m_e)^2 } = \sqrt{v_c^2 q_1 ^ 2 + ( q_1 ^ 2/4 m_e)^2 } \pm \hbar c_s in most superconductors , @xmath14 , can being estimated using critical current density @xcite , is roughly the orders of ten meters per second or below .
thus @xmath14 is orders of magnitude smaller than @xmath26 .
one then can realize that unless the @xmath30 ( @xmath31 ) in the phonon emission ( absorption ) process is roughly equal or larger than @xmath32 , eq .
4 can not be satisfied . for a cooper pair with a momentum of @xmath33 ,
the energy is roughly @xmath34 and the corresponding temperature is @xmath35 where @xmath36 is the boltzmann constant .
thus at low temperature @xmath37 , one - phonon scattering process is absent , and the scattering process of cooper pairs must involve at least two phonons .
one can invoke boltzmann transport equation to determine the temperature dependence of resistance of the cooper pair system .
however , unlike the case of a fermionic system where the existence of fermi surface and pauli blocking are essential , the analysis of the ( bosonic ) cooper pair system can be simplified . at @xmath38 ,
the one - phonon scattering process can bring the momentum of a cooper pair ( with an energy of @xmath39 or less ) to zero or to the opposite direction , thus effectively causing the dissipation of the current .
the probability of one phonon process in low temperature is proportional to @xmath40 ( see , _
e.g. _ , @xcite ) , thus the resistance @xmath41 is linear in @xmath40 . at @xmath42 , one can find that probability of two - phonons process is proportional to @xmath43 , thus @xmath44 . in metals where temperature dependence of resistance is determined by electron phonon scattering , the power law of @xmath45 at low temperature is different , with an exponent being 5 ( see , _
e.g. _ , @xcite@xcite@xcite ) .
thus one can distinguish between cooper pairs and electrons by checking the powering law of @xmath45 in the above critical current regime . in the so called strange metal phase of some high-@xmath10 cuprates
, the resistance has also a linear temperature dependence .
one might wildly speculate that this linear behavior could be caused by the scattering of cooper pairs . in order for this speculation to be valid
, cooper pairs shall exist above @xmath10 in some systems .
an example is that cold fermi atom gases which can be tuned to go through bcs - bec crossover . in the bec side , the binding energy of cooper pairs ( or molecules )
can be orders of magnitude larger than superfluid transition temperature @xmath10 , since @xmath10 can be made small by decreasing the density of atom gases .
we suggest that , under some circumstance , cooper pairs could exist in a superconductor above critical current , and the system has a different power law of @xmath45 from the case where electrons are current carriers . in superconductors ,
galileo invariance is not exact but is a good approximation when the center of mass motion is not large .
there might be some possibility that the dispersion energy of normal state ( without pairing ) could be smaller than the dispersion energy of pairing state within a current regime somewhere between @xmath46 and the first supercurrent , we ignore this case here .
f. b. silsbee , _ journal of the washington academy of sciences _ * 6 * , 79 ( 1916 ) . for an analogy with a bose system ,
see x. g. wen , quantum field theory of many - body systems ( oxford university press , london , 2004 ) .
we obtain @xmath14 using @xmath47 , where @xmath48 is the critical current density , @xmath49 is the density of cooper pairs , @xmath50 is the charge of a cooper pair .
we assume that all conducting electrons are paired up , thus @xmath51 , where @xmath52 is the density of electrons . | arxiv |
A problem with the BCS energy expectation value of an excited state
I want to calculate the energy expectation value of the following state.
\begin{align}
|\Psi\_{ex}\rangle = \hat{c}\_{-k'\downarrow}^\dagger \hat{c}\_{k''\uparrow}^\dagger \prod\_{k \neq k', k''}(u\_{k} + v\_{k}\hat{c}\_{k\uparrow}^\dagger \hat{c}\_{-k\downarrow}^\dagger)|0\rangle
\end{align}
The hamiltonian is the reduced BCS hamiltonian:
\begin{align}
\hat{H} &= \sum\_{k, \: \sigma}\zeta\_{k} \hat{c}\_{k\sigma}^\dagger\hat{c}\_{k\sigma} + \frac{1}{\Omega}\sum\_{k,k'}V\_{k'-k} \hat{c}\_{k'\uparrow}^\dagger \hat{c}\_{-k'\downarrow}^\dagger \hat{c}\_{-k\downarrow} \hat{c}\_{k\uparrow}
\end{align}
I tried this before but I got a wrong result (which I know is wrong when I compare it with the original BCS paper):
\begin{align}
E\_{ex} = \sum\_{k \neq k', k''}2\zeta\_{k}|v\_{k}|^2 + \frac{1}{\Omega}\sum\_{k,l \neq k', k''}V\_{l-k}u\_{k}^\*v\_{k}v\_{l}^\*u\_{l}
\end{align}
It seems to be almost right, except some missing terms. In the kinetic energy part, you should have the additional $\zeta\_{-k'}+\zeta\_{k''}.$ This is because when evaluating $\left< \Psi\_{ex}|\epsilon\_k\hat{c}\_{-k'\downarrow}^\dagger\hat{c}\_{-k'\downarrow}|\Psi\_{ex} \right>$, you will get a $1$ instead of $v\_{-k'}$ when you move $\hat{c}\_{-k'\downarrow}$ toward $\left.|0\right>$, which is multiplied to $1$ instead of $v\_{k'}^\*$ when you move $\hat{c}\_{k'\downarrow}^\dagger$ toward $\left<0|\right.$.
The interaction term for this particular excitation is actually what you suspected $0$. but the actual excitation is really what is described by a combination of $\hat{c}$ on top of the BCS ground state which can be described by the Bogoliubov procedure $\hat{b}$, which turns the $k$ related term into $-v^\*\_k+u^\*\_k\hat{c}\_{k\uparrow}^\dagger\hat{c}\_{-k\downarrow}^\dagger$.
| stackexchange/physics |
a core principle of both financial investment and biology is that diversity leads to strength . in biology ,
hybrid vigor produces healthy organisms , because each parental genome contributes complementary strengths and balances the other 's weaknesses . in investing
, diversity spreads risk , maximizing the chances of finding some big winners while reducing the chances of collapse based on sudden declines in a few companies ' fortunes .
diversity at all levels from the kinds of science to the regions in which it is conducted to the backgrounds of the people conducting it strengthens the institute 's research portfolio and should lead to the best returns on the taxpayers ' investments .
it is impossible to know where or when the next big advances will arise , and history tells us that they frequently spring from unexpected sources .
it is also impossible to know what threads of foundational knowledge will be woven together to produce a new breakthrough .
supporting a wide variety of lines of inquiry will improve the chances of important discoveries being made .
this includes studying a diversity of organisms , because important and useful processes almost certainly remain to be discovered in areas of biology we have not yet explored .
scientists ' past or current experiences have a significant impact on the problems they choose to study and on the ideas they have for approaching these problems .
health burdens from specific diseases differ from state to state and population to population , and these variances can drive the kinds of questions researchers ask .
in addition to variations in regional health burdens , other environmental factors such as local plants and animals can influence an investigator 's research directions .
for example , baldomero olivera , now a prominent researcher at the university of utah , began studying deadly cone snail venom while he was working in the philippines , where the animals are endemic and people routinely died of snail stings ( telis , 2014 ) .
olivera 's work on cone snail toxins has transformed neuroscience and has already led to one food and drug administration approved drug and several more in clinical trials .
we also need to consider the identification and development of scientific talent when planning how we invest in biomedical research .
for example , if cutting - edge biomedical research were only being conducted in 25 states , it would mean that high school and college students in the other 25 states could get research experience only if they were willing and able to move .
the loss of talent to science in the united states caused by this research experience gap would be severe .
in addition to the value of supporting a diverse research portfolio , it is important to recognize that the best ideas come from investigators themselves . although there are times when management and top - down direction can help break through systemic barriers or open up bottlenecks particularly when the development of new technologies is required fundamental research works best when investigators are following their noses and setting their own directions . during the national institutes of health ( nih ) budget - doubling period ( 19982003 ) , the fraction of the nigms portfolio dedicated to investigator - initiated research declined from 99 to 80% because of increasing use of programmatic initiatives ( figure 1 ) ; that is , funding targeted at specific scientific areas . with the budget doubling more than a decade behind us ,
it is time to return the institute 's focus to investigator - initiated research , to ensure that new scientific territory is opened for exploration by adventurous investigators .
the fraction of the nigms portfolio committed to investigator - initiated research has declined over the past two decades .
the blue bars ( left axis ) show the funds nigms committed to funding opportunity announcements ( foas ) targeted at specific areas of research in each fiscal year shown .
the red line with triangles shows the change in the percentage of the nigms portfolio dedicated to investigator - initiated research .
the analysis does not include fellowship , career development , and training awards ; programs transferred to nigms from the former national center for research resources ; and some other programs .
a criticism of nigms ' renewed emphasis on investigator - initiated research has been that it will disadvantage team science and collaboration .
but the dichotomy is not between investigator - initiated research and team science ; it is between investigator - initiated research and targeted or top - down research , in which funds are earmarked for specific scientific areas .
team science aimed at studying fundamental biomedical problems can and usually should be investigator - initiated .
interdisciplinary team science is undoubtedly extremely important and will become increasingly so as we delve deeper into the complexities of biological systems .
one way to support team science is for independently funded principal investigators ( pis ) to form collaborations organically based on common interests and complementary skills , a method that , for fundamental research , seems likely to yield better results than collaboration borne of incentives such as targeted funding
nih also has several mechanisms dedicated to supporting investigator - initiated team science , including multi - pi r01s and program project grants ( p01s ) .
the centers of biomedical research excellence within the nigms institutional development award program also support team science , with a focus on developing the careers of junior investigators ( nigms , 2015 ) . moving forward
, we plan to try to understand what kinds of teams benefit the most from unified grant mechanisms such as multi - pi r01s and p01s .
press coverage , prizes , and renown all revolve around the concepts of discoveries and breakthroughs .
eureka moments in which a paradigm shift occurs . and yet most major advances in science actually happen when a series of small steps coalesce into an important new understanding .
for example , the discovery of restriction enzymes , a truly transformative advance that propelled biomedical research in the 1970s into the age of molecular biology and launched the biotechnology industry , began in the 1950s with the description of bacterial resistance to phage infection
. dozens of papers published in various journals led to the insights that brought the nobel prize to warner arber , daniel nathans , and hamilton smith in 1978 ( loenen et al . , 2014 ) .
discoveries arise from a complex web of knowledge , and without the network created by the steady progress of many researchers , they would not occur . as discussed earlier , it is impossible to know in advance where in this web the next big breakthroughs will arise or which strands of knowledge will be required to make them .
the original observation of crispr sequences , for example , was made at the end of a 1987 journal of bacteriology paper that was otherwise devoted to reporting the sequence of the gene for the escherichia coli alkaline phosphatase isozyme converting protein iap ( ishino et al .
describing the mysterious repeat sequences , the paper ends with the sentence , so far no sequence homologous to these has been found elsewhere in procaryotes , and the biological significance is not known .
slowly , through years of careful characterization of the crispr pathway , our understanding of what this initial observation meant fueled the development of a novel technology that has dramatically improved our ability to replace genes in living cells , paving the way for advances in medicine and biotechnology .
this and many other instances like it show how important it is for us to support as wide a web of research as possible .
in 1985 , bruce alberts wrote a prescient commentary in which he laid out the inefficiencies created in the basic biomedical research enterprise when labs become too large ( alberts , 1985 ) .
there are a number of reasons for these inefficiencies , but they mostly come down to bandwidth . for example , the more people a pi has in his or her lab , the less time he or she can devote to training and supervising each one .
in addition , the bigger a lab gets , the more time the pi must spend on the grant - writing and administrative tasks needed to keep the operation running and the less time he or she has for actually doing research . for these reasons
, alberts argued that the per capita output of a lab would generally diminish above a certain size and that nih and other agencies should cap pi funding , thereby limiting lab size and optimizing scientific productivity and quality . in 2010 , nigms conducted an analysis of the productivity and scientific impact of the research the institute funds as a function of each nigms investigator 's total direct - cost support from nih ( figure 2 ) .
this study showed that , on average , these metrics increase only shallowly with funding above a moderate level ( $250,000300,000 ) and then actually decrease above $750,000 ( berg , 2010a , b ) .
although a few investigators beat the averages and increase their productivity at a proportional or better rate as their funding increases , other well - funded investigators perform even worse than the averages .
similar results have recently been published for chemical and biological research supported by other agencies ( fortin and currie , 2013 ; gallo et al . , 2014 ) and by the nih ( berg , 2015 ; danthi et al . , 2015
a 2010 analysis of researchers funded by nigms showed that , on average , productivity did not scale proportionally with funding beyond a relatively moderate direct - cost threshold .
( top panel ) average number of publications associated with nih grants of nigms - funded investigators as a function of their total nih direct costs ( red line with circles ) and the average impact factor of the journals in which each set of investigators published ( blue line with squares ) .
( bottom panel ) the unbinned data used to generate the averages shown in the top panel .
jeremy berg , paul sheehy , and matt eblen ( nigms ) performed the data analysis .
thinking about these data from the perspective of an investor of taxpayer funds , one can do a simple back - of - the - envelope calculation to determine what the best investment strategy for fundamental research should be .
the first is from a talented established investigator and is for a new r01 , which would be his third , bringing him from $ 400,000 to $ 600,000 in total direct funding .
in the first case , the additional $ 200,000 would buy taxpayers , on average , approximately one more paper during the funding period over what the established pi would have produced with $ 400,000 ( figure 2 ) . in the second case ,
the new pi would produce five papers on average in the funding period if she were awarded the grant .
thus the choice seems obvious : taxpayers net four more papers by funding the new pi than by giving the established pi a third grant .
, some biomedical research simply costs more money than the average , and this needs to be considered when grant budgets are set . and
a difficulty here is that recent analyses have indicated that the peer - review process does not have sufficient resolution to accurately distinguish among the most promising applications , with at best modest correlations between score and productivity or impact for funded applications ( berg , 2011 , 2013 ; gallo et al . , 2014 ;
so , for example , if the established pi 's application scored in the fifth percentile , and the new pi 's scored in the 15th percentile , could we really be confident that the former is likely to produce more important work than the latter ? along these same lines ,
as mentioned earlier , although we fund some pis who beat the average productivity versus funding curve , we also fund some who are below it , again indicating that picking the high performers is not easy , at least with the current process .
these considerations suggest that we should be very selective in allowing pis to accumulate high funding levels and that , in general , funding more investigators at a moderate level rather than a few at a high level will yield the best payoffs .
a question that at first glance may seem trivial but is , i believe , a significant one is whether our key metric for how we use the funds we invest in biomedical research should be the number of grants we award or the number of investigators we support .
for example , we report to the scientific community and congress on the success rate for grant funding : how many grants we awarded in a year divided by the number of grant applications we received . in theory , focusing on grants tells us how many projects we are funding . however , because pis can have more than one nigms research grant , this focus distances our funding decisions from the key question of how many investigators are in our portfolio .
if we instead used the number of pis we support as the key parameter to drive our funding and programmatic decisions , it would reduce the number of variables , allowing us to focus on the most important ones .
for example , once we decided on the optimal number of nigms - supported investigators , we could then set a mean and median direct - cost target per investigator based on our total research budget .
once we had established the total number of investigators who should be supported by the institute , we could determine how many new pis should enter and how many established pis should exit the system each year .
we would also be better able to ensure the diversity and breadth of the institute 's research portfolio .
overall this seemingly simple shift in how we view our mission could be a useful catalyst for reequilibrating the biomedical research enterprise to maximize its effectiveness , efficiency , and sustainability .
promoting this shift is something we are working on at nigms , both as part of our new strategic plan and through a new funding mechanism , described in the following section .
reequilibrating the biomedical research enterprise to make it more efficient and sustainable will require major changes in every part of the system . because we do not know a priori which changes will work best and because there is always a risk of unintended negative consequences
, the soundest approach will be to experiment and to expand initiatives that succeed and abandon those that do not .
this model requires us to define in advance the outcomes we hope to achieve and to collect the necessary data to measure them as the experiments progress .
one such experiment is the nigms maximizing investigators ' research award ( mira ; preusch , 2015 ) .
the mira program aims to transform how we support fundamental biomedical research , shifting away from the current paradigm of funding specific , predefined projects to one in which we focus on supporting the overall research program in each investigator 's lab .
the goals of the mira pilot are to 1 ) increase funding stability for investigators to enhance their ability to take on ambitious research and approach problems creatively ; 2 ) increase flexibility for investigators to follow new directions as ideas and opportunities arise , which should help maximize the chances for breakthroughs ; 3 ) improve the distribution of funding , allowing the institute to support an optimally broad and diverse portfolio of investigators ; and 4 ) reduce the amount of time spent writing and reviewing grant applications , freeing up time to focus on research , training , and mentoring .
each of these goals aims to help maximize the scientific returns on taxpayers ' investments .
much discussion of the problems facing the biomedical research enterprise ( e.g. , ioannidis , 2011 ; bourne , 2013b , c ; alberts et al . , 2014 ) .
among the many challenges , perhaps the most worrying is that junior scientists are becoming increasingly discouraged about their career prospects ( bourne , 2013a ; polka and krukenberg , 2014 ) , a growing crisis that could leave a serious deficit in the nation 's scientific capacity for years to come . but despite the many challenges we face , there are reasons to be optimistic about the future .
scientifically , our deepening and expanding knowledge is opening up incredible new frontiers in research , and developments in technology are allowing us to address questions that a decade ago seemed completely inaccessible .
although i have not discussed it here , renewed focus on improving scientific education , training , and career development seems likely to lead to an even more skilled , productive , and efficient workforce in the coming years .
there is a growing recognition that we owe it to the nation and future generations to reoptimize the biomedical research enterprise ( lorsch , 2015 ) , and momentum is building in many sectors to make the changes this reoptimization will require .
for example , the nih ( rockey , 2012 , 2015 ; maas , 2015 ) , members of congress ( harris and young , 2014 ; hearing on the fy 2016 national institutes of health budget request , 2015 ) , professional societies ( federation of the american societies for experimental biology , 2015 ) , and academic leaders ( daniels , 2015 ) are focusing attention on the challenges facing junior scientists and are trying to develop strategies to help this critically important group . if these trends continue , and all of the stakeholders take on their share of the responsibility , i am confident we can develop a more efficient and sustainable biomedical research enterprise and , in the process , accelerate advances in human health and prosperity . | pubmed |
presently a wide - spread program of investigations of the structure of the lightest nuclei is under consideration .
there are new proposals to study the polarization characteristics of the deuteron using both hadron @xcite and electro - magnetic probes ( cf
. refs .
the future experiments are very interesting since a complete reconstruction of the amplitude of the process @xcite and an overall investigation of the nuclear momentum distribution @xcite seems achievable . among the simplest reactions with hadron probes are processes of forward or backward scattering of protons off the deuteron .
the intensive experimental study of these reactions has started a decade ago at dubna and saclay ( see , for instance , refs .
@xcite ) and is also planed to be continued in the nearest future at cosy @xcite .
the measured momentum of the fragments is directly related to the argument of the deuteron wave function in the momentum space . in this way one
hopes that a direct experimental investigation of the momentum distribution in the deuteron in a large interval of the internal momenta is possible . by using polarized particles
one may investigate as well different aspects of spin - orbital interaction in the deuteron and can obtain important information about the role of `` non - traditional '' degrees of freedom ( like @xmath0 isobars , @xmath1 excitation and so on ) in the deuteron wave function .
nowadays a renewed interest receives the elastic backward @xmath2 scattering with polarized protons and deuterons .
a distinguished peculiarity of this process is that in the impulse approximation the cross section is proportional to the fourth power of the deuteron wave function ( contrary to the break - up and quasi - elastic reactions which are proportional to the second power of the wave function ) .
this makes the processes of elastic scattering much more sensitive to the theoretically assumed mechanisms and the deuteron wave function .
another peculiarity of elastic backward or forward @xmath2 reactions is that the amplitude of the process is determined by only four complex helicity amplitudes , and a set - up of experiments for a complete reconstruction of these amplitudes is rather possible . for this
it is sufficient to measure 10 independent observables as proposed in refs .
@xcite .
first measurements of polarization observables , such as the tensor analyzing power @xmath3 and deuteron - proton polarization transfer @xmath4 , have been performed at dubna @xcite and saclay @xcite . theoretically the elastic @xmath2 scattering has been studied by several authors @xcite .
it has been shown that the cross section can not be satisfactorily described within the impulse approximation and that other mechanisms , such as meson exchange or triangle diagrams @xcite , may become important .
it is expected that the role of virtual meson production becomes important at moderate energies of the incoming proton , @xmath5 gev / c ( or equivalently , at momenta of the outgoing proton @xmath6 gev / c ) , corresponding to the range of excitations of @xmath0 isobars during the interaction .
namely at these energies the experimental cross section exhibits a relatively broad bump ( cf .
@xcite ) , which may be considered as an evidence of the @xmath0 excitations in the process of elastic backward @xmath2 scattering . consequently
, an investigation of the contribution of such diagrams to the unpolarized cross section and to the polarization observables , which are more sensitive to the reaction mechanism , is of interest .
we focus our attention here on a study of the contribution of virtual meson production in the elastic @xmath2 amplitude within the bethe - salpeter ( bs ) approach by using a numerical solution of the bs equation obtained with a realistic one - boson exchange interaction @xcite . for the triangle diagrams we consider only the positive energy waves ( the largest ones ) , because the negative @xmath7 waves are expected to provide a negligible contribution to the total amplitude . within the present approach the effects of relativistic fermi motion ,
lorenz boosts and spin transformations of the relevant amplitudes are treated in a fully covariant way .
the total amplitude of the process is presented as a sum of the amplitudes of the one - nucleon exchange mechanism ( investigated in details in a previous paper @xcite ) and the one - meson exchange diagrams .
it is explicitly shown that the total amplitude is time - reversal invariant .
our paper is organized as follows . in section
ii we present the kinematics and notation .
section iii contains the relevant formulae of both the one - nucleon exchange process and , in more detail , the triangle diagrams .
results ( such as numerical calculations of the cross section , tensor analyzing power @xmath3 , polarization transfer from deuteron to proton @xmath4 and from proton to proton @xmath8 ) are discussed in section iv and summarized in section v. some important technical details are presented in the appendices .
we consider the elastic backward @xmath2 scattering of the type @xmath9 the differential cross section of the reaction ( [ reaction ] ) in the center of mass of the colliding particles reads @xmath10 where @xmath11 is the mandelstam variable denoting the total energy in the center of mass , and @xmath12 is the invariant amplitude of the process . in the case of backward scattering
the cross section eq .
( [ cross ] ) depends only on one kinematical variable , which is usually chosen to be @xmath11 .
other variables can be expressed via @xmath11 by using the energy conservation law ; for instance , the mandelstam variable @xmath13 is @xmath14 , the center of mass momentum reads @xmath15 etc . here
@xmath16 and @xmath17 stand for the deuteron and nucleon masses , respectively . in the laboratory system
we define the relevant kinematical variables as follows @xmath18 and the components of the polarization vector of the deuteron with the polarization index @xmath19 are fixed by @xmath20 the dirac spinors , normalized as @xmath21 and @xmath22 , read @xmath23 where @xmath24 , and @xmath25 denotes the usual two - dimensional pauli spinor .
the general properties of the amplitude @xmath12 for the elastic scattering of the spin type @xmath26 have been studied in detail and are well known ( see , for instance , refs .
@xcite ) ; here we recall only the most important characteristics of @xmath12 . in principle , the process of the elastic @xmath2 scattering is determined by 12 independent partial amplitudes . however , in case of forward or backward scattering , because of the conservation of the total spin projection , only four amplitudes remain independent and these four amplitudes determine all the possible polarization observables of the process .
there are many possible choices of representing these four amplitudes . in order to emphasize explicitly the transition between initial and final states with fixed spin projections it is convenient to represent @xmath12 in the center of mass in the two - dimensional spin space of the proton spinors and three - dimensional space of the deuteron spin characteristics .
in such a representation of the amplitude it is possible , by using eqs .
( [ moms ] ) - ( [ spinors ] ) , to express all the partial spin amplitudes via the corresponding quantities evaluated in the deuteron s rest frame . then using the same notation as adopted in refs .
@xcite , the total amplitude is written in the form @xmath27 with @xmath28)\nonumber\\[2 mm ] & + & \i \ , { \cal d}\,(\bsigma\bn)(\bn\cdot [ \bxi_m\times\bxi^+_{m ' } ] ) , \label{amplit}\end{aligned}\ ] ] where @xmath29 is a unit vector parallel to the beam direction , and @xmath30 are the partial amplitudes of the @xmath2 elastic scattering depending on the initial energy . the cross section ( [ cross ] ) for unpolarized particles is determined by @xmath31 .
the four scalar amplitudes @xmath32 , @xmath33 are related to the partial spin amplitudes @xmath34 via @xmath35 & & { { \cal m}}_{\frac{1}{2}-1}^{\frac{1}{2}-1}={{\cal a}}- { { \cal c}}-{{\cal d}},\quad { { \cal m}}_{\frac{1}{2}0}^{-\frac{1}{2}1}=\sqrt{2}{{\cal c}}.\label{spinampl}\end{aligned}\ ] ] the differential cross section and polarization observables under consideration read @xcite @xmath36 t_{20 } & = & -\frac{1}{\sqrt{2 } } \frac{4\left ( 2 \re \left [ { { \cal a}}{{\cal b}}^ * \right ] + |{{\cal b}}|^2 - 2 \re \left [ { { \cal c}}{{\cal d}}^*\right ] -|{{\cal d}}|^2\right ) } { \mbox{tr } \left ( { { \cal f}}{{\cal f}}^+\right ) } , \label{t20}\\[2 mm ] \kappa_{d\to p } & = & \frac{6\left ( \re \left [ ( 2{{\cal a}}^*+{{\cal b}}^*+{{\cal d}}^*){{\cal c}}\right ] + |{{\cal c}}|^2 \right ) } { \mbox{tr } \left ( { { \cal f}}{{\cal f}}^+\right ) } , \label{dtop}\\[2 mm ] \kappa_{p\to p } & = & \frac{2 \left ( 3|{{\cal a}}|^2 + 2 \re ( { { \cal a}}{{\cal b}}^ * ) + |{{\cal b}}|^2 -2|{{\cal c}}|^2 -4 \re ( { { \cal c}}{{\cal d}}^*)-2|{{\cal d}}|^2\right ) } { \mbox{tr } \left ( { { \cal f}}{{\cal f}}^+\right ) } , \label{ptop}\end{aligned}\ ] ] with @xmath37 + |{{\cal b}}|^2 + 6|{{\cal c}}|^2 + 4 \re \left [ { { \cal c}}{{\cal d}}^*\right ] + 2|{{\cal d}}|^2 ) .
\label{trace}\ ] ]
in what follows we investigate the contribution of the relativistic one - nucleon exchange and one - meson exchange diagrams to the process ( [ reaction ] ) as depicted in figs .
correspondingly , the amplitude reads @xmath38 where @xmath39 stands for the one - nucleon exchange amplitude , and @xmath40 and @xmath41 denote the contributions of the triangle diagrams in figs .
1b and 1c .
the contribution of the one - nucleon exchange mechanism in @xmath2 reactions has been investigated within the bs formalism in detail elsewhere ( cf.refs .
therefore , we briefly recall only the main results for the one - nucleon exchange diagram . using the kinematics shown in fig . 1 the one - nucleon exchange contribution to the elastic amplitude within the bs formalism is @xmath42 where @xmath43 denotes the bs vertex function of the deuteron , @xmath44 is the modified propagator of the exchanged ( second ) particle ( see fig .
1a ) . by making use of eqs .
( [ moms ] ) - ( [ spinors ] ) the covariant amplitude ( [ gn ] ) may be expressed in the form ( [ amplit ] ) .
the result ( only for positive bs waves ) is @xcite : @xmath45 { \cal a}_0 & = & 16\pi m p_{lab}^2\,\left ( \psi_s(p_{lab})-\frac{\psi_d(p_{lab})}{\sqrt{2}}\right ) ^2 , \label{abs}\\ { \cal b}_0 & = & 16\pi m p_{lab}^2\ \frac{3}{2}\psi_d(p_{lab})\,\left ( 2\sqrt{2}\psi_s(p_{lab } ) + \psi_d(p_{lab})\right ) , \label{bbs}\\ { \cal c}_0 & = & 16\pi mp_{lab}^2\,\left ( \psi_s(p_{lab } ) -\frac{\psi_d(p_{lab})}{\sqrt{2}}\right ) \left(\psi_s(p_{lab})+\sqrt{2}\psi_d(p_{lab})\right ) , \label{cbs}\\ { \cal d}_0 & = & -\,16\pi mp_{lab}^2\ , \frac{3}{\sqrt{2}}\psi_d(p_{lab } ) \left ( \psi_s(p_{lab})-\frac{\psi_d(p_{lab})}{\sqrt{2}}\right ) , \label{dbs}\end{aligned}\ ] ] where we employ the notion of bs wave functions with @xcite @xmath46 with @xmath47 , @xmath48 , and @xmath49 as the partial vertices with positive @xmath50 spins .
note , that within the one - nucleon exchange approximation the bs formalism with only positive - energy waves provides exactly the same form of polarization observables as in the non - relativistic impulse approximation @xcite , whereas an account of the negative - energy @xmath7 waves leads to more complicate relations among the polarization observables and the deuteron wave function @xcite .
now we proceed with an investigation of the triangle diagram depicted in fig .
1b . the corresponding amplitude , in case when the exchanged particles are a proton and a @xmath51 , has the form @xmath52 where @xmath53 is the @xmath54 coupling constant , @xmath55 is the pion mass , @xmath56 the bs amplitude , and the operator @xmath57 describes the off - mass shell process @xmath58 . besides the amplitude ( [ triangl1 ] )
, there is another diagram with neutron and @xmath59 exchange , which is related to ( [ triangl1 ] ) by an isospin factor of @xmath60 . for the sake of consistency ,
the operator @xmath61 which is a @xmath62 matrix in the spinor space should be computed within the same framework of the effective meson - nucleon theory as the bs equation is solved . however ,
this is a rather cumbersome and ambitiouse problem . to avoid uncertainties connected with calculations of @xmath61 , in this paper
we express it via the amplitude @xmath63 of the subprocess @xmath64 with real on - mass shell particles by @xmath65 the bs amplitude @xmath56 is related to the deuteron bs vertex @xmath66 it is seen , at first sight , from eqs .
( [ triangl1 ] ) and ( [ vert ] ) that there are six poles in the integrand ( [ triangl1 ] ) : three located in the upper half - plane of @xmath67 , the other three ones in the lower half - plane .
actually , the two nucleon propagators in ( [ vert ] ) contain only two poles , as it may be shown , for instance , by performing an explicit partial decomposition of the amplitude @xmath56 in the spin - angular basis @xcite , hence the integrand ( [ triangl1 ] ) contains two poles in the upper half - plane and two poles in the lower one .
inserting eqs .
( [ fpid ] ) and ( [ xilab ] ) - ( [ spinors ] ) into eq .
( [ triangl1 ] ) and keeping in the amplitude @xmath56 only partial waves with positive relative energy ( the explicit form of @xmath56 in terms of positive waves is given in appendix [ sec : app1 ] ) the contribution of the triangle diagram reads @xmath68 & \times & \left [ \frac { g_{s^{++ } } ( q_0,|{\bf q}| ) - g_{d^{++ } } ( q_0,|{\bf q}|)/\sqrt{2 } } { ( m_d-2e_q)^2 - 4q_0 ^ 2 + \i \varepsilon } \chi^+_{s ' } \left ( ( \bsigma { \bf \cal k})(\bsigma\bxi_m ) \right ) \widetilde \chi_{s_2 } \right . \nonumber\\[2 mm ] + & & \left .
\frac{3\ , g_{d^{++ } } ( q_0,|{\bf q}| ) } { ( m_d-2e_q)^2 - 4q_0 ^ 2 + \i \varepsilon } ( \bxi_m { \bf q } ) \chi^+_{s ' } \left ( 1 -\frac{e_q+m}{e_{lab}+m } \frac{(\bsigma { \bf q } ) ( \bsigma \bp)}{{\bf q}^2 } \right ) \widetilde \chi_{s_2 } \right ] , \nonumber\end{aligned}\ ] ] where @xmath69 , @xmath70 and @xmath71 . equation ( [ triang3 ] ) may be simplified by observing that the amplitude @xmath40 is a function of external momenta of the process ( [ reaction ] ) , for which only one independent three - vector may be defined , for instance the vector @xmath72 from ( [ amplit ] ) .
then one obtains @xmath73 \widetilde\chi_{s_2 } , \label{simple}\end{aligned}\ ] ] where we introduced two scalar functions as follows @xmath74 & \times & f^{m'}_{s_2,s}(p , p_2;\pi , d ' ) , \nonumber\\[2 mm ] d_{s_2,s}^{m ' } & = & -\frac{\i 3g_{\pi nn}}{\sqrt{8\pi } } \int\frac{d^4 q}{(2\pi)^4}\frac{1 } { \pi^2 - \mu^2 + \i \varepsilon } \sqrt{\displaystyle\frac{e_{lab}+m}{e_q+m}}\frac{2}{e_q } \frac{1 } { \pi^2 - \mu^2 + \i \varepsilon } \label{triang5}\\[2 mm ] & \times & \frac { g_{d^{++ } } ( q_0,|{\bf q}|)}{(m_d-2e_q)^2 - 4q_0 ^ 2 + \i \varepsilon } \left ( |{\bf q}|\cos\theta + \frac{e_q+m}{e_{lab}+m } |\bp'|\cos^2\theta \right)\nonumber\\[2 mm ] & \times & f^{m'}_{s_2,s}(p , p_2;\pi , d ' ) .
\nonumber\end{aligned}\ ] ] then the invariant amplitude @xmath75 is computed by using eqs .
( [ ampf ] ) - ( [ spinampl ] ) and ( [ triang4 ] ) - ( [ triang5 ] ) . within the bs formalism in numerical calculations of integrals with bs amplitudes one usually performs a wick rotation and all calculations are done in the euclidean space .
this is possible when singularities in integrands are well located and there are no poles in the first and third quadrant of @xmath67 . in our case
the pion pole is a `` moving '' one and accidentally , at some values of @xmath76 , it may cross the imaginary axis @xmath67 thus hindering the standard procedure of a wick rotation . in this case
one needs to compute either the contribution of the residue of this pole or abandon the wick rotation and to compute the integral by closing the contour in the upper half - plane and evaluating the residue in each pole appearing in the integrand .
as mentioned , in our case in the upper half - plane there are two poles , one from the nucleon propagator , another one from the pion propagator .
an analysis of the contribution of the pion pole has been performed in ref .
@xcite and it is found to be relatively small , and with an accuracy of @xmath77 ( where @xmath78 is the deuteron binding energy ) it may be neglected .
then the main contribution to the integrals ( [ triang4 ] ) and ( [ triang5 ] ) comes from the residue at @xmath79 , where the exchanged proton is on mass shell , i.e. @xmath80 , and the neutron is off mass shell , i.e. @xmath81 .
here it is worth emphasizing that when calculating loop and triangle diagrams in quantum field theory , after performing integrations on @xmath67 in one propagator , the second one remains singular in @xmath82 .
these singularities , known as landau ghosts @xcite , are unphysical and they ought to be removed by properly choosing a subtraction procedure . in our case these ghosts may appear in the pion propagator after the integration of the nucleon pole is carried out and the remaining integral on @xmath82 is extended to infinity .
within effective meson - nucleon theories there are no rigorous regularization schemes to subtract singularities in triangle diagrams .
usually they are removed either numerically , for instance by using cut - off parameters in the integrations , or by choosing adequate physical approximations .
we proceed now as follows . at the nucleon pole
the pion propagator reads @xmath83 it is seen that singularities may appear at large values of @xmath84 , which correspond to large @xmath76 in the integrals ( [ triang4 ] ) and ( [ triang5 ] ) ; however at such @xmath76 the bs waves functions and the subprocess @xmath85 vanish so that in numerical calculations this range of @xmath76 should be eliminated . following refs .
@xcite we introduce in the laboratory system the kinetic energies of particles on - mass shell , @xmath86 and due to the fact that in the process ( [ reaction ] ) the momentum of the outgoing proton is kinematically restricted ( since @xmath87 in the whole range of @xmath88 ) we neglect in eq .
( [ approximation ] ) terms @xmath89 and @xmath90 , i.e. @xmath91 plugging eq .
( [ approximat ] ) into eqs .
( [ triang4 ] ) and ( [ triang5 ] ) we obtain @xmath92 & \times & \left ( \psi_s(q_0,|{\bf q}|)-\psi_d(q_0,|{\bf q}| ) \frac{1}{\sqrt{2 } } \right ) \left ( |{\bf q}|\cos\theta + \frac{e_q+m}{e_{lab}+m } |\bp'|\right ) \nonumber\\[2 mm ] & \times & f^{m'}_{s_2,s}(p , p_2;\pi , d'),\nonumber\\[4 mm ] d_{s_2,s}^{m ' } & = & -\frac{6g_{\pi nn}}{(4\pi)^{3/2 } } \sqrt{m_d } \int\frac{{\bf q}^2 d |{\bf q}|d\cos\theta}{({\bf q}-{\bf p}')^2+\mu^2 } \frac{1}{e_q}\sqrt{\displaystyle\frac{e_{lab}+m}{e_q+m } } \label{dnew}\\[2 mm ] & \times & \psi_d(q_0,|{\bf q| } ) \left ( |{\bf q}|\cos\theta + \frac{e_q+m}{e_{lab}+m } |\bp'|\cos^2\theta\right ) f^{m'}_{s_2,s}(p , p_2;\pi , d ' ) .
\nonumber\end{aligned}\ ] ] our ansatz , eq .
( [ approximat ] ) , is very similar to that one adopted in ref .
@xcite , however , there is a difference in the treatment of the kinetic energy of the off - mass shell neutron . in ref .
@xcite the neutron kinetic energy has been taken to be identical to the one of the exchanged proton .
this leads to a violation of the energy conservation of the deuteron in the laboratory frame .
however , at low and moderate values of @xmath93 numerically both approximations provide nearly the same results .
note that in the extreme non - relativistic case , @xmath94 , eq . ( [ approximat ] ) yields @xmath95 , i.e. exactly the pion propagator used in ref .
@xcite . finally , after an explicit evaluation of the spin matrix elements in eq .
( [ simple ] ) ( see also , appendix [ sec : app2 ] ) the amplitude corresponding to the diagram fig .
1b may be cast in the form @xmath96 & + & \left .
a_{s_2,s}^{m ' } \left ( -\sqrt{2}\delta_{m1}\delta_{s_2\frac{1}{2 } } \delta_{s'\frac{1}{2 } } + \sqrt{2}\delta_{m-1}\delta_{s_2-\frac{1}{2 } } \delta_{s'-\frac{1}{2 } } \right ) \right\ } , \label{tot}\end{aligned}\ ] ] with @xmath97 and @xmath98 given by eqs .
( [ anew ] ) and ( [ dnew ] ) , respectively . for explicit calculations of the amplitude ( [ tot ] )
the amplitude @xmath99 of the elementary process @xmath100 is needed at an unphysical value of the mass of the virtual pion , and so there is an ambiguity related to the value to be used .
since the amplitude depends on two invariant variables , and the mandelstam @xmath13 is common for both the process ( [ reaction ] ) and the subprocess @xmath100 , we choose the independent variables for @xmath101 to be @xmath13 and @xmath102 . then assuming that the amplitude does not vary as a function of the pion mass
, one may reconstruct the amplitude by using the experimental data for the real process @xmath100 at given @xmath103 and @xmath13 . in our calculation
we use the partial amplitudes @xmath104 from the combined analysis of arndt et al.@xcite , which are available via telnet in an interactive regime ( see references in @xcite ) . in our calculations
we need the partial amplitudes in the laboratory frame where the vectors @xmath105 and @xmath106 are not collinear , while the experimental amplitudes are given in the center of mass of colliding particles .
consequently , a lorenz boost of the amplitudes from the center of mass to the laboratory system is needed . as a result two
additional rotations of the amplitude ( the wick helicity rotation @xcite to adjust the helicity amplitudes in two systems , and a wigner rotation from @xmath107 axis parallel to @xmath108 to the @xmath109 axis along the vector @xmath110 ) have to be employed ( see appendix [ sec : app3 ] ) .
the contribution to the invariant amplitude @xmath12 from the diagram fig .
1c is computed in the frame where the outgoing deuteron is at rest and it is found to be related to the contribution of the diagram 1b via @xmath111 it is seen that the sum of the two diagrams 1b and 1c ensures the total amplitude @xmath112 to be time reversal invariant .
in fig . 2 results of numerical calculation of the differential cross section are presented .
the dashed line is the contribution of the one - nucleon exchange mechanism @xcite .
it is seen that within the impulse approximation a satisfactorily description of data can not be achieved .
the contribution of one - meson exchange diagrams ( dotted line ) is significant in the region @xmath113 gev / c ( corresponding to the range of the initial momentum @xmath114 gev / c ) , which is the region ( enlarged by
fermi motion
effects ) where the experimental data give evidence for @xmath0 excitations in the amplitude @xmath64 @xcite . beyond this region
the amplitude @xmath64 vanishes rather rapidly as also the triangle amplitude does .
the total cross section is represented by solid lines , where the line labeled by ( a ) is the result of calculations with taking into account the full bs solution ( including @xmath7 waves ) , the label ( b ) depicts the bs result with only positive - energy waves .
it may be seen that an account for @xmath0 excitations ( through the @xmath64 amplitudes ) essentially improves the description of the experimental data .
contrary to this , the polarization observables are less sensitive to the contribution of the triangle diagrams . as seen in figs . 3 and 4 the agreement with data of tensor analyzing power @xmath3 and polarization transfer @xmath4 is not improved .
5 demonstrates that also the polarization transfer @xmath8 is essentially unaffected by the triangular diagrams . to understand this insensitivity one has to recall that within the one - nucleon exchange approximation the corresponding expressions for the polarization observables ( but not for the cross sections and with positive bs waves only ) are analytically identical for all the backward @xmath2 processes , elastic , quasi - elastic and break - up reactions @xcite
this is due to a factorization of contributions from upper and lower vertices in diagrams like the one depicted in fig .
1a . the triangle diagram , eqs .
( [ anew ] ) and ( [ dnew ] ) , is implicitly proportional to the second power of the deuteron wave function ( the amplitude @xmath115 itself is proportional to the first power of the wave function of the outgoing deuteron ) , so that the contribution to the cross section is @xmath116 as is the cross section in the one - nucleon exchange approximation .
however , our numerical results for polarization observables , figs . 3 - 5 , and a comparison with those obtained within one - nucleon exchange approximation @xcite , persuades us that the amplitude for triangle diagrams may be also approximately presented as a factorization between the upper vertex ( the amplitude @xmath115 in fig .
1b ) and the lower vertex , characterizing the structure of the target deuteron . consequently , potentially large effects in the cross section cancel in the ratios , which define the polarization observables .
moreover , it seems that canonical approaches , treating the deuteron solely by nucleon degrees of freedom , should be supplemented by different `` exotics '' ( e.g. @xmath0 - @xmath0 components ) .
more experimental data on polarization characteristics of backward @xmath2 reactions will provide more complete information about the deuteron structure and reaction mechanisms .
in summary , we present an explicit analysis of pion - exchange effects in elastic backward scattering of protons off deuterons within the bethe - salpeter formalism with realistic interaction kernel . the total amplitude of the process is presented as a sum of contributions of the one - nucleon exchange mechanism and the triangle diagrams with virtual @xmath0 excitations .
the four partial spin amplitudes of the process have been computed explicitly within the bethe salpeter approach .
effects of relativistic fermi motion and lorenz transformations of the amplitudes have been taken into account in a fully covariant way .
numerical estimates of effects of pion exchanges in the cross section and polarization observable , e.g. tensor analyzing power and polarization transfers , at kinematical conditions of operating @xcite and forthcoming experiments @xcite , are performed .
it is found that the one - pion exchange mechanism plays a crucial role in describing the spin averaged cross section , while for the considered polarization observables the role of triangle diagrams is less important .
it is shown that the one - nucleon and one - pion exchange exchange mechanisms are not the predominant ones in describing various polarization observables and future experiments mainly will highlight effects beyond these mechanisms .
we thank r. arndt and i. strakovsky for useful discussions and explanations of how to use the said program in an interactive regime to obtain their partial amplitudes for the @xmath100 reaction .
we especially thank r. arndt which provide us with fortran codes to compute the helicity amplitudes @xmath117 .
useful discussions with a.yu .
umnikov , yu .
kalinovsky , l. naumann and f. santos are gratefully acknowledged .
two of the authors ( l.p.k . and s.s.s .
) would like to thank for the warm hospitality in the research center rossendorf .
this work is supported within the heisenberg - landau jinr - frg collaboration project , and by bmbf 06 dr 829/1 and rfbr no.95 - 15 - 96123 .
the bethe salpeter amplitudes in the laboratory system are of the form @xcite
@xmath118 \phi_m^{d^{++}}(p_1,p_2 ) & = & -\frac{{\cal n}}{\sqrt{2 } } ( \hat k_1+m ) \frac{1+\gamma_0}{2 } \left ( \hat\xi_m + \frac{3}{2|{\bf p}|^2 } ( \hat k_1-\hat k_2)(p\xi_m)\right ) ( \hat k_2-m ) \phi_d ( p_0,|{\bf p}|),\nonumber \ ] ] where @xmath119 are on - mass shell four - vectors related to the off - mass shell vectors @xmath120 as follows @xmath121 and @xmath122 are the partial scalar amplitudes , related to the corresponding partial vertices as @xmath123 in eq . ( [ psis ] )
the normalization factor is @xmath124 .
here we present some explicit formulae which may be useful in computing the spinor matrix elements in eq .
( [ triang3 ] ) and in deriving eq .
( [ tot ] ) : @xmath125 & & ( \bsigma\,{\bn})(\bsigma\,\bxi_m)=(\bn\,\bxi_m ) + \i \left ( \bsigma\,[\bn\times\bxi_m]\right ) ; \nonumber\\[2 mm ] & & -\i \left ( \bsigma\,[\bn\times\bxi_m]\right ) \
, \i \sigma_y=(\bxi_m)_x -\i ( \bxi_m)_y\sigma_z = \left \ { \begin{array}{cc } -\sqrt{2}\hat p_+ & \quad m=+1\\ 0 & \quad m=0\\ \sqrt{2}\hat p_- & \quad m=-1 \end{array } \right . , \end{aligned}\ ] ] where @xmath126 is the spin-@xmath60 projection operator on states with positive ( negative ) spin projections , @xmath127 .
by definition , a state with given momentum @xmath128 and helicity @xmath129 in a frame of reference @xmath130 is that obtained by a lorenz transformation of a state with given spin projection @xmath131 from the rest system @xmath132 to @xmath130 , i.e. : where @xmath134 .
as usually , a lorenz transformation @xmath135 $ ] is presented by a sequence of two operations : a boost along the @xmath107 axis , @xmath136 , where @xmath137 is the speed of the state in @xmath130 , and a rotation from @xmath107 direction to the direction of @xmath128 , i.e. @xmath138 .
let us suppose now that one has a state @xmath139 given in the frame @xmath130 and one wishes to know how it reads in another frame @xmath140 obtained by a lorenz transformation @xmath141 on @xmath130 @xmath142 from the definition of the helicity states one has @xmath143)| \stackrel{0}{p};\lambda\rangle , \label{b3}\ ] ] where @xmath135 $ ] is the corresponding lorenz transformation @xmath144 . then multiplying eq .
( [ b3 ] ) by unity , @xmath145)u^{-1}[h[(\bp')]=1 $ ] , where @xmath146 $ ] is the helicity transformation that would define a state @xmath147)| \stackrel{0}{p},\lambda\rangle $ ] with @xmath110 being the same vector as obtained by transforming @xmath128 from @xmath130 to @xmath140 , one obtains : @xmath148){\cal r}| \stackrel{0}{p},\lambda\rangle , \ ] ] where @xmath149u(l^{-1})u[h(\bp)]$ ] is a sequence of transformations @xmath150 , i.e. nothing but a rotation
. then latexmath:[\[|\bp,\lambda\rangle_{{{\cal o } } ' } = d^{(s)}_{\lambda\lambda'}(\omega ) angles describing the rotation . in case
when the lorenz transformation is a simple boost along the @xmath107 direction with the speed @xmath152 then @xmath153 is just an angle , describing a rotation about the @xmath154 axis , @xmath155 with @xmath156 and @xmath157 are the polar angles of @xmath128 in the systems @xmath130 and @xmath140 , respectively .
this is known as wick helicity rotation , contrary to wigner s canonical spin rotation . in our case
the relevant @xmath107 axis is the one along the @xmath158 direction .
then , obtaining the helicity amplitudes in the laboratory frame we need an additional rotation to change from the helicity basis to the spin projections
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with the current understanding of the mechanism of coronary artery disease , acute st segment elevation myocardial infarction , non - st segment elevation myocardial infarction , and unstable angina can be classified as acute coronary syndrome ( acs ) .
acute myocardial infarction ( ami ) is one of the most common cardiovascular diseases , having the highest morbidity and mortality in the world [ 13 ] . in the year 2010 ,
more than 6 million patients were hospitalized for treatment of ami in the united states .
owing to china s aging population , the incidence rate of this disease has increased drastically .
according to official estimates , more than 16 million people annually will succumb to ami by 2020 .
patients suffer ami due to myocardial necrosis , an ischemic injury that leads to the deformation of mitral annulus .
the effects of mild ischemic mvr include left ventricular remodeling and left ventricular enlargement . in severe cases , it can lead to left ventricular dysfunction and left ventricular failure , which is a life - threatening condition . when ischemic mvr is severe , the survival rate is just 1 year in more than 60% cases
. coronary artery bypass grafting ( cabg ) and mitral valve repair or replacement ( mvrr ) surgery are carried out on patients who develop significant ischemic mvr after myocardial infarction .
these surgical treatments can remove coronary artery blockages and mvr simultaneously , helping restore normal left ventricle geometry . according to current guidelines ,
surgical intervention is the conventional method for treating ischemic mvr with an ejection fraction ( ef ) of 30% or greater ( class i recommendation ) ; a class ii b recommendation is when the ef is 30% or less .
however , several studies have reported that the survival rate is not significantly different when patients with ischemic mvr are treated with mvrr and cabg [ 914 ] .
in other words , medical researchers are still dubious that mvrr surgery is suitable for treating patients who develop ischemic mvr after myocardial infarction . in this study
, we pooled results of recent studies and performed a meta - analysis to investigate the efficacy and patient prognosis of cabg combined with or without mvrr .
a comprehensive search was performed in ovidsp , pubmed , cochrane library , and embase to access medical literature from january 1986 to march 2015 .
we identified and reviewed all the studies that described the trials comparing the efficacy of only cabg with the combined treatment of cabg and mvrr , which were used to treat patients with moderate to severe ischemic mvr ( > 2 + grade ) after acs .
in pubmed , search terms were presented in text string format as follows : ischemic mitral valve regurgitation or ischemic mitral valve insufficiency ) and ( mitral valve repair or mitral valve annuloplasty or mitral valve replacement ) and ( coronary bypass grafting or surgical revascularization ) and ( acute myocardial infarction or acute coronary syndrome or acs ) .
we performed the meta - analysis to compare the differences in the short - term ( mean hospital mortality rate ) and long - term survival rates of patients treated with cabg only and those treated with both cabg and mvrr .
secondary outcomes were compared with the preoperative and postoperative degree of mvr , left ventricular end - systolic volume ( lvesv ) , left ventricular ejection fraction ( lvef ) , and new york heart association ( nyha ) class .
the criteria for excluding the articles were as follows : ( 1 ) no direct comparison between only cabg and the combined technique of cabg and mvrr ; ( 2 ) etiologies for mvr were myxomatous , rheumatic , infectious , congenital , or degenerative ; ( 3 ) mitral valve regurgitation was accompanied by mitral valve prolapse , tendon rupture , or papillary muscle rupture ; ( 4 ) no survival curves or hazard ratios ; ( 5 ) articles were not written in english .
the quality of each included study was evaluated by 2 researchers who cross - checked the extracted data from the selected case control study or randomized controlled trials .
if they had differences of opinion , then they sought the opinion of a third researcher .
baseline characteristics were described using proportions of discrete variables , while medians and standard deviation were calculated for continuous variables . to compare discrete variables of different groups ,
the kruskal - wallis test was conducted . in each individual study , the odds ratio was calculated for short - term survival , while hazard ratios were calculated for determining long - term survival . in each study , the survival curves compared the efficacy of only cabg with the combined technique of cabg and mvrr .
these survival curves were checked and evaluated for time intervals of 2 , 3 , or 6 months depending on their mean follow - up years .
the heterogeneity of patients and treatment procedures were incorporated in the random - effects model , including the study of statistical data and the 95% confidence intervals ( cis ) .
the heterogeneity of patients was examined using cochran s q test and the i statistic .
the degree of heterogeneity was divided into 3 grades : low ( < 25% ) , moderate ( 25%75% ) , and high ( > 75% ) .
meta - analysis was conducted using review manager , version 5.3 ( the cochrane collaboration , update software , oxford ) .
a comprehensive search was performed in ovidsp , pubmed , cochrane library , and embase to access medical literature from january 1986 to march 2015 .
we identified and reviewed all the studies that described the trials comparing the efficacy of only cabg with the combined treatment of cabg and mvrr , which were used to treat patients with moderate to severe ischemic mvr ( > 2 + grade ) after acs .
in pubmed , search terms were presented in text string format as follows : ischemic mitral valve regurgitation or ischemic mitral valve insufficiency ) and ( mitral valve repair or mitral valve annuloplasty or mitral valve replacement ) and ( coronary bypass grafting or surgical revascularization ) and ( acute myocardial infarction or acute coronary syndrome or acs ) .
we performed the meta - analysis to compare the differences in the short - term ( mean hospital mortality rate ) and long - term survival rates of patients treated with cabg only and those treated with both cabg and mvrr .
secondary outcomes were compared with the preoperative and postoperative degree of mvr , left ventricular end - systolic volume ( lvesv ) , left ventricular ejection fraction ( lvef ) , and new york heart association ( nyha ) class .
the criteria for excluding the articles were as follows : ( 1 ) no direct comparison between only cabg and the combined technique of cabg and mvrr ; ( 2 ) etiologies for mvr were myxomatous , rheumatic , infectious , congenital , or degenerative ; ( 3 ) mitral valve regurgitation was accompanied by mitral valve prolapse , tendon rupture , or papillary muscle rupture ; ( 4 ) no survival curves or hazard ratios ; ( 5 ) articles were not written in english .
the quality of each included study was evaluated by 2 researchers who cross - checked the extracted data from the selected case control study or randomized controlled trials . if they had differences of opinion
baseline characteristics were described using proportions of discrete variables , while medians and standard deviation were calculated for continuous variables . to compare discrete variables of different groups ,
the pearson test was performed . to compare continuous variables of different groups , the kruskal - wallis test was conducted . in each individual study , the odds ratio was calculated for short - term survival , while hazard ratios were calculated for determining long - term survival . in each study , the survival curves compared the efficacy of only cabg with the combined technique of cabg and mvrr .
these survival curves were checked and evaluated for time intervals of 2 , 3 , or 6 months depending on their mean follow - up years .
the heterogeneity of patients and treatment procedures were incorporated in the random - effects model , including the study of statistical data and the 95% confidence intervals ( cis ) .
the heterogeneity of patients was examined using cochran s q test and the i statistic .
the degree of heterogeneity was divided into 3 grades : low ( < 25% ) , moderate ( 25%75% ) , and high ( > 75% ) .
meta - analysis was conducted using review manager , version 5.3 ( the cochrane collaboration , update software , oxford ) .
in total , we reviewed 1183 studies , including 1159 studies in ovidsp and 24 studies in pubmed ; however , we could not find any related studies in embase or cochrane library .
while perusing through title , abstract , and full text of manuscripts , we found that a cohort of 5 studies met the inclusion criteria [ 9,11,1618 ] . among them , only 1 study was a prospective randomized trial , while the other studies were retrospective observational trials ( figure 1 ) .
a total of 3120 patients were included in all the studies that met our inclusion criteria . among them ,
2545 ( 82% ) patients were treated with only cabg , while 575 ( 18% ) patients underwent both cabg and mvrr .
the average age of the study population was 67 years ; the patients were in the age group of 61 to 70 years .
the mean percentage of male patients was 61% . in the analyzed studies , the proportion of male patients varied from 26% to 81% .
the study presented by kang had no published data on the number of patients with hypertension . however , in other studies more than half of the included patients also suffered from hypertension .
the degree of mvr was more than 2 + in all the patients that were included preoperatively .
after performing revascularization surgery , the degree of residual mvr in patients treated with only cabg was less than 1 + , but the degree of mvr was lower in patients treated with both cabg and mvrr ( 0.90.6 vs. 0.60.6 ) . nevertheless , there was no significant difference between the 2 groups .
cabg combined with mvrr was better than only cabg in reducing the mean lvesv and nyha classes , but only 1 study indicated that there were significant differences between the 2 surgical procedures . in the improvement of the mean lvef ,
the results of the 2 surgical procedures were similar , except for 1 study showing no improvement in cabg combined with mvrr .
short - term survival was defined as patients who died within 30 days despite being admitted in a hospital . in 3 studies ,
the total hospital mortality rate in patients treated with both cabg and mvrr techniques was 4.8% ( 5/104 ) , which was higher than the 2.8% hospital mortality rate of patients treated with only cabg ( 6/216 ) .
however , there was no significant difference in the hospital mortality rates of these patients ( p=0.358 ) .
odds ratio ( or ) range varied from 1.00 ( no favoring ) to 8.47 ( favoring cabg only ) .
we also assessed the heterogeneity of patients included in the studies ( chi=1.24 , p=0.54 , and i=0% ) .
the pooled or was 2.54 ( 95% ci , 0.659.95 ; p=0.18 ) ( figure 2 ) , indicating that the hospital mortality in patients treated with both cabg and mvrr techniques was similar to that witnessed in patients treated with only cabg . through the short - term funnel plots
, we deduced that there was no publication bias in the included studies ( figure 3 ) .
the shortest observation period of these studies was approximately 5 years , while the longest observation period was over 10 years . because these studies were not randomized controlled trials , the chosen survival curves were adjusted before analyzing .
the study hazard ratios varied from 1.22 to 5.16 ( figure 4 ) . while assessing potential heterogeneity , ( chi=2.55 and p=0.28 ) we found that there was no significant heterogeneity in patients included in various studies .
furthermore , i=21% , so the variability between these studies was due to low heterogeneity . in summary ,
the pooled study population showed that compared to the cabg group , long - term survival was more pronounced in the group treated with both cabg and mvrr techniques .
moreover , there was no publication bias in the included articles ( figure 5 ) .
a total of 3120 patients were included in all the studies that met our inclusion criteria . among them ,
2545 ( 82% ) patients were treated with only cabg , while 575 ( 18% ) patients underwent both cabg and mvrr .
the average age of the study population was 67 years ; the patients were in the age group of 61 to 70 years .
the mean percentage of male patients was 61% . in the analyzed studies , the proportion of male patients varied from 26% to 81% .
the study presented by kang had no published data on the number of patients with hypertension . however , in other studies more than half of the included patients also suffered from hypertension .
the degree of mvr was more than 2 + in all the patients that were included preoperatively .
after performing revascularization surgery , the degree of residual mvr in patients treated with only cabg was less than 1 + , but the degree of mvr was lower in patients treated with both cabg and mvrr ( 0.90.6 vs. 0.60.6 ) . nevertheless , there was no significant difference between the 2 groups .
cabg combined with mvrr was better than only cabg in reducing the mean lvesv and nyha classes , but only 1 study indicated that there were significant differences between the 2 surgical procedures . in the improvement of the mean lvef ,
the results of the 2 surgical procedures were similar , except for 1 study showing no improvement in cabg combined with mvrr .
short - term survival was defined as patients who died within 30 days despite being admitted in a hospital . in 3 studies ,
the total hospital mortality rate in patients treated with both cabg and mvrr techniques was 4.8% ( 5/104 ) , which was higher than the 2.8% hospital mortality rate of patients treated with only cabg ( 6/216 ) .
however , there was no significant difference in the hospital mortality rates of these patients ( p=0.358 ) .
odds ratio ( or ) range varied from 1.00 ( no favoring ) to 8.47 ( favoring cabg only ) .
we also assessed the heterogeneity of patients included in the studies ( chi=1.24 , p=0.54 , and i=0% ) .
the pooled or was 2.54 ( 95% ci , 0.659.95 ; p=0.18 ) ( figure 2 ) , indicating that the hospital mortality in patients treated with both cabg and mvrr techniques was similar to that witnessed in patients treated with only cabg . through the short - term funnel plots
, we deduced that there was no publication bias in the included studies ( figure 3 ) .
the shortest observation period of these studies was approximately 5 years , while the longest observation period was over 10 years . because these studies were not randomized controlled trials , the chosen survival curves were adjusted before analyzing .
the study hazard ratios varied from 1.22 to 5.16 ( figure 4 ) . while assessing potential heterogeneity , ( chi=2.55 and p=0.28 )
furthermore , i=21% , so the variability between these studies was due to low heterogeneity . in summary ,
the pooled study population showed that compared to the cabg group , long - term survival was more pronounced in the group treated with both cabg and mvrr techniques .
moreover , there was no publication bias in the included articles ( figure 5 ) .
this complication is more pronounced in patients who suffer ami : the incidence rate of ischemic mvr is up to 1350% in patients who have suffered ami . in most patients with mild mvr ,
the symptoms are not very obvious . however , in patients with moderate to severe mvr , the typical symptoms include palpitation , angina , heart failure , or even death
. therefore , many scholars dispute whether patients with ischemic mvr must be treated with concomitant mitral valve surgery .
ischemic mvr leads to left ventricular volume overload , resulting in left ventricular remodeling that aggravates mvr .
therefore , mvrr surgery can reduce left ventricular volume overload by reducing the mitral valve flow , which is also beneficial in left ventricular remodeling .
we found that after the surgery , the degree of residual mvr in patients treated with both cabg and mvrr was lower than that in patients treated with only cabg .
the combinatorial technique of cabg and mvrr was also better than that of only cabg , regardless of the mean of lvesv , lvef , or nyha classes .
these results had been confirmed by most studies , and they were also suitable for patients with end - stage cardiomyopathy . except for the gangemi study ,
no improvement was reported in the heart function of patients treated with mvrr surgery , perhaps because preoperative left ventricular function had been overestimated in these studies .
several studies reported that the prognosis of patients improved when they were treated with both cabg and mvrr surgeries . in a case - controlled study ,
the long - term survival rates in 58 patients with moderate mvr were similar to the 58 case - matched patients without mvr .
several studies , including a multicenter randomized trial by deja et al . , have reported that mv repair can significantly improve the survival rate of patients as compared to only cabg [ 2632 ] .
the risk associated with surgical and postoperative mortality does not increase in patients treated with combinatorial techniques of cabg and mvrr surgeries , although the operation time increases as compared to patients treated with only cabg .
however , in guiding clinical management of ischemic mvr , the results of our meta - analyses have some limitations : most studies were carried out on a small number of patients , so the sample size is small in most studies
. furthermore , outdated studies do not include current ischemic mvr assessment techniques adequately , increasing perioperative surgical risk .
the comparison of different groups could not fully summarize the total range of treatment modalities , including cabg with or without mvrr [ 2630 ] . according to our meta - analysis ,
compared to patients treated with only cabg , long - term survival rates were lower in patients treated with both cabg and mvrr .
several studies , including a 2009 meta - analysis , have reported that there is no enhancement in the survival rates of patients with ischemic mvr when they are treated with both cabg and mvrr [ 914 ] .
ischemic mvr occurs because of left ventricular ( lv ) remodeling and dilatation after myocardial infarction , which tethers and pulls the mitral valve apart ; the mitral valve is normal in structure but is incompetent as a result of a dilated and dysfunctional left ventricle .
therefore , ischemic mvr can be corrected with only cabg ; this surgical intervention can successfully restore coronary flow .
therefore , the survival rate of patients treated with only cabg might be higher than those treated by both cabg and mvrr techniques .
the search method was very limited and failed to include all the published literature , including published papers of organizations and conferences .
we only reviewed manuscripts that were published in english , so papers published in other languages were not included .
therefore , we may have missed out some important findings of research studies published in other languages .
the keyword search included ischemic mitral valve regurgitation , functional mitral valve regurgitation , ischemic mitral valve insufficiency and mitral valve repair , mitral valve annuloplasty , mitral valve replacement or mvs , and coronary bypass grafting or surgical revascularization .
although these keywords were consistent with other studies [ 3638 ] , we also included acute myocardial infarction or acute coronary syndrome .
therefore , our selected literature may not be same as the meta - analysis of 2009 . thus , different studies were included and reviewed in our meta - analysis .
most patients with serious mvr were treated with both cabg and mvrr techniques , so there could be bias in selected population .
myocardial viability also plays an important role in the surgical management of ischemic mvr . after performing the cabg technique , the dysfunctional yet viable myocardium undergoes significant recovery .
we did not perform routine tests to determine the myocardial viability of patients . in the near future
the search method was very limited and failed to include all the published literature , including published papers of organizations and conferences .
we only reviewed manuscripts that were published in english , so papers published in other languages were not included .
therefore , we may have missed out some important findings of research studies published in other languages .
the keyword search included ischemic mitral valve regurgitation , functional mitral valve regurgitation , ischemic mitral valve insufficiency and mitral valve repair , mitral valve annuloplasty , mitral valve replacement or mvs , and coronary bypass grafting or surgical revascularization .
although these keywords were consistent with other studies [ 3638 ] , we also included acute myocardial infarction or acute coronary syndrome .
therefore , our selected literature may not be same as the meta - analysis of 2009 . thus , different studies were included and reviewed in our meta - analysis .
most patients with serious mvr were treated with both cabg and mvrr techniques , so there could be bias in selected population .
myocardial viability also plays an important role in the surgical management of ischemic mvr . after performing the cabg technique
we did not perform routine tests to determine the myocardial viability of patients . in the near future
the patients with acs complicated with ischemic mvr can achieve reduced mitral regurgitation and improved left ventricular function through either only cabg or both cabg and mvrr surgery .
there is still no evidence that the long - term survival rate of cabg combined with mvrr is superior to that of only cabg , while the hospital mortality and secondary outcomes were similar in both .
we expect that the new technology of mitral valve surgery can bring about some changes .
the optimal surgery plan still needs to be adjusted according to the individual situation of the patient . | pubmed |
the mose ( modelling eso sites ) project is a feasibility study whose principal goal is to prove the possibility to forecast all the most relevant classical atmospheric parameters for astronomical applications ( wind speed intensity and direction , temperature and relative humidity ) and the optical turbulence ( ot ) that means @xmath0 profiles with the integrated astroclimatic parameters derived from the @xmath0 ( i.e. seeing @xmath1 , isoplanatic angle @xmath2 and wavefront coherence time @xmath3 ) above the two european southern observatory ( eso ) sites of cerro paranal , the site of the very large telescope ( vlt ) and cerro armazones , the site of the european extremely large telescope ( e - elt ) . the ultimate goal of the project is to investigate the possibility to implement an automatic and operational system for the forecast of these parameters at the vlt and at the e - elt . in this paper
we will treat the optical turbulence that , as will see later on , is the most difficult but also the most challenging parameter to be forecasted among those we treated . in previous papers related to the mose project we treated the abilities of the model in reconstructing wind speed and direction , temperature and relative humidity all along the atmosphere ( @xmath5 20 km i.e. vertical stratification of the atmospheric parameters ) @xcite and in reconstructing the same atmospheric parameters close to the surface @xcite . in all cases results indicated excellent model performances . in this paper
we will focus our attention on results we obtained on the analysis of the model performances in reconstructing the optical turbulence i.e. the astroclimatic parameters ( @xmath0 profiles , the seeing @xmath1 , the isoplanatic angle @xmath2 and the wavefront coherence time @xmath3 ) that are commonly used to optimized the observations supported by the adaptive optics ( ao ) .
this paper completes therefore the whole feasibility study carried out for eso .
the forecast of the optical turbulence is crucial for the success of the new generation telescopes .
we refer the reader to the introduction of @xcite for a detailed description of the scientific challenges related to the forecast of the optical turbulence .
we remind here the key elements .
the traditional scheduling of scientific program using as a criterion only the quality of the scientific program has , indeed , important drawbacks and limitations .
it has been widely accepted by the astronomical community that we had to take into account simultaneously the quality of the scientific program but also the status of the optical turbulence to optimize the use of the telescope otherwise we risk that the most challenging scientific programs are not carried out and the most important potentials of telescopes and instrumentation are not exploited as they could .
the forecast of the ot is therefore extremely important to schedule the scientific programs , to select the typology of instruments to be used at a specific time of the night and to optimize the adaptive optics ( ao ) systems performances .
the ao techniques can be very powerful , at present , in correcting the perturbations induced by the optical turbulence on the wavefronts but the ao performances are strongly dependent on the status of the optical turbulence and , under particular conditions , they can hardly run or they can even not run at all . more in general
the forecast of the optical turbulence is crucial for the service mode i.e. the observation mode of all the top - class facilities of present time and it will be the observing mode of all new generation facilities .
it is the observing strategy that will maximize the possibility to achieve outstanding scientific goals with the elts .
the service mode implies the knowledge in advance of the status of the atmosphere ( atmospheric parameters and optical turbulence ) and the rank of the scientific programs .
forecast _ of these parameters plays therefore a crucial role in the context of the high - angular resolution ground - based astronomy .
besides , we have not to forget that the cost of a night of observations is of the order of a hundred thousand us dollars and it is therefore immediate to understand that the forecasts plays a crucial role not only in scientific but also in economical terms .
the forecast we are dealing about aims to provide information in advance on a time scale @xmath6 t that is not inferior to 20 minutes .
this is the typical time required to a beam to be shifted from an instrument to another in a configuration of permanents instruments placed in different focal stations .
this is the configuration planned for new generation telescopes .
our approach implies the use of atmospheric non - hydrostatic mesoscale models , more precisely a model called meso - nh @xcite for the atmospheric parameters joint with a dedicated code developed for the optical turbulence @xcite . for simplicity
we call this model astro - meso - nh model .
we refer the reader to the introduction of @xcite to know why mesoscale models are necessary instead of other typologies of models ( general circulation models ( gcm ) , direct numerical simulations ( dns ) , large eddy simulations ( les ) ) .
mesoscale model are applied on limited areas of the earth .
there are different typologies of mesoscale models depending on the typical extension of the limited area and the horizontal resolution used .
we used here limited areas having a size between 800 and 10 kilometers square and a subkilometric horizontal resolution in the innermost domain in the neighboring of the site of interest . the optical turbulence ( ot )
is completely parameterized in the mesoscale models .
these characteristics guarantee to the astro - meso - nh model to reconstruct the ot maintaining the link with the spatio - temporal evolution of the atmospheric flow external to the limited areas i.e. to realize a real forecast of the ot .
the astro - meso - nh model has been applied in the last decades to many among the most important astronomical sites such as cerro paranal in chile @xcite , san pedro mrtir in mexico ( @xcite ) , roque de los muchachos in canaries islands @xcite , mt . graham in arizona @xcite , dome c in antarctica ( @xcite ) . for completeness
we remind that other studies concerning the ot forecast on the whole atmosphere have been carried out using other mesoscale or general circulation models and similar ( or different ) approaches in the astronomical context ( @xcite ) .
we highlight three important considerations : * ( 1 ) * the paper contains necessarily only a selection of the most relevant results obtained for the ot related to an extended study lasted a few years ( and completed recently ) that provided a clear indication of the good efficiency of the astro - meso - nh model for an application to the service mode .
these convincing results have induced eso to propose us to implement a demonstrator for an automatic operational version of the astro - meso - nh model applied to the sites of the vlt and the e - elt .
this project will start in the next months . even if the research on the ot forecast is in a continuum evolution ( as well as that of the weather forecast ) and there is always space for improvements , in this feasibility study we achieved important steps ahead in terms of estimation of the model performances . due to the fact that we are entering in the new phase of the operational demonstration and more and more observatories are
interested on such a kind of application it is important to provide the state of the art of the performances of our system . *
( 2 ) * thanks to the development of our most recent algorithm of the @xmath0 we could prove to be able to achieve a vertical resolution of the @xmath0 all along the whole atmosphere up to roughly 150 m. this is a crucial achievement that opens interesting new perspectives for the most sophisticated adaptive optics systems i.e. the wide field adaptive optics ( wfao ) such as the ground layer adaptive optics ( glao ) @xcite , multi conjugated adaptive optics ( mcao ) ( @xcite ) , laser tomography adaptive optics ( ltao ) @xcite and multi objects adaptive optics ( moao ) @xcite . *
( 3 ) * as expected , the model performances in forecasting the optical turbulence are not as good as in forecasting the atmospheric parameters ( at least so far ) .
this is due to the fact that the spatio - temporal scales on which the ot fluctuates are much smaller than the grid - size and also to the fact that the turbulence is a stochastic quantity .
this means that it is more difficult to describe numerically the optical turbulence .
however , in spite of these intrinsic difficulties , we will see that results we achieved are very impressive and , even more important , are objectively already of great support for the service mode .
the plan of the paper is the following : in section [ obs ] we will describe the observations that we used as a reference to calibrate and to validate the model . in section [ astro - meso - nh ] we will described the model configuration used for this study . in section [ method ] we will describe the strategy used to calibrate and validate the model and in section [ results ] we will show the results obtained . in section [ cn2_hvr ]
we show the model performances in reconstructing @xmath0 profiles with very high vertical resolution . in section [ concl ]
we will present the conclusions and perspectives of this study .
measurements provided by different instruments have been used to carry out this study . considering the scarcity of ot measurements related to cerro armazones , in agreement with eso
the study on the optical turbulence has been performed only above cerro paranal .
an important preliminary analysis having the goal to assure and test the reliability of the measurements has been performed with part of the instruments of the par2007 site testing campaign @xcite useful in our context : ( 1 ) a generalized - scidar ( more precisely the cute - scidar iii ) developed by the istituto de astrofisica de canarias ( iac ) team @xcite and corrected by @xcite to eliminate the error induced by the normalization of the autocorrelation of the scintillation maps by the autocorrelation of the mean pupil ( problem identified by @xcite and @xcite ) , ( 2 ) a multi - aperture scintillation sensor ( mass ) developed by the kornilov & tokovinin team @xcite and ( 3 ) a differential image motion monitor ( dimm ) an instrument that since 1988 is running at cerro paranal to monitor the seeing i.e. the integration of the optical turbulence developed all along the whole atmosphere @xcite .
we had simultaneous gs and dimm measurements related to 20 nights .
mass measurements were simultaneous to gs on a sub - sample of 14 nights .
we note that the three instruments are located at basically the same height ( gs at 5 m above ground level ( a.g.l ) , dimm and mass at 6 m a.g.l . ) .
moreover the vlt is basically a plateau and this guarantees a fair comparison between measurements .
the re - calibration of the gs measurements was fundamental to assure us a reliable reference .
as we will see later on , we decided to use the gs as a reference for the calibration of the astro - meso - nh model .
besides , a detailed analysis of comparisons of measurements from the gs , mass and dimm @xcite permitted us to conclude that the mass could not be taken as a reference because of three main problems : * ( 1 ) * it underestimates the integrated turbulence ( j or seeing ) in the free atmosphere with respect to the gs with a relative error of -32@xmath7 in terms of the seeing ( -48@xmath7 in terms of j ) ; * ( 2 ) * we found important discrepancies between mass and gs in all the individual layers ( reaching relative errors as high as -65% in terms of seeing and -82% in terms of j ) with exception of the layers located at 2 and 16 km ( layers 3 and 6 ) in which the relative error remains limited to + 18% in terms of seeing ( + 20% in terms of j ) .
a previous study on a similar topic @xcite ( even if it was applied on a poorer statistical sample ) found relative errors on individual layers as large as those we found in @xcite ; * ( 3 ) * the particular weighting functions ( wfs ) of the mass , having a triangle shape , do not permit to identify precisely the height of the boundary layer and in general the height separating a layer from the contiguous one .
this represents an important limitation for the calibration of the astro - meso - nh model .
thanks to dimm measurements ( a third independent instrument during the par2007 campaign together with gs and mass ) we could prove that the problem causing the discrepancies between gs and mass came from the mass .
we cite here just the elements useful to justify why mass measurements could not be used to calibrate the astro - meso - nh model .
an accurate estimate of the @xmath0 is indeed important for the model calibration and , because of the reasons we have just discussed , the mass could not assure that .
besides , we remind that @xcite proved that the isoplanatic angle @xmath2 coming from the mass is reliable ( mainly thanks to the good reliability of the ot estimate in layer 6 located at 16 km above the ground ) and the @xmath3 measurements are reliable too ( just a few warnings with respect to this parameter - see the cited paper ) .
this information is useful for the analysis done in this paper . with these elements in mind we concluded we could use mass measurements of @xmath2 and @xmath3 to validate the model with respect to these parameters ( see section [ cal_val ] ) .
mass is , indeed , an instrument currently running above cerro paranal at vlt observatory .
after the model calibration , we could therefore validate the model with a more extended sample of nights not belonging to the par2007 campaign .
.astro - meso - nh model grid - nesting configuration for the ot simulation . in the second column
the number of horizontal grid - points , in the third column the domain extension and in the fourth column the horizontal resolution @xmath6x . [ cols="^,^,^,^ " , ] | arxiv |
Hubbard model with magnetic field
The Hamiltonian for a 1D Hubbard model reads
$$H= -t \sum\_i c\_i^\dagger c\_{i+1} + c\_{i+1}^\dagger c\_{i} + U\sum\_i n\_{i\uparrow}n\_{i\downarrow}.$$
The two parameters $t$ and $U$ for the hopping and onsite interaction are usually both assumed to be of the order of electron Volts. If one wants to introduce an external magnetic field, a Zeeman coupling term is introduced:
$$H= -t \sum\_i c\_i^\dagger c\_{i+1} + c\_{i+1}^\dagger c\_{i} + U\sum\_i n\_{i\uparrow}n\_{i\downarrow} + h\_B \sum\_i (n\_{i\uparrow} - n\_{i\downarrow})$$
If this term should have any significance, the parameter $h\_B$ should be of the same order of magnitude as $t$ and $U$, so also in the eV range.
Well, the Zeeman coupling term in SI units usually reads (see e.g. [here](https://books.google.de/books?id=Dm31BwAAQBAJ&lpg=PA127&ots=ilVZr3tOeV&dq=zeeman%20term%20hubbard&hl=de&pg=PA127#v=onepage&q=zeeman%20term%20hubbard&f=false))
$$H\_{Z}= g\_s \mu\_B\; B \; \hat{s}\_z = \frac{1}{2} g\_s \mu\_B\; B \; (\hat{n}\_\uparrow - n\_\downarrow)$$
With $\mu\_B$ the Bohr magneton. One can then identify $h\_B \hat{=} \frac{1}{2} g\_s \mu\_B\; B = \mu\_B\; B$ (because $g\_s=2$).
If now $h\_B=1$eV, then $B$ would have to be of the order of $20000$T! That appears to be completely unreasonable.
Where did I make my mistake?
You presume that the order of magnitude of a relevant magnetic field should be the same as the order of magnitude of the other parameters. That intuition is correct if there is only one parameter in play, e.g. if $U$ is very small. Indeed let's take $U=0$ such that we have a free fermion hopping problem. At half-filling, we have two (disconnected) half-filled bands (one for spin up, the other for spin down). If we now start adding a small magnetic field, it indeed won't do too much: it will only slightly favor spins along the magnetic field. To really cause a phase transition, i.e. to polarize our spins, we need to make the magnetic field of the order of the band width (which completely forces one of the two bands to be full, the other empty). So in that case if $t$ is of the order eV, then so must the magnetic field be, which corresponds to a ridiculously large magnetic field as you point out.
But interactions change everything! Indeed, it's well-known that for large $U$ and at half-filling, our effective Hamiltonian becomes the Heisenberg antiferromagnet $H = \frac{4t^2}{U} \sum \mathbf{S}\_i \mathbf \cdot \mathbf{S}\_{i+1}$. To fully polarize this system, we need to only apply a magnetic field of the order of $\sim \frac{t^2}{U}$ (more precisely and generally, the critical magnetic field at half-filling is $2\left( \sqrt{t^2+U^2} - U \right)$, ref: page 198 of [The one-dimensional Hubbard Model](http://max2.physics.sunysb.edu/~korepin/Hubbard.pdf)).
Still, despite $\frac{t^2}{U}$ being a smaller quantity, it typically still corresponds to quite large magnetic fields. Even if we take the rather weak $t = .5$ eV and strong $ U = 10$ eV, we would need a magnetic field corresponding to $0.025$ eV, or $\sim 500$ Tesla! So part of the answer is: you're right, the magnetic fields needed to cause a phase transition are quite big (at least at half filling, it goes down quite a bit at lower filling, again see the above reference). Note though: that is to actually get a phase transition, this of course implies you can already start seeing appreciable effects with lower fields.
| stackexchange/physics |
condensed - matter and particle physics are cross - fertilizing fields . for instance
, exclusion of magnetic flux from a superconductor was interpreted by anderson as generation of mass for a gauge boson.@xcite popularized in particle physics by higgs,@xcite this effect plays a central role in the electroweak theory . in the other direction , statistical ( chern - simons ) gauge fields , a field - theorist s toy , facilitate better understanding of the quantum hall effect.@xcite a closely related phenomenon , parity anomaly in @xmath0-dimensional electrodynamics , still awaits its experimental discovery in condensed matter . in a nutshell ,
the effect is rather simple .
two - component dirac fermions with a mass @xmath1 react in a peculiar way to an external magnetic field @xmath2 .
the symmetry between occupied ( fermi - sea ) and empty fermion states is violated and a nonzero fermion density appears in the vacuum state . the density of fermions each carrying charge @xmath3is such that the average flux per particle is @xmath4 : @xmath5 by relativistic invariance , application of an electric field in the plane induces a hall current with quantized conductivity : @xmath6 both the induction of charge by magnetic field ( [ cs-0 ] ) and the appearance of a chern - simons current ( [ cs-1 ] ) violate the symmetries of parity and time reversal , hence the name `` parity anomaly '' . in certain materials ,
electrons behave as dirac fermions , albeit with a small `` speed of light '' , so it seems natural to look for the anomaly in condensed matter . on a deeper level
, there is a subtle problem , known as fermion doubling , which often prevents the anomaly .
for example , electron states in a sheet of graphite are well described at low energies as 2-component massless dirac fermions in 2 + 1 dimensions . because the unit cell contains 2 lattice sites , there are 2 fermion species living at inequivalent fermi points in the brillouin zone .
semenoff observed that a symmetry breaking mass term @xmath1 will be induced if the inequivalent sites are populated by different atoms .
unfortunately , the 2 species have mass terms of opposite signs.@xcite the total anomalous current ( [ cs-1 ] ) vanishes .
later , fradkin , dagotto and boyanovsky@xcite ( fdb ) suggested a possible way to circumvent the problem of fermion doubling .
lead chalcogenides pbte , pbse , and pbs are semiconductors with a narrow gap ( @xmath7@xmath8 ev ) between conduction and valence bands.@xcite low - energy fermion quasiparticles are concentrated around 4 inequivalent l points in the brillouin zone , @xmath9 and three others related by cubic symmetry .
the band structure near each l point is such that the quasiparticles resemble 4-component massive dirac fermions ( in 3 + 1 dimensions ) .
4 components result from 2 inequivalent sites in a unit cell and 2 possible projections of a spin @xmath10 .
fdb pointed out that a stack fault in a crystal creates a domain wall , on which one finds 2 + 1 dimensional massless dirac fermions . in this
setting , certain perturbations can induce a mass term of _ the same _ sign in all 4 fermion species . the anomalous current ( [ cs-1 ] )
does not have to vanish . in a more detailed paper,@xcite fdb suggested that a symmetry - breaking mass term @xmath1 can be induced by a peierls distortion , which is present in some lead chalcogenides.@xcite that does not sound right : a peierls distortion violates parity but leaves time reversal intact , therefore it can not possibly induce a chern - simons current ( [ cs-1 ] ) .
haldane has argued that this incarnation of parity anomaly is caused by an unphysical lattice hamiltonian used by fdb , which is ( or seems to be ) odd under time reversal.@xcite upon further reflection , this argument does not work : if a continuum limit derives from a model with lattice potential and spin - orbit interaction , it can not violate the time - reversal symmetry .
then why does the fdb hamiltonian couple spin and linear momentum via the term @xmath11 that seems to break @xmath12 ?
the answer : the @xmath13 matrices here are _ not _ the electron spin variables .
symmetry under time reversal need not be broken .
the existence of the anomalous chern - simons current is then questionable .
being field theorists , fdb did nt bother to derive their hamiltonian ( nor its continuum version ) from any physical model of electrons in a lattice potential and with the spin - orbit interaction .
their phenomenological hamiltonian was merely tailored to correctly reproduce the energy spectrum of the conduction and valence bands near the fermi level .
therefore the @xmath13 matrices in it have nothing to do with the actual electron spin . but without knowing which physical variables the @xmath13 matrices represent , one can not learn how this or that physical perturbation ( e.g. , a peierls distortion ) couples to the fermion zero modes .
then it is impossible to determine correctly the sign of charge or the direction of hall current induced by a symmetry - breaking perturbation . to clear up the matter ,
i have derived a correct continuum approximation for low - lying electron states both by appealing to symmetry arguments ( the easy way ) and by using the standard @xmath14 method combined with a tight - binding approximation@xcite ( see appendix ) .
i have studied the behavior of massless fermions bound to a domain wall and enumerated _ all _ symmetry - breaking perturbations that raise or lower the zero modes in magnetic field , thus inducing surface charge ( [ cs-0 ] ) .
the results of this study are unambiguous .
already from eq .
[ cs-0 ] it is clear that @xmath1 should be odd under both parity and time reversal ( a pseudoscalar ) . a peierls distortion therefore will not work because @xmath15 is a genuine scalar ( @xmath16 is the vector of atomic displacement and @xmath17 is the normal to the domain wall ) . on the other hand , certain kinds of magnetic order may induce an anomalous hall current .
the fdb hamiltonian ( in the continuum limit ) can be derived from a tight - binding model of noninteracting electrons that includes electron kinetic energy , periodic lattice potential , and spin - orbit interaction:@xcite @xmath18\cdot { \bf p}}{4m^2c^2}.\ ] ] this hamiltonian is invariant under parity and time reversal .
the triplet of pauli matrices @xmath19 denotes the spin operators . introduce operators of isospin @xmath20 to describe the two sublattices in the rocksalt structure .
eigenvalues @xmath21 correspond to lead and chalcogen sites . near each of the four l points ,
lowest - energy states have a 4-component wavefunction ( 2 spin components @xmath22 2 sublattices ) and resemble dirac fermions . by symmetry arguments alone , one can anticipate the correct form of the hamiltonian in the continuum limit .
define the operations of parity and time reversal as @xmath23 the minus sign accounts for odd parity of @xmath24 orbitals .
near an l point in the brillouin zone , e.g. , @xmath25 , the one - particle hamiltonian of a dirac fermion is limited to the following @xmath26 and @xmath12-invariant terms : @xmath27 \cdot \nabla ) + \tau_3 mv^2 . \label{dirac3
+ 1}\ ] ] here @xmath28 is odd under both parity and time reversal ( directions @xmath29 and @xmath30 describe the same l point ) ; @xmath31 is the relative strength of the spin - orbit interaction , and @xmath32 is a fermion velocity . for simplicity ,
i set @xmath33 , which gives a spherically symmetric energy spectrum near the l points .
the same form of @xmath34 is obtained from a tight - binding model , see appendix [ appendix ] .
the low - energy hamiltonian thus has a dirac form @xmath35 .
the standard dirac matrices have the following representation : @xmath36 , & \beta = \gamma^0 = \tau_3 , \\
-i\vec{\gamma } = -i\beta\vec{\alpha } = \tau_2 \hat{\bf p } - \tau_1 [ \vec\sigma \times \hat{\bf p } ] , & \gamma^5 = -\tau_1(\vec\sigma\!\cdot\!\hat{\bf p } ) , \\ \vec\sigma = -\gamma^5\vec\alpha = ( \vec\sigma\!\cdot\!\hat{\bf p})\hat{\bf p } + \tau_3\ ,
\hat{\bf p}\!\times\![\vec\sigma\!\times\!\hat{\bf p } ] , & i\gamma^0\gamma^5 = \tau_2(\vec\sigma\!\cdot\!\hat{\bf p } ) \end{array}\ ] ]
consider a stack fault ( pb @xmath37 te ) in a plane perpendicular to a unit vector @xmath17 .
then @xmath38 is a function of @xmath39 .
more specifically , the normal to the domain wall @xmath17 points in the direction of increasing @xmath38 : @xmath40 energy eigenstates bound to the domain wall can be written in the form @xmath41 , where @xmath42 $ ] are coordinates within the plane .
the scalar @xmath43 and bispinor @xmath44 satisfy the following equations:@xcite @xmath45 the first two equations ( [ eqn - x - par][gamma - n - eigen ] ) indicate that these states are fermion zero modes in the direction perpendicular to the wall.@xcite the last two ( [ gamma - n - eigen]-[eqn - x - perp ] ) describe 2-component massless fermions in 2 + 1 dimensions with the hamiltonian @xmath46 application of magnetic field @xmath47 perpendicular to the domain wall results in a spectrum with landau levels:@xcite @xmath48 the energy spectrum is symmetric with respect to charge conjugation : @xmath49 zero modes ( @xmath50 ) are eigenstates of the `` spin '' component @xmath51 with the eigenvalue @xmath52 .
all landau levels have orbital degeneracy @xmath53 per unit area . in a half - filled system ( no dopants ) , the zero modes are exactly at the fermi level and thus have occupation numbers @xmath10 .
the energy spectrum is particle - hole symmetric and the domain wall is not charged .
an arbitrarily small perturbation can shift the zero modes above or below the chemical potential ( assuming it stays pinned at 0 ) . with
the particle - hole symmetry broken , the domain wall gets charged : each zero mode contributes charge @xmath54 ( empty ) or @xmath55 ( filled ) to the domain wall ( @xmath56).@xcite although a condensed - matter system lacks the true relativistic invariance and quantization of hall conductivity ( [ cs-1 ] ) does not follow automatically from eq .
[ cs-0 ] , there is a thermodynamic identity that establishes this relation:@xcite @xmath57 with the derivative taken at a constant chemical potential .
this result is valid in the absence of low - energy excitations .
imagine now that a uniform perturbation @xmath58 ( such as a peierls distortion or the actual zeeman term ) is applied to fermions on the domain wall . in the presence of the landau gap ,
the shift of the zero modes can be computed to first order in @xmath58 using the standard perturbation theory . because there is no spin or isospin degeneracy and @xmath58 is uniform , @xmath59 .
recall that @xmath60 is an eigenstate of 3 commuting matrices : @xmath61 ( the third matrix @xmath62 is simply the product of the first two . ) to compute @xmath63 , one can write @xmath58 as a superposition of 15 traceless hermitian @xmath64 matrices @xmath65 @xmath66 because operators @xmath67 either commute or anticommute with one another , only 3 of them ( [ sigma - n][gamma-05 ] ) need to be included in the sum : if some @xmath68 anticommutes with one of them , its expectation value in the state @xmath60 vanishes . thus operators ( [ sigma - n][gamma-05 ] ) exhaust all the handles through which external perturbations can tickle the zero modes and possibly induce charge on a domain wall .
such a perturbation will contain @xmath69 , @xmath70 , or @xmath71 .
the symmetry breaking term @xmath72 is a pseudovector , @xmath73 is a vector , and @xmath74 is a pseudoscalar .
the area density of charge induced by them on a domain wall ( for a single fermion species ) is @xmath75 it is now evident that a vector perturbation @xmath76 , such as a peierls distortion , can not induce a chern - simons current : the sign of induced charge is not sensitive to the direction of magnetic field . by the thermodynamic identity ( [ cs-1 cm ] ) , there will be a normal hall effect with current reversing the direction when magnetic field does .
one obviously needs a pseudoscalar perturbation ( odd under both @xmath26 and @xmath12 ) in order to relate a scalar ( charge ) to the pseudoscalar @xmath77 .
this is why a pseudoscalar @xmath74 will work ( and a vector @xmath76 will not ) .
alternatively , one can use a pseudovector @xmath72 ( e.g. , staggered field of an antiferromagnetic order parameter ) to construct a pseudoscalar @xmath78 . to corroborate these general considerations ,
i discuss in some detail several symmetry - breaking terms that might exist in a physical system .
we need to add to the @xmath79 dimensional dirac hamiltonian ( [ dirac3 + 1 ] ) a term that breaks @xmath26 but not @xmath12 and does not affect electron spin .
such a term is @xmath80 ( both @xmath81 and @xmath29 are @xmath12-odd ) .
the vector @xmath16 characterizes the direction and length of the peierls distortion .
it couples to the operator @xmath82 ( [ gamma - n ] ) . with the aid of eq .
[ 15terms ] , @xmath83 the charge density is _ unchanged _ when magnetic field is reversed @xmath84 . by extension ( [ cs-1 cm ] ) , the hall conductivity is sensitive to the direction of @xmath85 . for a wall perpendicular to @xmath16 , summation over the four l points gives @xmath86 this describes a perfectly normal hall current , not a chern - simons current ( [ cs-1 ] ) .
no parity anomaly here .
consider zeeman interaction @xmath87 induced by uniform magnetic field @xmath85 perpendicular to the domain wall .
@xmath88 at a constant chemical potential , @xmath89 again , a normal hall effect results : @xmath90 in a system with antiferromagnetic order , one expects staggered magnetic field @xmath91 to induce a zeeman term @xmath92 .
it couples to the same operator of dirac `` spin '' ( [ sigma - n ] ) : @xmath93 \!\cdot\!\hat{\bf
\label{zeeman - staggered}\ ] ] in the simple case with @xmath94 , @xmath95 and @xmath96 the hall current depends on the direction of the staggered field @xmath97 and not of the uniform field @xmath85 .
one can call this a parity anomaly , but clearly there is no magic involved : this is a hall effect caused by the staggered magnetic field .
finally , one can imagine coupling directly to the third conserved quantity ( [ gamma-05 ] ) .
the only perturbation that will do is @xmath98 the sign of induced charge depends on the direction of magnetic field : @xmath99 hall conductivity is insensitive to the sign of @xmath2 : @xmath100 this term definitely generates a chern - simons current .
i must admit though that i do not understand what perturbation could cause it .
i have presented a critique of the parity anomaly ( eqs .
[ cs-0 ] and [ cs-1 ] ) suggested for @xmath101 dimensional fermions in a narrow - gap semiconductor.@xcite both symmetry considerations and a correct continuum treatment of the model indicate that a parity anomaly requires a pseudoscalar ( @xmath26 and @xmath12-odd ) or pseudovector ( @xmath26-even and @xmath12-odd ) symmetry - breaking term .
therefore , a peierls distortion , which is a vector ( @xmath26-odd and @xmath12-even ) , can not generate a parity anomaly , contrary to the suggestion of fdb .
antiferromagnetic order , which violates the time - reversal symmetry , could lead to an observable chern - simons current in the system .
unfortunately , the prospects of observing such an effect are rather dim : not only would this require antiferromagnetism , but also the nel order parameter must be ( anti)parallel to the applied magnetic field . in a heisenberg antiferromagnet , @xmath102 stays orthogonal to @xmath85 , in which case the entire effect vanishes . in hindsight , this foray into the dreamworld of field theory is a reminder to a condensed - matter physicist : trust your intuition .
anomalous hall current of dirac fermions , whether directly in @xmath103 dimensions or on a domain wall in @xmath104 , is always caused by magnetic order present in the system.@xcite
i thank n. nagaosa , l. p. pryadko and f. wilczek for helpful discussions and b. jank for hospitality during my stay at argonne .
research was supported by doe grant no .
de - fg02 - 90er40542 and doe office of science under contract no .
w-31 - 109-eng-38 .
lead and a chalcogen have 2 and 4 electrons in their 3 external @xmath24 orbitals ( @xmath105 orbitals give deeply lying bands , which can be ignored ) .
the @xmath24 bands are thus half filled .
the one - particle hamiltonian including lattice potential and spin - orbit interaction is @xmath106\cdot(-i\nabla)}{4m^2c^2}. \label{h - full}\ ] ] omitting spin for clarity , one can write an energy eigenfunction in the bloch form @xmath107 here @xmath108 labels unit cells in the rocksalt lattice , @xmath109 are the coordinates of site @xmath110 within a unit cell and @xmath111 is the wavefunction of the @xmath112-th orbital on sublattice @xmath110
. we are to find the bloch coefficients @xmath113 . with spin
included , @xmath114 is a 12-component wave function .
it follows from symmetry considerations alone@xcite that the two sublattices ( lead and chalcogen sites ) are decoupled at the l points , such as @xmath115 . in this case
, the hamiltonian takes on a simple form@xcite @xmath116 where the first term comes from the overlap of different @xmath24 orbitals ( between second neighbors ) and the second , from the spin - orbit interaction .
the eigenstates of the hamiltonian ( [ h0 ] ) are kramers doublets with @xmath117 or @xmath118 . according to volkov _
et al._,@xcite the spin - orbit coupling is the weakest perturbation and the two bands around the fermi level are derived from states with @xmath119 . in this approximation,@xcite the eigenstates are @xmath120 in the basis of @xmath121 orbitals . to calculate the matrix elements of the hamiltonian near an l point , at lattice momentum @xmath122 , i use the standard `` @xmath14 ''
method.@xcite instead of shifting momentum away from a symmetry point @xmath123 in the wavefunctions ( [ psi ] ) , one transforms the hamiltonian @xmath124 the matrix elements of the second term `` @xmath125 '' are then evaluated in the hilbert space of the two kramers doublets closest to the fermi level at the l point .
this is a good approximation for small @xmath126 , provided that other states lie at energies much larger than the gap @xmath127 . in the tight - binding limit ,
overlap of @xmath128 orbitals on different sublattices occurs along the @xmath129 direction only . in the case of @xmath128 orbitals at momentum @xmath130 ( fig .
[ fig - px ] ) , operators @xmath131 and @xmath132 have the following nonzero matrix elements : @xmath133 where @xmath134 and @xmath135 are some real constants . in the basis of states
@xmath136 , @xmath137 , the resulting @xmath138 term reads @xmath139 near the l point @xmath25 .
the operators of isospin @xmath140 act according to @xmath141 matrix elements of the complete hamiltonian between the states ( [ jz - states ] ) are : @xmath142 & \nonumber \\ & + \frac{1}{2}(e_{\rm pb } - e_{\rm te } ) \tau_3.&\end{aligned}\ ] ] this yields the anticipated continuum result ( [ dirac3 + 1 ] ) @xmath143})\ , \tau_2 + mv^2\ , \tau_3,\ ] ] where @xmath29 is the unit vector in the direction of the l point @xmath25 .
an identical result is obtained for the 3 other l points , which differ by the direction @xmath29 . on a final note ,
the unit vector @xmath28 is odd under parity and time reversal defined in eq .
it can be made even by redefining them as @xmath144 this is the familiar standard representation of parity and time reversal in relativistic field theory.@xcite the form of the hamiltonian in the continuum limit ( [ dirac3 + 1 ] ) is strongly constrained by symmetry requirements .
it is therefore not sensitive to the approximation made here .
i have checked that the same result holds in the opposite limit , when the spin - orbit coupling in eq .
[ h0 ] dominates .
then @xmath146 is the total angular momentum of an electron . | arxiv |
Warren Harding 18651923 was the 29th President of the United States.
Warren Harding may also refer to:
Warren G. Harding Texas politician 19212005
Warren G. Harding High School
Warren Harding High School
Warren Harding climber 19242002 | wikipedia |
Bishop's House is a heritage-listed villa at 73 Margaret Street, East Toowoomba, Toowoomba, Toowoomba Region, Queensland, Australia. It was designed by Henry Marks and built from 1910 to and from 1939 to . It is also known as Dalmally and Kilallah. It was added to the Queensland Heritage Register on 21 October 1992.
History
Bishop's House, designed by Henry Marks, was constructed in 1911 as the home of Toowoomba businessman, William Charles Peak. In 1939 the house was purchased by the Roman Catholic Church and became home to the Bishop of the recently created Toowoomba Diocese.
Settlement of what was to become the Toowoomba area commenced at Drayton, now a suburb of Toowoomba, in the early 1840s. Thomas Alford opened a general store in the area in 1843. In the same year, residents of Drayton petitioned the Governor to form a township. A survey of the town was prepared in 1849. In laying out Drayton, Government Surveyor James Charles Burnett was instructed to mark out suburban allotments for Garden and Agricultural purposes. The ideal site for what was known as the Drayton Swamp Agricultural Reserve, later to become Toowoomba, was an area approximately three to four miles northeast of Drayton where two swampy creeks joined to form the headwaters of Gowrie Creek. The Agricultural Reserve included 12 allotments bounded by the left bank of the west swamp, and the present Bridge, West and Stephen streets.
Six of the 12 Swamp allotments were first offered at auction in November 1849, however some were not sold until 1853. By late 1857, the name Toowoomba had gradually taken over from The Swamp, as the town continued to expand. At the time of its incorporation into a municipality in November 1860, Toowoomba had well outgrown Drayton. Toowoomba continued to develop as the service centre for the upper Darling Downs. It became the urban home of many pastoralists and businessman during the early twentieth century.
One of the many people who constructed houses during this period of expansion was William Charles Peak, born in Drayton in 1867 as the eldest son of a local councillor WJ Peak. In 1881 William Peak entered the company of Wilcox Bros, general merchants of Toowoomba and within fifteen years was the owner. He took an interest in the development of Toowoomba and held many positions in local industry and development including President of the local Chamber of Commerce 191415; Chairman of the Toowoomba Permanent Society; as well as being the instigator of the Greenmount Dairy Factory Co Ltd, who established one of the first cheese factories in the state. He was involved with the foundation of the Anderson Malting Company, the Darling Downs Building Society; the Toowoomba Steam Laundry and the Security Trust Company. Peak's other local involvements included the Royal Agricultural Society; the local Cricket Union and the Traders' Association. Today, two memorials to Peak are found in Toowoomba, one at the Toowoomba showground and another in Queen's Park where a drinking fountain is named in his honour.
In about 1910 as a reflection of his importance in the local community, WC Peak commissioned local architect Henry J Marks to design a house, initially known as Kilallah, for the Peak family at the corner of Lindsay and Margaret Streets, Toowoomba, adjacent to Queen's Park.
Henry Marks was a member of a prominent Toowoomba architectural family. James Marks, Henry's father, arrived in Queensland from England in 1866 and practised as an architect and builder in Dalby before starting his successful family practice in Toowoomba in the 1870s which remained active until 1962. Henry joined his father in practice in 1892 when the business became known as James Marks and Son.
Henry Marks was an innovative and creative architect, who invented and patented several products including pot-bellied ventilation flues and chimney shafts, windows and a walling system. He employed his inventions on many of his buildings and this helps to identify the buildings for which he was responsible. Several of these innovations are found at Kilallah, now known as the Bishop's House, including window openings and chimney stacks. Marks designed windows which allowed maximum opening capacity and also directed airflow around the opening. The windows designed for the end bays of the Bishop's House were extendable casements. Also on the house were several of Marks' patented design for Improved Chimney Top and Ventilator introducing a rounded base to the shaft of the chimney top directing air flow and with a V-shaped catchment plate and run-off for rainwater.
The planning of the Bishop's House reflects Marks' concern with air flow and natural lighting; a large ventilated roof light over the intersection of the entrance hall and the transverse corridor terminated at the east and west ends of the building with semi-open octagonal bays.
In her thesis on the Marks family architectural practice in Toowoomba, Morag Papi, describes the building as one of the best examples of Harry Mark's work. Certainly the sophistication of the detailing, the composition of the exterior and regard to environmental issues suggest that this is a well considered building. His other numerous Toowoomba buildings include the halls at both St Luke's and St James' Churches St James hall is known as the James Taylor Memorial Institute St Mary's Christian Brothers building; Holy Name Convent; buildings at the General Hospital; White Horse Hotel; Union Bank and City Chambers.
The Peak family remained at Kilallah for only a few years when the house was purchased by a Mr Horrigan who sold it to the Fletcher family. The house was then rented out to a number of people until its purchase by the Roman Catholic Church of Toowoomba as a Bishop's residence in 1939.
The Catholic Church was established in Toowoomba in the early 1860s when a pastor was appointed. Robert Dunne, later Archbishop of Brisbane, was appointed as a parish priest in Toowoomba in 1868. The Roman Catholic Church in Queensland developed with the population increases and by 1928 Archbishop James Duhig announced that two new dioceses, Toowoomba and Townsville were to be created, raising the number of diocese to four, alongside Brisbane and Rockhampton.
The first Bishop appointed to Toowoomba was James Byrne, born in Ireland in 1840 and educated at St Patrick's College, Thurles, County Tipperary. Byrne was ordained by the Archbishop of Cashel on 21 July 1896 and volunteered to work in the Archdiocese of Brisbane. After work in Brisbane for many years he was appointed Domestic Prelate in 1923 and then was appointed as the Bishop of Toowoomba in 1929. St Patrick's Church in Toowoomba, constructed in 1883-89 to a design by James Marks, was consecrated as a cathedral on 1 September 1929.
The residence originally used by James Byrne was the brick presbytery alongside St Patrick's Cathedral, constructed in 1927 for a parish priest before the archdiocese was formed, to a design by Jack Donoghue. This was deemed too small to house both the bishop, parish priests and administrators of the growing parish and therefore a dedicated residence for the bishop was found in Unara in 1939. Previously, Unara was the residence of Sir Littleton Groom, Member of the Australian House of Representatives for the Darling Downs and was leased from Lady Groom by the Diocese for one year with the option of purchase at the end of this time. However, because the location of Unara, near the eastern boundary of the Diocese, was considered inconvenient the purchase option was not exercised.
Instead the Diocese bought WC Peak's 1911 residence, then known as Dalmally, along with a timber house on property adjoining the main house on Lindsay Street. The house was called Dalmally by a lessee, Captain Serisier, in remembrance of a village in Scotland.
To facilitate the use of the house as a Bishop's residence extensive internal alterations and some external renovations were carried out to a design by local architects, Messrs Hodgen and Hodgen, a partnership of William Hodgen Jnr and his son. Hodgen was born in Toowoomba where he did an apprenticeship in the building trade before joining the Queensland Colonial Architect's Office as a cadet in 1886. He then travelled to London to broaden his professional experience and returned to Queensland in 1896 and began private practice in Toowoomba in February 1897 where he remained until his death in 1943.
The alterations designed by Hodgen for the Bishop's House, as it became known after its purchase by the Roman Catholic Church, were principally internal. Pressed metal ceilings by Wunderlich used in most of the rooms were retained along with the general floor plan of the building. Changes introduced included forming an entrance vestibule on the front loggia/verandah; alterations of the semi-octagonal end bays with the removal and bricking up of several sash windows; a room was planned as a chapel; a bathroom was added to the eastern end of the house in an extension designed for that purpose and some internal rearrangement of existing walls and doors was carried out to facilitate access to this extension. External signage, BISHOP'S HOUSE was added to the pediment above the entrance doors and sections of the front verandah/loggia were enclosed with glazing. Internally almost every room of the house was wall-papered to the picture rail.
Alterations to the grounds around the house included the demolition of the stables and replacement with a skillion roofed garage and construction of new entrance gates off Lindsay Street for motor-car access. A timber and concrete laundry was erected to the northwest of the house.
The various Bishops of Toowoomba remained at Bishop's House until recently, when another residence was constructed to the rear, northeast side of the building. Bishop's House has been refurnished as offices for the diocesan administration and the Catholic Education Office.
Description
Bishop's House, located opposite Queen's Park on the corner of Lindsay Street fronting Margaret Street to the south, is a single-storeyed masonry building with rendered quoining and detailing. The building has a corrugated iron roof with projecting gables, a central clerestory surmounted by a cross, and three HJ Marks patented pot bellied chimney stacks.
The symmetrical south elevation has a central enclosed loggia consisting of five arches with rendered voussoirs, keystones and columns, supporting a parapet wall surmounted by two small triangular projections either side of a central gable with the name BISHOP'S HOUSE in raised lettering. The loggia is flanked by projecting bays at either end, and is enclosed with arched sash window units and masonry panels on the western side, and sliding aluminium window units on the eastern side of the entry. The central entry has steps leading to a timber door with leadlight panel insert, sidelights and fanlight depicting a crest. The projecting bays have sash windows, but evidence of the original HJ Marks patented extendable casement windows is visible. The bays are surmounted by projecting boarded gables, above which are semi-circular windows with rendered voussoirs in the gable to the roof.
The north elevation has an enclosed verandah with an accommodation wing attached at the northwest corner, which consists of a masonry section with a timber framed and fibrous cement clad addition with concrete stumps. The verandah is enclosed with vertically jointed boarding to sill height and multi-paned sliding timber windows with fixed green glass panels above. The east and west ends have a projecting five-sided bay room with masonry to sill height and extendable casement windows above. These windows have been replaced by aluminium sliding windows on the west bay. A small brick addition with a parapet wall and sash window has been constructed on the southern side of the east bay room.
Internally, the building has plastered walls with wide east-west and north-south halls which intersect below a central clerestory. Principal rooms open to the south enclosed loggia, with French doors and an arched sash window with rendered voussoirs. However, the original loggia wall to the west of the entry has been removed to create one large office into the loggia space. Secondary rooms open to the north enclosed verandah which is lined with fibrous cement and has a sash window painted to imitate stained glass opening from the former chapel. A large arched doorway containing a timber door with leadlight sidelights and fanlight opens to the rear of the central hall. The foyer has timber wall panelling, and throughout the building many of the doors, architraves and skirtings have an obscure grained finish. Ceilings are pressed metal of various designs, most of the doors and windows have patterned glass panels, and fireplace surrounds are of narrow face brick. At either end of the east-west hall are panelled timber doors with leadlight panel insert, sidelights and fanlight. The east bay room has coloured glass door and windows, and a partition wall has been constructed to create a hall leading to the south addition.
The northwest accommodation wing contains an office and kitchen in the masonry section, with a bedroom and bathroom in the fibrous cement section. The masonry section has rendered walls with boarded ceilings, and the addition has timber framed fibrous cement walls and ceiling.
The site has a low brick fence along the south and west boundaries, with driveway access at the southeast and to the northwest of the building. A metal front gate is located at the corner of Lindsay and Margaret Streets, with a path leading to the main entrance. The grounds contain substantial mature trees to the south and southwest, with a bitumen carpark to the southeast and carports to the northwest.
The site also contains the Marian Community Centre, a single-storeyed masonry building to the northwest, and a two-storeyed masonry residence for the Bishop to the northeast of the building.
Heritage listing
Bishop's House was listed on the Queensland Heritage Register on 21 October 1992 having satisfied the following criteria.
The place is important in demonstrating the evolution or pattern of Queensland's history.
Constructed in 1911, Bishop's House is a substantial brick house which demonstrates the growth of this area of Toowoomba during the 1910s, a period of commercial and social expansion for the town following closer settlement. The building's use by the Roman Catholic Church illustrates the development of the church in Queensland, in particular internal growth which saw the establishment of another two dioceses in 1929.
The place is important in demonstrating the principal characteristics of a particular class of cultural places.
The building is a very good example of the work of architect Henry Marks, combining much of his innovative detailing with a general concern for ventilation and natural lighting.
The place is important because of its aesthetic significance.
Bishop's House, together with its mature plantings, makes a significant aesthetic contribution to the Margaret Street streetscape and Toowoomba townscape. The form and fabric of the building illustrate a creative and skilled design approach, and the detailing of the materials and finishes reflects a fine quality of workmanship.
The place is important in demonstrating a high degree of creative or technical achievement at a particular period.
The use of the extendable casement window and pot-bellied chimney stacks, as patented designs, are important in demonstrating a high degree of technical achievement by the architect Henry Marks during the early twentieth century.
The place has a strong or special association with a particular community or cultural group for social, cultural or spiritual reasons.
The building is important to members of the Roman Catholic community in Toowoomba as the home of the Bishop of their Diocese for many years.
The place has a special association with the life or work of a particular person, group or organisation of importance in Queensland's history.
The building is associated with Henry Marks, a prominent and prolific local architect; with WC Peak an important early Toowoomba businessman for whom it was constructed, and with the hierarchy of the Roman Catholic Church in Toowoomba who have owned the building as their principal residence since 1939.
References
Attribution
External links
Category:Queensland Heritage Register
Category:East Toowoomba, Queensland
Category:Houses in Queensland
Category:Articles incorporating text from the Queensland Heritage Register
Category:Houses completed in 1911
Category:1911 establishments in Australia
Category:Roman Catholic Diocese of Toowoomba | wikipedia |
Iegorievsk (en ) est une ville de l'oblast de Moscou, en Russie, et le centre administratif du raïon de Iegorievsk. Sa population s'élevait à habitants en 2014.
Géographie
Iegorievsk est située sur la rive droite de la rivière Gouslitsa et se trouve à au sud-est du centre de Moscou.
Histoire
Un village du nom de Vyssokoïe (Высокое) est connu depuis 1462. Son église Saint-Georges a été édifiée au . Le nom de la ville vient de Igor, variante russe du prénom « Georges. » Au , la ville acuueille une foire annuelle très fréquentée compte tenu de sa position favorable, au carrefour des routes entre Moscou et Riazan d'une part, de Vladimir et de Kolomna d'autre part. La localité, qui s'appla d'abord Iegoriev, a le statut de ville depuis 1778.
Elle s'agrandit tout au long du avec l'installation de manufactures, notamment de filatures, la création d'une école et la réparation des édifices religieux. Iegorjevsk devient un bastion des vieux-orthodoxes de la région de Moscou, ce que rappelle certains bas-reliefs de la nouvelle église Saint-Georges (1882).
Iegorievsk abrite de nombreux bâtiments historiques des et s, ainsi qu'un musée présentant des objets artistiques et de la vie quotidienne des siècles précédents.
Population
Recensements (*) ou estimations de la population :
Personnalités
Grigory Spassky (1783-1864), explorateur et historien, né à Iegorievsk
Edouard Ouspenski (né en 1932), écrivain
Aliya Mustafina (née en 1994) gymnaste septuple médaillée olympique et 12 fois médaillée des championnats du monde.
Notes et références
Liens externes
Informations sur Iegorievsk
Cartes topographiques
Division administrative fondée en 1462 | slim_pajama |
the development of artificial bioengineered constructs largely depends on adequate vascularization to guarantee sufficient oxygen supply . the arteriovenous
( av ) loop model is an established method to obtain transplantable bioartificial tissue in vivo .
originally based on the findings of erol and spira and subsequently modified by murphy et al . and tanaka et al .
this model of benign angio - inductive behavior triggers the formation of novel vessel sprouts remarkably without additional extrinsic and angio - inductive factors . in brief , a femoral vein is dissected , harvested , and as an autologous graft , interposed between the contralateral femoral artery and vein .
this results in an arteriovenous fistula , which is then embedded in a fibrin - filled teflon chamber .
a mature microcirculatory system originates mainly from the venous graft , thereby facilitating cultivation , harvesting , and transfer of rudimentary organ - like structures to a secondary defect site , thus minimizing donor site morbidity [ 69 ] .
as vascularization is crucial to promote clinical implementation of bioengineered constructs , tremendous research efforts have been undertaken to further optimize vessel formation within the av loop .
the current understanding of angiogenesis is evolving , as the underlying nature and mediating signaling pathways fundamentally differ in various types of angiogenesis .
watson et al . demonstrated that vascular flow is essential for hypoxia - driven angiogenesis in embryonic development .
furthermore , we recently pointed out that distinct av associated changes of the hemodynamic load namely the shear rate are responsible for triggering the angio - inductive behavior of endothelial cells within the venous graft .
both of these observations fundamentally rely on the presence of angio - inductive endothelial cells and a viable venous graft . however , polykandriotis et al . and westerband et al
moreover , zdolsek et al . demonstrated that utterly decellularized and avital vein allografts are continuously able to maintain angio - inductive properties within the av loop . due to the constant progress in reconstructive surgery and due to improved and standardized microsurgical treatment algorithms , the range of medical indications for reconstructive vascularized tissue transfers has increased dramatically during the last decades .
thus , microvascular flaps are exposed to high - dose radiation after defect coverage with increasing frequency . for this reason , the vascular behavior of novel reconstructive approaches , such as intrinsically vascularized av loop - based constructs ,
allows an excellent evaluation of the accompanying angiogenesis , and is of special interest in evaluating the response to radiation .
furthermore , the understanding of the av loop associated angiogenesis is of special translational importance .
there is an ongoing discussion as to whether the interposed venous graft is vitally important for the induction of angiogenesis under conditions of high flow . in order to alter the cellular hemostasis specifically within the grafted vein we exposed the graft intraoperatively to 2 gy of ionizing radiation ( a level of radiation considered a relevant rat dose - rate ) .
we wanted to demonstrate that the graft possessed vital intrinsic factors that were at least partially responsible for triggering flow - mediated angiogenesis in the av loop model , and we generally wanted to investigate the effect of radiation in the developing av loop microvasculature . beside three - dimensional micro - ct
, a previously described observer - independent automatic software algorithm was used to assess vessel number , density , and area by analyzing two - dimensional histological cross sections in order to characterize the differences of angiogenesis in detail .
all operations were performed by the same investigator ( jmc ) using a surgical microscope ( magnification 16 , opmi ifc , carl zeiss , oberkochen , germany ) .
2 to 4 month old male lewis rats ( n=14 ) with an average body mass of 340 g were obtained from charles river laboratories ( sulzfeld , germany ) .
all experiments were approved by the institutional animal care and use committee of the regierungsprsidium mittelfranken ( az 54 - 2532.1 - 34/09 ) and in accordance with the german animal welfare act .
for induction of anesthesia , the rats received 5% isoflurane ( baxter , vienna , austria ) inhalation . before surgery
, they received buprenorphin for analgesia , ( 0.3 mg / kg body weight , temgesic , essex chemie ag , luzern , switzerland ) , as well as heparin anticoagulation ( 80 iu / kg liquemin , ratiopharm ulm , germany ) .
the right femoral vascular bundle was exposed by a mid - ventral incision . the femoral vein was dissected and a 20 mm long venous graft was harvested .
the grafts either underwent irradiation or were directly interposed as a loop ( figure 1 ) between the contralateral femoral artery and vein using 11/0 nylon sutures ( ethilon , ethicon , norderstedt , germany ) after similar incubation in sodium heparin solution ( sham treatment , 10,000 ie / l ) .
the av loop was embedded in the isolation chamber , which was filled with 800 l of fibrin sealant ( tissucol , baxter ) composed of fibrinogen ( 10 mg / ml ) , thrombin ( 2 iu / ml ) and aprotinin ( 1,500 kie / ml ) as described previously .
the chamber was sutured subcutaneously onto the underlying adductor fascia with 6 - 0 polypropylene ( prolene 6/0 , ethicon , norderstedt , germany ) . for wound closure ,
interrupted vertical mattress sutures with vicryl 4 - 0 ( ethicon , norderstedt , germany ) were used .
all rats received buprenorphin and heparin ( 80 iu / kg liquemin , ratiopharm ulm , germany ) postoperatively .
the rats were kept at a 12-hour dark / light cycle in the animal facility of the university of erlangen medical centre with free access to standard chow ( sniff ) and water . at the end of the experiment ,
the rats were sacrificed under deep anesthesia ( 5% isoflurane ) by exsanguination , and subsequent reperfusion with india ink or microfil ( flowtech , ma , usa ) . the autologous venous graft was harvested and rinsed in sodium heparin solution ( 10,000 ie / l ) .
a dose of 2 gy ionizing radiation was applied to the vein graft within 30 seconds using an isovolt titan x - ray machine with a 120 kv power supply ( ge sensing & inspection technologies , ahrensburg , germany ) .
after 15 days , an abdominal midline incision was performed and newly formed vessels along the main vessel axis were detected by cannulating the distal descending aorta using a 24-gauge catheter .
the descending vascular system was cleansed with 100 ml of prewarmed ( 37c ) isotonic salt solution containing heparin ( 100 ie / ml ) and subsequently perfused with 30 ml of prewarmed ( 37c ) india ink solution [ 50% v / v india ink ( rohrer & klinger ) ] in 5% gelatin and 4% mannitol in order to detect additional vessels around the constructed av loop .
micro - ct analysis required the reperfusion of the circulatory system with 20 ml of warmed yellow microfil ( mv-122 ) containing 5% of mv curing agent ( flowtech inc . , carver , usa ) .
incubation at 4c for 24 hours allowed the gelatin and mannitol to solidify before continuing with downstream applications . for histological analysis
then 5 m histological sections in standardized planes perpendicular to the longitudinal av loop axis were produced using a microtome ( leica microsystems , wetzlar , germany ) .
hematoxylin and eosin ( h&e ) staining was performed using an autostainer ( st5010 , leica microsystems ) according to standard protocol .
isolectin b4 ( sigma l 2140 , sigma - aldrich , hamburg , germany ) staining was used to detect luminal endothelial cells by means of immunohistochemistry as described elsewhere .
histological cross sections were visualized using an inversed microscopy ( olympus ix81 , 10 magnification , olympus corporation , hamburg , germany ) and analyzed using an automatic two - dimensional quantification algorithm established previously by our group for superior morphometric quantification .
high - resolution micro - ct scans were acquired on a cone - beam micro - ct scanner at the institute of medical physics , university erlangen , germany ( forbild scanner ) .
further technical specifications and specialized algorithms for optimization and enhancement of images obtained were described in detail elsewhere . for statistical analysis and figures , originpro 2015 ( b9.2.214 , originlab corp . ,
for analysis of more than two groups , analysis of variance ( one - way anova ) was used .
all operations were performed by the same investigator ( jmc ) using a surgical microscope ( magnification 16 , opmi ifc , carl zeiss , oberkochen , germany ) .
2 to 4 month old male lewis rats ( n=14 ) with an average body mass of 340 g were obtained from charles river laboratories ( sulzfeld , germany ) .
all experiments were approved by the institutional animal care and use committee of the regierungsprsidium mittelfranken ( az 54 - 2532.1 - 34/09 ) and in accordance with the german animal welfare act .
for induction of anesthesia , the rats received 5% isoflurane ( baxter , vienna , austria ) inhalation . before surgery
, they received buprenorphin for analgesia , ( 0.3 mg / kg body weight , temgesic , essex chemie ag , luzern , switzerland ) , as well as heparin anticoagulation ( 80 iu / kg liquemin , ratiopharm ulm , germany ) .
the right femoral vascular bundle was exposed by a mid - ventral incision . the femoral vein was dissected and a 20 mm long venous graft was harvested .
the grafts either underwent irradiation or were directly interposed as a loop ( figure 1 ) between the contralateral femoral artery and vein using 11/0 nylon sutures ( ethilon , ethicon , norderstedt , germany ) after similar incubation in sodium heparin solution ( sham treatment , 10,000 ie / l ) .
the av loop was embedded in the isolation chamber , which was filled with 800 l of fibrin sealant ( tissucol , baxter ) composed of fibrinogen ( 10 mg / ml ) , thrombin ( 2 iu / ml ) and aprotinin ( 1,500 kie / ml ) as described previously .
the chamber was sutured subcutaneously onto the underlying adductor fascia with 6 - 0 polypropylene ( prolene 6/0 , ethicon , norderstedt , germany ) . for wound closure ,
interrupted vertical mattress sutures with vicryl 4 - 0 ( ethicon , norderstedt , germany ) were used .
all rats received buprenorphin and heparin ( 80 iu / kg liquemin , ratiopharm ulm , germany ) postoperatively .
the rats were kept at a 12-hour dark / light cycle in the animal facility of the university of erlangen medical centre with free access to standard chow ( sniff ) and water . at the end of the experiment ,
the rats were sacrificed under deep anesthesia ( 5% isoflurane ) by exsanguination , and subsequent reperfusion with india ink or microfil ( flowtech , ma , usa ) .
the autologous venous graft was harvested and rinsed in sodium heparin solution ( 10,000 ie / l ) .
a dose of 2 gy ionizing radiation was applied to the vein graft within 30 seconds using an isovolt titan x - ray machine with a 120 kv power supply ( ge sensing & inspection technologies , ahrensburg , germany ) .
after 15 days , an abdominal midline incision was performed and newly formed vessels along the main vessel axis were detected by cannulating the distal descending aorta using a 24-gauge catheter .
the descending vascular system was cleansed with 100 ml of prewarmed ( 37c ) isotonic salt solution containing heparin ( 100 ie / ml ) and subsequently perfused with 30 ml of prewarmed ( 37c ) india ink solution [ 50% v / v india ink ( rohrer & klinger ) ] in 5% gelatin and 4% mannitol in order to detect additional vessels around the constructed av loop .
micro - ct analysis required the reperfusion of the circulatory system with 20 ml of warmed yellow microfil ( mv-122 ) containing 5% of mv curing agent ( flowtech inc . , carver , usa ) .
incubation at 4c for 24 hours allowed the gelatin and mannitol to solidify before continuing with downstream applications . for histological analysis , the chambers with the av loop were explanted .
formalin - fixed , paraffin - embedded tissue sections were obtained using standard protocols . then 5 m histological sections in standardized planes perpendicular to the longitudinal av loop axis were produced using a microtome ( leica microsystems , wetzlar , germany ) .
hematoxylin and eosin ( h&e ) staining was performed using an autostainer ( st5010 , leica microsystems ) according to standard protocol .
isolectin b4 ( sigma l 2140 , sigma - aldrich , hamburg , germany ) staining was used to detect luminal endothelial cells by means of immunohistochemistry as described elsewhere .
histological cross sections were visualized using an inversed microscopy ( olympus ix81 , 10 magnification , olympus corporation , hamburg , germany ) and analyzed using an automatic two - dimensional quantification algorithm established previously by our group for superior morphometric quantification .
high - resolution micro - ct scans were acquired on a cone - beam micro - ct scanner at the institute of medical physics , university erlangen , germany ( forbild scanner ) .
further technical specifications and specialized algorithms for optimization and enhancement of images obtained were described in detail elsewhere .
for statistical analysis and figures , originpro 2015 ( b9.2.214 , originlab corp . , northampton , ma , usa ) was used .
all data are presented as mean sem and compared using unpaired t - test . for analysis of more than two groups , analysis of variance ( one - way anova )
all rats survived the experiments and tolerated the anesthesia and surgical procedures well ( n=14 ) .
one rat in the control group had a significant swelling in the groin in the first week after surgery most likely due to seroma formation .
after explantation of the chamber , the peripheral tissue was examined by macroscopic assessment . the matrix embedding the av loop within the chambers had a milky translucent appearance at implantation .
stained main vessel axis was visible in all rats indicating a successful reperfusion and patency of the av loop at the time of reperfusion .
fifteen days after the loop implantation , angiogenesis was visualized by three - dimensional micro - ct analysis in two rats from each group . in line with previous results , control loops showed homogenous vessel sprouting that originated predominantly from the lumen of the graft ( figure 2a ) . local graft irradiation considerably impaired neovessel formation along the graft ( figure 2b ) .
lumina of the microcirculatory system along the graft appeared darkly stained in h&e and lectin stained cross sections of india ink - or microfil - perfused av loop constructs .
the microcirculatory system along irradiated grafts was predominantly aligned in close proximity to the main vessel axis . when a non - irradiated control graft was used , however , newly formed vessels extended further peripherally from the main vessel axis ( figure 3 ) .
the degree of vascular sprouts was assessed by an automatic observer - independent quantification algorithm , as described earlier , and yielded a total amount of 739111 ( n=7 ) vessels per cross section .
no significant morphometrical differences were found between the inflow ( 43183 , n=7 ) and the outflow tract ( 30843 , n=7 ) of non - irradiated control grafts ( figure 4a ) .
the amount of vessels of the graft inflow ( 17458 , n=7 ) was not statistically different from the graft outflow ( 13738 n=7 ) .
mean vessel area ( figure 4b ) assessed by cross section analysis within constructs where control grafts were used amounted to 238,92463,126 m and , similar to the vessel number , there were no statistical significant differences among control grafts with an area of 151,73051,975 m ( n=7 ) at inflow segments and 84,33722,964 m ( n=7 ) at outflow segments .
irradiated grafts behaved correspondingly with an area of 21,9986,850 m , n=7 ( graft inflow ) and 21,1405,897 m , n=7 ( graft outflow ) respectively .
although luminal sprouting was strongly impaired , the formation of new vessels from the luminal graft was not thoroughly abolished .
single - dose irradiation of 2 gy reduced the mean number of vessel sprouts to 31173 ( n=7 ) and was significantly different from the control ( figure 4a ) .
irradiation reduced mean vessel area to 43,13710,224 m ( n=7 ) compared to 238,92463,126 m ( n=7 ) in corresponding control grafts ( figure 4b ) .
the mean number of vessels and area of irradiated grafts were significantly lower when compared to non - irradiated control grafts ( figure 4a and 4b ) . while not statistical significant , mean vessel diameter after graft irradiation ( 141.8 m , n=7 ) tended to be lower compared to control grafts ( 192.6 m , n=7 , figure 5 ) .
densities of neovessels were differently distributed when comparing av loop constructs with control and irradiated grafts .
vessel formation aroused primarily within a peripheral radius of 401600 m when normalized to the main vessel axis .
in contrast , mean vessel diameter began to differ at radii greater than 400 m , suggesting that radiation may have negative effects on peripheral maturation of newly formed vessels ( figure 6b ) .
all rats survived the experiments and tolerated the anesthesia and surgical procedures well ( n=14 ) .
one rat in the control group had a significant swelling in the groin in the first week after surgery most likely due to seroma formation .
after explantation of the chamber , the peripheral tissue was examined by macroscopic assessment . the matrix embedding the av loop within the chambers had a milky translucent appearance at implantation .
stained main vessel axis was visible in all rats indicating a successful reperfusion and patency of the av loop at the time of reperfusion .
fifteen days after the loop implantation , angiogenesis was visualized by three - dimensional micro - ct analysis in two rats from each group . in line with previous results , control loops showed homogenous vessel sprouting that originated predominantly from the lumen of the graft ( figure 2a ) . local graft irradiation considerably impaired neovessel formation along the graft ( figure 2b ) .
lumina of the microcirculatory system along the graft appeared darkly stained in h&e and lectin stained cross sections of india ink - or microfil - perfused av loop constructs .
the microcirculatory system along irradiated grafts was predominantly aligned in close proximity to the main vessel axis .
when a non - irradiated control graft was used , however , newly formed vessels extended further peripherally from the main vessel axis ( figure 3 ) .
the degree of vascular sprouts was assessed by an automatic observer - independent quantification algorithm , as described earlier , and yielded a total amount of 739111 ( n=7 ) vessels per cross section .
no significant morphometrical differences were found between the inflow ( 43183 , n=7 ) and the outflow tract ( 30843 , n=7 ) of non - irradiated control grafts ( figure 4a ) .
the amount of vessels of the graft inflow ( 17458 , n=7 ) was not statistically different from the graft outflow ( 13738 n=7 ) .
mean vessel area ( figure 4b ) assessed by cross section analysis within constructs where control grafts were used amounted to 238,92463,126 m and , similar to the vessel number , there were no statistical significant differences among control grafts with an area of 151,73051,975 m ( n=7 ) at inflow segments and 84,33722,964 m ( n=7 ) at outflow segments .
irradiated grafts behaved correspondingly with an area of 21,9986,850 m , n=7 ( graft inflow ) and 21,1405,897 m , n=7 ( graft outflow ) respectively .
although luminal sprouting was strongly impaired , the formation of new vessels from the luminal graft was not thoroughly abolished . single - dose irradiation of 2 gy reduced the mean number of vessel sprouts to 31173 ( n=7 ) and was significantly different from the control ( figure 4a ) .
irradiation reduced mean vessel area to 43,13710,224 m ( n=7 ) compared to 238,92463,126 m ( n=7 ) in corresponding control grafts ( figure 4b ) .
the mean number of vessels and area of irradiated grafts were significantly lower when compared to non - irradiated control grafts ( figure 4a and 4b ) . while not statistical significant , mean vessel diameter after graft irradiation ( 141.8 m , n=7 ) tended to be lower compared to control grafts ( 192.6 m , n=7 , figure 5 ) .
densities of neovessels were differently distributed when comparing av loop constructs with control and irradiated grafts .
vessel formation aroused primarily within a peripheral radius of 401600 m when normalized to the main vessel axis .
in contrast , mean vessel diameter began to differ at radii greater than 400 m , suggesting that radiation may have negative effects on peripheral maturation of newly formed vessels ( figure 6b ) .
to the best of our knowledge , this is the first study investigating the effects of ionizing radiation within an av loop - based neovascular system .
grafts were exposed intraoperatively to a single dose of 2 gy ionizing radiation prior to loop construction in order to elucidate whether they provide angio - inductive features under conditions of high flow that are mandatory for av loop associated angiogenesis . as assessed by three - dimensional micro - ct analysis and two - dimensional quantification of mean vessel number and area
, we demonstrated that vessel sprouting was significantly impaired when irradiated vein grafts were used for av loop construction . further dissecting this angio - inductive phenomenon histologically , we provided evidence that the emerging microcirculatory system was homogeneously distributed along the main vessel axis
additionally , we illustrated that radiation compromises neovessel stabilization and maturation as mean vessel diameter primarily decreased in more peripheral regions of constructs containing irradiated vein grafts .
changes in mechanical load following vein grafting into an arteriovenous shunt flow have been shown to foster angio - inductive properties in the graft endothelium .
however , it has also been demonstrated that vascular grafts are exposed to a significant amount of endothelial denudation .
notably , even decelluarized and avital vascular allografts seem sufficient to provide angiogenesis in the av loop .
thus , it has been proposed that the venous graft merely serves as a connecting prosthesis providing sufficient length to ensure a tension - free av anastomosis .
contrary to this believe , we repeatedly observed luminal sprouts emerging from the grafted vein .
observed by means of scanning electron microscopy ( sem ) of corrosion casts , that luminal sprouting was present in the vein and the grafted vein but not in the arterial segment between day 10 and 14 after av loop creation .
we previously pointed out that , in contrast to pulsatile flow , increased vascular shear rate induced specific cellular responses linked to angio - inductive behavior .
notably , intercellular gap junction protein connexin ( cx ) 43 is specifically upregulated in vein graft endothelium , and it has been suggested that it is vital for angiogenic signaling and vessel growth .
thus , we believe that the interposed graft transduces mechanosensitive stimuli after exposure to high flow .
the detrimental effects of ionizing radiation have long been recognized and are widely used in adjuvant and neoadjuvant treatment options worldwide .
hydroxyl radicals ( oh ) alter cellular lipid hemostasis , membrane transport , and constitute significant genotoxic stressors on vascular cells .
double - strand dna breaks ultimately activate proto - oncogenes and propel malignant cell transformation .
the molecular mechanisms behind radiation - induced genetic alterations are for the time being largely unidentified but may , among others factors , be linked to dysfunctional expression and nuclear translocation of cytoplasmic transcription factors . within blood vessels , endothelial cells are the most vulnerable to irradiation .
radiation - induced vascular injury correlates histologically with desquamated endothelial cells , which leads to small vessel obstruction and subsequent tissue ischemia .
it has been previously demonstrated that the acute effect of radiation - induced vascular injury depends on vessel diameter .
severity of adventitial fibrosis and medial hyalinization are most distinctively recognized in vessels < 500 m . in the presented study
, we showed that single - dose graft irradiation with 2 gy impaired the development of a functional microcirculatory system likely due to dysfunctional graft - specific and angio - inductive properties .
the clinical management of head and neck tumors and extended extremity sarcomas continue to challenge reconstructive surgeons worldwide ; av loop - based tissue transfer may provide an essential adjunct for vascularized tissue transfer after oncologic resection .
as the majority of these patients regularly require adjuvant radiotherapy , the effect of radiation on av loop vascularization is of great clinical importance .
although strongly decreased , vessel sprouting was not fully abolished after irradiation in our study .
hence , vascular shear rate might constitute a fairly sturdy and vital determinant for loop - associated neoangiogenesis even after isolated and high - dose radiation of the mediating vein . nevertheless , we only examined short - term effects of radiation on av loop associated angiogenesis .
as vascular tissue mainly consists of slowly proliferating cells , single - dose local graft irradiation may impede vascular hemostasis of bioengineered constructs primarily in the long term .
further analysis of radiation - mediated ramifications of the av loop model may contribute to safe clinical implementation and adequate patient selection .
the isolated and homogeneous chamber environment , as well as the established quantification algorithms , render the av loop model eligible for compartment - specific characterization of newly developing vascular networks .
as various malignant microenvironments induce different dynamic and angio - inductive behavior , the av loop model may conceivably be a useful tool for further in vivo characterization of anti - angiogenic treatment options .
dynamic and molecular interactions of various cancer stem cells with a defined vascular supply , as well as their intrinsic susceptibility to radiotherapy and other novel and locally restricted treatment options , may conveniently and separately be studied within the av loop chamber . in the presented study , we investigated the effects of radiation in a benign angiogenesis rat model .
these findings provide a useful tool for further molecular characterization of tumor growth ; especially as various tumor cells differently interact with vascular structures thereby altering radiation sensitivity .
taken together , we provided evidence that the venous graft constitutes a vital part of the av loop model and is essential to initiate vascular luminal sprouts .
it remains speculative whether reduced graft viability or cellular alterations are responsible , as irradiation induces a plethora of vascular and metabolic changes within the vascular tissue .
although not completely impaired , graft - specific irradiation negatively influences av loop associated vascularization .
radiation compromises neovessel stabilization and maturation primarily in peripheral regions of av loop - based constructs .
these results add to the current understanding of av loop - based neovascularization and suggest clinical implications for patients relying on combined av loop - based tissue transfer and adjuvant radiotherapy . | pubmed |
Lost Girl 1. What do I want ?
**Take me away**
**Chapitre 1 : **What do i want ?
Assise à son bureau, elle soupira longuement, essayant de relâcher toute la pression de ces derniers jours, de ces dernières semaines voire de ces cinq dernières années. Elle pourrait, ainsi, essayer de se concentrer sur le présent et sur la nouvelle qu'elle venait d'apprendre. Pour être honnête, ce n'était pas vraiment surprise, mais plutôt une confirmation, cela faisait presque deux semaines que de multiples indices lui avait déjà permis de soupçonner ce qu'il se passait. Mais en avoir la preuve, devant elle, dans ses mains était presque trop.
Pas certaine de savoir comment elle devait réagir, elle se mit à regarder fixement le mur blanc devant elle, comme si les réponses à toutes ses questions allaient s'afficher par magie.
Instinctivement, elle se mit à jouer avec l'objet qu'elle tenait entre les mains, espérant trouver un petit bouton, un mot, n'importe quoi qui lui indiquerait que tout ceux-ci n'était qu'une mauvaise blague. Quelque chose qui lui permettrait de pouvoir recommencer à dormir la nuit et faire comme si rien de tout cela n'était vraie. Elle ne put s'empêcher de rire devant sa réaction plus qu'absurde, elle avait elle-même acheté l'objet dans une pharmacie à l'autre côté de la ville, là où personne ne la connaissait. Personne n'était au courant de sa présente situation.
Le docteur en elle, la gifla mentalement.
« _Il faut que tu te reprennes si tu ne veux pas perdre le contrôle des évènements ! »_, cette pensée l'obligea à se redresser, détourner son regard du mur et poser l'objet sur le bureau. Elle ferma les yeux un instant et soupira une seconde fois.
Ainsi, elle commença un débat mental.
_« Qu'est-ce que je suis supposé faire maintenant ? En parler ? A qui ? » _
Elle secoua la tête un peu plus brutalement que nécessaire, pour chasser cette stupide idée de son esprit.
_« Personne ne te croira, ce genre de chose n'est jamais arrivé… Tu ne ferais qu'attirer plus de problèmes que tu n'en as déjà. Tu n'es qu'une humaine, c'est ta parole contre celle de Fae respectés qui ont vécu des centaines voire des milliers d'années. De plus, même si tu arrivais à le prouver scientifiquement, c'est une erreur de la nature, ils te tueront à coup sûr… »_
_**Mais si je n'en parlais qu'à Bo ? Elle saurait sûrement quoi faire, et serait capable de te protéger, ce n'est pas comme si j'étais la seule responsable dans cette histoire… Elle a joué un rôle plus qu'important dans cette histoire, elle a le droit de savoir non ?**_
_« Dois-je te rappeler qu'elle t'a abandonnée ? Que vous n'êtes plus ensemble ? Même après avoir éclaircis tes intentions sur les derniers événements, elle ne te refera plus confiance, pas comme avant en tout cas. Elle ne veut rien de tout cela, si tu l'informe, elle se sentira obligée de te protéger, et ce n'est pas ce que tu veux. Être un fardeau ne fera que votre malheur à tous les deux »._
A la mention de la jeune femme, son cœur se mit à battre plus rapidement que nécessaire, comme si il essayait de sortir de sa cage thoracique, qui commençait à ressembler plus à une prison qu'à autre chose. Sentant ses mains devenir moites, elle les essuya doucement contre son jean avant de les poser à plat contre le bureau, cherchant un appui, de peur que ses jambes ne soient plus capables de la tenir bien longtemps.
Il n'y a pas si longtemps, lorsqu'elle pensait à la femme avec qui elle pensait qu'elle allait vivre une belle et longue histoire d'amour, elle ne ressentait que du bonheur, même lorsqu'elles n'étaient pas encore ensemble. Un sentiment de liberté, comme si elle puisait en elle la force de croire que tout était possible.
_« Tu es tellement stupide, tous les signes étaient là, une humaine faible comme toi, n'aurait jamais pu la rendre heureuse. Tu t'es baignée dans des rêves… »_
Le réveil avait été plus que brutal, un peu comme si on l'avait poignardée dans le dos. Son agression par l'adolescent du camp, il y a quelques semaines de cela, semblait presque agréable à côté de sa séparation avec Bo.
_« Tu vas devoir trouver une solution pour gérer tout cela toute seule »._
Seule. Cela faisait 5 ans qu'elle l'était. Même si cette dernière année, elle avait eu l'impression d'avoir des amis. Trick, Hale et dernièrement Kenzi et Dyson. Après l'histoire avec le Garuda, elle avait eu la sentiment de faire partie de la bande, traînant ensemble au Dal, riant lorsqu'ils écoutaient les histoires de Kenzi, plus loufoques les unes que les autres.
Mais très vite, elle avait comprit que ce n'était que pour le bien de Bo, qu'ils la supportaient. Lorsque celle-ci l'a rejeté il y a deux semaines, personne n'avait demandé de ses nouvelles, le téléphone n'a plus sonné, ni la sonnette de l'appartement. Elle a vécu ces derniers jours dans un silence presque épuisant. I ans, elle ne s'en serait pas plainte, après tout, elle n'est qu'une esclave des Fae. Mais elle s'était surprise à aimer la compagnie, espérer qu'on lui demande comment elle allait, ce qu'elle pouvait ressentir, qu'on l'invite à prendre un verre.
Encore une fois, le retour à la réalité avait été bien brutal.
_« Tu es intelligente, tu es l'un des meilleurs docteurs parmi les Fae ! I aucune raison pour que tu perdes tes moyens ici, tu peux le faire. Réfléchis._ _Comment tu peux te sortir de cette situation ? Dire la vérité est bien évidemment hors de question. Mais tu vas devoir avouer quelque chose, si tu veux avoir une chance de t'en sortir, et répondre aux questions qu'on te posera éventuellement dans le futur. »_
Que dire ? Que cacher ?
En quelques secondes, des dizaines de scénarios effleurèrent son esprit, elle utilisa sa logique scientifique pour trouver les défauts de chacun d'entre eux, lesquels serait les plus plausibles, ceux qui attireraient trop l'attention, ceux qui la mettraient en danger.
_**Tu sais qu'il y a un moyen assez simple de mettre un terme à cette situation. Ainsi personne n'aura à savoir quoi que ce soit, **_lui suggéra une voix intérieure qu'elle n'avait plus entendue depuis plusieurs années. Elle représentait une part de sa personnalité qu'elle avait décidez d'abandonner il y a un certain temps, celle qui ne se souciait que d'elle, qui l'autorisait à être égoïste.
_**Pourquoi t'attacher à quelque chose que tu n'as pas demandé ? Personne ne sera là pour toi. L'opération peut-être discrète et tu as des contacts prêts à t'aider et à se taire. Tout serait tellement plus simple si tu le faisais.**_
_« Ce n'est pas faux, tu peux choisir le chemin le plus simple et te sortir de tout ceci. Ou tu peux choisir les chemins pleins d'obstacles, où ta vie deviendra un mensonge constant. Est-ce que tu es sûre de pouvoir le faire ? De pouvoir assumer cette responsabilité ? »_
S'il y a une chose qu'elle avait apprit de ces dernières années avec les Fae, c'est que rien n'était facile. Mais si elle s'en donnait les moyens, elle pouvait se sortir de toutes les situations et assumer les conséquences. Tout en étant une esclave, elle est devenue l'un des meilleurs scientifiques, trouvant des remèdes à presque toutes les épidémies qu'elle rencontrait au fil des années.
Pour ce qui est d'assumer les conséquences de ses actes, elle était une experte. Après que Nadia soit tombée dans le coma, elle a supportée cinq années de souffrances pour essayer de la sauver. Après sa première nuit avec Bo, elle n'avait pas insisté lorsque celle-ci avait décidée de l'ignorer durant des semaines. Même aujourd'hui, elle assumait le fait d'avoir dupée Bo, pour pouvoir la sauver, elle et Dyson. Cela avait fini par Bo, lui demandant de sortir définitivement de sa vie.
_« A ce stade, la seule question que tu dois te poser c'est, qu'est-ce que tu veux ? »._
Les larmes menaçaient de couler le long de ses joues, mais elle résista essayant de se montrer forte même s'il n'y avait personne avec elle. S'agrippant plus fortement à son bureau, elle commençait à ressentir la douleur du bois qui s'enfonçait dans ses paumes, mais elle l'ignora, comme si elle avait besoin de se punir, de ressentir cette douleur, cette peine.
Rouvrant doucement les yeux, elle lança un dernier regard au test de grossesse qu'elle avait posé devant elle, mais surtout au « + » affiché sur le petit écran.
**Qu'est-ce que je veux ?**, Lauren Lewis se le demandait encore une fois.
2. Milk and mornings
**AN:** _Salut tout le monde ! Alors je suis encore en train d'apprendre à poster sur FF c'est pour cela qu'il n y avait aucune explication sur le premier chapitre car je ne savais pas comment ça marchait ! _
_Alors je vais continuez de poster en Français car j'écris d'abord en français avant de le traduire en anglais et vous êtes deux à lire apparamant donc pour vous je posterais en français._
_Alors la fic se passe à la fin de la saison 3, avec la seule modification que Hale est toujours Ash, Voilà ! _
**Chapitre 2 : Mornings and Milk**
8 ans plus tard...
"Merde !"
Ce dernier mot fut très vite suivit pas un énorme bruit de verre cassée. Elle n'eut pas besoin de se retourner pour savoir ce qui venait de se passer, ce qui la fit sourire malgré elle, le jeune garçon était très maladroit, des fois beaucoup trop pour son bien.
"Ethan Dyson Lewis ! Combien de fois dois-je te rappeler de faire attention à ton langage ?!" Le gronda-t-elle en se levant brusquement de son bureau pour aller nettoyer l'énorme flaque de lait et les morceaux du bol que son fils venait de faire tomber.
Il prit un air penaud, dont il avait le secret pour essayer d'échapper au pire situation ou avoir ce qu'il voulait, dans ces moments-là son cœur se mît à lui faire mal. Cette expression lui rappelait beaucoup trop la personne qu'elle avait mis des années à oublier, elle n'était pas sûre d'avoir réussi d'ailleurs.
Soupirant doucement, elle se reprit et lui jeta un regard sévère qui voulait clairement dire "tu peux toujours essayer, ça ne marche pas sur moi". Il baissa la tête, pour se rendre compte des dégâts qu'il venait de causer.
"Mais Maman le dit toujours et pourtant tu ne lui dis rien !" Tenta-t-il, une chose qu'il tenait d'elle. Elle lui avait appris à ne pas se laisser faire et toujours justifier ses actions, malheureusement cela s'est très rapidement retourné contre elle.
"Pour une fois qu'il prend compte de mes conseils" grommela-t-elle de façon très basse afin qu'elle seule puisse l'entendre.
"Ce n'est pas parce que ta mère fait quelque chose que c'est n'est pas une bêtise, on en fait tous même les adultes, le plus important est de s'en rendre compte et de se corriger, d'ailleurs dans cet esprit c'est toi qui va nettoyer le sol, peut-être que la prochaine fois tu feras plus attention".
Une fois, qu'elle eut finit de ramasser les morceaux de verre, le but était de lui apprendre une leçon et non pas de le blesser et vue à quel point il pouvait être maladroit, le laisser manipuler des objets tranchants n'était pas une bonne idée. Elle lui tendit la serpillère, qu'il prit non sans soupirer un bon coup.
"Tu n'es pas fun" ajouta-t-il en se mettant à la tâche.
La blonde leva les yeux au ciel remarquant que le jeune brun ne savait pas manipuler le simple tissu. Après avoir lâché la serpillère sur la flaque, il utilisa son pied pour recouvrir toute la surface qui avait été touché par sa maladresse. Aggravant les dégâts plus qu'autre chose.
"J'y crois pas ! Tu penses sérieusement que c'est comme ça que je fais lorsque je nettoie ?
- Bah quoi ? C'est comme ça que Maman fait !
- On parle de moi ?".
La nouvelle voix surgit de la chambre située près du salon, connu comme étant la chambre parentale. Ce qui poussa Lauren et Ethan à détourner le regard pour se concentrer sur la blonde qui venait de se réveiller d'après l'état de ses cheveux. Si elle n'était pas énerver par l'incompétence du jeune garçon pour nettoyer une simple tâche de lait, elle aurait trouvé sa compagne irrésistible, du levée jusqu'au couché du soleil elle était tout simplement à couper le souffle.
"Ton fils vient de m'apprendre comment tu t'occupais des tâches ménagères".
La déclaration poussa la jeune femme à ouvrir les yeux grands comme un enfant venant de se faire prendre en flagrant délit. Encore une des choses qui aurait fait craquer le docteur dans n'importe qu'elle autre situation. La coupable baissa les yeux pour se concentrer sur le jeune garçon lui lançant une expression que Lauren interpréta comme un "c'était censé rester entre nous !". Il ne répondit qu'en haussant les épaules "Si je tombe, tu tombes aussi".
Balançant son regard de son fils vers sa compagne, Lauren ne put s'empêcher de jalouser leur relation, ils étaient très proches l'un de l'autre arrivant à communiquer sans parler, des fois elle se demandait s'ils n'avaient pas finit par établir une connexion télépathique dont elle n'était pas au courant.
"Quelque chose à dire pour ta défense ? Finit-elle par ajouter lorsqu'elle comprit que la blonde n'avait pas l'intention de se justifier.
"Je t'aime ?", elle prit un air de chien battu qui poussa Lauren à soupirer et lever les yeux au ciel comme signe d'abandon. Le temps passait et Ethan avait école de plus même si elle ne l'admettrait jamais, elle avait bien dû mal à résister lorsque la blonde utilisait cette expression.
"Finit de te préparer, elle se tourna pour refaire face à son fils, le bus scolaire devrait passer d'une seconde à l'autre et prend une barre de céréales avec toi, ton petit déjeuner étant par terre je ne veux pas que tu nous fasses une crise d'hypoglycémie à l'école".
Un peu comme pour appuyer ses propos, un bruit de Klaxon se fit attendre, il ne lui fallut qu'un regard furtif vers la fenêtre pour apercevoir le bus jaune.
C'est dans ce genre de cas qu'elle se félicitait de réveiller son fils 15 plus tôt que nécessaire ainsi, malgré l'incident il ne serait pas en retard et ne raterai pas le bus, ce qui n'étais jamais arrivé jusque-là et était bien déterminé à ce que ça n'arrive pas. Cependant, son fils n'était pas hors d'affaire, elle allait définitivement devoir commencer à l'inclure dans les tâches ménagères.
Heureux de pouvoir échapper à la situation qui commençait a devenir pesante, il se pressa à l'entrée pour mettre ses chaussures et prendre son manteau. Son cartable déjà positionné prêt de la porte, ce que vérifiait sa mère tous les soirs avant de l'envoyer se coucher, il n'eut plus qu'à aller embrassé rapidement ses deux mères avant de se diriger vers la porte.
"Au revoir mon poussin, travaille bien !".
Il lui sourit avant de disparaître.
Puis, comme tous les matins elle se positionna près de la fenêtre pour être sûr qu'Ethan soit bel et bien entrer dans le bus. Elle ne put s'empêcher de sourire légèrement lorsqu'elle le vit jeter un dernier coup d'œil vers la fenêtre avant de monter dans le véhicule, il savait qu'elle était la à le surveiller.
Ainsi, elle se retourna vers fiancée sans dire un mot le sourcil levé et un regard accusateur sur le visage.
"Oh allez Lo' ! Tu ne penses pas que tu exagères un peu ?, elle comprit que même si son fils avait pu y échapper elle n'aurait pas la même chance
"Il se servait de la serpillère comme d'un skateboard au-dessus de la tâche !, puis se rappelant que personne s'en était occupé elle se dirigea vers la cuisine pour s'en occuper.
Elle était bien contente de n'avoir pas suivi l'avis de sa compagne qui voulait du parquet, mais avoir opté pour du carrelage comme son l'instant lui avait suggéré, sinon cela fait bien longtemps qu'il aurait été foutu.
Regardant Lauren s'étalé à la corvée et se senti un tantinet coupable, elle décida de se diriger vers la cafetière pour lui faire du café.
"Il n'a que 7 ans ! Il l'aura le temps d'apprendre a faire ce genre de chose.
-Oh mais je le sais bien, mais toi ? Il vient de me dire que c'est en te regardant faire qu'il avait appris cette méthode... Dois-je commencer a me demander comment tu t'occupes du reste des tâches que je te donne a faire ? Après 8 ans de vie commune j'aurais pensé avoir détache sur toi.
-Tu l'as fait crois-moi si tu savais comment je m'occupais du ménage avant toi, j'ai bien peut que tu n'y survivrais pas !".
Ce commentaire arracha un sourire a Lauren qui venant de finir avec la serpillère et le sol de la cuisine, se lava rapidement les mains et se faufila derrière la blonde pour l'enlacer par derrière, ce qui lui valu un soupir de satisfaction de la femme.
"Je pensais que tu vivais dans ta voiture ?, doucement elle lui embrassa le cou.
"Hum... Il y avait ça aussi".
Se retournant elle retournait l'attention de la blonde en l'embrassant tendrement sur la bouche. Mais son regard tomba sur la petite horloge accroche sur le mur lui indiquant qu'elle était en retard pour le travail.
"Merde !, Commença-t-elle ce qui lui valut un regard sévère de la blonde qui se souvint qu'elle avait réprimandé son fils ce matin pour avoir utilisé l'expression, Il faut que je file si je ne veux pas avoir le capitaine sur le dos" dit-elle en se détachant a contre cœur de sa fiancé pour aller se préparer rapidement.
Une fois habille, coiffé et maquille, elle attrapa sa veste pour se diriger vers la porte. Rapidement Lauren lui lança une barre de céréales.
"Je viens de demander a notre fils de ne pas nous faire un malaise, essaye d'en faire de même, lança-t-elle avec un petit sourire.
"Bye, Lo' je t'aime !
-Bye Tamsin".
3. Chapter 3
_AN: Je sais que ça fait longtemps que j'ai pas posté mais j'ai été prise par les cours, mais aussi par la traduction du deuxième chapitre en anglais qui m'a pris pas mal de temps.
Ne vous inquiétez pas, il y aura plein de flash back expliquant ce qu'il s'est passé ces dernières années, d'ailleurs ce chapitre en est un =)._
Chapitre 3:
Souriant bêtement après que Tamsin ai quitté la maison au quart de tour, il lui fallut quelques secondes pour se reprendre. Soupirant de bien être cette fois-ci, elle prit le temps d'apprécier le présent. I ans elle n'aurait cru jamais tous ceux-ci possibles.
Perdue, seule et effrayé, c'est l'état d'esprit dans lequel elle était lorsqu'elle apprit qu'elle était enceinte d'Ethan. Repensant aux minutes où elle pensait à avorter, se disant que tout serait plus simple ainsi, personne n'en saurait rien et elle aurait pu continuer à vivre sa vie.
Et qu'elle vie ?
Celle d'une esclave pour les Fae, traitée comme un être inférieur malgré toute sa contribution à la science, tous les remèdes qu'elle avait trouvé et toutes les vies qu'elle avait sauvé.
Celle d'une femme brisé par un passé familial plus que douloureux, la prison, la guerre en Afghanistan, le Congo, la perte de sa petite amie puis le rejet violent de la femme qu'elle considéra longtemps comme le grand amour de sa vie.
Celle d'une femme froide qui se serait définitivement fermé au reste du monde après avoir tout perdu, pour être sûr de ne plus jamais souffrir comme elle l'a fait.
Sans s'en rendre compte elle avait commencé à faire les cent pas dans le salon, une habitude qu'elle avait lorsqu'elle était plongé profondément dans ses pensées ce qui faisait bien rire Tamsin, qui des fois prenait un malin plaisir à l'observer s'agiter, avoir d'intense débat mentale avec elle-même, caché dans un coin de la maison pour se moquer légèrement de sa "geekitude" qu'elle apprit à trouver irrésistible avec le temps.
Finalement elle décida de se poser sur le canapé et se mis à se remémorer, l'événement qui lui a permis de se retrouver là où elle était en ce moment.
Il a suffi d'une seule promenade...
(Flashback)
"Qu'est-ce que tu veux ?" Cette question se répéta dans sa tête telle un CD rayé, comme si plus elle se le demandait plus vite elle trouvera une réponse.
Malheureusement rien n'était aussi facile et elle se surprit a chassé avec son pouce des larmes qui se mirent à couler le long de ses joues sans son autorisation.
"Tu es faible, tu le sais ça ?" Se réprimanda-t-elle.
Mais plus elle essaya de combattre sa peine, plus celle-ci redoublait de force, sa détermination à ne pas s'effondrer ne servant que de nourriture au gigantesque trou qu'elle ressentait au fond de son être.
En moins de temps qui ne fallait pour le dire, ses bras et ses jambes n'eurent plus la force de la soutenir et elle se retrouva genoux par terre, essayant de retrouver son souffle face au déluge de souffrances et de détresses qui cherchait un moyen de sortir de son corps.
C'est ainsi qu'elle se mît à pleurer, assise par terre, le menton sur ses genoux et les mains recouvrant son visage, pendant ce qui sembla une éternité.
Même si elle paraissait pathétique de l'extérieur, pleurant comme une enfant à qui on refusait un jouet, chaque larme qu'elle relâchait était une libération.
Elle relâchât la tension et pression de ces deniers mois. Se vidant peu à peu d'un énorme poids qu'elle ne savait pas qu'elle possédait.
La dernière fois qu'elle eut une crise de ce genre était le soir de la mort de Nadia, après que Bo lui ai enfoncé sa dague dans l'estomac avant de s'enfuir la laissant seul avec le cadavre.
Une fois qu'elle eut finit de pleurer, sûrement parce qu'elle venait de vider toutes les larmes de son corps, elle se sentit incroyablement légère.
Comme une résurrection, prête pour un nouveau départ, une fois qu'elle eut mis le passé derrière elle, l'idée d'avancer dans la vie ne lui fut plus aussi peur, ne lui semblait plus aussi compliqué.
Relâchant un très léger sourire, tellement discret que personne n'aurait deviné que s'en était un, elle se releva et s'étira après s'être rendu compte qu'elle n'avait pas opté pour la plus confortable des positions durant sa breakdown.
Elle lança un regard sur le test toujours posé sur le bureau et soupira. Il fallait vraiment qu'elle commence à mettre ses idées au clair afin de prendre très rapidement des décisions, qui elle le savait l'affecteront le reste de sa vie.
Se sentant soudainement claustrophobique, elle se dirigea dans sa salle de bain afin de s'asperger d'eau sur le visage et effacer le fait qu'elle venait de pleurer.
Puis, après s'être regarder rapidement dans le miroir et expirer un bon coup, elle prit ses clés et sa veste, décidant qu'une bonne petite promenade ne pourrait pas lui faire de mal.
C'est ainsi, qu'elle se retrouva à errer dans les rues de son quartier au moment où le soleil se couchait. Il ne faisait ni chaud ni froid avec une légère brise qui la rafraîchit et lui fit le plus grand bien, c'était un temps tout simplement parfait.
Oubliant presque tous ses problèmes, elle se mît à observer ce qui l'entourait, le voisinage, les maisons, jardins, magasins qui bordait son appartement. Travaillant jour et nuit pour les Fae, elle n'avait jamais le temps de faire ce genre de chose, pour être tout à fait honnête cela ne l'intéressait pas non plus, son monde à elle était la science, la discipline pour laquelle elle consacrait bien volontiers tout son temps, aimant être dans le concret que son travail lui apportait, s'était la seule distraction dont elle avait besoin pour s'échapper de sa condition.
Laissant ses jambes la guider, elle ne fit pas attention où elle allait, juste continuant droit devant elle. L'idée qu'elle pouvait se perdre ne l'effleura pas un seul instant, le paysage était beaucoup trop intéressant. Comme pour essayer de comprendre un monde qu'elle avait quitté il y'a longtemps, elle observait chaque être humain que son regard croisait, se demandant s'ils savaient à quel point ils étaient chanceux de ne rien savoir à propos des Fae, d'être maître de leur propre vie, elle avait renoncé à ce privilège et en subissait les conséquences chaque jour.
"Heureux sont les ignorants" disait le dicton, elle ne pouvait qu'approuver.
Mais alors qu'elle observait une mère et sa fille jouant ensemble dans le jardin, elle éprouva un léger pincement au cœur et sans s'en rendre compte elle posa sa main sur son ventre.
Elle voulut se rapprocher de cet attendrissant spectacle comme attiré par une force magnétique mais elle se retrouva brusquement par terre bousculé par une énorme masse.
Secouée par l'interaction il lui fallut plusieurs secondes pour comprendre ce qu'il venait de se passer et prendre conscience que quelqu'un s'adressait à elle.
"Merde ! Je suis désole Lauren je ne regardais pas où est-ce que j'allais ! Tu vas bien ?" Demanda Dyson en lui proposant sa main pour l'aider à se lever.
Ne s'attendant pas à tomber sur le loup, la blonde ne dit rien, lui adressant simplement un léger sourire, pour le rassurer de son état, avant d'accepter sa main pour se relever.
Il la regarda un instant dans les yeux, comme s'il essayait de lire ses pensées avant de lui rendre son sourire. Il semblait sincèrement inquiet pour elle, ce qui eut l'effet de la réconforter un peu, ne sachant pas pourquoi elle se sentait en sécurité près de l'homme.
Un peu comme si après avoir essayé pendant presque deux ans de se supporter ils avaient fini inconsciemment par devenir ami, mais se rappelant avoir subi le traitement du silence de sa part également après l'incident avec Isaac, son corps se tendit.
« Non c'est moi, j'aurais dû faire plus attention désolé »
« Qu'est-ce que tu fais aussi loin du compound ? Je ne t'ai jamais vu te promener par ici », cette dernière réflexion poussa Lauren à regarder autour d'elle, se rendant compte qu'elle n'était pas loin du commissariat où Dyson travaillait. Elle se demanda soudainement depuis combien de temps elle traînait, dans sa contemplation elle avait perdu la notion du temps.
Voyant qu'elle n'était pas prête à répondre il se remit a parler.
« Peu importe, je suis bien content de tomber sur toi, j'avais envie de voir comment tu allais après les derniers événements de la semaine dernière malheureusement avec la Morrigan et sa nouvelle loi décrivant tous les humains comme des terroristes je n'ai pas eu une seule seconde à moi », son sourire semblait extrêmement sincère mais Lauren resta septique.
"Vraiment ?"
Il sembla comprendre sa méfiance et posa sa main son épaule pour lui montrer son affection.
« Je sais qu'on a jamais été en très bon termes mais avec tout ce qu'on a subi ces dernières j'ai appris à t'apprécier et à te respecter Lauren, je m'inquiète sincèrement pour toi. Je suis désolé de n'être pas passé prendre de tes nouvelles plutôt ».
Elle se détendît. Malgré toute la haine qu'elle avait pu éprouver pour le loup, elle aussi avait fini par le compter parmi ses amis. A partir du moment où il retrouvé son amour quelque chose avait changé en lui, surtout vis-à-vis des humains, il ne la traitait plus comme l'esclave des Fae qu'elle était mais comme une personne à part entière. Venant de lui, avec leur passé assez tendue, cela la touchait profondément. Elle avait été plus qu'heureuse de l'avoir autour d'elle ces derniers mois.
_Kenzi a beaucoup de mérites mais le plus grand est certainement d'avoir ramené l'ancien Dyson parmi nous._
_**Peut-être que je ne suis pas tout à fait seul après tout.**_
Souriant, elle posa doucement sa main sur la sienne, toujours positionné sur son épaule.
Au contact, l'expression du loup changea brusquement comme s'il avait été brûlé et il retira rapidement sa main, la regardant comme cherchant vraisemblablement une blessure ou cicatrice.
Surprise par sa réaction, Lauren fit un pas en arrière pour se protéger, elle eut soudainement peur qu'il l'attaque.
Mais en observant son expression, elle se rendit compte qu'il n'y avait rien d'hostile dans son regard, c'était un peu comme s'il avait subi un choc.
Ne comprenant pas ce qu'il venait de se passer, elle attendit qu'il dise quelque chose, qu'il lui explique. Levant la tête il la regarda doucement, on aurait dit qu'il essayait d'accepter une perturbante information.
A ce moment elle s'attendait à tout, mais il réussit tout de même à la surprendre.
"Tu es enceinte !"
(Fin du flashback)
Un léger bruit la soutira de ses pensées, son corps se tendit lorsque son odorat développé l'informa qu'une présence étrangère était proche. Son corps se mît instinctivement en alerte, devinant le danger.
Elle éclair doré lui traversa les yeux.
Se concentra sur son ouïe, elle essaya de deviner d'où venait le cliquetis qui l'avait perturbé, lorsqu'elle se rendit compte qu'il provenait de l'extérieur, devant la porte de l'entrée plus précisément, elle se leva brusquement pour attraper son portable qui était sur le comptoir de la cuisine.
Des gens s'introduisaient dans sa maison et à leur odeur, ils n'avaient rien d'humains...
End file.
| fanfiction |
Does increasing the entropy of a system cause it to absorb heat?
This is my first time posting here, so bear with me. It was stated (in this video: <https://youtu.be/7jT5rbE69ho?t=325>) (Watch about the next fifteen seconds, until 5:40) that an increase in entropy leads to a decrease in heat (or temperature or absorbs energy - unsure of the correct terminology). (If I'm understanding correctly.) Now, I've never taken a thermodynamics class or anything past high school chemistry, but this is a little confusing to me and I'm hoping to get an explanation. What follows below is my best attempt at understanding why. It is most likely mis-guided, so feel free to correct at will.
1. I understand that entropy can be partially understood as disorder. When the Helium-3 enters the Helium-4, that constitutes an increase in entropy.
2. The change in entropy is defined as Heat/Temperature (see below)
>
> Rudolf Clausius invented the idea of entropy in such a way that the change in entropy is the ratio of the heat exchanged in any process and the absolute temperature at which that heat is exchanged. That is, he defined the change in entropy DS of an object which either absorbs or gives off heat Q at some temperature T as simply the ratio Q/T.
>
>
>
3. I then figured that maybe the Q-T ratio (entropy) increased by the total energy (of the helium system) increasing, requiring it to pull heat from somewhere
Miscellaneous thought: My above reasoning confused me because I thought it required energy to decrease entropy locally (add order to a system), so it seems strange that a system increasing in entropy
(like my helium example) would absorb energy.
I consider watching any video a waste of time, so I'll be judging from your words alone. (Anyway, your question is essentially self-consistent, which is good.)
1. Yes, entropy is a measure of disorder (sort of).
2. No, $dS={\delta Q\over T}$ [only for ***reversible*** processes](https://en.wikipedia.org/wiki/Second_law_of_thermodynamics#Introduction).
3. And no, entropy is not the Q-T ratio for two reasons. First, because the above formula deals with infinitesimal increments and not with finite quantities. Second, because like I just said, that formula is not universally applicable.
All in all, the increase of entropy alone **is not** necessarily accompanied by the heat flow to the system. It may be so, but it may be otherwise. You may imagine pretty much any kind of possible outcome:
* You dissolve some $\ce{NH4NO3}$ in water (which surely increases entropy), and the beaker gets palpably cold. The system starts sucking heat from the surroundings, just like you anticipated.
* You mix your $\rm^3He$ with $\rm^4He$, and... *nothing* happens (except the increase in entropy, of course, but that's a thing you can't see or touch). There are no thermal effects to speak about, and hence no heat flow.
* You burn a candle in a closed vessel (supposedly, containing enough air), and guess what? Entropy increased, but heat is flowing *outside*.
As for your last remark: true, it takes some energy to decrease entropy locally (say, in your fridge). But in doing so, we inevitably increase entropy *elsewhere*, so the overall balance is positive.
So it goes.
| stackexchange/chemistry |
What does Ehrenfest's theorem actually mean?
I am told that Ehrenfest's theorem, applied to a physical observable $\hat A$, is:
$$\frac{d\langle\hat A\rangle}{dt}= \frac{i}{\bar h}\langle[\hat H,\hat A]\rangle$$
I don't understand how to use this equation or what it means intuitively.
The equations describes the time evolution of an expectation value of an operator (which is the expectation value of the value measured when doing many measurements on identically prepared systems). The expectation values are taken with respect to the state of the system at time $t$. This answer will show how to use the Ehrenfest theorem by applying it to an example. As for the intuition: Intuition is always a dangerous business with respect to quantum mechanics.
In some cases, you can use the Ehrenfest theorem to calculate the evolution of expectation values without solving the Schrödinger equation, if the commutator results in a sufficiently simple operator, or at least get results for the behaviour of sharp wave packets. Consider for example the Hamiltonian of a particle in a potential $V(x)$
$$H = \frac{p^2}{2m} + V(x).$$
Then you can compute $[H, x]$ and $[H, p]$:
$$[H, x] = \frac{1}{2m} [p^2, x] = \frac{p}{2m} [p,x] + \frac{1}{2m} [p,x] p = -i\hbar \frac{p}{m},$$
$$[H, p] = [V(x), p] = [V(x), -i\hbar\nabla] = i\hbar \nabla V(x).$$
Plugging this in the Ehrenfest theorem gives the following equations of motion for the expectation values of $x$ and $p$:
$$d\_t \left< p \right> = - \left<\nabla V(x)\right> $$
$$d\_t \left< x \right> = \frac{p}{m} $$
Those are almost the classical equations of motion for position and momentum. The only difference is that the "force" $-\nabla V(x)$ is averaged over the state and not taken *at* the central position, for a wave packet which is small compared to the variation scale of $V(x)$ this therefore leads to the classical equations of motion in good approximation. So we have used the Ehrenfest theorem to show how and under which circumstances Newtonian mechanics arise from quantum mechanics.
There is a special case where the resulting equations of motion can be solved without reference to the state, namely the harmonic oscillator $V(x) = \frac 1 2 k (x-x\_0)^2$, here we get
$$\left< - \nabla V(x)\right> = -k \left<x - x\_0\right> = -k\big(\left<x\right> - x\_0\big),$$
so the equations of motion for the averages are exactly the classical equations of motion for the harmonic oscillator.
| stackexchange/physics |
the mandate of any professional society is to work for the welfare of its members and the profession it serves . to this end , it organises many activities and programmes , and occasionally involves people from allied and other professions . the choice of activities carried out depends on the constitutional mandate , the vision of the president and the committee and most importantly , the needs of the community .
associations have had a role in advocacy , creating a community of learning , mentoring new professionals , policy making and creating guidelines and practice parameters ( chamberlain et al .
associations are known to conduct research , gather information and present it to the authorities and thus shape policy making ( schwartz , 1984 ; scott et al . , 2008 ) .
two areas of work , which need to be added are :
accreditation of the society as a means of certifying for continuing professional development ( cpd ) ; andan active role in creating societal awareness of suicide .
accreditation of the society as a means of certifying for continuing professional development ( cpd ) ; and an active role in creating societal awareness of suicide .
a doctor needs to be a lifelong learner and the symposia , and academic activities provide avenues for enriching the professionals knowledge and skills .
however our regulatory body , the medical council of india ( mci ) , has mandated that doctors need to renew their licence to practice every 5 years .
further a criterion for renewal is that the specialist should have attended academic activities to upgrade his proficiency . to this end
, they laid a rule requiring 30 credit points to be earned in 5 years . while this is with regard to academic activity , mumbai , in the previous year , that is , 2009 ,
had witnessed a surge of suicide in children and adolescents . in response to this crisis ,
the bombay psychiatric society ( bps ) needs to create awareness about suicide and its prevention in children and adolescents .
education is structured and follows rules and regulations . in contrast , specialists have to engage in activities , which will not only keep them updated with the cutting edge of research and technology , but also enhance their leadership , administrative and research skills .
this learning is therefore beyond the concept of simply continuing medical education as it encompasses personal and professional development .
thus , one needs to plan for autonomous , self - directed learners who have a wealth of knowledge .
new learning occurs in response to perceived need , which requires practical application of new skills or knowledge , and this new learning is built on previous knowledge and experiences ( bennett et al . , 2000 ) .
in fact a needs analysis of the members would be the first step in planning cpd activities .
this is followed by deciding learning strategies and eventually assessing if the objectives are met ( ghosh , 2008 ) .
globally various medical institutes , professional associations , non - governmental organisations , pharmaceutical and other industries have been known to be providers for cpd .
while in some countries , medical institutes provide systematic cpd activities , in many countries this is now structured by private organisations . however , there is wide variation in the availability and accessibility of cpd activities .
some medical bodies have insisted on identifying the accredited courses attended , some have looked at recertification of specialists
. another important method of self - monitoring by the professional is by creating a portfolio of activities , which would prove the efforts at self - improvement . to ensure the quality of education ,
the world federation of medical education has provided a framework , which can be used by all ( wfme , 2003 ) . addressing the predisposing , the enabling and the reinforcing factors
while the predisposing factors act as catalysts influencing the specialist to change , the enabling factors facilitate the new learning in practice , and the reinforcing factors reflect the positive outcome and , therefore , maintain and enhance the changes . motivating factors for the specialist for participating will be the choice of topic for the symposium or seminar .
while this has been the practice in our society , in response to the requirement of the mci , we need to make modifications .
realising the exponential growth of information and the need for optimum care of patients , mci has insisted on doctors keeping abreast of new information , skills and technology . as a proof of this they needed to earn credit points : 30 points over 5 years ( imc , 2002 ) .
these could be earned by attending conferences , symposia , writing papers , chapters and/or being a teaching faculty .
this learning occurs formally through organised activities and informally by discussion with colleagues and reflection on one 's practice .
while cpd has professional and regulatory aspects , it should not be reduced to a mere formality of collecting credit points .
involvement of peers has shown to be beneficial in this respect ( bouch , 2006 ) .
bombay psychiatric society should be an institution that facilitates this process by accrediting the learning of its members .
the society thus needs to get registered with the maharashtra medical council*. once this status is achieved , the details of programmes and speakers have to be sent to the council , which would decide on the number of credit points to be allocated .
it is necessary to maintain an attendance record , and there is a possibility of an observer of the council attending these programmes .
these measures would result in not only good attendance , but also benefit our members .
however , there does remain an element of doubt on the efficacy of learning that occurs .
many have therefore suggested that assessment of the learning would ensure motivation to learn and improve the quality of learning .
we need to work further and develop a system for continuous assessment of needs , planning objectives and implementing different programmes to achieve our needs .
while it may be viewed as bothersome , assessment of the learning is imperative as it is that which often drives learning .
when children believe that death is the only option for them , it is indeed a sad state of affairs .
worldwide suicide is the second leading cause of death in teenagers ( hawton et al . , 2012 ;
the aetiology of suicide and self - harm is multi - factorial with genetics , psychosocial , familial and cultural factors playing a role . in this age group ,
the role of media and the spread of contagion suicide is also a cause of concern . due to a wide variety of factors leading to suicide
evidence - based activities that work in prevention of suicide are targeting different groups and are classified as universal , selective and indicated interventions .
nearly 28 countries around the world have a national suicide prevention strategy ( who , 2014 ) .
being an important but underreported and preventable cause of death , a large amount of research and activities are working in prevention .
the international association of suicide prevention marks 10 september as the world suicide prevention day . over time
, there has been a legal shift with many countries decriminalising suicide and india too is following suit .
most plans which concentrate on youth suicides have components of health promotion , prevention , intervention and postvention .
prevention programmes have been implemented in various settings such as schools , communities and in health care settings .
the prevention activities currently implemented are such that they address increasing awareness , screening for at risk , gatekeeper philosophy , creating peer leadership , and skills training ( katz et al . , 2013 ) .
in the year 20092010 , there was a sharp rise in child and adolescent suicide in mumbai and in the month of january , 2010 , there were 32 cases ( ahmed , 2010 ) .
it is known that indian society places a high premium on academic achievement and underachievers suffer from shame , low self - esteem and other psychopathology ( shah , 2005 ) .
this troubling crisis evoked strong reaction from the public , and they demanded appropriate health strategies from our fraternity . in response to the unrest in the community ,
our society should decide to take a proactive step in organising a campaign for suicide prevention .
on one hand , we will work to increase awareness of suicide , the causes , and the ability to identify predisposing and precipitating factors , and also facilitate seeking of help from a professional .
it is imperative that we burst the myths of suicide and clear misconceptions about depression , its treatment and outcomes .
research has shown that teachers have poor knowledge of mental illness and have reported increased motivation in working with children following training .
we , therefore , have to empower teachers and students to listen , identify high - risk situations and take proactive measures .
prevention is either to the targeted high risk or to the general pool of children and adolescents .
one envisages that in our setting working with the department of education , we could work with schools to implement the programme .
mental health professionals would visit schools and conduct workshops for students and staff regarding the above issues . to ensure uniformity and facilitate easy availability of resources , a common presentation would be made , which could be used by our members .
it is known that prevention programmes do help in reducing suicide ( aseltine and de martino , 2004 ; mann et al . , 2005 ) .
longer and sustained programmes would be more effective ( aseltine and demartino , 2004 ) .
besides the prevention of suicide , this initiative would provide an opportunity to create a link between schools and mental health professionals .
considering the stigma associated with mental health and visiting psychiatrists , most schools , teachers and parents resist taking help from services available .
however with a background of an alarming rise in suicide , the resistance of the teachers and parents is likely to get lowered .
it is for us to convert this crisis into an opportunity for partnering with the education system in building resilience in our children .
after all emotional well - being is a known protective factor in children ( hawton et al . , 2012 ) .
simultaneously , it would indeed be beneficial to interact with people in the media and discuss their role , especially the method of reporting such cases .
research from our country has revealed that most reporting does not follow international standards in reporting such cases ( chandra et al . , 2013 ) .
sensible reporting prevents the contagion effect seen so often ( chandra et al . , 2014 ) .
thus such a campaign , publicised through various media channels , would be a valuable tool to combat the rising tide of suicide .
today , we need to respond to the local crisis and as a fraternity contribute to their well - being . our association has always worked tirelessly to serve the fraternity , the profession and the community .
individually each of us had various academic and networking benefits arising out of our membership .
it is imperative that we too participate proactively in the programmes planned so as to reap benefits for the collective good of all and for the society and the community .
every professional association has to choose a path based on the vision and the context of the times .
the crucial roles that need to be carried out in the present context are two - fold : one directly concerned with members and their personal and professional development ( cpd ) , and other related to the mental health of our society at large ( suicide prevention in children and adolescents ) . with good planning , judicious use of resources and a collaborative effort we could be successful in achieving our goals
. our society can be accredited by the medical council , and the activities would be awarded credit points .
these will ensure ease in recertification and also aid in the enhancement of professional knowledge and skills of our members .
our work in the field of suicide prevention in children and adolescents highlights our commitment to the community and our responsibility of ensuring that every child counts .
let our society and members prove that we care , not only for ourselves , but also for our profession and above all for those we serve .
together we can ensure that we are a well - qualified fraternity , which will thoughtfully create programmes and activities , which will have a positive ripple effect on its members and the community .
let us arm ourselves with knowledge and skills that can be translated towards enhancing the quality of our practice .
let us also remember those suicide in general and those in children and adolescents , in particular , are preventable and mental health professionals have a major role in their prevention .
how do we ensure that the cpd actually leads to improvement in practice in our context?what method of suicide prevention is effective and also cost efficient in our school settings?how can mental health professionals partner with other sectors in suicide prevention ?
how do we ensure that the cpd actually leads to improvement in practice in our context ?
what method of suicide prevention is effective and also cost efficient in our school settings ?
henal shah md has done her mbbs from tn medical college and her master 's in psychiatry ( md ) from gs medical college and kem hospital , mumbai , india . following this she has had experience at the child psychiatry department of the royal hospital for sick children at glasgow .
she has obtained her fellowship in medical education from gsmc - fri ( 2006 - 2008 ) and from faimer , philadelphia ( 2008 - 2010 ) , a master 's ( mhpe ) in the same from the university of maastricht , netherlands .
her current designation is professor ( additional ) in the department of psychiatry at the topiwala national medical college & byl nair ch .
she is keenly interested in the field of child and adolescent psychiatry and presented and published in this field | pubmed |
the cyg ob 7 molecular cloud is a giant molecular cloud ( gmc ) located at a distance of 800 pc @xcite in the direction of the cygnus region ( e.g. , * ? ? ?
the cloud has an apparent size of @xmath7 centered at @xmath8 and @xmath9 , and has a total molecular mass of @xmath10 @xmath1 @xcite .
figure [ fig : location](a ) shows the entire extents of the cloud .
there are two well - known star forming sites in the cloud .
one is the region known as ldn 988 @xcite where a number of pre - main sequence stars are forming ( e.g. , * ? ? ?
* ; * ? ? ?
* ) , and the other is a massive dense core known as the northern coal sack ( ncs ) producing a massive class 0 object @xcite . except for these two regions , star formation is much less active in this cloud compared to other gmcs with a similar mass ( e.g. , orion a , * ? ? ?
* ) , and there is no extended h regions associated with the cloud .
the cyg ob 7 molecular cloud is also characterized by its low temperature ( @xmath11 k ) and a large turbulence ( @xmath12 km s@xmath13 in @xmath14co , * ? ? ?
* ) , and has been regarded as a gmc in an early stage of cloud evolution prior to an active massive star formation . in the all - sky visual ( vis ) and near - infrared ( nir ) extinction maps derived from the digitized sky survey ( dss , * ? ? ? * ) and the 2 micron all sky survey ( 2mass , * ? ? ?
* ; * ? ? ?
* ) , we found a massive dense core in the northern part of the cyg ob 7 molecular cloud . in the dss - based extinction map ,
the core is cataloged as tguh 541p1 by @xcite which corresponds to the eastern end of the dark nebula ldn 1004 @xcite . in the optically thinner 2mass - based extinction map , it splits into several smaller condensations such as
the one numbered no.2996 in the catalog compiled by @xcite .
hereafter , we shall refer to this core as l1004e in this paper . in figure
[ fig : location](b ) , we show the location of l1004e in the @xmath15 map produced by @xcite .
as seen in the figure , the core is very large and is the densest in the entire cyg ob 7 cloud with the maximum @xmath15 of @xmath16 mag .
based on the @xmath15 map , we estimate its total mass to be at least @xmath17 @xmath1 . in spite of its huge mass ,
l1004e is not accompanied by any h regions or bright infrared sources representing massive young stellar objects ( ysos ) , indicating that l1004e is a core in an initial stage of massive star formation or cluster formation .
l1004e should provide us a precious opportunity to investigate the initial conditions of such massive cores , because the initial conditions can be easily destroyed by the strong stellar wind and uv radiation from ob stars soon after they are formed in the cores .
the angular resolutions of the 2mass- and dss- based extinction maps ( @xmath18 ) that we used to find l1004e are not sufficient to resolve the structure of the core .
we therefore carried out molecular line observations at a high angular resolution using the 45 m telescope ( hpbw@xmath19 at 115 ghz ) at nobeyama radio observatory ( nro ) , which should also provide us information on the velocity field of the core .
the purpose of the present paper is to report results of the observations with the 45 m telescope .
we observed the core in various molecular lines such as c@xmath4o .
the observational procedures are described in section [ sec : observations ] . based mainly on the c@xmath4o data
, we analyzed the spatial and velocity structure of the core , and we also searched for candidates of ysos associated with the core using some infrared point source catalogs ( pscs ) open to the public .
we found that the core has a huge total mass of @xmath0 @xmath1 and is consisting of a number of massive filaments and core - like structures with a mass of @xmath6 @xmath1 , which appears similar to the filamentary structures recently evidenced in other molecular clouds ( e.g. , * ? ? ?
to our surprise , some of the filaments are apparently colliding against each other , and some candidates of ysos are located around the intersections of the filaments as if they were induced by the collisions of the filaments .
we present these observational results in section [ sec : results ] . in order to understand how the colliding filaments were formed in the core , we performed numerical simulations of core evolution assuming a model core with an initial mass and size similar to those of l1004e . in section
[ sec : discussion ] , we describe the method and results of the simulations , and discuss what initial conditions are needed for the formation of such colliding filaments which should play an important role for massive star formation and cluster formation in massive cores .
conclusions of this paper are summarized in section [ sec : conclusions ] .
observations were carried out with the 45 m telescope at nro .
we observed thirteen molecular lines in total , i.e. , @xmath20co@xmath21 , @xmath14co@xmath21 , c@xmath4o@xmath21 , cs@xmath22 , c@xmath23s@xmath22 , hco@xmath24 , h@xmath14co@xmath24 , hc@xmath25n@xmath26 , ccs@xmath27 , nh@xmath28 , nh@xmath29 , nh@xmath30 , and nh@xmath31 . the @xmath14co@xmath21 emission line was observed for 4 days in 2010 january , and the other lines were observed for 22 days in the period between 2009 february and 2009 may .
our observations can be divided into two modes .
one is the mapping observations to reveal the entire molecular distributions of l1004e , and the other is one - point observations made only toward the protostellar candidate iras 21025 + 5221 found in the core .
the mapping observations were carried out with 6 molecular lines as summarized in table [ tab : mapping_obs ] .
we used the 25 beam array receiver system ( bears ) to observe the emission lines of co and its isotopes .
we also used an sis receiver named s40 to observe the hc@xmath25n and ccs lines at 45 ghz as well as a cooled hemt receiver named h22 to observe the nh@xmath32 line at 24 ghz .
spectrometers were auto - correlators ( ac ) covering a band - width of either 32 mhz or 16 mhz with 1024 channels with a frequency resolution of 38 khz or 19 khz , respectively .
we mapped an area of @xmath33 around the core using the on - the - fly ( otf ) technique @xcite , and calibrated the spectral data with the standard chopper - wheel method @xcite .
reference positions ( i.e. , the emission - free off positions ) were ( @xmath34 , @xmath35)@xmath36 ( 20@[email protected]@xmath39 , 51@xmath4047@xmath4102@xmath42 ) , ( 20@[email protected]@xmath39 , 51@xmath4048@xmath4100@xmath42 ) , ( 20@[email protected]@xmath39 , 51@xmath4036@xmath4159@xmath42 ) , ( 21@[email protected]@xmath39 , 52@xmath4033@xmath4147@xmath42 ) for the @xmath20co , c@xmath4o , nh@xmath25 , and the other emission lines , respectively .
we used the reduction software package nostar available at nro to subtract a linear baseline from the raw data and to resample the spectral data onto @xmath43 or @xmath44 grid along the equatorial coordinates .
we then applied a correction for the main beam efficiencies which vary in the range @xmath45 % depending on the frequencies to the baseline - subtracted data in order to scale them to units of @xmath46 .
further corrections for the side - band ratio were applied for the data obtained by bears , because it is a double - side - band ( dsb ) receiver .
velocity channels are resampled onto 0.1 km s@xmath13 or 0.2 km s@xmath13 velocity grid , which resulted in a velocity resolution of @xmath47 km s@xmath13 .
noise levels of the resulting data are @xmath48 k at these velocity resolutions as summarized in table [ tab : mapping_obs ] .
one - point observations toward iras 21025 + 5221 were made with molecular lines as summarized in table [ tab : point_obs ] .
for these observations , we used waveguide - type dual - polarization sideband - separating sis receivers called t100h / v @xcite to observe cs , c@xmath23s , hco@xmath49 , and h@xmath14co@xmath49 lines , and also used the h22 receiver to observe four nh@xmath50 lines of @xmath51 transitions .
spectrometers were acousto - optical spectrometers ( aoss ) with a bandwidth of 40 mhz and a frequency resolution of 37 khz corresponding to a velocity resolution of @xmath52 km s@xmath13 .
the baseline removal was done by using the reduction package newstar .
the data were scaled up to units of @xmath46 in the same way as for the mapping data .
the system noise temperatures @xmath53 were in the range @xmath54 k depending on the receivers including the atmosphere . pointing accuracy was better than @xmath55 as was checked by observing the sio maser t - cep at 43 ghz every 2 hours during the observations .
figure [ fig : ii_maps ] shows the integrated intensity distributions of the observed emission line listed in table [ tab : mapping_obs ] . as seen in the figure , the c@xmath4o map in panel ( a ) reveals the filamentary structure of the core . on the other hand , the @xmath14co map in panel ( b ) shows rather flat distribution , because the line is heavily saturated .
the @xmath20co emission line ( not shown ) extends all over the mapped area , and it appears much flatter .
the other molecular emission lines , ie . , hc@xmath25n , css , and nh@xmath25 in panels ( c)(e ) , show clumpy distributions , and they are concentrated especially around iras 21025 + 5221 . in figure [
fig : w3 ] , we show the 12 @xmath56 image taken by the wise satellite .
it is noteworthy that the c@xmath4o map in figure [ fig : ii_maps](a ) is very similar to the dust distribution revealed by wise , indicating that the molecular line is a good tracer of the total molecular column density @xmath57 . in order to estimate the mass of l1004e
, we therefore derived @xmath57 at each observed position by analyzing the c@xmath4o data using a standard method assuming the local thermodynamic equilibrium ( lte , e.g. , see * ? ? ?
* ) . for this
, we first estimated the excitation temperature of c@xmath4o from the @xmath20co spectra at each observed position assuming that the @xmath20co emission line is optically very thick .
we then calculated @xmath58(c@xmath4o ) the optical depth of the c@xmath4o emission line and its column density @xmath59(c@xmath4o ) , and converted @xmath59(c@xmath4o ) to @xmath59(h@xmath60 ) using an empirical conversion relation found by @xcite .
we summarize the method in the appendix .
the analyses of the c@xmath4o and @xmath20co data infer that l1004e has a huge mass of @xmath61 @xmath1 within the region mapped in c@xmath4o ( figure [ fig : ii_maps](a ) ) .
this mass is much higher than other single dense cores found in low - mass star forming regions such as taurus ( @xmath62 @xmath1 , * ? ? ? * ) or in massive star forming regions found in the vicinity of some h regions ( @xmath6 @xmath1 , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) suggesting that l1004e may comprise a number of distinct smaller cores . actually , as shown in section [ subset : filaments ] , l1004e is very likely to consist of several massive filaments having a mass of @xmath6 @xmath1 .
it is also noteworthy that the c@xmath4o column density of l1004e is very high compared with cores in other star forming regions .
in fact , we found that the c@xmath4o emission line which is often optically thin ( @xmath63 ) in molecular clouds has a high optical depth of @xmath64 at the peak intensity positions in figure [ fig : ii_maps](a ) .
figure [ fig : column_density ] shows the frequency distributions of @xmath59(c@xmath4o ) in l1004e compared with those of hlc 2 and ldn 1551 observed by the same nro 45 m telescope ( the data of these regions are open to the public at the website of nro , http://www.nro.nao.ac.jp/@xmath65nro45mrt/results/data.html ) . as seen in the figure , l1004e exhibits much higher @xmath59(c@xmath4o ) than the others .
on the basis of statistical studies of dense cores in taurus , @xcite showed that all of the cores with column density greater than @xmath59(h@xmath66)@xmath67 @xmath68 are accompanied by ysos selected from iras sources , and they suggested that the cores start to form stars immediately as soon as the column density exceeds the value .
this critical value of @xmath59(h@xmath66 ) corresponds to @xmath59(c@xmath4o)@xmath69 @xmath68 ( see equation ( [ eq : nh2 ] ) in the appendix ) .
as shown in the next subsection , there are only two iras sources as promising candidates of protostars in this massive core , suggesting that the core may be in a stage prior to an active star formation or may have just initiated forming stars .
l1004e is also characterized by its low temperature . within the observed region ,
the excitation temperature derived from the @xmath20co emission line varies in the range @xmath70 k with a mean value of @xmath71 k , which is lower than those in other gmcs with a similar size ( e.g. , @xmath72 k , * ? ? ?
* ) , but close to those in smaller dark clouds such as the one in taurus ( e.g. , @xmath11 k , * ? ? ?
in addition , there is a clear tendency that @xmath73 is lower in the central part of the core than in the outskirts by a few kelvin .
similarly , the observed line width measured by applying a single gaussian fitting to the c@xmath4o emission line varies in the range @xmath74 km s@xmath13 with a mean value of @xmath752 km s@xmath13 in the region surrounded by the lowest contour in figure [ fig : ii_maps](a ) , and it tends to be smaller where the c@xmath4o intensity is higher , suggesting dissipation of turbulence in the central part of the core .
we summarize the global properties of l1004e found through the above @xmath20co and c@xmath4o analyses in table [ tab : core ] . finally , we show the velocity distributions of molecular gas in a series of channel maps in figures [ fig : channelmap_13co_0][fig : channelmap_c18o_1 ] . molecular emission lines , especially the @xmath20co line ( not shown ) , spread over a wide velocity range of @xmath76 km s@xmath13 , but the other emission lines concentrate in a rather limited range around @xmath77 km s@xmath13 ( see figure [ fig : channelmap_13co_0 ] displaying the @xmath14co distributions ) .
figures [ fig : channelmap_13co_1 ] and [ fig : channelmap_c18o_1 ] show channel maps of @xmath14co and c@xmath4o , respectively , produced at a higher velocity resolution of 0.5 km s@xmath13 .
these figures show that denser parts of the core exhibits an elongated structure , and the core apparently consist of a number of filaments having slightly different velocities .
the filaments are clearer in the c@xmath4o channel maps in figure [ fig : channelmap_c18o_1 ]
. we will attempt to identify the individual filaments and will further analyze their stability and interactions in section [ subset : filaments ] . in order to search for ysos in the observed region , we selected candidates of ysos in the iras psc using the criteria suggested by @xcite for a search of ysos in the taurus cloud complex : we selected sources detected at least 3 bands including 25 @xmath56 and 60 @xmath56 satisfying the conditions log@xmath78 and log@xmath79 where @xmath80 means a flux density at 12 @xmath56 , and so on . as a result , we found only 2 iras sources in the observed region .
they are iras 21005 + 5217 and 21025 + 5221 whose properties are listed in table [ tab : iras ] . both of the iras sources have a cold fir spectra typical of ysos ( e.g. , * ? ? ?
* ) , having a total far - infrared ( fir ) luminosity @xmath81 and @xmath82 @xmath83 .
note that these are the bolometric luminosities detected only in the four iras bands ( including the correction for wavelengths longer than100 @xmath56 , * ? ? ?
* ) , and the flux in the wavelengths shorter than 12 @xmath56 is not included .
we further searched for ysos in the wise psc using the selection criteria suggested by @xcite , which is to select candidates of class i and class ii sources @xcite from the wise psc .
the criteria require detection in the wise 3.4 @xmath56 , 4.6 @xmath56 , and 12 @xmath56 bands with rather complex limitations in magnitudes and colors in the 3 bands to exclude non - ysos objects such as galaxies , active galactic nuclei ( agns ) , unresolved knots of shock emission due to outflows , and so on ( for details , see the appendix of * ? ? ?
* ) . as a result
, we found a score of candidates for class i or class ii sources in the observed region , but they are mostly located outside of the denser parts of the core , suggesting that many of them are the sources either in the foreground or background , not having physical association with the core .
we should note , however , that there may be more faint ysos in the wise psc , which were excluded by the tight selection criteria of @xcite . as they state in their paper , it is difficult in general to establish definite criteria to select ysos perfectly .
their criteria have a strong restriction especially on the magnitudes of the sources in order to exclude agns , i.e. , the apparent magnitudes at 3.4 @xmath56 and 4.6 @xmath56 have to be brighter than 14.0 and 13.5 mag , respectively ( see their section a.1 ) .
if we disregard these restrictions to exclude agns , we would find more candidates of faint ysos .
actually , we found a score of such faint sources lying along the filaments of the core , which are likely to be ysos forming therein . in the original wise psc , however , it seems that there are a certain fraction of false detections probably caused by the algorithm to extract point sources from the wise images .
in order to avoid such false detections , we checked by eyes the locations of the point sources on the wise images , and selected only those having an apparent counterpart at least in one of the four band images of wise ( i.e. , 3.4 , 4.6 , 12 , and 22 @xmath56 ) . as a result
, we found 83 candidates of ysos ( i.e. , 50 class i sources and 33 class ii sources ) within the area mapped in c@xmath4o including the above faint sources without the restrictions to exclude agns . the 2 iras sources are also included in these numbers because they have a counterpart in the selected wise sources .
we show locations of the these sources in figure [ fig : ysos ] , and we shall regard them as ysos forming in l1004e . here
we attempt to estimate the star formation efficiency ( sfe ) of l1004e .
a certain fraction of the 83 sources should be agns or ysos unrelated to the core , but for simplicity , we shall assume that all of them are ysos forming in the core .
we also assume that their average mass is @xmath84 @xmath1 which is the mean value of stars following the salpeter s mass function ( @xmath85 , * ? ? ?
* ) over the range @xmath86 @xmath1 .
these assumptions yield an estimate of the sfe of only @xmath87 % , because the total molecular mass of the core is @xmath88 @xmath1 ( see table [ tab : core ] ) .
this value of sfe is much lower compared with other massive cores forming clusters ( e.g. , sfe@xmath89 % on the average , * ? ? ?
note that this is the maximum estimate for the sfe , because a certain fraction of the wise sources should be unrelated to l1004e . in an extreme case ,
if we take that only the 2 iras sources and several bright wise sources which are located where the c@xmath4o emission is strong are promising ysos forming in l1004e , a very low sfe of only @xmath90 % would inferred , which should be the minimum estimate of the sfe in l1004e .
we found that the 2 iras sources selected as candidates of ysos have a counterpart not only in the wise psc but also in the 2mass psc , as summarized in table [ tab : counterparts ] .
iras 21025 + 5221 is probably a younger yso than iras 21005 + 5217 , because it is not detected in the @xmath91 and @xmath92 bands of 2mass , while iras 21005 + 5217 is not detected in the iras 100 @xmath56 band . in order to better access the stellar properties of these sources such as the ages , masses , and luminosities , we employed a recent stellar model developed by robitaille et al . @xcite .
the model was first developed by @xcite , and it comprises several parameters for the central star , circumstellar disk , and envelope , to calculate the spectral energy distributions ( seds ) for a wide range of wavelengths that can be compared with the observations .
tools for the model fitting are available on their website ( http://caravan.astro.wisc.edu/ ) which provide us 10,000 sets of the model parameters to fit observational data sorted according to the resulting @xmath93 .
we utilized their tools on the web to fit the seds of the 2 iras sources using the observed parameters listed in tables [ tab : iras ] and [ tab : counterparts ] . resulting seds of the model best fitting
the data are shown in figure [ fig : sed ] , and some of the best model parameters with the minimum @xmath93 are summarized in table [ tab : modelpara ] .
the @xmath94 values in the first column of the table are the fitted total extinction along the line - of - sight to the stellar envelope , which is consistent with what we would expected from the observed column density of c@xmath4o .
the other parameters ( age , mass , and luminosity ) are the best fitting parameters for the central star .
looking into the best 10 sets of the model parameters with the smallest @xmath93 , these parameters summarized in the table seem to be well determined with small variations in the case of iras 21005 + 5217 , while the parameters are rather ambiguous in the case of iras 21025 + 5221 varying in the range @xmath95 yr , @xmath96 @xmath1 , and @xmath97 @xmath83 , which is mostly due to the lack of the data points in the @xmath91 and @xmath92 bands ( there are only the upper limits for these data points ) . in any case , iras 21025 + 5221 is obviously younger than the other source .
we found that iras 21025 + 5221 is accompanied by a small and well - defined molecular condensation which should be the direct parental core of the iras source , while the other iras source is not accompanied by such a very evident condensation .
figure [ fig : iimaps_iras21025 ] displays the close up view of the condensation traced by some molecular emission lines , and figure [ fig : sample_spectra ] shows spectra of various molecular lines observed toward the iras source . as seen in figure [ fig : iimaps_iras21025 ] , the condensation is evident especially in hc@xmath25n , ccs , and nh@xmath25 .
ratio of the nh@xmath98 and @xmath99 emission lines infers the gas temperature of the condensation of @xmath100 k ( e.g. , * ? ? ?
* ; * ? ? ?
* ) , which is close to the excitation temperature @xmath101 k derived from the @xmath20co emission line .
as shown in section [ subset : filaments ] , we estimate the total mass , radius , and mean molecule density of the condensation to be @xmath102 @xmath1 , @xmath103 pc , and @xmath104 @xmath105 ( see no.1 in table [ tab : filaments ] ) , respectively , based on the c@xmath4o data in the same way as described in section [ sec : distributions ] .
note that the condensation is accompanied by iras 21025 + 5221 and many other faint ysos selected from the wise psc , indicating that the condensation is probably a young dense core that has just initiated to form a star cluster .
the idea that the condensation is very young can be supported also by the ccs and hc@xmath25n data .
it is known that these molecules are abundant in an early stage of chemical evolution of dense cores ( @xmath106 yr ) , and they rapidly disappear along with the core evolution ( @xmath107 yr , * ? ? ? * ; * ? ? ?
based on the ccs and hc@xmath25n spectra shown in figure [ fig : sample_spectra ] , we calculated the fractional abundances of these molecules , i.e. , @xmath108 where @xmath109ccs or hc@xmath25n , using the same method as ( * ? ? ? *
see their section 3.2 ) , and we found @xmath110 and @xmath111 .
we compare the results with those measured in dense cores in other star forming regions as well as with a model calculation performed by @xcite in figure [ fig : abundances ] which is quoted from figure 9 of @xcite who studied starless cores in the polaris cirrus ( see their table 9 for data points of the other cores ) .
there is an apparent tendency in the figure that data points for dense cores not associated with ysos ( represented by the open circles ) are located in the upper - right side of the diagram having higher @xmath112 and @xmath113 , while those associated with ysos ( filled circles ) are more widely distributed in rather bottom - left side .
it is interesting to note that the condensation associated with iras 21025 + 5221 ( the open square labeled l1004e ) is located between the two distributions , suggesting that the condensation is a young core which has just started star formation .
finally , we should note that there are some noticeable features in a series of spectra shown in figure [ fig : sample_spectra ] .
most of the spectra have a peak radial velocity of @xmath114 km s@xmath13 which should represent the systemic velocity of gas around iras 21025 + 5221 .
however , the hco@xmath115 and cs emission lines exhibit a double - peaked profile with a greater blue - shifted velocity component .
such a profile is often seen around protostars in optically thick emission lines like hco@xmath115 , and is considered as a sign of collapsing motion of dense cores ( e.g. , * ? ? ?
it is also noteworthy that the @xmath20co emission exhibits a very broad line width extending over the velocity range @xmath116 km s@xmath13 .
this could be due to a molecular outflow possibly associated with iras 21025 + 5221 , although it is difficult to confirm its red and blue shifted wings because the @xmath20co line around the iras source is heavily contaminated by the emission from the diffuse ambient gas over a wide velocity range ( especially at @xmath117 km s@xmath13 ) .
the wing - like features are also seen in the spectra of hco@xmath49 and cs which should be more free from such contamination , but we have only limited data for these lines .
observations of these molecular lines at a higher angular resolution using interferometers such as sma and bima would be needed to confirm and resolve the outflow as well as the collapsing motion of the condensation .
as seen in the c@xmath4o total intensity map in figure [ fig : ii_maps](a ) , l1004e has an elongated morphology consisting of several filaments and core - like structures . in order to characterize the filaments
, we attempted to identify the individual filaments based on the c@xmath4o data .
we first tried to find a systematic way to define the filaments , but we found that it is very difficult to find a numerical definition to separate the filaments reliably .
after some trials , we finally decided to pick up relatively large filaments by eye inspection in an iso - temperature map of c@xmath4o in 3 dimension ( figure [ fig : filaments ] ) .
we then determined the velocity range where the identified filaments are detected , and produced a c@xmath4o intensity map integrated over the velocity range for each of the filaments to measure their physical properties such as the mass , size , and line width .
although our method to define the filaments is tentative , we will analyze the filaments identified in this manner , because our main purpose is not to compile a complete list of the filaments but to investigate their typical properties , gravitational stabilities , and velocity structures . in total
, we picked up 12 filaments as labeled in figure [ fig : filaments ] .
the condensation associated with iras 21025 + 5221 shown in section [ subset : iras21025 ] corresponds to the one labeled no.1 .
some of the filaments including the condensation have a round shape , and it may be more appropriate to call them cores " or subcores " rather than filaments " . in order to see how much the filaments are round or elongated , we fitted the c@xmath4o intensity distribution of the individual filaments by an elliptic 2 dimensional gaussian function , and derived their major and minor radii ( @xmath118 and @xmath119 ) to determine their ellipticities @xmath120 ( @xmath121 ) which can be a measure of their elongated shapes ( e.g. , @xmath122 is for a spherical shape ) . in this subsection ,
we call filaments with @xmath123 filaments " and call the others with with @xmath124 subcores " .
four of the 12 filaments we identified ( nos . 1 , 2 , 8 , and 9 in figure [ fig : filaments ] ) can be classified to subcores .
other than the ellipticities , we measured some properties of the filaments and subcores which are summarized in table [ tab : filaments ] .
in the table , the parameter @xmath125 is the velocity range that we used to define the filaments and subcores , and @xmath34 and @xmath35 are their peak positions in the c@xmath4o intensity maps integrated over @xmath125 .
@xmath59(h@xmath66 ) and @xmath126 are the molecular column density and the line width ( defined at fwhm ) measured at the peak positions , respectively , and @xmath127 is the mass derived from the c@xmath4o intensity in the same way as described in section [ sec : distributions ] .
we defined the surface area of the filaments and subcores @xmath128 at the half maximum of the peak c@xmath4o intensity integrated over @xmath125 , and defined their radii as @xmath129 .
we also derived c@xmath4o spectra averaged over @xmath128 , and fitted them by gaussian functions to measure the mean line width @xmath130 . in order to check the gravitational stability of the filaments and subcores
, we also calculated their virial mass in a standard way ( e.g. , * ? ? ?
* ) as @xmath131 as summarized in the table , we found that the identified filaments and subcores have a mass , line width , and column density of @xmath132 @xmath1 , @xmath133 km s@xmath13 , and @xmath134 @xmath68 with a mean value of 341 @xmath1 , 1.7 km s@xmath13 , @xmath135 @xmath68 , respectively .
these quantities are comparable to those of cores forming massive stars ( e.g. , * ? ? ?
* ; * ? ? ?
* ) or star clusters ( e.g. , * ? ? ?
* ; * ? ? ?
we also found that the masses of the filaments and subcores @xmath127 are roughly consistent with @xmath136 as shown in figure [ fig : mvir](a ) , indicating that they are likely to be in the virial equilibrium . however , dispersion in the @xmath136 vs. @xmath127 diagram is large , probably because @xmath136 in equation ( [ eq : mvir ] ) is for an ideal sphere while many of the filaments and subcores have an elongated shape .
actually , the difference between @xmath127 and @xmath136 tends to be larger for the filaments and subcores with lower ellipticities , e.g. , @xmath127 is a few times higher than @xmath136 for many of the filaments with @xmath123 . in order to better investigate the gravitational stability of highly elongated filaments
, we employed a simple model of isothermal cylindrical gas with infinite length ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
. the cylindrical gas can be gravitationally stable when the mass density @xmath137 as a function of radius @xmath138 from its axis follows the equation @xmath139^ { - 2}}\ ] ] where @xmath140 is an effective radius written as @xmath141 and @xmath142 , @xmath143 , and @xmath144 are the gravitational constant , the speed of sound , and the density at @xmath145 , respectively .
integration of equation ( [ eq : cylindrical ] ) from @xmath145 to infinity yields @xmath146 the mass per unit length of the gravitationally stable filaments , which can be expressed as @xmath147 if we assume that @xmath143 is equal to the observed line width @xmath126 because the internal motion of the observed filaments is apparently dominated by turbulence rather than thermal motion , @xmath146 can be written in the following useful form , @xmath148 using the above equation , we calculated @xmath146 of the filaments by inserting @xmath126 in table [ tab : filaments ] , assuming that we are observing the filaments orthogonally to their elongation .
we also calculated the observed gas mass per unit length of the filaments as @xmath149 where @xmath150 is the lengths of the filaments estimated as @xmath151 , which can be compared with @xmath146 .
we summarize these values in the last columns of table [ tab : filaments ] , and compare @xmath146 and @xmath149 in figure [ fig : mvir](b ) . as seen in the figure
, @xmath146 and @xmath149 do not match for the subcores with high ellipticities ( @xmath124 shown by open circles ) , because @xmath146 is almost meaningless for the subcores .
about half of the elongated filaments ( @xmath123 , filled circles ) have @xmath149 close to @xmath146 , indicating that they can be gravitationally stable .
the other half of the elongated filaments ( such as no.12 ) have @xmath146 a few times higher than @xmath149 , suggesting that they might be gravitationally unbound being dispersed into the interstellar medium .
however , we should note that the c@xmath4o spectra of such filaments with @xmath152 are often contaminated by faint emission from other filaments at different velocities .
it is difficult to separate them reliably to measure @xmath126 precisely at the present sensitivity of our c@xmath4o data .
such contamination can easily cause an overestimation of @xmath146 by a factor of a few .
in fact , the difference between @xmath146 and @xmath149 is larger for filaments with larger @xmath126 .
more sensitive c@xmath4o dataset with much better signal - to - noise ratio is needed to verify the gravitational stability of the filaments , especially for those appearing gravitationally unbound . as can be seen in the c@xmath4o channel map in figure [ fig : channelmap_c18o_1 ] , the filaments and subcores often have slightly different radial velocities .
it is noteworthy that some of them show an apparent anti - correlation to each other in the channel map , i.e. , ridge of a filament corresponds to valley or hole of another filament .
a typical example of the anti - correlations is shown in figure [ fig : collision ] .
filaments labeled 4 and 5 ( table [ tab : filaments ] ) in panel ( b ) of the figure correspond to a hole between subcore 2 and filament 6 in panel ( a ) .
similarly , another filament labeled 7 in panel ( b ) corresponds to a hole in fainter c@xmath4o intensity distribution in panel ( a ) .
we suggest that some of these anti - correlations represent collisions between the filaments and subcores . in oder to find an evidence for such collisions , we made position - velocity ( pv ) diagrams along the cuts labeled a b , c d , and e f in panel ( a ) of figure [ fig : collision ] .
resulting diagrams are displayed in panels ( c)(e ) of the figure .
as seen in panel ( c ) , the filaments 4 and 5 have a similar velocity , and the filament 6 is located in between having slightly shifted peak velocity by @xmath750.5 km s@xmath13 , and the three filaments appear physically connected to each other with fainter c@xmath4o emission . another pv diagram in panel ( d ) for the cut c
d shows a similar feature .
these features seen in the pv diagrams can be naturally accounted for if we assume that the filaments 4 and 5 used to be one continuous filament and the subcore 2 and filament 6 used to be another continuous filament , and they collided and passed through each other .
the filaments 4 and 5 in panel ( b ) are shifted by @xmath153 ( @xmath36 0.12 pc ) from the corresponding hole in panel ( a ) .
if we take that the relative velocity of the filaments to be 0.51 km s@xmath13 as seen in panels ( c ) and ( d ) , their collision may have occurred 0.1 0.2 myr ago . as described in section [ sec : discussion ] , we have performed numerical simulations to investigate the formation and evolution of the filaments in a very massive core having the same total mass as l1004e ( @xmath154 @xmath1 ) .
the simulations can reproduce filaments inside of the model core , and some of them collide against each other to form stars .
it is noteworthy that pv diagrams taken around such colliding filaments in the simulations ( e.g. , see figure [ fig : simulation_color](c ) ) often appear very similar to those actually observed as displayed in figure [ fig : collision](c ) and ( d ) , strongly suggesting that the anti - correlations seen in the c@xmath4o channel map ( figure [ fig : channelmap_c18o_1 ] ) represent collisions of the filaments . in the case of the anti - correlation seen around the filament 7 in figure [ fig : collision ] ( a ) and ( b )
, however , there is no abrupt jump in velocity in the pv diagram ( see panel ( c ) ) .
although such a pv map can also be seen in our simulations for a filament drifting in the shear or for distinct filaments colliding with a small relative velocity , it is difficult to judge whether the anti - correlations in the channel maps are due to collisions of the filaments or merely trace velocity gradients along a single filament without collisions .
we will further investigate the velocity structure of the filaments and subcores around the 2 iras sources .
as shown in section [ subset : iras21025 ] , iras 21025 + 5221 is a promising candidate of ysos forming in subcore 1 .
there are @xmath155 wise sources in the vicinity ( figure [ fig : iimaps_iras21025 ] ) , suggesting that the subcore has just started to form a small star cluster .
a careful inspection of the c@xmath4o data and the wise 12 @xmath56 image indicates that the subcore is a part of a small filament extending to the north - east direction .
we delineate its outline by the white broken line in figure [ fig : pv_iras1](a ) ( labeled 1 in the circle ) . in addition , the small filament is crossed by another filament which is an extension of filament 3 in the north - west of the iras source . as can be seen in the channel maps and the pv diagrams shown in panels ( b)(e ) of figure [ fig : pv_iras1 ] , these filaments ( 1 and 3 ) have different velocities that can be divided at @xmath156 km s@xmath13 , and subcore 1
is located at their intersection where the 2 velocity components are merged .
these pictures infer that the small filament 1 was collided by filament 3 in the past , and they were merged at the intersection to form subcore 1 .
we suggest that the collision induced the formation of the subcore and then the small star cluster . in the case of the other iras source ( 21005 + 5217 ) ,
filaments showing such apparent collisions are difficult to identify .
several ysos including the iras source are located between filaments 7 and 12 as shown in figure [ fig : pv_iras2 ] .
filament 7 has a branch labeled 7 in the figure which has the same radial velocity as the main body of the filament and is extending to the west close to the boundary of filament 12 .
as seen in panels ( e ) of the figure , the branch and filament 12 have slightly different radial velocities by @xmath157 km s@xmath13 , and their interface exhibits rather complex velocity field , which might reflect the interaction between the branch of filament 7 and filament 12 .
however , it is difficult to confirm the possible interaction and its influence on the formation of ysos only with the present dataset . to summarize
, subcore 1 is very likely to be collided by a part of filament 3 , which may have influenced on the formation of iras 21025 + 5221 and the other @xmath155 ysos . in the case of iras 21005 + 5217
, there are 2 filaments ( 7 and 12 ) showing complex velocity field in the vicinity , though it is difficult to confirm their possible collision and its influence on star formation . a clear evidence of collisions between molecular clouds was first found in sgr b @xcite , and since then on , similar collisions as well as star formation induced by the collisions have been evidenced in some star forming regions ( e.g. , * ? ?
* ; * ? ? ?
* ) . however , these are the collisions between clouds or clumps on much larger scales .
note that what we suggest in this paper is the collisions between filaments inside of a single massive dense core , which may be a direct trigger of formation of massive stars or star clusters .
we will discuss the origin of the colliding filaments in section [ sec : discussion ] .
to summarize the results of our observations , l1004e has a huge mass of @xmath158 @xmath1 and it consists of a number of filaments having a mass of @xmath6 @xmath1 .
some of the filaments are apparently colliding against each other , and it is likely that some ysos are forming around the regions where the filaments are colliding ( e.g. , around iras 22025 + 5221 in figure [ fig : pv_iras1 ] ) .
it is probably natural to assume that such collisions induce star formation in the filaments .
actually , according to recent numerical simulations @xcite , collisions of spherical clumps can yield high sfes of @xmath159 % which is a typical value of ir clusters @xcite , but head - on collisions are needed for the high sfes .
note that collisions of filaments can be partially regarded as equivalent to the head - on collisions of spherical clumps , and formation and collisions of giant filaments in a massive core like l1004e may play a key role for cluster formation . here is a problem , however , to understand the collisions of the filaments .
there have been a number of numerical simulations on the evolution of dense cores ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) . in general ,
the simulations show that filaments can form easily in the cores , but they scarcely collide against each other . the core studied here might have extraordinary parameters ( e.g. , too high mass or density ) , or there might be an unknown mechanism to cause their collisions , which have not been taken into account in the earlier simulations . in order to find what physical conditions are needed for the collisions of filaments , we performed self - gravitational hydrodynamics simulations using the adaptive mesh refinement ( amr ) technique developed by @xcite . for the initial conditions
, we assumed a uniform core with a huge mass ( @xmath160 @xmath1 ) and size ( @xmath161 pc@xmath162 ) corresponding to an average density of @xmath163 @xmath105 , which are similar to those found in l1004e .
turbulence typically of an order of mach 10 ( @xmath164 km s@xmath13 ) is imposed in the initial core ( see for detial * ? ? ?
the initial velocity field is incompressible with a power spectrum of @xmath165 , generated following @xcite , where @xmath166 is the wavenumber .
this power spectrum results in a velocity dispersion of @xmath167 , in agreement with the larson scaling relations @xcite .
we calculated decaying turbulence with the self - gravity , and we did not consider a driving force of turbulence during the evolution ( c.f .
the gas was assumed to be isothermal with a temperature of 10 k. evolution of the core was followed from @xmath168 0 myr to @xmath84 myr , and we observed the formation and evolution of the resulting filaments in 2-dimensional velocity channel maps and 3-dimensional iso - density maps which are equivalent to those in figures [ fig : channelmap_c18o_1 ] and [ fig : filaments ] . details of the simulations will be presented in a subsequent publication ( matsumoto et al .
2014 , in preparation ) . in this paper
, we describe a summary as in the following points ( 1)(3 ) , and show some snapshots of the evolution of the column densities observed from two different directions ( @xmath169 and @xmath170 ) at some different epochs in figure [ fig : amr_simulation](a)(f ) : + * ( 1 ) * filaments are formed in the core at @xmath171 myr , and stars are formed in the filaments spontaneously at @xmath172 myr . in total , 209 stars are formed at the end of the simulations ( @xmath173 myr ) . + * ( 2 )
* apparent collisions of the filaments are not observed throughout the calculation time . + * ( 3 ) * in the velocity channel maps , we sometimes observe a hole and bump showing anti - correlations at different velocities , which appears similar to those seen in figures [ fig : channelmap_c18o_1 ] and [ fig : collision](a)(b ) .
the anti - correlations observed in the simulations , however , represent relatively large - scale transient structures drifting in the shear , but they are not well - defined filaments forming stars .
we repeated the simulations for several sets of different initial parameters , but the results are essentially the same as described in the above .
the holes and bumps on a rather large scale described in the point ( 3 ) may account for a part of the observations , but we could not reproduce the well - defined colliding filaments forming stars by the above simulations , and we concluded that simple increment of mass and size of the initial core does not result in collisions of the filaments . an additional condition is apparently needed to account for the collisions . after some trials , we finally found that the filaments can collide when there is a large velocity gradient across the initial core in a sense to compress it .
in other words , we have to force the filaments to collide by giving the velocity gradient .
an example of the simulations incorporating the velocity gradient can be summarized as in the following point ( 4 ) : + * ( 4 ) * if we assume a velocity gradient of @xmath174 km s@xmath13 pc@xmath13 in one direction across the initial core , which is provided by a sinusoidal flow with an amplitude of mach 10 , in the @xmath169-direction on the initial core for the range @xmath175 pc where @xmath176 and @xmath177 are the mach number of the flow and the sound velocity , respectively .
this flow provides the maximum velocity gradient @xmath178 km s@xmath13 pc@xmath13 at @xmath179 pc . ]
the filaments are formed at @xmath180 myr in the same way as described in the point ( 1 ) , and some of them start to collide against each other ( or cross each other ) to form stars at @xmath181 myr .
stars are often formed at the intersections of the filaments , but they are also formed spontaneously along the ridge of dense filaments without collisions . roughly , @xmath182 @xmath183 of the stars are formed directly by collisions . in total ,
479 stars are formed at the end of the simulation , which is @xmath184 times larger than in the case of no initial velocity gradient .
some snapshots of the above simulations are displayed in figure [ fig : amr_simulation](g)(l ) .
characteristic features observed in the c@xmath4o data , i.e. , the anti - correlations in the channel maps and the velocity jumps in the pv diagrams ( figures [ fig : collision][fig : pv_iras1 ] ) , are often seen in the simulated data . in figure
[ fig : simulation_color ] , we demonstrate an example of such features seen in the simulations .
panel ( a ) of the figure displays the column density distributions in different velocity ranges ( colored in red and blue ) exhibiting anti - correlations at some places .
as shown in panel ( b ) , the first star observed in the simulation ( indicated by the star symbol ) was formed in one of the blue filaments @xmath185 myr after another red filament ( indicated by the ellipse with broken line ) collided and passed through it .
we can see a clear velocity jump in the pv diagram in panel ( c ) measured along the filaments .
panels ( d ) and ( e ) display the column density distributions in the two different velocity ranges in panel ( a ) separately , but the data are smoothed to a lower resolution ( @xmath186 pc @xmath187 at 800 pc ) similar to that of the c@xmath4o data . some noticeable anti - correlations including the one around the first star mentioned in the above
are indicated by boxes , and they appear similar to those seen in the c@xmath4o data in figure [ fig : collision ] .
it is noteworthy that some elongated condensations in panels ( d ) and ( e ) of figure [ fig : simulation_color ] which would be regarded as one filament actually consist of a bunch of thinner filaments that can be seen at a higher spatial resolution ( @xmath188 pc ) in panel ( a ) .
filaments observed in the c@xmath4o data may probably have similar substructures which would be resolved by interferometer observations with higher angular resolutions of a few arcsec .
actually , such thin filaments were recently evidenced in the taurus region by @xcite who found bundles of small and gravitationally stable filaments with a typical length of @xmath157 pc , which may correspond to the thin filaments observed in our simulations .
as we can see in figure [ fig : amr_simulation](k ) , the point of the simulations is that the velocity gradient generates a layer of high density gas containing a number of filaments in the middle of the initial core . in such a layer ,
star formation should occur more frequently , not only because the free - fall time should be shorter due to the gas compression , but also because the collision rate of the filaments should be higher .
though it is not easy to separate clearly the contributions of the two effects to star formation , roughly @xmath182 @xmath183 of the stars are formed directly by collisions of the filaments .
this is consistent with the fact that there are 83 candidates of ysos selected in l1004e ( see section [ subset : protostars ] ) and @xmath155 of them are located where collisions of the filaments are inferred ( figures [ fig : pv_iras1 ] and [ fig : pv_iras2 ] ) . in the above simulations , the layer has a thickness of @xmath189 pc and and its edge - on view appears similar to the c@xmath4o intensity map in figure [ fig : ii_maps](a ) .
we suggest that this is the case for l1004e . to be more precise
, l1004e may not be a complete edge - on view of the layer but it may be an oblique view .
in fact , the @xmath14co channel maps ( figure [ fig : channelmap_13co_1 ] ) shows that there is a velocity gradient of @xmath190 km s@xmath13pc@xmath13 in the direction orthogonal to the elongation of l1004e ( i.e. , from the south - east to north - west , see panels for @xmath191 km s@xmath13 in the figure ) . for
now , it is not yet very clear how large initial velocity gradient is needed to cause the collisions of the resultant filaments , but it should be greater than that necessary to make the crossing time @xmath192 shorter than the free fall time @xmath193 myr of the initial core . in the case of l1004e ,
@xmath194 myr for the average density @xmath195 @xmath105 , and @xmath196 myr if we take @xmath192 is the reciprocal of the observed velocity gradient @xmath197 ( @xmath198 km s@xmath13pc@xmath13 ) .
it is not clear either how the initial velocity gradients influence on the final sfes of the cores , because we have results only for the two cases with ( @xmath199 km s@xmath13pc@xmath13 ) and without ( @xmath200 km s@xmath13pc@xmath13 ) the velocity gradients at the moment .
we would expect higher sfes for larger velocity gradients because the initial cores can be compressed more sufficiently , but it should be clarified by additional simulations .
the velocity gradient necessary for collisions of the resultant filaments can be caused by an external effect , e.g. , shock fronts of snrs or h regions to compress the initial core .
actually , there have been a number of studies for such molecular clouds influenced by snrs ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) or h regions ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
it is noteworthy that the cyg ob7 molecular cloud has been suggested to be interacting with the nearby snr hb21 ( cataloged as g89.0 + 4.7 by * ? ? ?
* ) by @xcite .
in addition , there are some other snrs ( i.e. , da530 , da551 , and 3c434.1 ) in the vicinity of the cyg ob7 cloud ( * ? ? ?
* see their figure 11 ) .
although distances to these snrs have not been determined well ( e.g. , * ? ? ?
* ) , it is very possible that they have influenced on the initial velocity fields of l1004e .
other than the influence of the snrs and h regions , stellar winds from nearby ob stars can also provide a similar effect on the velocity field of the initial cores .
note that there have been found several young ob stars located @xmath201 pc away from l1004e @xcite . in figure
[ fig : illustration ] , we summarize the suggested scenario for the formation of the colliding filaments . the collision of the filaments in massive cloud cores may be essential for cluster formation .
the ubiquitousness of the scenario , however , has to be confirmed especially by observing other massive star forming regions or cluster forming regions such as m17 and ori kl , because , at the moment , l1004e is probably only the core where such collisions of giant filaments are found .
we have carried out millimeter - wave observations of a massive dense core l1004e in the cyg ob 7 molecular cloud in various molecular lines such as @xmath20co , @xmath14co , c@xmath4o , ccs , hc@xmath25n , and nh@xmath25 , using the 45 m telescope at the nobeyama radio observatory .
main findings of this paper are summarized below .
\(1 ) the molecular observations revealed the total extent and velocity structures of l1004e .
based on the c@xmath4o data , we find that the core has a huge mass and size of @xmath202 @xmath1 and @xmath203 pc@xmath3 , respectively .
the core is also characterized by the cold temperature @xmath204 k as measured in the @xmath20co and nh@xmath25 molecular lines .
the maximum column density observed is @xmath205 @xmath68 at the peak position of the c@xmath4o intensity map .
turbulent motion measured from the line width varies in the range @xmath206 km s@xmath13 over the core .
\(2 ) we searched for candidates of ysos in the iras psc , and found that there are only 2 sources that can be regarded as promising ysos .
they are iras 21005 + 5217 and 21025 + 5221 .
we employed a stellar model developed by @xcite to access the age , mass , and luminosity of the iras sources .
we searched for ysos also in the wise psc which is much more sensitive than the iras psc by using the selection criteria proposed by @xcite .
if we disregard one of their criteria to exclude agns , there found 83 candidates for ysos in the observed region , and @xmath155 of them are concentrated in a condensation around iras 21025 + 5221 . assuming that all of the wise sources are real ysos , we estimated the star formation efficiency of the entire core to be @xmath207 % at most .
\(3 ) we find that the core consists of a number of filaments and some core - like structures . in the velocity channel maps of c@xmath4o
, these filaments appear apparently colliding against each other , and some candidates of ysos are located near the intersections of the filaments .
we identified 12 major filaments and core - like condensations , and estimated their masses to be @xmath6 @xmath1 .
we investigated their gravitational stability to find at least half of the filaments and core - like condensations are likely to be in the virial equilibrium , and the others might be gravitationally unbound .
\(4 ) using the adaptive mesh regiment technique @xcite , we performed numerical simulations to reproduce the collisions of the filaments .
as the initial conditions of the core , we assumed a high mass , size , and density similar to those observed toward l1004e .
results of the simulations indicate that the filaments are formed in the core , but they never collide against each other during their evolution .
after some trials , we finally found that the filaments can collide only when there is a large velocity gradient in the initial core in a sense to compress it , which can be generated by an external energetic effect such as the shock fronts of snrs .
there are actually some snrs in the vicinity of the cyg ob 7 molecular cloud including hb21 that has been suggested to be interacting with the cloud .
we suggest that l1004e was influenced by such an external effect ( possibly by hb21 ) to have the initial velocity gradient , which results in the formation of the colliding filaments .
this research was financially supported by grant - in - aid for scientific research ( nos .
22340040 , 23540270 , 23540270 , 24244017 , 24700866 , 26287030 , 26350186 , 26400233 , and 26610045 ) of japan society for the promotion of science ( jsps ) , and also by the mitsubishi foundation .
the 45 m radio telescope is operated by nro , a branch of national astronomical observatory of japan .
this research has made use of the nasa/ ipac infrared science archive , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration .
the wide - field infrared survey explorer is a joint project of the university of california , los angeles , and the jet propulsion laboratory ( jpl ) , california institute of technology ( caltech ) , funded by the national aeronautics and space administration ( nasa ) .
the two micron all sky survey is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation .
we derived the total mass of the observed core as summarized in the following .
the method we used assumes the lte , and is a standard way to derive the total molecular mass from the c@xmath4o emission line .
details of the method can be found in some literature ( e.g. , * ? ? ?
* ) . in general , observed brightness temperature of a certain molecular line @xmath46(@xmath169 ) ( e.g. , @xmath109c@xmath4o , @xmath20co , etc . )
can be expressed as @xmath208\left [ { 1 - { { \mathop{\rm e}\nolimits } ^ { - \tau ( x ) } } } \right]\ ] ] where @xmath209 , and @xmath210 is a constant ( @xmath210=5.27 k for c@xmath4o and 5.53 k for @xmath20co ) . @xmath73 and @xmath211 are the excitation temperature and the cosmic background ( 2.7 k ) , respectively , and @xmath212 is the optical depth .
we first estimated @xmath73 at each observed position by solving the above equation for @xmath46(@xmath20co ) measured at the peak velocity of the c@xmath4o spectra assuming @xmath58(@xmath20co)@xmath213 .
we then derived @xmath58(c@xmath4o ) and @xmath59(c@xmath4o ) , and converted @xmath59(c@xmath4o ) to @xmath57 to estimate the total mass @xmath214 by summing up the derived @xmath57 over the observed area .
the process of the derivation can be summarized in the following equations ; where @xmath219 and @xmath57 are in units of @xmath68 , and the constant @xmath220 is @xmath221 @xmath68 k@xmath13 ( km s@xmath13)@xmath13 for the c@xmath4o@xmath21 emission line .
@xmath222 , @xmath223 , and @xmath224 in the last equation are the mean molecular weight taken to be 2.4 , the hydrogen mass , and the area of the pixels of the c@xmath4o map ( @xmath225 cm@xmath3 at the assumed distance 800 pc ) .
summation in the right side of equation ( [ eq : mass ] ) is made for the total area observed in c@xmath4o shown in figure [ fig : ii_maps](a ) .
equation ( [ eq : nh2 ] ) is derived from an empirical relationship between @xmath94 and @xmath59(c@xmath4o ) @xcite as well as between @xmath94 and @xmath59(h@xmath66 ) for @xmath227 @xcite .
note that @xmath57 calculated using equation ( [ eq : nh2 ] ) and then @xmath214 calculated using equation ( [ eq : mass ] ) may be the minimum estimates for the true values , because c@xmath4o is known to be depleted onto dust grains in very dense cloud interior like l1004e ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) , while we assume the linear @xmath59(c@xmath4o)@xmath59(h@xmath60 ) conversion relation based on the results of @xcite whose measurements were done in much less dense regions .
however , we shall use the simple conversion relation in equation ( [ eq : nh2 ] ) in this paper , because it is difficult at the moment to assess precisely how much the depletion of c@xmath4o is occurring in l1004e .
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, & kobayashi , h. 2011 , , 63 , 1259 zhou , s. , evans ii , n. , j. , kmpe , c. , & walmsley , c. m. 1993 , , 404 , 232 lcrcccccccccc @xmath20co & @xmath5 & 115.271204 & 15 & bears & 340 & & ac & 32 & 38 & 1.25 & 0.22 & 10 + @xmath14co & @xmath5 & 110.201353 & 16 & bears & 320 & & ac & 32 & 38 & 0.94 & 0.14 & 10 + c@xmath4o & @xmath5 & 109.782182 & 16 & bears & 310 & & ac & 32 & 38 & 0.53 & 0.14 & 10 + hc@xmath50n & @xmath228 & 45.490319 & 40 & s40 & 230 & & ac & 32 & 38 & 0.14 & 0.32 & 30 + ccs & @xmath229 & 45.379033 & 40 & s40 & 230 & & ac & 32 & 38 & 0.15 & 0.32 & 30 + nh@xmath25 & @xmath230 & 23.694506 & 75 & h22 & 140 & & ac & 16 & 19 & 0.08 & 0.34 & 30 + lcrccccccccc cs & @xmath231 & 97.980968 & 18 & t100h & 160 & & aos & 40 & 37 & 0.09 & 0.11 + c@xmath23s & @xmath231 & 96.412982 & 18 & t100h & 160 & & aos & 40 & 37 & 0.25 & 0.12 + hco@xmath49 & @xmath5 & 89.188518 & 19 & t100v & 430 & & aos & 40 & 37 & 0.04 & 0.12 + h@xmath14co@xmath49 & @xmath5 & 86.754330 & 19 & t100h & 160 & & aos & 40 & 37 & 0.04 & 0.13 + nh@xmath25 & @xmath230 & 24.139417 & 75 & h22 & 140 & & aos & 40 & 37 & 0.03 & 0.46 + nh@xmath25 & @xmath232 & 23.870129 & 75 & h22 & 140 & & aos & 40 & 37 & 0.03 & 0.47 + nh@xmath25 & @xmath233 & 23.722633 & 75 & h22 & 140 & & aos & 40 & 37 & 0.02 & 0.47 + nh@xmath25 & @xmath234 & 23.694506 & 75 & h22 & 140 & & aos & 40 & 37 & 0.02 & 0.47 + cccccccrccc @xmath243 & @xmath244 & @xmath245 & & 0.9932(6 ) & 2.580(5 ) & 7.521(9 ) & @xmath246 ...
@xmath247 & 3331 & aaab & 21.8 + @xmath248 & @xmath249 & @xmath250 & & 0.3691(11 ) & 1.907(28 ) & 8.101(10 ) & 39.96(17 ) & 3333 & caaa & 35.9 + ccccccccc @xmath243 & @xmath251 & @xmath252 & @xmath253 & @xmath254 & & @xmath255 & @xmath256 & @xmath257 + @xmath248 & @xmath258 & @xmath259 & @xmath260 & @xmath261 & & @xmath262 & @xmath263 & @xmath264 + cccccccccccccc 1&@xmath269&@xmath270 & @xmath271 & 3.1&1.58 & 170&1.70 & 0.34&0.33 & 199&1.00 & 1158 & 259 + 2&@xmath272&@xmath273 & @xmath274 & 2.1&0.44&230&1.52 & 0.52&0.41 & 196&0.91 & 90 & 277 + 3&@xmath275&@xmath276 & @xmath277 & 1.9&0.63&177&1.08&0.45&0.38 & 91&0.17 & 186 & 96 + 4&@xmath275&@xmath278 & @xmath279 & 2.1&0.77&326&1.04&0.64&0.45 & 102&0.37 & 277 & 221 + 5&@xmath275&@xmath280 & @xmath281 & 2.1&1.20&420&1.39&0.76&0.49 & 200&0.20 & 668 & 192 + 6&@xmath282&@xmath283 & @xmath284 & 1.9&0.73&590&1.88&1.30&0.64 & 478&0.42 & 249 & 295 + 7&@xmath285&@xmath286 & @xmath287 & 4.5&1.78&793&1.78&1.04&0.57 & 380&0.50 & 1471 & 488 + 8&@xmath288&@xmath289 & @xmath290 & 3.0&1.48&212&1.89&0.22&0.27 & 197&0.63 & 1021 & 314 + 9&@xmath291&@xmath292 & @xmath293 & 3.0&2.54&165&2.94&0.32&0.32 & 579&0.77 & 2994 & 223 + 10&@xmath294&@xmath295 & @xmath296 & 1.9&0.42&107&1.26&0.35&0.33 & 110&0.43 & 82 & 106 + 11&@xmath297&@xmath298 & @xmath299 & 2.1&1.09&415&2.42&0.95&0.55 & 670&0.48 & 551 & 261 + 12&@xmath300&@xmath301 & @xmath302 & 2.1&1.45&491&1.51&0.81&0.51 & 240&0.28 & 983 & 255 + o column densities of l1004e ( thick solid line ) , hcl 2 ( thin solid line ) , and ldn 1551 ( broken line ) observed with the 45 m telescope .
the maximum number of pixels in the vertical axis is normalized to unity for each region .
[ fig : column_density ] ] image .
class i and class ii sources selected following the criteria of @xcite are shown by the filled and open circles , respectively .
small plus signs indicate the sources which would be regarded as ysos ( class i or ii ) without one of their criteria to exclude angs ( see section [ subset : protostars ] ) .
point sources which are likely to be false detections in the original wise psc without apparent counterparts in none of the four band wise images ( i.e. , 3.4 , 4.6 , 12 , and 22 @xmath56 ) are excluded .
[ fig : ysos ] ] and [ tab : counterparts ] .
the open circles denote the upper limits .
the solid line is the model of @xcite best fitting the observed fluxes , which was calculated using their tools available on the web ( http://caravan.astro.wisc.edu ) .
the dashed line shows the stellar photosphere of the central star best fitting the observed data , as we would observe in the absence of circumstellar dust but including interstellar extinction .
[ fig : sed ] ] n versus that of ccs observed toward l1004e ( square ) compared with those in other dense cores in literature such as tmc-1(cp ) and tmc-2a corrected by @xcite who studied starless cores in polaris .
open and filled circles denote cores with and without ysos , and those accompanied by molecular outflows are indicated by plus signs .
arrows denote the upper limits .
results of model calculations performed by @xcite for densities of @xmath303(h@xmath66)=10@xmath304 and @xmath305 @xmath105 are shown for comparison by open circles and hexagons .
numbers in the symbols denote the reaction time in units of 10@xmath306 yr . [ fig : abundances ] ] | arxiv |
the processes of dust formation and mass loss in evolved giants and supergiants remains poorly understood despite its manifold and profound implications to the cycle of matter through stars and back into the ism .
an extensive observational and phenomenological literature ( see e.g. @xcite for a review ) bears witness to the barrage of astrophysical techniques applied to this problem , and progress has been considerable in many important areas .
however , fundamental uncertainties remain over the mechanisms of elevation of material , chemical nucleation of the dust , and subsequent outflow and global properties of the wind . as an example of the gap in our understanding
, there has been to date no self - consistent physical model of the atmosphere of an evolved o - rich giant which encompasses the upper regions including even the most important basic phenomena : non - grey radiative transfer , pulsation , shocks , convection , non - equilibrium dust formation and the molecular atmosphere . from an observational perspective
, progress has been hampered until now by the difficulties inherent in imaging material on size scales of a few au which encompass the photospheres themselves and the dust formation and acceleration regions .
although modern long - baseline optical / ir interferometry is capable of accessing these scales , imaging is not straightforward as targets can be complex , deeply embedded and often asymmetric . in particular for many mira - type variables ,
the relatively low surface - brightness material in the outflow can be very difficult to detect against the high luminosity stellar flux .
the stellar photosphere and circumstellar dust shell are usually treated as completely separate regimes , as justified by the following simple argument . as a first approximation
, one might consider that dust grains in an optically thin envelope are grey or nearly so , and exist in thermal equilibrium with the radiation field .
furthermore , we can approximate the star as having a small angular extent , so that the mean intensity , @xmath0 at the dust condensation radius @xmath1 is equal to the luminosity of the central star @xmath2 divided by @xmath3 . in this case equation [ eqndustgrey ] gives an estimate of the dust formation radius ( here @xmath4 the radius of the central star , @xmath5 the effective temperature of the star and @xmath6 the dust condensation temperature ) . given an effective temperature of 3000k and a dust condensation temperature of 1100k , the dust formation radius is 3.7 stellar radii , which means that the physics of the photosphere and the circumstellar environment could be considered well - separated . where dust is considered to be non - grey , but the dust formation radius still lies well - outside the photosphere , conservation of energy and radiative equilibrium gives equation [ eqndustaway ] , where @xmath7 is the absorption coefficient of the dust and @xmath8 is the planck function in the form which gives power per unit area per steradian per unit wavelength
. further discussion of these kinds of approximations can be found in @xcite .
@xmath9 @xmath10 the absorption coefficients for dust around o - rich mira are often assumed to be those of `` dirty '' silicates @xcite .
these silicates have optical constants very similar to amorphous olivine mg@xmath11fe@xmath12sio@xmath13 with @xmath14 @xcite , with the exception of the spectral range 2 - 8@xmath15 m , where inclusions such as solid fe are required to match observationally derived optical constants .
olivine with @xmath14 can form only slightly closer to the star than grey dust . using
the emitted flux from a 3000k effective temperature mira model from ireland et al .
( 2004a ) ( the m09n model ) , the optical constants from @xcite and an assumed condensation temperature of 1100k , this olivine can form at a radius of 6.4 stellar radii : still a comfortable distance from the upper atmosphere of the star . apart from the optical properties , the other factor governing grain survival at smaller radii is the sublimation temperature .
the dust species often considered to be the first to form in higher effective temperature stars from semi - empirical considerations is corundum @xcite , al@xmath16o@xmath17 , which is stable at considerably higher temperatures than silicates @xcite .
its formation radius for this same 3000k model star is 2.1 stellar radii , using the optical constants from @xcite and an assumed condensation temperature of 1400k .
the multi - wavelength diameter measurements of six mira - like variables made by ireland et al .
( 2004b ) show an increase in apparent diameter from 900 nm to 700 nm with a component which appears uncorrelated with the strength of tio bands .
these observations are best explained by scattering from dust closer than a few stellar radii ( although molecular line blanketing makes quantitative interpretation difficult ) .
the presence of extensive dust this close is , as discussed above , difficult to reconcile with the conventional wisdom on dust formation around agb stars . despite the fact that the net polarisation arising from a spherically symmetric dust shell is zero ,
it is possible to separate it from the unpolarised photosphere with a polarisation - sensitive high - resolution measurement . scattering from the dust shell
will have a polarisation at any point with the e field in an azimuthal direction with respect to the stellar centre .
this is due to the simple relationship that scattered light from small particles in the rayleigh limit is polarised orthogonal to the plane containing the source , scatterer and observer .
if we now consider the response of a long - baseline interferometer which measures the fourier components ( called visibilities when total flux is normalised to unity ) of such an image , these will have different amplitudes and phases in different polarisations .
for a partially - resolved circularly symmetric source , the linear polarisation with the e field parallel to the baseline of observation will have a lower amplitude and the same phase as the visibility measured using the polarisation perpendicular to the baseline .
an attempt was made using this technique to detect scattering by free electrons around @xmath18 orionis using the long - baseline narrabri stellar intensity interferometer @xcite , but the instrument lacked the required sensitivity .
here we report the first successful use of this technique on a long - baseline optical interferometer .
the observational technique is described in the following section , while section [ sectmodel ] gives the results and section [ sectdiscuss ] a discussion and astrophysical interpretation .
the sydney university stellar interferometer ( susi ) is a long baseline optical interferometer with presently operational baselines from 5 to 160 m ( further details can be found in @xcite ) .
the observations presented here used 5 and 10 m baselines and a filter with central wavelength of 900 nm and full - width half - maximum 80 nm .
this filter was chosen so as to minimise contamination from the strongest features caused by the tio molecule .
it is in principle possible to measure visibilities at arbitrary polarisations through the use of quarter - wave plates and polarisers at arbitrary orientations . for a discussion of a general way to calibrate a long baseline interferometer for imaging in all stokes parameters ,
see @xcite .
due to polarisation - dependent phase - shifts and mirror reflectivities over the many mirrors in the susi optical chain , arbitrary initial polarisation states are not well preserved .
the measurements therefore are restricted to states with pure vertical and horizontal electric field orientation with respect to the optical path . while they will be attenuated
, these states should not suffer mixing from any reflection with the exception of the initial reflection off the siderostat when observing away from the meridian .
care was taken to only observe stellar targets when near the meridian .
given susi s north - south baseline orientation , this observing strategy resulted in visibility measurements with the e field at all times being within 19 degrees of perpendicular ( @xmath19 ) or parallel ( @xmath20 ) to the baseline . for crucial observations where a direct comparison was made between the visibilities in these two polarisations ,
data were restricted further to lie within 8 degrees of these orientations . the beam combining system used for these observations consisted of a pupil - plane beam combiner feeding two avalanche photo - diode ( apd ) detectors . by repeatedly scanning the optical delay linearly through the white - light fringe position ,
the light detected from each output of the combining beamsplitter is modulated at a frequency that depends on the scanning rate and the observing wavelength , with the fringe signals 180 degrees out of phase at the two outputs .
a description of a similar system can be found in @xcite , and further details of the beam combining system used for these observations will be found in @xcite ( in preparation ) .
although the two outputs are usually used differentially to reduce the effects of scintillation noise , it is possible to obtain an estimate for the fringe visibility from only one output , as in figure [ figpowerspectra ] .
the use of only one detector means that the bias in the power spectrum is not flat due to scintillation , and incorrect subtraction of this bias becomes an additional error source for low @xmath21 .
the observational strategy employed consisted of two separate parts : the first aimed at measuring @xmath19 and @xmath20 separately , while the second measured the ratio @xmath22 .
these are described in turn below .
firstly , polarisers were co - aligned and placed in front of the two outputs of the beam combiner , enabling a high signal - to - noise measurement of the correlation in linear polarised light .
as is usual with optical interferometry measurements , observations of targets were interleaved with un- or partially - resolved reference stars to calibrate the system correlation ( the @xmath21 response to a point source ) as a function of time . before use in adjusting the science measurements
, this system response was also corrected for the known nonzero diameters of the reference stars given in table [ tblcalstars ] . in this phase of the observational program , measurements were predominantly made of @xmath19 which had a much higher signal - to - noise than @xmath20 .
this is mainly due to partially polarising beamsplitters used at susi to split off light to the tip / tilt adaptive optics camera , which had the effect of significantly lowering the system throughput for @xmath20 .
.assumed diameters for the calibrator stars used for these observations [ cols= " < , < , < " , ] [ tblfitparams ]
the dust free ( ud only ) fits in table [ tblfitparams ] are clearly eliminated for both stars .
the high @xmath23 values have their origin in the inability of this scattering - free model to generate any polarisation signal . of the two models with dust ,
the thin shell model is a better fit than the outflow model for both stars .
the best - fit condensation radii in the outflow models are also uncomfortably close to the continuum - forming photospheres for both stars .
although there may be dust types that could plausibly exist in thermal equilibrium with the radiation field at these radii ( as discussed below ) , the gas temperatures in the model star of section 1 are 2000k at 1.1 stellar radii , much too high for grain nucleation ( e.g. see the discussion in @xcite ) .
the only way dust could exist so close to the continuum - forming photosphere is if it had formed at near - minimum phases and then fallen in .
however , this kind of motion is in conflict with the general assumptions of the outflow model .
the two epochs of r car do not show statistically significant differences , but the small differences at the level of about 1-@xmath24 are in the expected direction .
the star appears to increase in apparent size from phase 0.08 to 0.15 , as predicted by the models , and the optical - depth in scattering appears to decrease , consistent with the dust being part of an infalling layer that is partially sublimating at these near - maximum phases . for rr sco ,
the discrepancy between the luminosity / model - predicted diameter and the best fit diameter is almost certainly due to contamination from the tio molecule . a moderate strength tio band at 850 nm is included in the wing of the susi filter profile which could account for the enlargement observed ,
although predicting the effects of such molecular contamination is made difficult by its strongly cycle - dependent nature ( ireland et al .
2004a ) . from the discussion of dust formation radii in section 1 ,
it is clear that `` dirty '' silicates can not form a major fraction of the optical depth in scattering due to dust around r car . for survival within the hostile environment close to the photosphere
, dust must have very low absorption between 1 and 4@xmath15 m where most of the radiation from the central star is emitted , and higher absorption coefficients at longer wavelengths promoting efficient radiative cooling .
corundum is a clear possibility here , but another obvious dust type that satisfies these criteria is forsterite , the mg - rich olivine that is predicted to be the first significant silicate to form in chemical equilibrium calculations @xcite . the optical constants for this dust species as given in @xcite result in absorption coefficients 300 times higher at 10@xmath15 m than at 2@xmath15 m .
this dust is stable at a radius of 1.2 stellar radii from the 3000k model star of section 1 . as a plausible and abundant dust candidate
, we will assume that the dust around these stars is made of forsterite for the following analysis of the implications of the dust model parameters .
low absorption at wavelengths where the bulk of the stellar radiation is emitted also results in lower radiation pressure on the dust .
assuming full dynamical coupling between the gas and dust and full mg condensation , we can calculate the radiative acceleration as a fraction of the gravitational acceleration for an optically - thin model dust shell . for a shell made of forsterite around the 3000k model star of section 1 using mie theory to calculate absorption and scattering coefficients ,
this fraction is 41% for spherical grains of radius 0.1@xmath15 m and 1.5% for grains of radius 0.02@xmath15 m .
we therefore propose that this dust is formed in material primarily elevated by shocks , which in turn means that significant temporal variation in the dust shell optical depth and/or radius is expected .
where the rayleigh limit of small particles with respect to the wavelength of scattered light applies , it is sufficient to approximate dust with a distribution of sizes as a homogeneous population with a single effective radius @xmath25 . for dust composed of forsterite , with a scattering optical depth of @xmath26 at 900 nm , typical of the observations presented here ,
the optical depth in absorption at 10@xmath15 m is 1 for @xmath25 = 55 nm .
results from a radiative transfer model of a geometrically thin shell of forsterite with a fixed temperature of 1100k and an optical - depth of 1 at two stellar radii from the centre of a spherical black - body 3000k star are displayed in figure [ figmidirspect ] .
it can be seen that there is no strong mid - infrared feature evident in either emission or absorption due to the dust shell .
it would seem that the dust here represents an intermediate case between the compact geometries typically yielding absorption features , and spectra exhibiting emission which is usually associated with extended geometries . this result was found to be robust , and insensitive to the optical - depth of the shell .
note , however , that a shell of forsterite with a 10 micron optical - depth much greater than 1 would heat up beyond its sublimation temperature at the inner edge of the thin dust shell . in order to meet this criteria while maintaining the observed 900 nm optical depth ,
the effective particle size @xmath25 is constrained to be larger than about 50 nm . from the point of view of energetics , the failure of the dust to have a profound impact on the spectrum is simply a consequence of its optical properties : its inability to absorb in the near - infrared means that it can not redistribute the bulk of the stellar flux .
the dust scattering measured by the technique in this paper is thus largely independent of the form of the infrared spectrum , and could therefore have remained hidden from investigations based on sed fitting . by this argument , the mid - infrared excess in the spectrum must come from a material that absorbs more strongly than forsterite in the near - infrared .
dust that has evolved and been enriched with iron ( that condenses at lower temperatures ) in an outflow consisting of shells partially ejected in previous pulsation cycles could satisfy this property .
more detailed mid - infrared spectral modeling is beyond the scope of this paper , but would need to include the emission from the extended molecular atmosphere as predicted by self - consistent modeling by @xcite and semi - empirical modeling of @xcite and @xcite .
m optical - depth of 1 at 2 stellar radii , illuminated by a star with a 3000k black - body spectrum .
flux is normalised to the 8@xmath15 m flux , and the 3000k black - body spectrum is overlaid for reference ( dotted line ) .
iras _ low resolution spectrometer ( lrs ) spectra are overplotted for r car ( crosses ) and rr sco ( diamonds ) .
the emission features in these spectra almost certainly come from a region geometrically more distant than that probed here ( see text ) . ]
the dust uncovered here is not inconsistent with the mid - infrared measurements of @xcite .
these authors fit an outflow model to r leo ( which has slightly more pronounced mid - infrared emission than either r car or rr sco ) , with an optical depth at 11@xmath15 m of 0.1 . for forsterite dust with @xmath25 = 55 nm , this corresponds to a 900 nm optical depth of 0.025 .
if a similar outflow were to exist around rr sco or r car in addition to the shell model , then its effect on the fit parameters in table [ tblfitparams ] would be roughly within the quoted errors . in order to measure scattering from such an outflow , shorter baselines and higher precision would be required . both r car and rr sco have relatively low mass - loss rates as constrained by co line observations .
@xcite modeled the mass loss rate for rr sco to be @xmath27 m@xmath28 per year and that of r car to be less than @xmath29 m@xmath28 per year . if we assume full mg condensation at solar metallicity , then our best fit model with a shell at 2 stellar radii and an optical - depth 0.15 in scattering at 900 nm has a total mass of @xmath30 if we continue our assumptions of dust composed of forsterite with @xmath31 nm and full condensation .
less than full condensation , or dust composed of the lower - abundance corundum would give an even higher mass shell .
this means that the observed mass - loss rates are only consistent with the thin - shell model as long as the shell is considered nearly static , taking hundreds or thousands of pulsational cycles for material in the shell to be fully ejected .
this is in turn consistent with the low radiative acceleration expected from dust that can exist so close to the stars .
outflow models , on the other hand , were not so easy to fit within a self - consistent picture of stellar mass loss . using the measured co outflow velocity from @xcite of 3km / s for rr sco we can calculate the mass - loss rate from a typical outflow model in table [ tblfitparams ] . again assuming full mg condensation at solar metallicity for forsterite dust with @xmath25 = 55 nm , the mass loss rate for a model with our best fit optical - depth 0.25 in scattering at 900 nm and condensation radius of 1.1 stellar radii is @xmath32 m@xmath28 per year , much higher than the observed mass - loss rates .
this demonstrates once again that the outflow model can be ruled out .
using optical interferometric polarimetry , we have spatially separated the component of flux at 900 nm scattered by dust around the mira variables r car and rr sco from their photospheric emission .
we found that the inner radius of dust formation around these stars to be less than three stellar radii , consistent with dust that is relatively transparent between 1 and 4@xmath15 m , such as iron - poor silicates or corundum .
this dust exists in a shell - like structure around these stars that may have little influence on their mid - infrared spectra and is not part of an outflow .
this result demonstrates the complexity of the circumstellar environment of mira variables where mass loss and dust formation are only made possible by pulsation .
simple outflow models are grossly inadequate , and it is necessary to consider the changing optical properties of dust as it evolves from the condensation radius outwards .
visual data for estimating the variability phases of targets at the times of the susi observations were obtained from the aavso website .
we thank m. scholz for many valuable discussions , and all the susi group members for their help in supporting the instrument .
this research was supported by the australian research council and the deutsche forschungsgemeinschaft within the linkage project `` red giants . ''
j. e. , boysen r. c. , cox g. c. , haniff c. a. , rogers j. , warner p. j. , wilson d. m. , mackay c. d. , 1994 , in proc .
2200 , p. 118 - 128 ,
amplitude and intensity spatial interferometry ii , james b. breckinridge ; ed . design and performance of coast . | arxiv |
Why do tealights burn violently when nearly burnt out
I'm not entirely sure if this is the right place for this question, but I decided that it's better than physics.se (and I had no other ideas). I hope this is a good match, otherwise please move the question where it would belong. :)
I often use a mildly scented tealight in my apartment to cover the lingering smell of food. I usually light them using a matchstick, and sometimes I would toss the matchsticks into the tealight after lighting it up.
Usually, the matchstick would burn out after a short while, and for most of the life of the tealight nothing interesting happens. However, when the tealight is very close to burning out with the remains of the matchstick inside, it starts burning very violently, with the flame forming fantastic shapes (it looks like the whole remaining volume of the wax is burning).
Once the flame was so violent it broke the heat resistant glass container I kept it in (I was careless and I let the side of the cup touch a thinner part of the glass, rather than just the bottom).
Why does this happen?
There are two factors that probably matter here. One is that, for most of the life of the tea light, only a small amount of wax is liquid and actually burning. Most of the flame is liquid wax burning in the wick with a small pool of liquid wax below the wick. But later, when most of the solid wax has gone *all* the wax will be liquid. The second is that the matchstick can act as a second wick.
When the wick is still vertical (and held there by the presence of solid wax) the area of melting is kept small as the flame is vertical and the area of melting is constrained. Later, the wick may fall over as there isn't enough solid wax left. Also the heat can spread wider as the volume of wax decreases as it is also conducted more effectively through the aluminium container (wax isn't a good conductor of heat). The net result is more liquid wax near the end of the candles life.
Then two other factors may intervene. If the wick falls over, there is now a larger area of wick where burning can happen and the whole wick (not just the tip) can burn. Sometimes the matchstick will now also act as a wick, increasing the area of flame. Both these effects make more flame and more heat in a sort of runaway reaction which might also cause enough heat to reach the flash point of the wax leading to an even bigger flame. Even if the flash point isn't reached, the flame from a bigger wick area and a match acting as a wick can be a lot bigger than the flame form a normal vertical wick.
When only about 3 mm of wax is left, the wax in the tea light becomes so hot that its flash point is reached, and it begins to burn independently of the wig as a yellow/orange flame, just as is well known to happen in a more bluish version with alcohol at room temperature. This effect has principally nothing to do with the matchstick, which has been thrown in (as mentioned in the question).
Given that the tea light is already burning independently of the wig, if one would now extinguish the flame by covering the vessel for a second, one could see that an extremely strong cloud of white fumes evaporates (which should not be inhaled!): this is inflammable gaseous wax, which may be torched again even if one removes the wick beforehand with tweezers.
In the case of a still full or half-full wax-vessel, it is not possible that the temperature of the wax raises to the flash point because the flame is then burning essentially above or on level with the rim of the vessel, so that the vessel and the wax are heated up much less. Additionally, when only few wax is left, this heating up is much more effective because the heat may then focus on less wax. (The heating effect is stronger if the wax is in an aluminium vessel, because metal reflects the heat back into the wax; however, the stronger effect is helpful to elucidate the real causal coherences.)
| stackexchange/chemistry |
Why does the density matrix $\rho$ obey a wrong-signed Heisenberg equation of motion?
The [density matrix](http://en.wikipedia.org/wiki/Density_matrix) is defined as
$$ \rho\_\psi ~:=~ \frac{\lvert\psi(t)\rangle \langle \psi(t)\vert}{ \langle \psi(t) |\psi(t)\rangle }$$
in the Schrödinger picture. $\rho\_\psi$ is obviously a time dependent projector, and the equation of motion on these projectors become:
$$
i\hbar\frac{d}{dt} \rho\_\psi ~=~ [H,\rho\_\psi] \tag{S}
$$
but my book also reports that the [Heisenberg equation of motion](http://en.wikipedia.org/wiki/Heisenberg_picture) on the operators/observables is:
$$
\mathrm{i}\hbar\frac{d}{dt} A ~=~ [A,H] . \tag{H}
$$
Why are the signs in eqs. (S) and (H) opposite?
Isn't $A$ an operator like $ \rho\_\psi$, although time independent? They belong to the same operator space, so I don't think I can apply duality, but I know that $A$ operate on the states to give us the expectation value through the relation
$$ \mathrm{Tr}( \rho\_\psi A)$$
so it should be in the dual space of the observables.
$\rho\_\psi$, the density matrix, is *not an observable/operator* evolving in the sense of the Heisenberg equation of motion
$$ \mathrm{i}\hbar\frac{\mathrm{d}}{\mathrm{d}t} A = - [H,A]$$
since it is defined, as you correctly write, as a projector on states, hence it is time-dependent in the Schrödinger picture (since there the states it projects on are time-dependent), obeying the [von Neumann equation](http://en.wikipedia.org/wiki/Density_matrix#The_Von_Neumann_equation_for_time_evolution)
$$ \mathrm{i}\hbar\frac{\mathrm{d}}{\mathrm{d}t}\rho\_\psi = [H,\rho\_\psi]$$
as a direct consequence of the Schrödinger equation. The von Neumann equation indeed differs from the Heisenberg equation of motion by a sign *because it is not an equation in the Heisenberg picture*, but in the Schrödinger picture.
In the Heisenberg picture, the states are time-independent, and the density matrix does consequently not evolve. In particular, it does *not* obey the Heisenberg equation of motion.
You can also look at this by considering that $\mathrm{Tr}(\rho\_\psi A)$ is the expectation value of a operator for a particular state. It takes to inputs - the "state input" $\rho\_\psi$ and the "operator input" $A$. In the Schrödinger and Heisenberg pictures, only *one* of these should be time-dependent, even if they both "look" like operators.
Your question apparently stems from a lack of understanding of the different pictures in quantum mechanics, that are Schrödinger picture, Heisenberg picture and Interaction picture.
In the Schrödinger picture, states are time-evolving, while observables are time-independent. The density matrix is another (more general) way of writing the state vector; its time evolution follows from the von-Neumann equation, which can be derived from the Schrödinger equation and its Hermitian conjugate, given by
$$ \mathrm i \hbar \frac{\partial}{\partial t} | \psi(t) \rangle\_\mathrm{S} = H | \psi \rangle\_\mathrm{S},$$
and
$$ -\mathrm i \hbar \frac{\partial}{\partial t} {}\_{\mathrm S}\langle \psi(t)| = {}\_{\mathrm S}\langle \psi(t)|H .$$
Take the time derivative of the density matrix here for a pure state (beware, there are partial derivatives, see <http://en.wikipedia.org/wiki/Liouville%27s_theorem_%28Hamiltonian%29#Quantum_Liouville_equation>), and use the product rule, you get
$$\mathrm i \hbar \frac{\partial}{\partial t}\rho\_{\mathrm S} (t) = \mathrm i \hbar \frac{\partial}{\partial t} | \psi(t) \rangle\_\mathrm{S} \langle \psi(t)| = \mathrm i \hbar \Bigl( \frac{\partial}{\partial t} | \psi(t) \rangle\_\mathrm{S} \Bigr) {}\_\mathrm{S} \langle \psi(t)| + \mathrm i \hbar | \psi(t) \rangle\_\mathrm{S} \Bigl( \frac{\partial}{\partial t} {}\_\mathrm{S} \langle \psi(t)|\Bigr) .$$
Now you can pull the $\mathrm i \hbar $ inside the bracket and substitute each of the brackets by the correspondings left hand sides of the Schrödinger equation and its Hermitian conjugate, to obtain
$$ \mathrm i \hbar \frac{\partial}{\partial t} | \psi(t) \rangle\_\mathrm{S} \langle \psi(t)| = H | \psi \rangle\_\mathrm{S} \langle \psi(t)| - | \psi(t) \rangle\_\mathrm{S} \langle \psi(t)|H = [H,\rho\_{\mathrm S}(t)]. $$
In the Heisenberg picture, the observables are evolving in time, while the states are constant.
The density matrix can be stated in any of these pictures, where you take the expectation value of an observable $A$ always via $\mathrm{Tr}[\rho\_{\mathrm S}(t) A\_{\mathrm S}] = \mathrm{Tr}[\rho\_{\mathrm H} A\_{\mathrm H}(t)] $.
Here $\mathrm S$
and $\mathrm H$ denote the Schrödinger and the Heisenberg picture.
Please note that
$$\rho\_{\mathrm S}(0) = \rho\_{\mathrm H} \text{ and } A\_{\mathrm H} (0) = A\_{\mathrm S} .$$
By using the unitary time evolution operator, we can show the equivalence of the pictures quite easy for the density matrix.
The unitary evolution operator is given (for time-independent Hamiltonian $H$)
$$ U(t) = \mathrm e^{-\mathrm i H t/\hbar} . $$
The density matrix at time $t$ is then given in the Schrödinger picture by
$$ \rho\_\mathrm{S} (t) = U(t) \rho\_{\mathrm S} (0) U^\dagger (t) ,$$
while the operators evolve in the Heisenberg picture as
$$ A\_\mathrm{H} (t) = U^\dagger(t) A\_{\mathrm H} (0) U (t) .$$
So we find for the expetation value for the observable $A$ the following:
$$ \langle A \rangle (t) = \mathrm{Tr}[\rho\_{\mathrm S}(t) A\_{\mathrm S}] = \mathrm{Tr} [ U(t) \rho\_{\mathrm S}(0) U^\dagger (t) A\_{\mathrm S} ]$$
in the Schrödinger picture. We can now very easy switch to the Heisenberg picture by using the cyclic property of the trace, i.e.
$$\mathrm{Tr} [ABC] = \mathrm{Tr} [BCA] = \mathrm{Tr} [CAB] ,$$
by cycling the first unitary operator to the end, so we obtain
$$\langle A \rangle (t) = \mathrm{Tr} [ \rho\_{\mathrm S}(0) U^\dagger (t) A\_{\mathrm S} U(t)] .$$
Using the equivalence of the two pictures at $t=0$, we can reqrite this as
$$\langle A \rangle (t) = \mathrm{Tr} [ \rho\_{\mathrm H} U^\dagger (t) A\_{\mathrm H}(0) U(t)] = \mathrm{Tr} [ \rho\_{\mathrm H} A\_{\mathrm H}(t)].$$
Actually, you can use duality:
the normal states of quantum mechanics are objects of the (unique) predual of the von Neumann algebra of quantum observables.
Using a concrete example: if the algebra of observables are the bounded operators on a Hilbert space, the predual are the trace class operators. Of them, the normal states are the ones positive, self-adjoint and of trace norm one.
It is then clear that by mutual duality the evolution on observables/states induces the evolution of states/observables; and that takes into account of the "minus sign" in the generator that is different between the two.
| stackexchange/physics |
clostridium difficile is responsible for 15% to 25% of antibiotic - associated diarrhoea and for more than 95% of pseudomembranous colitis .
this gram - positive spore - forming bacterium is the major cause of hospital - acquired diarrhoea . since 2003 , many countries have reported outbreaks of severe c. difficile infections ( cdi ) .
this trend is assumed to be due in part to the emergence and rapid dissemination of an epidemic clone of c. difficile named nap1/bi/027 .
other changes have been observed in the epidemiology of cdi : ( a ) community cases of cdi have increased and have been described in people previously considered to be at low risk , ( b ) another clone , named 078 , involved in severe cdi has been described , ( c ) c. difficile has been recognized as a pathogen or commensal in numerous animals and ( 4 ) detection of c. difficile in food products has been reported .
the main virulence factors of c. difficile are two large clostridial toxins , toxins a ( tcda ) and b ( tcdb ) , encoded by the genes tcda and tcdb , respectively .
these two genes are located within a locus of pathogenicity ( paloc ) with three accessory genes : tcdc , tcdr and tcde .
sequencing of the paloc has indicated a series of genetic polymorphisms . on the basis of pcr
restriction fragment length polymorphism of this locus , c. difficile strains are currently divided into 31 toxinotypes ( or toxin variant strains ) that are characterized by insertions , deletions and sequence mutations compared to the reference strain , vpi 10463 ( toxinotype 0 ) . among the 31 toxinotypes ,
only the toxinotype xi strains do not produce tcda and tcdb ( ab strains ) related to an absence of the tcdb gene and the presence of a large deletion in the 5 region of the tcda gene .
a third toxin , called binary toxin or cdt , was isolated for the first time by popoff et al .
in a patient with severe pseudomembranous colitis .
this toxin is detected in 17% to 23% of c. difficile strains in nonoutbreak situations [ 1315 ] .
this toxin is encoded by two genes , cdta and cdtb , located on the cdt locus ( cdtloc ) , which is separated from the paloc on the c. difficile chromosome .
strains carrying the cdtloc belonged to specific toxinotypes , e.g. toxinotypes iii , iv , v and xi , or , more rarely , to strains for which the paloc is absent .
five nonepidemiologically related c. difficile strains , characterized by the absence of tcdb gene but the presence of the binary toxin genes , and suspected to belong to the toxinotype xi ( abcdt ) , were sent to the national reference center ( nrc ) for c. difficile in paris , france , between december 2011 and february 2013 .
the objectives of this study were to confirm the toxinotype of those strains , to describe the clinical features of the five patients in whom these strains were isolated and to estimate the prevalence of such strains that produce binary toxin but not large clostridial toxins .
between december 2011 and february 2013 , five strains with atypical toxin - encoding gene content were sent to the nrc for c. difficile in paris .
three of five strains were identified as bcdt using the molecular method xpert
c. difficile ( cepheid , sunnyvale , ca , usa ) and were sent by the biologists to the nrc for confirmation of this particular result and to exclude a genetic drift in tcdb .
the two other strains were characterized as abcdt by the nrc performing routine pcr targeting tcda , tcdb , cdta and cdtb genes on dna extracted from c. difficile cultures .
dna extraction from colonies of c. difficile was performed with the instagene matrix kit ( bio - rad laboratories , hercules , ca , usa ) .
amplification by pcr of tcda , tcdb , tcdc , cdta and cdtb genes coding for toxin a , toxin b , tcdc and the binary toxin , respectively , was performed using primers described elsewhere .
the toxinotypes were determined according to the method described by rupnik et al .
.
briefly , amplification of a2 and a3 fragments of tcda and b1 , b2 and b3 fragments of tcdb was performed as described .
in vitro toxin production was tested by inoculating two to five colonies into brain
heart infusion broth ( oxoid , hampshire , england , uk ) that was incubated 5 days under an anaerobic atmosphere . the supernatant was filtered ( 0.22 m pore size ) , and the filtrate was inoculated on mrc-5 cells .
toxin detection was also tested by c. diff quik chek complete ( alere , orlando , fl , usa ) performed directly on colonies .
clinical data were reviewed and analyzed for the five patients harbouring these strains . to estimate the frequency of abcdt strains , 220 consecutive nontoxinogenic strains ( ab ) isolated in paris ( north of france ) ( n = 84 ) and montpellier ( south of france ) ( n = 136 ) between july 2011 and april 2013 were screened .
all strains were isolated from patients with diarrhoea who were suspected of having cdi , who were admitted in saint antoine ( paris ) or arnaud de villeneuve ( montpellier ) hospitals and strains were characterized as nontoxinogenic strains by toxigenic culture ( tc ) .
the in vitro determination of c. difficile isolates ability to produce toxins ( tc ) was performed either by inoculating supernatant from a 5-day brain heart infusion broth ( oxoid ) on mrc-5 cells ( paris ) or by using immunocard toxins a&b ( meridian bioscience , cincinnati , oh , usa ) directly on colonies as recommended by the manufacturer ( montpellier ) .
absence of the paloc was confirmed as described elsewhere by obtaining an amplification of about 700 bp using primers lok1 and lok3 anchored outside the targeting paloc . in case of a negative result ( i.e. , absence of the paloc
was not confirmed ) , amplification by pcr of tcda , tcdb , tcdc , cdta and cdtb genes , toxinotyping and pcr ribotyping were performed as described above .
amplification of b1 , b2 and b3 fragments of tcdb was confirmed as negative for the five strains ( data not shown ) . only the 3 region ( a2 and a3 fragments ) of the tcda gene was amplified for all the strains .
binary toxin genes and a 39 bp deletion in tcdc were identified in the five isolates .
three isolates were defined as toxinotype xia ( ecori restriction pattern of a3 pcr fragment was of type 5d ) and two isolates as xib ( ecori restriction pattern of a3 pcr fragment was of type 8) ( fig . 1 ) .
the five strains showed either a similar or slightly different pcr ribotyping banding pattern as reference strains ( r11402 , 542 and cd219 ) , suggesting that the five strains belonged to the same lineage ( fig .
the strains tested negative for their in vitro toxin production either by the cytotoxicity assay on mrc-5 cells or the c. diff quik chek complete assay .
clinical and biological data of the five patients were analyzed ( table 1 ) .
the five patients were hospitalized in french hospitals in different areas , and their infections were considered to be epidemiologically unrelated .
all five patients were symptomatic ( diarrheic stools ) and had risk factors for cdi ( antibiotics n = 5 , age > 65 years n = 3 ) . four of five patients harbouring toxinotype xi strains were considered truly infected by their treating physician and were specifically treated with oral metronidazole .
the clinical presentation of one patient was atypical because diarrhoea was probably the manifestation of ileal cdi , as the patient had previously undergone a total colectomy ( table 1 , patient 1 ) .
one patient was not treated for cdi , but symptomatic treatment was started and diarrhoea resolved in the following days ( patient 3 ) . among the 220 studied strains ,
an amplification was obtained with primers lok1 and lok3 , confirming the absence of the paloc , for 219 strains ( 99.5% ) .
absence of amplification with primers lok1 and lok3 was observed for one strain ( 0.5% ) .
further amplifications for tcda and tcdb showed the presence of the 3 region of tcda only .
this strain belonged to the same pcr ribotype ( 033/033-like ) as the five toxinotype xi strains previously identified in our laboratory ( fig .
clinical data for the patient hospitalized in hpital saint antoine , paris , and harbouring this strain were sparse ; no specific treatment was initiated despite clinical symptoms , probably because the strain was reported as nontoxigenic by tc to the physician ( table 1 , patient 6 ) .
we report here the six first strains of toxinotype xi isolated in patients suspected of having cdi in france .
toxinotype xi strains produce only binary toxin but not the common large clostridial toxins tcda and tcdb .
only portion of the 3 end region of paloc is present , bearing part of the sequence of tcda and tcdc , and the 5 region covering tcdb , tcdr and tcde is deleted .
described heterogeneity in the a3 region of tcda that leads to distinguish two subtypes , xia and xib .
so far , toxinotype xi is the only c. difficile toxinotype to be positive for binary toxin but negative for tcda and tcdb production ( abcdt ) ( http://www.mf.uni-mb.si/tox/images/table1_toxinotypes-characteristics.pdf ) . uncertainties still remain about the clinical significance of toxinotype xi in the pathogenesis of cdi because the role of binary toxin as a virulence factor is still controversial .
this toxin is produced by the highly virulent nap1/bi/027 clone , which has caused severe outbreaks in north america and europe , and by the emerging 078 clone , suggesting that it may serve as an additional virulence factor and may act in synergy with the large clostridial toxins . a few clinical and epidemiological studies that compared data from infections with strains producing binary toxin in addition to tcda and tcdb and infections with strains producing only tcda and tcdb suggested that there could be a correlation between the production of binary toxin and the severity of cdi [ 2325 ] .
a case control study conducted in 2005 compared the clinical presentation of 26 patients infected with strains producing binary toxin in addition to toxins a and b to 42 controls infected with strains producing only toxins a and b. using univariate analysis , diarrhoea due to a binary toxin
positive strain was more often community acquired ( p = 0.017 ) and associated with abdominal pain ( p = 0.07 ) than diarrhoea due to binary toxin negative strains .
diarrhoea was more often the cause of hospitalization in cases than in controls ( p = 0.003 ) .
a more recent study reported that patients infected with c. difficile harbouring genes for toxins a and b and binary toxin had higher case - fatality rates than patients infected with c. difficile harbouring genes for toxin a and b without binary toxin .
another study has shown that the presence of the binary toxin gene in c. difficile isolates was the only independent predictive factor for recurrent cdi .
in the rabbit ileal loop model , inoculation of supernatants from culture of binary toxin positive strains that produced neither tcda nor tcdb leads to enterotoxic response , suggesting that binary toxin may act as a virulence factor .
nevertheless , in the hamster model of ileocolitis , these strains produced no symptoms despite colonization .
recent in vitro experiments have shown that binary toxin induces redistribution of microtubules and formation of long microtubule - based protrusions at the surface of intestinal epithelial cells .
the cdt - induced microtubule protrusions form a dense mesh work at the cell surface , which wrap and embed bacterial cells , thereby largely increasing the adherence of c. difficile
.
finally , the importance of binary toxin was demonstrated using isogenic toxin mutants ( abcdt ) of nap1/027/bi strains producing only binary toxin inoculated to the hamsters .
, this pcr ribotype is the second most common strain isolated in cattle and calves .
however , very few cases of human cdi due to toxinotype xi have been described in the literature . among the five cases reported by geric et al .
, three were from asymptomatic patients and one was from a symptomatic patient ; no clinical information was available for the remaining case . in the present report , c. difficile strains were isolated from six symptomatic patients with several risk factors for cdi , including advanced age and previous broad - spectrum antibiotic treatment .
these data support the conclusion that diarrhoea in four patients was really due to c. difficile .
only a few studies have estimated the prevalence of toxinotype xi strains . in this study
, we found a prevalence of 0.5% ( 1/220 ) . in a european study , 411 clinical c. difficile isolates from 38 hospitals in 14 european countries were characterized by toxinotyping .
isolates , 268 ( 75.7% ) were from toxinotype 0 ; 86 strains ( 24.3% ) belonged to nine variant toxinotypes , but none was of toxinotype xi .
a large collection ( 5000 isolates ) of c. difficile isolates from the united states and other sources over a 20-year period was examined for the presence of binary toxin genes among strains that do not produce tcda and tcdb .
eight isolates have been reported as ab but cdt
. among these eight isolates , five had a truncated paloc characteristic of toxinotype xi ( including two toxinotype xia and three toxinotype xib isolates ) .
however , most of the toxinotype xi strains isolated in that study were recovered from asymptomatic patients .
all these data indicate that the prevalence of strains from toxinotype xi in humans seems very low . however ,
indeed , the microbiological diagnosis of cdi in france is mostly based on the detection of tcda or tcdb in stool samples , and clinical laboratories do not specifically look for binary toxin . as a consequence ,
strains from toxinotype xi would be likely reported as nontoxigenic isolates when tested in a clinical laboratory . since 2009 ,
most of the assays only target the tcda or tcdb genes of c. difficile . among these tests ,
the xpert
c. difficile assay simultaneously detects three targets , including tcdb , binary toxin genes and the deletion in position 117 within the tcdc gene .
this assay was initially developed in order to presumptively identify cdi due to the epidemic strain nap1/bi/027 . in recent years , this assay has been widely used in many laboratories in france for the routine diagnosis of cdi .
three cases of toxinotype xi that we report here were detected in clinical laboratories using the xpert c. difficile assay and were suspected only because of the presence of binary toxin gene .
it is likely that the increasing use of this test will enable a better recognition of toxinotype xi and therefore of its potential role in clinical disease . in conclusion
, the present study suggests that c. difficile strains producing only binary toxin seem to be pathogenic despite the lack of tcda and tcdb .
a result of c. difficile testing that would be only positive by pcr for binary toxin should be taken into account and may reveal a toxinotype xi strain . | pubmed |
this is the second paper in a series of two where we discuss stationary solutions to the nlse on metric graphs that is _ nonlinear quantum graphs_. in the first paper @xcite we have developed a framework that allows to reduce the solution of the wave equation with matching conditions at the vertices to a finite set of nonlinear algebraic equations and we have derived a low intensity approximation scheme for the nonlinear transfer operator that expresses the wave function and its derivative at one end of an edge in terms of their values at the other end .
+ nonlinear quantum graphs have received increasing attention in the mathematical and theoretical physics literature recently as a model that allows to study the interplay between topology and nonlinear wave propagation in a relatively simple but non - trivial setting .
we refer to our first paper @xcite for a detailed overview of the recent literature .
+ in this paper we focus on the stationary cubic nlse and we apply the framework and the approximation scheme to a number of basic open and closed graph structures . in order to keep this
paper self - contained we summarise the relevant exact framework for nonlinear quantum graphs and the approximate solutions of the cubic nlse using canonical perturbation theory in the remainder of this section . in section [ stationary ]
we consider the spectral curves of some basic examples with increasing complexity : the interval , the ring , star graphs and the tadpole ( aka lollipop or lasso ) graph .
for all these examples we derive a finite set of nonlinear algebraic equations that describe the spectrum of the nonlinear graph and the corresponding wave functions . in the low - intensity limit
we show how the equations reduce to a single secular equation for the spectrum that is well known for linear quantum graphs . in a short wavelength
limit we show how canonical perturbation theory simplifies the nonlinear equations and may be used in order to describe genuine nonlinear effects such as the appearance of new solutions via bifurcations .
+ in section [ scattering ] we consider stationary scattering on open graphs where one or two nonlinear edges are connected to a small number of leads .
we assume linear wave propagation on the leads and derive exact equations that describe the nonlinear scattering of stationary waves . in the small wavelength limit
we show how canonical perturbation theory simplifies the nonlinear equations that describe genuine nonlinear effects .
we explicitly show how multi - stability occurs in some settings .
+ in section [ conclusion ] we conclude with an outlook and the proposition to use the approximate description based on canonical perturbation theory as a genuine model for nonlinear stationary waves on metric graphs .
+ the definitions of the elliptic integrals used in the main text are summarised in the appendix . a nonlinear quantum graph consists of a metric graph , a nonlinear wave equation on the edges of the graph and matching conditions for the wave functions at the vertices .
each edge @xmath0 has a length @xmath1 and a coordinate @xmath2 $ ] .
some edges may be half - infinite intervals with @xmath3 and one end at @xmath4 adjacent to one vertex .
we call such edges _ leads _ while edges of finite length ( adjacent to vertices on both ends ) will be called _
bonds_. graphs that contain ( do not contain ) leads are _ open _ ( _ closed _ ) .
+ in this paper we consider the stationary cubic nlse for a complex valued scalar wave function @xmath5 on any edge @xmath0 @xmath6 here @xmath7 is the nonlinear coupling constant and @xmath8 the chemical potential . the nonlinear interaction is called repulsive for @xmath9 and attractive for @xmath10 .
we use units ( of energy ) where the coefficient of the second derivative in is unity .
the wave equation needs to be complemented by matching conditions at the vertices .
we will introduce these below in section [ sec : matching ] after discussing the solutions of the wave equation on one edge .
let us consider one edge without any conditions at its ends .
we omit the index @xmath0 until we come back to solutions on the graph . all local solutions to the stationary cubic nlse on an interval
are known and may be expressed in terms of elliptic functions ( see @xcite for a complete overview ) . in this paper
we only consider solutions @xmath11 with a positive chemical potential @xmath12 ( @xmath13 ) .
we will also restrict our attention to sufficiently low intensities where @xmath14 such that all solutions remain bounded when extended to the infinite line .
the bounded solutions are characterized by the maximal and minimal values @xmath15 of the local intensity @xmath16 @xmath17 the amplitude is a periodic function @xmath18 with period @xmath19 where @xmath20 is the complete elliptic integral of first kind ( see appendix [ appendix ] for our conventions for elliptic functions and integrals ) and we introduced the two constants @xmath21 it is explicitly given in terms of the @xmath22-periodic elliptic sine function @xmath23 as @xmath24 the phase @xmath25 is a monotonic function that is non - decreasing in the direction of the constant current @xmath26 in the interval @xmath27 the phase is given by @xmath28 where @xmath29 is the incomplete elliptic integral of third kind and @xmath30 for @xmath31 the phase function is continued in a smooth way using @xmath32 note that the change of phase over a period @xmath33 is in general not commensurate with @xmath34 .
+ the stationary wave functions simplify considerably if the current vanishes @xmath35 . for the bounded wave functions this is the case if and only if there are nodal points such that @xmath36 .
the corresponding wave functions are given by @xmath37 these wave functions are essentially real as they only contain a global phase factor @xmath38 .
the wave function on the graph @xmath39 ( where @xmath40 is the set of edges of the graph ) is just the collection of all scalar wave functions on the edges .
we choose standard matching conditions at all vertices ( also known as kirchhoff or neumann matching conditions for quantum graphs ) . at the vertex @xmath41
these are defined as follows .
let @xmath42 be the set of edges connected to @xmath41 .
we may assume that @xmath4 at the vertex @xmath41 for all @xmath43 .
we now require the following conditions : ( i. ) continuity of the wave function @xmath44 for all @xmath45 , and ( ii . ) a vanishing sum of outward derivatives @xmath46 . if @xmath47 is the valency of the vertex @xmath41 these conditions imply @xmath48 complex equations that couple the wave functions on different edges .
it is useful to write these conditions in terms of amplitudes and phases . with @xmath49 continuity of the wave function
just implies continuity of amplitudes and phases @xmath50 the condition on the outward derivatives then becomes @xmath51 [ eq : derivativesum ] where @xmath52 is the ( constant ) current along edge @xmath41 .
the second equation is just kirchhoff s rule that the sum of all currents at a vertex must vanish .
the exact solutions of the one - dimensional nlse described in section [ sec : elliptic_wf ] may be used to find solutions on a graph .
the matching conditions and lead to a finite set of nonlinear algebraic equations for the parameters @xmath53 , @xmath54 and @xmath55 of the exact solution on each edge . even for simple network structures these equations
are usually too complex to be solved analytically .
an approximation method that may take into account the effect of week nonlinearity has been developed in @xcite using canonical perturbation theory after rewriting the nlse as an equivalent integrable hamiltonian system with two degrees of freedom and ` time ' @xmath56 . in this approximation scheme
the unperturbed system is the corresponding linear schrdinger equation obtained by setting @xmath57 .
the approximation is locally valid for sufficiently small nonlinearities @xmath58 ( where @xmath59 ) .
we will use the dimensionless parameter @xmath60 to denote the order of the approximation . with few exceptions we will only require first - order perturbation theory in this manuscript .
the corresponding approximate solutions may best be described introducing action - angle variables in the zero - order ( linear ) wave equations . with @xmath61 the solution in higher order perturbation theory is written as @xmath62 where @xmath63 while @xmath64 can take arbitrary real values .
the action variable @xmath64 is constant for arbitrary value of @xmath65 while @xmath66 is only constant for @xmath57 .
indeed for @xmath57 one has @xmath67 and @xmath68 such that eq .
reduces to a superposition of two plane waves with opposite current directions . in first - order perturbation theory
one finds @xcite @xmath69 [ eq : actionangle ] where @xmath70 and @xmath71 are the constant action variables of the nonlinear system and [ eq : phasedynamics ] @xmath72 note that one action variable is equivalent to the current @xmath73 .
equations and reveal two entirely different effects of a weak nonlinearity on a solution .
the first effect seen in is a local deformation of the linear solution .
the second effect seen in is a change of the phase dynamics where we see a shift in the ` nonlinear wave numbers ' @xmath74 and @xmath75 .
the latter changes may accumulate over large distances and lead to a dephasing between the two angles which is not present in the linear case where the two nonlinear wave numbers have the exact ratio two . in the setting of a nonlinear quantum graph
we need to specify the parameters @xmath76 , @xmath71 , @xmath77 and @xmath78 on each edge separately such that the given matching conditions are satisfied at the vertices .
it may then happen that though the local deformations ( which are of order @xmath79 ( where @xmath80 ) are tiny while the accumulated change in the phase @xmath81 along an edge of length @xmath82 is of order unity which implies that the global spectral characteristics of the graph ( such as the nonlinear spectrum ) completely change .
we thus have a second dimensionless parameter @xmath83 that may characterise different asymptotic regimes .
especially short wave length limits @xmath84 will be of interest . in the latter locally weak nonlinearity @xmath85 does not imply globally weak nonlinearity @xmath86 .
-@xmath87 plane where the asymptotic regimes r1 , r2 , r3 are applicable .
the dimensionless parameters @xmath88 and @xmath83 define the lines @xmath89 , @xmath90 and @xmath91 with are shown .
the dashed ( red ) line @xmath92 marks the complete breakdown of canonical perturbation theory which requires @xmath85 .
regimes r1 and r2 require @xmath93 and @xmath94 and thus break down near the dash - dotted ( green ) line @xmath95 .
regime r3 only requires @xmath96 while @xmath97 may not be negligible . along the dash - dotted ( green )
line @xmath95 only first - order perturbation theory gives a non - negligible contribution .
along the dotted line @xmath98 second - order contributions are required .
, scaledwidth=65.0% ] we may identify three different regimes that are consistent with the canonical perturbation expansion ( @xmath85 ) and may lead to additional simplifications .
we explain their range of validity in the following and illustrate it in figure [ fig : asymptotic_regimes ] . *
the _ low - intensity asymptotic regime _
@xmath96 at fixed @xmath99 ( see illustration in figure [ fig : asymptotic_regimes ] ) .
this regime is weak in both the local and the global sense . for the leading nonlinear effects one may expand the oscillatory functions with respect to the small phase shifts ( where this leads to a simplification ) .
we will see that this regime allows explicit analytical results that include nonlinear effects to lowest order . *
the _ short wavelength globally weak nonlinear asymptotic regime _
@xmath84 with @xmath100 ( see illustration in figure [ fig : asymptotic_regimes ] ) . this is a special case of the low - intensity regime which leads to additional simplifications as the dominant nonlinear effects all come from the shift in the nonlinear wave numbers @xmath74 and @xmath75 . * the _ short wavelength asymptotic regime with moderately large intensities _ @xmath101 and @xmath96
( see illustration in figure [ fig : asymptotic_regimes ] ) .
this regime is weakly nonlinear only in the local but not ( necessarily ) in the global sense and the intensity is allowed to have moderately large values . as in the globally weak short wavelength regime
the leading effect is the change of the nonlinear wave numbers @xmath74 and @xmath75 which leads to phase shifts of order @xmath102 .
as these phase shifts may be large we may _ not _ expand the oscillatory terms and the nonlinear effect in the wave function comes in the leading order .
if we are only interested in the leading effect we may neglect all other deformations . in this regime the equations that describe the stationary states on nonlinear quantum graphs simplify considerably but remain nonlinear .
+ a final note on this regime : we have only given the leading shift of the nonlinear wave numbers in .
this is consistent as long as the intensity is only growing moderately as @xmath103 ( at fixed @xmath82 and @xmath65 ) .
the regime however allows a larger growth @xmath104 but this requires to calculate the nonlinear wave numbers @xmath74 and @xmath75 to higher orders : if @xmath105 then we need to calculate @xmath74 and @xmath75 to @xmath106-th order .
while this is possible in principle ( see @xcite ) we will confine our discussions to @xmath107 ( or , equivalently @xmath108 ) with one exception : in our discussion of multi - stability in section [ sec : scatt_interval1 ] we will consider @xmath109 and @xmath110 . apart from finding analytical or numerical solutions in the above mentioned cases we will also discuss to some extent whether the regimes allow for a quantitative or at least qualitative description of nonlinear effects such as multi - stability of scattering solutions or bifurcations of spectral curves .
our focus here is on how the complexity of the description of example graphs reduces with an appropriate perturbation theory
. therefore we will usually not give the complete discussion of nonlinear effects that each example graph may deserve .
we believe that the methods we present here will be useful for such a detailed analysis in the near future .
finally let us state how equations and simplify for essentially real wave functions ( real modulo a global complex phase ) where the current @xmath71 vanishes .
these equations appear to be singular at @xmath111 .
the limit @xmath112 is however well defined and after an appropriate shift of the angle variable @xmath113 they reduce to @xmath114 [ eq : real_perturbation_sol ] where @xmath38 is a fixed global phase of the solution .
note that we have included a term proportional to @xmath115 in @xmath74 .
this term can be obtained straight forwardly using canonical perturbation theory to second order in @xmath116 . in most of our discussion
this term will be negligible ( apart from section [ sec : scatt_interval1 ] ) .
let us now discuss a few examples of closed nonlinear quantum graphs @xmath117 .
exact solutions for the interval and the ring are well - known and are used here to illustrate approximations using canonical perturbation theory the star and the lasso are added to illustrate how proper graph topologies behave .
our main aim in this section is to describe the spectral curves @xmath118 that give the nonlinear eigenvalues as a function of the @xmath119-norm or _ total intensity _ @xmath120 which is physically proportional to the number of particles in a bose - einstein condensate or the number of photons in an optical setting . in each case we will reduce the problem of solving the generalized nonlinear eigenproblem to a set of ( coupled ) nonlinear equations with a finite number of unknown variables .
where analytical solutions are available we will give them , but will sometimes have to rely on numerical solutions .
the stationary nlse on the interval ( as a graph with a single edge connecting two vertices , see figure [ fig : closed_graphs]a ) ) @xmath121 $ ] with dirichlet conditions at both ends @xmath122 is straight forward to solve @xcite . in this case
the current @xmath123 vanishes which leads to the essentially real exact solutions where we set the arbitrary phase @xmath124 .
the dirichlet condition at @xmath125 implies @xmath126 .
the remaining parameters in the solution are the wave number @xmath127 and @xmath128 .
the latter is a dimensionless measure of the strength of nonlinearity and proportional to the intensity with @xmath129}(g |\phi(x)|^2/k^2)= \rho_+$ ] ( for @xmath130 it is bounded by @xmath131 ) . in order to obey the second dirichlet condition @xmath132 as well the wave number @xmath133 has to be quantised according to @xmath134 for any positive integer @xmath106 . for @xmath135
one finds the usual spectrum @xmath136 of the linear schrdinger equation .
the total intensity can now be evaluated as @xmath137 } { g } & \text{if $ g>0$}\\ \frac{2n k_n(\rho_+ ) ( 2+\rho_+)\left[\pi\left ( 1 , \frac{\rho_+}{2(\rho_++1 ) } , \frac{\rho_+}{2(\rho_++1 ) } \right ) -k\left ( \frac{\rho_+}{2(\rho_++1 ) } \right)\right ] } { |g|\sqrt{\rho_++1 } } & \text{if $ g<0$. } \end{cases } \label{eq : interval_norm}\ ] ] equations and implicitly define the nonlinear wave number spectrum @xmath138 which is shown in figure [ fig : interval_spectrum ] together with some corresponding wave functions @xmath139 .
are shown dashed .
on the left the regime @xmath140 , on the right the regime @xmath130 is considered .
the upper panels focus on small values of @xmath83 , the lower panels on large values of @xmath99 .
( for the purpose of this graph we have defined @xmath141 which is numerically smaller but of the same order compared to the definition in the text . ) , title="fig:",scaledwidth=45.0% ] are shown dashed . on the left the regime @xmath140 , on the right the regime @xmath130 is considered .
the upper panels focus on small values of @xmath83 , the lower panels on large values of @xmath99 .
( for the purpose of this graph we have defined @xmath141 which is numerically smaller but of the same order compared to the definition in the text . ) , title="fig:",scaledwidth=45.0% ] + are shown dashed . on the left the regime @xmath140 , on the right the regime @xmath130 is considered .
the upper panels focus on small values of @xmath83 , the lower panels on large values of @xmath99 .
( for the purpose of this graph we have defined @xmath141 which is numerically smaller but of the same order compared to the definition in the text . ) , title="fig:",scaledwidth=45.0% ] are shown dashed . on the left the regime @xmath140 , on the right the regime @xmath130 is considered .
the upper panels focus on small values of @xmath83 , the lower panels on large values of @xmath99 .
( for the purpose of this graph we have defined @xmath141 which is numerically smaller but of the same order compared to the definition in the text . ) , title="fig:",scaledwidth=45.0% ] with the full solution available for the interval we may use this as a test ground for using the perturbative local solutions that have been developed in section iii of @xcite . in first order perturbation theory the wave function is given by .
the first dirichlet condition implies @xmath142 and we may again set @xmath143 .
the nodal points @xmath144 with @xmath145 then satisfy @xmath146 . requiring @xmath132 thus leads to the condition @xmath147 on the wave number . note that @xmath148 .
the total intensity of the corresponding wave function is @xmath149 which allows us to write @xmath150 explicitly in terms of the total intensity @xmath151 which is consistent with expanding and for small @xmath152 and solving for @xmath138 including first - order corrections ( for either sign of @xmath65 ) .
note that @xmath153 .
figure [ fig : interval_spectrum ] compares the exact spectrum and wave functions to the ones obtained using perturbation theory . as expected from the error estimate in the agreement
extends to much higher intensities for large values of @xmath99 .
+ note that no further assumptions than locally weak nonlinearity ( in first - order canonical perturbation theory ) have been used to derive which is thus valid in the low - intensity and both small wave length regimes introduced in sec .
[ sec : canonpert ] .
the small wave length limit corresponds here to @xmath154 where includes the regime r3 where @xmath155 should grow not faster than @xmath106 .
only the first - order shift in the nonlinear wave number @xmath156 enters into the explicit first - order correction term to @xmath157 in and @xmath138 in . for @xmath157
higher - order corrections follow directly from higher - order corrections in the nonlinear wave number @xmath158 .
the explicitly given first - order correction ( and any higher order corrections ) to the intensity @xmath159 in result from corrections to @xmath158 _ and _ the deformations of the wave form .
this implies that apart from the shift in the nonlinear wave number also the deformations are relevant in higher - order corrections of @xmath138 .
+ for consistency let us compare maximal amplitudes in the exact and approximate solutions .
one then finds @xmath160 which allows us to express @xmath161 which is indeed the first - order expansion in @xmath152 of the exact expression .
+ while the shift of the nonlinear wave number and the deformation of the plane wave solution are both affected by the nonlinearity in first - order perturbation theory we see that even for the simplest graph the two effects enter in different ways and that some leading nonlinear corrections to spectral curves may be found by only referring to the shift .
a star graph consists of @xmath162 edges ( which we enumerate @xmath163 ) with lengths @xmath164 , one vertex of degree @xmath162 ( the _ center _ of the graph to which all edges are adjacent ) and @xmath162 vertices of degree one where we assume dirichlet conditions .
for @xmath165 the corresponding graph is depicted in figure [ fig : closed_graphs]b ) .
the ground states of nonlinear star graphs and their stability ( with respect to the time - dependent nlse dynamics ) have been the subject of recent research @xcite .
+ we will use the convention that the variable @xmath166 on edge @xmath0 increases towards the center where @xmath167 while @xmath4 corresponds to the other end .
we will also assume that the coupling constant takes the same constant value @xmath168 on all edges .
as there is no cycle in the graph the current has to vanish everywhere and the wave function @xmath169 may be chosen real . + if some of the edges have rational ratios then we may immediately construct some solutions with a nodal point at the central vertex from the known solutions on the interval . for instance
if @xmath170 assume that @xmath171 is a solution of the nlse on the interval @xmath172 that we continue smoothly to the edge such that @xmath173 . defining @xmath174 to be the corresponding continuation along edge @xmath175 ( that is @xmath176 ) and @xmath177 on all remaining edges we have constructed a solution on the star with a nodal point in the centre . moreover there will be a corresponding spectral curve @xmath178 such that the central vertex remains a nodal point for the solutions of this spectral curve . if all edges have rationally independent lengths then we are not able to build any solutions as easily from the solutions on the interval .
there will generally still be some solutions with a nodal point at the centre ( and a wave function which is supported by a few edges ) but these features can not be expected to be stable along any spectral curve .
+ let us now consider the problem of finding spectral curves under the assumption that there is no nodal point at the centre . by continuity we can extend this to spectral curves with isolated points with a nodal point at the centre .
we first reduce the problem of finding exact stationary solutions on a star to a set of nonlinear equations that may be solved numerically in an efficient way . for a given ( unperturbed ) wave number @xmath133 the wave function on each edge is given by . the dirichlet conditions
@xmath179 imply @xmath180 . the remaining parameters @xmath181 and @xmath182 have to be found by considering the matching conditions at the centre
let @xmath183 be the value of the wave function at the central vertex . by choosing a global phase
we assume @xmath184 the wave function is then real and @xmath185 .
the parameters @xmath181 can be found in terms of @xmath186 by solving the nonlinear equation @xmath187 .
this is a nonlinear equation which has in general many solutions @xmath188 for @xmath189 the sign @xmath190 then follows from requiring @xmath191 . choosing one solution branch @xmath192 on each edge this leaves @xmath186 and the wave number @xmath133 as free parameters .
however we have one more condition to satisfy which is @xmath193 this condition can be compactly written as [ eq : star_nonlinearquantisation ] @xmath194 we have omitted the explicit dependence of @xmath195 .
we may write the solutions of as spectral curves @xmath196 ( where @xmath106 enumerates disconnected spectral curves ) .
the total intensity @xmath197 is then calculated straight forwardly from the corresponding parameters @xmath181 .
this implies that we implicitly know @xmath138 . note that as @xmath198 all amplitudes @xmath199 have to vanish and the condition reduces to @xmath200 which is the secular equation for @xmath133 to be in the spectrum of the corresponding linear star graph where @xmath57 ( for rationally independent lengths this gives the complete spectrum ) .
+ numerically , if one point on a spectral curve @xmath201 is found one may use newton - raphson methods to extend this numerically to a finite part of the curve .
if one is only interested in spectral curves that connect to the spectrum of the corresponding linear graph it may be numerically more efficient to first solve for the linear spectrum and then extend the curves using newton - raphson methods .
+ while we have reduced the coupled nonlinear problem of finding @xmath162 parameters @xmath181 ( and corresponding signs ) to a sequence of @xmath202 relatively benign nonlinear equations that can be solved numerically it remains a formidable task to find all solutions in a given spectral interval ( and some restrictions on the maximal local or total intensities ) .
+ we now turn to the perturbative solutions for locally weak nonlinearity @xmath203 .
the wave function @xmath5 on each edge @xmath0 is then given in terms of with @xmath204 and @xmath205 .
we need to find a set of @xmath162 action variables @xmath206 such that the matching conditions at the centre are satisfied .
the continuity condition @xmath207 leads to the nonlinear implicit equation @xmath208 for @xmath209 .
we will later see that the asymptotic regimes r1 and r2 allow us to obtain explicit unique expressions for @xmath209 in terms of @xmath210
. in general may have many solutions which are easy to obtain numerically . before discussing the asymptotic regimes
let us continue with the general expressions based on first - order perturbation theory .
once the parameters @xmath209 are found such that is satisfied we may calculate the total intensity @xmath211 which at this stage is a function of @xmath186 .
the remaining matching condition @xmath212 may be reduced to @xmath213=0 \ .
\label{eq : star_quantization_pert}\ ] ] here @xmath214 , @xmath215 and @xmath216 , so that one obtains @xmath217 in leading order which is consistent with the linear limit where @xmath218 .
equations , and implicitly define the spectral curves @xmath138 . while they are simpler than the corresponding exact equations based on jacobi elliptic functions they generally remain nonlinear .
+ let us now turn to the three asymptotic regimes r1 , r2 , and r3 where additional simplifications allow for a more explicit form of the solutions . in the low intensity regime
r1 @xmath219 where @xmath220 is bounded one may expand oscillatory functions such as @xmath221 ( note that @xmath222 ) . after this expansion equation may be solved explicitly for the action variable @xmath223 we keep error terms involving low orders in @xmath99 for later use .
we may use above expression in order to give an explicit expression for the leading nonlinear correction in .
the latter correction is proportional to the total intensity @xmath224 for which we only give the required leading term .
equation now reduces to @xmath225 which implicitly defines the spectral curves @xmath226 .
one may worry about the terms @xmath227 that appear in various denominators and give rise to poles for @xmath228 .
note that we have already assumed that there is no nodal point in the centre @xmath229 moreover in the low intensity regime r1 one has @xmath230 which implies @xmath231 as well .
+ if @xmath232 is in the spectrum of the linear graph it satisfies @xmath233 and the spectral curve @xmath178 emanating from there can be evaluated from as @xmath234 next let us consider the short wave length regime r2 where @xmath235 with bounded total intensity ( @xmath84 and @xmath236 in terms of dimensionless quantitites ) .
the expansions performed in the low intensity regime r1 remain valid .
note that in expressions , , , and we have kept track of the dependence of error terms on the wave number @xmath133 .
neglecting subdominant terms allows us to simplify and [ eq : star_r2 ] @xmath237 which shows that the slope of the spectral curves decreases fast when @xmath238 . while the regimes r1 and r2 allowed us to express the spectral curves @xmath178 implicitly as the zeros of an explicit function of @xmath133 and @xmath155 the corresponding results may as well have been derived by expanding the exact expressions in terms of elliptic functions in terms of the local amplitudes @xmath181 .
one strength of the approach based on canonical perturbation theory is that it remains valid even for moderately strong total intensities at small wave lengths .
this is the regime r3 where @xmath239 with a total intensity @xmath240 that may grow proportional to the wave number ( or equivalently , the actions may grow as @xmath241 ; in terms of dimensionless parameters @xmath242 , @xmath243 where @xmath244 ) . in this case
we are not allowed to expand oscillating terms completely .
e.g. , in a term @xmath245 the phase @xmath246 can not be considered small .
indeed these phases give the leading nonlinear effect which is of order unity .
neglecting all other nonlinear effects leads to the set of equations [ eq : star_r3 ] @xmath247 where the neglected term falls off at least as @xmath248 ( if the total intensity is allowed to grow @xmath249 ) .
note that these equations remain nonlinear and allow in principle for effects such as bifurcation of spectral curves that remain absent in the regimes with globally weak nonlinearity ( r1 and r2 ) .
for instance eq . at fixed
@xmath133 and @xmath186 has generally more than one solution that is consistent with the range of validity of these equations . ,
@xmath250 and @xmath251 .
( for the purpose of this graph we have defined @xmath141 which is numerically different but of the same order compared to the definition in the text.),title="fig:",scaledwidth=45.0% ] , @xmath250 and @xmath251 .
( for the purpose of this graph we have defined @xmath141 which is numerically different but of the same order compared to the definition in the text.),title="fig:",scaledwidth=45.0% ] + , @xmath250 and @xmath251 .
( for the purpose of this graph we have defined @xmath141 which is numerically different but of the same order compared to the definition in the text.),title="fig:",scaledwidth=45.0% ] , @xmath250 and @xmath251 .
( for the purpose of this graph we have defined @xmath141 which is numerically different but of the same order compared to the definition in the text.),title="fig:",scaledwidth=45.0% ] + , @xmath250 and @xmath251 .
( for the purpose of this graph we have defined @xmath141 which is numerically different but of the same order compared to the definition in the text.),title="fig:",scaledwidth=45.0% ] , @xmath250 and @xmath251 .
( for the purpose of this graph we have defined @xmath141 which is numerically different but of the same order compared to the definition in the text.),title="fig:",scaledwidth=45.0% ] indeed one can find bifurcations of spectral curves in the exact spectral curves and these are well described by the asymptotic approximation in the short wave length regime r3 .
this can be seen in figure [ fig : graph_spectrum ] where we compare the spectral curves obtained from exact solutions with approximative solutions based on .
the agreement of the curves clearly improves with increasing wave number @xmath133 and extends to higher total intensities @xmath155 as @xmath133 is increased .
we have found some new spectral curves appearing at higher intensities which are not connected to the linear spectrum at @xmath252 .
we do not want to suggest that we have found all spectral curves in the shown intervals .
the spectral curves that extend to the linear spectrum were found using a newton raphson method by deforming the ( easily available ) linear solution .
we would like to note that the computations using the asymptotic approximation were considerably quicker .
indeed the bifurcations where new spectral curves appear at larger intensities have usually first to be found using the asymptotic equations before ( which could then be used as a starting point to find the exact ones ) . in a very different regime ( negative chemical potential )
bifurcations in the ground state have been analyzed in @xcite .
next let us consider a ring of total length @xmath82 illustrated in figure [ fig : closed_graphs]c ) where the spectrum of the linear case is just the collection of eigenvalues @xmath253 for @xmath254 ( we will always assume @xmath255 ) . here
, @xmath256 corresponds to the constant function and eigenvalues @xmath257 are double degenerate with corresponding eigenfunctions of the form @xmath258 such that the intensity @xmath259 is constant for @xmath260 or @xmath261 and has discrete nodal points for @xmath262 .
the exact solutions in the nonlinear case have been studied in detail before in terms of jacobi elliptic equations for repulsive @xcite and attractive nonlinearity @xcite . here
we want to give a short overview how the equations simplify for locally weak nonlinearity where first - order canonical perturbation theory applies .
the main new feature compared to the interval or star graphs is that the wave functions may be genuinely complex valued .
this is accompanied by the fact that there are now two distinct periodicities described by the nonlinear wave numbers @xmath74 and @xmath75 . in the linear
limit their ratio takes a unique value @xmath263 and we will see that in the nonlinear case this ratio can take other ( rational ) values .
+ let us start with stating the conditions for an exact solution @xmath264 which is locally given by and with @xmath126 ( by choice of origin ) and with the periodicity condition @xmath265 for all @xmath56 .
this implies [ eq : ring_periodicity ] @xmath266 the solutions and depend on two parameters @xmath267 such that @xmath268 . for a given value of the wave number @xmath133
the two conditions can be satisfied for a discrete set of values @xmath269 . with the total intensity @xmath270 each of the solutions
@xmath269 then defines a spectral curve @xmath271 .
+ we want to discuss these curves using canonical perturbation theory to first order where the wave function is given by equations and ( with @xmath272 by choice of origin and global phase ) .
these solutions depend on the two action variables @xmath70 and @xmath71 which need to be determined through conditions .
complex conjugation of a solution gives a new solution that is given by replacing @xmath273 .
we may thus confine our discussion to non - negative values @xmath274 . for @xmath275
the periodicity conditions imply [ eq : circle_conditions ] @xmath276 where @xmath106 and @xmath277 are integers . here
@xmath278 may take any positive value which is obvious from the second equation .
we will see later that @xmath279 takes non - negative values and this is the reason for writing @xmath280 in the first condition . if @xmath281 the intensity is constant and only the second condition applies which then reduces to @xmath282 note that in this case the integer @xmath277 is not defined .
with @xmath283 one obtains a spectral curve @xmath284 these spectral curves connect to the linear spectrum as @xmath285 .
+ setting @xmath286 in leads to another set of spectral curves that connect to the linear spectrum . in this case
@xmath111 and we have an essentially real wave function ( modulo choice of a global phase ) with @xmath287 nodal points such that the problem reduces to the nonlinear interval of length @xmath288 .
the corresponding spectral curves are given by @xmath289 where @xmath290 .
note that so far the discussion has been consistent with the globally weak asymptotic regimes r1 and r2 as well as the short wave length regime with moderate intensities r3 .
let us now discuss the case @xmath291 . first note that eliminating @xmath106 from gives @xmath292 which is manifestly non - negative ( as we confined the discussion to @xmath293 without loss of generality ) , so that @xmath294 is a non - negative integer as stated above .
moreover , if we want to have @xmath291 then shows that this is not consistent with globally weak nonlinearity ( regimes r1 and r2 ) where the right - hand side becomes arbitrarily small in the asymptotic limit . on the other hand
the short wave length regime r3 with modestly large intensities allows for the right - hand side to be of order unity ( as @xmath71 is allowed to take values @xmath295 ) .
the rest of the discussion will be confined to this regime where the @xmath71 and @xmath76 are of order @xmath295 and @xmath296 ( so @xmath297 ) while @xmath298 takes small integer values ( @xmath299 ) .
solving for the action variables gives @xmath300 note that the second equation implies that @xmath76 changes sign at @xmath301 .
as @xmath76 is manifestly positive this defines an endpoint of a spectral curve where @xmath302 is not vanishing at the same time . with @xmath303
the corresponding spectral curve @xmath304 does not connect directly to the linear spectrum .
rather it bifurcates from the spectral curve @xmath138 given by at a finite total intensity @xmath305 .
this bifurcation scenario is depicted in figure [ fig_bifurc ] .
( see eq . )
is shown for @xmath306 together with the spectral curves @xmath307 ( see eq . ) that bifurcate above a critical intensity .
the approximations are valid in the high wave number asymptotic regime r3 .
, title="fig:",scaledwidth=45.0% ] ( see eq . ) is shown for @xmath306 together with the spectral curves @xmath307 ( see eq . ) that bifurcate above a critical intensity .
the approximations are valid in the high wave number asymptotic regime r3 . , title="fig:",scaledwidth=45.0% ] + the tadpole graph consists of a ring graph of length @xmath308 to which one dangling edge of length @xmath309 is attached at one end , see figure [ fig : closed_graphs]d ) .
we choose the coordinates on the ring such that @xmath310 where @xmath311 ( and equivalently @xmath312 ) is the position of the vertex where the dangling edge is attached .
the coordinate on the dangling edge will be chosen such that @xmath313 with @xmath314 for the vertex of degree one and @xmath315 for the vertex that connects to the ring .
we assume dirichlet boundary conditions @xmath316 at the dangling vertex and standard matching conditions [ tadpole - matching - condition ] @xmath317 at the vertex on the ring .
one may observe that the real solutions of the ring considered in the section [ sec : ring ] can be extended to a solution on the tadpole : if one of the nodal points is on the vertex and we set @xmath318 then all matching conditions are satisfied .
if we try to extend the ( non - trivially ) complex solutions on the ring ( with a finite current ) to the tadpole then , due to the lack of nodal points , this can only be done with a non - vanishing solution on the dangling edge such that @xmath319 .
this can in general not be satisfied at the same time as continuity .
however , there is also the additional rotational freedom of solutions on the ring
so the problem of extending a ring solution to the tadpole reduces to the condition @xmath319 where @xmath320 .
while this may not work for arbitrary ring solutions one expects that at least some ( non - trivially ) complex nonlinear ring solutions can be extended to the tadpole for any values of the lengths @xmath308 and @xmath309 .
interestingly , in the linear case ( @xmath57 ) this is generally not the case because solutions do not change with the overall scaling .
+ in the linear case complex solutions with a finite current around the ring only exist for wave numbers @xmath133 that satisfy @xmath321 and @xmath322 at the same time .
this in turn implies that the quotient of the two lengths is rational @xmath323 ( where @xmath324 and @xmath325 are integers ) .
the linear wave number spectrum is then discrete and non - degenerate .
one half of the spectrum @xmath326 for positive integers
@xmath106 corresponds to wave functions @xmath327 on the ring with a nodal point on the vertex while the other half can only be given implicitly as the zeros of the equation @xmath328 the wave functions corresponding to the latter solutions are of the form @xmath329 which have a non - vanishing value @xmath330 at the vertex which follows from condition and the assumption that @xmath331 is irrational . in the nonlinear case
the exact solutions were classified in @xcite and their stability and bifurcations were studied in @xcite .
we will now establish a few complex solutions using canonical perturbation theory in the generic case where @xmath331 is irrational . in the previous sections we have seen that the asymptotic low - intensity regimes r1 and the globally weakly nonlinear short wave length regime r2 describe how nonlinear solutions connect to the linear solutions while not being able to describe any bifurcations .
the same applies in the present context , so we immediately consider the short wave length asymptotic regime r3 and try to find solutions of the form @xmath332 where the form of @xmath171 ensures that @xmath333 .
we have also chosen @xmath334 such that complex solutions have a current along the ring in increasing direction of @xmath335 . by complex conjugation one
then finds a new solution with opposite current ( i.e. the corresponding solution with negative @xmath336 ) . + before considering how some complex solutions can be described let us first consider the appreciable simpler case of real solutions where @xmath337 and @xmath338 . in that case the two choices of the sign in @xmath171 lead to @xmath339 it is straight forward to see from @xmath340 that the sine solutions must have a nodal point at the vertex which implies @xmath341 and that the wave function on the dangling bond is identically zero @xmath318 .
we identify these solutions as the nonlinear solutions on the ring .
the corresponding spectral curves are given by and connect to the corresponding part of the linear spectrum .
choosing the cosine in leads to the condition @xmath342 which together define spectral curves @xmath178 . in the limit @xmath198
we have @xmath343 and @xmath344 and the condition becomes the implicit equation for the corresponding linear spectrum .
altogether we found a clear correspondence between the real nonlinear solutions and corresponding linear solutions of the tadpole graph .
+ in addition to the real solutions there may be a large number of complex solutions . with the canonical perturbation approach
we have reduced the problem of finding all complex solutions to a finite set of non - linear conditions that can in general be solved numerically . in the present setting we restrict ourselves to establish the existence of some complex solutions analytically .
let us consider only the leading behaviour and look for solutions that satisfy the additional condition @xmath345 .
this condition implies that the intensity on the ring is constant , @xmath346 . in this case
the matching condition @xmath347 implies @xmath348 for some integer @xmath324 . in this case
@xmath349 which reduces the matching condition to @xmath319 or @xmath350 for a positive integer @xmath351 .
the remaining matching conditions @xmath352 just implies @xmath353 .
we may replace one of the two conditions and by the quotient @xmath354 this is a single condition for the combination @xmath355 .
if it is satisfied the individual conditions and are straight forwardly satisfied by considering @xmath133 and @xmath356 independently .
so let us show that can indeed be satisfied in the short wave length regime . in this regime one may choose @xmath357 and @xmath358 large such that the ratio @xmath359 is a rational approximant to ( the irrational number ) @xmath360 or @xmath361 where @xmath362 may be positive or negative and arbitrarily small .
choosing @xmath363 then satisfies the condition ( in leading order ) .
+ we see that a relatively simple graph such as the tadpole already has a rich set of solutions . within canonical perturbation theory
we have shown straight forwardly that there exist solutions to the nonlinear tadpole which are not just deformations of the solutions of the corresponding linear problem .
it would certainly be interesting to study the full bifurcation scenario of the spectral curves @xmath178 in this case using canonical perturbation theory in the present paper we confine ourself to initial steps in a variety of simple graphs and thus leave this as an open problem for later investigation .
in this section we discuss stationary scattering from nonlinear graphs .
we will consider a few simple graphs with some nonlinear bonds and linear leads .
we will fix incoming wave amplitudes on the leads and be interested in reflection and transmission amplitudes through the nonlinear graph . in the linear setting these amplitudes are described by a scattering matrix @xcite .
scattering through nonlinear graphs was studied previously by different methods in @xcite .
we will use canonical perturbation theory to show how the nonlinear setting connects to the known linear description at low intensities and also discuss how multi - stability as a proper nonlinear effect can be described in this framework . as before we do not aim at a complete description of each example graph .
we consider a nonlinear interval of length @xmath82 with dirichlet boundary condition at @xmath125 and a linear interval coupled at @xmath364 ( see fig . [
fig : scattgraphs]a ) ) .
it is ideal for testing the power of the canonical perturbation theory for a scattering setup .
we write the wave function as @xmath365 where @xmath366 is a real nonlinear solution given in equation ( with @xmath126 to satisfy the dirichlet condition and @xmath367 ) .
the parameter @xmath368 in is the current of the incoming wave .
the reflected wave contains an additional scattering amplitude @xmath369 . in an experiment one
sets the current @xmath368 and the wave number @xmath133 and measures the scattering phase @xmath362 as a function of @xmath133 and @xmath368 . in the linear case
the scattering phase is @xmath370 ( or @xmath371 ) which follows from the dirichlet condition at @xmath125 . at a given wave number @xmath133 the nonlinear wave function @xmath366 depends on the single parameter @xmath152 .
if we fix @xmath152 we may determine @xmath368 and @xmath362 from the continuity of the wave function and its derivative at @xmath364 .
this is equivalent to considering the point @xmath364 as a vertex on graph with two edges ( a finite bond and an infinite lead ) with the standard matching conditions described in section [ sec : matching ] .
this leads to the exact and unique relation between @xmath368 and @xmath152 @xmath372 & \text{if $ g>0$}\\ \frac{k^3}{|g|}\frac{\rho_+(2+\rho_+)}{8(1+\rho_+ ) } \left [ \frac { \mathrm{sn}^2\left(k\sqrt{1+\rho_+}\ell,\frac{\rho_+}{2(1+\rho_+)}\right ) } { \mathrm{dn}^2\left(k\sqrt{1+\rho_+}\ell,\frac{\rho_+}{2(1+\rho_+)}\right ) } + ( 1+\rho_+ ) \frac { \mathrm{cn}^2\left(k\sqrt{1+\rho_+}\ell,\frac{\rho_+}{2(1+\rho_+)}\right ) } { \mathrm{dn}^4\left(k\sqrt{1+\rho_+}\ell,\frac{\rho_+}{2(1+\rho_+)}\right)}\right ] . &
\text{if $ g<0$. } \end{cases } \label{eq : scatt_int_flow}\end{aligned}\ ] ] the scattering amplitude may generally be expressed as @xmath373 which leads to the phase shift @xmath374 implicitly this defines the scattering phase @xmath362 as a function of the incoming flow @xmath368 .
it is well - known that multi - stability and related hysteresis effects occur already in the most basic nonlinear scattering systems such as the one considered here . in the present context hysteresis
physically implies that the outcome of an experiment where @xmath368 and @xmath133 are given and @xmath362 is measured depends on the history of the experiment which selects one ( stable ) branch out of many .
numerically this is indeed seen straight forwardly .
this is shown in fig.[fig : intervalscatt ] where @xmath375 is depicted for some values of @xmath133 .
as can be seen there is a critical value @xmath376 such that multi - stability sets in above @xmath377 and this value increases with @xmath133 . .
the blue curves depict the exact results whereas the results based on canonical perturbation theory are shown as yellow curves .
the flow is plotted in natural dimensionless units as @xmath378.,title="fig:",scaledwidth=45.0% ] .
the blue curves depict the exact results whereas the results based on canonical perturbation theory are shown as yellow curves .
the flow is plotted in natural dimensionless units as @xmath378.,title="fig:",scaledwidth=45.0% ] + .
the blue curves depict the exact results whereas the results based on canonical perturbation theory are shown as yellow curves .
the flow is plotted in natural dimensionless units as @xmath378.,title="fig:",scaledwidth=45.0% ] .
the blue curves depict the exact results whereas the results based on canonical perturbation theory are shown as yellow curves .
the flow is plotted in natural dimensionless units as @xmath378.,title="fig:",scaledwidth=45.0% ] in the remainder of this chapter we want to use canonical perturbation theory in order to approximate the nonlinear effects in the scattering phase and to give an analytical estimate how the critical flow @xmath376 increases with @xmath133 .
the wave function @xmath366 is then given by equation ( with @xmath142 and @xmath367 ) .
the scattering amplitude can then be expressed as @xmath379 } { 2kj_r(\ell)+e^{i\beta_r(\ell)/2 } \left[(\beta'_r(\ell)-2k)j_r(\ell)\cos(\beta_r(\ell)/2 ) + j'_r(\ell ) \sin(\beta_r(\ell)/2)\right ] } \label{eq : scatt_phase_interval_cp}\ ] ] and the incoming flow as @xmath380 ^ 2 \label{eq : scatt_flow_interval_cp}\ ] ] the low intensity regimes r1 and r2 do not allow for multi - stability because the asymptotic limit is not compatible with describing nonlinear effects above a critical value .
+ let us now turn to the short wavelength regime @xmath381 . in this regime @xmath382 and @xmath383 . in all previous examples we could capture interesting nonlinear effects by only considering the leading order corrections of order @xmath384 to the phase while neglecting contributions @xmath385 to the phase and @xmath386 ( relative to the leading term ) to the amplitude .
we will show that the critical value @xmath376 scales like @xmath387 which implies that @xmath388 can not be neglected as @xmath389 .
the detailed calculation can then only be performed consistently if one also keeps corrections @xmath386 to the amplitude . using and
one then obtains @xmath390 \label{eq : scatt_interval_r3_ilir}\ ] ] and @xmath391 where @xmath392 fig .
[ fig : intervalscatt ] shows the scattering phase @xmath375 by numerically solving and and compares it to the numerical solution of the exact equations .
as can be seen multi - stability can be accurately described numerically .
+ the expressions can also be used for analytical estimates .
a unique function is only obtained if the function is a monotonic function of @xmath76 .
if @xmath393 is the smallest value such that @xmath394 then multi - stability sets in for @xmath395 , and since the incoming flow @xmath368 is equal to @xmath76 to leading order we get multi - stability for incoming flows @xmath396 . this value can be estimated straight forwardly from by taking the derivative @xmath397 which shows that the derivative can only vanish if @xmath398 is of order unity which gives the estimate @xmath399 fig .
[ fig : critflow ] compares this estimate @xmath376 to the numerically obtained critical value using the exact equations . as a function of the wave number above which multi - stability sets in for scattering from a nonlinear interval with one ( linear )
lead attached at one end : a ) attractive case ; b ) repulsive .
the wave number is expressed in a natural dimensionless way by @xmath400 . + thick blue lines : numerical data using exact equations .
+ thin yellow lines : numerical data using canonical perturbation theory ( see text ) .
+ dashed lines give the analytically found scaling law @xmath401 in very good agreement with numerically found data . , title="fig:",scaledwidth=45.0% ] as a function of the wave number above which multi - stability sets in for scattering from a nonlinear interval with one ( linear ) lead attached at one end : a ) attractive case ; b ) repulsive .
the wave number is expressed in a natural dimensionless way by @xmath400 . + thick blue lines : numerical data using exact equations .
+ thin yellow lines : numerical data using canonical perturbation theory ( see text ) .
+ dashed lines give the analytically found scaling law @xmath401 in very good agreement with numerically found data .
, title="fig:",scaledwidth=45.0% ] next let us consider a nonlinear interval of length @xmath82 that is connected to linear leads at both ends ( see fig .
[ fig : scattgraphs]b ) ) .
here a plane wave with flow @xmath368 and wave number @xmath133 comes in through one lead and is partially reflected and partially transmitted through the interval .
the wave function may written as @xmath402 here @xmath403 and @xmath404 are complex transmission and reflection coefficients that depend on the incoming flow @xmath368 and the wave number @xmath133 .
flow conservation implies @xmath405 . inside
the nonlinear lead @xmath366 is a complex solution of the nlse .
+ we do not aim at a complete discussion of the solutions .
rather we want to show how the solution simplifies in the leading order when one considers the short wavelength regime r3 where @xmath406 and @xmath407 while @xmath97 need not be small . neglecting terms of order @xmath386
we can write @xmath408 where @xmath409 , @xmath410 , and we have used that the flow @xmath71 through the interval is positive . requiring that the wave function and its first derivative are continuous at the two ends of the interval it is straight forward to show that assuming @xmath411 is consistent with these requirements . in this case there is negligible reflection and the wave passes through unhindered .
the only effect is a non - negligible phase shift that can easily be calculated as @xmath412 it is well known @xcite that transport through a nonlinear interval shows multi - stability .
our calculation here shows that this can not be analysed by only considering the nonlinear phase shifts which are the dominant nonlinear effect in the short wavelength asymptotic regime r3 .
multi - stability can only be analysed if the reflection coefficient is not neglected
so one needs to take into account terms of order @xmath413 in the nonlinear wave function @xmath366 .
this is analogous to the scattering from the nonlinear interval with a single lead : in order to get a consistent description of multi - stability we had to add terms that change the shape of the wave function in addition .
the main reason why seemingly small contributions are important when considering multi - stability is the necessity to use the implicit function theorem to get @xmath414 and @xmath415 as a locally unique function of @xmath368 and @xmath133 .
multi - stability can be analysed by considering the breakdown of the implicit function theorem this involves derivatives of the wave function with respect to all parameters .
a consistent description of these derivatives in the presence of large phase shifts generally requires also that the corrections @xmath413 to the shape are used in sufficient high order . in that sense equations
have to be taken with care if one assumes that one obtains a unique solution . however solving the equations for @xmath414 and @xmath415 starting from using the implicit function theorem
may still reveal that there are additional solutions .
+ any further analysis in the present case would follow similar lines as for the case with one lead .
a detailed discussion of this case would certainly also be of interest but at present our aim is just to show the power and the limitations of the approach using canonical perturbation theory .
we now consider a nonlinear ring with ( circumference ) length @xmath82 and a variable @xmath416 $ ] with one infinite linear lead attached at @xmath417 ( see fig .
[ fig : scattgraphs]c ) ) .
we denote the variable on the lead as @xmath418 with the vertex on the ring being at @xmath419 .
the configuration is similar to the finite tadpole discussed above where the finite nonlinear interval is replaced by an infinite linear lead .
+ the wave function in the lead is @xmath420 where @xmath368 is the incoming flow and @xmath421 is a scattering phase and the wave function @xmath422 on the ring is a complex solution of the nlse .
+ one special feature of this scattering system is the existence of bound states in the continuum , i.e. states that have a finite amplitude on the ring but vanish on the lead .
this implies @xmath423 and @xmath424 which are just the conditions for finding real solutions to the nlse on the ring as discussed in chapter [ sec : ring ] in the linear limit this leads to the standard quantisation condition @xmath425 .
the existence of such solutions gives rise to severe limitations to any kind of perturbation theory because assuming that the incoming flow @xmath368 is sufficiently small does in general not imply that the intensities on the ring are small as well .
+ our aim is to show in a concise way how canonical perturbation theory can be used in this context to find some solutions .
we focus again on the short wavelength regime r3 where the leading effect is a nonlinear phase shift in a superposition of plane waves and other changes being neglected @xmath426 where @xmath427 and @xmath428 .
we have chosen @xmath429 solutions with the opposite direction of flow can be obtained by complex conjugation . for the bound states in the continuum we have no current @xmath71 . confining our discussions to scattering states that are ` close ' to the bound states we will focus on solutions with @xmath430 .
the wave function simplifies to @xmath431 where we implicitly redefined the ( still undetermined ) phase @xmath432 .
continuity at the vertex then implies @xmath433 which has two types of solutions : either @xmath434 with arbitrary @xmath432 or @xmath435 with no restrictions on @xmath74 . in the first case
@xmath434 we have @xmath436 and @xmath424 which are the conditions for a solution on the ring .
this in term implies that @xmath437 or that the scattering phase is @xmath438 . the bound state is thus embedded in a one - parameter family of solutions with finite incoming flow where the scattering phase vanishes . in fact
this can easily be seen using the exact equations . + finally let us turn to solutions with @xmath435 where two conditions still need to be satisfied @xmath439 using that @xmath440 and consistently neglecting terms @xmath386 these equations simplify to @xmath441 , @xmath442 and a scattering phase @xmath443 while our calculations again show that some solutions can easily be explored using canonical perturbation theory caution needs to be applied when uniqueness of these solutions is considered ( see the previous discussion for the interval with two leads ) .
note that the existence of bound states did not obstruct a consistent derivation of some solutions in the perturbative regime .
this is mainly due to the restricted topology and our restriction to solutions without flow around the ring .
narrow resonances in a scattering graph pose a challenge to any perturbation theory based on ( relatively ) low intensities .
if the corresponding linear quantum graph has a narrow resonance at some wave number @xmath232 then this implies that the wave is ` trapped ' inside the graph where constructive interference leads to intensities inside the graph that may be much higher than on the lead . in the nonlinear case
any nonlinearity is then magnified .
indeed it has been observed @xcite that nonlinear effects such as multi - stability in quantum graphs occur generically already when the incoming flow is very low due to a generic mechanism for narrow resonances , the so - called topological resonances @xcite .
we refer to @xcite for a more detailed discussion of topological resonances in linear quantum graphs and to @xcite for a numerical analysis how topological resonances magnify nonlinearities and lead to multi - stability for arbitrarily small incoming flows . here
we want to describe this mechanism briefly for two example graphs .
we leave the detailed nonlinear analysis as a challenging problems in future research and restrict ourselves to explain the challenge .
+ the first example is the y - structure shown in fig .
[ fig : scattgraphs ] ( d ) .
two nonlinear bonds of lengths @xmath308 and @xmath309 are connected to a linear lead . in the linear case
it can easily be seen that there are bound states if the bond lengths are rationally related @xmath444 for some integers @xmath357 and @xmath358 in that case it is straight forward to construct sine waves on the bonds such that there is a nodal point on the vertex , so that the solution can be continued on the lead by a vanishing wave function .
however for a generic choice of lengths no integers @xmath357 and @xmath358 exist ( the lengths are incommensurate ) and thus no bound states . while there are
no bound states where the wave function has a nodal point on the vertex there are many scattering solutions where a nodal point comes arbitrarily close to the vertex in that case the intensity on the two bonds may be orders of magnitude higher than on the attached lead .
indeed , just as any irrational number can be approximated by a rational number to arbitrary precision one can find resonances where the intensity on the bonds is arbitrarily high . in a nonlinear graph this leads to arbitrarily high magnifications of all nonlinear effects .
if @xmath133 ranges in a certain spectral interval the strongest topological resonance will limit any _ uniform _ application of perturbation theory ( though it may break down only in a tiny interval around the resonance ) .
+ the y - graph is the simplest structure where the effect of such topological resonances may be studied .
one reason for being simple is that all scattering solutions are essentially real ( they can be made real by a global gauge transformation ) and total flows on all edges vanish .
the simplest graph with fundamentally complex scattering solutions consists of two bonds of lengths @xmath308 and @xmath309 and two leads , see fig .
[ fig : scattgraphs ] ( e ) .
the two bonds form a ring with two vertices by connecting each end of one bond to an end of the other and the leads are connected . in the linear case
we again find bound states for rationally related lengths in that case one can construct sine functions around the ring that have nodal points at both vertices .
for incommensurate lengths one finds again no bound states but one does find topological resonances that are arbitrarily ` close ' to a bound state ( in the sense that the intensity outside may be arbitrarily small ) @xcite .
if one wants to consider nonlinear effects of topological resonances in a graph with complex wave functions and particle flows this structure is probably the simplest case though it remains a challenge for future research .
note , however that it is sufficient to assume that one of the two bonds responds nonlinearly which does simplify the problem to some extent .
to summarise , we studied applications of canonical perturbation theory for the stationary nonlinear schrdinger equation developed in @xcite to some specific quantum graphs . depending on wave number , the strength of the nonlinear interaction and the lengths of the edges in the graphs we identified three different asymptotic regimes .
the first two regimes can be equivalently obtained by linearizing the stationary wave function and the chemical potential around the results obtained for vanishing nonlinearity .
the resulting equations are simple to solve as they allow for a recursive treatment , however effects like multistabilities and bifurcations typical for systems with nonlinear dynamics can not be obtained .
the third regime describing quantum graphs with weak nonlinear interaction but moderately large intensities at large wave numbers ( or large bond lengths ) allows to describe multistabilities and bifurcations as the underlying equations connecting the solutions at the vertices remain nonlinear . compared to an exact analysis , this regime offers a reduced complexity .
numerically this leads to much shorter computation times .
analytically it opens the way to find some asymptotic solutions and their nonlinear properties .
+ in the case of closed graphs , we focused on determining spectral curves @xmath138 , i.e. we determined the discrete allowed values indexed by @xmath106 of the wave number as a function of the norm @xmath155 of the wave function .
we considered here the nonlinear interval , star graphs , the ring and the tadpole graph and explained the simplifications induced by the canonical perturbation theory .
e.g. for the nonlinear interval we obtain an explicit expression for the spectral curves within canonical perturbation theory , whereas only an implicit expression was available from exact calculations . for star graphs we could show numerically that the asymptotic description captures the bifurcations present in the exact solutions . for the ring we could analyse the bifurcation scenario within canonical perturbation theory . for the tadpole graph we established some complex solutions in the asymptotic large wave number regime . + for open graphs we focused on the transmitted intensity and scattering phase . for the nonlinear interval connected to one lead we derived in our perturbative approach a simple condition for the onset of multistabilities that we confirmed numerically .
we also calculated the scattering phase for the nonlinear interval connected to two leads and the infinite tadpole .
+ canonical perturbation theory is usually used to describe either small perturbations of an integrable hamiltonian system or the vicinity of a periodic orbit with elliptic stability . to our knowledge
, our work is the first extending this analysis to quantum graphs with nonlinear interaction on the bonds .
thus the aim of our work is to give a first overview over the possibilities provided by canonical perturbation theory leaving plenty of open questions : the bifurcation scenarios and classification of spectral curves for the closed star graph and the tadpole graph remain incomplete . characterizing bifurcation scenarios by canonical perturbation theory in more complicated nonlinear scattering systems would be of interest as well . a first step would be to consider here the nonlinear interval connected to two leads or the infinite tadpole .
another interesting question is if there is any way to approximate the exact solutions obtained at negative chemical potential by canonical perturbation theory .
+ here we focussed on the cubic nlse
the approach has also been developed to the non - cubic case ( see @xcite ) and may be extended to other nonlinear wave equations on quantum graphs .
furthermore , several interesting modifications and applications of quantum graphs without nonlinearity have been developed in the past , that call for including effects of nonzero nonlinearity .
one example are fat graphs consisting of bonds with finite widths @xcite .
what is the effect of nonlinear interaction on quantum spectral filters modelled by star graphs @xcite ?
+ nonlinear equations play in general a fundamental role for describing the dynamics in physical systems .
an extension of the method applied here to networks with the dynamics determined by the burgers equation , the dirac equation with nonlinearity @xcite , korteweg - de vries @xcite or the sine - gordon equation @xcite could lead to new insights into bifurcations present in these systems .
+ finally , all of the results of the paper are obtained using the model of quantum graphs .
it would be interesting how well such a model can be realized and our predicted effects can be confirmed in experiments by considering optical fiber networks or one dimensional ( cigar - like ) bose - einstein condensates .
we would like to thank uzy smilansky for initial discussions during research stays of both authors at the weizmann institute and the weizmann institute of science for hospitality .
d.w . acknowledges financial support from the minerva foundation making this research stay possible .
s.g . would like to thank the technion for hospitality and the joan and reginald coleman - cohen fund for support .
we use the following notation for elliptic integrals where @xmath446 , @xmath447 and @xmath448 .
jacobi s elliptic function @xmath449 , the elliptic sine , is defined as the inverse of @xmath450 @xmath451 extended to a periodic function with period @xmath452 .
the corresponding elliptic cosine @xmath453 is @xmath454 such that @xmath455 .
we also use the non - negative function @xmath456 10 s. gnutzmann , d. waltner , phys .
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Effect on rate of diffusion in addition of an inert gas
What will be the effect on the rate of diffusion on addition of an inert gas to the gaseous mixture?
I think the rate of diffusion should increase as the addition of extra gas will increase the inside pressure. But the given answer contradicts my proposed explanation. Where am I wrong? And why is the rate of diffusion decreasing?
My question does not ask about the effect of addition of an inert gas on a reaction equilibrium.
The inter-diffusion caused by two gasses is described by the Stefan-Maxwell equation.
If $x\_1,x\_2$ are the mole fractions of the two gasses, $\bar v$, the average speed and $\lambda$ the mean free path then
$$D\_{1,2}= \frac{x\_2}{2}\bar v\_1\lambda\_1+ \frac{x\_1}{2}\bar v\_2\lambda\_2$$
where $D\_{1,2}$ is the inter-diffusion coefficient. Substituting for the mean free paths does not lead to a useful result because terms that involve collision between molecules of the same kind cannot have any extra effect compared to when only one gas is present, and so these are ignored. The result is
$$D\_{1,2}= \frac{1}{\pi\sigma\_{1,2}^2(n\_1+n\_2)} \left( \frac{2k\_BT}{\pi\mu} \right)^{1/2}$$
where $\sigma\_{1,2}$ is the sum of the radii of the two molecule types and $n\_1, n\_2$ number of molecules/m$^3$ of each, the reduced mass is $\mu$ kg ($\mu=m\_1m\_2/(m\_1+m\_2)$).
This equation shows that the inter-diffusion depends on the total concentration at a given temperature, a result that is close to that observed experimentally. So your intuition was correct.
(ref chapter (II). E. Moelwyn-Hughes, 'Physical Chemistry')
| stackexchange/chemistry |
Magnetic field induced by a rotating charged disk
Let's assume that there is a disk of total electric charge $Q$ rotating about its axis with a
constant angular velocity $\vec{\omega}$. I know that one can easily compute the magnetic field
generated on the axis of the rotation of the disk, which is possible due to the symmetry of the
problem.
My question is the following: Is there any way to use the Biot-Savart law (or any other method)
in order to compute the magnetic field on an arbitrary point on the plane of the disk itself?
I would, probably naively, think of somehow reducing the problem to a $2D$ one, but fail to implement it.
Your rotating charged disk can be thought of as many concentric rings of current. Each ring can be thought of a many short elements of current, each of which contributes to the magnet field at any chosen point as predicted by Biot-Savart. Not being a mathematician, if I had to do this I would let a computer do a numeric summation. (Decades ago, I did a similar calculation for selected points within the field of a Helmholtz coil.)
| stackexchange/physics |
Single-particle states vs. basis states vs. eigenkets vs. quantum numbers
I am confused between these terms that we usually find in quantum mechanics.
In my understanding, we can write any operator in a given Hilbert space in terms of the eigen-kets of any operator. For example, if we have an operator $\hat{A}$ which has eigen-kets $\{|a\_i\rangle \}$, then any other operator $\hat{B}$ can be written in terms of $\{|a\_i\rangle \}$ as $\hat{B}=\sum\_{ij}|a\_i\rangle\langle a\_i|\hat{B}|a\_j\rangle\langle a\_j|$. Similarly, we could have eigen-kets of the Hamiltonian operator $\{|E\_i\rangle\}$.
My confusions are:
1. Are eigen-kets $\{|a\_i\rangle \}$ of any operator called the single-particle states? Or the eigen-kets of only Hamiltonian, $\{|E\_i\rangle\}$, are called single-particle states?
2. Are eigen-kets $\{|a\_i\rangle \}$ and "basis states" same thing?
3. What are quantum numbers? Are eigen-kets $\{|a\_i\rangle \}$ the quantum numbers?
**(Orthonormal) basis**
A set of ket $\{|\psi\_i\rangle:i\in I\}$ is a (orthonormal basis) if the kets are orthonormal $\langle \psi\_i|\psi\_j\rangle = \delta\_{ij}$ and satisfy the completeness relation :
$$1 = \sum\_i |\psi\_i\rangle\langle \psi\_i|$$
**Eigen-kets**
Given a self-adjoint operator $\hat A$, a ket $|\psi\rangle$ is an eigen-ket of $\hat A$ if there is a complex number $a$ such that :
$$\hat A|\psi\rangle =a|\psi\rangle $$
In this case, $a$ is called the eigenvalue.
The spectral theorem ensures that there exists an orthonormal basis $\{|\psi\_i\rangle, i\in I\}$ whose kets are all eigenkets of $\hat A$ :
$$\hat A|\psi\_i\rangle =a\_i|\psi\_i\rangle$$
If $|\psi\rangle,|\phi\rangle$ are eigenkets of $\hat A$ *with the same eigenvalue*, then any linear combination of them is also an eigenkets. If $|\psi\rangle,|\phi\rangle$ are eigenkets of $\hat A$ *with different eigenvalues*, then they are orthogonal.
Therefore, if $\hat A$ has no degeneracy, we can construct an eigen-basis of $\hat A$ by choosing one eigenket $|a\rangle$ for any eigenvalue $a$.
**Quantum numbers**
Often, operators have degeneracy. In this case, we want to find a maximal set of commuting observables. This is a set $\hat A\_1,\ldots, \hat A\_n$ of self-adjoint operators which commute with each other (and therefore, by the spectral theorem, we can find a basis whose kets are eigen-kets of all the $A\_k$) and such that for any set $(a\_1,\ldots,a\_n)$ of eigenvalue, there is at most one ket (up to normalization and phase) such that :
$$\hat A\_k|\psi\rangle = a\_k|\psi\rangle$$
In this context, the eigenvalues $(a\_1,\ldots,a\_n)$ are called the quantum numbers of the state $|\psi\rangle$. Since they determine it uniquely, we often write $|\psi\rangle = |a\_1,\ldots,a\_n\rangle$
**Single particle states**
This only make sense for a Hilbert space which also contain multi-particle space (eg Fock spaces). In this case, there should be a particle number operator $\hat N$ and single-particle states are eigenstates with the eigenvalue $1$ :
$$\hat N|\psi\rangle = |\psi\rangle$$
We can write any operator $\hat{B}$ in terms of $\{|\alpha\_i\rangle\}$ because of the completeness relation the set of eigenkets of $\hat{A}$, namely $\{|\alpha\_i\rangle\}$, satisfies,
$$\sum\_{i=1}^n|\alpha\_i\rangle\langle\alpha\_i|=\textbf{1}\_{n\times n}$$
where $n$ is the dimensionality of the basis.
Having said that,
1. Neither $|\alpha\_i\rangle$, nor $|E\_i\rangle$ need be one-particle states. They can be many particle states. They can also be one-particle states. In particular, $|E\_i\rangle$ can be a one-particle state if the Hamiltonian is a Hamiltonian that time-evolves a one-particle system.
2. If the eigenkets are orthonormal and they form a complete set (i.e. span the vector space), then yes, they are the same.
3. The quantum numbers are the eigenvalues of some operators. Usually, with the same eigenvalues we also label the corresponding arrays (or states), i.e. take as an example the total spin operator and its eigenstates of the spin operator
$$S^2|s\rangle=\hbar s(s+1)|s\rangle$$
The label $s$ denotes the quantum number of spin.
I hope this helps. If there are any questions, please comment.
Firstly, not all operators have a well defined set of eigenstates. Even if they have right-eigenstates, they may not have left-eigenstates. Or the eigenstates may not be complete. The eigenstates of an operator are not necessarily single-particle state. Consider for example the annihilation operators. It has right-eigenstates, called the coherent states
$$ \hat{a} |\alpha\rangle = |\alpha\rangle\alpha . $$
These coherent states are not in general single particle-states.
Hermitian operators do in general (as far as I know) always have complete sets of orthogonal eigenstates. (Even if it has degenerate eigenvalues, one can define an orthogonal basis). So if $\hat{A}$ is Hermitian, then we can represent it as
$$ \hat{A} = \sum\_m |m\rangle \lambda\_m \langle m| , $$
where $|m\rangle$ is the eigenstates and $\lambda\_m$ the eigenvalues. A complete set of orthogonal states can serve as a basis. Therefore, such a set of eigenstates can serve as a basis.
The quantum numbers are quantities that represent the degrees of freedom of a system. It could for instance be represented by the index $m$, depending on the context.
| stackexchange/physics |
QED vacuum as a classical dielectric medium?
I have heard this analogy a few times, particularly in the context of vacuum polarization. To what extent can the QED vacuum be modeled as a classical dielectric medium? Can one compute effective linear and nonlinear susceptibilities of this medium from QED? I am aware of the Born-Infeld theory and its relation to QED vacuum polarization, but I am also interested in higher-order effects like photon-photon scattering, which would involve third-order nonlinear susceptibility.
[WP quote](https://en.wikipedia.org/wiki/QED_vacuum):
*"When Planck's constant is hypothetically allowed to approach zero, QED vacuum is converted to classical vacuum, which is to say, the vacuum of classical electromagnetism."*
As long you fulfill the above condition you should be able to reach the same results with the $ε\_{0}$, $μ\_{0}$, classical dielectric vacuum using QED.
By nullifying the Planck's constant space is no more quantized and becomes a continuum.
**Note:** Classical vacuum is not a **material medium**, but a reference state used to define the SI units. Its permittivity is the electric constant and its permeability is the magnetic constant, both of which are exactly known by definition, and are not measured properties. See Mackay & Lakhtakia, p. 20, footnote 6
| stackexchange/physics |
How many atoms exist within a continuum body?
Materials, such as solids, liquids and gases, are composed of molecules separated by "empty" space. On a microscopic scale, materials have cracks and discontinuities. However, certain physical phenomena can be modelled assuming the materials exist as a continuum, meaning the matter in the body is continuously distributed and fills the entire region of space it occupies.
How many atoms exist within a continuum body?
The number of atoms (or molecules) in a body is given by [Avogadro's constant](http://en.wikipedia.org/wiki/Avogadro_constant), or $6.022 \times 10^{23}$ per mole. A mole is the amount of material, in grams, equal to the atomic or molecular mass of the substance in question.
For example, for water ($H\_2O$), 1 mole equals 18 grams. To get this number, remember that hydrogen ($H$) has an atomic mass of $1$. Oxygen ($O$) has an atomic mass of $16$, so the total mass of a water molecule is equal to $2\times1+16=18$ atomic mass units. It follows from Avogardo's constant that 18 grams of water have $6.022 \times 10^{23}$ molecules of water.
Similar calculations can be done for other elements or compounds, and for different masses. For instance, the atomic mass of iron is $55.845$, so there are $6.022 \times 10^{23}$ iron atoms in $55.845$ grams of iron, or $0.107 \times 10^{23}$ iron atoms per gram.
With those kind of numbers, normal bodies can easily be considered to be continuous, as the number of atoms in them is near enough to infinite for everyday practical purposes.
The simple answer to find the average number of atoms/molecules per unit volume is....
N/V (average atoms or molecules/$m^3$ ) = density ($kg/m^3$) \* 1000 / atomic(or molecular) mass \* $N\_a$
where $N\_a$ is Avogadro's number (~$6 \times 10^{23}$)
In general in solid or liquid the distance between the nuclei of atoms is approximately 1 Angstrom = $10^{-10}$ m
| stackexchange/physics |
Srđan Kljajević Cyrillic: Crђaн Kљajeвић, born 23 November 1974 is a Montenegrin goalkeeping coach and former player.
Club career
Born in Titograd, Kljajević began playing football with the youth side of FK Bokelj. He played for FK Zeta, before joining Greek Superleague side Panachaiki F.C. in July 2002. He would next play for fellow Superleague club Egaleo F.C., before moving to Serbian FK Rad Belgrade and already back in Montenegro, FK Grbalj. Since the winter-break of the 200910 season, he has been playing with FK Kom.
References
External links
Profile at Srbijafudbal.
Category:Living people
Category:1974 births
Category:Sportspeople from Podgorica
Category:Montenegrin footballers
Category:Montenegrin expatriate footballers
Category:FK Zeta players
Category:Panachaiki F.C. players
Category:Egaleo F.C. players
Category:Expatriate footballers in Greece
Category:FK Rad players
Category:OFK Grbalj players
Category:FK Mornar players
Category:FK Kom players
Category:Association football goalkeepers | wikipedia |
The Last Kids on Earth is a children's illustrated novel and subsequent book series by American author Max Brallier, illustrated by Douglas Holgate, with audiobook format narrated by Robbie Daymond. Novels in the series have been recognized on Best Seller lists of both The New York Times and USA Today. This book is highly recommended for teens/pre-teens in the middle school demographic. The series currently includes five books and has been adapted into an animated series by Netflix.
In the initial story, a foster child and optimistic loner named Jack finds himself abandoned in a cartoonish end-of-the-world apocalypse. He thrives on freedom, junk food and video games while building a team of his classmates to fight off zombies as well as a trove of campy monsters who have also somehow appeared. The series treats its subject matter with lighthearted humor rather than adult horror.
Subsequent books continue the same comic dystopian scenario with the team of mismatched school kids facing new antagonists, new monsters and new challenges.
Series titles
The Last Kids on Earth 2015
The Last Kids on Earth and the Zombie Parade 2016
The Last Kids on Earth and the Nightmare King 2017
The Last Kids on Earth and the Cosmic Beyond 2018
The Last Kids on Earth and the Midnight Blade September 17, 2019
The Last Kids on Earth: June's Wild Flight 2020
The Last Kids on Earth and the Skeleton Road 2020
Summary
The seven books follow a thirteen-year-old boy named Jack Sullivan, who lives in his foster brother's tree house after a zombie outbreak hits his hometown, Wakefield, Indiana. He is accompanied by his best friend Quint Baker, who loves experimenting; June Del Toro, who is Jack's love interest; and Dirk Savage, the local bully with exceptional fighting skills. The friends fight one monster in each book, while trying to stay alive, and stop an entity named Rezzoch, who wants to take over the Earth.
Reception
The series is recognized as a bestseller on both The New York Times and USA Today book lists, with the publisher boasting one million copies in print.
Animated series
On February 26, 2018, it was announced that Netflix had a series order to an animated television adaptation of the book series. The first season, a single hourlong special covering the plot of the first book, was released in September 2019 to coincide with the release of the fifth novel. The second season, covering the plot of the second book, is expected to air in 2020 and will consist of ten episodes. Production companies involved in the series include Thunderbird Entertainment's animation studio Atomic Cartoons.
References
Further reading
Category:Series of children's books | wikipedia |
What is a non-classical carbocation?
* What is a non-classical carbocation?
* How is it different from a classical carbocation?
I am confused as I have come across this term many times on Chem.SE but there seems to be nothing for my level of understanding on the Internet!
Here is a picture of a "classical" carbocation, there is an electron deficient carbon bearing a positive charge.
There are many examples of "non-classical" carbocations, but the [2-norbornyl carbocation](http://en.wikipedia.org/wiki/2-Norbornyl_cation) is among the best known.
[](https://i.stack.imgur.com/f2mqy.png)
Labeling experiments have shown that the positive charge resides on more than one carbon in the 2-norbornyl ion. Early on, the data was explained by equilibrating classical ions, but soon another possibility emerged - one involving a single non-classical ion.
The problem comes down to: are the equilibrating classical ions ground state structures with the non-classical ion serving as the transition state, or is the non-classical ion the ground state? This debate went on for a very long period of time, but now most agree that the non-classical structure is the ground state in the 2-norbornyl system. In fact, a recent, and difficult to obtain, [crystal structure for the 2-norbornyl cation](http://www.sciencemag.org/content/341/6141/62) has been published proving that the ion exists with the non-classical geometry (thanks to Klaus for finding this reference, see his comment below).
**A key difference between classical and non-classical structures is the bonding**. As illustrated above, a classical ion has a carbon with a sextet of electrons and 3 other bonds. The non-classical ion, on the other hand, involves 3 carbons with 2 electrons spread over them. This is called a [3-center 2-electron bond](http://en.wikipedia.org/wiki/Three-center_two-electron_bond) ([hypercoordinate bonding](http://en.wikipedia.org/wiki/Hypervalent_molecule)) and is **a clear marker for a non-classical ion**. Notice if you count all of the bonds to any of these 3 carbon atoms (solid and dashed lines) you count 5! Sounds strange, but such "hypercoordinate bonding" is a permitted consequence of the 3-center 2-electron bond.
[](https://i.stack.imgur.com/LVZBR.png)
Here is a [link](https://chemistry.stackexchange.com/questions/29000/which-carbocation-is-more-stable-the-ethyl-or-1-propyl-carbocation/31729#31729) to a simpler non-classical carbocation discussed here yesterday.
| stackexchange/chemistry |
The 1982 Toronto Blue Jays season was the franchise's sixth season of Major League Baseball. It resulted in the Blue Jays finishing sixth in the American League East with a record of 78 wins and 84 losses. Bobby Cox became the third field manager in team history.
Dave Stieb established himself as one of the top pitchers in the American League, as he led the AL with 19 complete games and 5 shutouts.
Offseason
November 17, 1981: Aurelio Rodríguez was traded by the New York Yankees to the Toronto Blue Jays for a player to be named later. The Toronto Blue Jays sent Mike Lebo minors December 9, 1981 to the New York Yankees to complete the trade.
November 27, 1981: Danny Ainge was released by the Blue Jays.
December 28, 1981: Paul Mirabella was traded by the Blue Jays to the Chicago Cubs for a player to be named later. The Cubs completed the deal by sending Dave Geisel to the Blue Jays on March 25.
March 25, 1982: Phil Huffman was traded by the Blue Jays to the Kansas City Royals for Rance Mulliniks.
Regular season
One of the key events of the season was that the Toronto Blue Jays sold its first beer. Exhibition Stadium was the only stadium in the major leagues that did not sell beer. The Ontario Legislature reached a decision on July 7, 1982. Dr. Robert Elgie, the minister of Consumer and Commercial Relations announced that beer would be sold on a trial basis at Exhibition Stadium along with Hamilton's Ivor Wynne Stadium and Ottawa's Lansdowne Park. On July 30, 1982, Paul Godfrey sold the first ceremonial beer at Exhibition Stadium to William Turner, a fan from London, Ontario.
Opening Day Lineup
Jesse Barfield
Mark Bomback
Dámaso García
Alfredo Griffin
John Mayberry
Lloyd Moseby
Rance Mulliniks
Willie Upshaw
Ernie Whitt
Al Woods
Season standings
Record vs. opponents
Notable transactions
April 2, 1982: Aurelio Rodríguez was traded by the Blue Jays to the Chicago White Sox for Wayne Nordhagen.
May 5, 1982: John Mayberry was traded by the Blue Jays to the New York Yankees for Dave Revering, Tom Dodd, and Jeff Reynolds minors.
June 7, 1982: 1982 Major League Baseball draft
Jimmy Key was drafted by the Blue Jays in the 3rd round. Player signed June 12, 1982.
Mike Henneman was drafted by the Blue Jays in the 27th round, but did not sign.
June 15, 1982: Wayne Nordhagen was traded by the Blue Jays to the Philadelphia Phillies for Dick Davis.
June 22, 1982: Dick Davis was traded by the Blue Jays to the Pittsburgh Pirates for a player to be named later. The Pirates completed the deal by sending Wayne Nordhagen to the Blue Jays on June 25.
Roster
Game log
Player stats
Batting
Starters by position
Note: G = Games played; AB = At bats; R = Runs scored; H = Hits; 2B = Doubles; 3B = Triples; HR = Home runs; RBI = Runs batted in; AVG = Batting average; SB = Stolen bases
Other batters
Pitching
Note: W = Wins; L = Losses; ERA = Earned run average; G = Games pitched; GS = Games started; SV = Saves; IP = Innings pitched; R = Runs allowed; ER = Earned runs allowed; BB = Walks allowed; K = Strikeouts
Award winners
Jim Clancy, American League All-Star Selection, Reserve
Dámaso García, 2B, Silver Slugger Award
Dave Stieb, The Sporting News Pitcher of the Year Award
Dave Stieb, American League Leader, 19 Complete Games
Dave Stieb, American League Leader, 5 Shutouts
Farm system
LEAGUE CHAMPIONS: Medicine Hat
Notes
References
External links
1982 Toronto Blue Jays at Baseball Reference
1982 Toronto Blue Jays at Baseball Almanac
Category:Toronto Blue Jays seasons
Toronto Blue Jays season
Category:1982 in Canadian sports
Category:1982 in Toronto | wikipedia |
we fabricate nanopores from glass capillaries using a programmable
laser puller ( p-2000 , sutter instruments ) .
the pore sizes are characterized
by direct imaging using an sem and from conductance measurements by
taking a current voltage ( i v ) curve .
the three pore diameters used are 15 3 ,
148 26 , and 1018 30 nm .
the pulled capillaries are assembled
into a pdms - based microfluidic sample cell which is sealed onto a
glass coverslide .
the capillary connects two reservoirs filled with
kcl of varying concentrations buffered by tris - edta ( te ) at ph 8 .
for concentrations greater than 100 mm , 1 ( 10 mm )
te is used ;
for lower concentrations the buffer is diluted to give a final concentration
of 10% ( i.e. , for a 10 mm kcl solution , 1 mm te is used ) .
because
it is not possible to change the salt concentration once the sample
cell is filled , it is necessary to fill a new capillary for measurements
at a different concentration . to take into account the variations
between pores , the results presented are an average over several pores
at each salt concentration .
the optical tweezer setup is a single - beam
gradient trap based on an inverted microscope .
we use a 5 w ytterbium fiber laser ( ylm-5-lp , ipg laser ) operating
at a wavelength of 1064 nm which backfills a 60 , na 1.2 olympus
uplansapo water immersion objective to create a stable three - dimensional
optical trap near the laser focus . real time position tracking with
a bandwidth of a few khz
the sample cell is mounted onto a piezoelectric
nanopositioning device ( p-517.43 and e-710.3 , physik instrumente )
which allows the relative position of the trap and pore to be adjusted
with an accuracy of 100 nm .
spherical 2 m streptavidin polystyrene
beads ( kisker ) are flushed into the reservoir and captured with the
trap .
force calibration is achieved for every trapped particle using
a power spectral density method ; the resulting trap stiffness is in
the range 1060 pn/m , corresponding to applied laser
powers of 50300 mw at the sample plane .
voltages
in the range + 1 to 1 v are applied using ag / agcl electrodes
connected to a commercial electrophysiology amplifier ( axopatch 200b ,
molecular devices ) , which also allow for simultaneous low - noise ionic
current recording .
the entire experimental setup is controlled using
custom - written labview software ( labview 2009 , national instruments ) .
it integrates a fast emccd camera ( andor ixon3 865 ) with ionic current
measurements and has been described previously .
a heka epc 800 electrophysiology amplifier is
used to apply voltages across the nanopore and record ionic currents .
the reservoir containing the nanopore is seeded with a dilute solution
of 540 nm diameter streptavidin coated polystyrene particles that
are embedded with the nilered dye ( spherotec ) . commercially available
solutions ( 0.1% w / v ) are centrifuged for 10 min at 5000 g , the supernatant removed , and the particles resuspended in a washing
buffer of 100 mm kcl buffered with 1 te at ph 8 .
this
is repeated thrice , after which the fluorescent particles are resuspended
in the measurement buffer of choice .
the particles can therefore be
added to the reservoir surrounding the nanopore without affecting
the salt concentration in the reservoir .
a green laser operating
at 1 mw ( laser quantum ) is used to illuminate a wide region ( 30
30 m ) surrounding the nanopore opening .
the motion of the fluorescent particles due to the flows is recorded
at 500 frames per second .
the emccd chip is cooled to 20 c
and operated at an emccd gain of 3 .
individual particles are tracked
using custom - written software ( labview 2009 , national instruments )
which allows for the extraction of average particle velocities at
each point in a grid surrounding the pore .
the stokeslet limit of the
landau squire solution describes the flow field resulting from
a point force applied to a quiescent fluid at a low reynolds number .
the stokes stream function for this solution is given by8where is the dynamic
viscosity , p the magnitude of force required to set
up the flow , and r and are spherical polar
coordinates centered at the pore .
the coordinate system is defined
with the polar axis coincident with the pore axis . from the stream
function we can obtain velocity components:910 by moving
the bead to different locations in the plane of the pore a force map
can be created , which is converted to a velocity map using the equation fi = 6rvi , where r is the bead radius and fi and vi are the i - th components of the force and velocity .
the self - similar
nature of the flow allows the data to be linearized : if we let
= cos /r and = sin /r , plotting ur against or u against
gives straight lines which allow p to be
determined.1112 in practice , once the landau
squire nature of the flow
has been verified , p can be determined from just
a single point measurement of force , as long as the coordinates r and ( or equivalently x and y ) are known .
boltzmann equation for
the electric potential , followed by the stokes equation for
the fluid velocity . when e/kbt < 1 , the poisson boltzmann
equation can be linearized , which permits analytic solutions .
although
at low salt concentrations this condition is not fulfilled , the qualitative
features of the analytic model are preserved . the linearized poisson
. we can solve for the
electric potential subject to the boundary condition that
does not diverge anywhere , and the gradient of at the glass
surface depends on the surface charge according to gauss s
theorem .
inside an infinite cylinder of radius a the
solution is given by14and outside the cylinder , by15 the velocity profiles are determined from the stokes equation
in the absence of pressure gradients . inside the cylinder , this is
given bywhere we have used relations from
the poisson and debye hckel equations , and finally
our solution for the potential to rewrite the result .
outside the
cylinder , the equation is given by19 we can directly integrate these equations to obtain the final
results for the velocity profiles inside and outside the cylinder:20and21 finite - element
simulations were carried out using the comsol multiphysics package ,
version 4.4 .
planck equations ( eqs 1 and 2 ) are solved in a first
step neglecting convection ( the ciu term ) , which outputs fluxes and concentrations ji , c , ci and hence the charge density
e(r ) and electric potential (r ) .
(r ) and e(r ) are the inputs for the body force in the stokes
equation ( eq 3 ) , which is solved in a second
step to produce the velocity and pressure fields , u(r ) and p(r ) . the ratio
of diffusion to convection in the nernst
emax
10 v / m and umax 0.1
m / s , giving a diffusive to convective ratio of around 100 ; thus the
neglect of convection in the first step of the simulations is a reasonable
approximation . after each run , quantities such as ionic current and
flow rate through the pore were calculated . in order to compare with
experiments ,
a quantity p was also extracted by measuring
the velocity at a point on the pore axis 1 m from the pore
opening .
this simulates placing a bead close to the pore and using
it to probe the local velocity ( although in reality the measured force
is due to an average velocity over the entire bead surface , which
is not taken into account here ) . | pubmed |
when two superconductors are in close proximity , they are influenced by each other via the tunneling of cooper pairs .
the cooper - pair tunneling results in the flow of a superconducting josephson current , which has been studied for decades and is used in various superconducting quantum devices @xcite .
the josephson current is governed by the phase difference of the order parameters of the two superconductors .
therefore , josephson junctions consisting of unconventional superconductors , where the superconducting order parameter changes its sign depending on the momentum direction , serve as a unique platform where novel phase - related phenomena , e.g. , spontaneous formation of half flux quanta in a tri - junction of cuprate superconductors @xcite , take place .
compared with the well - investigated josephson currents , the spatial and energy dependence of the superconducting order parameter and quasiparticle states around these junctions remain to be understood .
recent progress in scanning tunneling microscopy ( stm ) and spectroscopy ( sts ) technologies opens up a way to directly visualize the spatial variation of the electronic states in superconducting hetero - structures @xcite .
however , stm / sts studies on superconducting junctions made of unconventional superconductors are still demanding .
there are two reasons which make it difficult to study unconventional junctions .
first , it is often challenging to artificially fabricate well - defined junctions of unconventional superconductors .
second , in most of unconventional superconductors , surfaces are not electronically neutral ; the resultant charge accumulation at the surfaces prevents stm / sts from accessing bulk superconducting properties . in this study
, we solve these problems by inspecting the twin boundaries ( tbs ) in the nodal iron - based superconductor fese @xcite .
the tb is a crystallographic plane in a crystal shared by two neighboring domains with one being the mirror image of the other .
the tbs are often formed by a tetragonal - to - orthorhombic structural phase transition , which reduces the four - fold ( @xmath4 ) symmetry at high temperature to two - fold ( @xmath5 ) symmetry at low temperature .
in such a case , the orthorhombic crystal may contain the tbs parallel to the ( 110 ) plane , which act as an atomically well - defined junction .
some unconventional - superconductor - related materials , such as yba@xmath6cu@xmath7o@xmath8 , ae(fe@xmath9co@xmath10)@xmath6as@xmath6 ( ae : alkali - earth element ) and nafeas , do form tbs upon the tetragonal - to - orthorhombic transition which were identified by stm / sts measurements @xcite
. however , unavoidable surface state formation and/or insufficient amount of chemical doping prevent the stm / sts measurements to access superconductivity near tbs in these materials .
fese ( superconducting transition temperature @xmath11 k @xcite ) is a promising candidate for studying the effects of tbs on unconventional superconductivity by stm / sts . among various iron - based superconductors , fese has the simplest crystal structure [ fig .
1(a ) ] in which electronically neutral two - dimensional fese layers are stacked along the @xmath12 axis @xcite .
this guarantees the perfect cleaved surface which is electronically neutral .
the tetragonal - to - orthorhombic structural phase transition , which is likely caused by the orbital ordering @xcite , occurs at @xmath13 k and the tbs are spontaneously formed in the orthorhombic phase as illustrated in fig .
band - structure calculations show that the fermi surface of fese consists of hole cylinders around the zone center and compensating electron cylinders around the zone corner @xcite .
several measurements , including penetration depth , quasiparticle interference , thermoelectric response @xcite , quantum oscillations @xcite , and angle - resolved photoemission spectroscopy ( arpes ) @xcite reveal that the fermi surface in the orthorhombic phase consists of one hole and one ( or two @xcite ) electron bands , both of which have very low carrier densities .
the tunneling spectrum @xcite , temperature dependence of the penetration depth down to 80 mk and the residual thermal conductivity at @xmath14 @xcite , all provide strong evidence that fese is an unconventional superconductor with line nodes in the superconducting gap .
the tbs in fese have been studied by low - temperature ( 4.2 k ) stm / sts in the films grown by molecular beam epitaxy and the suppression of superconductivity by the tbs has been reported @xcite .
we performed stm / sts measurements at much lower temperature ( @xmath15 k ) in vapor - grown single crystals to examine the details of the superconducting gap and quasiparticle excitations near the tbs .
stm / sts experiments were conducted in a constant - current mode with a commercial ultra - high vacuum very - low temperature stm ( unisoku , usm-1300 ) modified by ourselves @xcite .
the samples used in this study were high - quality bulk single crystals grown using the vapor transport method @xcite .
superconducting transition temperature defined at zero resistance is about 9 k. these crystals are undoped and stoichiometric , enabling us to investigate uniform and clean tbs .
samples were cleaved _ in - situ _ at liquid n@xmath6 temperature to prepare clean and flat ( 001 ) surfaces . immediately after cleaving , the samples were transferred to the stm unit kept below 10 k. we used electrochemically - etched polycrystalline tungsten wires for the scanning tips which were cleaned and sharpened _ in - situ _ by field evaporation using field - ion microscopy .
the tunneling conductance @xmath16 reflecting the local density of states ( ldos ) at a position @xmath17 and energy @xmath18 , was acquired by standard lock - in technique . here ,
@xmath19 and @xmath20 denote the tunneling current and the sample - bias voltage , respectively .
figure 1(c ) depicts an stm image of the cleaved surface of an fese single crystal at temperature @xmath21 k. the image demonstrates the extremely small concentration of defects , i.e. about one defect per 5000 fe atoms in the ( 001 ) plane .
there is a shallow `` groove '' running along the [ 110 ] direction of the fe lattice across which the unidirectional feature around the point defect is rotated by @xmath0 , indicating that the `` groove '' represents the tb .
we also observed that the elongated vortex cores @xcite , which were imaged by mapping @xmath22 in a magnetic field , are rotated by @xmath0 across the tb [ fig .
what is intriguing is that the vortices trapped at the tb are not elongated along the tb , demonstrating that the critical current density across the tb is comparable to that of the bulk .
the stm image of the tb at a lower bias voltage is not a `` groove '' but a `` ridge '' [ figs .
this suggests that the apparent corrugations near the tb are primarily associated with the electronic - state variations ; the actual surface topography near the tb may be essentially flat . a magnified stm image near the tb is shown in fig .
1(f ) . a regular square lattice of the top - most se atoms
is well maintained even in the close vicinity of the tb .
these observations indicate that the tb in fese is an atomically sharp superconducting junction with minimal strain to the lattice .
( a detailed argument regarding the absence of strain is given in appendix a. ) we examined the ldos evolution across the tb by taking a series of @xmath23 along the line indicated in fig .
2(a ) . here and in the following
, we are interested only in the evolution of @xmath23 along the @xmath24 axis running perpendicular to the tb leaving the @xmath25 coordinate constant , hence @xmath26 .
figure 2(b ) shows an intensity plot of @xmath23 .
individual spectra taken at representative points are depicted in fig .
at the position far away from the tb ( i ) , @xmath23 exhibits a superconducting gap with clear quasiparticle peaks at @xmath27 mev .
in addition to this main feature , there is a shoulder outside of the main peaks ( @xmath28 mev ) , which may represent multiple superconducting gaps @xcite .
in contrast to the case of fully - gapped superconductors in which @xmath29 in an extended @xmath18 region near @xmath30 , @xmath23 in fese approaches zero only for @xmath31 and apparently v - shaped , indicating the presence of line nodes @xcite .
even right at the tb ( iii ) , the residual ldos at @xmath30 is negligibly small , indicating that the tb hardly gives rise to a pair breaking effect . in the vicinity of the tb , the quasiparticle peak and the shoulder associated with the superconducting gap diminish , and instead , sharp particle - hole symmetric peaks appear at @xmath32 mev . in the crossover region ( ii ) , the 1.5 mev peak coexists with the 2.5 mev peak , meaning that the former is not associated with the suppressed superconducting gap .
the 1.5 mev peak diminishes within a distance of about 5 nm from the tb , which is close to the `` averaged '' in - plane coherence length @xmath33 nm obtained from the upper critical field @xmath3415 t @xcite .
these results suggest that the 1.5 mev peak represents the bound state induced by the tb .
another interesting observation is that low - energy quasiparticle excitations are modified over a very long distance from the tb .
high - resolution @xmath23 spectra at the positions of ( i ) , ( ii ) and ( iii ) are plotted in fig .
while the overall v - shaped behavior is maintained , the exact shape near the bottom of the gap depends on the position . in order to examine this behavior ,
we fit an empirical power - law @xmath35 to the low - energy ( @xmath36 mev ) spectra and plot the exponent @xmath37 as a function of the distance from the tb at @xmath38 [ fig .
2(e ) ] . except close to the tb ( @xmath39 ) where the 1.5 mev peaks dominate
, @xmath37 increases gradually with decreasing @xmath24 by about @xmath40% .
this implies the suppression of the low - energy quasiparticle excitations , most probably due to the opening of a small gap induced by the tb .
the salient feature is that @xmath37 continues to change even at @xmath41 ( @xmath42 nm ) , indicating an unexpectedly long - distance influence of the tb .
the long - distance tb effect on the ldos can be seen in a more dramatic way in two junctions in series formed by two tbs . as shown in fig .
3(a ) we find an area where two tbs are running parallel to each other .
the distance between the tbs is 34 nm , which is about 7 times larger than @xmath1 .
figure 3(b ) shows the spatial evolution of @xmath23 across the double tbs .
individual spectra at representative points are plotted in fig .
the overall spectral features , the 2.5 mev peak , the 3.5 mev shoulder and the 1.5 mev peak observed near a single tb are all reproduced ( positions i , ii , and iii ) . however
, the low - energy spectrum taken inside the central domain ( position iv ) shows a striking anomaly which is absent in the case of a single tb . figure 3(d ) depicts @xmath23 spectra at low energies .
it is clear that , in between the double tbs , there is a finite energy range where @xmath23 is almost completely zero .
the noticeable difference of the gap structure between inside and outside the central domain is clearly seen in fig .
3(e ) , which shows the exponent @xmath37 plotted as a function of the distance from one of the tbs ; @xmath37 is strongly enhanced in the central domain and peaks at the middle of the domain .
the large power @xmath43 , which is @xmath44 times larger than the values at large @xmath24 , essentially indistinguishable from an exponential energy dependence .
this apparent large power again corroborates the finite gap opening in the excitation spectrum of quasiparticle .
the above observations , the tb - induced bound states at finite energies and the suppression of the low - energy quasiparticle excitations over a length scale much longer than @xmath1 , suggest a novel role of the tb in an unconventional superconductor . before discussing the origin of these anomalies , we briefly review what can be expected at a tb of fese .
recent high - resolution laser - arpes measurements of fese indicate that the hole cylinder is fully gapped @xcite , implying that the line nodes are present on the electron cylinder , as has been also inferred from vortex imaging @xcite . given this information ,
we consider two possible phase structures for symmetry of the superconducting gap across a tb as illustrated in fig . 4 , where either the global phase of the superconducting gap is fixed to the crystallographic axis [ fig .
4(a ) ] or is flipped across the tb [ fig .
it should be noted that the sign of either the nodal gap or the nodeless gap is reversed between the two domains in fig .
4(a ) or fig . 4(b ) , respectively .
this means that the amplitude of at least one of the gaps vanishes at the tb , giving rise to the zero - energy quasiparticle state that should appear as a zero - energy peak in @xmath23 .
this argument applies not only for the particular phase structure shown in fig . 4 but also for a general case in which nodal and nodeless gaps reside on multiple fermi surfaces .
the observed bound - state peak at 1.5 mev apparently contradicts this conjecture and suggests instead that the tb induces an additional gap component which shifts the position of a zero - energy peak to a finite energy .
we point out that , as long as the induced gap is real , a sum of the bulk gap and the tb - induced gap reverses its sign at a finite distance from the tb and still gives rise to a zero - energy peak .
however , as shown in fig .
2(b ) , we did not observe a zero - energy peak in @xmath23 over more than 100 nm from the tb .
thus , we speculate that the induced gap has an imaginary component , which means that time reversal symmetry is locally broken near the tb .
in such a case , bound state peaks are located at finite energies @xmath45 because the phase shift @xmath46 on the tb is reduced from @xmath47 @xcite . here
, @xmath48 is the amplitude of the superconducting gap .
the possibility of the tb - induced time - reversal - symmetry - broken state has been argued theoretically in @xmath49-wave yba@xmath6cu@xmath7o@xmath8 with a small @xmath50-wave component @xcite , but the experimental observation is still lacking . in order to substantiate the relevance of this scenario , we have calculated the spatial evolution of the ldos for a model order parameter with broken time - reversal symmetry near tbs .
the @xmath5-symmetric order parameter is represented by a sum of the isotropic component @xmath51 and the four - fold nodal component @xmath52 , @xmath53 where @xmath54 is the azimuthal angle in the momentum space ; see fig . 4 .
we assume that the global phase of the order parameter is fixed to the crystallographic axis , that is , the nodal component changes its sign across a tb as shown in fig .
the spatial variation of @xmath55 around a tb at @xmath56 is modeled by the form @xmath57\cos\theta(x)+i\sin\theta(x)\},\ ] ] where the @xmath24 axis is taken to be perpendicular to the tb , and @xmath58 is the amplitude of @xmath55 in the bulk .
the phase @xmath59 of @xmath60 equals @xmath61 for @xmath62 and @xmath63 for @xmath64 .
the phase variable @xmath61 is assumed to take a nonvanishing value near the tb and exponentially decay with another length scale @xmath65 .
it is important to note that the characteristic length @xmath66 for the local time - reversal symmetry breaking can be much longer than the coherence length @xmath67 @xcite .
( the derivation of the length @xmath66 is given in appendix b. ) to account for low - energy excitations near the nodes observed in the ldos , we focus on the electron cylinder with nodal gaps by setting the parameters @xmath68 and @xmath69 .
as a model order parameter with a tb at @xmath70 , we take @xmath71 with @xmath72 , which gives @xmath73 .
the order parameter @xmath60 is shown in fig .
5(a ) , where @xmath74 changes with the length scale @xmath67 while @xmath75 decays with the longer length scale @xmath66 .
the phase @xmath59 abruptly changes near the tb and gradually approaches @xmath76 or @xmath47 . using this order parameter
, we calculate the spatial dependence of the ldos within the quasi - classical approximation @xcite .
figure 5(b ) shows the global peak structure of the ldos at representative points calculated with energy smearing of @xmath77 .
far from the tb , namely in the bulk ( i ) , the ldos has peaks at @xmath78 . on the tb ( iii ) ,
the peaks observed in the bulk are suppressed , and alternative peaks appear at @xmath79 , which correspond to the bound states whose energies are shifted from @xmath30 due to the local time - reversal symmetry breaking in @xmath55 .
the bound - state peaks disappear at @xmath80 ( ii ) since their wave functions decay into the bulk with the length scale @xmath67 .
these features of the calculated ldos arising from the bound states are consistent with the ldos peaks observed at @xmath81 mev by stm .
we show in fig .
5(c ) the ldos at lower energy scale which has been calculated with a much smaller smearing factor @xmath82 .
the clear v - shaped ldos in the bulk ( i ) changes to the u - shaped ldos upon approaching the tb , in agreement with the increase of the exponent @xmath37 evaluated from the experimental data [ fig .
the low - energy ldos is finite at @xmath38 ( iii ) and @xmath80 ( ii ) because low - energy quasiparticles with momenta along the nodal directions of the bulk gap can linger over long distance and reach the tb , even though the local gap , @xmath83 ^ 2 + [ { \rm im}(\delta_{4\phi})\sin(2\phi)]^2},\ ] ] does not vanish near the tb where @xmath84 .
we also calculate the ldos for double tbs located at @xmath85 , taking the model order parameter of the form @xmath86\tanh[(x+x_0)/\xi]\cos\theta(x ) + i\sin\theta(x)\},\ ] ] shown in fig .
we assume that the distance @xmath87 between the tbs is in the range @xmath88 .
the phase @xmath61 is an even function of @xmath24 and takes a maximum value at @xmath38 .
the global peak structure of the ldos and its low - energy blowup are shown for representative points along the @xmath24 direction in fig .
5(e ) and 5(f ) , respectively . the large peaks at @xmath89 on a tb ( iii ) and the small peaks at @xmath90 at the middle point @xmath38 between the tbs ( iv ) in fig .
5(e ) originate from the same dispersive mode of bound states at a tb . the calculated ldos spectrum at @xmath38 between the double tbs ( iv ) in fig .
5(f ) exhibits a clear energy gap extending over the region @xmath91 , reflecting the existence of a larger local gap at @xmath38 , where the bulk low - energy quasiparticles can not reach .
we conclude that the local gap enhanced by the local time - reversal symmetry breaking near tbs over the length scale @xmath65 can explain the strong suppression of the ldos between the two tbs observed in our stm / sts experiments .
we have reported on the visualization of the atomic scale variation of the quasiparticle states of the nodal superconductor fese near tbs that enforce a sign inversion at least one of the superconducting gaps opening on multiple fermi cylinders .
in contrast to the expectation that the sign inversion generates a zero - energy quasiparticle bound state near the tb , the tb - induced quasiparticle states are not at zero but at finite energies @xmath92 mev . moreover , the low - energy excitation spectrum is affected by the tb over an extremely long distance , which is a few tens of times larger than @xmath1 .
an even more dramatic change in the low - energy spectrum has been detected in the region between double tbs separated by a distance @xmath93 , where the quasiparticle weight near the fermi energy is almost completely removed in the energy range @xmath94 mev .
these observations are qualitatively reproduced by a phenomenological model which assumes that the tb induces locally a superconducting state that breaks time - reversal symmetry .
our results suggest several important directions for future studies . a microscopic mechanism that induces the time - reversal symmetry
broken state is elusive and should be investigated theoretically .
it is also interesting to go beyond the quasi - classical approximation because fese is a unique superconductor whose fermi energy is of the same order as the superconducting gap , placing this system in the bcs - bec crossover regime @xcite .
experiments that directly probe the time - reversal symmetry breaking , such as muon - spin rotation and local magnetometry , are highly desirable and would give us further insights into the unconventional superconducting junctions .
we anticipate that the tbs in fese will stimulate further research on the role of the phase of the superconducting order parameter near the interface , which has been difficult to access experimentally
. this work has been supported by japan
germany research cooperative program , kakenhi from jsps and project no .
56393598 from daad , and the topological quantum phenomena " ( no .
25103713 ) kakenhi on innovative areas from mext of japan .
although stm has a high spatial resolution , possible creep in the piezoelectric scanner and/or the thermal drift make it difficult to estimate the small distortions in the topographic image .
here we utilize the so - called lawler - fujita algorithm @xcite to deduce the lattice distortion and show that the tb - induced strain is negligibly small .
first we briefly explain the principle of the methodology .
the observed stm topography @xmath95 , which mainly represents the top - most se lattice , can be expressed as @xmath96+\cdots.\end{aligned}\ ] ] here , @xmath97 is the amplitude of the se - lattice modulation , @xmath98 and @xmath99 are wave vectors for the se lattice , and @xmath100 represent all other modulations .
the distortions from the perfect lattice is described by the displacement field @xmath101 that can be regarded as a spatially varying phase of the @xmath98 and @xmath99 modulations .
this approximation is justified as long as the length scale of distortions is much longer than the se - se distance @xmath102 .
standard phase - sensitive detection scheme can be used to evaluate @xmath101 . by multiplying @xmath95 and the reference signal @xmath103 , we get @xmath104\nonumber\\ & + \cdots.\end{aligned}\ ] ] all
terms except the first exhibit periodic spatial modulations , which can be removed by low - pass fourier filtering @xmath105 .
@xmath106 by using the quadrature reference @xmath107 , we get @xmath108 therefore , we obtain @xmath109 , the @xmath24 component of @xmath101 as @xmath110 the @xmath25 component @xmath111 can also be deduced as @xmath112 a schematic model of atomic arrangement near the tb is shown in fig .
we expect that the orthorhombic distortion affects the atomic arrangement along the @xmath25 direction across the tb , while the periodicity along the @xmath24 direction remains intact . in order to verify this model and to check if there is an additional lattice distortion , we calculated @xmath109 and @xmath111 of the high - resolution stm image containing a tb running along the @xmath25 direction [ fig 6(b ) ] .
reference wave vectors @xmath98 and @xmath99 were obtained by the fourier analysis in the left domain . for low - pass fourier filtering ,
we picked up only long - wavelength components by using a gaussian mask with half width at the half maximum of @xmath113 . since there is a translational symmetry along the tb , we average @xmath109 and @xmath111 along the @xmath25 direction , yielding @xmath114 and @xmath115 , respectively .
this significantly enhances the signal - to - noise ratio .
figures 6(c ) and ( d ) show @xmath114 and its @xmath24 derivative .
there is no noticeable anomaly in both @xmath114 and @xmath116 , except for the smooth background associated with the creep of the piezoelectric scanner .
by contrast , @xmath115 exhibits a sharp kink at the tb [ fig .
these features are consistent with the model shown in fig .
it should be noted that @xmath117 shown in fig .
6(f ) is almost completely constant in both domains , indicating that the tb - induced strain to the lattice is negligibly small .
the observed value of @xmath118 in the right domain means that the angle @xmath119 defined in fig .
6(a ) is + 0.63@xmath120 .
this means that orthorhombic distortion @xmath121 , being consistent with the x - ray result @xcite .
even if there were an additional lattice distortion associated with the tb , it should be much smaller than this tiny orthorhombic distortion which we have clearly detected .
we derive asymptotic forms of the order parameter far from tbs using the ginzburg - landau ( gl ) theory .
we consider the gl free - energy functional for tetragonal symmetric systems @xcite as an expansion in the isotropic @xmath50-wave component @xmath51 and the four - fold @xmath49-wave component @xmath55 of the order parameter : @xmath122 = \int dv\left\{\sum_{\mu={\rm iso},4\phi } \left [ \tilde{a}_{\mu}(t)|\delta_{\mu}|^2 + b_{\mu}|\delta_{\mu}|^4 + k_{\mu}|\bm{\nabla}\delta_{\mu}|^2\right ] + \gamma_1|\delta_{\rm iso}|^2|\delta_{4\phi}|^2 \right.\\ \left .
+ \frac{\gamma_2}{2}\left(\delta_{\rm iso}^{*2}\delta_{4\phi}^2 + \delta_{\rm iso}^2\delta_{4\phi}^{*2}\right ) + \frac{\widetilde{k}}{2}\left [ ( \partial_a\delta_{\rm iso})^*(\partial_a\delta_{4\phi } ) -(\partial_b\delta_{\rm iso})^*(\partial_b\delta_{4\phi } ) + { \rm c.c.}\right]\right\},\end{gathered}\ ] ] where we have neglected the vector potential as it does not play an important role in our discussion .
the coefficients @xmath123 , @xmath124 , and @xmath125 are positive and @xmath126 with positive @xmath127 .
the differential operator @xmath128 is defined according to the crystal axes @xmath129 and @xmath130 . as in ref . , we assume @xmath131 , so that the free energy is minimized at @xmath132 , and the time - reversal - symmetry - broken @xmath133 state is stabilized when both @xmath51 and @xmath55 are finite . the effect of orthorhombic distortion is taken into account by adding the following term to the free - energy functional @xcite : @xmath134 where @xmath12 is a positive parameter and @xmath135 is the parameter of the orthorhombic lattice distortion . the total free energy for a uniform state in the bulk is then given by where @xmath137 and the relative phase @xmath138 .
if @xmath139 , then the free energy is minimized at @xmath140 for @xmath141 and at @xmath142 for @xmath143 . in the following discussion
we assume that this inequality is satisfied and the time reversal symmetric @xmath144 state is realized in the bulk .
next , we consider a tb located at @xmath56 along the @xmath25 axis , where the @xmath24 and @xmath25 axes are rotated by 45@xmath120 from the crystalline axes , @xmath145 and @xmath146 . the orthorhombic lattice distortion parameter @xmath147 changes its sign across the tb .
we assume @xmath148 for @xmath149 , so that the @xmath144 state is realized in @xmath149 . near the tb where @xmath150 is small ,
the @xmath133 state is favored .
then , the area density of the total free energy is given by @xmath151.\end{aligned}\ ] ] let us first assume that @xmath51 is a real and uniform order parameter while @xmath55 changes its sign across the tb , as shown in fig .
if we restrict @xmath55 to be real , then @xmath55 varies over the coherence length @xcite @xmath152 where @xmath153 is the amplitude of @xmath55 in the bulk .
however , we expect that time - reversal symmetry should be locally broken at the tb .
thus , we allow @xmath55 to be complex , @xmath154 . with this order parameter ,
the total free energy is given by @xmath155\bigg].\end{aligned}\ ] ] in the bulk region ( @xmath62 ) where @xmath156 and @xmath157 , the gl differential equation to minimize @xmath158 is @xmath159.\end{aligned}\ ] ] since @xmath160 far away from the tb , we can linearize the differential equation and find the relative phase to decay as @xmath161 with the characteristic length @xmath162 the characteristic length diverges when approaching the phase boundary , where @xmath163 , between the time reversal symmetric @xmath144 state and the time - reversal - symmetry - broken @xmath133 state . finally , we consider double tbs at @xmath164 , where @xmath165 .
we assume @xmath143 between the double tbs and @xmath141 otherwise . at the center @xmath38 between the double tbs
, we can set @xmath166 because @xmath167 . with this approximation ,
the gl differential equation to minimize @xmath158 for @xmath168 is @xmath169.\end{aligned}\ ] ] integration of the differential equation yields where the integration constant is determined from the conditions @xmath171 and @xmath172 . since we assume the distance between the tbs is in the range @xmath173 , the relative phase does not reach @xmath47 at @xmath38 , i.e. , @xmath174 . for @xmath175 near @xmath38
, the differential equation has the solution @xmath176 for the model order parameter shown in fig .
5(d ) , we have determined @xmath177 and @xmath178 by the continuity condition at @xmath179 , that is , by imposing that @xmath180 and @xmath181 in eq .
are smoothly connected at @xmath179 .
we note that different choices of the connecting position yield little change in the value of @xmath59 .
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Sherlock 1. Chapter 1
Mormor/Johnlock fanfic
**This is my first fanfic ever so if you could give me some feedback (negative is well appreciated), it would be great, thanks!
**I do not own any of the characters involved in the story
* * *
Sebastian burst loudly in through the out door looking very angry. Despite the ruckus, Jim didn't even blink an eye and continued staring at the book he held in his hands, although it didn't seem like he was really reading it.
"You bastard."
Seb's intention had been to shout at Jim, but it came out a lot weaker than he had expected, so Jim could barely hear him. He looked up from his book and tried hiding the smile that almost broke it's way to his face.
"What is it, Seb?"
He acted as if he had no idea what Seb was angry about and stared at him with a blank expression on his face.
Seb paced around the room looking very pissed-off.
"I thought you were dead", he said after a little while. He had stopped pacing, and now stood in the middle of the room staring at Jim.
"Oh, Seb, it was nothing personal", Jim said in a mocking tone. He put the book away, stood up and walked towards Seb. Seb, however, backed away.
"This isn't funny, Jim. I had been grieving for more than two years, you know how hard this was for me? And to hear that you're alive from the television, couldn't you have at least sent a letter or something?"
Seb was almost yelling at this point. Jim's face had gone from a sarcastic smirk to being very serious as he watched the veins in Seb's neck getting bigger and bigger.
"Now, now, don't make a scene. This was necessary. I'm sorry, I really am, but there was no way I could have let you know."
Seb looked straight into Jim's eyes and saw immediately that he was being serious.
"Well... just don't do it again, I was lost without my boss"
His head was hanging halfway down, but he still kept eye contact with Jim.
"I promise"
Jim smirked and reached up to give Seb a kiss.
2. Chapter 2
Mormor/Johnlock fanfic
**This is my first fanfic ever so if you could give me some feedback (negative is well appreciated), it would be great, thanks!
**I do not own any of the characters involved in the story
* * *
John looked worried. Moriarty's voice echoed inside his head.
"Did you miss me?"
He stepped inside the flat and sat down in his chair. Sherlock followed but didn't sit down, instead he started pacing back and forth around the flat. After a while John got tired of Sherlock's pacing.
"Sherlock, could you please sit down", he said and it was obvious on the tone of his voice that he wanted to shout that.
Sherlock walked up to his chair, sat down and put his hands together, as he normally did when he was deep in thought.
"So...", John hesitated. He didn't want to bother Sherlock with his useless blabbering, but he had gotten tired of the silence.
"No, John, I don't know what we're going to do", Sherlock said with a hint of annoyance in his voice.
"I guess we're just going to wait then", John muttered and stood up from his chair to make himself a cuppa. "You want some?"
"Please", Sherlock said. He still sat in the exact same position as before and stared at the coffee table.
John wondered what could be going to Sherlock's mind. He wished he could help in some way, but he knew that if he tried to help in any way he'd just be bothering Sherlock.
Sherlock noticed the carpet had been vacuumed not that long ago. Mrs. Hudson had been there. Where could she have gone? She would surely be in their flat asking many annoying questions about Moriarty if she was anywhere in the house.
"Where do you think Mrs. Hudson went?", he asked John.
"She's not in her flat?" John wasn't surprised that Sherlock seemed to know this, but he still felt the need to ask the question.
"Of course not, John", Sherlock said with an irritated tone in his voice. "She's gone somewhere. Oh well, it's not like I care."
"Of course you don't", John muttered. "Here's your cuppa". He handed Sherlock the cup and sat down in his chair with his own. "So, any progress on the Moriarty... uh, situation?"
"Of course, John. I have thought of 11 possible ways of how he could have done it. And still working on some more".
"Wow. That's... impressive. Don't you want to take a break though? Relax a bit", John hoped Sherlock would understand what he meant.
"How can I relax at this time?"
John sighed. He'd have to explain further, and he hated that.
"Well, I know of a few ways that can help a lot in these kind of situations", John said and put his cup down, moved forward in his chair and looked into Sherlock's eyes.
"Oh? You have some on you right now?", Sherlock suddenly got very interested.
"Have what... oh no, no, no, no, Sherlock I'm not talking about drugs, good god why would you think that? And you said you quit!", John was disappointed and annoyed.
"Well then, what are you talking about John? You know it bothers me when I don't know what people are thinking".
John was tired of trying to think of more hints, and he knew it would take a lot for Sherlock to get it. So he decided to take action. He stood up from his chair and signed Sherlock to follow him.
Confused, Sherlock followed John into the bedroom.
Half an hour later Mrs. Hudson came in through the front door of 221b Baker Street with her arms full of grocery bags. When she had shut the door she suddenly stopped, looked up and smiled.
"Oh those boys, they're at it again", she muttered to herself giggling, and carried on into her flat.
End file.
| fanfiction |
the present paper elaborates on the notion of @xmath0-curve of stahl @xcite and of gonchar and rakhmanov @xcite . among the many applications of @xmath0-curves ( see for instance section 6.3 of @xcite and references therein ) , we pay special attention to the theory of nonhermitian orthogonal polynomials @xmath1 @xmath2 the classical theory of orthogonal polynomials corresponds to the hermitian case , in which the integration path @xmath3 is typically a real interval and the weight is a positive real function on @xmath3 . but
more recently the nonhermitian case , in which @xmath3 can be a more general curve in the complex plane and the weight can be a complex function , has received much attention . in the mathematical literature
these polynomials first appeared as denominators of pad and other types of rational approximants @xcite , but the corresponding theory quickly developed and found applications into such fields as the riemann - hilbert approach to strong asymptotics , random matrix theory @xcite and , consequently , in the study of dualities between supersymmetric gauge theories and string models @xcite .
more concretely , our aim is to apply the general theory of @xmath0-curves as developed in @xcite to study the asymptotic distribution of zeros of orthogonal polynomials and the phase structure of the asymptotic distribution of eigenvalues as @xmath4 of random matrix problems of the form @xcite @xmath5 where the eigenvalues of the @xmath6 matrices @xmath7 are constrained to lie on @xmath3 . throughout our discussion
we assume that @xmath8 is a complex polynomial and @xmath3 is a simple analytic curve connecting two different convergence sectors ( @xmath9 ) at infinity of ( [ pol1 ] ) .
a fundamental result of gonchar and rakhmanov @xcite asserts that if @xmath3 is an @xmath0-curve , then the asymptotic zero distribution of @xmath10 exists and is given by the equilibrium charge density @xcite that minimizes the electrostatic energy ( among normalized charge densities supported on the curve @xmath3 ) in the presence of the external electrostatic potential @xmath11 .
note that the integral ( [ pol1 ] ) is invariant under deformations of the curve @xmath3 into curves in the same homology class and connecting the same two convergence sectors at infinity .
this freedom to deform @xmath3 means that only for special choices of @xmath3 the asymptotic zero distribution has support on @xmath3 .
according to recent results by rakhmanov @xcite , given a family of orthogonal polynomials of the form ( [ pol1 ] ) we can always deform @xmath3 into an appropriate @xmath0-curve .
we use an analytic scheme , to be implemented in general with the help of numerical analysis , based on the study of certain algebraic curves which arise as a direct consequence of the @xmath0-property @xcite .
these _ spectral curves _ have the form @xmath12 where @xmath13 is a polynomial such that @xmath14 .
the main parameters that determine the @xmath0-curves and the associated equilibrium densities are the branch points of @xmath15 , which turn out to be the endpoints of the ( in general , several disjoint ) arcs ( cuts ) that support the equilibrium density . systems of equations for these branch points can be formulated in terms of period integrals of @xmath15 and are known in several equivalent forms .
we select one of these forms that in the hermitian case reduces to the system of equations derived in @xcite .
the corresponding cuts are characterized as stokes lines of the polynomial @xmath16 or , equivalently , as trajectories of the quadratic differential @xmath17 . at this point
we use numerical analysis not only to solve the equations for the cut endpoints but also to analyze the existence of cuts satisfying the @xmath0-property .
recently bertola and mo @xcite and bertola @xcite have used the notion of boutroux curves to characterize the support of the asymptotic distribution of zeros of families of nonhermitian orthogonal polynomials .
both the calculations of the present paper and the approach of @xcite do not rely on the minimization of a functional but on the characterization of spectral curves ( [ eq : c0 ] ) with appropriate cuts .
this characterization is formulated in @xcite in terms of admissible boutroux curves which are determined from certain combinatorial and metric data in the space of polynomials @xmath18 .
it can be proved that the branch cut structure of admissible boutroux curves consists of arcs satisfying the @xmath0-property and , consequently , the method of @xcite can also be applied to characterize @xmath0-curves . however , as we explained in the previous paragraph , our calculations are based on an explicit system of equations for the cut endpoints .
in contrast , the generation of nontrivial explicit examples in @xcite amounts to imposing directly period conditions by means of a numerical algorithm involving the minimization of a functional that vanishes precisely for admissible boutroux curves .
the paper is organized as follows . in section
[ sec : zdop ] we review the basic results on equilibrium densities of electrostatic models under the action of external fields . then we introduce the notions of @xmath0-curve and @xmath0-property , and discuss their relevance to characterize asymptotic zero densities of orthogonal polynomials . to obtain an equivalent but computationally more efficient formulation of the @xmath0-property it is convenient to introduce the complex counterpart of the electrostatic potential .
this formulation leads naturally to the notion of spectral curve . in section [ sec : ced ] we recall the theoretical background to construct equilibrium densities on @xmath0-curves for a given polynomial @xmath8 and use the theory of abelian differentials in riemann surfaces to derive a system of equations for the cut endpoints .
we also discuss the characterization of cuts as stokes lines and the process of embedding the cuts into @xmath0-curves . in section
[ sec : tcm ] we apply the former results to perform a complete analysis of the cubic model @xmath19 with a varying complex coefficient @xmath20 .
we determine @xmath0-curves and equilibrium densities for the two possible cases corresponding to equilibrium densities supported on one or two disjoint arcs .
our analysis combines theoretical properties with numerical calculations and allows us to characterize critical processes of merging , splitting , birth and death at a distance of cuts . as a consequence
we describe the phase structure of the corresponding families of orthogonal polynomials on different paths @xmath3 .
the consistency of our results is checked by superimposing the cuts and the zeros of the corresponding orthogonal polynomials @xmath21 with degree @xmath22 .
thus we find a complete agreement with the gonchar - rakhmanov theorem @xcite ( theorem 1 below ) . finally , in section
[ sec : gcr ] we briefly discuss a generalization of the @xmath0-property which arises in the study of dualities between supersymmetric gauge theories and string models on local calabi - yau manifolds .
some technical aspects of the theoretical discussion are treated in appendix a.
according to the general theory of logarithmic potentials with external fields @xcite , given an analytic curve @xmath3 in the complex plane and a real - valued external potential @xmath23 , there exists a unique charge density @xmath24 that minimizes the total electrostatic energy @xmath25 = \int_{\gamma } |\rmd z| \rho(z ) v(z ) - \int_{\gamma } |\rmd z| \int_{\gamma } |\rmd z'| \log |z - z'| \rho(z ) \rho(z')\ ] ] among all positive densities supported on @xmath3 such that @xmath26 this density @xmath24 is called the _ equilibrium density _ , and its support @xmath27 is a finite union of disjoint analytic arcs @xmath28 ( cuts ) contained in @xmath3 : @xmath29 in terms of the total electrostatic potential @xmath30 the equilibrium density is characterized by the existence of a real constant @xmath31 such that @xmath32 @xmath33 the property that relates this minimization problem to the asymptotic zero density of orthogonal polynomials is called the _ s - property _ , and was singled out by stahl @xcite , elaborated by gonchar and rakhmanov @xcite , and more recently extended by martnez - finkelshtein and rakhmanov @xcite .
a curve @xmath3 is said to be an _
@xmath0-curve _ with respect to the external field @xmath23 if for every interior point @xmath34 of the support @xmath27 of the equilibrium density the total potential ( [ loge ] ) satisfies @xmath35 where @xmath36 denote the two normal vectors to @xmath27 at @xmath34 pointing in the opposite directions . in this case
it is said that @xmath27 satisfies the @xmath0-property .
the condition ( [ s0 ] ) means that the electric fields at each side are opposite , @xmath37 .
let @xmath38 be a family of monic orthogonal polynomials on a curve @xmath3 with respect to an exponential weight @xmath39 , @xmath40 here and henceforth we assume that @xmath8 is a complex polynomial of degree @xmath41 @xmath42 and that @xmath3 is an oriented simple analytic curve which as @xmath43 connects two different sectors of convergence of ( [ pol1b ] ) .
the notion of @xmath0-curve is crucial in the analysis of the limit as @xmath44 of the zero density @xmath45 of @xmath10 .
the following theorem ( see @xcite , section 3 ) states the close relation between the asymptotic zero distribution of orthogonal polynomials and the equilibrium densities on @xmath0-curves : let @xmath38 be a family of orthogonal polynomials on a curve @xmath3 with respect to an exponential weight @xmath39 . if @xmath3 is an @xmath0-curve with respect to the external potential @xmath11 , then the equilibrium density on @xmath3 is the weak limit as @xmath44 of the zero density of @xmath10 .
it often occurs in the applications that the orthogonal polynomials @xmath10 are initially defined on a curve @xmath3 which is not an @xmath0-curve .
this problem raises the question of the existence of an @xmath0-curve in the same homology class of @xmath3 connecting the same pair of convergence sectors at infinity ( and therefore defining the same family of orthogonal polynomials ) .
this question has been recently solved in the affirmative by rakhmanov ( see @xcite , section 5.3 ) . note also that although this @xmath0-curve is not unique , the associated equilibrium density is certainly unique .
equilibrium densities on @xmath0-curves are also expected to describe the asymptotic eigenvalue distribution as @xmath44 of random matrix models with partition function ( [ mm0 ] ) . according to heine s formula @xcite ,
the polynomials ( [ pol1 ] ) are the expectation values of the characteristic polynomials of the matrices @xmath7 of the ensemble , @xmath46 in terms of the zeros @xmath47 of @xmath10 and of the eigenvalues @xmath48 of @xmath7 , this result means that the expectation value of the function @xmath49 is the function @xmath50 . therefore it is natural to conjecture that the asymptotic distributions of zeros of @xmath10 and of eigenvalues of @xmath7 coincide .
this conjecture has been rigorously proved in the hermitian case , i.e. , when @xmath51 and the polynomial @xmath8 has real coefficients @xcite , and indeed orthogonal polynomials are a widely used tool in many aspects of hermitian random matrix theory ( for some recent applications see @xcite ) .
the @xmath0-property can be formulated in a more convenient form to our goals using a complex counterpart of the electrostatic potential ( [ loge ] ) .
thus , we define @xmath52 where @xmath53 is the analytic function in @xmath54 given by @xmath55 here we assume that the logarithmic branch is taken in such a way that for every @xmath56 the function @xmath57 is an analytic function of @xmath34 in @xmath58 minus the semi - infinite arc of @xmath3 ending at @xmath59 . as usual @xmath60 and
@xmath61 denote the limits of the function @xmath62 as @xmath59 tends to @xmath34 from the left and from the right of the oriented curve @xmath3 respectively .
it is clear that @xmath63 and therefore the equilibrium condition ( [ cm ] ) can be rewritten as @xmath64 furthermore , it follows from the cauchy - riemann equations that the @xmath0-property ( [ s0 ] ) is verified if and only if the imaginary part of @xmath65 is constant on each arc @xmath66 of @xmath27 ( usually stated as `` locally constant on @xmath27 '' ) @xcite : @xmath67 note that , in essence , the @xmath0-property embodies the possibility of analytically continuing the derivative of the complex equilibrium potential through the support . in some physical applications @xcite the values @xmath68 are especially relevant , and equations ( [ mina1 ] ) and ( [ s20 ] ) are ( trivially ) restated by saying that @xmath3 is an @xmath0-curve if and only if the complex potential @xmath65 is locally constant on @xmath27 @xmath69 and the constants @xmath70 have the same real part @xmath71 next we will see how equations ( [ s2 ] ) lead to the notion of spectral curve .
( in section [ sec : eqendpts ] we will see that equations ( [ s22 ] ) are essential to formulate the system of equations for the cut endpoints in the multicut case . ) in fact , condition ( [ s2 ] ) can be rewritten in a form especially suited for practical applications in terms of a new function @xmath15 defined by @xmath72 the complex potential @xmath65 is locally constant on @xmath27 if and only if the square of @xmath15 is a polynomial of the form @xmath73 where @xmath13 is a polynomial of degree @xmath14 .
_ condition ( [ s2 ] ) is equivalent to @xmath74 where @xmath75 and therefore ( [ s3 ] ) can be written as @xmath76 the function @xmath15 is analytic in @xmath77 and , due to ( [ rh ] ) , its square is continuous on @xmath27 .
hence @xmath78 is analytic in the whole @xmath58 .
furthermore , since @xmath79 we have that @xmath80 and liouville s theorem implies that @xmath78 is a polynomial of degree @xmath81 with @xmath82 .
therefore , we have @xmath83 where @xmath84 is a polynomial of degree @xmath85 .
reciprocally , given @xmath24 , if the function ( [ y ] ) is such that its square is a polynomial then it satisfies ( [ rh ] ) and consequently ( [ s3 ] ) .
equation ( [ c1b ] ) defines an algebraic curve referred to as a _
spectral curve _ , which determines the equilibrium charge density via ( [ y ] ) , @xmath86 where @xmath27 has the orientation inherited by the orientation of @xmath3 .
hermitian families of orthogonal polynomials correspond to @xmath51 and @xmath8 with real coefficients . in this hermitian case
it is clear that the real line @xmath51 is an @xmath0-curve , because taking @xmath57 as the principal branch of the logarithm we have @xmath87 hence ( [ s20 ] ) holds because @xmath88=0,\quad x\in \gamma\subset \mathbb{r}.\ ] ] there is a well stablished theory for characterizing the asymptotic distribution of zeros for hermitian orthogonal polynomials and the asymptotic distribution of eigenvalues for hermitian matrix models @xcite .
in particular , a method of analysis of the phase structure and critical processes for multicut hermitian matrix models was recently presented in @xcite .
in this section we discuss the theoretical background underlying the determination of @xmath0-curves . using proposition 1 ,
we begin by looking for spectral curves ( [ c1b ] ) where @xmath89 . obviously , the number @xmath90 of possible cuts for a fixed @xmath8 is at most @xmath91 .
we assume for simplicity that @xmath78 has only simple or double roots .
the simple roots will be denoted by @xmath92 and the double roots by @xmath93 .
the simple roots @xmath94 will be the endpoints of the cut @xmath66 , and therefore @xmath95 . to determine the branch of @xmath15 that verifies ( [ asy ] ) in the @xmath90-cut case , we write @xmath15 in the form @xmath96 @xmath97 and take the branch of @xmath98 such that @xmath99 the factor @xmath100 in ( [ y1 ] ) is then given by @xmath101 where @xmath102 stands for the sum of the nonnegative powers of the laurent series at infinity . hence the function @xmath15 is completely determined by its branch points @xmath92 , and satisfies @xmath103 our first task is to find a system of equations for the cut endpoints @xmath92 .
we use the theory of abelian differentials in riemann surfaces to find a system of equations satisfied by the cut endpoints ( see appendix a for definitions and notations ) .
let us denote by @xmath7 the hyperelliptic riemann surface associated to the curve @xmath104 we introduce the meromorphic differential @xmath105 in @xmath7 , where @xmath106 is the extension of the function ( [ y1 ] ) to the riemann surface @xmath7 in terms of two branches of @xmath106 in @xmath7 given by @xmath107 .
the asymptotic condition ( [ asy ] ) implies @xmath108 since the only poles of @xmath105 are at @xmath109 and @xmath110 , equation ( [ 1.4 ] ) shows that ( with @xmath111 ) @xmath112 is a first kind abelian differential in @xmath7 .
hence it admits a decomposition in the canonical basis @xmath113 for some complex coefficients @xmath114 .
thus , we may write @xmath115 let us now denote by @xmath66 a set of oriented cuts joining the pairs @xmath116 and @xmath117 of the function ( [ y1 ] ) , and by @xmath118 an arbitrary point in @xmath66 .
the @xmath119-periods of the differential @xmath105 can be written as @xmath120 since @xmath107 , we have that @xmath121 .
hence from ( [ y ] ) and ( [ s22 ] ) we get @xmath122 -2 \left[w(z_j)-\left(g(z_{j+})+g(z_{j-})\right)\right]\\ = 2 ( l_{j+1}-l_j ) = 2 \rmi ( m_{j+1}-m_j)\in \rmi\mathbb{r } .\end{aligned}\ ] ] as a consequence , the coefficients @xmath123 in ( [ idy ] ) are given by @xmath124 furthermore , from ( [ mes ] ) we find that the @xmath125-periods are @xmath126 and consequently ( [ idy ] ) implies @xmath127 since the matrix of periods @xmath128 is positive definite @xcite , the linear system ( [ fina ] ) uniquely determines the coefficients @xmath129 as functions of the cut endpoints @xmath130 and the coefficients @xmath131 of the potential @xmath8 .
therefore , we have the following method to find a system of equations for the cut endpoints : ( 1 ) : : we start with a function @xmath15 of the form ( [ y1])([y2 ] ) and use the identity @xmath132 to determine the double roots @xmath133 of @xmath78 in terms of the cut endpoints
. then we express the coefficients of the polynomial @xmath134 in terms of the cut endpoints and the coefficients of @xmath8 .
( 2 ) : : from ( [ y1])([ache ] ) it is clear that @xmath135 \\ & = \mathcal{o}\left(z^{n+s-1}\right),\quad z\rightarrow \infty .
\end{aligned}\ ] ] moreover , in order to satisfy ( [ sc2 ] ) , we impose that @xmath136 therefore , we equate to zero the coefficients of the powers @xmath137 and to -@xmath138 the coefficient of @xmath139 in ( [ sh1 ] ) .
thus we obtain @xmath140 equations for the @xmath141 cut endpoints .
( 3 ) : : finally , to obtain @xmath142 additional equations , we express the differentials @xmath143 and @xmath144 in terms of the cut endpoints and solve the system ( [ fina ] ) to determine the unknowns @xmath129 as functions of the cut endpoints and of the coefficients of @xmath8 .
then , in view of ( [ idy])([idy2 ] ) we impose @xmath145 there is an alternative and more intrinsic scheme for finding the cut endpoints using the expressions of the abelian differentials .
indeed , as a consequence of the identities ( [ nho ] ) , ( [ diff1 ] ) and ( [ diff10 ] ) of appendix a we have @xmath146 hence if we set @xmath147 in this identity we find @xmath148 in particular for the hermitian case ( see subsection 1.3 ) @xmath149 so that ( [ ce ] ) simplifies to @xmath150 which is the standard system used in hermitian random matrix models to determine the asymptotic eigenvalue support @xcite . in section [ subsec : twocutcase ]
we will illustrate for the usual cubic model how the new terms in the general equations ( [ ce ] ) are reduced ( via real parts and imaginary parts of periods of abelian differentials ) to the calculation of standard integrals , which in this particular case can be expressed in closed form in terms of elliptic functions .
once a solution of the endpoint equations has been obtained , the @xmath151-function ( [ y1 ] ) is completely determined .
the next step is to find the cuts @xmath66 connecting the respective pairs of cut endpoints @xmath94 and such that the @xmath24 defined by ( [ mes ] ) is a normalized positive density and the @xmath0-property on @xmath152 is satisfied . let us define the function @xmath153 from ( [ cm ] ) and ( [ y ] ) we have that the @xmath151-function must satisfy @xmath154 \\ & = u(z)-l , \quad z\in \mathbb{c}\setminus \gamma,\end{aligned}\ ] ] where @xmath155 is the electrostatic potential ( [ loge ] ) and @xmath31 is some real constant .
hence , in terms of @xmath156 the equilibrium condition ( [ cm ] ) reads @xmath157 note that different choices of the base point among the branch points @xmath116 in the integral ( [ g ] ) lead to conditions equivalent to ( [ cmp ] ) .
given a root @xmath158 of @xmath78 with multiplicity @xmath159 , there are @xmath160 maximal connected components ( excluding any zeros of @xmath78 ) of the level curve @xmath161 which stem from @xmath158 @xcite .
these maximal components are called the stokes lines outgoing from @xmath158 associated to the polynomial @xmath78 .
stokes lines for a polynomial can not make loops and end necessarily either at a different zero of @xmath15 ( lines of _ short _ type ) or at infinity ( lines of _ leg _ type ) .
therefore , the condition ( [ cmp ] ) means that the cuts @xmath66 must be short type lines with cut endpoints @xmath94 of the polynomial @xmath78 .
it should be noticed that the function @xmath15 is continuous on those short type lines which are not cuts . in what follows
we will denote by @xmath162 the set of all the stokes lines emerging from the simple roots @xmath94 of @xmath15 and by @xmath163 the set of all the stokes lines emerging from all the roots of @xmath78 .
the positivity of the corresponding density ( [ mes ] ) also imposes that @xmath164 however , the scheme of the above subsection implies @xmath165 so that ( [ norm ] ) holds .
therefore if ( [ cmp2 ] ) is verified on @xmath142 cuts and the total charge on these cuts is smaller than unity , then ( [ cmp2 ] ) is also verified on the remaining cut .
it is straightforward that if the cuts satisfy ( [ cmp ] ) and ( [ cmp2 ] ) then the @xmath0-property is verified on @xmath27 , and that we may characterize @xmath0-curves @xmath3 by imposing the following two additional conditions : ( s1 ) : : @xmath3 contains @xmath27 .
( s2 ) : : @xmath3 does not cross any region of the complex plane where @xmath166 . indeed , as a consequence of ( s1 ) the path @xmath3 verifies the @xmath0-property with respect to the external potential @xmath23 .
moreover , using ( [ idl ] ) we have that ( s2 ) implies the condition ( [ cm1 ] ) , so that @xmath24 is an equilibrium measure on @xmath3 . to implement condition ( s2 )
we need an explicit description of the set @xmath167 in the complex plane .
it is helpful to observe that points in the neighborhood of a cut satisfy @xmath166 , while the remaining connected lines of the level set @xmath168 separate regions where @xmath166 from regions where @xmath167 .
these properties can be proved as follows .
from ( [ g ] ) we have that the derivatives of @xmath169 with respect to the cartesian coordinates are @xmath170 then take for instance a point @xmath171 near to a point @xmath172 of a cut and to the left of the cut ( i.e. @xmath173 ) .
then since @xmath174 and using ( [ dg ] ) we have @xmath175 the same result is obtained for points
@xmath176 near to a point @xmath177 of a cut and to the right of the cut ( i.e. @xmath178 ) taking into account that @xmath179 .
the corresponding statement for the other connected lines verifying @xmath168 follows similarly using the continuity of @xmath15 on them .
equation ( [ dg ] ) also shows that if a stokes line @xmath180 emerging from one cut endpoint @xmath94 meets a zero @xmath181 of @xmath15 different from @xmath182 and @xmath183 both partial derivatives of the curve @xmath184 vanish at @xmath181 and therefore @xmath180 has a critical point at @xmath181 .
these situations arise in particular at phase transitions of equilibrium densities in which the number of cuts changes . in the one - cut case we will drop the general notation and denote the cut endpoints by @xmath185 and @xmath186 respectively .
the scheme of section [ sec : eqendpts ] to determine the cut endpoints reduces to identifying the coefficients of @xmath139 and @xmath187 in ( [ sh1 ] ) , where @xmath188 the resulting equations for @xmath189 and @xmath190 are often simpler when expressed in terms of @xmath191 moreover , in this case the function @xmath192 is given by @xmath193 to prove this identity we recall the form of the function @xmath194 and look for a decomposition @xmath195 where @xmath196 is a polynomial and @xmath180 a complex constant . differentiating this equation with respect to @xmath34 and multiplying by @xmath98
we get @xmath197 with @xmath198 hence @xmath199 and @xmath200 for a certain complex constant @xmath201 .
since @xmath196 is a polynomial , the logarithmic terms in @xmath202 must cancel , and taking into account that @xmath203 we get that @xmath204 and @xmath205 a simple illustration of the above method is provided by the gaussian model @xmath206 in this case only spectral curves with one cut may arise . moreover , @xmath207 and @xmath208 .
then ( [ c1b ] ) leads to @xmath209 if we take the cut @xmath27 as the interval @xmath210 $ ] then @xmath211 and @xmath27 satisfies the @xmath0-property .
figure [ fig : ga ] shows the stokes lines emerging from the cut endpoints of the gaussian model as well as the set @xmath212 where the cut may be continued into an @xmath0-curve .
a possible choice is @xmath51 .
then we may define @xmath57 as the principal branch of the logarithm and we have @xmath87 and the regions @xmath212 ( shadowed regions ) for the gaussian model.[fig : ga ] ]
we will now discuss the cubic model @xmath213 where @xmath20 is an arbitrary complex number . for @xmath214
the model has been rigorously studied by deao , huybrechs and kuijlaars @xcite .
recent results for @xmath215 have been communicated by lejon @xcite .
the phase structure of the corresponding random matrix model has been studied by david @xcite and mario @xcite . using the notation specific for the one - cut case introduced in section [ sec:1cut ] we have @xmath216 and ( [ sh1 ] ) and ( [ sh2 ] ) lead to the following system of equations for the cut endpoints : @xmath217 @xmath218 therefore @xmath219 satisfies the cubic equation @xmath220 and @xmath221
is determined by @xmath222 the cubic equation ( [ eq : beta ] ) defines a three - sheeted riemann surface @xmath223 of genus zero for @xmath219 as a function of @xmath20 .
the function @xmath224 is determined in terms of three branches @xmath225 where @xmath226{\frac{1}{2 } + \sqrt{\frac{1}{4 } - \left(\frac{t}{3}\right)^3}}\ ] ] and where the roots take their respective principal values .
there are three finite branch points @xmath227 at which @xmath228 , @xmath229 , and @xmath230 respectively . in the three separate plots of figure [ fig : rs ]
we show the real parts of the three branches of the riemann surface ( [ eq : beta ] ) . as an aid to guide the eye
, we also plot two paths on the surface .
the first path starts at the origin @xmath214 in @xmath231 ( i.e. , at @xmath232 ) and proceeds to the left without leaving this sheet .
the second path corresponds to @xmath233 ( larger than the modulus of the branch points @xmath234 ) : note that the path stays in the branch @xmath231 from the real axis @xmath235 to @xmath236 , proceeds to the @xmath237 branch from @xmath236 to @xmath238 , then to @xmath239 from @xmath240 to @xmath241 , and back to the branch @xmath231 form @xmath241 to the real axis @xmath242 .
.[fig : rs],width=566 ] of stokes lines calculated according to the branch @xmath231 starting at @xmath214 and proceeding along the negative @xmath20 axis ( path to the left in figure [ fig : rs ] ) .
the shaded areas are regions with @xmath167 .
[ fig : pathneg ] ] figure [ fig : pathneg ] shows the sets @xmath162 of all the stokes lines of the roots @xmath243 of the function @xmath78 corresponding to @xmath231 for negative real values of @xmath20 .
the path on @xmath231 starts at @xmath214 and proceeds along the negative @xmath20 axis ( the path to the left in figure [ fig : rs ] ) .
note the two simple zeros @xmath189 and @xmath190 , each one with three stokes lines stemming at equal angles of @xmath244 . in the two first plots , corresponding to @xmath214 and @xmath245 , we find a short connecting @xmath189 and @xmath190 , so that we get a cut satisfying the @xmath0-property .
however , for a critical value @xmath246 the double zero of @xmath78 meets this cut giving rise to a singular curve , and beyond that point there is no stokes line joining @xmath189 to @xmath190 .
this indicates that for @xmath247 the branch @xmath231 does not lead to a cut satisfying the @xmath0-property .
( this interpretation is in agreement with the main theorem in @xcite . ) in fact , we can find an analytic condition ( which , however , has to be solved numerically ) for the set of complex values of @xmath20 such that @xmath248 , where @xmath162 is the set of stokes lines of @xmath189 and @xmath190 . using ( [ ge ] ) we find that the @xmath249 functions corresponding to the branches @xmath250 are @xmath251 hence the condition for @xmath252 is @xmath253 where @xmath254 in figure [ fig : ph ] we show the curves in the complex @xmath20-plane determined by the solutions of ( [ eq : gabc ] ) , with colors matching those of the corresponding branches in figure [ fig : rs ] .
in addition each region has been identified with a number that will be used in our forthcoming discussion of the phase structure . ) for @xmath255 , with colors matching those of the respective branches in figure [ fig : rs ] .
the dashed lines are the cuts ( @xmath256 ) of the riemann surface ( [ eq : beta]).[fig : ph ] ] in the two - cut case we will denote @xmath257 , @xmath258 , @xmath259 , @xmath260 and @xmath261 .
now we have @xmath262 and ( [ sh1 ] ) , ( [ sh2 ] ) and ( [ periods ] ) lead the following system of equations for the four cut endpoints @xmath263 we recall that @xmath264 is given in terms of @xmath125-periods @xmath265 ( we drop the subindex , i.e. , @xmath266 ) by equation ( [ fina ] ) @xmath267 taking into account that ( [ eq : y2h1])([eq : y2h3 ] ) imply @xmath268 it follows that @xmath269 where @xmath270 , @xmath271 denote the integrals @xmath272 and @xmath273 it is clear that in general the system ( [ eq : y2h1])([eq : y2h4 ] ) must be solved numerically . but even so , it would be very difficult to attempt a direct numerical solution without a well identified initial approximation .
however , we can take advantage of our knowledge of the critical curves ( [ eq : gabc ] ) and the corresponding explicit solutions for the one - cut endpoints given by ( [ eq : betak ] ) , and proceed iteratively by small increments in @xmath20 using as initial approximation at each step the results of the previous one .
once the cut endpoints @xmath189 , @xmath190 , @xmath180 and @xmath274 for a certain value of @xmath20 have been calculated , the corresponding stokes lines are also calculated numerically .
figures [ fig:1 - 10 ] and [ fig:1 - 9 ] show the sets @xmath275 of all the stokes lines stemming from the simple roots @xmath189 , @xmath190 , @xmath180 and @xmath274 for values of @xmath20 crossing critical lines of figure [ fig : ph ] . in figure
[ fig:1 - 10 ] we proceed along the negative @xmath20 axis beyond the critical value @xmath246 ( i.e. , to the part of the path corresponding to @xmath276 in the first graph of figure [ fig : rs ] ) and we find a `` splitting of a cut '' at the crossing from region 1 to region 9 in figure [ fig : ph ] , in agreement with the theoretical result of @xcite . in figure
[ fig:1 - 9 ] we have crossed vertically from region 8 into region 9 , and find a process of `` birth of a cut at a distance '' with cut endpoints @xmath180 and @xmath274 ; the graph corresponding to @xmath277 , not shown in the figure , is precisely the last graph in figure [ fig:1 - 10 ] ; and as we proceed further down from region 9 to region 10 we find the symmetric `` death of a cut at a distance '' with cut endpoints @xmath189 and @xmath190 . in the next section these interpretations are confirmed by numerical calculations of zeros of orthogonal polynomials . ] ] as we discussed in section [ sec : eds ] , to determine the asymptotic zero distribution of a given family of orthogonal polynomials ( [ pol1 ] ) on a path @xmath3 , we must find an @xmath0-curve in the same homology class as @xmath3 and connecting the same pair of convergence sectors at infinity .
then the desired zero counting measure is the equilibrium measure on the @xmath0-curve . ]
the cubic exponential weight @xmath278 decays in three sectors @xmath279 of opening @xmath280 of the complex @xmath34 plane centered around the rays @xmath281 , @xmath255 .
let us denote by @xmath282 @xmath283 simple paths with asymptotic directions @xmath284 and @xmath123 as indicated in figure [ fig:3n ] and , for concreteness , consider the problem of determining @xmath0-curves @xmath3 in the same homology class and with the same asymptotic directions of @xmath285 .
the graph corresponding to @xmath214 in figure [ fig : pathneg ] shows that the cut @xmath286 can be prolonged both upwards and downwards into the shaded regions which contain the asymptotic directions @xmath287 and @xmath288 respectively , and therefore into a full @xmath0-curve homologous to @xmath285 .
this is no longer true for @xmath247 , as the graph corresponding to @xmath289 in figure [ fig : pathneg ] shows : in fact , the cut @xmath286 has disappeared .
however , the graph for @xmath289 in figure [ fig:1 - 10 ] features the two cuts @xmath286 and @xmath290 , which can be prolonged into the same sectors via the shaded region in the right part of the figure .
therefore , for this value of @xmath20 we have a full two - cut @xmath0-curve .
this type of analysis which combines the theoretical results of section [ sec : ced ] with numerical calculations show that in the case of @xmath285 the branches @xmath291 , @xmath292 and @xmath293 can be used to generate a one - cut @xmath0-curve for the cubic model when @xmath20 is in the regions 1 to 7 , 8 and 10 of figure [ fig : ph ] , respectively . for @xmath285
the encircled region 9 represents the two - cut region .
similar ( symmetric ) situations arise for the cases of @xmath294 and @xmath295 , for which the two - cut regions are the encircled regions 3 and 6 respectively . as a check of the consistency of these results with theorem 1 , in figures [ fig : zd1 ] , [ fig : zd2 ] and [ fig : zd3 ] we superimpose to the graphs of figures [ fig : pathneg ] , [ fig:1 - 10 ] and [ fig:1 - 9 ] the zeros of the corresponding polynomials @xmath21 with degree @xmath22 , which we have generated by recurrence formulas to minimize numerical errors . in figures [ fig : zd1 ] and [ fig : zd2 ] , which exemplify the splitting of a cut , as @xmath20 decreases along the negative real axis and due to the symmetry of the situation , the 24 zeros split evenly into the two sets of 12 zeros following closely the positions of the cuts that correspond to the limit @xmath296 . in figure [ fig : zd3 ] , which exemplifies the birth and death of a cut at a distance , what we find numerically as the value of @xmath20 descends vertically from @xmath297 to @xmath298 is that all the 24 zeros lie initially on the lower cut @xmath286 , and start travelling upwards one by one , thus populating the upper cut @xmath290 and depopulating the lower @xmath286 .
this behavior is particularly clear in the second graph ( corresponding to @xmath299 ) , in which the fourth zero is `` arriving '' at the upper cut , and in the symmetric graph ( corresponding to @xmath300 ) , in which the 21st zero is `` leaving '' the lower cut . superimposed to the splitting of a cut in figure [ fig : pathneg].[fig : zd1 ] ] superimposed to the splitting of a cut in figure [ fig:1 - 10].[fig : zd2 ] ] superimposed to the birth and death of a cut at a distance in figure [ fig:1 - 9].[fig : zd3 ] ] a phase diagram for the cubic random matrix model with a two - cut region with the same shape as region 3 in figure [ fig : ph ] was presented in @xcite .
it is also worth noticing that in terms of the variable @xmath301 the curve ( [ eq : gabc ] ) looks quite similar to the genus 0 _ breaking curve _ found in @xcite for the family of orthogonal polynomials associated to the quartic potential @xmath302 however , the curve in @xcite is only symmetric with respect the real @xmath303-axis , while the curve for the cubic model is symmetric with respect both real and imaginary axes .
another important difference between the curve for the cubic model and that for the quartic model is that for this later there exist genus 0 and genus 1 _ breaking curves _ ( see figure 4 in @xcite ) , although implicit equations for genus 1 curves are provided only for the symmetric case @xcite .
a generalization of the @xmath0-property ( [ s20 ] ) arises in the study of dualities between supersymmetric gauge theories and string models on local calabi - yau manifolds @xmath304 of the form @xcite @xmath305 where @xmath8 and @xmath13 are polynomials such that @xmath306 .
the manifold @xmath304 can be regarded as a fibration of two - dimensional complex spheres on the spectral curve @xmath307 .
most of the string model information encoded in @xmath304 can be described in terms of the spectral curve , and its associated complex density ( [ mes ] ) .
these spectral curves satisfy the condition ( [ s20 ] ) for the @xmath0-property , but they do not determine an equilibrium density since ( [ mes ] ) provides in general a complex density . as a consequence the complex electrostatic potential is locally constant on the support of @xmath24 @xmath308 but the real parts of the constants @xmath70 are , in general , different . in this case
the cut endpoints are determined by ( [ sh1 ] ) , ( [ sh2 ] ) and , instead of ( [ periods ] ) , by the constraints @xmath309 where @xmath24 is the complex density ( [ mes ] ) and @xmath310 are a given set of nonzero complex values ( t hooft parameters ) .
finally , instead of the single quadratic differential @xmath311 , in this case @xmath90 in general different quadratic differentials @xmath312 are required to determine the cuts @xmath66 as stokes lines @xmath313 we believe that these more general spectral curves can be characterized and classified using an analysis similar to that of the present paper .
we thank prof . a. martnez finkelshtein for useful conversations and for calling our attention to the work @xcite .
the financial support of the ministerio de ciencia e innovacin under projects fis2008 - 00200 and fis2011 - 22566 is gratefully acknowledged .
in this appendix we briefly discuss the elements of the theory of abelian differentials in riemann surfaces that we use in section [ sec : eqendpts ] .
let us denote by @xmath7 the hyperelliptic riemann surface associated to the curve ( [ 1.1 ] ) .
the two branches @xmath314 and @xmath315 characterize @xmath7 as a double - sheeted covering of the extended complex plane : @xmath316 the homology basis @xmath317 of cycles in @xmath7 is defined as shown in figure [ fig : hb ] , and the corresponding periods of a differential @xmath318 in @xmath7 will be denoted by @xmath319 ] we introduce the following abelian differentials in @xmath7 : ( 1 ) : : the canonical basis of first kind ( i.e. , holomorphic ) abelian differentials @xmath320 with the normalization @xmath321 .
these differentials can be written as @xmath322 where the @xmath323 are polynomials of degree not greater than @xmath324 uniquely determined by the normalization conditions .
( 2 ) : : the second kind abelian differentials @xmath325 @xmath326 whose only poles are at @xmath109 , such that @xmath327 and normalization @xmath328 @xmath329 .
it is easy to see that @xmath330 where the @xmath331 are polynomials of the form @xmath332 and the coefficients @xmath333 are uniquely determined by the normalization conditions .
( 3 ) : : the third kind abelian differential @xmath334 whose only poles are at @xmath109 and @xmath110 , such that @xmath335 and normalization @xmath336 for all @xmath337 .
it follows that @xmath338 where @xmath339 is a polynomial of the form @xmath340 and the coefficients @xmath341 are uniquely determined by the normalization conditions . for instance , in the one - cut case ( @xmath342 )
we have @xmath343 and the first three polynomials are @xmath344
10 url # 1#1urlprefix[2][]#2 stahl h 1985 _ complex variables theory appl . _ * 4 * 311 | arxiv |
One of the biggest names in the medical cannabis sector seems poised to enter the United States market soon.
The British company GW Pharma, known for its marijuana-derived drug Epidiolex, reportedly could get approval for the drug from the US Food and Drug Administration (FDA) in early 2016.
Epidiolex contains the medical cannabis substance cannabidiol (CBD) and is primarily used to treat epilepsy. Currently, the drug has a fast-track status from the FDA. It is also in its final Phase 3 study for the treatment of pediatric epilepsy disorders, and results are expected in the first quarter of 2016, reported the Huffington Post.
Writing for the publication, medical cannabis advocate Alice O'Leary Randall said that Epidiolex is anticipated to "breeze through this final stage". If it does, it could be on the US market in the first half of next year.
Because Epidiolex is a marijuana product, shipping it from the UK would be highly complicated, especially in the face of US federal regulations. GW Pharmaceuticals will likely need to invest in infrastructure in order to grow cannabis within the US, and then manufacture the drug in the states where it wants to sell it. | slim_pajama |
U.S. Supreme Court Justice Anthony Kennedy To Host T.V. Show On The Mystery Channel
Entertainment News Syndicate-
The Mystery Channel, the newest entry into an already crowded field of cable television stations, debuted last week…to general critical acclaim.
The nascent network's most anticipated show is titled, "Anthony Kennedy's Divining Rod," and features the Chief Justice Himself trying to find various people, things- and even concepts- that have famously gone lost or missing over time. The pilot airs tomorrow night, Tuesday, October 13th at 8 p.m. E.S.T.
The new network's president stated, "We feel that if he could find the absolute right to gay marriage in the Constitution, that he should have a real chance of putting an end to some of the most mysterious disappearances that have plagued and intrigued humanity over the millennia."
The Mystery Channel has 12 episodes (13 weeks) currently "in the can" for season one, with the following schedule synopsis:
Pilot (Ep. 1; "Elvis, Is That You?")- Anthony, or "K.K." (King Kennedy), as he's often referred to in the show, attempts to track down Elvis Presley.
Ep. 2; "It's Plane To See"- In this thrilling episode, K.K. will do his best to locate the remains of Malaysian Flight 370!
Ep. 3; "Re-Union"- K.K. seeks Jimmy Hoffa.
Ep. 4; "She Flew The Coop"- Just back from his previous expedition, Justice Kennedy is on the hunt for Amelia Earhart.
Ep. 5; "Exit, Stage Left"- The Chief takes on his most challenging task to date: locating the Democratic Party of Harry Truman and JFK.
Ep. 6; "And It Used To Have A Soul, Too"- Our favorite man in black goes in search of the Republican Party's spine.
Ep. 7; "Didn't You Use To Be America?"- Tony tries to track down limited government of, by and for…the people.
Ep. 8; "She-mails"- Chief Justice Anthony Kennedy is his name and crime is his game. This time he tries to hunt down the missing Hillary Clinton State Department e-mails. Two-part episode.
Ep. 9; "Two If By Sea?"- K.K.'s off to find the Ark of the Covenant.
Ep. 10; "Is it not U.S.?"- The robed-wonder tries to conjure up the Lost City of Atlantis.
Ep. 11; "Is There An App For That?"- K.K. frantically looks for Bristol Palin's virginity!
Ep. 12; "Umm, Like, Whatever Dude?!"- In the breathtaking first-season finale', the Chosen One is off in search of…intelligent life on Earth.
Cecil And Samson
The New Evil Empire
The United States Declares Its Independence From T...
Satanic Statue Unveiled In Detroit
U.S. Declaring Independence From Thomas Jefferson
President Barack Obama And "The Only Options"
Planned Parenthood Newsletter (Parody)
Intolerant Insanity (Or P.C. B.S.)
President Obama, What Was Your Half-Mast Excuse?
Bill Cosby And The Presidential Medal Of Freedom
Stone Mountain And The Repeal Of History
Nuclear Accord With Iran
Pope Francis And The Communist Crucifix
Near-Future Headlines
Conservative Restraint, Liberal Attack
Fifty Shades Of...Shabani?
U.S. Supreme Court Justice Anthony Kennedy To Host...
The U.S. Supreme Court Redefines Lightning
Taking Charge Of America On A LARC!
Monuments To Freedom? (Obamacare, Marriage Equalit...
Fourth Of July Symbolism And Substance
United States Capital To Change Name?
The Obergefell Decision And The U.S. Extreme Court
An Urgenda Agenda
A King's Ransom | slim_pajama |
in the last years , the extended hubbard model ( ehm ) was introduced to explain some interesting phenomena including metal - insulator transition mott1,mott2,mott3,mott4,mott5 , antiferromagnetism sanna , nie , antif3,antij , and high-@xmath6 superconductivity mc , supra2,halb .
this ehm is a standard simple model of interacting itinerant electrons in a solid @xcite .
although this model is too idealized to be regarded as a quantitatively reliable model of real solids , it contains physically essential features of interacting itinerant electron systems . despite being one of the most studied models to describe strongly correlated electrons system , many questions concerning the hubbard model remain as open problems .
in applied , we have applied the self consistent random phase approximation ( scrpa ) @xcite to solve the ehm in @xmath7 , where , we have shown that this approach treat the correlations of closed chains with a rigours manner .
the behaviour of our scrpa ground state and gap energies shows that the repulsive off - site interaction between the electrons of the neighbouring atoms induces supplementary conductivity , since , the scrpa energy gap vanishes when the closed chains of the ehm are governed by a strong repulsive on - site and an intermediate repulsive off - site interactions .
but , due to the restricted motion along one direction in space , the hubbard model chain does nt exhibit any ferromagnetic feature .
thus , the @xmath7 hubbard is a nice prototype to describe , only , the @xmath7 classical conductors .
stimulated by the discovery of high-@xmath6 superconductivity in the cuprate plans , the @xmath8 hubbard model have attracted a great attention in the recent two decades @xcite . in spite of its simple description in square lattice ,
it is not obvious to solve the 2d hubbard model in the general case .
the exact solution of @xmath8 hubbard model is not still reached , but , a great variety of approximate treatments have been proposed @xcite . very recently , e. kovacs et al .
@xcite proposed an exact solution of the usual hubbard model for @xmath9 cluster with low concentration , where each cluster presents four electrons .
the dynamics of these electrons is described by the usual kinetic of electrons with hopping energy @xmath10 and the repulsive on - site interaction between electrons in the same site with interaction energy @xmath0 . in the present paper , we purpose to apply this method to an extended hubbard model which takes into account the off - site interaction with an interaction energy @xmath1 this paper is organized as follows . in sec.2 , we present the model and the calculation procedure which allows us to construct the hamiltonian matrix of dimension @xmath5 . in sec.3 , we present our results for ground state and gap energies and discuss the effect of the off - site interaction on the dynamics of system . finally , in sec.4 we give our conclusions .
the two - dimensional extended hubbard model on a square lattice is given by:@xmath11 where @xmath12 ( @xmath13 ) are the creation ( annihilation ) operators for a fermion of spin @xmath14 at site @xmath15 ( @xmath16 ) with periodic boundary conditions .
thus , @xmath10 is the hopping term from the site @xmath16 to the site @xmath15 , where @xmath17 sums over nearest neighbour sites .
the second term describes the local repulsive interaction with parameter @xmath0 .
the last term takes into account the nearest - neighbour repulsion between electrons with energy @xmath1 .
the resolution of the model ( @xmath18 ) in case of finite size system , gives the exact solution of some physical quantities as the ground state energy , the energy gap and the occupation numbers .
we consider , thus , a two dimensional @xmath19 square lattice at one - eighth filling ( four electrons per cluster ) , with periodic boundary conditions in both directions .
for this considered system , three types of particle configurations may occur .
first , we can have two double occupancies at sites @xmath15 and @xmath16 ( @xmath20 ) .
second , we may have a double occupancy at site @xmath15 and two electrons with opposite spins at sites @xmath16 and @xmath21 ( @xmath20 , @xmath22 and @xmath23 ) . finally , we may have four single occupancies placed on different sites of this @xmath24 square lattice .
these three possible configurations provide , respectively , the three states : @xmath25 @xmath26 @xmath27 where @xmath28 represents the state vacuum with no electron present .
the states @xmath29 , @xmath30 and @xmath31 generate @xmath32 states , which describe all possible distributions of our four electrons in the @xmath2 cluster . in order to construct a @xmath3 basis , it is convient to define a linear operator @xmath33 @xcite , which verifies the relation : @xmath34 where @xmath35 and @xmath36 represent the particle configurations as mentioned in fig . 1 , @xmath37 is the linear combination of the @xmath38 contributions obtained by the translation of the configuration @xmath35 to each site of the @xmath2 cluster .
using this linear operator and taking into account the symmetry proprieties of the @xmath2 cluster in @xmath3 representation , we can regroup these @xmath39 states in @xmath4 cluster states denoted by @xmath40 , where @xmath41 , and are all orthogonal vectors .
for example , @xmath42 is the linear combination of all states @xmath29 with @xmath43 , where @xmath44 ( @xmath45 ) is the lattice position of the site @xmath15 ( @xmath16 ) and @xmath46 is the square lattice parameter .
@xmath47 is the linear combination of all states @xmath30 with @xmath48 and @xmath49 . whereas @xmath50 is ,
also , the linear combination of all states @xmath30 with @xmath51 but @xmath52 ( for the definition of the other 82 vectors , see ref .
@xcite ) .
the application of the hamiltonian @xmath53 on the basis vector @xmath54 gives : @xmath55 it is clear that the hamiltonian would not be diagonal in our @xmath3 basis , since the application of the kinetic term @xmath56 on a vector @xmath57 gives , always , the new states @xmath58 after the creation and the annihilation of electrons in the different lattice sites .
thus , it is necessary to define the matrix energy @xmath59 as : @xmath60 where @xmath40 and @xmath61 are two vectors of the @xmath3 basis . in order to study the local properties of the @xmath2 square lattice ,
it is appropriate to determine , numerically , the eigenvalues and the eigenvectors of the matrix energy @xmath59 .
we consider the obtained first and second minimums of the eigenvalues as , respectively , the ground state and the first excited energies .
first , we disregarded the off - site interaction , and we have plotted in fig.2 and fig.3 the ground state and the first excited state energies , respectively , as function of the on - site interaction energy @xmath0 .
the corresponding curves of this case @xmath62 show that the ground state energy has smooth ( less than linear ) @xmath0 dependence , whereas the first excited state energy is @xmath0 independent and fixed at @xmath63 for any value of @xmath0 .
thus , it is clear that the first excited state is an eigenvector of the kinetic energy @xmath64 , since this excited state avoid totally the double occupancy . whereas , the ground state is not eigenstate of the kinetic energy or the on - site interacting part of @xmath65 only , but is eigenvector for the sum of both .
thus , at the ground state , the dynamics of the electrons system is governed by a competition between the habitual kinetic and the on - site interaction .
then , we have taken into account the off - site interaction @xmath66 and we have plotted in in the same previous figures ( fig.2 and fig.3 ) the ground state and the first excited state energies , respectively , as function of the on - site interaction energy @xmath0 for two values of @xmath67 . the fig .
2 shows that the energy @xmath68 has a smooth @xmath0 dependence and a linear @xmath1 dependence .
this behaviour is similar to the one obtained for the ground state energy of the chains extended hubbard model with the self consistent random phase approximation ( scrpa ) @xcite , where we have also , defined the matrix energy but in the basis of vectors impulsion - space ( @xmath69 ) and not in @xmath3 representation .
the curves of fig . 2 show , also , that @xmath68 decreases with @xmath1 for a fixed value of @xmath0 .
thus , we can conclude that this off - site interaction imposes the electron system to avoid partially the double occupancy in this ground state .
3 shows that the first exited state energy becomes @xmath0 dependent for @xmath70 .
thus , the off - site interaction encourages the existence of the double occupancies in this exited state . for a weak off - site interaction ( @xmath71 )
, the corresponding curve shows that @xmath72 becomes @xmath0 independent for the high values of @xmath0 .
but for an intermediate off - site interaction ( @xmath73 ) , @xmath72 still remains dependent @xmath0 ; since , we have the opportunity to have the double occupancies even for high values of @xmath0 . in order to analyze the on - site and off - site interactions effects on the repartition of our four electrons in the above system
, we define the double occupancy coefficient in the first exited state @xmath74 as the probability to have a couple of electrons @xmath75 on the same site in this exited state , @xmath76 where the sum over all @xmath2 cluster sites and the mean values @xmath77 are taken in the corresponding eigenvector to @xmath72 .
the double occupancy coefficient @xmath74 in the first exited state is shown in fig.4 as function of @xmath78 for different values of @xmath67 .
for @xmath79 , we have @xmath80 .
thus , effectively , our system avoids completely the double occupancy at this exited state .
but , after taking into account the off - site interaction , we have @xmath81 . for @xmath73 , we have @xmath81 even for the strong values of @xmath78 .
but , for @xmath82 , the coefficient @xmath74 vanishes for the strong value of @xmath78 , where the off - site interaction becomes very weak before the on - site interaction .
thus , the behaviour of our system in this regime ( @xmath83 ) is similar to the one found in ref .
@xcite . where the authors have shown that @xmath84 of the excited states of the @xmath2 cluster are @xmath0 independent .
but , it is clear that the number of this @xmath0 independent exited states decreases if we take into account the off - site interaction , since this interaction encourage the formation of the double occupancies in the exited states .
finally , in order to analyze the effect of the off - site interaction on the dynamics of electrons , we define the energy gap @xmath85 as the difference between the first excited state energy @xmath72 and the ground state energy @xmath68 @xmath86 in fig . 5
, we plot the variation of this energy gap @xmath85 as function of the repulsive on - site interaction energy @xmath0 for different values of the off - site interaction energy @xmath1 . for a fixed value of @xmath67
, the energy gap decreases with @xmath0 .
we deduce that the repulsive on - site interaction ( @xmath87 ) increases the conductivity of the system , since the repulsion between the two electrons of the same site encourages every electron to jump to the neighbouring site .
moreover , this curves show that the off- site interaction increases also the conductivity of this @xmath2 cluster . for a weak off - site interaction ( @xmath88 ) ,
the effect of @xmath1 is remarkable only for the weak on - site interaction whereas it becomes practically non - existent for strong on - site interaction .
but , for an intermediate off - site interaction ( @xmath73 ) , the effect remains remarkable even for the strong values of @xmath78 .
thus , we can conclude that with a strong on - site and an intermediate off - site interactions , our @xmath2 cluster have an important conductivity .
in this paper , an exact diagonalization in the @xmath3 was proposed to solve the two dimensional extended hubbard model for finite size system . in particular , we have considered a two dimensional @xmath19 square lattice at one - eighth filling with respecting the periodic boundary conditions in both directions . first , the numeric diagonalization of our hamiltonian matrix allow us to determine some interesting local properties of our @xmath2 square lattice as : the ground state energy @xmath89 , the first excited state energy @xmath72 , the gap energie @xmath85 and the double occupation number per site @xmath74 .
then , the analysis of the behaviours of these obtained local properties as function of @xmath0 and @xmath1 allows as to study the distribution and the dynamics of the elctrons system in two interesting states : ground and first exited states .
thus , we have found that our system has always the double occupancies in the ground state for any value of @xmath0 and @xmath1 . in the first exited state
, we have shown that the off - site site interaction encourages the electrons system to form the double occupancies , where the coefficient @xmath74 vanishes for @xmath90 .
whereas , for an intermediate off - site interaction , we found that we have always the probability to have these double occupancies .
but , this probability vanishes for strong on - site and weak off - site interactions , where , the electrons system avoids completely the double occupancy .
thus , the behaviour of our system in this regime ( @xmath91 ) is similar to the one found in ref .
finally , the analysis of the off - site interaction effect on the energy gap shows that the repulsive off - site interaction induces supplementary conductivity of the system , where , this effect of @xmath1 is more remarkable for an intermediate off - site interaction , since we have a reduction of order @xmath92 in this regime . | arxiv |
What's the Propagator in the Free Particle Case? (Path Integrals with Source Term)
If I take the Lagrangian to be,
$$L(t)=\frac{1}{2}m \dot q(t)^2$$
The Euclidean Path Integral is supposed to be,
$$K=\int D[q(t)] \ e^{-\int L(\dot q) d \tau}$$
If I add a source term $J(\tau)$ we obtain,
$$K[J]=\int D[q(t)] \ e^{-\int L(\dot q) -J(\tau) \cdot q(\tau) d\tau}$$
All the books say that the integral is equal to,
$$K[J]=e^{\int \int \ J(\tau) G(\tau,\tau') J(\tau') \ d\tau d\tau'}$$
Where $G(\tau,\tau')$ is the propagator, Green's Function, for the Lagrangian. However, I can't figure out a sensible propagator here. If I plug the Lagrangian into the Euler-Lagrange formula, and add the inhomogeneous term, I get,
$$\frac{m}{2} \partial\_t^2 G(\tau-\tau')=\delta(\tau-\tau')$$
Which seems reasonable. However, I wish to calculate $\langle \int q(t)^2 \rangle$, so I need to be able to take the second variational derivative, with respect to $J$. This yields, according to some version of Wick's Theorem,
$$\int d\tau \left( \cfrac{\delta}{\delta J} \right)^2 K[J]=\left \langle \int q(t)^2 \right \rangle=\int 2 \cdot G(\tau-\tau) \ d \tau$$
However, $G(0)$ could be anything, according to the differential for the Green's Function. How do I generally pick boundary conditions for the Green's Function so I can get proper results? I want to be able to try this later with $L(t)=\frac{1}{2}m \dot q(t)^2+\lambda \cdot q(t)$ and after that with a quadratic. So hopefully, the answer can help guide me towards getting correct answers.
For the bounty: I want to see the derivation for the integral with a source term. I also want to see an example of taking the second functional derivative of this derived functional integral.
Jean Zinn-Justin has a [great way](https://global.oup.com/academic/product/phase-transitions-and-renormalization-group-9780199665167?cc=us&lang=en&) of teaching path integral techniques starting with finite dimensional random variables (sometimes called "0-dimensional fields"). Here, you should think of these as discrete lattice approximations to continuous fields. In the spirit of Zinn-Justin's approach, I'll describe how this is done for the 1D free particle system you describe above.
Assuming that $q(t)$ vanishes in the infinite past and infinite future, your Lagrangian $L[q]=\int dt\frac{1}{2}m\dot q^2(t)$ can be rewritten as $\int dt\big[-\frac{1}{2}m q \ddot q\big]$, using integration by parts. In this notation, you can think of this as a bilinear $\int dt\big[\frac{1}{2}mq(t)(-\partial\_t^2)q(t)\big]=\frac{1}{2}m\langle q,-\partial\_t^2q\rangle=\frac{1}{2}q^T A q$. The last expression uses notation from finite dimensional linear algebra in order to temporarily demystify some of the steps. Here, $A$ is thought of as some sort of matrix realization of the linear operator $-m\partial\_t^2$. We can also assume that $A=A^T$.
The way to derive the explicit expression for the generating functional $Z[J]$ is by *completing the square* in the path integral, performing a linear change of variables. To do this, we need to use some notion of the *inverse* of $A$:
\begin{align\*}
\int \mathcal D q \exp\bigg[-\frac{1}{2}q^TAq - J\cdot q\bigg]=&\int\mathcal D q\exp\bigg[-\frac{1}{2}(q+A^{-1}J)^TA(q+A^{-1}J)+\frac{1}{2}J^TA^{-1}J\bigg]\\
=&\int\mathcal Dq\exp\bigg[-\frac{1}{2}q^T A q\bigg]\exp\bigg[\frac{1}{2}J^TA^{-1}J\bigg]\\
=& Z\_0\exp\bigg[\frac{1}{2}J^TA^{-1}J^T\bigg].
\end{align\*}
To complete the derivation, we need to solve (and pick a convention) for $A^{-1}$, which is called the Green function. This is tricky in general, because of the existence of harmonic functions $f$ that satisfy $Af=0$ (i.e. $A=-m\partial\_t^2$ has a non-trivial kernel, consisting of constant functions and a drift term). Physically, you can interpret these harmonic functions more generally as radiation from sources located in the distant past (or less physically, in the far future), and they lead to the distinction between advanced and retarded Green functions. In general, it is conventional to choose the harmonic part of the Green function so that boundary conditions are easily satisfied with linearly independent combinations of the Green function. For example, the retarded Green function is determined by the causality condition that it should vanish in the distant past.
Naturally, the space of allowed $J$'s is restricted to the domain on which $A^{-1}$ makes sense. In practice, the $J$'s satisfy conservation laws, and must decay sufficiently quickly at the boundaries.
At a purely formal level, computing functional derivatives with respect to $J$ of $Z[J]$ is exactly analogous to computing partial derivatives with respect to $\vec J$ of some discrete finite dimensional approximation to the partition function: in economical finite dimensional notation, $\frac{1}{Z\_0}\frac{\delta^2}{\delta J\_1 \delta J\_2}Z[ J]\Big|\_{J=0}:= \frac{\delta^2}{\delta J\_1 \delta J\_2}\exp\Big[\frac{1}{2}J\_i A\_{ij}^{-1}J\_j\Big]\Big|\_{J=0}=\frac{\delta}{\delta J\_1}\frac{1}{2}(J\_iA\_{i2}^{-1}+A\_{2i}^{-1}J\_i)\exp(\frac{1}{2}J\_iA\_{ij}^{-1}J\_j)\Big|\_{J=0}=\frac{1}{2}(A\_{12}^{-1}+A\_{21}^{-1})\exp(\frac{1}{2}J\_iA\_{ij}J\_j)\Big|\_{J=0}+\mathcal O (J^2)\Big|\_{J=0}=A\_{12}^{-1}=:G(\tau\_1,\tau\_2)$.
The Green function can be viewed as an elementary solution to the inhomogeneous version of a linear differential equation. The 2-point correlation function in your example happens to be a Green function for the 1D diffusion equation, but there is a certain amount of freedom in deciding on the Green function depending on the number of independent harmonic modes. Even the correlation function depends on how the space of fields that is integrated over is defined. One common way to choose a Green function is to impose vanishing boundary conditions. For Brownian motion, the choice of boundary conditions can be interpreted as a choice of reference frame.
Now for an explicit example. Consider a fluctuating elastic 'string' with $q(0)=q(L)=0$. To find the correlation function, we first choose an appropriate basis for describing fluctuations: here, we can expand configurations $q(s)$ in Fourier modes $S\_n(s)=\sqrt{\frac{2}{L}}\sin(\frac{n\pi s}{L})$, where $n\in\mathbb N$. In this basis, the operator $-\partial\_s^2$ acts as $-\partial\_s^2 S\_n(s)=\left(\frac{n\pi}{L}\right)^2S\_n(s)$. Hence, it can be inverted by defining $(-\partial\_s^2)^{-1} S\_n(s)=\frac{L^2}{\pi^2n^2}S\_n(s)$, extending by linearity. To find the integral kernel representation of $(-\partial\_s^2)^{-1}$ in position space, we need to evaluate
\begin{align\*}
\sum\_{n\geq 1} \frac{L^2}{\pi^2n^2}S\_n(s')S\_n(s)=-\frac{L}{\pi^2}\sum\_{n\geq 1} \frac{1}{n^2}\bigg[\cos(\frac{\pi n}{L}(s+s'))-\cos(\frac{\pi n}{L}(s-s'))\bigg]
\end{align\*}
In the limit of large $L$, the sum over $n$ can be replaced by an integral over $\omega\equiv\frac{\pi n}{L}$:
\begin{align\*}
G(s,s')= -\int\_{\frac{\pi}{L}}^\infty\frac{d\omega}{\pi}\frac{1}{\omega^2}\bigg[\cos(\omega(s+s'))-\cos(\omega(s-s'))\bigg]
\end{align\*}
This integral can be performed in general by taking appropriate limits of sums of contour integrals (where the sum of integrands, restricted to the real line, must approach the original function $\frac{1-\cos(x)}{x^2}$). Here, a valid sequence of approximations is
\begin{align\*}
G\_\epsilon(s,s')=-\int\_{-\infty}^\infty \frac{d\omega}{2\pi}\frac{1}{\omega^2+\epsilon}\bigg[\cos(\omega(s+s'))-\cos(\omega(s-s'))\bigg],\quad \epsilon\rightarrow 0^+.
\end{align\*}
To perform the contour integrals, the above function can be broken into positive and negative frequency parts, which have poles at $\omega=\pm i\epsilon$. The result of the limiting integration when $s \geq s'$ is $G(s,s')=s'$, or in general $G(s,s')=\min(s,s')$ from the symmetry between $s$ and $s'$ in this case (and also since $s$ and $s'$ are positive). [Note that this result is valid in the limit as $L$ approaches infinity. Near the opposite boundary, a similar formula for $G(s,s')$ holds, except with $s\mapsto L-s$.]
| stackexchange/physics |
Is it possible for the remaining solute of a saturated solution to form a single even phase from top to bottom (similar to that of a colloid)?
If a solute that dissolves in a liquid solvent has reached high enough levels to cause saturation within the solution, is it possible for the remaining solute particles to form an evenly distributed phase from top to bottom similar to that of a colloid (where **settling** would not occur or take very long to occur)? I realize behavior varies depending on the solute and solvent in question, I am just curious if this is possible. Thanks so much!
The density of the solute relative to that of the solvent will primarily determine whether the excess solute will float, sink or tend to disperse throughout the solution. Additionally, the particle size and porosity will play a role in the *rate* of settling or floating, as will the viscosity of the solvent, but it is the density that determines whether the particles will float or sink.
But, the answer to your question is no. Even if the density of the undissolved solute is essentially the same as that of the solvent, and the undissolved solute is very fine, then you could have a uniform *looking* solution, but it would still be a two-phase solution, with a solid phase suspended in a liquid phase.
| stackexchange/chemistry |
Sun, Sea & Trails!
Poldhu 10k Summer Sessions beach race
Two ORCs, Jo Page and Jeremy Tandy, made the trip to Poldhu Cove, Cornwall, on Thursday 11th July for the third instalment of Freedom Racing's Summer Sessions 10k races. Hot, sunny weather gave way to a muggy evening and eventual drizzle – but that didn't dampen anyone's spirits! Setting off north from Poldhu Cove, the route headed up and over the headland to Church Cove and onward along the "undulating" coastal path through Gunwalloe before turning back and making the runners climb all those hills again. Fortunately, the stunning coastal scenery provided ample distraction from the pain in the legs! Jeremy Tandy finished in 7th place, with a time of 47min 06sec, and Jo Page finished in 17th place, 51min 33sec, as second place lady.
Haytor Heller
ORCs Tom Andrew and Jeremy Tandy tackled the Haytor Heller on Saturday 13th July. Organised by the Teignbridge Trotters, this was the 34th year of the 6-mile off road race. Starting halfway up Haytor (thankfully!) the route headed directly up to Haytor Rocks before heading into the stunning Dartmoor landscape. Out to Holwell Tor, then boulder-hopping down technical single track to Becka Brook before heading up the steep ascent to Hound Tor and then down again through more twisty single track and across the brook once more (wet feet this time!). The route then climbed to Black Hill and then, with runners gasping for breath, all the way back up to Haytor Rocks and a steep grassy descent to the finishing line. Jeremy Tandy, in his second race of the day, finished in 19th place with a time of 48min 45sec (and third in MV45 category). Tom Andrew finished in 150th place with a big smile on his face and a time of 66min 50seconds. ORCs will definitely be back in 2020 for this gem of a race!
Lydford Dash
The third running of the Lydford Dash took place on Saturday (13th) and attracted 11 Okehampton Running Club runners. The weather was overcast which made conditions better than during the preceding week. The race took place alongside other events in the Lydford Summer Fair. The route was multi terrain, being fairly rough in places. It was basically a figure of 8 course, running on paths and tracks, including the West Devon Way and up and across Fernworthy Down where the runners had excellent views of the moor and surrounding countryside, not that they stopped to look!! First ORC home was Jeremy Tandy in an excellent 32.01 and he was 2nd M40, followed by Andy Vernon who finished in 34.00 and was placed 2nd in the M50 category. First ORC lady to finish was Jo Page in 36.13 and she was 2nd lady overall. Molly Marvin had a great run, forging ahead of her mum to finish 3rd lady, in 37.44. Phil Read finished just ahead of Sarah Marvin in 39.14 and 40.07 respectively. Sarah won first prize in the W40 age category. Ian Page came in next in 41.21 and he was placed 3rd in the M60 category. Christine Fritsch crossed the line in 46.08 and was 3rd in the W40 category. Mags Jarvis came home in 47.21 and she was 2nd in the W60 age category. Janet White was happy that she completed the race in under an hour, in 59.32. Fiona Porter looked like she had really enjoyed the race when she crossed the line 61.34. Andy, Jo, Christine and Janet were all very pleased that their times were faster than they ran last year.
Having run her first 55mile Ultra Marathon successfully three weeks ago, Okehampton runner Jane Jackson moved up to attempt a 100k Ultra last Saturday. The Race To The Stones is an iconic 64miler starting in the Oxford Chilterns and following the ancient Ridgeway west to finish at the Avebury Stone Circle in Wiltshire. Jane's morning didn't start well when the bus taking runners from the finish to the start was so held up in traffic that the runners gave up, got off and walked in adding an extra mile to their day. Twelve miles into the race Jane was one of many to fall, victims of a path full of tree roots, suffering cuts and bruising her ribs. She continued on, determined to finish the race despite having to breathe in shallow breaths. The day was hot and with very little shade on the ridgeway it all made for an uncomfortable day. From 40miles on Jane experienced the nausea she had at the end of her previous ultra and kept going on small sips of water and no food, eventually finishing in 17.03.30, having not enjoyed the experience at all but pleased to have completed.
PrevPreviousA busy week of running for Team ORC.
NextA Busy Week in the Sun.Next | slim_pajama |
Are all esterification reactions reversible? What is their general mechanism?
For example the reaction of ethanoic acid with ethanol is reversible, however is this true for **all** esters? I'm not quite whether it is as easy for a reversible reaction to occur both ways. Is there a limit to the complexity an ester can be? What would be the general mechanism for these reactions? I assume there is no limit on the complexity (carbon chain length) of esters, other than the frequency of longer-chain carboxylic acids and alcohols needed to form them. Is this true?
I'll start this answer off with saying that both of these answers were the first result when searching for Google.
Yes, [The esterification reaction is both slow and reversible](http://www.chemguide.co.uk/organicprops/alcohols/esterification.html)
and here is the mechanism from an image search
| stackexchange/chemistry |
Doctor Who Everyone Is Immortal Until They Die
The Doctor looked impressed, which was rare, Clara thought to herself. Ever since he had regenerated he had been a lot grumpier but only on the outside though. Different but the same, he was still the curious child at heart, running through the stars trying to complete the impossible task of seeing the entire universe.
After the incident with the dream crabs Clara felt different too. It had felt so real growing old, living an entire life without the Doctor. Like all dreams though it faded but the impression it left on Clara didn't. Growing old scared her. Before she hadn't really thought about it, with Danny she didn't care but he was gone and now with the Doctor? Was he immortal? Now the timelords had given him a whole new regeneration cycle who knew. She had asked him before but his response was cryptic as ever.
'Everyone is immortal until they die Clara.' He had said in his strong Scottish accent. What did that even mean? She liked it though. It seemed hopeful in a weird sort of way. Something only someone like the Doctor could come up with. Either way with the exception of Trenzelore the Doctor had never really had to deal with old age. She often wondered how that had been for him but now she'd lived it too. Waking up and looking in the mirror at her wrinkled reflection. Gradually losing her mobility and strength and she'd been alone.
Second chances are rare but sometimes there are miracles especially at Christmas and Clara was intent to keep hold of this one.
'Clara.' A voice broke her train of thought. 'Clara?' Snapping out of her thought stream Clara focused once again on the Doctor. Before the invasion it had been a month since Danny's death, a month since she lied to the Doctor and let him leave her behind. But unlike the Doctor she still wasn't telling the complete truth now she thought with discomfort.
'Sorry.' She looked him feeling guilty about her secret. She wasn't sure why though. In fact she wasn't even sure why she couldn't tell him.
'Still thinking about the dream crabs?' he asked with slight concern.
'Yeah.' She said quietly. 'Not just them.' She thought.
'I scanned the Earth before we left. No more dream crabs. As for the old thing...' he paused. 'I'm older than you.' He finished eventually. The Doctor wished he could be of more comfort to Clara but he didn't know how. Aging and death are the biggest fears shared by the large majority of humanity in any time. 'Distract her.' He thought and pulled out the latest object of his tremendous curiosity. The orb shone with a pale blue light and hummed steadily indicating its intent to do more than be what it seemed. 'I've been working on this.' He told her enthusiastically.
'What is it?' Clara asked already intrigued.
'A map.' The Doctor pressed the orb between his hands and the humming sound grew exponentially like an old computer booting up. Then it faded out once more and in a burst of light the orb split apart suspended in mid air revealing a complex holographic map which surrounded the pair. It wasn't like any map Clara had ever seen though. There weren't roads or lines, it wasn't even a star map but instead a big ball of wibbly wobbly timey stuff as the Doctor had once so eloquently put it. The words were foreign to her even with the TARDIS's help she couldn't recognise any of it. The Doctor began to interact with the space moving the hologram enhancing and changing the patterns in the mess of the holograms blue light. Clara turned to him for an explanation but she realised from the concentration in his eyes she would have to wait until he had finished to get one without receiving a grumpy shut up. Intently she watched him trying to understand something in this complicated swirl but she got nothing. Even his movement seemed random to her but the Doctor knew what he was doing. Mostly.
It didn't take him long to finish whatever it was he was doing.
'So what do you think?' he asked her excited for her response but Clara didn't know what to say. 'Well?' he prompted.
'What is it?' he sighed. He had hoped not to have to explain.
'A map.' He said again.
'Temporal spatial map?' she asked. He nodded with a smile, she did know after all. 'But a map to where?'
'Oh of course you can't read it can you?' he asked rhetorically mentally scolding himself. 'There is a seed of truth to every myth Clara.'
'Like you then.' She smiled at him. 'A little bit impossible.'
'The elixir of life.' he clarified ignoring her comment. 'This map is impossibly old. Made by a race of ancient being knowledge beyond even the timelords. They are gone now but parts of their society remain scattered throughout all the plains of the universe. I found this in the time vortex and if I'm right it leads the source of immortality.'
Authors Note: To readers of my other stories, not dead and I so sorry! Life got crazy, I went to university and stuff, I'm going to try and be better this year. I hope I will because I really enjoy writing and I just need to force myself to make time for it. Happy new year and I hope you like the story
End file.
| fanfiction |
Chaetae may refer to:
Chaetae town in ancient Macedon
Chaeta, an anatomical feature of invertebrates | wikipedia |
Fantasy Island 1. Chapter 1
**A/N:** _Looks like I managed to finish the next installment of this series earlier than I thought. It's been a long time since I wrote one that quickly! Here's a late Christmas gift; hope you enjoy!_
* * *
><p>§ § § – September 27, 2008<p>
It was so late when the charter approached Fantasy Island that only the stars were out to witness their disembarkation at the plane dock. Roarke had instructed the pilot to radio ahead so that some of his employees would be waiting at the dock with rovers and extra manpower to unload all the crates and boxes they had brought from Italy. Lucan was asleep and Marina looked as if she wanted to be; Rogan yawned every few minutes, scowling from time to time. The gentle bump of their landing didn't disturb Lucan at all; since Marina had to carry him, they allowed her out of the plane first, then followed her with two or three boxes apiece. After that, a steady stream of natives, working by floodlights set up near the clearing, completed unloading the plane and transferring everything to the waiting cars. Rogan glanced around as he headed back for another box or two. "I'm looking forward to getting back home to Julie and Rory," he muttered through another yawn. "I hope like hell we don't have to go back to Italy, if we can't find a cure here."
"There would be no point," Marina said, glaring at him. "If we can't find a cure here, on this island, then we'll find it nowhere, for it won't exist."
"Save your energy," Roarke advised. "We must get everything hidden away in the greenhouse before we retire for the night, I'm afraid. Remember," and here he raised his voice for the benefit of the natives, "none of you is to breathe a word to anyone else about this. What little you do know, you must keep to yourselves." There was a murmured consensus, but the natives never stopped moving.
At last the cars were loaded and heading for the bed-and-breakfast inn that Julie ran. Marina rubbed one eye, still holding her son, and peered at what she could see of it in the softly lit night. "How pretty," she mused. "Oh, Mr. Roarke...where will Lucan and I stay?"
"The cottage that once belonged to my former assistant Tattoo is empty," Roarke told her. "We normally use it only when there are more guests than accommodations. Since everything else is full, you and Lucan may make that your home while you're here."
"You'll feel like Gulliver," Rogan commented with sleepy humor. "It's sized for him, so everything's miniaturized. The lad'll fit in fine, but you may find yourself sleeping on the floor under a rug."
"Rogan, I think it might be the better part of discretion for you to cease and desist," Roarke scolded him. "The cottage was renovated after Tattoo left the island, Marina, so you should feel comfortable there. For the moment, let's get to work."
It took fifteen minutes to unload everything again and take it into the greenhouse; then Rogan, with a slurred good-night farewell, headed for the big stone house nearby while Roarke delivered Marina and Lucan to the cottage. He found it a great relief to reach the main house and let himself in; the study was empty and dark, though as he crossed it toward the stairs, the grandfather clock softly chimed 1 AM. Roarke hoped there would be too much preoccupation with the fantasies for Leslie to ask many questions; he planned to tell her eventually, but he wanted to keep Christian in the dark for now. There was too much at stake and Christian was too volatile when it came to amakarna, and they had made far too little progress for Roarke to have much more than hope and determination about their research. He glanced into Leslie's old room, where she and Christian were both sound asleep, and smiled faintly before retreating into his own room for a good night's rest.
§ § §
Dawn was only just beginning to stain the eastern sky; but though Leslie's old dormer room in the main house faced east, the windowshade was down so that there was no sign of daybreak in the room. It wasn't much past five; so when Christian's cell phone began playing the _jordisk_ national anthem, it had all the impact of a thunderclap. Both Enstads jerked awake, moaning in chorus. "Who the hell is _that?"_ Leslie complained sleepily.
Christian muttered something in _jordiska_ that Leslie suspected was objectionable, a phrase he had yet to teach her since she didn't understand it, and reached out to slap the table on his side of the bed till his hand landed on the phone. "Enstad," he muttered, then stifled a groan. "Ben?" His voice was ominous, despite its sleep-induced scratchiness. "Do you realize what time it is here?"
For a moment Leslie frowned, then placed the name: Ben Keller, the manager of Christian's Boston office. Keller had run the place with a deft hand ever since Christian had completed the hiring when it had first opened; thus Christian had never yet been back. She wondered what had happened. The light snapped on and she screwed her eyes more tightly shut in protest.
The mattress began to jiggle and quake, violently enough for Leslie to open her eyes and see Christian pushing himself into a seated position. A scowl bloomed and deepened on his face; at last he demanded, "When did this happen?" Keller's answer made him close his eyes and shake his head. "No, don't do anything yet—just have Janine draft a newspaper ad and call it in. What's the local paper there again? Yes, the _Globe_. No, it's all right that you called me—you were right, I'll want to see to this myself. I'll give you a call and update you when I get my flights scheduled. All right, yes, do that. Goodbye." He ended the call before Keller could trap him into a run-on conversation and looked wearily at Leslie.
"What's wrong?" she asked.
He sighed. "I know you're not feeling well, and I'm sorry, my Rose, but there's an emergency of sorts in Boston. Keller just informed me that I'm going to have to hire two new computer technicians. One quit because her husband is being transferred to another state; and the other had a massive heart attack, which as I understand it will confine him to bed rest indefinitely, if not permanently. I'll have to fly out to Boston and oversee the hiring of replacements." He smiled wryly. "I'm sure you'll remember Keller's demeanor—hell bent for suede and that sort of thing—"
"Hell bent for leather, my love, not suede," Leslie corrected him with a snicker.
"My apologies," said Christian with that raised brow. She grinned at him, and he chuckled back, relaxing a little. "In any case, it means I'll have to fly out of here as soon as I can make flight reservations and pack some things. Likely I'll be gone at least a week, more like two, depending on how long it takes to find good candidates."
Leslie's smile vanished and she went limp where she lay, sighing heavily. "You're right, I still don't feel well, and I'm pretty sure I've got whatever bug Noelle and Lauren came down with. Probably some sort of stomach flu." She blew out an exasperated breath. "I just hope I can last till the guests go home tomorrow morning. It'll be bad enough as it is, but it's always worse if you're gone, for some reason."
Christian smiled at her and stroked her hair. "You know perfectly well I'd rather take you with me, but obviously that just wouldn't work. All I can do is promise that I'll be back as soon as humanly possible." He lifted the phone again. "To that end, let me start making airline reservations. The sooner I go, the sooner I come home."
An hour later, with Christian scheduled to depart on the ten-o'clock charter, they were both up and awaiting breakfast in the study while he watched her go through more of the bills that Roarke's business tended to generate so many of. "I don't suppose you'll join me for the morning repast," Christian said humorously.
She shot him a look from under her bangs, without lifting her head. "If I do, I'll be strictly a spectator. No doubt Mariki's going to accuse me of starving myself again."
"If she does," remarked a voice from the stairs, "I'll explain things to her." Leslie and Christian looked sharply around and goggled at sight of Roarke.
"Father! You're back early!" Leslie exclaimed, with great relief.
"You have quite the sense of timing, Mr. Roarke," Christian commented. "Leslie's been doing quite well, I think, since you left; but lately there have been problems. Noelle and Lauren have taken ill, and it looks as if Leslie is beginning to come down with whatever they have. And I myself have to leave for Boston because it's necessary for me to replace two of my employees there."
"I see," Roarke said, coming into the room. "Perhaps you two can fill me in more fully over breakfast. Leave the bills for later, Leslie; I'll handle them after you've updated me. I presume the children are still asleep?"
"They'll be awake before much longer, if habit holds true," Christian said, checking his Rolex. "I have to admit, I'm hungry this morning. It's just as well, because I suspect they won't be feeding me, even on the long-distance flights."
They were just about to go out to the veranda for breakfast when the triplets came thundering down the stairs in all their pajama-clad splendor. The moment they spied Roarke, they all shrieked in joyful welcome and threw themselves at him for hugs. Christian and Leslie watched, laughing softly, as Roarke managed to devote sufficient attention to all three children that they were soon a little calmer, though they clustered around him as the family made their way to the breakfast table.
The children chattered at their grandfather as Mariki appeared and began doling out serving dishes; the adults let them carry on for a minute, as it prevented Mariki from asking questions about Leslie's lack of enthusiasm for the meal. When she was gone and Christian had filled his plate, he lifted a hand. "Enough, the three of you. Your grandfather can't make any sense of your words if you all talk at the same time. Let him choose one of you and you can take turns telling your stories."
"Me first!" Tobias insisted immediately.
Susanna and Karina glared at their brother, but Roarke chuckled and indulged him. "All right, Tobias, go ahead." Tobias promptly started talking, and Susanna chimed in here and there till she got her turn. As Leslie listened, she got the sense that Roarke—unusually tolerant of his grandchildren's eager gabbing—was allowing them to have their say for more reasons than merely giving them a chance to let off steam. She considered asking, but she had learned over time that Roarke would talk when he was ready, and not till then.
_"Herregud,"_ Christian remarked when Susanna finally wound up her report, "even I didn't know about some of that. I'm sure much of it was exaggerated." He glanced at Leslie as he said this, and she grinned. "That leaves one. It's your turn, Karina."
"What have you been doing lately, sweetheart?" Roarke inquired of her.
Karina looked at Roarke with shining eyes. "I got to do Mommy's job!"
"You did not!" Susanna blared out, her face radiating outrage.
"Did so!" Karina shot back smugly. "You be quiet, it's my turn—Daddy said." So saying, she proceeded to tell Roarke about Tobias', Susanna's and Kevin's transgressions with her plush cat (which she had brought to the breakfast table and showed off to her grandfather with an indignant zeal that made Christian and Leslie grin at each other), and how in the aftermath Leslie had made the other children hunt down the missing toy while Karina was given the privilege of accompanying her mother on some rounds. This got them through most of the remainder of breakfast; Susanna and Tobias, eyeing Karina with black glares, finished eating while Karina talked. Brianna appeared as she finished and Christian checked his Rolex again before helping himself to more of Mariki's breakfast casserole.
The children were excused, and they tumbled out of their chairs, Karina grabbing her bedraggled plush cat as she left. Roarke nodded a greeting to Brianna before turning to his daughter and son-in-law. "So...how much of that was accurate?" he asked teasingly.
Christian and Leslie laughed. "Most of it was right," Leslie said. "What they failed to mention was that I'm not feeling so well myself, and that apparently Karina bragged about what she got to do, because Susanna came down late yesterday afternoon before Christian got off work and tried to talk me into letting her come along to make my last check on the Reardon fantasy for the day. I had to turn her down—after all, it's a time-travel fantasy, and I don't think we're quite ready to turn a four-year-old loose in the past."
Roarke chuckled. "A wise choice," he lauded. "Christian, you seem to be in something of a hurry, and I don't think I've ever seen you eat that much."
Christian smiled ruefully. "I'm quite hungry for some reason." He glanced at his wife. "I expected to worry about Leslie while I was gone, but with you back I'll have less of a burden on my mind." He drew in a breath and shifted gears, his expression sobering. "I presume your trip was fruitless. I can't say I'm surprised; amakarna is apparently one of those unavoidable evils of life."
"We returned a little early primarily because Giancarlo Ognissanti did the same," said Roarke. Leslie noticed he had dodged addressing Christian's assumption, and filed it away to ask him about later. "It was felt it might be best to avoid any confrontation."
Christian stilled and stared at him. "Giancarlo Ognissanti?" he repeated. "Are you telling me you were in Italy, at the LiSciola villa? Well, for fate's sake, what exactly were you doing there, and why did you have to take Rogan with you?"
Roarke, too, went still and studied the prince before replying, "Christian, I believe your flight out is scheduled to leave within the next eighty minutes, and you undoubtedly have a fair amount of packing to do. News of the trip will keep; you have other concerns to think about, and Leslie and I need to see to the fantasies."
Christian peered at him, enormous suspicion on his face, but gave in. Leslie had to smile; Christian, too, had learned when not to push Roarke. "Very well, but I do expect to have a full update at the earliest opportunity. You know perfectly well I'm interested in anything to do with that spice, because of my nieces. But you're right about the time, so I'll let it go this once. Leslie, my Rose, would you mind helping me pack?"
Leslie acquiesced; she had heard that inevitable imperial tone in her husband's voice, but knew at the same time that Roarke could be the immovable object to Christian's unstoppable force when it was necessary. She followed him out to the car and settled into the passenger seat while he piloted the vehicle out of the lane and on toward home.
After a few miles he glanced at her. "I've been thinking. Presumably Mr. Roarke got back sometime last night when we were asleep. He hasn't even mentioned whether they had a good flight, or even if Rogan came back with him." He flicked a glance into the rearview mirror before continuing, "But since he's never left the island for any reason before this, I have no way of knowing if his uncommunicative way is normal with him."
Leslie giggled. "Don't ask me, I don't know either. Christian, my love, I wouldn't worry about it if I were you. You've got other things to handle right now. And I admit, I'm actually less interested in Father's trip, and the reason he went, than I am in wishing _you_ didn't have to go. I always miss you when you're gone."
"I miss you too, my Rose, believe me," Christian assured her. His soft look grew into a teasing grin. "But I don't think you or even I need worry about Janine Polidari. I've had nothing but excellent reports about her from Keller, so I'm satisfied that she's truly matured and I won't have any trouble from her." She laughed, as he'd hoped, and he squeezed her hand and turned his full attention back to his driving.
At the plane dock a bit more than an hour later, Christian—now dressed in a suit and tie, which merely made him all the more irresistible to Leslie—glanced at the plane, consulted his Rolex for the dozenth time that morning, and set down the laptop case he carried in order to give each triplet a hug. "Where you going, Daddy?" Tobias wanted to know.
"A place called Boston, very far from here," Christian explained. "I have an office there that's just like the one here in town. I have to fix some problems there, but I promise I'll be coming back, so Mommy will bring you here to meet me then if she can."
"I want to go with you, Daddy," Susanna said.
"Sorry, _lillan min,"_ Christian said with a little laugh, tousling her hair. "Another time, perhaps. Maybe while I'm gone, you can help your mother and Ingrid around the house, and if Grandfather says it's all right, you might help him a little with something too. In fact, all three of you, why don't you go over and ask him if he has something for you to do for him?" He watched the triplets light up at this idea and flock to Roarke, all clamoring at once; then he grinned and sauntered to Leslie, drawing her into his embrace.
"Sneaky," Leslie said, half accusing, half laughing.
"You know there was a good reason I did that. I want to say a proper goodbye, and I know you'd have been thoroughly annoyed with me if I didn't," he retorted with a grin. "If you don't mind, let me say that goodbye before I miss the plane." Without giving her a chance to respond, he lowered his head and kissed her, as always making a complete job of it so that she wanted only to hold onto him and never let him loose.
"You really do say a hell of a goodbye," she admitted breathlessly when he released her. "Trouble is, it makes me not want to say goodbye at all."
He grinned at that. "In that case, let's make it a little easier." He popped a quick, perfunctory peck on her cheek and lifted the laptop case, turning away as if to leave.
"Oh no you don't, Christian Enstad," she shot out threateningly, grabbing his arm, and he dropped the case again and let her tug him back, laughing. Chuckling back, she pulled him into a long hug, sobering. "Be safe, my darling, and please call me when you land in Boston, will you? I wish you had a more certain timetable. These open-ended trips are a real pain in the butt because I don't know when you'll be home."
"You think I live for these things, then?" he retorted with a slight chuckle. "I promise to give you word as soon as the pilot gives clearance for passengers to place phone calls. I suspect Keller will be there again, trying to treat me like royalty, and I admit I'm not really looking forward to dealing with him. I mean...he means well, but he doesn't realize how overpowering and wearying he can be. I'm worried he'll insist on putting me up in his own home." He rolled his eyes while she snickered. "Not to worry, I'll get around that." His expression softened again and he gently smoothed her hair back from her face, placing a soft kiss on her lips. "I love you, my Leslie Rose, and I'll call when I get there."
"I love you too, Christian, my darling. I'll be waiting." They shared one last kiss just as the final boarding call came, and Christian released a resigned sigh before squeezing her, letting her go, picking up the laptop case and hurrying for the dock in his customary hasty leavetaking. She watched him, already feeling lonelier.
"Did you have sufficient time to render proper farewells, then?" inquired Roarke in a wry tone from beside her, and she looked around to see him shift his glance to the plane, where the attendants were just closing the hatch after Christian. The triplets were chasing each other around the clearing, shrieking and laughing.
"Of course we did, Christian saw to that," she said with a smirk, and he chuckled, shaking his head. Leslie let her attention drift back to the plane. "He promised to call, but I think he's afraid Keller's going to try to play host when he gets to Boston."
"I have no doubt Christian will be deft at handling Ben Keller," Roarke assured her, ushering her along toward the waiting car with a hand between her shoulder blades. "We'd better return to the main house; there's plenty to be done."
2. Chapter 2
§ § § – September 27, 2008
Leslie called for the triplets, and within a few minutes they were back in Roarke's study, with the children having gone out with Brianna for an excursion in the little wading pool near the regular adult swimming pool. They had been gone less than five minutes when Roarke set aside the checkbook he and Leslie had been working with earlier that morning and focused on his daughter. "Since we are finally alone here and Christian is well and truly out of earshot," he said, completely serious, "I think it's safe to talk."
"About what?" Leslie asked, setting aside the letter she had been about to slit open.
"My true purpose in taking Rogan to Italy," he said. She sat up in surprise, and he smiled privately; she had been absentmindedly massaging her stomach ever since they'd returned to the main house, but seemed to forget all about it now. "I wanted to wait till Christian in particular could not overhear, because I'm afraid his reaction would be far too violent. His journey to Boston was extremely fortuitous." Leslie eyed him with some suspicion, and he gave her a mildly reproving look. "No, that was not my doing."
She snorted softly, but relented. "Okay, okay. But just why do you want Christian kept in the dark?"
In the next few minutes Roarke filled her in on what he and Rogan had been doing in Italy, while her eyes got bigger and bigger. "As you're aware now, we returned last night, very late, and brought with us all the equipment we will need to continue the research." He waited a beat, then added, "We also brought back Marina and her young son."
Leslie's spine snapped even straighter in the chair and she blew out a breath, her eyes all but round by now. "Whoo. Then it _is_ a good thing Christian's not here." Roarke nodded, and she considered what she had heard. "So...Marina thought she had found the antidote, but in the end it didn't work after all."
"That's not quite true, my child," Roarke corrected her. "It did work, at least for a few days. Since it does seem to have had some effect, even only a temporary one, I feel that avenue is worth pursuit. However, it's clear that this is not the full answer; besides, we aren't sure precisely what property of the spice is affected by this particular plant."
"What plant was it?" she asked.
Roarke frowned. "Jimsonweed."
"I thought that was a narcotic," said Leslie, astonished. "Oh boy! Rogan must've really blown his top when she told you what she was taking."
"Indeed. In any case, since he has such extensive botanical knowledge, he will continue to test various plants in the hope of discovering others that may have some effect; and I will research the history and traditional uses of the spice among the clans, so that perhaps we will find additional clues in the texts."
"What's Marina going to do? For that matter, why did she insist on coming to the island in the first place?" Leslie asked. "Because, speaking of blown tops, Christian's will go sky-high if he finds out she's here. Well, not _if_, more like _when."_
"You had better hope that Christian spends the maximum time in Boston and that it takes us the minimum time to find a proper counter-agent," Roarke said with a touch of humor, "or else if I am to believe your words, all hell will break loose around here." She grinned reluctantly; he noticed her hand had strayed back to her stomach and was massaging again, probably without her knowing it. "To answer your question, Marina insists on being the test subject for each substance...the guinea pig, if you will."
"But that could be fatal," Leslie said. This merely got an _oh really?_ look from her father, and she smiled sheepishly. "Sorry, I'm stating the obvious. I think all three of us—Michiko and Lauren and I—have been sort of channeling Tattoo lately. Isn't there some other way to test possible cures, or antidotes, or whatever you want to call them?"
"If there were any other way, we would try it," Roarke said. "Unfortunately, as I have managed to ascertain, no other living creature on earth is susceptible in any way to the effects of amakarna—only human beings. Since it is necessary for Marina to have a daily dose of the spice anyhow, she insisted on being our living proving ground. She felt it unwise in the extreme to remain in Italy after her husband's return, for fear that he would discover what she was trying to do and perhaps retaliate in some fashion."
"Well, why on earth would he do that?" Leslie asked.
Roarke relaxed back in his chair. "I think Marina can best explain that to you," he said. "Suffice it for me to say for the moment that she brought her son, Lucan, with her for the child's own safety, as I understand it."
Leslie, whose hand had once more been moving restlessly over her abdomen, stilled again; Roarke nodded, knowing she had read between the lines. After a moment she asked, "Why would she fear for Lucan's safety? I thought she adored her husband—Christian told me once that she mentioned to Arnulf, the day he annulled their marriage, that she'd been in love with Giancarlo since she was nine years old and couldn't wait to be his wife."
"That was then, Leslie," said Roarke gently. "I've been given to understand that he is a much changed man, thanks to the trade in black lightning, for which he is solely responsible. It is he who produces the drug, distributes it to his dealers in various parts of the world, and collects the payment for it each month. After his many failures at all manner of other jobs, I suspect at first Marina's father, the count, was relieved to find that Giancarlo had at last stumbled upon something he could succeed at. But the acquisition of wealth seems to have altered his personality—whether irrevocably or not, I don't know. It's Marina's hope that if we are able to eradicate black lightning and its addictive properties, Giancarlo will be forced to find some other vocation, and perhaps as a result he will revert to the man she once knew. Her words, her hopes." His eyes had gone unfocused and distant. "Love may be all-conquering, my dear daughter, but sometimes it needs a little help."
"Well, then, I suppose you should get started," Leslie suggested with a little smile.
Roarke came back to the moment and chuckled. "Not immediately. We were all quite tired from the long flights, and there is jet lag to consider; so I'll concentrate on the fantasies for the remainder of the weekend, and allow Rogan, Marina and Lucan the chance to recuperate and adjust to the local time zone. Lucan is only a year younger than the triplets, so perhaps they will become playmates. Brianna may find herself earning a great deal of extra babysitting money, between watching Lauren's son and now Marina's."
"Noelle too, I think," Leslie agreed, "once she gets over whatever she has." As if the words were a signal of some sort, she suddenly hiccuped and wrapped both arms around her stomach. "Be right back," she croaked before leaping from the chair and racing upstairs as though there were wings on her feet. Roarke watched her go, shaking his head, smiling ruefully. It appeared he'd come home just in time!
§ § § - September 29, 2008
There was no word from Christian till after Leslie had taken the children home on Monday morning, nursing a stomach that refused to give her a second's respite. Ingrid noted her mistress' condition and insisted she go to bed, that she would take care of the triplets and handle everything else. Once Leslie had changed into her most comfortable sleepwear and had been lying quietly in bed for an hour or so, her stomach had at last consented to calm down enough that she was dozing lightly, on her way to a deeper sleep.
Then the phone in the library jolted her awake and her stomach began doing a long series of somersaults. Cursing silently to herself, Leslie squeezed her eyes shut, opening them only when Ingrid poked her head around the wall partition that split the stairway off from the master bedroom and said in _jordiska_, "Princess Leslie, it's Prince Christian."
"Oh, thank goodness," Leslie blurted in English, before managing to dredge her somewhat shaky _jordiska_ out of her memory. "Bring me the phone from the library, Ingrid, would you please?" The servant complied, and Leslie smiled her thanks and lifted it to her ear, relieved to switch back to English. "Hi, my love, what took you so long to call?"
Christian grunted. "I'm sorry, my Rose, I should have called earlier, but when I landed at Logan Airport, I discovered my phone had died and needed recharging. By the time there was enough power to make a call, it was too late in your part of the world, so I left it till I knew it would be less intrusive. I changed my watch to Boston time just for the sake of expediency, but my phone still shows Fantasy Island time, so I knew you would most likely be home by now. How do you feel?"
"Like crap," said Leslie bluntly, and he laughed. "I threw up half a dozen times yesterday, but I wasn't about to desert Father, what with Lauren and Noelle still out and Michiko in that fantasy. Which is a whole separate story in itself, actually, but first—tell me what's going on. Have you found out anything new?"
"No, I really haven't. For one thing, it's still Sunday here, and for another, it wasn't Keller who met me at the airport: it was Janine Polidari. There was something odd about her; she seemed a little skittish, as if she were afraid of something."
"Probably you," Leslie said humorously, "considering she'll likely never forget that one humiliating afternoon when she threw herself at you..."
"It's not that," Christian interrupted her, and her amusement died at his tone. "I could see something was bothering her and asked her if anything was wrong, but she said only that it was better if I got to a hotel as soon as possible and she would talk to me tomorrow. Today for you. Ach, this time-zone business is such a pile of fishtails."
She laughed at his translated _jordisk_ slang. "Nothing we can do about it. Did she give you any hint at all as to what might be bugging her?"
"Nothing. I did ask her where Keller is, and she said he had called her, along with all the other employees here, to tell them that I was on my way and that they should appear at the office tomorrow so that I could talk to them. She said then that she asked him if he would be there as well, and he told her he was feeling quite ill and would have to skip it. It sounds like nothing, and I was inclined to dismiss it as such, but Janine insists this is the first time Keller has ever been too sick to work."
"That still doesn't mean anything, necessarily," Leslie observed. "Sooner or later we all get laid low by something. It was just his turn, that's all."
"Mmm, that's my thought as well. But Janine seems to be of another mind entirely, so I suppose I'll have to draw her out. In the meantime, she handed me a small stack of paper applications that have been on file for the last year or so, and an ad will be appearing in the newspapers here starting tomorrow; so at least I have something to do."
"Well, good, then you won't be bored and have to resort to watching trashy reality crap on TV. Have you had a chance to go through them yet?"
"A few, but mostly I've taken it easy. My sense of time is completely skewed, and I need to try to nap a little. Not too much, so that when local night falls tomorrow, I'll be tired enough to sleep properly and that will complete my readjustment. So...as to you...it seems you've officially caught whatever Lauren and Noelle have."
"Yup. Father sent me home this morning right after we got back from the plane dock. It was just us, because when Michiko came out of the Reardon fantasy, she was so upset and unhappy that she couldn't talk about whatever had happened. She asked Father if she could be excused and go back to her mother's place, and he agreed, but he told her not to hold it in for too long and to talk to someone about it. I'm not a hundred percent certain of this, but I got a clue about it this morning."
"Oh? Now what fantasy was this, my Rose?"
"Mitchell Reardon—the guy from North Dakota who wanted to take part in a big Hollywood movie musical, circa 1948 or so. Michiko was supposed to be one of the background dancers in the movie he was making. But back then you never saw anything other than Caucasian dancers in these things, so Father left a potion for Michiko to use to turn her into a statuesque platinum blonde."
"Well enough, I follow you so far. What do you think may have happened?"
"Something might've developed between Michiko and Reardon, because when we said goodbye at the plane dock, he looked a little depressed. He mentioned a beautiful blonde chorus girl with an amazing voice and wished he could see her again. Like I said, I'm not sure it was Michiko, but what with her reaction and her refusal to come to the plane dock today, and the way he described her in her disguise, my gut says they must have had a fling and it affected Michiko more than she thought."
"Problems, problems everywhere," Christian mused through a sigh. His voice was light, though, and Leslie had to smile. "We'll get to the bottom of them, never fear, my Rose. It just takes some time."
"I know. We have our share of that, for sure..." She gasped as her stomach pitched, and cried, "Stay on the line, please, I'll be right back!" Dropping the cordless phone, she rolled off the bed and fled to the bathroom, where she threw up whatever she had tried to drink that morning at breakfast and then endured a couple of rounds of dry heaves before her stomach stopped spasming. She rinsed out her mouth, wiped her face and picked her way back to the bed. She could hear Christian's voice from the phone and lifted it to her ear. "Calm down, my love, it's okay now...I just threw up again."
_"Heilige hjusande ödet,"_ he swore, and she grinned weakly at the oath, which had been one of his late father's favorites. "I wasn't sure that's what it was. All I could hear were horrible gagging noises in the distance. Are you really all right?"
"As all right as I can be under the circumstances. Ingrid's handling the housework and watching out for the kids, so—" She caught herself when a small face peered around the partition at the stairway; it belonged to Susanna. "Hold on a second, my love. What's the matter, sweetie?"
"Ingrid said you're sick," Susanna said, padding into the room, eyes wide.
"I am, sweetie, and I just threw up again. What is it? I'm on the phone."
"Who is it?" Susanna asked, and when Leslie told her, she lit up. "Can I talk to Daddy, please, Mommy? I wanna tell him what we did yesterday."
"Hang on," Leslie said and relayed their daughter's request to Christian, who laughed and told her to put Susanna on the line. While the child was talking, Leslie resettled herself into the bed, moving gingerly in an attempt to keep her stomach from inciting another violent rebellion, and listened with half an ear to Susanna's chatter, thinking about Michiko all the while and wondering if she should give her friend a call at some point. Michiko was still dealing with Cat's chilly aloofness, so she hardly needed whatever was bothering her in the wake of this past weekend.
"Okay, Daddy," Susanna said suddenly. "Bye." She handed Leslie the phone. "Daddy wants to talk to you again."
Leslie took the phone and smiled a little. "I guess you're all updated now."
"Seems so...apparently the children were busy little bees yesterday. Don't let her hang around you too much, my Rose, you don't need the burden of nursemaiding any of the children as long as you yourself are ill." His voice gentled. "For that matter, I should let you rest. Shoo her out, my darling, and then try to take a nap; it might help you feel better."
"I hate to hang up, but I guess you're right. Well, give me a call when you have something worth telling me about, will you?"
"I will, I promise you that. Give my love to Tobias and Karina, and remember, I love you very much. Get well."
"You stay well, my love. Talk to you later," she murmured, and they disconnected.
"Is Daddy coming home soon?" Susanna asked.
"Honey, he only just got there. It's going to be a while. I need to try to rest, so why don't you go find your brother and sister and play with them. I don't want you to catch what I have, or you'll be throwing up all over the place too."
Susanna sighed. "Okay." With a hangdog look that made her mother grin, she plodded off to the stairs and disappeared, and Leslie finally succeeded in falling asleep this time, still mulling over Michiko.
3. Chapter 3
§ § § – September 29, 2008 – Boston, Massachusetts
By the time Monday was well under way in the northeastern US, Christian had been in his computer-repair office for an hour or so, having been brought over by a taxi called for him at the hotel's front desk. It was almost nine and he expected his employees to begin arriving any moment now; because of the absences of three of his staff, he had decided to close the office till noon. This office served all of southern New England, which was the reason his staff here was larger than in his other branches; there were eleven employees in all, including Keller and Janine. He expected to see only eight.
He had just finished a long phone conversation with Jörgen, the manager in his original Sundborg branch in Lilla Jordsö, when his local staff began to trickle in. They gave him deferential greetings and settled nervously at their desks; it was only the second time they had seen him, and he realized he probably seemed larger than life. He sighed inwardly; he'd have to do his best to put them at ease before he started digging into what was going on around here. He leaned back in his seat and suddenly grinned to himself; it had been a few years since he'd taken over this storefront, but he swore he could still catch the occasional whiff of the products from the perfumery that had previously occupied the space.
Janine arrived in the company of another woman; they were the last to appear, and when they did, Christian got up and locked the door behind them, leaving the sign in the window displayed to _CLOSED_. Then he wandered back to Keller's desk, where he had been sitting, and surveyed the small group. "Well," he said by way of greeting, "I'm sorry my first visit back here had to be under such unfortunate circumstances, but I must say it's good to see you. Now before I really disgrace myself, please introduce yourselves to me, if you will. I already know Janine." He smiled at his receptionist, still the youngest of his staff here, and she managed a return smile.
Names went around, and he made careful note of each one before nodding. "Thank you for coming. Now it's my understanding that Ellen Hazelton had to quit because she and her husband are moving to another state, and that Howard Welles was felled by a massive heart attack."
"Ellen Baselton, Your Highness," ventured the woman who had come in with Janine. She had introduced herself as Katherine Anderson; Christian thought she looked no more than about thirty, if that. "But yes, you're right. Howard had the attack Saturday night, and Ben called us all yesterday morning to let us know. He's at Mass General, and I guess it's bad enough that only his family can see him—and even then only for a few minutes."
Christian nodded. "I see, thank you, Katherine—and for the correction as well. Now, as to Ben...Janine has informed me he's ill, so we won't see him here today." Surprised looks ran around the group, and he noted this with a slight frown, especially when he caught Janine's latest spooked expression. He really had to talk to her. Settling on the edge of Keller's desk, he took in the faces and drew in a breath. "I'm going to be here for at least a week, possibly two—unless we have difficulties in hiring someone to replace Ellen and a temporary worker for Howard. I took a little inventory when I came in here, and I can see you folks are very busy indeed." He got a chorus of chuckles in response and smiled. "What I need to know right now is the average turnaround time for repair projects, whether you have busier periods and slower periods, and how much work is waiting to be done as I speak. Andrew, suppose you give me the statistics."
Having taken charge, he saw he had put his staff a bit more at ease, and the meeting went smoothly, though he still sensed a nervous reserve in the air. As soon as business had been conducted, he resettled himself on the edge of Keller's desk and regarded the group with a thoughtful look. "All right...with that cleared up, I should mention that I'll be in here each day, and I'll help out with repairs and design projects where needed, in between conducting interviews. Janine was kind enough to give me some applications, and I've made a few phone calls already; but we have an ad in the _Globe_, and I expect a fair amount of foot traffic in here through the next week or two. If you think this will disturb you in any way, let me know, and I'll make accommodations."
"It might work out better if you have the interviews right there at Ben's desk," said Tracey Savage, a thirtyish graphic designer who appeared to be good friends with Katherine Anderson. "We'd sort of like to get the measure of the different candidates. Ben's opened up another business up in Danvers, and he had to do some of the interviews right there at his desk. So we had a chance to see those folks."
Christian leaned forward slightly with surprise. "He has another business? In what field, if I might ask?"
"This has to do with computers too," said Tracey, "but it's sales, not repair. He's got about eight people there. He spends roughly six hours a day at each location, every single day. I have no idea where he gets the energy." This met with soft laughter, and Christian grinned as well, recalling the gung-ho Bostonian who'd so brazenly strolled into his Fantasy Island office and proposed managing a branch office for him.
"No wonder he finally fell ill," the prince commented with a chuckle. "Well, all right then. I'll keep the office closed till noon so you can play a little catch-up, but I'm also here to talk individually with each of you through the day. Tracey, why don't you come sit over here at Ben's desk, and we'll have a little chat. Janine, you're likely to get phone calls in regard to the open positions, so go ahead and take them, and tell them they can pick up applications after twelve." Janine nodded and headed for her desk; the others scattered, and Christian retreated behind Keller's desk to talk with Tracey Savage.
By the end of the day, which was at six, Christian had had fairly in-depth discussions with six of his eight employees; this left only Katherine Anderson and Janine, and he had it in mind to talk with them the next day. Gathering up a new stack of applications that had been filled out throughout the afternoon, he let Janine, Katherine and Tracey out ahead of him and meandered some steps behind them toward the nearby parking garage, fishing for his cell phone so he could call a taxi.
As he got off the line, he became aware that the three women had stopped near the street entrance to the garage, talking earnestly. Before he could decide whether to join them while waiting for his taxi, he overheard Katherine Anderson's voice: "Come on, Janine, you know you have to tell, if you actually saw something."
"Why should I?" Janine asked. "Nobody believes me. Even you two don't believe me."
"Because if you suspect something and you don't report it, and it turns out to be right, and something horrible happens..." Tracey began, trailing off as she became aware that Christian was within earshot. He took note that they'd spotted him at the same moment Janine and Katherine realized he was there, and they stared at him as if they'd been caught in the act of stealing computers out of the office.
Christian's suspicions had bloomed all of a sudden, and he signaled sternly at them. "I think we'd all better have a chat," he said firmly. "It's going to be some time before my taxi arrives, so we may as well go back into the office and have our talk there." He pulled the keys from another pocket and waited till the women had caught up with him before ushering them along in front of him, then letting them all back into the office and locking it again behind them. He gestured at the desks and told them to bring the nearest three chairs over in front of Keller's desk, and watched them go about this while he took his seat there once more and waited for them to settle down.
"Now what exactly is going on?" he wanted to know. "Janine, if you have something to tell me, I think it's best you just come out with it. To be honest, I've wondered what's been bothering you ever since you picked me up at the airport." He watched Janine cringe and her face grow crimson, and drummed his fingers on the desktop for a moment before focusing on Tracey. "What has she told you, then?"
Tracey glanced at Janine, then cleared her throat. "Well, you see, Your Highness, it started about a month ago. Maybe a little more than that, I'm not completely sure. Anyway, Ben let it be known that he'd been thinking about opening up yet a third business. We all thought either he was the world's worst workaholic, or he must have some sort of gambling problem he was trying to pay for." She essayed a nervous giggle that elicited a like response from Katherine; Janine tried to shrink in her chair, and Christian humored Tracey with a quick half-smile, gesturing for her to go on. "But we didn't really think that much about it. Ben's always been a go-getter. We just wished him luck and went on with the business. But in the last few weeks, he's been out more than he's been in, and we assumed he was splitting his time between here and Danvers and running around town looking for a new location for this latest business venture. The weird thing was, he never seemed to get tired. I don't even remember seeing him so much as yawn."
Katherine nodded. "Some of us told him he was going to work himself right into an early grave, but he just laughed and said he was having the time of his life. He's been losing weight, and his marriage fell apart shortly after he opened the place in Danvers, but nothing seemed to bother him. It was like he was obsessed."
"And then last week, Janine says she saw him in the back room where we keep all the spare parts," Tracey said. "It was after hours, I think, and she came back in here for some odd reason or another. We all have a key in case of emergencies—Ben saw to that—and I think she forgot something in here. I don't know what. She half confided in Katherine and me at lunch, but we didn't know whether to believe her or not, and now she refuses to tell anyone. But she keeps acting like someone's after her, so we've been trying to get her to open up. It was almost a relief when Ellen said she had to move and Howard had that heart attack, because that finally put Ben in over his head and he had to contact you."
"So that brings us to the present moment," Christian said, "and to you, Janine." The young woman flinched, and he sat up and leaned over the desk, modulating his voice as if he were consoling one of his children. "Janine, let me assure you right now, you need have no fear of any kind of reprisal. I'll see to it myself. But if you're this badly frightened by what Tracey says you apparently saw, it's best if you let me know."
He watched Janine flick a skittish glance up at him before huddling even farther into herself, shaking her head. Christian thought back for a moment; he could still remember the brash, brazen, homesick teenager who'd so boldly come on to him the summer the triplets were born, and since that time she had matured physically as well as mentally. She was 21 now, attractive and somewhat exotic-looking with her face accented by the Asian features she had inherited from her mother, Camille's sister Andrea. But right this moment, she looked like nothing so much as a terrified little girl.
Katherine finally urged, "Janine, come on, tell him."
Janine threw her a desperate glance, then at last met Christian's gaze head-on and demanded, "They don't really believe me, so why would you?"
Christian sat up again and let himself settle back in the chair, folding his arms over his chest and regarding her with a neutral an expression as he could create. "That depends on just how serious it is, whatever you claim to have seen."
Apparently that was more than Janine could bear, for she cringed again and shook her head violently. "Then I really can't tell you. It'll...it'll get me in so much trouble."
Tracey looked exasperated. "Why on earth would you think that, for Pete's sake?"
"I wish you'd just leave me alone," Janine cried, now quaking visibly. Her face and eyes grew red with the onset of tears and panic. "Stop _pushing_ me!"
Christian made a decision and got to his feet. "All right then...Katherine, Tracey, you two can go on home." They seemed startled, but neither of them protested his edict, though he thought Tracey looked as though she wanted to. He let them out, wished them a safe drive home, and locked himself in with Janine once again, this time taking the chair Tracey had sat in and laying a comforting hand on Janine's arm. "No one else has to know, Janine. You can tell me here and now, and I'll keep it in strict confidence."
"I can't," Janine protested, but more weakly now. Christian reached over to the desk and whipped a tissue out of a box that sat beside the monitor, handing it to her and waiting while she mopped her cheeks. After a moment or two she risked a peek at him and mumbled, "I don't even deserve this nice treatment..."
Christian smiled wryly. "I thought we had agreed to put that behind us when I hired you two and a half years ago."
Janine reddened visibly at that, in addition to her already-flushed features, and ducked her head while he grinned to himself for just a second. "It...it's hard not to remember that," Janine admitted low. "Though I try not to. Even more with you right here."
Christian laughed. "People have done far worse than that, you know." He resettled himself in the chair, regarding her with a more sober mien. "Janine, whatever may have happened in the past, you must understand that if you think you saw something serious that needs to be reported, then it's only right—it's imperative—that you do."
"No revenge from anybody?" Janine asked in a small voice. "Really?"
"Truly. I'm a man of my word," Christian told her. "Now tell me, please."
She nodded a few times, still dabbing at her eyes with the tissue, then slowly filled her lungs to capacity before releasing an even longer exhalation and folding her hands in her lap. She looked up to find Christian watching her expectantly. "Well, Mr. Enstad, it...it's Mr. Keller. I think...I think he's on drugs."
Christian stilled completely for about five seconds, gaping at her, before regaining enough equilibrium to urge sharply, "Explain to me just what you saw."
"It was last week, like Tracey said. I left a little early because I had a date—my boy-friend and I were going out to see a show at the Schubert Theater. But I got halfway home and I realized I forgot my cell phone in my desk, so I came all the way back to get it. I live with my grandparents, and I usually take the T and walk here from the closest station," she explained. Christian nodded, and she continued, "By the time I got back, it was past closing time, so I had to let myself in with my key. I got my phone and I was about to leave, but then I noticed the door to that back room was open a little, and I heard somebody. I thought Mr. Keller was there and I had something I wanted to ask him anyway, so I went over to do that." Her voice broke and she closed her eyes, shuddering. "I was about to ask my question when I saw him pull a needle out of his arm. It was like...like a doctor's syringe, the kind they use to vaccinate you, you know?" Again Christian nodded, encouraging her. "I was just so shocked, I couldn't move for a minute. Then Mr. Keller started to turn around, and I was so afraid he'd catch me there, I just ran. I ran right out the door and didn't even bother locking it. I didn't want him to know I saw him in there." She blew out a shaky breath and stared at Christian in appeal. "That's all I saw, but I know I saw a needle."
Christian muttered something potent in _jordiska_ and let himself go limp in the chair, considering Janine's words. It certainly sounded incriminating enough, but if Janine had been the only one to see him, how could they possibly prove anything? He grew aware that she was watching him, and he managed a smile. "All right, Janine, you can go on home now. Thank you for telling me." Looking relieved, Janine thanked him, erupted from the chair and made her escape, leaving Christian staring out the window wondering what in the world he was going to do now.
4. Chapter 4
§ § § – October 6, 2008 – Fantasy Island
By the time another weekend had come and gone, Roarke had begun to worry about Leslie. Noelle and Lauren had gotten over their stomach flu through the course of a weekend; but though Leslie had quit vomiting as frequently and violently, she seemed to retain vestiges of the illness even well after she should have gotten over it. Roarke noticed she was more fretful lately, and attributed that to Christian's absence—not to mention the fact that he had called only twice since leaving the island and, the second time at least, had said little other than that he was very busy interviewing prospective hires.
This Monday morning marked eight days since Christian's departure; the triplets had stopped asking when he would be coming home, as if they had finally understood that he had to be away for some time. Leslie, still nursing a somewhat irritable stomach, had gone home without fuss, leaving Roarke free to dispatch his numerous staff to their usual duties and a few of those he himself normally did, before going over to Rogan's greenhouse to check on any progress. He found the Irishman in the back room peering into pots filled with long, spindly herbs that sported clusters of tiny yellow-green flowers, muttering to himself in what sounded to Roarke like the Irish Gaelic he recalled hearing from his more distant relatives in times long past. "What word have you, if any?" he inquired.
Rogan glanced up for a second, then went back to squinting into the pots—or, as Roarke shortly ascertained, the flowers. "What do you know about lady's mantle?"
_"Alchemilla xanthochlora,_ known in the vernacular as 'heavenly dew', and _alchemilla mollis,_ sometimes called dewcup. They both grow wild in the interior here, and the dew that collects in the flowers has been said to have magical powers." Roarke approached the pots and studied the flowers; nearly all of them had a few dewdrops inside, thanks to the high humidity in the greenhouse. "I rarely use it, but I've added the dew to the tea of two very pregnant guests I had many years ago, to help prevent premature labor."
Rogan peered at him with interest. "Oh? Y'don't suppose it might have any conceivable use against amakarna, do you?"
"Anything is possible," Roarke allowed. "I had no idea you were growing it in here; it might be useful to collect the dew each morning. In a more mundane application, its infusion is a great aid to the female reproductive system."
Rogan made an interested noise, gently pinching a stem between his thumb and fore-finger and twisting the plant back and forth a bit. "Sounds as if I should experiment with this thing. I was talkin' with Dr. Ordoñez the other day, and he said something about how his wife has been looking for various nausea medications."
"Then it could be to your advantage to work with this. I came to ask about whatever progress you may have made in your research. I myself have gleaned little from the literature I have, but I learned enough to suggest that you may wish to work with valerian, digitalis and mistletoe. One of my sources states that amakarna had a neutralizing effect against these plants."
Rogan squinted skeptically at him. "Ye're aware that mistletoe's poisonous, uncle, I assume. So ye're sayin' amakarna can negate the stuff?"
"So it would seem. I think you should try testing it and tell me what you come up with. Meantime, I'll use the telephone in the front room and call Leslie."
"Go right ahead," murmured Rogan and returned to muttering in Irish Gaelic while Roarke went out and put the call through. When Leslie answered, he inquired as to her condition, which made her scoff in disgust.
"Nothing's changed, in case you were hoping. I really wish Christian would come home—I bet if he were here, I'd be over this by now. Anyway, what's Rogan up to, have you seen him yet?"
"Yes, in fact, I'm calling you from his greenhouse. I've suggested he work with a few plants that affect the heart, which I've learned amakarna can neutralize. It's reasonable to assume that they may have some sort of effect on the spice in return." He paused for a second or two, then queried, "Leslie, who in Christian's family is currently taking the spice?"
"Just Arnulf's daughters—Anna-Kristina, Gabriella and Margareta. Why?"
"Tell me what effects amakarna has had on them," Roarke requested.
Leslie made a contemplative noise, then said, "Oh yeah, I remember now, because Christian got so upset on their behalf when we all found out. They're all sterile; they can never bear children of their own. It was thought, at least by _jordiska_ doctors, that amakarna had affected their DNA in some way. I remember thinking at the time that that seemed like a heck of a stretch, but I suppose anything's possible with that stuff."
"I see," Roarke said slowly, making a mental note. "And has Christian enlightened you on who in his family has ever been on the spice, from the time the LiSciola clan first began selling it to them?"
"It started with his great-grandfather, King Erik XIII," Leslie said after a moment's rumination. "That's what I remember from what the current count said, that time he tried to sell Christian's soul to Mephistopheles. King Erik's only child was King Lukas VI, Christian's grandfather, and he was on it...and of course, so were Christian's father and oldest brother, the two King Arnulfs."
"And how did amakarna affect them, do you know?" Roarke asked.
"Their hearts," Leslie said. "Christian says they all died of heart problems associated with amakarna—all prematurely, except in his father's case for some reason. Father, what are you trying to get at here? I thought Marina was your guinea pig."
"She is, but if we are to have any hope of finding out how to combat the need for amakarna in ordinary earth humans, it's best to collect symptoms from those who are on the spice. It seemed logical to begin by asking about Christian's family. I'll make some inquiries along that line. Thank you for your assistance, and try to take things easy if you can. Have you been able to eat much?"
"I had some of Karina's _grömmagraut_ for breakfast this morning, and that seems to be acceptable as far as my stomach's concerned. I was surprised—it makes me think of baby food for some reason, but it tastes wonderful. No wonder my daughter's addicted to it." They laughed. "Anyway, I hope I was able to help."
"Yes, I think you've provided a good beginning for us to work with. Thank you, my child, and get some rest." They said their farewells, and Roarke hung up, thinking for a few seconds before letting Rogan know he was leaving. He had a few leads on other amakarna users; it was time to make some contacts and ask some questions.
§ § § - October 9, 2008 - Boston, Massachusetts
Janine's startling revelation was still prowling the back of Christian's mind over a week later, like a shark patrolling coastal waters, but he hadn't had time to really examine it since he'd wormed it out of her. Caught up as he had been in the vortex of the business—a very popular one with many Boston firms—he had found himself having to stay after hours to hold interviews, because he had taken on two design projects, all of Ellen Baselton's unfinished repair work, and a lucrative system-installation deal for a nearby bank branch that included maintenance and repair on a permanent basis. His employees, astonished at the burden he'd put himself under, kept asking if he needed any help; but he felt driven for some reason. He'd had no word at all from Ben Keller, and notice had come from Howard Welles' family that his heart attack had been serious enough that his doctor had decided it was best that he retire altogether. When he'd heard that, Christian had expanded store hours so that the office was open on weekends as well, in an attempt to give himself and his staff some time to catch up on the backlog. There had been no complaints, for in the bad economy of the moment, they were grateful to be working.
But Christian wasn't so immersed that he couldn't see what was going to happen to him if he didn't delegate some of his own tasks as soon as possible. What with all the work he had taken on in the office, he had to go over applications and select candidates after he'd returned to his hotel room for the night; and he hadn't been able to call Leslie except for one brief phone conversation in the middle of the previous weekend. Worry for her was lurking in the back of his brain as well, since she'd reported she still wasn't fully recovered from her bout with stomach flu and was now catering to Susanna, who had indeed managed to come down with it. Sketching out the rudiments of a website design for a client who'd contracted with the company only two days before Christian had arrived in Boston, he promised himself he would call Leslie on Sunday, and put his mind back to the task at hand.
There had been at least one bright spot on this chilly Friday morning: he had already hired on a new employee, a recent MIT grad who had been getting by on a Dunkin Donuts job since receiving his degree in June. Christian had put the young man through a series of tests after conducting his interview, and he'd been so thoroughly impressed by Morgan Sweeney's abilities that he had offered him the job on the spot, installing him at Howard Welles' desk and turning over all of Welles' remaining projects to him. It had taken some of the burden off the rest of his staff, and Morgan had been roundly welcomed by everyone.
Christian had a to-do list that he intended to tackle that very day no matter what; so he put the finishing touches on three repair projects, moved them to the table reserved for customer pickup, had Janine inform the owners that their machines were ready, and sent Andrew Hardy, Tony DiMeo and Katherine Anderson out to continue the installation job at the bank. Then he sat back, leaning the chair as far back as it would go, and took a breather, considering what he needed to do. With Keller AWOL and incommunicado, he himself was _de facto_ manager for the moment, and was handling the projects he'd taken on around calls to his other branches and consultations with his accountants, including the one here in Boston, Ian Forester. His own frantic activity, he realized as he closed his eyes, was well on the way to wearing him out. He still had to hire a replacement for Ellen, and the workload was enough to make him consider hiring an additional tech—but there was one chore he could no longer ignore. He had to track down Ben Keller; he had tried Keller's cell phone several times that week in his rare free moments, with no results.
He sat up, threw a quick glance around the office to make sure things were running smoothly, and then woke up the computer, bringing up Keller's master list of telephone numbers and emergency contacts. After swiftly entering the information Morgan Sweeney had provided when Christian had hired him, the prince shifted to Ben Keller's file and eyed the emergency contact listed there, a Rachel Keller, who lived in Watertown. There were a home number and a cell-phone number; Christian, assuming the woman was Keller's ex-wife and that she had to work, tried the cell first. He waited through three rings; then a harried-sounding female voice answered. "Hello?"
"Hello, my name is Christian Enstad, of Enstad Computer Services. Are you Mrs. Ben Keller, by any chance?" he asked.
"I was," she said sourly. "Who...oh, wait a minute—you're his boss, right?" Her voice grew deferential, and he sighed inwardly, wishing people would just treat him civilly with-out feeling forced to do so because of his station in life.
"Yes, and I haven't heard from nor seen him since I arrived here nearly two weeks ago. I was wondering if he might have contacted you, or if perhaps you know where he is or where I can reach him."
"I don't talk much with him," said Rachel Keller. "We've been divorced almost a year, and our kids are both grown, so there's not much reason to contact him. Why do you ask?"
"The last I heard," Christian said, choosing his words, "he had fallen ill suddenly, and that was just before I got into town. He seems to have disappeared, and no one has heard anything from him that I'm aware of."
"Well, I don't know...I assume you've tried his cell," Rachel said, and Christian confirmed this. "If he's sick, he could be at home in bed somewhere. Not that that helps. He doesn't have a landline—our son let me know that. You might have to go out to his place and confront him in person." She sighed. "I knew it was gonna happen one of these days. He never stops moving. He's...you know, frenetic. Can't stay still, always has to be doing something or else he gets antsy. I don't know how he does it. He used to wear me out just watching him. Anyway..." She paused a moment, then suggested, "If you can't find him at his place, then contact my son Nolan. He's in pretty regular touch with Ben." She gave Christian her son's number, and Christian thanked her and ended the call, studying Keller's information on the monitor screen. His address was listed as an apartment in Cambridge; Christian tried Keller's cell phone one more time, got nowhere again, and shook his head. It looked as if he'd have to go over there.
He arose and signaled at Ian Forester. "Ian, are you too busy for an excursion?"
Ian stood up too. "No suh, Your Highness, what can I do for you?" Ian had a Boston accent too, but his wasn't as thick as Keller's, so Christian had no trouble understanding him. "I actually just got done with last month's inventory and I could do with a walk."
Christian chuckled. "It's not going to be a walk, I'm afraid. How well do you know this city, if I might ask?"
Ian came to the desk. "Lived here all my life—born and raised, bringin' up my kids heah...this is my home and I know it like the back o'my hand, pahdon the cliché." He grinned. "Where do you want to go?"
"Ben Keller's apartment. I assume you know where this address is." He showed Ian the screen; Ian peered at it and nodded.
"Yeah...Clarendon Ave., off Broadway. That's close to the Arlington line. I can get you there, no problem. Might take a while—traffic in town is always insane."
Christian smiled a little grimly. "Whatever it takes. Thank you, Ian." He raised his voice to address the group. "Ian and I are going on an errand; I don't know how long it'll take, but with some luck we'll be back by lunchtime or a little later. I'll call if it takes longer. Janine, please file these for me and cull out some more—keep an eye out for graduates from the Massachusetts Institute of Technology. I seem to have had good luck with that."
He glanced over at Morgan Sweeney, who grinned in sheepish acknowledgment and said, "You know, Your Highness, you can just call it MIT like everybody else. It's a lot quicker and easier to say."
Christian laughed. "I'll keep that in mind, Morgan, thank you. All right, Ian, let's go."
The office was tucked into the corner of a building on a narrow roadway called Batterymarch Street, so Ian had to do some winding to get them out of Boston and across the Charles River into Cambridge. He had been right about the traffic, and Christian was glad he hadn't bothered to rent a car here. It took them most of half an hour to reach the address Keller lived at, and Ian muttered a couple of mild oaths as he searched for a place to park. It took some time, but he finally snagged one a couple of blocks away and accompanied Christian back to Keller's building. The apartment was on the second floor, so they buzzed a couple of times without a response, before Ian snorted under his breath and began buzzing other apartments till he finally hit pay dirt. An older woman with a suspicious expression on her face came to the street door and cracked it open just enough to ask, "What?"
"We're trying to find Ben Keller," Christian explained. "He lives in the second-floor flat, and we haven't seen him in almost two weeks. Do you know if he's home?"
The woman had been squinting at him as he spoke, and now recognition registered in her features, softening them considerably. "Oh...you're the prince with the computer business in the Financial District, aren'tcha? Keller work for you or somethin'?"
"Yes, he's my office manager," said Christian. "Is he at home? Have you seen him?"
The woman grew thoughtful. "Well, come t'think of it, there was an ambulance here a couple weekends ago. Sunday night, I think. Don't know who they took out, but it coulda been your guy. Might wanna start with Symmes Hospital over in Arlington—that's the nearest one to here."
Ian and Christian both thanked her and returned to Ian's car; it was a surprisingly straightforward trip to the hospital and took no more than ten minutes. It was Christian's notoriety as a prince that got them answers again, for the nurse at the admissions desk told him, "Yeah—as a matter of fact, his son's here now, visiting him. I'll call for you."
"Wonder what happened to Ben?" Ian mused idly. "It's weird to have him out sick—he was never sick before this. In fact..." He looked at Christian with some envy. "He was always so disgustingly healthy. Me, I get wasted by a damn cold."
Christian laughed, though without much humor. "If we're fortunate, we'll have an explanation soon."
The nurse turned to them. "Mr. Keller's son told me to send you both up. He's on the fourth floor." She gave them directions to the elevator and Keller's room.
A young man who couldn't be much past his twenty-fifth birthday or so met them at the door to the room in question; he was muscular and looked as if he played football or boxed. "Mr. Forester, hi," he said, shaking hands with Ian, then peering at Christian with some trepidation. "Hello, sir..."
"Just call me Mr. Enstad," Christian suggested, seizing the chance to dispense with the honorific that normally came with his title. "You must be Ben's son."
The young man nodded, accepting Christian's handshake. "Nolan Keller," he said. "Uh, you can come in if you want...but my dad isn't awake. Actually, he's been in a coma since they brought him here ten days ago."
"Crap," said Ian with great surprise. "That musta been some wicked bad case of...of whatever he's got. How's he look, Nolan?"
"Not good," Nolan said frankly. "C'mon in and take a look for yourselves." He led the two men into the room, and Christian stopped short for a second, taken quite off guard by the sight before him. The figure in the bed was attached to several IV lines and a couple of machines, one of which was clearly a heart monitor; Ben Keller looked like a scarecrow, his emaciated form sallow and his hair sparse and dull. His closed eyes seemed sunken, and his breathing was a little raspy. For some reason the sound poked Christian hard in the deeper recesses of his memory, but try though he might, he couldn't make a connection. He frowned, drifting toward the bed, unable to keep from staring at the man lying in it.
"Damn," Ian breathed from beside him. "Nolan, I'm sorry."
Nolan sighed wearily. "He's been like this ever since they brought him in. I come in every day and talk to him, just in case he wakes up, but he hasn't moved. Well, I mean, the nurses move him to keep him from getting bedsores, you know, but he doesn't move on his own." He stared helplessly at Christian, who had been watching him. "I hadn't seen him in a couple months—my schedule's crazy—but he didn't look nearly this bad. Not even a hint." He caught himself. "Well, I mean...he was too skinny actually, but he was in good health. Said he'd never felt better in his life."
"What did they find in his system that could be pinpointed as a cause?" Christian asked, wishing his memory would quit ringing bells to doors he couldn't open. He knew there had to be a connection there somewhere, but it just wouldn't surface.
"That's just it—nothing," Nolan exclaimed, throwing his hands in the air in a helpless gesture. "Nothing at all! His system was clean! Whaddaya make of that?"
Ian shrugged; Christian racked his brain, to no avail, and finally gave up with a sigh. "I'm trying to figure out why this seems familiar, but I can't just yet. However...there's something I think needs investigating. Nolan, do you have a key to your father's flat? With your permission, I'd like to get a look around."
Nolan shrugged agreeably. "Sure, we can go over there right now if you want, Mr. Enstad. I probably need to muck out Dad's kitchen anyway." He grinned weakly, and Ian and Christian chuckled and accompanied him out, Christian casting one last glance back at the shrunken form of Ben Keller as they went.
5. Chapter 5
§ § § – October 9, 2008 – Boston, Massachusetts
Back in Cambridge, Nolan buzzed them in through the same woman who had spoken with Christian earlier. She turned out to be the landlady, and looked aghast when they told her what had happened. "Hope they can help him over there," she said. "Go on up and do whatever you gotta do. Good luck." She patted Nolan's shoulder and watched them climb the stairs before retreating.
In Keller's apartment, they detected a faint but definite odor of food in the process of spoiling, and Nolan groaned. "That's what I thought. Mr. Enstad, I, uh...what were you thinking you might find around here?"
"I have a hunch," Christian said. "If I may, I'd like to get a look around."
"Go ahead," said Nolan. "I figure if you find anything, it might help them bring my dad back to health."
Ian decided to lend Nolan a hand in the kitchen, so Christian wandered through the flat alone. It was sparsely furnished, but the detritus of a long married existence spilled over onto everything: table surfaces, furniture, even the floor. The few shelves were overloaded with books and DVDs; three stacks of CDs teetered on a windowsill; magazines and newspapers were scattered over it all like jimmies on a doughnut; and everything bore a dusty film, as though it hadn't been touched in much longer than the ten days Keller had been in the hospital. Christian tried to imagine how much junk Keller must have had to cart over to this little place from the house he'd probably once shared with his ex-wife, and shook his head, hoping he and Leslie never acquired that much but wryly suspecting they might someday. He made a point of skipping the bathroom after no more than a glance inside; it was an unholy mess, and he wanted nothing to do with it unless Keller's son was there.
He felt even less comfortable with breaching the bedroom, which was in as bad shape as the rest of the place. The unmade bed lacked a spread; the pillows were smashed against the headboard, making Christian think for some reason of squashed insects; and books and papers covered the small tables that flanked the bed. Clothes lay in haphazardly folded piles on the bed, the dresser and the chest of drawers; the closet door stood ajar and contained a lot of empty hangers. There was a peculiar odor in the room that made Christian wrinkle his nose with distaste. He wanted to back out, but instead flipped on the ceiling light and began to gingerly explore the room. Slowly he allowed himself more leeway, peering under piles of clothing at first, then examining the interior of the closet. The books and papers offered no clues either. The smell in the room grew more pervasive when Christian made his way toward the far wall, where a clothes hamper reposed. It was full, and turned out to be the source of the odor. Making another face, the prince set aside two more messy stacks of CDs on the wide sill so he could open the window for a bit.
As he reached for the frame to shove it up, his hand brushed against an opaque black plastic container, half hidden behind the curtain, that toppled over and fell to the floor with a thud; Christian heard the slosh of liquid inside, and stared at it for a moment before forgetting the window and even the smell to pick it up. He shook it experimentally, but only the sloshing sound greeted him. He hesitated a long moment before unscrewing the cap and cautiously sniffing the contents; he detected a peculiar sweetish odor, but because of the color of the container, he couldn't really see what was inside.
He could hear Ian and Nolan in the kitchen, reminding him abruptly that he wasn't alone. He screwed the cap tightly back onto the container and went straight to the kitchen, where Nolan and Ian looked around in surprise. "Find anything?" Ian asked.
Wordlessly Christian raised the container; they stared at it for a few long moments before Nolan questioned, "Where was that?"
"In the bedroom, sitting on the windowsill. Is there something I can use to pour out a little of what's inside?" Christian asked.
Nolan poked in cabinets and finally extracted a shot glass; Christian cleared dirty plates aside on the table and swept a pile of old _Boston Globe_s off a chair with one hand, heedless of where they landed. He twisted the cap off again and carefully poured out a small amount of the liquid into the shot glass. The sweet odor, almost like soda, wafted around his head as he poured; the stuff collecting in the glass was very dark in color.
"What in hell is that?" Nolan demanded in disbelief.
Something tickled Christian's memory again, and he caught his breath, thinking back on all the clues he'd been gathering since he'd arrived. Keller was running a second business and trying to start up a third; he had a lot of energy and never seemed tired; he'd lost a shocking amount of weight and was now in the hospital; the doctors had found nothing in his system... It hit Christian then, and he hissed a quick string of ugly _jordiska_ curses that made Nolan and Ian trade glances.
"What's wrong, Your Highness?" Ian asked.
Christian closed his eyes and shook his head. "This substance is a drug called black lightning—and I'm sorry, Nolan, but I truly believe your father is hooked on it."
§ § § - October 10, 2008 - Fantasy Island
It was early enough on Saturday morning that Roarke and a still-queasy Leslie had just seen their guests off into their fantasies when the desk phone rang. Roarke answered; surprise crossed his features and he said aloud, "Christian?" Leslie's head snapped up.
"Yes, she's right here," Roarke said. "One moment." He handed the phone to his eager daughter, whose face had lit the moment he'd said her husband's name.
"Christian?" she exclaimed. "Where've you been all week?"
"I'm so sorry, my Rose," he said, and she could hear in his voice that he truly meant it. "If I told you what's been going on here, I'm not sure you'd believe it. I've had to take on my share of the backlog at the office here, and atop that I needed to find Ben Keller—which I did. To shorten this very long story, he's in the hospital because it appears he's a long-term user of black lightning."
Leslie gasped. "Are you serious?" She shot Roarke a look and hastily pressed the button that would put Christian on the speakerphone. "How on earth did you find out?"
She and Roarke listened in shock while Christian told them about his investigations. "We've just left Keller's flat and we're on the way to the hospital. Before we left, however, we went through the bathroom, and Keller's son found three or four syringes. There was a small collection of prescription medicines in the cabinet as well, and we took them all, just in case any of them have anything to do with Keller's current condition. But I strongly suspect black lightning is the sole culprit. I would ask your father for the antidote, if he happens to have any on hand and can send it here via overnight express."
"Well, I don't know...it's been quite a while since we needed it," Leslie said slowly, staring at Roarke, remembering a guest named Shara Foster who had visited the island with her cousin and sisters and turned out also to be an addict. "Father...?"
"The last time I needed it was twelve years ago, yes," Roarke confirmed, "and it has a shelf life. But simply shipping out a supply of the antidote may not be the full answer. For one thing, we're lacking some information. Do you know how long Mr. Keller has been using the drug? That has strong bearing on the effectiveness of the antidote."
"Does it?" Christian said, sounding startled. "One moment, Mr. Roarke." They could hear his voice, a bit muffled, asking questions; it wasn't long before he was back on. "Keller's son tells me he wasn't aware his father was using _any_ kind of drug. In any case, I need answers, and the only way we can get them is if Keller awakens. He's in a coma."
Roarke was silent for a moment before he met Leslie's gaze; they were both thinking the same thing. "We woke up Shara Foster the same night she collapsed," Leslie said aloud, "remember, Father?"
"Yes, and she had been on the drug for approximately three years, as she told us," he said, for Christian's benefit. "How long has Mr. Keller been in his current condition?"
"Since the day I arrived here," Christian said. "Janine picked me up at Logan when I was expecting Keller to do it, and told me he had called her and said he was too sick. He must have collapsed not very long thereafter, since it's my understanding that he was taken to the hospital that same night."
"You may be able to make educated guesses at some of the answers we need if you ask Mr. Keller's son a few questions," Roarke said.
"I'm afraid I don't know what I should ask," Christian protested.
"Leave that to me. Before you do, tell me whether you personally have ever noticed anything about Ben Keller that would fit the signs of one addicted to black lightning."
Christian sighed audibly into the phone before speaking. "Nothing that struck me as unusual, although now that I look back, I recall Keller telling me during our first-ever meeting that he had operated several businesses around the Boston area and was looking to work for me in particular. I recall him as appearing fit and trim back then, and I remember thinking he was quite forward, very eager, almost...almost capsizing the boat in his zeal to get started on the whole idea."
"Capsizing what boat?" Leslie put in.
Christian laughed. "Forgive me—I translated one of our slang phrases. It means that he wanted so badly to begin carrying out his plans that he could barely be restrained from leaping ahead with it and perhaps doing something rash."
"We'd say 'champing at the bit'," Leslie said, "but I see what you're getting at. So in other words, it looked like he had a lot of get-up-and-go."
"Get up and...?" Christian began.
Leslie rolled her eyes and said through a laugh, "Energy, my love. Well, that _is_ one sign, but that doesn't necessarily mean he was on it then."
"I'm not an expert," Christian said. "I met him only that one time there, and then not so long thereafter when I was ready to begin hiring the staff. He still seemed the same at the time, and if he had changed at all, it was too subtle for me to notice."
"Very well then...ask Mr. Keller's son if his father has always been as energetic as he appeared to be to you," Roarke instructed. "And if not, how long he has been so."
They heard Christian relay the question, and a moment later he delivered the reply: "He says he can recall his father being less active when he was a child, up till about the time he reached his mid-teens or so. Then he had much more energy and enthusiasm, was always restless and trying to find something else to do. He became a workaholic, as I believe the word goes, and there were quite a few occasions when Nolan says his father was holding down two jobs at once without breaking stride." He paused, and they heard a fainter voice adding something in the background. "Oh, and Nolan tells me he has never before seen his father sick—this is the first time ever that he knows of."
"Interesting," Roarke mused. "What about Mr. Keller's sleep habits?"
"He apparently doesn't seem to need to sleep more than three or four hours a night," Christian passed on Nolan Keller's response. "And Nolan says he can recall that within a couple of months after his father gained all that extra energy, there was visible weight loss. It sounds to me like a classic case of black-lightning addiction."
"Ask Nolan how long ago he first noticed this. As exactly as possible," said Leslie.
Christian's pause was broken by a muffled oath in _jordiska_ before he told them, "He says it's been just about ten years. He's twenty-four now and says he had just begun high school when all this became noticeable."
"Ten years!" blurted Leslie, staring at Roarke, who wore an uncharacteristic look of utter surprise. "Is that average, Father?"
"It's extraordinary," Roarke said, letting his amazement show in his voice. "By all rights, Ben Keller should have long since perished of the addiction. The drug draws on the body's deepest, innermost reserves to provide the extra energy, and that reserve cannot last forever. On the average it takes approximately four years—less for some. Mr. Keller's is a most unusual case indeed." He paused for a second or two. "I'll have to make up a fresh batch of the antidote, Christian, but I'll see to it that it goes out on the very next charter and leave explicit instructions that it be delivered to you overnight. Will you be at your office?"
"Yes, I've had to open on weekends—including Sundays—to give us all a chance to try to catch up on the work that my two missing employees left behind. I'll give you the Batterymarch Street address." Leslie grabbed a pen and notepad, and wrote down the infor-mation as Christian dictated it. "And now that I know what I know, I'm deeply sorry again, Leslie, my Rose, but it looks as if I'll have to hire a temporary manager to keep the place going until Keller can return to work, if that's possible. Which, damn everything, will extend my timetable another week. I'm sorry."
Leslie blew out a breath. "Well," she said, trying to put a good face on it, "it's already been almost two weeks since you left, so that's something. Just take care of yourself, and we promise the antidote will be on its way in a couple of hours at the most."
Once they had broken contact, she stared at Roarke. "Ten years! Do you think Keller will actually bounce back from that?"
Roarke folded his hands in front of him on the desktop, his expression grim. "I don't know, Leslie. Only time will tell." He focused on her and arose. "If you'll handle things for me here, I'll go and prepare the antidote."
Leslie watched him depart the room, wondering what progress Rogan and Marina might have made on their own research. _Research and...whatever else they call it. Dare we call it a cure?_ She sighed and hoped that the extra time Christian was away would give them a little better chance of coming across something, but she wasn't very optimistic.
Roarke got the antidote on the next charter as promised, then took Leslie with him to the B&B and around back to the greenhouse. This time Marina was in the back room with Rogan, while Lucan sat beneath the table containing the amakarna plants, shooting marbles with the unprocessed seeds that Rogan was just now harvesting. Leslie laughed. "Hey, that's a great way to kill the boredom." She glanced up and focused on Marina, who smiled. "Hi, Marina, how are you?"
"Hello, Leslie. We could be better. I don't want to insult you, but you don't look as well as you should either."
"Oh, it's just this stupid stomach flu that won't let up. I don't throw up every day though, so maybe I'm coming out of it. I take it this is your son."
"Yes, that's Lucan. He and Rogan's son have become friends, and they seem to have a lot of fun together even though Rory's so much older."
"I think Rory likes the idea of being a big brother," Rogan commented, pulling the last amakarna seed off its parent plant and squatting to round up the loose seeds that Lucan was playing with. "I presume you've come over here to see what progress we've made."
"Yes, do you have anything at all?" Roarke asked.
Rogan straightened up and grinned. "For a change, we've good news, uncle. You were right about the standoff between amakarna on the one side and digitalis, valerian and even mistletoe on the other. I'm amazed, really. It's funny how in small doses, those three herbs are beneficial for the heart...Marina was more than willing to try each one of them, and they all work, but..." He caught himself and his expression shifted. "Unfortunately, none of them have a permanent effect. Within a couple of days, she goes back to needing the spice again. What have _you_ learned, then?"
"That, among earth humans on the spice, the affected systems follow a very strict pattern with no exceptions that I've discovered. In men, amakarna affects the cardiovascular system, specifically the heart itself; in women, it's the reproductive system, most particularly the ovaries. I have asked those users whom I've contacted to try to find others and to get this information from them; if we are to have any success with this project, we must reach as many people as we can."
"There're always exceptions to every rule," Rogan mused, "and I'm sure we'll hear from some of them eventually. But it seems so far that if we can bring this line of work to fruition, we should be able to help the majority of people on the stuff. So what works on women, then? We've found the best plants for the heart, let's see what would be good for the reproductive system."
Leslie and Marina looked at each other, and Marina leaned over, tilting her head, to peer at Rogan. "Oh, that I know. I've worked with those herbs myself for years—I think it was the only way I was able to conceive and bear Lucan." Roarke and Rogan turned to her expectantly, and she glanced past Rogan into the main section of the greenhouse. "We will need yarrow—pink or white, it doesn't matter which. We can also try the stems of a plant called waterpepper, and there's the essential oil from rue. They all helped me, I think."
Leslie's mind started to run. "You took all those things while you were trying to get pregnant?" she asked.
"At different times, yes," said Marina. "Why?"
Leslie thought a little, half aware of everyone's attention on her. "And I guess you tried each of those heart medicines in succession," she murmured. "Yet you said they worked only a couple of days at a time."
"What're you getting at?" Rogan pressed her.
Leslie looked up at her cousin. "Why don't you try using all of them in the same solution, at the same time? It sounds to me like each one has some potential on its own, but not quite enough. If you combine them, maybe their aggregate strength will be enough to do the trick." Rogan's mouth dropped open; Roarke smiled with gentle pride, and even Marina looked impressed. "Hey, it's worth a try, isn't it?"
"Why didn't I think of that? Maybe you have something there!" Rogan burst out, as excited as Leslie had ever seen him.
"Perhaps it would work the same way with the herbs for the reproductive system," Marina added; Rogan's enthusiasm seemed to be contagious. "I'll help you gather the items we need, Rogan, and we'll distill the essences so that they can be soluble in a liquid."
"Don't forget the dewdrops from the lady's myrtle," Roarke offered. "As I said, I have had occasion to use them only twice, but they didn't fail me."
"Right," Rogan said, already on his way into the main room of the greenhouse. "I just happen to have all those plants here, actually, thanks to all the experimental tisanes Dr. Ordoñez' wife was asking after." He strode into the room with Marina flitting after him, and Roarke and Leslie looked at each other.
"Very good thinking, my child," Roarke said, grasping her shoulder. "As for you—I think it's time you went to your doctor. You've been dealing with this stomach flu entirely too long, and sooner or later I'll need you in a fantasy—thus we can't have you rushing off to the bathroom at an inopportune moment. I'm sure Dr. Lambert will be able to find a medication that will help you recover once and for all."
"Okay, okay. I suppose you want me to go today," Leslie pretended to grumble. In truth, she'd been considering the idea herself for a while, since both Lauren and Noelle had long since gotten back to normal from their own rounds with the illness and were as good as new. "But since it hasn't been that long since we sent the guests off, I think you have the time to spare to come with me."
Roarke chuckled. "Very well, if only to see that you actually go to Dr. Lambert's office. However, I'll have to drop you off there, as I have some appointments on the other side of the island that cannot be missed. I'm sure Dr. Lambert will be able to help."
"I hope so. I'm just sick and tired of the constant queasiness, and I'm especially fed up with Mariki's badgering. You know," she remarked as she accompanied Roarke out of the greenhouse and to the rover, "sometimes I think she doesn't believe it when I get sick, and she just picks on me for something to break the tedium." She grinned when Roarke laughed, and found herself looking forward to talking with her doctor.
6. Chapter 6
§ § § - October 11, 2008 - Boston, Massachusetts
The package arrived special delivery for Christian at his office, and he accepted it with relieved thanks. By now his entire staff here knew what had happened to Ben Keller, since Christian had found it necessary to quell a few rumors circulating among them and thought it was best that they know the truth. He had managed to hire a replacement tech for Ellen Baselton during the afternoon; Roger Wong—another MIT graduate—was due to begin work on Monday.
Christian kept the office open this Saturday till five, then sent everyone except Ian Forester home for the night and prevailed upon him to go over to the hospital in Arlington for another visit to Keller's room. They had by this time gained an anxious ally in Keller's son, who insisted on coming with them; so they waited till he met them at the office before going out to the parking garage and taking Ian's car to Arlington.
On the way there, Christian opened the package and found inside a note from Leslie, which read: _Hi, my love, here's the antidote. If it works, please let us know. Father made up only enough for one dose, because he's so low on the supply of some of the ingredients and will need time to collect more. But he isn't sure even fresh antidote will be successful, only because of the length of time Keller's been on that drug. So Father's very interested in the results. Call as soon as you can—I love you! Love, Leslie._
He smiled at the note, folded it and slipped it into an inside pocket of his suit jacket; then he lifted out one of Roarke's signature mini-decanters, made of ornate lead crystal in a complex raised-relief design with a matching stopper that had an overly large knob. The liquid inside was pale gold in color and completely filled the bottle; Roarke had sealed it so that it wouldn't spill or leak in transit, and as Christian tilted the little jar, he wondered whether Roarke expected him to use the entire contents. Considering how long Keller had evidently been using black lightning, he presumed they'd have to.
He pocketed the decanter as Ian pulled into the hospital parking lot, and Nolan got them in with no trouble at all. "Did you get the stuff for Dad, Mr. Enstad?" he asked once they were in the elevator.
Christian nodded. "My father-in-law sent it overnight." He withdrew the decanter and examined the contents again, then looked wryly at his companions. "So tell me, do we get a nurse, tell her the truth of our suspicions, and have her administer the antidote...or do we try to figure out how to sneak it into one of his IV tubes?"
Nolan and Ian grinned tentatively at each other, clearly both hoping Christian was joking; their smiles died when they realized he was waiting expectantly. Nolan shrugged. "Well, unless one of us knows how to fill up and connect an IV bag, maybe we oughta find a nurse and explain to her what the stuff is and what it's for."
"This is one time your fame might come in handy, Your Highness," Ian added.
"Ach, please don't even mention that," Christian groaned, making them chuckle as the elevator reached the fourth floor and the doors slid open. "Although you have a point; some things are unavoidable, it seems."
There was a nurse in Keller's room when they came in, just changing out an empty IV bag for a full one. "Excuse me...before you put that new one in, could you administer this stuff to my dad?" Nolan asked her, pointing at the decanter Christian held.
The nurse squinted suspiciously at it. "What is it?"
"It's a medicine," Christian explained. "My father-in-law sent it specifically for this patient, and the sooner we administer it, the better. There's a rare and particular something wrong with this man, which has no hope of resolution other than this."
The nurse recognized him, but held her ground nonetheless. "Prince Christian, I'll have to ask you to explain more fully. We can't just give him some kind of mysterious medicine on your say-so alone, or even his son's."
Nolan caught Christian's frown and blurted out with a trace of desperation in his voice, "We figured out my dad's been using that drug black lightning, and this is the only thing that'll get him out of his coma."
The nurse stared at him, then at Christian, who nodded once or twice. She threw Nolan another skeptical look, then reached for the chart on the clipboard that hung on the wall near Keller's bed. "Let me review the details," she muttered.
"Go ahead," Nolan said, "but I'm the one who answered all the doctor's questions when my dad was first brought in. It's all there. The weight loss, the complete exhaustion, the whole thing."
The nurse read the chart at least twice by Christian's calculation; then she looked up, heaved a long sigh and replaced the clipboard. "I'd better get Mr. Keller's doctor." She left the room, and Christian snorted impatiently and dropped the decanter back into his pocket, letting himself stare at Keller openly for the first time since they'd arrived. He looked as if he hadn't moved at all since the previous day; now that the nurse had departed and they were waiting in silence, Christian noticed the raspy quality of Keller's breathing again. He looked at Nolan and asked, "Do you hear that?"
Nolan followed Christian's gaze as the prince returned it to Keller, tipped his head slightly and listened, then frowned. "That doesn't sound good. He wasn't breathing like that when he was first admitted."
"Does he have asthma or some other sort of respiratory illness?" Christian asked.
"No...he's perfectly healthy. Or at least he was, before this happened." Nolan snapped his mouth shut as the nurse returned with a doctor, a woman some years older than Christian whose hair was mostly gray and whose face bore an intricate network of lifelines, but was kindly. She recognized Christian and nodded deferentially; he nodded back.
"You have some sort of...special medication for Mr. Keller, I hear?" she asked.
Christian displayed the decanter again and explained what it was and why he wanted to administer it. When the doctor heard the words "black lightning", she scowled so fiercely that he did a slight double take. "That crap," she muttered.
"You're familiar with it?" Christian asked, astonished.
The doctor nodded grimly, then backtracked. "Well, I wouldn't say _familiar,_ exactly, but I've had a little experience. I dealt with a case of black-lightning overdose about ten or eleven years ago. It was long enough ago that I didn't remember it well enough off the top of my head to associate Mr. Keller's condition with it. But now that you mention the drug, it all fits." She eyed Keller. "Not that I've ever seen anyone who looked as...as wasted away as he does. But yes, let's give him this antidote." Christian gave her the decanter; she peered at it, commented on the jar, then enlisted the nurse's help in finding a syringe big enough to hold the full contents. The three men watched the doctor fill the syringe and then inject the golden liquid into a vein on Keller's right arm.
"How long will it take to kick in?" Nolan asked.
Everyone looked at Christian, who shrugged. "I don't know. I'm told that the fact he's been on the drug for some ten years may affect the potency of the antidote."
"Ten years? My overdose case had been on the stuff for only two or three, I think," the doctor said, staring at Keller in amazement. "I've seen enough info on black lightning to know that ten years is probably unheard of for length of usage."
They waited for a few minutes; the doctor sent the nurse back on her rounds, but otherwise no one spoke. The sound of Keller's breathing filled the air; the doctor read over the chart again, but said nothing about it. Christian wondered how long Keller had been sounding like that.
Then there came a weak moan from the bed, galvanizing them; Nolan grabbed his father's hand. "Dad? It's me, Nolan. Wake up, Dad."
Ben Keller groaned again in response; then his eyes fluttered open and he stared at Nolan, then at Ian, then finally at Christian, upon which they widened. "Yaw Highness," he managed, in no more than a hoarse whisper. "Wasn't expecting you heah."
"You may recall sending for me," Christian reminded him dryly. "Ben, we know what happened to you. Nolan filled us in on some things, and I found a little incriminating evi-dence. Just how long have you been using black lightning?"
Shock registered in Keller's eyes and he closed them again, despair settling over his pale face. "Little ovah ten yee-ahs. I had to. I needed it."
"For what?" Christian pressed him, consciously moderating his voice.
Keller winced; the doctor straightened and peered at Christian with a jaundiced eye. "Your Highness, he may be awake and lucid, but he's very weak. I wouldn't push him if I were you, no matter how urgent this may be."
"Doc, I gotta tell him," Keller insisted in his rough whisper. "Lemme do it while I can." He shifted his gaze to Christian without waiting for the doctor's consent. "I needed a second job aftah my kids stahtid high school. But it was takin' a lot outta me, so I needed a boostah, some kinda energy source. They-uh was a guy outta Southie who had access to it—I went to school with 'im. Sawr 'im at somebody's birthday pahty and we got to talkin'. I told 'im what I was doin', and he gave me a sample o'the drug. Really did the trick. Had energy to burn, y'know? I was nevah sick, so this just made me feel even bettah."
"How did you pay for it?" Christian wanted to know. "It's quite expensive."
"I was gettin' good deals for yee-ahs, but f'some reason the supply got scarce and the prices went up. That's when I first came to you about stahtin' a branch of yaw computer-repay-uh business. Knew it was a real moneymakah and I wouldn't hafta worry about findin' the cash to pay faw the drug. But my source kept hikin' the rate, and I hadda staht a second business...and a third just a few weeks ago." He closed his eyes again and tried to shake his head, but succeeded only in a few feeble movements back and forth. "I guess it all musta caught up to me."
"More than you know," Christian told him. "You may be a unique case; even my father-in-law was shocked when he heard how long you've been on it. I think he'd like to know how you managed all these years before finally succumbing to the complete drain of your last energy reserves."
"I dunno," Keller whispered. His breathing seemed to have gotten louder; he sounded a little like Darth Vader, Christian found himself thinking. "All's I know is, I'm in heah. Aw, Doc..." He began to gasp. "Doc, I can't—I can't breathe!"
"Dad, hang on!" Nolan urged frantically, while the doctor punched the call button and Keller closed his eyes again, dragging air into his lungs like a long-unused bellows. Once more Christian was visited with the sense that he'd seen this before, had gone through this same experience—and when the rasp of Keller's breathing hit a new and higher volume, it struck him exactly what and when. His father had sounded like this in the last two days before his death, sucking in air with all his concentration, barely able to speak.
"Keller, you take amakarna, don't you?" Christian exploded.
They all gaped at him, then stared at Keller, whose exhausted features had filled with pure resignation. Since it was all he could do just to obtain oxygen, he gave one weak nod and shut his eyes yet again.
Fury and anguish boiled up inside Christian and he turned away from the bed, his head hanging, his ears roaring. _The stupidity,_ he thought in disbelief, _the sheer stupid futility of it. Why, why, __why__?_ He left the room, stumbling a little, trying to find a place he could be alone long enough to collect himself and at last settling for a stall in the men's room, where he silently cursed the fates.
7. Chapter 7
§ § § - October 12, 2008 - Fantasy Island
Leslie was still lying awake in the bed in her old room when her cell phone struck up the chorus to one of her favorite 80s songs. The sound startled her and she twitched in the bed before leaning off the mattress, grabbing her purse and pulling the phone out of the special pocket where she kept it. The ID told her it was Christian. "Hi, my love," she said.
"Leslie...I wish to fate you were here," he said, in a tortured voice she hadn't heard him use for quite a few years. "Right this minute I need you."
"What's wrong?" she exclaimed in alarm.
"This afternoon...this evening...I learned some things I wish I never had to know," he muttered, making her frown in bewilderment. "I've been sitting here in the men's room at a hospital near Boston for the last hour, because I'm not fit to face people. So I had to be..." His voice broke and he tried again. "I had to be tracked down to be informed that Ben Keller died about fifteen minutes ago."
Leslie gasped loudly. "Ohmigod, Christian, oh no," she breathed. "That's such a shame...but why do you sound so broken up over it?"
"Because it was amakarna that killed him," Christian told her, his voice now flat but shaky with his effort at control. "He was put on amakarna in his infancy. No one had any idea, including his son, and I have no idea how on earth he kept it a secret for so long. And I...I realized it because...because his breathing was loud and labored—just as my father's was in his last days. If they do an autopsy, and I suspect they will, they'll find traces of the spice in his heart, as with my father and grandfather." He fell silent while Leslie goggled at the wall, in that numb moment of shock before the avalanche of full acceptance; then he spat, _"Amakarna!"_ and she flinched. "That damn spice! How I loathe it!"
Leslie crammed a fist against her lips, closed her eyes and rocked back and forth in her seated position in the bed. In that moment she wanted so desperately to tell Christian about Rogan and Marina's research that she felt crushed under the weight of her promise to Roarke that she wouldn't. Only when Christian called her name did she dare respond. "I'm here, my love. Oh, I can't believe this..." She swallowed thickly. "Christian, my love, didn't the antidote work?"
"Yes, it did," he assured her. "It woke him up long enough for him to answer my questions about his addiction to black lightning. But his breathing began to get exponentially worse, and I finally remembered where I'd encountered that before—with my father, as I said. He had been breathing like that last night when my accountant here brought me in to see him. I just couldn't recall why I was feeling déjà vu, till it got so bad in Keller's last moments. And that's when I knew he took the spice too."
"I'd tell Father, but he's still out, and I decided to go to bed a little early. I wasn't asleep, though." She had a good reason for not being asleep, but she wasn't ready to tell anyone, not even her husband. "But I'll let him know when he gets in. Oh, Christian, I'm so sorry. What a shock. I guess you'll be there even longer now."
"Possibly. I did at least hire two new techs, and since now it seems I'll be here long enough to attend Keller's funeral, all I can do is promise that I'll try my best to find a new manager in the time we're waiting while the arrangements are made. I've been considering taking on an extra technician, but I haven't made a final decision on that yet. As badly as this place needs a manager, I feel guilty about arranging for a replacement so quickly."
"You can't help it, my love," Leslie said, feeling her own guilt again for leaving Christian out of the loop on the research issue. "I...I just wish you didn't feel as if you have to vet every single new hire, in every branch. With your offices so far-flung, it's just incredibly inconvenient for you to personally screen and hire all your employees."
"My darling, you know I've always been like that," he said. "It's just one of my quirks, I'm afraid. But I'll go to all the lengths I can to get them hired as soon as possible. I'm more than ready to come home, especially now, but I can't."
Her throat began to close and the backs of her eyes to sting. "I wish you could come home right now myself. I still don't feel that great, but at least I've been to the doctor and she gave me something for the nausea." She bit her lip before she revealed any more, terrified of his reaction when he was already under enough strain.
"Good, my Rose, I'm glad to hear that. Tell me, how are the children?"
It was almost a relief to turn to something more lighthearted as she updated him on the triplets' antics and other mundane matters. They shared a few chuckles; then Christian let out a sigh and said, "Well, all right, I guess I'd better get myself together and face the world once more. Thank fate, it really helped me to talk to you. When I have more news, I'll call again. Sleep well, my Rose, and I love you."
"I love you too, my darling," she said, and he murmured a goodnight and ended the call in his characteristic blunt way. She dropped the phone, cursed sharply and slammed a fist onto the mattress, and then burst into tears.
§ § §
In the morning she met Roarke at breakfast, with the triplets, after a fitful night's sleep. He studied her curiously as she got the children settled at the table; when she took her own chair, he inquired, "How did you sleep, Leslie?"
"Not that well," she admitted, knowing from long experience the futility of trying to put one over on her father once he'd taken note of something.
"You didn't tell me what happened at Dr. Lambert's office yesterday," Roarke commented, helping Tobias put some fruit on his plate.
A hot-and-cold feeling swept through Leslie from head to toe and back again, like reverberating ripples in a pond, but she managed to sound dismissive. "Oh, she just heard me out and gave me some nausea medication, and told me to come back in a month if I wasn't feeling any better." It was a partial prevarication; she had her reasons for it. "That's all there was to it." She pulled in a breath and changed the subject before Roarke could attempt further pursuit. "Christian called last night, late."
"Oh? What news did he have?" asked Roarke, now filling his own plate.
Leslie winced. "Well, for one thing...Ben Keller died."
That stilled Roarke completely; he stared at Leslie in astonishment. "Indeed! I am sure it came as quite a shock to Christian."
"More than you know." She told Roarke what Christian had told her, and when she revealed that Christian had deduced that Keller was on amakarna, Roarke closed his eyes for just a second, then shook his head and set down his plate.
"A double tragedy," he said softly. "And it explains why he was able to tolerate black lightning for so long. It would have boosted his health to an optimum level so that he could use the drug for longer than most addicts, although even at that, I am still impressed at the sheer length of time he took it." He focused on Leslie. "Presumably that sets back Christian's expected arrival home even farther."
She nodded glumly. "He said he's already hired the two replacements he needed for the other employees, but now he has to find a new manager, and he's thinking of taking on an extra worker too. Oh, Father, he was so upset about the reason for Keller's death...I wanted to tell him about Rogan and Marina's project so badly."
"Not until there are concrete results, Leslie," Roarke warned her. "Especially now, in light of Mr. Keller's decease, I see no need to inform Christian unless we have a favorable outcome. You'll say nothing until then."
"I know...I won't," she agreed reluctantly. "I just don't like it, that's all."
Roarke smiled. "I understand completely, my child, but it's best this way. Now, if Dr. Lambert's medication is working, I suggest you have some breakfast; it will be a busy day."
He was right, and Leslie's enforced running around and tending to the demands of her father's business kept her mind distracted for the most part. The weekend passed with no further incident, except just after supper on Sunday. The fantasies had been brought to a close and Roarke was tending to paperwork, while Leslie sorted through the mail. At that point there was a knock, and Leslie looked up in surprise while Roarke called, "Come in."
Their visitor was Michiko, whom Leslie hadn't seen since the Hollywood-musical fantasy in which she had participated. "Come on in and sit down," Leslie urged, her mood lightening considerably. "I'm really glad to see you."
"Good...now I feel less guilty about intruding on you at this hour," Michiko said with a wan smile. Leslie grinned back and set the envelopes on the tea table as Michiko sank into a chair. Roarke glanced up at them with a small smile and returned to his work. "I finally decided I needed to let it out, like Mr. Roarke advised me to a few weeks ago. Mostly I procrastinated because I kept telling myself there wasn't any hope."
"Hope for what?" Leslie asked.
"For this relationship." Michiko drew in a breath. "I swear I don't understand it at all. It should never have happened to me, only a couple of months after Errico's death. It makes me feel as if I'm just discarding his memory and moving right along."
Leslie recalled Michiko's mood after she'd been released from her role in Mitchell Reardon's fantasy, and Reardon's wistful longing for a certain blonde chorus girl as he departed that Monday morning. "Then it's just what I was thinking...you and Mitchell Reardon started falling in love that weekend, didn't you?"
Michiko hung her head, nodding it a little in desolation. "That's why I said I kept telling myself it was best this way. He has no clue at all who I really am, and I shouldn't even be thinking of falling for someone else when I'm still in mourning for Errico...and especially when Cat and I are still barely speaking. She already thinks Errico's death is my fault, and she refuses to forgive me for making her leave Arcolos. I'd never get her blessing for another relationship. I need to mend fences with my daughter before I can consider anything else, in any case. I know it—I know what I'm doing is the best thing for us all. But I have dreams at night, now and then. Mitch was everything I once daydreamed about in a love interest, and it was such a beautiful weekend."
For the first time Roarke spoke from his desk. "Michiko, has it not occurred to you that perhaps you are merely idealizing this man? You're right to be cautious, and you have many reasons for it—in addition to those you stated, there is also the fact that you had a mere two days of companionship, and under your circumstances you could hardly expect to build a solid, lasting relationship on such a meager base."
"Don't think that hasn't occurred to me too, Mr. Roarke," Michiko assured him. "But the ugly truth is that those feelings and dreams just refuse to go away." She ran both hands through her hair, despair engulfing her even as Leslie watched. "My life's fallen apart in just the space of a few months. My husband's dead, my daughter hates me, and my life has no purpose. If I'd...if I had died along with Errico, at least Cat could have stayed in Arcolos and grown up under her brother's protection. Sometimes I think that's what she wants."
"Michiko, stop thinking like that," said Leslie angrily. "Fine, so Errico's gone, and maybe that means you have to stay within certain societal parameters, especially someone as well-known as you. But that doesn't mean you don't deserve a life of your own, to lead as you please; and besides, you can't control the machinations of love. Love does what it wants, when it wants. The problem is..." She hesitated, her voice softening. "Father's right. You've got an awful dilemma here. You're getting the worst of it, too—Mitchell Reardon thinks he just had a quick romance with someone from the past, and he'll move on. It's as you said, he wouldn't have the least idea it was you, Queen Michiko of Arcolos, that he was really falling for, instead of a struggling, anonymous chorus girl in a 1940s movie."
"And as harsh as it sounds," Roarke added, not without sympathy, "you may very well find that Mr. Reardon would have fallen readily for the chorus girl, but not at all for the queen of Arcolos."
Michiko's face crumpled and she nodded again, looking beaten. "I know," she mumbled, barely audibly. "I know it, but I guess I had to be made to see it for myself. I...I have other things to resolve anyway, more important things."
"Never give up hope, Michiko," Roarke advised gently. "One day things may be different, and by then perhaps you will have regained your equilibrium. Until then, however, as you said, you have more immediate concerns. I wish you luck."
"Thank you, Mr. Roarke. Thank you both." Michiko pushed herself to her feet, took a deep breath and let her head fall back. "At least my house is about half finished, and the builders think they might get done ahead of schedule after all, so that's one thing in my life that's going right. I just wish I knew what to do about Cat."
"Cat's a stubborn kid," Leslie remarked with a wry grin. "Not to mention that she's probably used to getting her way just because she's royalty. She gets that from Errico. It might be better after your house is done and you two move in; then she'll have a room of her own and all her own things around her again, and it might give her enough of a sense of security to start rebuilding the bridge. So hang in there."
Michiko smiled as Leslie accompanied her to the inner-foyer door. "I'll keep that in mind. Thank you, Leslie...I knew I came to the right place."
The two friends hugged each other, and Leslie whispered, "And who knows—maybe someday Mitchell Reardon will be back, looking for that chorus girl." They snickered softly, then bid each other good night.
October 17, 2008
By the end of the week there was extremely good news from Rogan and Marina: after taking three doses of their latest infusion—which turned out to be mixed in a base solution of liquid chlorophyll—Marina had stopped using amakarna and so far had been doing fine for three days. "Look here," Rogan said, displaying a plain glass carafe of greenish liquid at them. "Chlorophyll normally is very unstable as a liquid and has to be produced as a powder so it doesn't get rancid and unusable—but I performed just a touch of the clan magic on it, so that it will remain stable, palatable and easily mixed with other liquids. No, Leslie, you aren't allowed to ask me what." He winked at the face Leslie made at him, and they both grinned. "We consulted a bit with Julie too, and she got in touch with her sister Delphine, and between them and the lore they unearthed, we have all the ingredients in the proper proportions. All we need do now is test it. It turns out, after all the experimenting I did with that green stuff Marina's been taking instead of the full spice, that it's a chlorophyll analogue, just as I thought, uncle."
"Chlorophyll?" Leslie said, amazed. "I didn't realize you could take it straight. I mean, I know we eat it all the time whenever we have green salads, but there can't be a whole lot of the stuff in there, or else nobody would need amakarna."
"Aye, that's good thinking. There's enough in three doses to equal a week's worth of large salads that include dark-green leaves, as opposed to simple lettuce. Between that and the plant tisanes we've extracted, we may just have something here. If Marina can go at least a full ten days without showing any deterioration, then I think it'll be safe to say she's cured of the need for the spice. You know it takes only five or six days at the most before the lack of the spice begins to take a toll on the body, uncle."
Roarke nodded. "That's how it averages out, yes. Some take longer, in some it begins sooner. However, I suggest giving the trial fifteen days. After that time has elapsed, all traces of the spice should be cleansed from the body, and if Marina is still in perfect health, we can pronounce the cure a success."
Leslie eyed them but said nothing; as if Roarke sensed something, he turned to her. "You have an objection?"
"No, but I'd like to point out one thing. Marina's part of the LiSciola clan—one of your people, you two. What about plain old run-of-the-mill human beings? Do you think it'll work on them too?"
Roarke gave Rogan a look, and Rogan sighed. "That's part of the problem. We don't have any handy human test subjects. Where do we find them?"
"Volunteers, I suppose," Leslie said. "I imagine there'd be no shortage of those."
Before either Rogan or Roarke could comment, her cell phone began singing, and she started. "I'll take it in the front room. Excuse me." She hurried out as far as the entrance to the greenhouse before answering what turned out to be a call from Christian. "Hi, my love, anything to report?"
"Thank the fates, yes...good news at last. The sad news first: Ben's funeral is to be held tomorrow, so I'm closing the office for the day so that everyone can attend. And that includes—here's the good news—my new manager and one more computer-repair technician. To tell the truth, when I saw Ben's condition in the hospital last week, I knew I would need at least a temporary replacement, so I had already been going through applications. That allowed me to cull out the best ones and conduct my interviews, and I made my choice just yesterday. The manager begins Saturday; I'm going to have the staff show her the ropes, as I've filled her in on whatever I do that's unique to my business methods. That means I'll be on a plane tomorrow night, my Rose, and you can expect to pick me up at the plane dock on the first charter Sunday morning."
"Oh good," Leslie blurted, relief and happiness washing through her—along with a touch of trepidation. She still hadn't told anyone her secret, for she was determined that Christian be the first to hear about it. She needed his reaction, and the comfort of having shared the burden with the most precious person in her life, before she could tell anyone else. "I can't wait to see you. There's a lot of news."
"Is there? Then I look forward to hearing it—but you know the first thing I want to do is be with you. I love you, my Rose—I'm afraid I need to go, there are still a lot of things I have to tie up before I can leave here with a clear conscience. Give the children my love, will you? Oh yes, and are you feeling all right?"
"Pretty much. I'll tell you about it when you get home. I love you too..."
"I know, my Rose. I'll see you soon." He hung up before she could respond, and she had to laugh. It was just so like Christian to steer clear of prolonged goodbyes.
She returned to the back room to find Rogan and Roarke discussing the issue of human volunteers for the untried amakarna cure. "You know, there's something else we haven't touched on yet," she said when there was a break in their conversation. "The cure for the addictive aspect of the stuff, namely. What about that?"
Rogan actually glared at her. "That, you _had_ to bring up, didn't you? This is what worries me about the cure." He scowled at the contents of the carafe he still held. "It so happens that the best cure I've ever found for addictive agents, at least in the clans, is thornapple, or more properly, alkaloids derived from it. It works in earth humans too, but the problem with it is that it's dangerous: it's both poisonous and hallucinogenic. That's the major risk any volunteer would have to face in testing this stuff."
"So the question is, do those on amakarna feel the risk is worth it?" Roarke said softly, glancing back and forth between Rogan and Leslie. "That's what we'll have to discover by sheer chance. How much did you need to add to the cure, Rogan?"
"Enough to make it scary for earth humans," Rogan told him solemnly. "It takes a bit more to be effective with our people, uncle, so that makes it just the more dangerous to them. When you put out the call for volunteers, you'll have to emphasize the drawbacks."
"We have no choice," Roarke said, straightening and gaining a quietly determined look. "Come, Leslie, we need to get the word out."
"Father," she said when they reached the main house, "I've been thinking...maybe I myself should ask Christian's nieces. I mean...we still haven't brought Christian into the loop, and I'm afraid of what he'll do when we finally let him in on it. If I e-mail his nieces, they can make the decision on their own, without any influence from him."
"You're likely to place a great burden indeed on your husband with this news," said Roarke sagely, "but perhaps it's best that we tell him. Yes, go ahead and inform his nieces of the need for test subjects for the cure. But, as Rogan said, make certain to delineate the risk factor very clearly. Only they can decide whether they feel it's worth it."
Leslie nodded and settled down at the computer, thinking nervously that Christian was going to have a burden on him in any case, no matter whether they ultimately told him about the potential cure or not. She swallowed back her trepidation and began drafting an e-mail message for Anna-Kristina, Gabriella and Margareta.
8. Chapter 8
§ § § - October 19, 2008
Leslie's stomach slalomed with a potent mixture of anticipation and dread as she stood at the plane dock Sunday morning, waiting for the eight-o'clock charter to arrive. She had considered waking the children and bringing them with her, but they had been sound asleep when she left and she didn't have the heart to wake them up. As the drone of the seaplane hit her ears and she watched it soar overhead, preparatory to landing, she began to wish, just a little, that she had brought them after all. Her nausea was returning, but it was due as much to nerves as to her lingering condition.
She was determined to tell her husband, no matter what happened. _ It's only fair that he know,_ she reminded herself. _After all, that's why you won't let on to anybody else. You need to know what he'll say, what he'll do—and not just about that, but about his nieces too. Oh, Christian, my love, I hope you won't hate me..._ She made a face at herself for this last absurd thought, but she still wasn't certain she would like his response to what she had to tell him.
The low sputtering of the charter's engine grew louder and she saw the craft round the bend in the lagoon, on its last approach to the dock. The more she watched, the more her gut somersaulted, and in the end she simply couldn't hold back anymore and plunged through the nearest bushes, where she lost what little was in her stomach—mostly acid. Her mouth burned as she spat out the last of it, and she stood for a moment breathing hard, wishing she had thought to bring something with her to settle the physical malaise. But she knew it was as much from nerves as illness. In the end, she gave in and pushed back into the clearing, surprising a few passengers who were crossing the grass as she came out. She smiled sheepishly at them and shifted her gaze to the hatch; her timing was perfect, for Christian was just now climbing out, laptop case in one hand.
He spotted her almost instantly. "Leslie!" he called out, and even from where she stood, she saw his face light up. She had to smile; despite her enormous trepidation, she was happy in the end that he was home, and returned his hard hug in kind, burying her face in his shoulder and breathing him in.
"Ah, my Rose," he murmured, nuzzling her hair. "What a relief to be home."
She wondered how relieved he would feel once he heard what she had to say, but she held her tongue for the moment, clinging to him. After a few more seconds he asked, "Are you all right, my darling? You haven't said a word."
"Don't kiss me," she muttered thickly into his shoulder. "I just threw up."
_"Herregud,"_ he said and laughed. "That's a hell of a welcome home." But his amusement died when she lifted her head and he saw the tears in her eyes. "What's this? Leslie, my Rose, what in the world is wrong? I thought you'd be happy to see me."
"I _am_ happy to see you," she said, sniffling a little. "It's just...I've got some news, and it's a real doozy. Both of them."
Christian loosened his hold on her and studied her face, his own growing concerned. "I'm not sure what a 'doozy' is, but from the look on your face, I suspect it's going to have quite an impact. Am I going to like this news?"
Leslie winced and ducked her head. "That's the problem—I don't know. But I have to tell you, here and now. You deserve to know." She opened her mouth to spill her secret, and at the last second balked. _Chicken!_ her inner voice taunted. She told it to shut up, and forced herself to look her husband directly in the eye, opting for the easier of the two pieces of news she had. "Well, first of all...there may, just may, be a cure for amakarna dependence. That's why Father and Rogan went to Italy."
He stared at her, frozen in place, for so long that she almost laughed. Before she could question him, though, he blinked and jutted his head forward, almost knocking her forehead with his chin. "A _cure_, you say? For the need for _amakarna?"_ His voice rose so high with incredulity that he sounded like a teenager just entering puberty.
"Well, we're hoping so. Father and Rogan had to have guinea pigs for it, so...well, they brought Marina back with them."
"Marina _LiSciola?"_ he yelped, shocked, and she nodded. He squeezed his eyes shut, gave his head a couple of sharp shakes, and drilled her with an ominous stare. "All right, Leslie, you'd better explain this whole thing to me."
She did so, taking comfort from the fact that he continued to hold her and that his expression grew more and more intrigued and hopeful as she talked. When she paused for a moment to catch her breath, he slowly began to shake his head. _"Herregud. _ I truly never thought such a thing would come to pass. If only Grandfather and Father and even Arnulf could have been with us to see this..."
Leslie cleared her throat, and the eagles with the seven-foot wingspans roared to life in her already queasy stomach once again. "Well, that's the catch, I'm afraid. It's still in the test stage; Marina's just started the trial period I told you about. The problem is that the cure also contains alkaloids from thornapple, to treat the addictive property of the spice...and Rogan said he had to put in a little more than was strictly safe, because of the needs of the clans. That might be more than a human can tolerate."
"And why would that be? What precisely is thornapple?" Christian asked.
"It's an herb that's used in medicine, in small quantities, to treat addiction, among other things. But it...it's a hallucinogenic, and it's poisonous to boot."
Christian muttered a curse in his own tongue and sighed. "It always has to be something, doesn't it. I don't suppose you've managed to find volunteers who are willing to take the risk for the chance of being freed from that damned spice."
Leslie nodded, taking a deep breath. "Yes, we did..." Her gaze skittered away from his as she said softly, "Gabriella volunteered."
His entire body twitched, stiffened, froze; he seized her upper arms and gaped at her. "You told my nieces about this? No, no, no—I won't allow it."
"It's too late," she said, a little frantic. "Gabriella's already on her way here from Lilla Jordsö. Christian, please, you're hurting me!"
It was as if he hadn't heard her. "Leslie Enstad, so help me, I refuse to let you use one of my nieces as a guinea pig when, first of all, no one yet knows whether the stuff will even work, and secondly, it may well be fatal! When Briella gets here, I'll lay down the law to her. She's not to be given that...that...whatever Rogan's brewed up. I simply won't take that chance, and that's the end of it."
"Christian," Leslie cried, and he suddenly saw what he was doing to her and let her go, hugging her hard and apologizing. "My love," she ventured, relaxing slightly, "you know you're going to get an argument from Briella when she gets here and you tell her that. She's of age, you know—she can decide these things for herself."
"I don't care," he muttered, and she could hear the stubbornness and that implacable imperial note in his voice. _Let Gabriella fight it out with him,_ she thought, for she had her own worries. He rocked her back and forth slightly for a few more seconds, then paused a moment before drawing back with a loud sigh and driving a hand through his dark hair, leaving it in disarray. "What else should I know?" he muttered rhetorically, lifting the laptop case he had put down when he first hugged her and going for the two suitcases that the dock attendants had delivered. "I can't imagine there could be any other news that would affect me as this did."
"Oh, I can," she mumbled to herself, watching him collect his luggage.
He had taken a few steps toward the rover waiting nearby before he realized she hadn't moved, and he stopped and turned to see her with her arms wrapped around her stomach. "Leslie, damn it, if there's more, you'd better tell me," he warned, unconsciously issuing a royal command.
She burst into sobs. "I'm pregnant!"
* * *
><p><em>How's that for some year-end bombshells? There will be more in January, so keep watching this space (or your e-mail for story alerts, LOL)...<em>
End file.
| fanfiction |
struct Pixel {
unsigned char r;
unsigned char g;
unsigned char b;
bool error;
// Constructing a Pixel.
Pixel(unsigned char, unsigned char, unsigned char);
Pixel();
// Summing the values in a Pixel.
int sum();
// Checking equality between pixels.
bool equals(Pixel);
bool operator==(Pixel);
// Getting the distance between two pixels.
int distance(Pixel);
// Getting the average between two pixels;
Pixel average(Pixel);
};
// Out of three pixels, check for the two pixels that are closest and choose
// the average of those two as the result.
Pixel choosePixel(Pixel, Pixel, Pixel);
#endif
| slim_pajama |
Smoke cobweb formations?
One day, my mom decides to light the house on fire, and after we put the fire out, all of the cobwebs in the house are black. Obviously, this is because of the smoke. Later, some renovations guy tells her something about how the cobwebs aren't really cobwebs and when a house fills with smoke, there is some weird chemical formation that makes a black cobweb-like-substance that just happens to show up right where cobwebs would be. Basically, the guy told my mom that those black cobwebs were chemical formations from smoke instead of cobwebs that became black after being in smoke. My mom will not believe me when I say that the renovations guy is wrong and they were obviously cobwebs. I ask her "What happened to the cobwebs we already had?" and "Why would a renovations guy know that it is a smoke formation if there are cobwebs in every house?"
I can't prove to my mom that she's wrong, so I'm asking a bunch of chemistry people to confirm that smoke doesn't stick to walls and form cobwebs.
Awkward. It just so happens that the renovations guy is right. The term you need to google is "[smokeweb](https://www.google.com.au/webhp?hl=en#hl=en-AU&q=smokewebs)".
The ionisation process of burning (particularly) synthetic materials like plastics, rubbers and polymers, creates charged smoke particles which can attract towards certain surfaces, and attract to each other creating chains, and ultimately web-like formations. They form under certain conditions called wet smoke, which involves low heat, or smoldering type environments. Smoke webs are typically sticky and pungent and will smudge easily and show up in particular areas where there is limited air flows, typically corners and edges of ceilings, in curtain folds, cabinets etc.
Spider webs will burn up very quickly in a real fire.
| stackexchange/chemistry |
WIN WIN
Written by
Tom McCarthy
EXT. WATCHUNG RESERVATION - DAWN.
It's a bitter cold January morning. The woods are quiet.
Desolate. In the far off distance a man is jogging. He banks
around the end of a small pond and runs right at us. This is
MIKE FLAHERTY, FORTY-TWO. He is running hard. Or at least as
hard as he can.
Suddenly TWO JOGGERS blow past him.
INT. HOUSE, BEDROOM - SAME.
A HOME MADE STAIN GLASS ANGEL hangs on a window. It falls to
the ground.
ABBY FLAHERTY, SIX-YEARS OLD, stirs and gets out of her bed
out. She picks up the Bird and inspects it. It's broken.
ABBY
Shit.
INT. HOUSE, BEDROOM - LATER.
JACKIE FLAHERTY, THIRTY-SEVEN is still sleeping. Abby walks
into the room. Jackie opens her eyes.
ABBY
(WHISPERS)
Mommy, can we play croquet today?
Jackie lifts Abby onto the bed.
ABBY (CONT'D)
Where's Daddy?
JACKIE
He's running.
ABBY
From what?
Jackie smiles.
INT. MIKE AND JACKIE'S HOUSE, BEDROOM - LATER.
STELLA, TWO YEARS OLD is standing up in her crib crying. Mike
comes in and picks her up.
MIKE
OK. OK. Hi there.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 2
INT. MIKE AND JACKIE'S HOUSE, KITCHEN - LATER.
Jackie prepares some food. She knocks a glass over into the
sink and it breaks.
JACKIE
Shit.
She looks over at Abby who is immersed in her coloring. Then
she sets the food down in front of Stella who is sitting in a
high chair. Mike enters wearing a suit and tie.
JACKIE (CONT'D)
How was the run?
MIKE JACKIE
Good. It was good. Abby, finish your cereal.
JACKIE (CONT'D)
(TO MIKE)
I'm very impressed with you keeping
it up.
Mike shrugs and takes a yogurt from the refrigerator.
ABBY
I don't like it.
JACKIE
You do too, so stop drawing and
eat.
MIKE ABBY
What brand is this? Daddy, look. It's your team.
JACKIE (CONT'D)
They're all the same.
Mike looks at the drawing. It looks nothing like a team.
MIKE
That's my team? That's great,
honey. Are they winning?
ABBY
Yeah.
JACKIE
Maybe you should show the team.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 3
CONTINUED:
Abby knocks over a glass of water. It spills onto the
drawing.
ABBY
Shit.
JACKIE
Honey, you can't use that word.
It's a bad word.
Off Mike's look.
JACKIE (CONT'D)
What? Don't look at me.
MIKE
Uh huh. Bye sweetie.
He kisses Abby.
ABBY MIKE
Bye daddy. Bye.
JACKIE
Hey. You OK?
MIKE
Yeah.
JACKIE
You sure?
MIKE
Yeah. I'm good. Why?
JACKIE
Just checking.
MIKE
OK. Bye guy's.
ABBY
Can I have more juice?
Mike leaves. Jackie is not convinced.
JACKIE
Just a minute.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 4
EXT. MIKE AND JACKIE'S HOUSE - LATER.
Mike walks outside toward his car. He opens the car door.
JACKIE
Mike?
Mike turns. Jackie is standing at the door.
JACKIE (CONT'D)
Did you call Fenn about the tree?
PAUL
No. I will today.
JACKIE
Please do. I don't want it coming
down on the house.
Mike looks at a VERY DEAD TREE in the side yard.
MIKE
Yeah. You're right. I will.
JACKIE
Mike?
MIKE
Yeah?
JACKIE
I love you.
MIKE
I love you too, sweetie. Bye.
Jackie shuts the door. Mike looks up at the tree.
MIKE (CONT'D)
Shit.
INT. DUNKIN' DONUTS - LATER.
Mike pays for his coffee and bagel and starts to leave. He
nods to a group of FIVE OLD MEN who wave him over. He tries
to keep moving but they continue to engage him. Finally he
joins the table. The group shares a laugh.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 5
EXT. MIKE'S OFFICE - LATER.
Mike's car pulls into a driveway of an OLD HOUSE that has
been converted into TWO OFFICES.
A SIGN on the lawn reads: "MICHAEL S. FLAHERTY, COUNSELOR AT
LAW" and "STEPHEN VIGMAN, CPA"
EXT. MIKE'S OFFICE, PARKING LOT - CONTINUOUS.
Mike parks his car as a WORKMAN walks up from the basement of
the house and gets into his VAN and pulls away.
Mike gets out of his car and walks toward the back door
carrying his briefcase. He stops at the basement steps.
MIKE
Vig?
VOICE
Down here.
Mike walks down the stairs.
INT. MIKE'S OFFICE, BASEMENT - CONTINUOUS.
It's an old, musty basement filled with endless shelves of
files.
MIKE
What's up, Vig?
VIGMAN
Donna's out sick and can't find
anything without her. It sucks.
STEPHEN VIGMAN, FIFTY, emerges carrying some files.
MIKE
Who was that guy?
VIGMAN
Oh, that sucks more. He's the
plumber. I called him to look at
that piece of crap of boiler.
Vigman points to an ANCIENT HOT WATER BOILER.
MIKE
Why?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 6
CONTINUED:
VIGMAN
That clanking is driving me nuts.
Can't you hear it down in your
office?
MIKE
Yeah. I just figured it's old.
VIGMAN
Well it is but he took one look at
it and said we should replace it
before it blows.
MIKE
What?! We just had it fixed three
months ago.
VIGMAN
Yeah, he said that job was crap.
The guy did crap work. Can you
believe that? That little scumbag!
MIKE VIGMAN
Jesus. All they care about is
getting paid. Makes me sick.
No one wants to do the work
anymore.
MIKE
How much to fix it, Vig? Did he
say?
VIGMAN
Six grand to replace everything.
MIKE
Holy shit.
VIGMAN
Tell me about it. I gotta be
honest, Mike, it's not a good time
for me. My business is off and my
step son wants to get Lasik.
MIKE
Really? Isn't he too young?
VIGMAN
I don't really care at this point.
If it makes him happy, he can have
it. I get nothing from that kid.
(MORE)
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 7
CONTINUED:
VIGMAN (CONT'D)
Nothing. He has an unnatural
attachment to his father.
MIKE
Right. So what do you want to do?
VIGMAN
Well I was thinking we could leave
it for now and just cover the file
cabinets in plastic to be safe. How
about you?
MIKE
Yeah. I guess I'm good with that.
CLANK. CLANK. CLANK. The boiler barks. They both jump.
VIGMAN
Let's get out of here before it
blows. I'll pick some up plastic
before practice.
They both hurry back up the stairs.
INT. MIKE'S OFFICE - LATER
Mike walks into his office. SHELLY, the receptionist, is at
her computer working. She's mid-20s and pure Jersey.
MIKE
Hey Shelly, How you doing?
SHELLY
I'm a little hung over and my
boyfriend's a moron.
MIKE
Oh. Sorry to hear that.
SHELLY
How'd the team do last night?
MIKE
We lost.
SHELLY
Bummer. Your noon canceled so you
just have a 10:30 and 3pm.
MIKE
OK. Anything else?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 8
CONTINUED:
SHELLY
The toilet isn't flushing again.
Should I just call someone this
time?
MIKE
No. I'll take a look at it. Who do
I have at ten-thirty?
SHELLY
(APOLOGETICALLY)
Frank.
MIKE
Great.
INT. MIKE'S OFFICE - LATER.
Mike is sitting with FRANK, an elderly man, jotting notes.
MIKE
And you think your son stole it?
FRANK
Yeah. I know he did.
MIKE
Why would he steal your cat, Frank?
FRANK
He's jealous of her. Very jealous.
INT. MIKE'S OFFICE - LATER
Mike is on his phone as he cleans his keyboard.
MIKE
I understand but that's my fee for
that particular service. Uh huh.
Right. Well maybe I can adjust that
a little bit.
INT. MIKE'S OFFICE - LATER
Mike is eating lunch at his desk. He hears a noise and looks
out the back window and see's Vigman pulling a LARGE ROLL OF
PLASTIC TARP out of the trunk of his car.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 9
INT. MIKE'S OFFICE, BATHROOM - LATER
Mike, on his knees, plunges the broken toilet.
INT. MIKE'S OFFICE - LATER
Mike is sitting with LEO POPLAR, 82 and his HOME HEALTH AID,
JOLIE, FORTY-FIVE and AFRICAN AMERICAN.
MIKE
Well Leo, remember you got lost and
the police had to help you a few
times. That's why we brought Jolie
into help you, right?
LEO
So now what happens?
MIKE
Well if that Judge deems you
incapacitated then you will need a
guardian. And if we can't find your
daughter then the state...
LEO
She can't find herself.
MIKE
OK but if we can't find her then
the State will have to become your
guardian.
LEO
Who's the state?
MIKE
You know...the state...of New
Jersey.
LEO
That's crazy. I don't need New
Jersey's help. I got Jolie now. And
there's no funny business between
us so you know.
MIKE
Right. I'm sure there's not. Let's
just first see if we can find your
daughter and then we'll go from
there.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 10
INT. SHELLY'S OFFICE.
SHELLY flips through some DOCUMENTS. The boiler sounds off.
CLANK CLANK CLANK. She jumps. She picks up the documents and
walks into Mike's office setting the documents down.
SHELLY
Am I still hung over or is that
noise getting louder?
MIKE
You're probably still hung over.
What's that?
SHELLY
Leo's financial statements. He's
loaded, huh?
MIKE
Yes, he is. You find his daughter?
SHELLY
No. That lady is gone and doesn't
want to be found.
MIKE
Crap.
Mike takes the STATEMENTS and puts them in LEO'S FILE.
SHELLY
Can't the state just leave him in
his home? That's what the guy
wants.
MIKE
They could but they never will.
It's too much work. They'll
probably move him into Oak Knoll.
Hand me one of their brochures?
Shelly grabs an OAK KNOLL BROCHURE from a stack.
SHELLY
But he has Jolie now. She can
handle it.
MIKE
No, she can't. His guardian still
has to make every single decision.
It's the difference between a baby
sitter and a parent.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 11
CONTINUED:
She hands it to Mike who takes it and paper clips in on the
inside of Leo's file.
SHELLY
I wish I could do it. I could use
an extra 1,500 bucks a month.
MIKE
$1,500. Is that what it is?
SHELLY
Yeah. It's in his file.
(Answering the phone)
Mike Flaherty's office.
Mike opens Leo's file.
INT. NEW PROVIDENCE HIGHSCHOOL GYM, THE PIT - LATER.
Mike and Vigman are coaching wrestling practice at the public
highschool. They are in the small, dingy back gym just off
the main gymnasium. This is a no-frills program.
The team of 12 WRESTLERS are doing a spinning drill. Vigman
holds up a singlet.
VIGMAN
Whose singlet is this? What did I
say about leaving them around?
A WRESTLER runs over and Vig flings it at him.
EXT. WATCHUNG RESERVATION - EARLY MORNING.
Mike and TERRY DELFINO are running. Terry is the same age as
Mike but dressed in a better gear. They are both breathing
hard.
TERRY
How's the team doing?
MIKE
Not good.
TERRY
What the hell happened? We used to
be good.
MIKE
Yeah, well we're not anymore.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 12
CONTINUED:
TERRY
Can we walk for a bit?
MIKE
Yeah.
They both stop. Terry is completely winded.
TERRY
That sucked. You're running good,
buddy. Kicking my ass.
Terry's blackberry beeps. He takes it out and reads it.
MIKE
Yeah. I've been getting out here a
bit more often.
TERRY
You gotta be kidding me.
MIKE
What?
TERRY
Lori's texting me at seven in the
morning to ask me if I want an
antique sewing table that we bought
together.
MIKE
Do you?
TERRY
No. I want my fucking house back!
MIKE
Is she still with that guy?
TERRY
You mean my contractor? The guy I
hired? Yeah, she is. I can just
picture that little scumbag walking
around my house wearing his tool
belt. Here.
He hands Mike his blackberry.
TERRY (CONT'D)
Take a picture for me.
Terry pulls down his pants and moons Mike.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 13
CONTINUED:
TERRY MIKE
Take it! Jesus, Ter!
TERRY (CONT'D)
Hurry! It's cold.
Mike takes the picture. Terry takes the blackberry back.
MIKE
Don't send it.
TERRY
Too late. I hate her.
They start to walk.
MIKE
Maybe you should move back into the
city? Get a new job. Shake it up a
bit.
TERRY
Nah. Finley called me. He's
starting up a new fund out here in
May so I'm gonna wait for that.
MIKE
That guy's starting another fund?
TERRY
Yeah. He's an animal. He prints
money. Come on, let's finish
strong.
Terry starts to run. Mike follows. After about thirty feet,
Mike pulls up. He's breathing is labored.
MIKE
Hold up!
TERRY
What?
MIKE
Just...hold up.
Mike is really breathing hard now. He's making some funny
noises.
TERRY
You alright?
Mike just holds up a hand. He can't really speak.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 14
CONTINUED:
TERRY (CONT'D) MIKE
Mike, what the fuck? What's (Barely audible)
wrong? Yeah. Fine. I just...
He drops to a knee. He's not alright.
TERRY (CONT'D)
Holy fuck! Mike? Hang on pal.
Terry takes out his black berry but immediately fumbles it
into the wet mud.
TERRY (CONT'D)
Fuck! Fuck!
He grabs it and shakes it out but it's dead.
TERRY (CONT'D)
You gotta be kidding me. Shit.
Mike is still wheezing. Terry turns his attention.
TERRY (CONT'D)
Is it your heart, buddy? Are you
having a heart attack?
MIKE
No! I'm not having a heart attack!
I just...can't breathe...
TERRY
That could be a heart attack, Mike.
You should lie down.
Terry tries to help him but it's only seems to annoy Mike.
MIKE TERRY
Get off me! Just lie down.
MIKE
No! It's wet. I don't want to lie
down.
TERRY
Who cares? You might be dying. Are
you cold? Do you feel cold?
MIKE
Yeah. I'm lying on the ground.
TERRY
Look into my eyes, Mike. Look into
my eyes.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 15
CONTINUED:
They are now engaged in a weird wrestling match.
WOMAN (O.S.)
Are you alright?
Terry looks to see TWO FORTY YEAR OLD WOMEN in jogging gear
staring at them.
EXT. PARKING LOT - LATER
An ambulance pulls away revealing Mike and Terry sitting in
the open back of Terry's LEXUS SUV.
TERRY
OK dude, how long has that been
happening?
MIKE
Couple of months. The doctor says
it's stress.
TERRY
Seriously? Did he prescribe
anything for you?
MIKE
Yeah. Jogging. Why the hell you
think I'm doing this?
TERRY
Jesus. That scared the shit out of
me. What are you so stressed about,
Mike?
MIKE
(SHEEPISH)
I don't know. Work. Money.
Everything.
TERRY
Is it that bad?
MIKE
Yeah. It is. I don't know how much
longer I can keep my practice
going.
TERRY
Really? Holy shit, Mike! What're
you gonna do?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 16
CONTINUED:
MIKE
I have no frickin' idea. I've been
trying everything.
TERRY
Have you told Jackie?
MIKE
Not yet. I don't want to freak her
out.
TERRY
Good call. So we just need a new
strategy, that's all. What about
that Judge that's always throwing
work your way? Can't she help you
out?
MIKE
Judge Lee, yeah. If it wasn't for
her I'd probably be out of business
already. I just need more.
TERRY
Is there anything else you can do
for money?
MIKE
What the hell am I gonna do?
Bartend? I'm a lawyer, Ter. I
practice law.
MIKE (CONT'D) TERRY
And it's not like I'm some I know.
scumbag. I help old people
for Christ sake. No offense
but your pal, Finley doesn't
give a crap about anything
but making money.
TERRY
Yeah. But that's why he makes it.
MIKE
No shit, Ter. Thanks for the
update.
INT. MIKE'S OFFICE - NIGHT
The office is dark aside from Mike's desk light. Shelly is
gone. Mike's blackberry rings.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 17
CONTINUED:
MIKE
Hi, honey. I'm still at the office.
Yeah. I came back after practice,
I'll be home in a bit.
(Checking his blackberry)
Oh, hey, let me go, Jack. I've been
waiting for this call. Bye.
Mike hangs up the phone and answers his blackberry.
MIKE (CONT'D)
Hey Tom. Thanks for getting back to
me. I'm good. I'm good. Yeah, I was
just following up to see if you had
any overflow. It's been a slow
month on this end and I was...
Mike listens. The news from Dunleavy isn't good.
MIKE (CONT'D)
Oh. OK. No, yeah of course. I
appreciate that. Thanks, Tom. Bye.
Mike hangs up the phone and sits at his desk. After a moment,
he slams his hand on the desk. And then something catches his
eye. It's LEO POPLAR'S FILE. He opens the file and see's the
PAMPHLET FOR OAK KNOLL. He flips through the file and lands
on a particular page and a particular line item.
Monthly Commission: $1,508.00.
EXT. UNION COUNTY COURT HOUSE - DAY
Mike walks with Leo Poplar up the steps of the courthouse.
INT. UNION COUNTY COURT HOUSE , SECURITY DESK - LATER.
Leo walks through the metal detector. Mike watches him and
then walks through himself but something beeps. The guards
stops Mike. Leo starts to wander away.
MIKE
Hey, Leo. Leo hold on!
(to the Guard)
Can you stop him, please?
INT. UNION COUNTY COURT HOUSE, COURTROOM - LATER.
It's a very drab, no frills courtroom. JUDGE LEE is seated on
the bench looking over some documents.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 18
CONTINUED:
Mike is sitting next Leo. Seated at the next table is STU
THATCHER, ATTORNEY FOR THE OFFICE OF PUBLIC GUARDIAN. Mike is
tapping his pen.
JUDGE LEE
Any word from his daughter? Mr.
Flaherty?
MIKE
Oh..no, Your Honor. I have the two
certified letters returned
unclaimed. And there is no phone
number for her. We can't find her.
JUDGE LEE
And she is the only living family,
is that correct?
MIKE
Yes, your Honor, she is. But Mr.
Poplar hasn't seen her for over
twenty years.
LEO
Who?
MIKE
Your daughter.
LEO
She's late? She's probably at the
store buying some crap or
something.
MIKE
OK.
Mike turns back to the Judge and shrugs.
JUDGE LEE
OK, then as, Mr. Poplar has been
deemed incapacitated by this court,
I'm appointing the Office of Public
Guardian to serve as the guardian
for his person and property. Do you
have the order for me to sign, Mr.
Thatcher?
THATCHER
Yes, I do, Your Honor.
JUDGE LEE
Then please approach.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 19
CONTINUED:
Thatcher stands and takes out the order. Mike's wheels are
spinning. He seizes his moment.
MIKE
Your Honor, if it pleases the
Court.
JUDGE LEE
Yes, Mr. Flaherty?
MIKE
I would be willing to serve as Mr.
Poplar's guardian.
THATCHER
(Stopping.)
Really?
MIKE
Yeah.
THATCHER
How long have you known him? Two
weeks?
Mike is suddenly put on the spot.
MIKE
More like five.
THATCHER
Really? And now you want to be his
guardian?
Mike looks at Leo and the Judge.
MIKE
May I approach, your honor?
JUDGE LEE
Council approach.
Mike collects himself and approaches.
JUDGE LEE (CONT'D)
What's going on Mike?
MIKE
Well Judge, I think I'd be a better
candidate then the state in this
case.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 20
CONTINUED:
THATCHER
Really?
MIKE
Yeah, and stop saying really, it's
annoying.
THE STENOGRAPHER raises in eyebrow.
MIKE (CONT'D) THATCHER
Your Honor, I live in the Proximity hardly qualifies
same town as Mr. Poplar... him as a guardian, Your
Honor.
MIKE (CONT'D)
And, as his lawyer, I feel like I'm
in a better position to execute
what my client wants.
THATCHER
Your Honor, Mr. Flaherty is Mr.
Poplar's court appointed
attorney...
JUDGE LEE
I know, Stu, I appointed him.
THATCHER
Yeah, well that hardly qualifies
him to be Leo's Guardian. What's
the motivation here?
Thatcher is turning up the heat. He obviously wants Poplar.
Mike is starting to feel it.
JUDGE LEE
Mike?
Mike looks back at Leo who is trying to unscrew the cap on
his water bottle, completely uninterested in the proceedings.
He makes a decision.
MIKE
Your Honor, Leo told me he wants
to live at home. He has the money
to do that and I want to make sure
that happens. If the State can do
that then fine.
THATCHER
Counsel knows we can't do that,
your Honor.
(MORE)
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 21
CONTINUED:
THATCHER (CONT'D)
We're spread too thin for that kind
of individual attention. But they
have an excellent elder care
facility in Mr. Poplar's town.
We'll put him there.
MIKE
Mr. Poplar wants to live at home.
JUDGE MALONE
(TO MIKE)
You can do that, Mike?
MIKE
Yes, I can.
(TO THATCHER)
Really.
Leo is putting papers in his briefcase. Mike sits down next
to him.
LEO
Did we win?
MIKE
Yeah. I think so.
LEO
Good.
EXT. LEO POPLAR'S HOUSE - DAY.
Mike walks toward his car carrying AN OLD TV SET. He puts it
into the back of his car which is packed with ITEMS from
Leo's house.
INT. MIKE'S CAR - LATER.
Mike and Leo are driving.
LEO
Are we going to the park?
MIKE
No. We're not, Leo. I'm gonna help
you get settled into a new place to
live right here in town.
LEO
I don't need a new place. I have a
house. I'm not fancy that way.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 22
CONTINUED:
MIKE
I know. But I need you to stay in
this new place for a while. It's
nice. You'll like it.
LEO
Is that what the judge said?
MIKE
Yeah, that's what he said.
Leo considers the news and looks out the window.
LEO
Ah shit.
EXT. OAK KNOLL SENIOR LIVING - DAY.
Mike and Leo arrive at Oak Knoll.
INT. OAK KNOLL SENIOR LIVING, PRIVATE ROOM - LATER.
It is a nice place. Mike sits on a small couch filling out
paperwork as a FEMALE STAFF MEMBER helps to prepare Leo's
room.
EXT. QUICK CHECK - DUSK.
Mike pulls up and walks into the Convenience Store. He buys
cigarettes and walks outside. He walks outside, around the
corner and then behind the store. He lights a cigarette and
then throws the pack into the dumpster. He stands there
smoking.
INT. OUR LADY OF PEACE CHURCH- MORNING.
AN ENORMOUS CRUCIFIX hangs over the alter. A COLLECTION
BASKET is passed from person to person. Abby deposits TWO
DOLLARS into the basket and looks up at Mike. He smiles.
EXT. OUR LADY OF PEACE CHURCH - LATER.
Jackie and Stella are waiting in the parking lot. Mike is
lagging behind carrying Abby and chatting with some OLDER
PARISHIONER'S. He's charming and he's working it. He finally
catches up with Jackie and they walk toward the car.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 23
CONTINUED:
JACKIE
Let's go, Mr. Mayor. It's cold and
I need to pick up some bagels for
your mom's.
MIKE
OK. OK. I just have to make one
stop first.
JACKIE
Where?
MIKE
I have to swing by a client's house
and shut off the water.
JACKIE
Why?
MIKE
Because it's freezing and I don't
want his pipes to burst.
JACKIE
No, I mean why are you doing it?
MIKE
(CASUALLY)
What? Oh, because I'm his guardian.
JACKIE
What? Since when?
MIKE ABBY
Just last week. Mommy, I want a bagel.
JACKIE (CONT'D)
That's a big deal, Mike. Were you
even gonna tell me?
MIKE JACKIE
It's not a big deal. And yes, It is too.
I was gonna tell you.
JACKIE (CONT'D)
You don't have time to be taking
care of some old man.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 24
CONTINUED:
MIKE
Jack, he's in Oak Knoll. They do
everything. I just have to check in
on him from time to time.
JACKIE
And who pays for that?
MIKE
He does. It comes out of his estate
and he can afford it. Trust me.
JACKIE
I don't get it. You've never done
it before.
MIKE
No I haven't.
JACKIE
So why are you doing it now?
MIKE
It's just...the right thing to do,
alright. We couldn't find his
daughter and I'm just trying to
help the guy. It's really not a big
deal.
JACKIE
Well, it sounds like a big deal.
And you should have told me.
ABBY
What's a big deal?
JACKIE
Ask your daddy, sweetie. Maybe
he'll tell you.
ABBY
Daddy, what's a big deal?
INT. MIKE'S CAR - LATER
Mike pulls up to Leo's house. It's a small house in a working
class section of town. A TEENAGER is sitting on the front
stoop.
JACKIE
Is that his house?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 25
CONTINUED:
MIKE
Yeah.
JACKIE
(Re: the Young Man)
Who's that?
MIKE
No idea.
Mike gets out of the car.
EXT. LEO POPLAR'S HOUSE - LATER
Mike walks up the front walk. The YOUNG MAN is listening to
his Ipod and smoking a cigarette. Mike approaches and waves.
The YOUNG MAN removes his headphones. He has a BRUISE on his
left eye.
MIKE
How you doing? Can I help you?
YOUNG MAN
No.
MIKE
Are you looking for Mr. Poplar?
YOUNG MAN
Yeah.
MIKE
Well, he doesn't live here anymore.
YOUNG MAN
Where does he live?
MIKE
You mind telling me why you're
looking for him first?
The Young Man sizes Mike up. Then...
YOUNG MAN
He's my Grandfather. I came to live
with him.
Mike is momentarily stunned by the news. Then he looks back
at the car where Jackie gives him a "What's going on?" look.
Uh oh.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 26
INT. MIKE'S CAR - LATER
Mike is driving. The Young Man is in the back seat next to
Abby and Stella.
JACKIE
So do you live around here, Kyle?
KYLE
No. Ohio.
Jackie looks at Mike who tries to avoid her piercing gaze.
JACKIE
Ohio? And where are your parents?
KYLE
It's just my mother and me. She's
back in Columbus. She couldn't
come.
JACKIE
So how did you get here?
KYLE
Bus.
JACKIE
Really? All by yourself?
KYLE
Yeah.
JACKIE
Wow.
ABBY
That sounds like a big deal.
Jackie looks at Mike. From the mouths of babes.
INT. OAK KNOLL SENIOR LIVING, HALLWAY - LATER
Mike knocks on Leo's door. After a moment, Leo opens it.
MIKE
Hey, Leo, you have a visitor.
LEO
Who? Him?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 27
CONTINUED:
MIKE
Yeah.
KYLE
Hi.
LEO
Come on in. I'll turn off the TV.
INT. OAK KNOLL SENIOR LIVING, LEO'S ROOM - SAME.
Leo turns off the TV and then turns and looks at Kyle. He
doesn't recognize him.
MIKE
This is Kyle Timmons, Leo. He's
your grandson. He came from Ohio to
see you.
LEO
I don't have a Grandson.
KYLE
Yeah, you do. We just never met.
LEO
Are you bringing me home?
Kyle looks to Mike, unsure of what to say.
MIKE
Kyle's just here for a visit, Leo.
LEO
Oh. You want to watch TV?
KYLE
OK.
Leo turns on the TV and sits down. Kyle joins him.
MIKE
OK. So I'll come back to pick you
up in an hour. You OK?
KYLE
Yeah.
MIKE
You alright, Leo?
(Leo doesn't respond)
OK, see you in a bit.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 28
CONTINUED:
Mike leaves.
INT. GINA FLAHERTY'S HOUSE - LATER.
The house is smaller than Mike's house. GINA, MIKE'S MOTHER,
and Jackie clean up after breakfast. Mike sits with Abby at
the kitchen table.
GINA
So did you call his mother?
JACKIE
No. Not yet. Oh and he was smoking
too. He's sixteen!
GINA
He's probably on drugs.
JACKIE
I know.
GINA
What are you going to do with him?
MIKE
We're going to send him back is
what we're going to do.
GINA
Well I hope so. You have your hands
full over there. And now taking
care of that old man too. That
sounds like a lot, Mike.
JACKIE
Thank you, Gina. I agree. He
somehow forgot to tell me about it.
MIKE
I told you.
JACKIE
Not until I asked.
GINA
His daughter should be taking care
of him. Not you. You have me to
worry about.
MIKE
I don't have to worry about him.
He's at Oak Knoll.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 29
CONTINUED:
ABBY
Daddy? Can we play croquet today?
GINA
The whole thing just sounds crazy.
JACKIE
It is crazy. It's crazy.
ABBY
(TO MIKE)
Who's crazy?
MIKE
Me.
EXT. OAK KNOLL SENIOR LIVING - LATER
Mike and Kyle exit he building and walk toward the parking
lot.
MIKE
How did the visit go?
KYLE
OK. He fell asleep watching TV. So
he lives there now?
MIKE
Yeah. Your grandfather is in the
early stages of dementia, Kyle. So
sometimes he does things and says
things that don't make sense.
KYLE
Are you a friend of his or
something?
MIKE
I'm his guardian.
KYLE
What's that mean?
MIKE
It means I make sure he's well
taken care of.
KYLE
That's cool.
Kyle lights a cigarette.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 30
INT. MIKE'S AND JACKIE'S HOUSE, BASEMENT - NIGHT.
Kyle's is fiddling with KID'S KEYBOARD. Jackie walks
downstairs.
JACKIE
Everything alright?
KYLE
Yeah.
JACKIE
Did you reach your mom?
KYLE
Yeah. I told her I was coming home.
JACKIE
Did she want to talk to me or
anything?
KYLE
No.
JACKIE
Well, I'm sorry you can't stay
longer but maybe you can come back
with your mom and visit again.
KYLE
Yeah. If I want to smoke should I
go outside?
JACKIE
You shouldn't be smoking.
KYLE
I know. But if I do.
Jackie decides not to engage.
JACKIE
Yeah. You should go outside.
KYLE
OK. Good night, Jackie.
JACKIE
Good night, Kyle.
Jackie nods and leaves.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 31
INT. MIKE AND JACKIE'S HOUSE, KITCHEN - SAME.
Mike is leaning against the counter eating ice cream. Jackie
emerges from the stairs, shuts basement door behind her and
slides a dead bolt locking it.
MIKE
What are you doing?
JACKIE
We have kids, Mike. I'm not taking
any chances with Eminem down there.
MIKE
There's not even a bathroom down
there.
Jackie thinks about this and then unlocks the door in a huff
and walks up stairs.
INT. OAK KNOLL SENIOR LIVING, DINING ROOM - DAY.
Mike and Kyle are sitting with Leo who is eating breakfast.
LEO
Hey Mike, could you talk to them
about getting Coco Puffs? I like
that kind.
MIKE
Sure thing, Leo.
LEO
(TO KYLE)
Mike's a stand up guy. You need
cereal then talk to him.
Kyle and Mike smile. Mike checks his watch.
MIKE
We should go, Kyle.
KYLE
OK. Bye Leo.
LEO
Are you going to work?
KYLE
No. I'm going home.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 32
CONTINUED:
LEO
Well, don't take any shit from any
of those guys.
Kyle smiles. He doesn't always understand this guy but he
likes him.
KYLE
I won't.
He leaves.
EXT. BUS STATION - LATER.
Mike and Kyle are waiting for the bus. Mike pulls out his
wallet.
MIKE
Here's fifty bucks in case you need
it.
Mike counts his cash.
KYLE
I have money.
MIKE
Actually it's only forty-three but
take it. You never know.
KYLE
I have enough money. But thanks.
The bus pulls up.
MIKE
Well, good luck, Kyle.
KYLE
Yeah. You too, Mike.
Kyle gets on the bus. Mike watches it pull away.
INT. MIKE'S AND JACKIE'S HOUSE, BEDROOM - NIGHT.
Mike and Jackie are sleeping. The phone rings and Mike
answers the phone.
MIKE
Hello? Yes, it is. Yes. OK.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 33
CONTINUED:
Jackie sits up and turns on the light.
MIKE (CONT'D)
OK. Thanks. I'll be right down.
He hangs up the phone.
JACKIE
What?
MIKE
It was the police. They have Kyle.
JACKIE
What? Why?
MIKE
Breaking and entering.
Mike gets up.
JACKIE
What?
EXT. POLICE STATION - LATER.
Mike and Kyle walk out of the New Providence Police Station.
MIKE
So what happened?
KYLE
I decided not to go home.
MIKE
And then you decided you'd break
into your Grandfather's house?
KYLE
You mind if I have a quick smoke?
MIKE
Yeah, I do. Get in the car.
INT. MIKE'S CAR - SAME.
Kyle fastens his seat belt.
MIKE
So you want to tell me what
happened?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 34
CONTINUED:
KYLE
Not really.
MIKE
Yeah. Well good luck with that,
pal.
Kyle looks at Mike.
MIKE (CONT'D)
You'll see.
INT. MIKE AND JACKIE'S HOUSE - LATER.
Jackie is waiting. Kyle is on the hot seat. Mike is watching.
JACKIE
Kyle?
Kyle can barely look at her.
JACKIE (CONT'D)
We can't help you if you don't tell
us what's going on. Is there a
reason you don't want to go home?
Kyle remains silent.
JACKIE (CONT'D)
What happened to your eye, Kyle?
Kyle shifts. Avoiding.
JACKIE (CONT'D)
Kyle. You can trust us.
Kyle looks up at them. Trust is obviously an issue.
KYLE
I can't live there anymore.
JACKIE
With your Mom? Did she do that to
your eye?
KYLE
No. She's not even there. She's in
a clinic or hospital or whatever.
I'm living with Craig.
JACKIE
Who's Craig?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 35
CONTINUED:
KYLE
Her boyfriend, I guess, but he's an
asshole.
JACKIE
Does she even know you're here?
KYLE
My mom? She doesn't care about me.
JACKIE
How do you know? She's probably
worried sick and just doesn't know
how to reach you.
Kyle reaches into his pocket and takes out his cell phone.
KYLE
She could've called, right?
The sincerity of his question is heartbreaking and Jackie is
cut to the quick. She looks at Mike. Brutal.
EXT. MIKE AND JACKIE'S HOUSE - LATER.
Kyle is sitting on the back steps and smoking a cigarette.
INT. MIKE'S AND JACKIE'S HOUSE, BEDROOM - LATER.
Mike is sitting up in bed. His wheels are spinning.
JACKIE (O.S.)
We don't have a choice now.
MIKE
So what are we gonna do? Adopt him?
Jackie walks into the room putting on face moisturizer.
JACKIE
No. But I'm not sending him back
until I talk to his mother. She
better freaking call me back.
MIKE
Honey, I know it's tough but we're
not in a position to take care of
another kid right now.
She gets in the bed.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 36
CONTINUED:
JACKIE
I don't care. I'm not sending him
back there, Mike. I can't. And for
the record, I'm not very happy
about it either!
MIKE
Then we don't have to do this.
JACKIE
Yes, we do, Mike! We do. It makes
me so angry and so damn sad to see
that poor kid in that kind of
situation. He's just a kid.
Jackie starts to break. Mike buckles.
MIKE
I know. I know. You're right.
JACKIE
I just want to go to Ohio
and...beat the crap out of his mom.
MIKE
Come on.
JACKIE
I do. I want to beat the crap out
of her and her stupid boyfriend.
MIKE
OK.
JACKIE
I'm serious.
MIKE
I know. I'm just not sure that
beating the crap out of everybody
is the best solution.
JACKIE
Well it feels like it. I'm leaving
her another message.
Jackie picks up her phone and dials.
MIKE
Now?
JACKIE
Yes. Now. Shush!
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 37
EXT. COUNTRYSIDE - DAY.
Terry is sitting in his parked car, talking on his cell.
TERRY (O.S.)
So get rid of him again.
INT. TERRY'S CAR - SAME.
Terry watches as a PICK UP TRUCK pulls into a beautiful
country house.
MIKE (O.S.)
I can't. Not until we figure what's
going on back there.
TERRY
Have you talked to his mother?
MIKE
No. Not yet. Jack's left her about
thirty messages.
A STRAPPING CONTRACTOR wearing a TOOL BELT gets out and walks
into the house.
TERRY
Mother fucker. He's wearing his
tool belt.
MIKE (O.S.)
What? Who?
TERRY
No. Sorry dude, I was distracted.
MIKE (O.S.)
Where are you? Are you watching
Lori's house again?
Terry quickly pulls out.
TERRY
It's my fucking house and no. I'm
just driving. Where's the kid now?
INT. MIKE'S OFFICE - CONTINUOUS.
Mike is sitting at his desk.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 38
CONTINUED:
MIKE
He's sitting in my waiting room.
Jackie made me take him with me.
TERRY (O.S.)
Alright, listen pal, this is not
the time to long that stock, you
know what I mean?
MIKE
No. What does that mean?
TERRY
It means you shouldn't be taking
care of another kid. Especially a
convict.
MIKE
(ON PHONE)
Yeah, well...
Shelly pops her head in.
SHELLY
I found her.
Mike spins in his chair.
MIKE
Let me call you back.
TERRY (O.S.)
Fine. But get rid of the convict,
Mike!
Mike hangs up.
SHELLY
She's in a drug treatment program
in Columbus. She has five weeks to
go.
MIKE
Jesus. Can I talk to her?
SHELLY
They said she would call you.
Mike shakes his head. Nothing is easy here.
SHELLY (CONT'D)
He's kind of a sweet kid but what's
up with hair?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 39
CONTINUED:
MIKE
Who knows?
A knock on the door.
MIKE (CONT'D)
Yeah.
Kyle opens it.
KYLE
Can I go visit Leo?
Mike looks to Shelly who just shrugs.
MIKE
Uh...yeah...OK. You know where it
is?
KYLE
Yeah. Just down the street.
MIKE
OK, yeah. Just stay there and I'll
pick you up at about three.
KYLE
OK.
Kyle shuts the door. Mike looks at Shelly.
SHELLY
That's some crazy hair, I'm just
saying.
INT. NEW PROVIDENCE HIGHSCHOOL GYM, THE PIT - LATER.
Kyle is sitting in the corner watching. Mike is standing and
watching. He doesn't like what he sees.
MIKE
Hey, Rew, what are you doing?
Coach, can you get on Pill.
VIGMAN
Get up, Rew.
REW gets up and Vigman gets down on the other wrestler, PILL.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 40
CONTINUED:
MIKE
Everyone watch because none of you
are doing it right. You want to put
your chest into his side.
Vig does it but he's a bit off.
MIKE (CONT'D)
Just slide back a bit, Vig. A bit
more. Yeah. Right there. Then you
give him your full weight. Go ahead
Vig.
Vig does. Pill starts to buckle. Vig is big.
MIKE (CONT'D)
Then you ride the crotch and break
him down with a cross-face.
Vigman grabs Pill under the crotch, applies a stiff cross-
face and then drives him hard to the mat. Another Wrestler,
STEMLER chimes in. Stemler is wearing a STAR WARS t-shirt.
STEMLER
Oh man, how'd that feel, Pill?
We'll just call you "pancake"!
Stemler's a bit off.
PILL
Shut up, Chewbaka.
STEMLER
Yeah, right. More like the "Secret
Apprentice".
FEENEY
What are you, ten years old,
Stemler?
Mike loses it.
MIKE
Hey! We're trying to teach you guys
something and you're all just
goofing off. Shut up!
VIG
Quiet!
MIKE
Last time I checked we haven't won
a match! Right coach?!
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 41
CONTINUED:
VIG
It's embarrassing, guys.
MIKE
It's embarrassing. But you're all
acting like you don't care! Well,
I'm not getting paid enough to just
jerk around here.
(gestures to Vig)
I don't know about you?
VIG
I'm not getting paid enough.
MIKE
I care about what I do and so
should you!
VIG
I care!
MIKE
So does coach Vig, and so should
you! Run em, Coach. I can't look
at them anymore!
VIG
Let's go ladies!
Mike storms out past Kyle who watches him go.
INT. MIKE AND JACKIE'S HOUSE, DINING ROOM - LATER.
Mike, Jackie, Abby and Kyle are eating dinner together. Abby
is coloring. Mike watches Kyle as he finishes his big glass
of milk.
JACKIE
Here, have some more corn.
She gives him the bowl of corn.
JACKIE (CONT'D)
I'll get you some more milk too.
Kyle finishes off the corn. Jackie gets up for the milk.
JACKIE (CONT'D)
Did you call Fenn about the tree,
Mike?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 42
CONTINUED:
MIKE
Uh...yeah I did but Terry said he'd
help and I think we can...
JACKIE
Mike. Don't start. You two are not
cutting down that tree. Just call
Fenn.
Stella starts to cry on the BABY MONITOR.
JACKIE (CONT'D)
I'm going to give her some Tylenol.
And Jackie is gone.
ABBY
(TO KYLE)
Do you want to play croquet?
KYLE
Now?
ABBY
When it's warm.
KYLE
Yeah, maybe.
Mike gets up and begins to load the dishwasher.
ABBY
Daddy, can I watch TV?
MIKE
Uh...yeah but just for a half hour.
Abby leaves. Kyle turns to Mike.
KYLE
Hey Mike, you think I could
practice with you guys tomorrow?
MIKE
Yeah, if you want. Sure. And by the
way, what I did in there today,
yelling like that. I don't usually
do that.
KYLE
You were right, they deserved it.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 43
INT. NEW PROVIDENCE HIGH SCHOOL, BACK GYM - DAY.
Mike and Kyle are walking into the gym.
KYLE
I don't have wrestling shoes.
MIKE
Don't worry about it. You ever
wrestle before?
KYLE
Yeah.
Vigman is already running the team through a drill.
VIGMAN
Get that ankle. Get that ankle!
Time!
MIKE
Hey Vig. Alright, guys, listen up!
Kyle's going to be working out with
us for a little while.
STEMLER
(LOUDLY)
What's up Kyle!
The team laughs. Kyle just nods to Stemler.
VIGMAN
Carlos, you and Jimmy rotate him
in.
Kyle nods and walks over to Carlos and Jimmy.
VIGMAN (CONT'D)
OK. Let's go. Ten seconds to get an
ankle. Then we switch it up. Ready?
Wrestle!
Jimmy sits against the wall and Mike blows his whistle again
the wrestlers all go at each other. Mike watches Kyle.
He moves well. Fluidly. Carlos keeps trying to grab Kyle's
ankle but Kyle easily defends against it. Mike checks his
watch. Then blows his whistle.
MIKE
Time. Switch. And...wrestle!
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 44
CONTINUED:
Mike blows his whistle again and Kyle goes on the offensive.
He gives Carlos a quick head fake and before Carlos knows
what's happened, Kyle has grabbed his ankle and tripped him
down to the mat.
Carlos looks shocked. Kyle pops back up but stays focused on
Carlos. Mike looks to Vigman who raises an eyebrow,
impressed. One thing is certain, Kyle can wrestle.
EXT. NEW PROVIDENCE HIGH SCHOOL PARKING LOT - NIGHT.
Kyle and Mike are walking toward the car.
MIKE
You have fun?
KYLE
Yeah.
MIKE
When's the last time you wrestled?
KYLE
A couple years ago.
MIKE
Why'd you stop?
KYLE
Just felt like it.
Kyle just shrugs and Mike let's it go. They arrive at Mike's
car and Mike talks to Kyle over the roof.
MIKE
So let me ask you something, Kyle.
How good are you?
Kyle just looks at Mike, almost blank.
KYLE
I'm pretty good.
INT. MIKE AND JACKIE'S HOUSE, MIKE'S OFFICE NOOK - LATER.
Mike is looking at his computer screen.
MIKE
Holy shit.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 45
INT. TERRY'S CONDO - LATER.
Mike runs inside. It's a sparsely furnished bachelor pad with
all the toys.
MIKE (O.S.)
You check out that link I sent you?
TERRY (O.S.)
Yeah. Kyle Timmons. That's the kid?
MIKE (O.S.)
Yeah. That's the kid!
TERRY
Holy shit!
MIKE
I know, right? Can you believe
that?!
Terry is in the den at his computer, reading excitedly.
TERRY
Holy shit! He was thirty-five and
one as a freshman!
MIKE
I know. He finished second at the
states. In Ohio!
Mike walks into the kitchen and grabs a beer.
TERRY
This kid had seventeen pins. He's a
killer.
MIKE
I know. It's nuts. And he quit
after his freshman year.
TERRY
Why?
MIKE
I don't know. He doesn't talk much.
He's kind of a weird kid. Why
can't I have one kid like that on
my team? Just one.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 46
CONTINUED:
TERRY
What're you talking about? You do.
You have him. You can take this kid
to the states, Mike.
MIKE
He's not on the team, Ter. He's not
even a student. He's been here for
three days.
TERRY
So what? Enroll him!
MIKE
I'm not enrolling him. He's just
here until we reach his mother and
figure this out.
TERRY
So he's gotta do something, right?
Let him wrestle. Look at this way,
you're helping out the old man and
this kid's a little bonus for doing
the right thing.
MIKE
I'm not just helping out the old
man, Ter. It's not like it's
charity work. I'm getting paid for
it.
TERRY
No. Shit, everyone gets paid, but
think about it, Mike. What are the
chances that this kid ends up on
your door step and he can wrestle
like that? It's a sign, pal.
This lands with Mike. Terry sits down at his computer.
TERRY (CONT'D)
Check this out. There's a video
link of him wrestling in some
tournament.
Terry presses play. It's grainy and amateur but good enough.
Mike looks on.
TERRY (CONT'D)
Look at that kid.
Mike gets sucked in.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 47
CONTINUED:
MIKE
Wow. He's gonna throw him. Look,
he's setting him up. He's setting
him up!
Mike and Terry explode. They high five and hug.
INT. MIKE AND JACKIE'S HOUSE, FOYER - MORNING.
Kyle is standing, waiting. Jackie walks out with her purse.
JACKIE
Here's five dollars for lunch. I
have no idea what it costs but let
me know when you find out.
KYLE
I have money.
JACKIE
Good for you. Save it. Now take
this, it's too early to argue.
Kyle takes it. Mike arrives.
MIKE
OK. Let's go, pal.
JACKIE
Bye Jackie.
Kyle leaves. Mike kisses Jackie.
JACKIE (CONT'D)
Hey, you sure we should do this?
MIKE
Why not? Whether he's here for two
more days or two weeks it gives him
something to do all day. Unless you
want him hanging out here?
JACKIE
OK. Go.
INT. NEW PROVIDENCE HIGHSCHOOL, MAIN OFFICE - DAY.
Mike and Kyle are waiting. After a moment, STEVE DELUCA, THE
PRINCIPAL, emerges from his office and greets them. They all
walk into his office.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 48
INT. MIKE'S OFFICE - DAY.
Mike is working at his desk. Shelly opens the door.
SHELLY
Hey Mike, we got a check from Leo
Poplar's trust for $1,500 but it's
made out to you and not the firm.
MIKE
Right. I'll take that.
Mike gets up and takes the check.
SHELLY
Shouldn't I deposit it in the
business account?
MIKE
No. It's not a legal fee. It's a
personal fee.
SHELLY
For what?
He puts on his coat.
MIKE
Oh, I ended up taking on Leo's
guardianship.
SHELLY
(SURPRISED)
Really?
MIKE
Yeah, I thought I mentioned that to
you.
SHELLY
No, you definitely didn't mention
that.
MIKE
Yeah, well, it just played out that
way. I have to get going.
He turns off his computer.
SHELLY
Well can we put some of that in the
business account so they don't take
our copier back?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 49
CONTINUED:
MIKE
Uh..not this time. Next month.
Promise.
He grabs his briefcase and leaves.
SHELLY
We need our copier, Mike.
MIKE
I know. Bye Shelly.
CLANK. CLANK. CLANK.
SHELLY
And that noise is getting louder.
I'm not hung over today!
EXT. BANK - LATER.
Mike walks out of the bank and dials his cell phone.
MIKE
Hey honey. I'm good. Could you do
me a favor and drop that health
insurance check in the mail? I just
forgot to mail it. Yeah, it's on my
desk. Thanks. I'll call you later.
INT. NEW PROVIDENCE HIGHSCHOOL, LOCKER ROOM - LATER.
Terry is walking through the locker room. A few WRESTLERS and
BASKETBALL PLAYERS are getting dressed.
TERRY
What's up Fella's? Hitting the
showers, huh?
(TO HIMSELF)
That sounded weird.
INT. NEW PROVIDENCE HIGHSCHOOL, COACHES OFFICE - SAME.
Mike and Vigman are in their office looking over a board.
TERRY
Oh yeah!
MIKE
Hey.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 50
CONTINUED:
TERRY
What's up? Hey Vig.
VIGMAN
Hi Terry.
MIKE
What are you doing here?
TERRY
What do you think? I have to see
this kid.
VIGMAN
He's incredible. Just incredible.
And he's good to wrestle.
TERRY
Great. So what's next?
Terry pulls up a stool.
MIKE
We're trying to figure out where he
can wrestle?
TERRY
Where ever the hell he wants,
right?
MIKE
No. Not right.
Kyle knocks at the door.
MIKE (CONT'D)
Hey Kyle. Come on in. How was
school?
KYLE
OK.
MIKE
This is my friend Terry.
Terry, pops up, a bit too excitedly.
TERRY
Hey man! Nice to meet you! Really
nice to meet you. Welcome.
KYLE
Thanks.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 51
CONTINUED:
Mike tries to cover.
MIKE
How the shoe's fit?
KYLE
Good.
MIKE
So let me ask you something, Kyle.
You think you might want to wrestle
in a match?
KYLE
OK.
MIKE
Great. We have a match on Saturday.
What do you wrestle?
KYLE
One-nineteen.
TERRY
Excellent. Done.
KYLE
Is anyone there now?
MIKE
Yeah. Jimmy Reed. But I think he
might be better off at 125.
KYLE
Don't you think we should wrestle
off?
MIKE/TERRY/VIG
Yeah.
INT. NEW PROVIDENCE HIGHSCHOOL, THE PIT - LATER.
KYLE's tying his NEW WRESTLING SHOES. The rest of the team is
sitting around the mat.
VIGMAN
Alright, let's go guys. Wrestle
off.
MIKE
Vig, you keep time?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 52
CONTINUED:
Mike holds up a stop watch.
VIGMAN
Yeah.
TERRY
I'll do it.
Terry grabs the watch from Mike.
TERRY (CONT'D)
You don't mind, do you?
VIGMAN
No. Go ahead.
Mike gives Terry a look. Vig minds. Kyle and JIMMY REED shake
hands. And set themselves on their marks.
VIGMAN (CONT'D)
Ready? And...wrestle.
Vigman blows his whistle and the room erupts in cheering.
Most of it for Jimmy Reed except for Stemler who is rooting
for Kyle.
Jimmy and Kyle lock arms but Kyle pushes him away. Jimmy
locks again but Kyle pushes him away again. Jimmy comes in
hard this time and Kyle uses his momentum to quickly throw
him to the ground.
Jimmy tries to scramble to his knees but Kyle is all over
him. He quickly locks Jimmy in a cradle and rocks him onto
his back. It looks easy. Vigman calls the pin. The room is
quiet...except for Terry.
TERRY
Wow!
Mike shoots Terry a look. Kyle helps Jimmy off the mat.
KYLE
Good match.
JIMMY
Didn't feel good.
Vigman turns to Mike and Terry.
VIGMAN
I don't think we can teach him
anything.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 53
INT. DIMAIO'S PIZZERIA - LATER.
Mike, Terry, Kyle, Jackie and the kids are eating pizza.
TERRY
I don't know why we didn't quit.
Just the smell of that room brought
back the memories. I hated it, it
was like a form of self-abuse.
KYLE
Were you guys that bad?
TERRY
Mike was average. I sucked. Sorry
Abby.
ABBY
It's OK.
Mike checks his watch.
MIKE
I gotta stop by the office and deal
with the computer. Should I...?
JACKIE
No, I'll take him.
TERRY
We both should have quit. Then we
could have joined the ski club and
gotten busy with Allison Shepard on
the overnights.
MIKE JACKIE
Hey! Yo! Terry!
ABBY
Who was busy?
JACKIE
Your Uncle Terry is just silly.
TERRY
Sorry Abby. Getting busy is bad.
Kyle cracks up. Terry catches his eye.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 54
INT. MIKE'S OFFICE - LATER.
Terry is sitting in Mike's office. A bottle of scotch and two
glasses on the desk.
KYLE
Hey, how do you think we'd do
against Kyle? Now?
MIKE (O.S.)
He'd kill us. Both of us. Together.
TERRY
Yeah, you're right. The kid has man
strength, dude.
Mike emerges from under the desk.
MIKE
Man strength?
TERRY
Yeah. You know. Not kid strength.
Man strength.
MIKE
Yeah...I wouldn't say that around
the locker room.
TERRY
What the hell are you doing anyway?
MIKE
Trying to figure out what's wrong
with my fricking back-up system.
TERRY
Just call your IT guy?
MIKE
I don't have an IT guy. IT guys
cost money.
TERRY
OK. I'm just gonna say what's on my
mind. I want to be an assistant
coach too.
MIKE
Seriously?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 55
CONTINUED:
TERRY
Yeah. Why not? I'm value added.
Especially compared to Vig.
MIKE
How are you value added?
TERRY
Well first of all I'm fun. No
denying that. And secondly, unlike
Vig, I actually used to wrestle.
MIKE
Yeah, but Ter, you sucked.
TERRY
That doesn't matter, your team
sucks. Plus I even look more like a
coach then Vig.
MIKE
Yeah, that's not really value
added.
TERRY
Look, Mike, I'm serious here. I
need some distraction in my life
right now. All I do is sit in my
condo and think about Lori and that
guy having sex in the jacuzzi I
paid for. It's fucking unhealthy.
I've been really kind of going
crazy. Really.
Mike looks at his friend. He can tell he's serious.
MIKE
We start at 3:30pm. Don't be late.
TERRY
My brother! I will not let you
down. To the team.
Terry raises his glass. Mike toasts.
TERRY (CONT'D)
Hey, what should I wear to
practice?
MIKE
Just a singlet.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 56
CONTINUED:
TERRY
Really?
MIKE
Yeah, so we can see your man
strength.
TERRY
Good one, Coach! See, it's already
fun.
INT. MIKE AND JACKIE'S HOUSE, BASEMENT - NIGHT.
Jackie is hanging laundry. She hears a phone ringing from the
laundry room. She peeks around the corner and sees that Kyle
is not there. She crosses to his phone and picks it up. It
reads "Mom". She answers it.
JACKIE
Hello? Hello, this Jackie Flaherty.
Kyle is staying with us. Hello?
(She closes the phone)
I'm gonna kill that lady.
She sets the phone down and turns. Kyle is standing on the
stairs. His hair is wet and he's carrying his towel.
JACKIE (CONT'D)
Oh. Hi. I heard your phone ringing
and...
KYLE
You answered it?
JACKIE
Yeah, well, I saw it was your Mom
and we've been waiting to hear from
her.
KYLE
What'd she say?
JACKIE
She didn't say anything. She hung
up. Have you talked to her?
KYLE
No. Can you not answer my phone
anymore?
JACKIE
Yeah. OK. I can do that. I'm sorry.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 57
CONTINUED:
Jackie heads back to laundry room. She stops at the stairs.
JACKIE (CONT'D)
Oh. Here's a bucket. You shouldn't
be smoking but if you do could you
put the cigarettes in here.
KYLE
I quit now that I'm wrestling
JACKIE
Oh. Good. OK.
She leaves. Kyle walks over the couch and picks up his phone.
INT. MIKE AND JACKIE'S HOUSE - EARLY MORNING.
Mike and Jackie are sleeping. A sound from downstairs. Then a
door opens and shut. Mike sits up and listens.
JACKIE
Is that Abby?
MIKE
If it is, she just ran away.
INT. MIKE AND JACKIE'S HOUSE, KITCHEN - CONTINUOUS.
Mike walks into the kitchen. Kyle is drinking water.
MIKE
Were you outside?
KYLE
Yeah. I went for a run.
MIKE
It's pretty early. You do this
every morning?
KYLE
In season, yeah. I like to get my
run in early and then drill some
moves for an hour before school.
MIKE
Oh. Wow.
KYLE
Yeah...so I'm gonna do it. See you.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 58
CONTINUED:
Kyle walks downstairs.
INT. MIKE'S AND JACKIE'S HOUSE, BEDROOM - LATER.
Mike climbs back into bed. Jackie barely moves.
MIKE
It was Kyle.
JACKIE
What's he doing?
MIKE
Working out.
JACKIE
Is he gonna do it every morning?
MIKE
In season. Yeah.
Beat.
JACKIE
I hate you.
MIKE
I know.
INT. NEW PROVIDENCE HIGHSCHOOL, LOCKER ROOM - DAY.
Kyle takes off his shirt and stands on the scale wearing only
his underwear. He's lean and muscular. He has a TATOO on his
right arm and PAIR OF WINGS TATOO on his shoulder blades.
VIGMAN
Jesus! Look at those tats.
TERRY
This kid is just fricking cool.
REF
Timmons. One nineteen. Good.
INT. NEW PROVIDENCE HIGHSCHOOL, MAIN GYM - LATER.
The New Providence team jogs out to the mat. There are maybe
twenty people there. A PUNK ROCK SONG is playing.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 59
CONTINUED:
TERRY
This song sucks.
VIGMAN
Rew picked it. He's an odd one.
TERRY
Hey Vig, which kid is yours anyway?
VIGMAN
None of them. He quit.
TERRY
Really? You're son quit?
VIGMAN
My step son and yes. Don't get me
started, I thought becoming a coach
might be a nice way for us to bond.
He said it wasn't fierce and he
quit.
TERRY
Harsh. So why you still doing it?
MIKE
Vig is leading by example. Winners
never quit.
VIGMAN
That's right, even if it sucks.
This team is just depressing
sometimes.
Terry sits next to Mike.
VIGMAN (CONT'D)
That's where I sit, Ter.
TERRY
Sorry buddy. I got to be near,
Mike. It's good luck.
VIGMAN
Say's who?
MIKE
Guys. I don't think we should fight
about our seats in front of the
kids.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 60
INT. NEW PROVIDENCE HIGHSCHOOL, MAIN GYM - LATER.
The Pioneers are getting beat. Carlos is wrestling and
putting up a good fight but time is running out and he's down
by three points. He tries a desperate takedown but it
backfires and the other wrestler picks up another two points.
The buzzer sounds. Match over.
The team gets up to greet Carlos. Kyle strips off his sweats
and buckles up his head gear. He walks up to Mike for a pep
talk.
MIKE
OK. You ready?
KYLE
Yeah.
MIKE
This kid is good. So just...you
know...be ready out there.
Terry gives Vigman a look. "Be ready?"
KYLE
Can you give me a slap?
MIKE
What?
KYLE
Give me a slap. Across the face.
Like your waking me up.
MIKE
Uh, OK.
Mike cuffs Kyle on the side of the head gear.
KYLE
Can you do it harder?
Mike slaps him hard. And Kyle sprints to the mat and takes
his stance.
The Ref blows the whistle and the wrestlers circle each
other. The OTHER WRESTLER is clearly on the offensive.
TERRY
Come on, Kyle. Take this punk out.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 61
CONTINUED:
MIKE
(Under his breath)
Ter! Cut the shit! You're a coach.
You're not sitting in the stands.
TERRY
Sorry. I'm just excited. You know
me.
The Other Wrestler shoots a single and takes Kyle down. Two
points.
TERRY (CONT'D)
What's he doing?
VIGMAN
Losing.
MIKE
It's his first match. Give him a
break.
The Other Wrestler is relentless. Kyle keeps trying to get up
and the kid keeps breaking him down. Kyle stands up and Other
Wrestler slams him to the mat. Kyle is getting beat up.
The two Wrestlers go out of bounds and the Ref stops the
action. Kyle gets up and Mike checks in with him.
MIKE (CONT'D)
Hey! You OK?
KYLE
(SLIGHT SMILE)
Yeah.
Kyle gets into the bottom position.
VIGMAN
Did he smile?
MIKE
Yeah. I think he did.
TERRY
Good. That's good, right?
The Ref blows the whistle and Kyle explodes to his feet,
kicking a leg back between the Other Wrestler's legs. He
lower's his body, reaches behind him and whips the Other
Wrestler to the mat.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 62
CONTINUED:
He drops down and puts him a double arm bar and runs the
Other Wrestler right up over his own shoulders. The Ref drops
to the mat and calls the pin. Match over. The Team jumps up
and cheers.
TERRY (CONT'D)
(TO VIGMAN)
See. I'm good luck.
VIGMAN
That's got nothing to do with luck.
Kyle shakes the other wrestler's hands and the Ref raises his
hand in victory. Kyle crosses to the opposing coaches and
shakes their hands. Then he runs to back to his bench. Mike
greets him with a handshake.
MIKE
How'd that feel? Pretty good?
KYLE
Yeah, pretty good.
Mike smiles and Kyle sits down. The next wrestler, Jimmy
steps up to Mike.
MIKE
You ready?
JIMMY
Yeah. Can you slap me too, Coach?
Mike laughs. And then he slaps him.
INT. MIKE AND JACKIE'S HOUSE, DEN - NIGHT.
Mike, Kyle and Abby are watching TV. Jackie walks in putting
on her coat.
JACKIE
I'm going to the market. I'll be
back in a bit.
KYLE
Can I go with you?
JACKIE
Uh...yeah OK.
Kyle gets up to get his coat. Jackie looks at Mike who just
shrugs.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 63
CONTINUED:
ABBY
I want to go with Kyle.
MIKE
No, honey. It's almost bed time.
INT. GROCERY STORE - LATER.
Jackie is shopping. Kyle catches up to her. He is carrying
two BOXES OF CEREAL. He doesn't put them in the basket.
JACKIE
Coco Puffs. Is that your brand?
KYLE
It's for Leo.
JACKIE
Nice. Drop it in, it's on me. Go
ahead.
(KYLE DOES)
How's he doing?
KYLE
He's doing OK. He can say some
pretty funny things. Yesterday he
told me I was fired.
JACKIE
Fired? For what?
KYLE
I don't know. He just fired me.
JACKIE
I think I have to meet this Leo.
KYLE
Yeah. He's a pretty funny dude.
JACKIE
You have any home work?
KYLE
A little but I already did it.
JACKIE
Impressive. You ever think about
going to college?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 64
CONTINUED:
KYLE
Yeah but just to wrestle. My old
coach thought I could get a
scholarship.
JACKIE
Yeah, I hear you're pretty good. So
why'd you quit?
Kyle just shrugs.
JACKIE (CONT'D)
You don't have to tell me. It's
alright.
They keep walking. Jackie grabs a box of tacos from the
shelf.
JACKIE (CONT'D)
Do you like tacos?
KYLE
Yeah.
JACKIE
Me, too. I make a mean taco.
INT. NEW PROVIDENCE HIGH SCHOOL, THE PIT - LATER.
The team is jogging in circles around the mat. Mike, Vigman,
and Terry, stand in the middle of the circle talking.
VIGMAN
Let's go! Circle up!
MIKE
Alright. I want to spend this week
working on bottom position. Did you
all see Kyle the other day? He
exploded up. Kyle, show the guys
what you did.
Kyle is caught off guard. He hesitates
KYLE
It's kind of my own thing.
MIKE
So can you share it with us?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 65
CONTINUED:
KYLE
Well, it's not a move or anything,
I just tell myself that the guy on
top is going to take my head and
shove it under water and kill me.
And if I don't want to die on the
bottom, I just gotta do what ever
the fuck it takes to get out.
This kid is intense. His words really land with Mike.
VIGMAN
OK. So the move is called "whatever
the fuck it takes." Let's go. Let's
work on it. Come on. "Whatever the
fuck it takes."
Vigman claps and the wrestlers start to move.
INT. OAK KNOLL SENIOR LIVING, COMMUNAL ROOM - DAY.
Kyle sitting in the communal room at a table with Leo. Kyle
is doing homework. Leo is staring out the window. Court TV is
playing in the background.
LEO
You're mother didn't want to come?
KYLE
No.
LEO
She's a tough kid that one. She
tell you bad things about me?
KYLE
Yeah. But I never believe her
anyway.
LEO
You should, she's your mother.
Respect that.
(Pointng to the TV)
Can you turn that down? I hate that
judge. I wouldn't be in this place
if it wasn't for her.
KYLE
But this place is pretty nice.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 66
CONTINUED:
LEO
It's not my damn house! I paid for
that house. Damn Judge. Turn it
off!
KYLE
You want to take a walk outside,
Leo?
LEO
Yeah. Let's go to my park.
KYLE
Your park, huh?
LEO
Yeah. My park.
EXT. MIKE AND JACKIE'S HOUSE - NIGHT.
Mike and Kyle get out of the car and unload a couple of small
mats from the backseat.
MIKE
You bring the tape?
KYLE
Yeah. It's in my bag.
Mike grabs his briefcase from the trunk.
KYLE (CONT'D)
Hey, Mike, can I ask you something?
MIKE
Yeah. Of course. What?
KYLE
Leo told me that some Judge made
him move into that place. Is that
true or is he just making that up?
Mike wasn't expecting this.
MIKE
No. That's true, pal.
KYLE
Why?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 67
CONTINUED:
MIKE
Well because they can take good
care of him there, Kyle.
Mike's phone rings.
KYLE
But he wants to live at home.
MIKE
I know, pal. Hang on a minute.
(Into cell phone)
Hello? Yes. This is him.
MIKE (CONT'D)
Oh. Can you hang for a moment?
(TO KYLE)
Hey, I have to take this. I'll be
right in, OK? We can talk in a
minute.
Kyle walks inside. Mike watches him go, already regretting
the lie. He exhales...
MIKE (CONT'D)
(INTO PHONE)
Hi. Sorry to keep you waiting.
Yeah. How are you doing?
INT. MIKE AND JACKIE'S HOUSE, KITCHEN - LATER.
Jackie it the sink. Stella is eating. Mike is sitting at
the table with a beer.
JACKIE
What? She doesn't even know us!
MIKE
Yeah, well I think she heard that
I'm a lawyer and I have a family
and that was good enough.
JACKIE
For how long?
MIKE
Another month, I guess, until she
gets out of rehab. She said that
Craig guy took off. She sounded
pretty shaky.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 68
CONTINUED:
JACKIE
I can't believe this lady.
Jackie joins Mike at the table.
MIKE
Yeah. I know. Where is he anyway?
JACKIE
In the basement with Abby.
(BEAT)
This is crazy.
MIKE
Yes, it is. So what do we do?
JACKIE
We let him stay. I don't know, do
we even have a choice?
MIKE
I guess we don't.
EXT. NEW JERSEY COUNTRY SIDE - DAY
A school bus drives through the New Jersey Farm country.
INT. SCHOOL BUS - DAY
Kyle is siting on the bus listening to his Ipod. Stemler is
sitting next to him.
STEMLER
You nervous?
KYLE
No.
STEMLER
I am.
KYLE
You're not wrestling.
STEMLER
I know. I'm just nervous a lot.
KYLE
You ever think about wrestling in a
match?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 69
CONTINUED:
STEMLER
Yeah. I'm just waiting for the
green light from Coach. But I'm
glad I'm not wrestling today. These
guys are ranked fourth in the
state. And you're wrestling Kenny
Randall. He's undefeated. He is
tough! Really tough.
KYLE
Thanks for letting me know.
Vigman stands up at the front of the bus.
VIGMAN
Hey! Cut the chatter! You should
all be playing the "what if" game.
What if he shoots a single leg?
What if he controls my wrists?
STEMLER
What if we all get pinned like last
year?
VIGMAN
Shut up, Stemler! Or I'll throw you
off the bus myself!
Vigman sits back down next to Terry.
TERRY
Did they really pin all of you?
VIGMAN
Just about. It's gonna be a fucking
bloodbath.
INT. MILBURN HIGH SCHOOL - LATER
Multiple Pins. It's a bloodbath. Jackie, Abby and Stella are
in the stands and they look depressed. Kyle's next up.
MIKE
OK. This is Kenny Randall. He's
very good.
KYLE
Yeah, I heard.
MIKE
But you have an advantage here, he
has no idea who you are, right?
(MORE)
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 70
CONTINUED:
MIKE (CONT'D)
So he's gonna be overconfident. You
take advantage of that and when you
get your shot, put him away.
Kyle nods and Mike slaps him across the face and Kyle sprints
to his place on the mat and gets ready. Mike turns to the
team.
MIKE (CONT'D)
See how he runs out there? I want
that kind of intensity from all of
you.
ABBY
Why did Daddy hit Kyle?
JACKIE
I don't know, honey.
The Ref blows the whistle and the match starts. As Mike
predicted KENNY RANDALL tries to end the match quickly with a
throw but Kyle is too strong and too good. Kyle counters and
throws Kenny to his back. Before anyone can blink, Kyle pins
him. Mike, Terry, and Vigman explode off their chairs.
MIKE (CONT'D) TERRY
Yeah! Holy shit!
VIGMAN
He just pinned Kenny Randall. Are
you kidding me?!
Kenny Randall looks shocked. He throws off his head gear and
gets up. The MILBURN COACHES look equally shocked. The Ref
raises Kyle's hands. Kyle runs over to shake the Milburn
Coaches hand and then he runs back to his bench and is
greeted by Mike.
KYLE
He know's who I am now.
Mike smiles as the team greets him.
INT. MIKE AND JACKIE'S HOUSE, DEN - LATER.
Jackie and Stella are sitting on the ground. Kyle walks in.
KYLE
Hi, can I watch TV in here?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 71
CONTINUED:
JACKIE
Yeah but I want to show you
something. Stella, who's that?
STELLA
Ky.
Kyle laughs.
JACKIE
She started saying it at the match
today.
KYLE
That's cool.
JACKIE
OK. So I have to ask, those tatoo's
must have hurt, right?
KYLE
Not really.
JACKIE
Don't lie to me. Look.
Jackie lifts her pant leg. She has a small tatoo on her
ankle.
JACKIE (CONT'D)
I got it on Spring Break. Hurt like
hell.
KYLE
What's it say?
JACKIE
JBJ. Jon Bon Jovi. I'm a fan. You
got a problem with that?
KYLE
No I do not.
JACKIE
That was fun today. You're good.
I'm glad you started wrestling
again.
KYLE
Yeah. Me too.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 72
CONTINUED:
JACKIE
No quitting this time, you got
that?
KYLE
Can I tell you something?
JACKIE
Of course.
KYLE
I didn't quit my old team. I got
thrown off.
JACKIE
Why?
KYLE
I stole a car.
JACKIE
What? You're don't even drive.
KYLE
Yeah. That was part of the problem.
JACKIE
Who's car did you steal?
KYLE
A teacher's.
JACKIE
Oh my God.
KYLE
It was really stupid.
JACKIE
Yeah. It was stupid. You could have
killed yourself.
KYLE
Yeah. Everything just got messed up
after that.
JACKIE
Yeah, well we all do stupid things.
But the best part is that you got a
another chance and now you're
kicking butt.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 73
CONTINUED:
KYLE
I guess.
JACKIE
It's true. And you know who would
agree with me?
KYLE
Mike?
Jackie lifts her leg.
JACKIE
Nope. JBJ.
Jackie lifts her leg exposing her tatoo. Kyle smiles.
INT. NEW PROVIDENCE HIGHSCHOOL, MAIN GYM - DAY.
The Pioneers race out onto the mat to do warm-ups before a
home match. They are fired up. There are more fans in the
stands. Terry and Vig bob their head to the music.
Kyle looks up at Jackie, Shelly and kids who are also rocking
out in the stands.
EXT. PARK - DAY.
Kyle and Jackie walk through a park with Leo.
INT. NEW PROVIDENCE HIGH SCHOOL, HALLWAY - DAY.
The wrestling team sprints through the empty hallways.
INT. STEMLER'S HOUSE - DAY.
Kyle and Stemler are battling it out on the Wii. Stemler is
wearing a helmet.
INT. MIKE'S AND JACKIE'S HOUSE, KITCHEN - MORNING.
Mike pours himself some coffee. Jackie is feeding the kids.
The basement door opens and Kyle walks out followed by
Feeney, Jimmy, Carlos, and Stemler. They are all sweating
profusely. Mike is about to sip his coffee when Terry walks
out. He nods and follows the gang.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 74
EXT. MIKE'S AND JACKIE'S HOUSE - DAY.
Terry and Kyle stand side by side holding onto two ropes.
Mike is cutting down the dead tree with a chain saw. Jackie
Abby watch from the front porch. Mike finishes cutting and
Terry and Kyle pull the tree over. Success. Mike lifts his
arms in triumph.
INT. NEW PROVIDENCE HIGHSCHOOL, COACHES OFFICE - DAY.
Mike, Vigman and Terry are preparing for the match.
VIGMAN
They don't have anyone at
heavyweight.
MIKE
Really? Korsic will be happy. Tell
him now so he doesn't puke.
TERRY
Why does he puke? He's a
heavyweight. He doesn't have to
lose weight.
VIGMAN
Nerves.
TERRY
Sweet Lord. This is a team for the
ages.
Kyle knocks on the door. Stemler is with him.
MIKE
What's up, guys?
KYLE
Stemler wants to wrestle today.
MIKE
You do?
STEMLER
Yeah, Coach. I'm pretty sure I'm
ready. Right?
KYLE
Right.
MIKE
Where you gonna wrestle?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 75
CONTINUED:
KYLE
He could wrestle 119. I could bump
up and get a pin at 125 and Jimmy
goes 130. Then we're only giving up
one weight class and we got a shot.
Vig and Terry look at Mike.
MIKE
Huh. Vig?
VIG
Yeah. He's right. It's possible.
TERRY
Have you ever wrestled in a match
before Stemler?
STEMLER
No, I have not.
KYLE
You're just waiting for the green
light, right?
STEMLER
Right. I think now is my time. I
can feel the force.
The three coaches all look at each other.
INT. NEW PROVIDENCE HIGHSCHOOL, LOCKER ROOM - LATER.
Terry holds up a CUP OF STICKS with weight classes written on
them. The BERKLEY HEIGHTS COACH selects a stick and reads the
weight.
BH COACH
One twenty-five.
Vigman reads off the roster.
VIGMAN
We start at 125 pounds. Depasquale
and Timmons. We'll finish at 119
pounds. Tomlinson and Stemler.
STEMLER (O.S.)
I'm ready Coach.
The Coaches all turn to see Stemler already wearing his
singlet and headgear.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 76
CONTINUED:
STEMLER (CONT'D)
Show time.
VIGMAN
Thanks for the update Stemler.
TERRY
We're dead.
MIKE
No. It's gonna be fine.
INT. NEW PROVIDENCE HIGHSCHOOL, MAIN GYM - LATER.
The SCORE BOARD reads 33- 31. The 112 pound weight class is
wrestling.
MIKE
Hook the arm! Carlos, hook the arm!
Carlos does and holds on for the win. The team cheers. Mike
turns to Vigman and Terry.
MIKE (CONT'D)
How we doing?
VIGMAN
With that win, we're up by five. If
Stemler doesn't get pinned, we win.
TERRY
That's a huge fucking "if".
STEMLER (O.S.)
I can hear you, Coach.
They all turn. Stemler is standing right there. He looks
petrified.
VIGMAN
Good job, Ter.
TERRY
Sorry, Stemler. You're a champ.
MIKE
Come here, Stemler.
Mike takes Stemler by the shoulders.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 77
CONTINUED:
MIKE (CONT'D)
You've been practicing for a long
time. You're ready for this. You
hear me?
Stemler nods.
MIKE (CONT'D)
If you get in trouble out there,
you just listen to me. I'm right
here, OK?
Stemler nods again. Too scared to respond.
MIKE (CONT'D)
OK. You are not going to get
pinned! You hear me! No way!
STEMLER
(BARELY AUDIBLE)
No way. No way.
MIKE
Good. Now I'm going to slap you.
Ready?
STEMLER
Yeah but not so hard.
Mike gives him an odd half-slap and Stemler runs out to the
mat and takes his place at the line. The team cheers.
But then the other WRESTLER runs out. He is wearing a BLACK
PROTECTIVE FACE MASK. Stemler spins away from the line and
looks pleading at Mike.
STEMLER (CONT'D)
Holy shit! It's Darth Vader! Are
you kidding me? No way!
He does look like Darth Vader. But in a singlet.
MIKE/TERRY/VIGMAN
Don't worry. It's just a mask. You
are ready! Get on that line. Now!
KYLE
Hey, Stemler. Come here.
Stemler walks over.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 78
CONTINUED:
KYLE (CONT'D)
If he's Darth Vader then you're the
Secret Apprentice. You got this.
Stemler buys it.
STEMLER
Yeah. You're right.
Stemler returns to the line slightly more confident. The Ref
blows the whistle and the match starts. Stemler is
immediately taken down. Terry looks at his feet.
TERRY
I can't watch.
LATER -
It's late in third period. Stemler is losing 13-0. Stemler
is flat on his belly and he's getting mauled. The Ref calls
him for stalling. One point. 14-0. Thirty seconds to go.
MIKE
Keep moving, Stemler. Keep working!
VIGMAN
(Reading score card)
Oh shit. Oh shit!
TERRY
What?
VIGMAN
He's one point away from a tech
fall and we'd lose on criteria.
MIKE
Shit. Really?
TERRY
What the hell does that mean?
VIGMAN
If he falls behind by fifteen
points it's a technical fall. They
get five team points. If that
happens the score would be tied but
we'd lose the match on criteria.
TERRY
Seriously?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 79
CONTINUED:
MIKE
Fuck this!
Mike drops to the mat.
MIKE (CONT'D)
Stemler! Stemler!!
Stemler looks over. His eyes are wild.
MIKE (CONT'D)
You need to get up! He's trying to
drown you! He wants you dead. But
you are not going to die on the
bottom! Do you hear me? Do you?!
Stemler manages a nod, albeit a terrified one.
MIKE (CONT'D)
Good! Now just do the move we
worked on in practice.
Off Stemler's confused look.
MIKE (CONT'D)
"Whatever the fuck it takes!"
Stemler almost manages a smile and then he hits "the move".
It's not pretty but somehow he manages to get up and out. The
team goes nuts. One point for Stemler. 15-1.
The Other kid frantically tries to take him down but Stemler
holds him off dancing wildly around the mat. The buzzer
sounds. The team goes nuts.
The Ref raises the other wrestler's hand in victory but it's
Stemler who celebrates as if he just won the states. He runs
off the mat and into the arms of his teammates.
INT. NEW PROVIDENCE HIGHSCHOOL, HALLWAY - LATER.
Mike and Kyle walk through the empty hallway.
MIKE
Hey, I'm proud of what you did
today. That win meant a lot to the
guys.
KYLE
Cool. It was good coaching with
Stemler.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 80
CONTINUED:
Mike laughs. Then he just looks at Kyle.
MIKE
Let me ask you something. What's it
like? Being as good as you are?
What's it feel like?
KYLE
I don't know. I guess it just feels
like I'm in control. Of everything.
You know what I mean?
MIKE
Yeah, I do. Must be nice.
KYLE
It is.
INT. UNION HIGHSCHOOL - DAY
The DISTRICT TOURNAMENT. Kyle is ahead in points going into
the second period. He chooses the top position. The Ref blows
the whistle and the OTHER WRESTLER sits out and Kyle simply
sucks him onto his back. It almost looks too easy.
VIGMAN
That's it.
MIKE
Yeah.
TERRY
District champ, baby.
VIGMAN
Pure fucking poetry.
The Ref slaps the mat and it's over.
INT. OAK KNOLL SENIOR LIVING - DAY.
Kyle walks into Leo's room.
KYLE
Hey, Leo. Guess who won the
Districts?
LEO
Who?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 81
CONTINUED:
KYLE
Me. And Mike said he got a call
from a college scout about me.
LEO
Oh.
VOICE (O.S.)
Hi baby.
A THIRTY-EIGHT YEAR OLD WOMAN standing in the door way. This
is CINDY TIMMONS. Kyle's mother.
KYLE
What are you doing here?
CINDY
I came to get you, honey. And to
see Grandpa. I missed you so much.
Can I have a hug, baby?
Kyle looks at Leo who just shrugs. Finally, he walks toward
her but then veers away and runs from the room.
LEO
Where's he going?
CINDY
Oh, he's just had to go somewhere,
Dad. Do you want some juice?
INT. MIKE AND JACKIE'S HOUSE, LIVING ROOM - NIGHT.
Mike is watching Stella who is playing on the ground. Jackie
comes up from the basement.
MIKE
How is he?
JACKIE
He's upset. I don't blame him. It's
weird that she just shows up like
that.
(Checking her watch)
And of course she's late, the
druggie.
MIKE
Honey. Can you stop, please?
JACKIE
You're gonna talk to her, right?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 82
CONTINUED:
MIKE
Yeah. I am. If you don't punch her
first.
Car lights in the window. Mike looks out the window.
MIKE (CONT'D)
It's a cab. It's her.
JACKIE
It's not my fault if I punch her.
MIKE
Yeah, it is. That will be your
fault.
Jackie picks up Stella. The door bell rings. Mike answers it.
Cindy is standing there. She looks nervous.
MIKE (CONT'D)
Hi. I'm Mike Flaherty. Come in,
please.
CINDY
Hi.
MIKE
And this is my wife, Jackie and my
daughter, Stella.
CINDY
Hi.
JACKIE
Hi, Cindy. Nice to meet you.
CINDY
She's very cute.
JACKIE
Thanks. Abby, our six year old, is
downstairs with Kyle.
CINDY
Oh. OK.
Awkward pause.
JACKIE
Do you want to sit down?
CINDY
Thanks. This is a very nice house.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 83
CONTINUED:
JACKIE
Thank you very much.
MIKE
Can I get you a drink or something?
Jackie shoots Mike a look. A drink?
MIKE (CONT'D)
Water or soda or anything?
CINDY
No. No thanks. I'm fine.
MIKE
Right. OK. So I'll go get Kyle.
Mike starts to go but Cindy doesn't quite seem ready.
CINDY
How's he doing?
MIKE
Oh, he's doing really well. He's
going to the high school here and
he's wrestling on the team
actually.
CINDY
Really? That's good. He loves
wrestling so much.
JACKIE
He's a really sweet kid. Our girls
love him.
CINDY
That's nice.
Cindy starts to tremble.
CINDY (CONT'D)
I am so sorry about this...it's
just been such a difficult time...
Jackie and Mike share a look. Then Jackie caves and slides
over next to her.
JACKIE
Oh hey...these things happen,
Cindy. And we've loved having him.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 84
CONTINUED:
Mike rolls his eyes. So much for beating the crap out of her.
Abby walks upstairs.
MIKE
Hi, honey. This is Abby.
CINDY
Hi Abby.
ABBY
Hi.
MIKE
Abby, can you go get Kyle for us?
ABBY
He left.
MIKE
He left? What do you mean?
ABBY
He left out the window.
INT. MIKE'S CAR - NIGHT.
Mike and Cindy are driving.
MIKE
I'm really sorry about this.
CINDY
That's okay. Thanks.
MIKE
You know Kyle's doing really well
with wrestling here, Cindy. The
regions are this weekend and if he
wins there then he goes to the
states.
CINDY
That's great.
MIKE
Yeah. It is and it could be really
good for him. It might even mean a
scholarship. Anyway, I was
wondering if you could stay here
for another three weeks until
that's all over.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 85
CONTINUED:
Cindy thinks about it.
CINDY
I'd like to but don't think I can
afford to stay in the hotel for
that long. Do you think we could
stay in my dad's house?
This is not what Mike wanted but he's stuck.
MIKE
Uhh...yeah. We could probably make
that work.
CINDY
Then, yeah, I could stay.
MIKE
OK. Good. That's great.
Mike's phone rings.
MIKE (CONT'D)
Hey.
TERRY (O.S.)
Hey. Kyle's here.
MIKE
Really?
(TO CINDY)
We found him.
INT. TERRY'S CONDO - SAME.
Terry looks into the other room. Kyle is playing on the Wii.
TERRY
Yeah. We're playing Wii Golf. I'm
destroying him. Dude, this kid
really hates his mother.
INT. MIKE'S CAR - SAME.
Mike is driving.
MIKE
Yeah, OK.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 86
CONTINUED:
TERRY (O.S.)
I mean like more then I hate my ex
wife.
MIKE
Great, Ter. Thanks. Bye.
(Mike hangs up)
He went to my friend's house. We
can go get him.
CINDY
Maybe I'll just go back to the
hotel. It might just be too much
for him tonight. I can see him
tomorrow.
MIKE
You sure?
CINDY
Yeah. I think maybe that's better.
I know how Kyle can be.
MIKE
OK. I'll drop you off.
Mike keeps driving.
INT. MIKE'S NEIGHBORHOOD - EARLY MORNING.
Mike and Kyle are jogging. Kyle's mood is dark.
KYLE
So when wrestling's over I have to
go?
MIKE
I'm afraid so, pal. She's staying
so you can finish the season.
That's pretty nice of her.
They arrive back at Mike's house. Mike is really winded.
MIKE (CONT'D)
I told her you'd go see her today,
Kyle.
KYLE
Where?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 87
CONTINUED:
MIKE
Where ever you want. She could come
here or we could go see her at
Leo's house. She moving in this
morning.
Kyle thinks.
KYLE
I'll go see her at Leo's before
practice. But I want to go alone.
MIKE
(HESITANT)
Yeah, that's OK but Kyle but you
have to promise me...
KYLE
Don't worry, Mike. I'll go.
Mike turns and spots his OLD NEIGHBOR watching him.
OLD NEIGHBOR
Hi Mike.
MIKE
Hi Betty. How's the foot?
BETTY
Better.
INT. MIKE'S OFFICE, BATHROOM - DAY.
Mike is attempting to plunge the toilet. Shelly approaches
him.
SHELLY
Mike? Cindy's here.
MIKE
Really? Did she say why?
SHELLY
No. But she's here with an
attorney.
Mike gets up and opens the door to his office. Eleanor and
Cindy stand to greet him.
MIKE
Hi Cindy. Hi, I'm Mike Flaherty.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 88
CONTINUED:
Cindy nods.
ELEANOR
Hi, I'm Eleanor Cohen.
MIKE
Please come in.
He leads them into his office.
MIKE (CONT'D)
I wasn't aware that Cindy was
represented by council.
ELEANOR
She retained me last week to help
sort out her father's situation.
MIKE
Last week? I thought she just
arrived two days ago.
(MIKE SITS)
How long have you been here?
ELEANOR
She wanted a little time to settle
in and spend some time with her
father.
MIKE
So how can I help?
ELEANOR
Cindy has decided that she wants a
more active role in her father's
care.
MIKE
What kind of a role is that?
CINDY
I want to take care of him.
MIKE
Really? So you want to move here?
ELEANOR
No. Cindy would like to bring her
father back to Columbus.
CINDY
That's where my support network is
now. It's home.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 89
CONTINUED:
MIKE
Well I'm not sure that's what Leo
wants.
CINDY
I already talked to him about it.
He seem to like the idea.
MIKE
I understand that, Cindy. But you
haven't seen Leo in a long time and
he's battling dementia now so it
puts me in a tough position here.
ELEANOR
She is the presumed Guardian, Mr
Flaherty.
MIKE
I understand that.
ELEANOR
And we do hope to avoid litigation.
MIKE
So do I and I'm sure we can. Now,
I'm sorry, but I actually have to
go see a client so we'll have to
set up another time to discuss
this.
CINDY
Kyle's still coming to see me
today, right?
MIKE
Yeah. Of course. After school.
ELEANOR
I'll have my office call. Come on
Cindy.
CINDY
Thanks Mike.
Mike nods and Eleanor and Cindy leave. Mike watches them go.
CLANK. CLANK. CLANK.
EXT. QUICK CHECK - LATER.
Mike walks out of the Convenience Store, around the corner
and behind the store. He lights a cigarette.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 90
CONTINUED:
TERRY (V.O.)
I don't get it. Is it that bad?
EXT. NEW PROVIDENCE HIGH SCHOOL - LATER.
Mike and Terry are standing outside talking.
MIKE
Yeah, it's that bad.
TERRY
Just take her to court, you'll kill
her.
MIKE
I can't.
TERRY
Why not? She's a freaking mess.
You're a pillar of the community,
Mike.
MIKE
I just can't go back in front of
Judge Lee, it won't look good,
trust me.
TERRY
So maybe you'll get a different
judge.
MIKE
She's the only Judge who handles
these cases and if I look bad in
front of her right now, I'm
screwed. I'll have to close my
fricking doors.
TERRY
Then dump it. Give her Poplar. It
sucks but you've got your practice
to worry about, right?
MIKE
Yeah, I do.
TERRY
Incoming, dude.
Mike turns. Kyle approaches.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 91
CONTINUED:
MIKE
Hey, pal.
KYLE
Do you know she wants to take Leo
back to Ohio?
MIKE
Yeah. She just told me today.
KYLE
You're not gonna let her do that
are you?
MIKE
I don't know Kyle. It's
complicated.
KYLE
What's complicated about it? She
doesn't give a shit about Leo. They
hate each other. You can't let her
take him.
MIKE
OK. OK. Look, just go get ready for
practice and I'll deal with it.
KYLE
Fine but I told her I'm staying
with you guys until we leave.
Kyle leaves. Terry just looks at Mike.
TERRY
Wow. What's your play?
MIKE
I have no idea. I have no freaking
idea!
TERRY
She's looking for a payout, dude.
Just buy her stake and give her an
exit.
MIKE
What the hell does that mean?
TERRY
Just give her some of Leo's money
and send her home. He's not gonna
miss it. He's in happy land.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 92
CONTINUED:
MIKE
No, I can't do that. She's not even
in his...
Mike stops. A flash of inspiration.
MIKE (CONT'D)
That's right. She's not and she
doesn't and that's my play.
TERRY
What's your play?
Mike takes out his phone and dials.
MIKE
Don't worry about it. I just need
to make a call. Can you get
practice started?
TERRY
Really? You want me to slap your
face? Get you psyched up for the
call?
MIKE
No. I really don't.
EXT. BUSINESS CENTER - DAY.
Mike walks into the brick and glass tower.
MIKE (O.S.)
Look, we're all concerned with
what's best for Leo so I'm hoping
we can settle this in an amicable
way.
INT. ELEANOR COHEN'S OFFICE - SAME.
Mike is siting down with Eleanor and Cindy.
ELEANOR
So do we.
MIKE
Good, well, I thought I'd start by
laying all the cards on the table,
so maybe you can understand why I'm
hesitating in turning Leo over to
Cindy.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 93
CONTINUED:
ELEANOR
OK.
MIKE
Cindy, your father disinherited you
from his will. Completely. And I'm
afraid that can't change now that
he's been declared incapacitated.
CINDY
(TO ELEANOR)
Is that true?
ELEANOR
We'll have to see a copy of the
will, Mike.
MIKE
Yeah. I actually brought you a
copy.
Mike reaches into his briefcase and puts the A COPY OF THE
WILL on Eleanor's desk.
CINDY
Who did he leave it too? Did he
leave it to Kyle?!
MIKE
No.
CINDY
Then who? You?
MIKE
No. He left everything to the
municipal parks system. He wanted
the town park dedicated in his
name.
CINDY
That scumbag! He never cared about
anyone but himself and his fucking
money. Did you know about this?
ELEANOR
Cindy please!
CINDY
Please what?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 94
CONTINUED:
ELEANOR
(Annoyed to Mike)
I'd like to discuss this with my
client, Mr. Flaherty.
CINDY
What's to discuss? I'm not taking
care of him if I'm not getting
anything for it.
ELEANOR
Cindy, please.
(TO MIKE)
We're finished here.
MIKE
OK.
Mike gets up and walks out. A smile creeps across his face.
INT. UNION HIGH SCHOOL, GYM - DAY.
Jackie, Gina and the kids settle into the bleachers. A LARGE
BANNER reads NORTHEAST REGIONAL TOURNAMENT.
INT. UNION HIGH SCHOOL, HALLWAY - DAY.
Mike and Terry walking down the hallway eating SNICKER BARS.
TERRY
Brass balls, buddy. Brass balls.
MIKE
Yeah. And she's gone back to the
motel.
TERRY
That's good.
MIKE
Yes, it is. Yeah, I think it
worked.
TERRY
It totally worked. They opened
their kimono and you made them eat
the trade.
MIKE
I don't what know what your talking
about half the time.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 95
CONTINUED:
TERRY
Really?
MIKE
Yeah. Really.
INT. UNION HIGHSCHOOL, BACK GYM - LATER.
Kyle is warming up. Vigman is watching. Mike and Terry enter.
MIKE
It's time, Coach.
(TO KYLE)
You ready?
Kyle just walks out of the warm-up room.
VIGMAN
He's ready.
TERRY
Yeah, he is.
INT. UNION HIGHSCHOOL GYM - LATER.
The four men walk into the huge gym. It's packed. Kyle is
completely focused.
VIGMAN
Wow. This is big time. I bet there
are scouts here.
TERRY
Definitely. And wait till we get to
the states! Atlantic City here we
come, baby.
VIGMAN
Atlantic City. Fierce.
Mike smiles but then his smile fades. Cindy Timmons is
standing against the wall. She steps forward and Kyle sees
HER
CINDY
Good luck, baby.
Kyle keeps his head down and keeps walking. Mike looks
shocked but also keeps walking.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 96
INT. UNION HIGH SCHOOL, GYM - LATER.
Mike and Kyle are face to face.
MIKE
Listen to me. One more win and we
are going to the states. That's
what counts. That's all that
matters. You hear me?
Kyle nods. Mike can tell that he's half listening.
MIKE (CONT'D)
Hey! Kyle. Stay in this, OK. This
is your place. You are in control,
remember! You control it. Now go
get him. Finish this!
Mike slaps him. And Kyle races to the mat.
The wrestlers slap hands and THE REF blows the whistle. Kyle
immediately shoots in for a double leg. The Other Wrestler
tries to sprawl but Kyle is in too deep. Kyle lifts him high
and dumps him hard to the mat. The audience reacts and the
Ref stops the action. The other wrestler bravely pops up but
he is obviously stung.
REF
Warning. Red. One point.
MIKE
Kyle! Hey! Control! Control!
Kyle looks at Mike and nods but his eyes are wild. The Ref
blows the whistle and Kyle and the Other Wrestler lock up.
They dance a bit and finally the Other Wrestler tries to wrap
Kyle up. Kyle back pedals and then literally throws the Other
Wrestler off the mat. The Ref has seen enough. He quickly
issues Kyle his second warning and disqualifies him from the
match. It's over.
The Other Wrestler pops up and runs at Kyle. Kyle responds.
The Coaches all intervene. It's a melee.
INT. UNION HIGH SCHOOL, LOCKER ROOM - DAY.
Kyle is sitting on the bench, perfectly still. Mike walks in
and sits down next to him.
MIKE
How you doing?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 97
CONTINUED:
Kyle stares at the floor.
KYLE
I'm sorry.
MIKE
Hey, it's alright.
Mike puts his arm on his shoulder and Kyle starts to cry.
Mike squeezes him.
KYLE
I don't want to go with her. I
don't.
MIKE
OK, pal. OK.
EXT. UNION HIGH SCHOOL, PARKING LOT - LATER.
Mike, Terry and Kyle walk out of the school. The entire
family is waiting for them. Jackie gives Kyle a big hug. Abby
takes his hand. They all get into their car. Mike is just
about to get in but then he sees Cindy standing by her car
watching. He shuts his door and crosses to her.
MIKE
Why are you here?
CINDY
I wanted to see my son wrestle.
MIKE
Yeah, well your son had a pretty
good chance to do something special
in there. Maybe even change his
life and that's gone now. I hope
you're happy.
CINDY
That's not my fault.
MIKE
It isn't? Why do you think he lost
his shit in there, huh?! What do
you want, lady?
CINDY
I want my father.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 98
CONTINUED:
MIKE
It didn't sound like that the other
day. It sounded like you hated the
guy.
CINDY
You have no idea what my father
used to be like. No idea! He wasn't
like he is now! He treated me like
shit and he was all I had!
MIKE
So now you want to return the
favor? Is that it?!
CINDY
I want that commission! That should
be mine!
MIKE
And that's why you're doing all
this? For fifteen hundred dollars a
month?
CINDY
Isn't that why you did it?
This stops Mike in his tracks.
MIKE
Alright, I'll tell you what. You
want the commission? You can have
it. And you don't even have to take
Leo. I'll take care of him for free
and I'll send you the check every
month. On one condition.
CINDY
What's that?
MIKE
You leave Kyle here. With us. Until
he finishes high school.
CINDY
I'm his mother. He belongs with me.
MIKE
Are you sure he feels that way?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 99
CONTINUED:
CINDY
Don't tell me what my son feels!
He's coming with me and there isn't
anything you can do about that.
MIKE
Then you can't have that
commission.
CINDY
We'll see about that.
MIKE
Yeah, we will.
Mike turns and walks away.
CINDY
I want to see my son!
MIKE
Then call him! You have his number!
INT. MIKE AND JACKIE'S HOUSE, BACK PORCH - DUSK.
Mike sits on the back porch nursing a beer. Terry stands in
the yard facing away from him.
TERRY
We were right there, Mike. Right
fucking there. And now we have
nothing. Nothing!
Terry screams. It's a primal scream. Mike just looks at him.
MIKE
You OK?
TERRY
No.
Terry drinks. Mike watches him. Jackie pops out from the
kitchen.
JACKIE
Mike, your mom's here and dinner's
almost ready. Have you seen Kyle?
MIKE
He's not in the basement?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 100
CONTINUED:
JACKIE
No.
TERRY
I'll track him down.
MIKE
Thanks, Terry.
TERRY
(TO JACKIE)
What a day, huh?
JACKIE
Yeah, right.
Terry goes inside. Jackie sits next to Mike.
JACKIE (CONT'D)
You OK?
Mike shrugs.
JACKIE (CONT'D)
What are we gonna do, Mike?
MIKE
There's nothing to do. I can't stop
her. She's gonna leave and she's
gonna take Kyle and Leo with her.
JACKIE
And you don't think you'd beat her
in court?
MIKE
No. I don't.
JACKIE
Why? It's so obvious she's just
wants him for the money.
Mike turns to Jackie. He wants to tell her but just can't.
MIKE
I just can't win this one, Jackie.
Trust me.
Jackie misinterprets Mike's guilt for pain. She backs off.
JACKIE
I do.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 101
INT. CINDY'S MOTEL ROOM - LATER.
Cindy is smoking next to the open window. She is nervous. A
knock on the door. She throws the cigarette out the window
and closes it. She checks herself in the mirror and opens the
door. Kyle is standing there.
CINDY
Kyle, honey, come in. I'm so glad
you came.
She steps back and he enters.
CINDY (CONT'D)
Have a seat, honey. Do you want a
soda or something?
He sits on one bed.
KYLE
No. What do you want?
She sits on the other facing him.
CINDY
I just wanted to say how sorry I
was about the match and if I did
anything to cause it then I will
never forgive myself. I know how
much wrestling means to you, baby.
KYLE
Is that why you called me. Just to
tell me that?
CINDY
No. I also wanted to say that I'll
do whatever you think is best for
Leo. I promise.
KYLE
Then leave him here. Where he is.
CINDY
OK. I will. If that's what you
want. But I have to be honest, I'm
not sure that's what Leo wants.
KYLE
What do you mean?
CINDY
Here. Read this.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 102
CONTINUED:
She hands him a piece of paper.
KYLE
What is it?
CINDY
It's the court transcript from when
Leo was in court. My lawyer got it.
Read the parts in yellow. See what
it says.
Kyle reluctantly reads it.
KYLE
This isn't real. The Judge told Leo
he had to live there.
CINDY
No, honey. This is official from
the court. It's what Mike said.
Kyle reads it again.
CINDY (CONT'D)
He gets paid for being Leo's
guardian, Kyle. And then he just
put him in that place so he didn't
have to worry about him.
Kyle stares at the page.
CINDY (CONT'D)
Leo belongs with us, Kyle.
KYLE
Why?
Cindy is caught of guard by the question.
CINDY
Why what?
KYLE
Why does he belong with us?
Cindy judges her son's look and speaks from the heart.
CINDY
Because we deserve that money,
Kyle. Not some lawyer. You're a big
boy. You can understand that.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 103
CONTINUED:
Kyle looks at the page on more time and then suddenly,
without warning, pounces on his mother pinning her to the
bed. She screams. He gets in her face.
KYLE
Shut up! Shut up!
She finally quiets. Terrified.
KYLE (CONT'D)
Listen to me! I don't care about
this. It's all bullshit. Leave Leo
alone. He belongs here. Do you hear
me? Do you?
Cindy can only cry and nod. Kyle grabs the paper and runs out
the door.
INT. MIKE'S HOUSE - LATER.
Mike paces around talking on the phone.
MIKE
OK. Thanks, Karen. I appreciate it.
Bye.
Jackie walks into the room.
JACKIE
Anything?
MIKE
He's not at Stemler's.
JACKIE
This is crazy, where could he be?
MIKE
I don't know, he's upset, maybe he
went for a walk.
JACKIE
Well we should take a drive, your
mom can stay with the kids.
His phone rings. Jackie stops.
MIKE
Hello. Yes, this is him. What?
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 104
INT. OAK KNOLL SENIOR LIVING, RECEPTION - LATER.
A STAFF MEMBER is at the desk.
STAFF MEMBER
Sir, stay calm, we'll find him.
MIKE
Stay calm? You've lost my ward!
JACKIE
Mike! Calm down.
MIKE TERRY
Calm down?! We are gonna sue you guys,
silly. He's a laywer!
The Staff Member picks up the phone.
STAFF MEMBER
Look, he's definitely not on the
premises. A lot of the time they
just try to go home. We're about to
go there.
Mike and Jackie share a look and leave. Terry turns to some
residents who are looking on.
TERRY
Hey folks, listen up! Watch out for
each other.
MIKE (O.S.)
Terry!
EXT. LEO POPLAR'S HOUSE - LATER.
Mike's car pulls up. They all get out and run up to the
house.
TERRY
There's a light on.
JACKIE
It's got to be him. Do have the
key?
MIKE
No. I didn't bring it with me.
They arrive at the front door. Mike tries the knob. It's
locked.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 105
CONTINUED:
MIKE (CONT'D)
Shit.
Mike goes to edge of the porch, climbs up onto the railing
and looks into the side window. Leo is sitting in a chair
watching TV.
MIKE (CONT'D)
There he is!
JACKIE
What's he doing?
MIKE
Watching TV.
TERRY
What's he watching?
JACKIE
Who cares?
MIKE
Leo? Hey Leo?
Mike knocks on the window. Leo doesn't register it.
MIKE (CONT'D)
He's not responding. Ring the bell.
Jackie does. Leo still doesn't respond.
MIKE (CONT'D)
Nothing. Fuck.
TERRY
This is freaking spooky.
Mike climbs down back onto the porch.
TERRY (CONT'D)
Should we break in?
MIKE
I have a key back at the office. I
could go get it.
JACKIE
Is he OK?
MIKE
He seems it. He's just sitting
there.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 106
CONTINUED:
Suddenly the door opens. Leo is standing there.
LEO
Hi.
MIKE/TERRY/JACKIE
Hi./Hey.
LEO
Come on in.
Leo walks away. They all follow him.
TERRY
OK. That is very creepy.
INT. LEO POPLAR'S HOUSE - SAME.
They walk into the house following Leo into the living room.
He sits back in his chair and start watching TV again.
MIKE
You OK, Leo?
Leo just watches TV.
MIKE (CONT'D)
How did you get here, pal?
Mike stoops over and tries to connect with Leo.
MIKE (CONT'D)
(GENTLY)
Did you walk here, Leo?
Leo turns and looks at them as if he is about to speak. The
all wait for his reply and then...
KYLE (O.S.)
I brought him here.
They all jump.
JACKIE MIKE
Kyle? You took Leo?
KYLE (CONT'D)
Yeah.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 107
CONTINUED:
MIKE
Have you lost your mind?! We've
been worried sick about him!
JACKIE
About both of you!
KYLE
You don't have to worry about us.
Kyle walks out of the room.
TERRY
OK. That's super spooky. Just
saying.
INT. LEO POPLAR'S KITCHEN - CONTINUOUS.
Kyle walks into the kitchen, he turns off a pot of boiling
water and strains some pasta.
MIKE
Kyle, What the hell are you doing?
KYLE
(VERY CALMLY)
Making spaghetti.
MIKE
Have you lost your mind?
KYLE
No.
JACKIE
Kyle, why did you do this? Please
just tell us. Leo needs to be in a
home.
KYLE
This is where he belongs.
JACKIE
Kyle he needs to be at Oak Knoll.
MIKE
Kyle, we talked about this.
KYLE
Yeah. We did! Listen to this.
Kyle takes a piece of paper out of his pocket.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 108
CONTINUED:
KYLE (CONT'D)
(READING)
Mike Flaherty: Mr. Poplar wants to
live at home. Judge Lee: You can do
that Mike? Mike Flaherty: Yes, I
can. Really.
JACKIE
What is that?
Jackie takes it and looks at it.
KYLE
It's from the court.
JACKIE
Where did you get this?
KYLE
From my mother.
(TO MIKE)
It's true isn't, Mike?
JACKIE
Mike?
Mike can't answer. Kyle's seen enough.
KYLE
You're just like her.
He runs out. They all give chase.
EXT. LEO POPLAR'S HOUSE - CONTINUOUS.
Mike runs outside and see's Kyle crossing the lawn. He
quickly catches up to him. Terry and Jackie follow close
behind.
MIKE
Hey. Hey, Kyle.
Kyle keeps walking.
MIKE (CONT'D)
Hey can you hold on a second?
KYLE
Leave me alone!
MIKE
Kyle please.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 109
CONTINUED:
Mike grabs Kyle one more time. Kyle rips his arm away and
tries to push Mike back.
KYLE
Don't touch me!
Mike deflects Kyle and Kyle spills to the ground.
TERRY
Oh shit.
Kyle gets up and starts to circle Mike. Mike has no choice
but reciprocate.
MIKE
Would you let me explain?!
KYLE
Explain what? How you lied to me?
How you lied to Leo?
Kyle head pumps. Mike takes the bait and jumps back.
MIKE TERRY
Kyle wait... Watch the head fake!
MIKE
Kyle I don't want to wrestle you.
JACKIE TERRY
Kyle, stop for a minute. Keep your hands out, Mike.
Hands out.
JACKIE
Terry, stop it!
TERRY
I'm just trying to help.
JACKIE
You're not helping.
Kyle head fakes again but this time he's in. Before Mike
knows what hits him, he's on his back.
MIKE TERRY
Ow! Oh shit.
JACKIE (CONT'D)
Mike, stop it!
Kyle is all over Mike. Mike's trying to fight back but it's
useless and even kind of pathetic.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 110
CONTINUED:
MIKE
I'm trying to stop it!
TERRY
Sit out Mike! Sit out!
JACKIE MIKE
Shut up, Terry! Kyle, stop it!
Mike gets up to hands and knees but Kyle drives him hard to
the ground.
MIKE (CONT'D) TERRY
Ow! Shit! Ouch! He's getting killed.
JACKIE
Would you stop coaching and break
that up!
Terry rushes in and tries to pull Kyle off but he's lost it.
Finally, he wraps his arms around Kyle and pulls him off.
Kyle spins free and fronts Terry. Terry immediately puts up
his hands.
TERRY
I'm the ref. I'm just the ref!
Kyle turns and runs off.
JACKIE
Kyle! Stop! Please!
He doesn't stop. Jackie turns to Mike.
JACKIE (CONT'D)
Is that true, Mike?
MIKE
Yeah, it is.
Mike gets up.
JACKIE
So why'd you move him if he wanted
to stay here.
MIKE
Because it would have been too much
work to leave him here. I couldn't
have done it.
JACKIE
Then you shouldn't have taken him.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 111
CONTINUED:
MIKE
I had to, alright?
JACKIE
Why?!
MIKE
Because I needed the money! We
needed the money.
JACKIE
You moved an old man out of his
house to make money? Have you lost
your freaking mind?
MIKE
No! I just didn't think it would
get this complicated.
JACKIE
Really? Or you just didn't think
you'd get caught?
This stops Mike in his tracks. He can't answer. Jackie turns
and walks away.
MIKE
Jack! Jack, where are you going?
JACKIE
Home!
She walks away.
137 INT. STEMLER HOUSE, BASEMENT - SAME. 137
Stemler is sleeping on one couch. Kyle on the other. Kyle's
cell phone rings. He wakes up and checks it. He answers it.
KYLE
Hello. Hello. Mom?
She's not there. He hangs up. Kyle starts to put on his
shoes.
STEMLER
Did your mom just crank call you?
KYLE
No.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 112
CONTINUED:
STEMLER
So you and Coach Mike get in a
fight because you lost?
KYLE
No. We got in a fight because he's
an asshole.
STEMLER
Really?
KYLE
Yeah, really, Stem.
STEMLER
Well I'm sure he'll make it up to
you, bro. You're the best wrestler
he's ever had. I mean he's always
been cool to me and I suck.
This comment lands with Kyle.
INT. OAK KNOLL SENIOR LIVING - MORNING.
Mike is sleeping on a love seat. He wakes up. Leo is sitting
there watching him.
MIKE
Hey Leo.
LEO
Hi.
MIKE
I fell asleep. I'm sorry.
LEO
Sorry for what?
That's a big question. Mike cuts to the chase.
MIKE
You want to go home?
LEO
Yeah.
INT. MIKE AND JACKIE'S HOUSE - LATER.
Jackie is sitting with Stella and a cup of coffee. The front
door opens and closes. Mike walks into the kitchen.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 113
CONTINUED:
JACKIE
Hi.
MIKE
Hi. Is he here?
JACKIE
No. He slept at Stemler's. How
about you?
MIKE
Oak Knoll.
(BEAT)
You're right, that's not who I am.
JACKIE
So what are you going to do?
MIKE
I have to go court.
JACKIE
You can't. You told the Judge you
were keeping Leo at home.
MIKE
I know.
JACKIE
So then tell her you changed your
mind. No one can question that.
MIKE
I can't, Jack.
JACKIE
Why not?
MIKE
Because it's not true.
JACKIE
Well I'm glad your done lying now,
just in time to lose your practice.
That's how we survive, Mike. Your
family. You ever think of that?
MIKE
Yeah. All the time.
Jackie quickly crosses to the sink. She starts to clean. She
breaks something.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 114
CONTINUED:
JACKIE
Shit.
She braces herself against the sink and exhales. Mike just
watches her.
MIKE
I'm sorry, Jack. I really am.
JACKIE
I know.
A noise from the basement. Mike heads down the stairs.
INT. MIKE AND JACKIE'S HOUSE, BASEMENT - CONTINUOUS.
Jackie and Mike walk downstairs. Kyle is angrily gathering
his stuff and putting it in his back pack.
JACKIE
Hey Kyle. How'd you get down here?
KYLE
The window.
JACKIE
Are you hungry? I was gonna make
some pancakes.
KYLE
No. I'm leaving. I just came to get
my shit.
They share a look and walk over to Kyle.
MIKE
Kyle, listen, I just wanted to say
I'm sorry...
KYLE
I know, Mike, you're sorry.
Everyone's always sorry.
MIKE
I moved Leo back home, Kyle. And
I'm gonna fight to keep him there.
KYLE
It's too late. You'll lose. My
mother's gonna take him.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 115
CONTINUED:
MIKE
Maybe but I'm still gonna try.
KYLE
So what?! You want me to forgive
you now? Is that it, Mike?!
MIKE
No. I just want you to give me
another chance. That's all I'm
asking.
Mike's sincerity is undeniable. Kyle looks to Jackie. They
connect. Kyle shakes his head, turns around, and then throws
his bag.
KYLE
This is bullshit!
Mike looks at Jackie.
MIKE
Hey, Kyle, listen -
KYLE
I want to be alone.
MIKE
What?
KYLE
(Without looking at them)
I JUST WANT TO BE DOWN HERE ALONE!
MIKE
OK. All right. Yeah.
Jackie and Mike turn and start to walk upstairs but Jackie
stops.
JACKIE
Kyle, I just wanna say - we love
you.
Kyle keeps his back turned to them as they continue up the
stairs.
INT. KITCHEN - LATER.
Tight on the Baby Monitor. We hear Stella crying and Jackie
talking to Abby.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 116
CONTINUED:
JACKIE (O.S.)
Abby, just pick a shirt and put it
on. Please.
Mike is sitting alone at the kitchen table drinking a cup of
coffee. The remnants of a pancake breakfast are on the table.
There is one clean plate where Kyle usually sits.
After a moment, Kyle comes up from the basement and sits down
at the table without saying anything.
He just looks at Mike. Then he serves himself a few pancakes.
Mike passes him the bottle of syrup. He takes it and puts
some on his pancakes.
He eats. Mike watches.
EXT. UNION COUNTY COURT HOUSE - DAYS LATER.
The group is walking up the front steps of the court house.
Terry joins.
TERRY
Hi guys.
MIKE
What are you doing here?
TERRY
Dude, I'm your assistant coach. And
just notice who isn't here.
Mike smiles.
TERRY (CONT'D)
Stephen Vigman.
MIKE
Yeah, I got it.
Terry puts his arm on his friend's shoulder.
INT. UNION COUNTY COURT HOUSE - LATER.
The whole gang is walking toward to the courtroom.
ELEANOR
Mike?
Mike turns. Eleanor approaches.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 117
CONTINUED:
MIKE
Hi Eleanor.
ELEANOR
Can I talk to you?
MIKE
Sure.
Mike and Eleanor step to the side. She looks at Mike.
ELEANOR
You know the transcript alone is
enough to hang you.
MIKE
Yeah, well, we'll see what happens.
Eleanor just looks at him, Judge and Jury. Mike blinks.
ELEANOR
Shame on you counselor.
MIKE
Is that it?
ELEANOR
No. My client would like to talk to
you.
Mike and Eleanor walk over to Cindy. She is barely holding it
together.
MIKE
Hi Cindy.
CINDY
Hi. Is your deal still available?
Mike tries to conceal his shock.
MIKE
What about Kyle?
Cindy and Eleanor share a look.
CINDY
He can stay.
MIKE
Then yes. It is.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 118
CONTINUED:
CINDY
And you'll send me the checks?
MIKE
Every month.
CINDY
You take good care of him.
MIKE
We will.
Cindy nods.
CINDY
I want to say goodbye.
Mike turns and waves Kyle over.
Kyle look to Jackie who gives him the OK. He walks over as
Mike steps away. He just looks at his mother. She gently
touches his face. He doesn't move.
Everyone looks on as Cindy says a few words to Kyle, hugs him
hard and then quickly turns and walks away. Kyle watches her
go.
EXT. MIKE AND JACKIE'S HOUSE - EARLY EVENING.
A croquet ball hits a stick.
ABBY (O.S.)
Your turn.
Abby, Kyle, and Stemler are playing on the front lawn.
STEMLER
I know. Don't rush me.
Stemler hits a shot and the ball goes into the garden.
STEMLER (CONT'D)
This mallet is crap! You see that?
Mike pulls up and gets out of his car, wearing a suit and
carrying his briefcase.
MIKE
Hi guys!
ABBY
Hi, Daddy. I'm winning.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 119
CONTINUED:
STEMLER KYLE
What's up, coach? Hi.
MIKE
That's great, honey. Kyle, can you
drag those garbage cans to the side
of the house for me?
KYLE
OK.
MIKE
Thanks, pal.
He runs inside.
INT. MIKE AND JACKIE'S HOUSE - CONTINOUS.
Mike drops his briefcase and takes off his coat.
MIKE
Hi Honey.
JACKIE (O.S.)
How was work?
MIKE
Good. I got stuck at the office
with a client.
Jackie walks in from the other room, gives Mike a kiss.
JACKIE
I know, Shelly called. Oh, I
dropped off the fan at Leo's today.
MIKE
Thanks for doing that.
Mike heads upstairs.
MIKE (CONT'D)
I'll be right back down.
JACKIE
Do you have time to eat.
MIKE
I'll eat there.
JACKIE
Make sure you do.
5/15/10 - FULL SHOOTING SCRIPT - WIN WIN 120
INT. MIKE AND JACKIE'S HOUSE, BEDROOM - LATER.
Mike takes off his suit and throws it on the bed. He puts on
a casual button down blue shirt.
He takes a hard look himself in the mirror, almost as if he's
steeling himself for something.
Mike smiles.
INT. BAR - NIGHT.
Terry walks in and crosses to the bar. He sits down.
TERRY
Can I get a banana daiquiri,
please?
The Bartender turns. It's Mike.
MIKE
Sure.
Mike opens a beer and sets it down in front of Terry.
MIKE (CONT'D)
You want an umbrella with that?
TERRY
Nah. I'm good. But keep these
coming.
Mike checks a ticket and prepares two drinks.
TERRY (CONT'D)
So how you doing, pal?
MIKE
Me? I'm pretty good.
We hold on Mike as he continues to work.
BLACK OUT.
Win Win
Writers : Tom McCarthy
Genres : Comedy Drama
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This is a list of the amphibians of the archipelago of Puerto Rico. The Puerto Rican archipelago consists of the main island of Puerto Rico, two island municipalities, Vieques and Culebra, one minor uninhabited island, Mona and several smaller islands and cays.
This list only includes animals with verifiable established populations in the archipelago of Puerto Rico. Many species of amphibians are introduced, both legally mainly through the pet industry and illegally, to the archipelago of Puerto Rico every year, with some of these species being subsequently released into the wild. However, non-viable breeding species do not constitute a breeding population and hence they lack inclusion in this list.
The following tags help provide additional information regarding the status of each species.
Endemic species.
Introduced species.
Extinct species.
Extirpated species
Amphibians
Family Bufonidae
Family Hylidae
Family Leptodactylidae
Family Ranidae
See also
Fauna of Puerto Rico
List of endemic fauna of Puerto Rico
List of endemic flora of Puerto Rico
List of mammals of Puerto Rico
List of birds of Puerto Rico
List of reptiles of Puerto Rico
Footnotes
This species is endemic to the archipelago of Puerto Rico.
This species is extinct.
This species no longer occurs in the archipelago Puerto Rico but other populations exist elsewhere.
This species was introduced to the archipelago of Puerto Rico.
This species occurs in Caja de Muertos Island.
This species occurs in Cayo Batata.
This species occurs in Cayo Santiago.
This species occurs in the island of Desecheo.
This species occurs in Magueyes island.
This species occurs in the island of Monito.
This species occurs in the island of Culebrita.
References
Rios-López, N. and R. Thomas. 2007. A new species of palustrine Eleutherodactylus Anura: Leptodactylidae from Puerto Rico. Zootaxa 1512: 5164
Amphibians
Puerto Rico
Amphibians
Puerto Rico | wikipedia |
Chamaecrista is a genus of flowering plants in the pea family, Fabaceae, subfamily Caesalpinioideae. Members of the genus are commonly known as sensitive pea. Several species are capable of rapid plant movement. Unlike the related genera Cassia and Senna, members of Chamaecrista form root nodules.
Species
Chamaecrista comprises the following species, organized into sections, subsections, and series:
Section Apoucouita Benth.
Series Apoucouita
Chamaecrista aiarana H.S.Irwin H.S.Irwin & Barneby
Chamaecrista apoucouita Aubl. H.S.Irwin & Barneby
Chamaecrista aspidiifolia H.S.Irwin & Barneby
Chamaecrista bahiae H.S.Irwin H.S.Irwin & Barneby
Chamaecrista boyanii H.S.Irwin & Barneby H.S.Irwin
Chamaecrista compitalis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista duartei H.S.Irwin H.S.Irwin & Barneby
Chamaecrista eitenorum H.S.Irwin & Barneby H.S.Irwin
var. eitenorum H.S.Irwin & Barneby H.S.Irwin
var. regana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista ensiformis Vell. H.S.Irwin & Barneby
var. ensiformis Vell. H.S.Irwin & Barneby
var. maranonica H.S.Irwin H.S.Irwin & Barneby
var. plurifoliolata Hoehne H.S.Irwin & Barneby
Chamaecrista hymenaeifolia Benth. H.S.Irwin & Barneby
Chamaecrista negrensis H.S.Irwin H.S.Irwin & Barneby
var. albuquerquei H.S.Irwin & Barneby H.S.Irwin
var. negrensis H.S.Irwin H.S.Irwin & Barneby
Chamaecrista onusta H.S.Irwin & Barneby
Chamaecrista polystachya Benth. H.S.Irwin & Barneby
Chamaecrista scleroxylon Ducke H.S.Irwin & Barneby
Chamaecrista subpeltata Rizzini H.S.Irwin & Barneby
Chamaecrista xinguensis Ducke H.S.Irwin & Barneby
Series Pteridophyllae
Chamaecrista adiantifolia Spruce ex Benth. H. S. Irwin & Barneby
var. adiantifolia Spruce ex Benth. H. S. Irwin & Barneby
var. pteridophylla Sandwith H.S.Irwin & Barneby
Chamaecrista aspleniifolia H.S.Irwin & Barneby H.S.Irwin
Section Absus DC. ex Colladon emend. Irwin & Barneby
Subsection Absus DC. ex Colladon
Series Absoideae
Chamaecrista acosmifolia Benth. H.S.Irwin & Barneby
var. acosmifolia Benth. H.S.Irwin & Barneby
var. euryloba H.S.Irwin & Barneby H.S.Irwin
var. oropedii H.S.Irwin & Barneby H.S.Irwin
Chamaecrista amiciella H.S.Irwin & Barneby H.S.Irwin
Chamaecrista andersonii H.S.Irwin & Barneby H.S.Irwin
Chamaecrista barbata Nees & Mart. H.S.Irwin & Barn
Chamaecrista belemii H.S.Irwin & Barneby H.S.Irwin
var. belemii H.S.Irwin & Barneby H.S.Irwin
var. paludicola H.S.Irwin & Barneby H.S.Irwin
Chamaecrista brevicalyx Benth. H.S.Irwin & Barneby
var. brevicalyx Benth. H.S.Irwin & Barneby
var. elliptica H.S.Irwin & Barneby H.S.Irwin
Chamaecrista campestris H.S.Irwin & Barneby
Chamaecrista carobinha H.S.Irwin & Barneby H.S.Irwin
Chamaecrista chapadae H.S.Irwin & Barneby H.S.Irwin
Chamaecrista egleri H.S.Irwin & Barneby H.S.Irwin
Chamaecrista fagonioides Vogel H.S.Irwin & Barneby
var. fagonioides Vogel H.S.Irwin & Barneby
var. macrocalyx H.S.Irwin & Barneby H.S.Irwin
Chamaecrista hispidula Vahl H.S.Irwin & Barneby
Chamaecrista jacobinea Benth. H.S.Irwin & Barneby
Chamaecrista juruenensis Hoehne H.S.Irwin & Barneby
Chamaecrista longicuspis Benth. H.S.Irwin & Barneby
Chamaecrista multiseta Benth. H.S.Irwin & Barneby
Chamaecrista paraunana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista punctulata Hook. & Arn. H.S.Irwin & Barn
Chamaecrista roncadorensis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista rugosula Benth. H.S.Irwin & Barneby
Chamaecrista salvatoris H.S.Irwin & Barneby H.S.Irwin
Chamaecrista souzana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista tetraphylla Britton & Rose
Chamaecrista viscosa Kunth H.S.Irwin & Barneby
var. major Benth. H.S.Irwin & Barneby
var. paraguayensis Chodat & Hassl. H.S.Irwin & Barneby
var. viscosa Kunth H.S.Irwin & Barneby
Chamaecrista zygophylloides Taub. H.S.Irwin & Barneby
var. caribaea H.S.Irwin & Barneby H.S.Irwin
var. colligans H.S.Irwin & Barneby H.S.Irwin
var. deamii Britton & Rose H.S.Irwin & Barneby
var. zygophylloides Taub. H.S.Irwin & Barneby
Series Adenophyllae
Chamaecrista adenophylla Taub. H.S.Irwin & Barneby
Chamaecrista chrysosepala H.S.Irwin & Barneby H.S.Irwin
Chamaecrista hatschbachii H.S.Irwin & Barneby
Chamaecrista itabiritoana H.S.Irwin & Barneby H.S.Irwin
Series Andromedeae
Chamaecrista andromedea Benth. H.S.Irwin & Barneby
Series Atroglandulosae
Chamaecrista atroglandulosa Harms H.S.Irwin & Barneby
Series Bracteolatae
Chamaecrista bracteolata Vogel H.S.Irwin & Barneby
Chamaecrista glaziovii Harms H.S.Irwin & Barneby
Chamaecrista phyllostachya Benth. H.S.Irwin & Barneby
Series Catharticae
Chamaecrista cathartica Mart. H.S.Irwin & Barneby
var. cathartica Mart. H.S.Irwin & Barneby
var. paucijuga H.S.Irwin & Barneby H.S.Irwin
Chamaecrista catharticoides H.S.Irwin & Barneby H.S.Irwin
Chamaecrista microsenna H.S.Irwin & Barneby H.S.Irwin
Series Confertae
Chamaecrista caespitosa Benth. H.S.Irwin & Barneby
Chamaecrista conferta Benth. H.S.Irwin & Barneby
var. conferta Benth. H.S.Irwin & Barneby
var. machrisiana Cowan H.S.Irwin & Barneby
var. simulans H.S.Irwin & Barneby H.S.Irwin
var. virgata H.S.Irwin & Barneby H.S.Irwin
Chamaecrista crommyotricha Harms H.S.Irwin & Barneby
Series Ericifoliae
Chamaecrista ericifolia Benth. H.S.Irwin & Barneby
Series Geminatae
Chamaecrista didyma H.S.Irwin & Barneby
Chamaecrista geminata Benth. H.S.Irwin & Barneby
Series Glutinosae
Chamaecrista caracensis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista catiarae H.S.Irwin & Barneby H.S.Irwin
Chamaecrista dentata Vogel H.S.Irwin & Barneby
Chamaecrista echinocarpa Benth. H.S.Irwin & Barneby
Chamaecrista fragilis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista kirkbridei H.S.Irwin & Barneby H.S.Irwin
Chamaecrista lentiscifolia Benth. H.S.Irwin & Barneby
Chamaecrista myrophenges H.S.Irwin & Barneby H.S.Irwin
Chamaecrista punctulifera Harms H.S.Irwin & Barneby
Chamaecrista semaphora H.S.Irwin & Barneby H.S.Irwin
Chamaecrista stillifera H.S.Irwin & Barneby H.S.Irwin
Series Gracillimae
Chamaecrista benthamii Ghesq. H.S.Irwin & Barneby
Series Hassleranae
Chamaecrista hassleri H.S.Irwin & Barneby H.S.Irwin
Series Hedysaroides
Chamaecrista hedysaroides Vogel H.S.Irwin & Barneby
Series Incanae
Chamaecrista incana Vogel H.S.Irwin & Barneby
Series Incurvatae
Chamaecrista incurvata Benth. H.S.Irwin & Barneby
var. incurvata Benth. H.S.Irwin & Barneby
var. zanclodes H.S.Irwin & Barneby H.S.Irwin
Chamaecrista lavradioides Benth. H.S.Irwin & Barneby
Chamaecrista linearifolia G.Don H.S.Irwin & Barneby
var. bradei Harms H.S.Irwin & Barneby
var. linearifolia G.Don H.S.Irwin & Barneby
Chamaecrista planifolia H.S.Irwin & Barneby H.S.Irwin
Series Lomatopodae
Chamaecrista lomatopoda Benth. H.S.Irwin & Barneby
Series Lucidae
Chamaecrista amambaya H.S.Irwin & Barneby H.S.Irwin
Chamaecrista caiapo H.S.Irwin & Barneby H.S.Irwin
Chamaecrista labouriaeae H.S.Irwin & Barneby H.S.Irwin
Chamaecrista lamprosperma Benth. H.S.Irwin & Barneby
Chamaecrista seticrenata H.S.Irwin & Barneby H.S.Irwin
Series Microphyllae
Chamaecrista adenophora Harms H.S.Irwin & Barneby
Chamaecrista cristalinae H.S.Irwin & Barneby H.S.Irwin
Chamaecrista dalbergiifolia Benth. H.S.Irwin & Barneby
Chamaecrista decrescens Benth. H.S.Irwin & Barneby
Chamaecrista dumalis Hoehne H.S.Irwin & Barneby
Chamaecrista elachistophylla Harms H.S.Irwin & Barneby
Chamaecrista foederalis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista harmsiana H.S.Irwin & Barneby
Chamaecrista huntii H.S.Irwin & Barneby H.S.Irwin
Chamaecrista imbricans H.S.Irwin & Barneby H.S.Irwin
Chamaecrista isidorea Benth. H.S.Irwin & Barneby
Chamaecrista neesiana Benth. H.S.Irwin & Barneby
var. goyazensis Taub. H.S.Irwin & Barneby
var. laxiracemosa Harms H.S.Irwin & Barneby
var. neesiana Benth. H.S.Irwin & Barneby
var. subnitida Taub. H.S.Irwin & Barneby
Chamaecrista nuda H.S.Irwin & Barneby H.S.Irwin
var. correntina H.S.Irwin & Barneby H.S.Irwin
var. huntii H.S.Irwin & Barneby H.S.Irwin
Chamaecrista pohliana Benth. H.S.Irwin & Barneby
Chamaecrista polymorpha Harms H.S.Irwin & Barneby
Chamaecrista psoraleopsis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista sincorana Harms H.S.Irwin & Barneby
Chamaecrista subdecrescens H.S.Irwin & Barneby H.S.Irwin
Series Nigricantes
Chamaecrista calixtana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista fodinarum H.S.Irwin & Barneby
Chamaecrista gilliesii Harms H.S.Irwin & Barneby
Chamaecrista glischrodes H.S.Irwin & Barneby
Chamaecrista itambana Benth. H.S.Irwin & Barneby
Chamaecrista lavradiiflora Harms H.S.Irwin & Barneby
Chamaecrista machaeriifolia Benth. H.S.Irwin & Barneby
Chamaecrista philippi H.S.Irwin & Barneby H.S.Irwin
Chamaecrista pilicarpa Harms H.S.Irwin & Barneby
Chamaecrista sophoroides Benth. H.S.Irwin & Barneby
Chamaecrista tephrosiifolia Benth. H.S.Irwin & Barneby
Chamaecrista urophyllidia H.S.Irwin & Barneby H.S.Irwin
Series Ochnaceae
Chamaecrista bifoliola Harms H.S.Irwin & Barneby
Chamaecrista cotinifolia G.Don H.S.Irwin & Barneby
var. cotinifolia G.Don H.S.Irwin & Barneby
var. glaberrima H.S.Irwin & Barneby H.S.Irwin
var. leptodictya H.S.Irwin & Barneby H.S.Irwin
var. percoriacea H.S.Irwin & Barneby H.S.Irwin
Chamaecrista crenulata Benth. H.S.Irwin & Barneby
Chamaecrista desertorum Benth. H.S.Irwin & Barneby
Chamaecrista geraldii H.S.Irwin & Barneby H.S.Irwin
Chamaecrista ochnacea Vogel H.S.Irwin & Barneby
var. latifolia Benth. H.S.Irwin & Barneby
var. mollis H.S.Irwin & Barneby H.S.Irwin
var. ochnacea Vogel H.S.Irwin & Barneby
var. purpurascens Benth. H.S.Irwin & Barneby
var. speluncae H.S.Irwin & Barneby H.S.Irwin
Chamaecrista punctata Vogel H.S.Irwin & Barneby
Chamaecrista vauthieri Benth. H.S.Irwin & Barneby
Series Oligospermae
Chamaecrista oligosperma Benth. H.S.Irwin & Barneby
Series Paniculatae
Chamaecrista celiae H.S.Irwin & Barneby H.S.Irwin
Chamaecrista claussenii Benth. H.S.Irwin & Barneby
var. claussenii Benth. H.S.Irwin & Barneby
var. cyclophylla H.S.Irwin & Barneby H.S.Irwin
var. megacycla H.S.Irwin & Barneby H.S.Irwin
Chamaecrista lundii Benth. H.S.Irwin & Barneby
Chamaecrista orbiculata Benth. H.S.Irwin & Barneby
var. cercidifolia H.S.Irwin & Barneby H.S.Irwin
var. orbiculata Benth. H.S.Irwin & Barneby
var. trichothyrsus Harms H.S.Irwin & Barneby
var. ustulata H.S.Irwin & Barneby H.S.Irwin
Chamaecrista pachyclada Harms H.S.Irwin & Barneby
Chamaecrista rigidifolia Benth. H.S.Irwin & Barneby
var. rigidifolia Benth. H.S.Irwin & Barneby
var. veadeirana H.S.Irwin & Barneby H.S.Irwin
Series Pinifoliae
Chamaecrista paniculata Benth. H.S.Irwin & Barneby
Series Rigidulae
Chamaecrista altoana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista azulana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista benthamiana Harms H.S.Irwin & Barneby
Chamaecrista brachyblepharis Harms H.S.Irwin & Barneby
Chamaecrista brachyrachis Harms H.S.Irwin & Barneby
Chamaecrista chaetostegia H.S.Irwin & Barneby H.S.Irwin
var. chaetostegia H.S.Irwin & Barneby H.S.Irwin
var. obolaria H.S.Irwin & Barneby H.S.Irwin
Chamaecrista ciliolata Benth. H.S.Irwin & Barneby
var. caprina H.S.Irwin & Barneby H.S.Irwin
var. ciliolata Benth. H.S.Irwin & Barneby
var. pulchella H.S.Irwin & Barneby H.S.Irwin
Chamaecrista cipoana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista dawsonii Cowan H.S.Irwin & Barneby
Chamaecrista decumbens Benth. H.S.Irwin & Barneby
Chamaecrista densifolia Benth. H.S.Irwin & Barneby
Chamaecrista feliciana H.S.Irwin & Barneby H.S.Irwin
Chamaecrista filicifolia Benth. H.S.Irwin & Barneby
Chamaecrista glaucofilix H.S.Irwin & Barneby H.S.Irwin
Chamaecrista gymnothyrsa H.S.Irwin & Barneby H.S.Irwin
Chamaecrista macedoi H.S.Irwin & Barneby H.S.Irwin
Chamaecrista mollicaulis Harms H.S.Irwin & Barneby
Chamaecrista multipennis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista nanodes H.S.Irwin & Barneby H.S.Irwin
Chamaecrista nummulariifolia Benth. H.S.Irwin & Barneby
Chamaecrista planaltoana Harms H.S.Irwin & Barneby
Chamaecrista polita H.S.Irwin & Barneby H.S.Irwin
Chamaecrista strictula H.S.Irwin & Barneby H.S.Irwin
Series Secundae
Chamaecrista secunda Benth. H.S.Irwin & Barneby
Series Setosae
Chamaecrista amphibola H.S.Irwin & Barneby H.S.Irwin
Chamaecrista auris-zerdae H.S.Irwin & Barneby H.S.Irwin
Chamaecrista campicola Harms H.S.Irwin & Barneby
Chamaecrista obtecta Benth. H.S.Irwin & Barneby
Chamaecrista ochrosperma H.S.Irwin & Barneby H.S.Irwin
Chamaecrista orenocensis Benth. H.S.Irwin & Barneby
Chamaecrista scabra Benth. H.S.Irwin & Barneby
Chamaecrista setosa Vogel H.S.Irwin & Barneby
var. detonsa Benth. H.S.Irwin & Barneby
var. paucivenia H.S.Irwin & Barneby H.S.Irwin
var. setosa Vogel H.S.Irwin & Barneby
var. subsetosa Malme H.S.Irwin & Barneby
Series Spinulosae
Chamaecrista spinulosa H.S.Irwin & Barneby H.S.Irwin
Series Strictifoliae
Chamaecrista strictifolia Benth. H.S.Irwin & Barneby
Series Trachycarpae
Chamaecrista cavalcantina H.S.Irwin & Barneby H.S.Irwin
Chamaecrista trachycarpa Vogel H.S.Irwin & Barneby
var. acutifolia Benth. H.S.Irwin & Barneby
var. trachycarpa Vogel H.S.Irwin & Barneby
Chamaecrista venatoria H.S.Irwin & Barneby H.S.Irwin
Series Unijugae
Chamaecrista catapodia H.S.Irwin & Barneby H.S.Irwin
Chamaecrista monticola Benth. H.S.Irwin & Barneby
Series Ursinae
Chamaecrista adamantina H.S.Irwin & Barneby H.S.Irwin
Chamaecrista astrochiton H.S.Irwin & Barneby H.S.Irwin
Chamaecrista aurivilla Benth. H.S.Irwin & Barneby
Chamaecrista centiflora H.S.Irwin & Barneby H.S.Irwin
Chamaecrista exsudans Benth. H.S.Irwin & Barneby
Chamaecrista fuscescens Benth. H.S.Irwin & Barneby
Chamaecrista ixodes H.S.Irwin & Barneby H.S.Irwin
Chamaecrista leucopilis Harms H.S.Irwin & Barneby
Chamaecrista ursina Benth. H.S.Irwin & Barneby
Chamaecrista virginis H.S.Irwin & Barneby H.S.Irwin
Chamaecrista xanthadena Benth. H.S.Irwin & Barneby
Subsection Adenophyllum Irwin & Barneby
Chamaecrista bucherae Moldenke H.S.Irwin & Barneby Cuba
Subsection Baseophyllum Colladon Irwin & Barneby
Chamaecrista coriacea Benth. H.S.Irwin & Barneby
Chamaecrista cytisoides DC. ex Collad. H. S. Irwin & Barneby
var. blanchetii Benth. H.S.Irwin & Barneby
var. brachystachya Benth. H.S.Irwin & Barneby
var. confertiformis H.S.Irwin & Barneby H.S.Irwin
var. cytisoides DC. ex Collad. H. S. Irwin & Barneby
var. decora H.S.Irwin & Barneby H.S.Irwin
var. micrantha H.S.Irwin & Barneby H.S.Irwin
var. unijuga Benth. H.S.Irwin & Barneby
Subsection Otophyllum Irwin & Barneby
Chamaecrista debilis Vogel H.S.Irwin & Barneby
Section Caliciopsis Irwin & Barneby
Chamaecrista calycioides DC. ex Collad. Greene
Chamaecrista duckeana P.Bezerra & Alf.Fern. H.S.Irwin
Section Chamaecrista Moench
Series Bauhinianae Colladon Irwin & Barneby
Chamaecrista basifolia Vogel H.S.Irwin & Barneby
Chamaecrista rotundifolia Pers. Greene
var. rotundifolia Pers. Greene
var. grandiflora Benth. H.S.Irwin & Barneby
Series Chamaecrista Moench
Chamaecrista chamaecristoides Collad. Greene
var. brandegeei Britton & Rose H.S.Irwin & Barneby
var. chamaecristoides Collad. Greene
var. cruziana Britton & Rose H.S.Irwin & Barneby
Chamaecrista cuprea H.S.Irwin & Barneby
Chamaecrista deeringiana Small & Pennell
Chamaecrista fasciculata Michx. GreeneShowy Partridge Pea
Chamaecrista glandulosa L. GreeneJamaican Broom
var. andicola H.S.Irwin & Barneby
var. andreana Britton & Killip H.S.Irwin & Barneby
var. brasiliensis Vogel H.S.Irwin & Barneby
var. flavicoma Kunth H.S.Irwin & Barneby
var. glandulosa L. Greene
var. mirabilis Pollard H.S.Irwin & Barneby
var. parralensis H.S.Irwin & Barneby H.S.Irwin
var. picardae Urb. H.S.Irwin & Barneby
var. swartzii Wikstr. H.S.Irwin & Barneby
var. tristicula Kunth H.S.Irwin & Barneby
Chamaecrista lineata Sw. Greene
var. brachyloba Griseb. H.S.Irwin & Barneby
var. brevipila Urb. H.S.Irwin & Barneby
var. jamaicensis Britton H.S.Irwin & Barneby
var. keyensis Pennell H.S.Irwin & Barneby
var. lineata Sw. Greene
var. pinoi Britton & Rose H.S.Irwin & Barneby
Chamaecrista mimosoides L. Greene
Chamaecrista nictitans L. Moench
subsp. brachypoda Benth. H.S.Irwin & Barneby
subsp. disadena Steud. H.S.Irwin & Barneby
subsp. nictitans L. Moench
subsp. patellaria Collad. H.S.Irwin & Barneby
var. aspera Elliott Torr. & A.Gray
var. diffusa DC. H.S. Irwin & Barneby
var. glabrata Vogel H.S. Irwin & Barneby
var. jaliscensis Greenm. H.S. Irwin & Barneby
var. mensalis Greenm. H.S.Irwin & Barneby
var. pilosa Benth. H.S. Irwin & Barneby
var. praetexta Vogel H.S. Irwin & Barneby
Chamaecrista obcordata Sw. Britton
Chamaecrista pascuorum Benth. H.S.Irwin & Barneby
Chamaecrista pedemontana H.S.Irwin & Barneby
Chamaecrista pedicellaris DC. Britton
var. adenosperma Urb. H.S.Irwin & Barneby
var. pedicellaris DC. Britton
Chamaecrista portoricensis Urb. O.F.Cook & G.N.Collins
Chamaecrista pygmaea DC. Britton
var. pygmaea DC. Britton
var. savannarum Britton H.S.Irwin & Barneby
Chamaecrista repens Vogel H.S.Irwin & Barneby
var. multijuga Benth. H.S.Irwin & Barneby
var. repens Vogel H.S.Irwin & Barneby
Chamaecrista rufa M.Martens & Galeotti Britton
Chamaecrista venturiana H.S.Irwin & Barneby
Chamaecrista vestita Vogel H.S.Irwin & Barneby
Series Coriaceae Bentham Irwin & Barneby
Chamaecrista anceps Benth. H.S.Irwin & Barneby
Chamaecrista aristata Benth. H.S.Irwin & Barneby
Chamaecrista burchellii Benth. H.S.Irwin & Barneby
Chamaecrista cardiostegia H.S.Irwin & Barneby
Chamaecrista caribaea Northr. Britton
var. caribaea Northr. Britton
var. inaguensis Britton H.S.Irwin & Barneby
var. lucayana Britton H.S.Irwin & Barneby
Chamaecrista choriophylla Vogel H.S.Irwin & Barneby
var. choriophylla Vogel H.S.Irwin & Barneby
var. latifolia Benth. H.S.Irwin & Barneby
var. rossicorum H.S.Irwin & Barneby
Chamaecrista cinerascens Vogel H.S.Irwin & Barneby
Chamaecrista distichoclada Benth. H.S.Irwin & Barneby
Chamaecrista lagotois H.S.Irwin & Barneby
Chamaecrista mucronata Spreng. H.S.Irwin & Barneby
Chamaecrista multinervia Benth. H.S.Irwin & Barneby
Chamaecrista olesiphylla Vogel H.S.Irwin & Barneby
Chamaecrista papillata H.S.Irwin & Barneby
Chamaecrista potentilla Benth. H.S.Irwin & Barneby
Chamaecrista roraimae Benth. Gleason
Chamaecrista rotundata Vogel H.S.Irwin & Barneby
var. rotundata Vogel H.S.Irwin & Barneby
var. grandistipula Vogel H.S.Irwin & Barneby
Chamaecrista simplifacta H.S.Irwin & Barneby
Chamaecrista tragacanthoides Benth. H.S.Irwin & Barneby
var. rasa H.S.Irwin & Barneby
var. tragacanthoides Benth. H.S.Irwin & Barneby
Chamaecrista ulmea H.S.Irwin & Barneby
Chamaecrista venulosa Benth. H.S.Irwin & Barneby
Series Flexuosae Irwin & Barneby
Chamaecrista flexuosa L. Greene
var. flexuosa L. Greene
var. texana Buckley H.S.Irwin & Barneby
Chamaecrista gononclada Benth. H.S.Irwin & Barneby
Chamaecrista parvistipula Benth. H.S.Irwin & Barneby
Chamaecrista swainsonii Benth. H.S.Irwin & Barneby
Series Greggianae Irwin & Barneby
Chamaecrista greggii A. Gray Pollard ex A. H. Heller
var. greggii A. Gray Pollard ex A. H. Heller
var. macdougaliana Rose H.S.Irwin & Barneby
var. potosina Britton & Rose H.S.Irwin & Barneby
Series Prostratae Bentham Irwin & Bameby
Chamaecrista cordistipula Mart. H.S.Irwin & Barneby
Chamaecrista kunthiana Schltdl. & Cham. H. S. Irwin & Barneby
Chamaecrista pilosa L. Greene
var. luxurians Benth. H.S.Irwin & Barneby
var. pilosa L. Greene
Chamaecrista serpens L. Greene
var. delicata Britton & Rose H.S.Irwin & Barneby
var. grandiflora Benth. H.S.Irwin & Barneby
var. mensarum A.R.Molina H.S.Irwin & Barneb
var. serpens L. Greene
var. wrightii A.Gray H.S.Irwin & Barneby
Chamaecrista supplex Benth. Britton & Killip
Chamaecrista tenuisepala Benth. H.S.Irwin & Barneby
Chamaecrista trichopoda Benth. Britton & Killip
Section Grimaldia Schrank Irwin & Barneby
Chamaecrista absus L. H.S.Irwin & Barneby
var. absus L. H.S.Irwin & Barneby
var. meonandra H.S.Irwin & Barneby H.S.Irwin
Section Xerocalyx Bentham Irwin & Barneby
Chamaecrista desvauxii Collad. Killip
var. brevipes Benth. H.S.Irwin & Barneby
var. desvauxii Collad. Killip
var. langsdorffii Kunth ex Vogel H.S.Irwin & Barneby
var. latifolia Benth. H.S.Irwin & Barneby
var. latistipula Benth. G.P.Lewis
var. linearis H.S.Irwin H.S.Irwin & Barneby
var. malacophylla Vogel H.S.Irwin & Barneby
var. mollissima Benth. H.S.Irwin & Barneby
var. pirebebuiensis Chodat & Hassl. H.S.Irwin & Barneby
var. saxatilis Amshoff H.S.Irwin & Barneby
var. triumviralis H.S.Irwin & Barneby
Chamaecrista diphylla L. Greene
Chamaecrista ramosa Vogel H.S.Irwin & Barneby
var. curvifolia Vogel G.P.Lewis
var. erythrocalyx Benth. H.S.Irwin & Barneby
var. lucida Benth. H.S.Irwin & Barneby
var. parvifoliola H.S.Irwin H.S.Irwin & Barneby
var. ramosa Vogel H.S.Irwin & Barneby
var. ventuarensis H.S.Irwin H.S.Irwin & Barneby
Incertae Sedis
Chamaecrista africana Steyaert Lock
Chamaecrista aldabrensis Hemsl. F. Friedmann
Chamaecrista amabilis H.S.Irwin & Barneby
Chamaecrista amorimii Barneby
Chamaecrista anamariae Conc., L.P. Queiroz & G.P. Lewis
Chamaecrista angustissima Lam. Greene
Chamaecrista ankaratrensis R.Vig. Du Puy
Chamaecrista arachiphylla Barneby
Chamaecrista arboae Barneby
Chamaecrista arenicola R.Vig. Du Puy
var. arenicola R.Vig. Du Puy
var. dunensis R.Vig. Du Puy
Chamaecrista auricoma Benth. V.Singh
Chamaecrista axilliflora H.S.Irwin & Barneby
Chamaecrista biensis Steyaert Lock
Chamaecrista botryoides Conc., L.P. Queiroz & G.P. Lewis
Chamaecrista brevifolia Lam. Greene
var. brevifolia Lam. Greene
var. glabra Brenan Du Puy
Chamaecrista capensis Thunb. E.Mey.
Chamaecrista caspariifolia Barneby
Chamaecrista catolesensis Conc., L.P. Queiroz & G.P. Lewis
Chamaecrista chiquitana Barneby
Chamaecrista comosa E.Mey.
var. comosa E.Mey.
var. capricornia Steyaert Lock
Chamaecrista concinna Benth. Pedley
Chamaecrista coradinii H.S. Irwin & Barneby
Chamaecrista decora H. S. Irwin & Barneby Conc. et al.
Chamaecrista deltoidea Hervencio & L.P. Queiroz
Chamaecrista depauperata Conc., L.P. Queiroz & G.P. Lewis
Chamaecrista dimidiata Buch.-Ham. ex Roxb. Lock
Chamaecrista duboisii Steyaert Lock
Chamaecrista dumaziana Brenan Du Puy
Chamaecrista dunensis Thulin
Chamaecrista exilis Vatke Lock
Chamaecrista fagifolia Bertol
Chamaecrista falcinella Oliv. Lock
var. falcinella Oliv. Lock
var. intermedia Brenan Lock
var. parviflora Steyaert Lock
Chamaecrista fallacina Chiov. Lock
Chamaecrista fenarolii Mendonca & Torre Lock
Chamaecrista fulgida Barneby
Chamaecrista garambiensis Hosokawa H.Ohashi, Tateshi & Nemoto
Chamaecrista ghesquiereana Brenan Lock
Chamaecrista gracilior Ghesq. Lock
Chamaecrista grantii Oliv. Standl.
Chamaecrista gumminans H.S.Irwin & Barneby
Chamaecrista harneyi Specht Govaerts
Chamaecrista hecatophylla DC. Greene
Chamaecrista hildebrandtii Vatke Lock
Chamaecrista huillensis Mendonca & Torre Lock
Chamaecrista jaegeri Keay Lock
Chamaecrista kalulensis Steyaert Lock
Chamaecrista katangensis Ghesq. Lock
var. katangensis Ghesq. Lock
var. nuda Steyaert Lock
Chamaecrista kirkii Oliv. Standl.
var. glabra Steyaert Lock
var. kirkii Oliv. Standl.
var. guineensis Steyaert Lock
Chamaecrista kleinii Wight & Arn. V.Singh
Chamaecrista kolabensis Kothari, Moorthy & M.P.Nayar V.Singh
Chamaecrista lateriticola R.Vig. Du Puy
Chamaecrista leptocarpa Benth.
Chamaecrista leschenaultiana DC. O. Deg.
Chamaecrista longipes Domin Pedley
Chamaecrista meelii Steyaert Lock
Chamaecrista mindanaensis Merr. K.Larsen
Chamaecrista newtonii Mendonca & Torre Lock
Chamaecrista nigricans Vahl Greene
Chamaecrista nilgirica V.Singh V.Singh
Chamaecrista nomame Sieber H.Ohashi
Chamaecrista paralias Brenan Lock
Chamaecrista parva Steyaert Lock
Chamaecrista plumosa E.Mey.
var. erecta Schorn & Gordon-Gray Lock
var. plumosa E.Mey.
Chamaecrista polytricha Brenan Lock
var. pauciflora Brenan Lock
var. polytricha Brenan Lock
var. pulchella Brenan Lock
Chamaecrista pratensis R.Vig. Du Puy
Chamaecrista pteropoda Barneby
Chamaecrista puccioniana Chiov. Lock
Chamaecrista pumila Lam. K.Larsen
Chamaecrista reducta Brenan Du Puy
Chamaecrista robynsiana Ghesq. Lock
Chamaecrista rupestrium H.S.Irwin & Barneby
Chamaecrista schmitzii Steyaert Lock
Chamaecrista speciosa Conc., L.P. Queiroz & G.P. Lewis
Chamaecrista stricta E.Mey.
Chamaecrista tagera L. Standl.
Chamaecrista telfairiana Hook.f. Lock
Chamaecrista usambarensis Taub. Standl.
Chamaecrista verruculosa Afr.Fern. & E.P. Nunes
Chamaecrista wallichiana DC. V.Singh
Chamaecrista wittei Ghesq. Lock
Chamaecrista zambesica Oliv. Lock
Species names with uncertain taxonomic status
The status of the following species is unresolved:
Chamaecrista bella Conc., L.P.Queiroz & G.P.Lewis
Chamaecrista biddulphiana Pedley
Chamaecrista bissei A.Barreto & Yakovlev
Chamaecrista ×blanchetiformis Conc., L.P.Queiroz & Borba
Chamaecrista blanchetii Benth. Conc., L.P.Queiroz & G.P.Lewis
Chamaecrista burmanni Eckl. & Zeyh.
Chamaecrista commixta auct.
Chamaecrista cupeyalensis A.Barreto & Yakovlev
Chamaecrista deserti Pedley
Chamaecrista exigua Pedley
Chamaecrista falcifoliolata A.Barreto & Yakovlev
Chamaecrista grisea Pedley
Chamaecrista guanensis A.Barreto & Yakovlev
Chamaecrista macambensis A.Barreto & Yakovlev
Chamaecrista maritima Pedley
Chamaecrista moorei Pedley
Chamaecrista mwangokae Gereau & G.M.Walters
Chamaecrista nana Conc., L.P.Queiroz & G.P.Lewis
Chamaecrista ×patyensis Conc., L.P.Queiroz & Borba
Chamaecrista rusbyi Britton & Rose ex Pittier
Chamaecrista symonii Pedley
Chamaecrista takhtajanii A.Barreto & Yakovlev
Chamaecrista vestita Vogel Govaerts
Chamaecrista xanthadena Mart. ex Benth. Govaerts
References
External links
Category:Fabaceae genera
Category:Cassieae | wikipedia |
Aston Wyatt Greathead 31 May 1921 18 July 2012 was a New Zealand artist. He was born in Napier, the second of the five children of William John Edwin Greathead and Jane Greathead née Wyatt, but the family soon moved to Timaru. Aston Greathead attended Waimataitai Primary School, where his drawings on the covers and page margins of his textbooks were sought-after by fellow pupils at the school's annual book sales. He never received art lessons, but was completely self-taught, developing his own natural talent from an early age. At one early art competition, the judges did not believe the work he submitted was his own, so he was locked in a room with a pencil and paper only to produce a work that amazed the judges.
Greathead did not attend secondary school, instead going directly into employment at S.W. Lewis and Sons in Timaru where he learnt signwriting.
During the Second World War, Greathead served in the New Zealand Army in the North African and Italian campaigns. His art was in demand by fellow soldiers who wanted to send home pictures.
He returned to New Zealand after the war, setting up his own signwriting business in Christchurch, but while the business flourished, the stress became too much and he was advised to give it up. He then sold up in 1960 and relocated his family wife Ethel 'Ett' née Taberner and their three daughters Suzanne Jean, Wendy Wilks and Denise Kay to their bach at Kaikoura. With only one motel in that town at the time, he bought some fishermen's cabins, which he let to tourists.
For three years or so, the family lived hand-to-mouth on the earnings form the cabins, plus the occasional sale of a painting. By the fourth year, art sales picked up, and his prospects brightened.
In 1966 he won Sir Henry Kelliher's Dawson Hallmark watercolour award, which propelled him to fame and brought him commissions. Many of the early commissions came from remote farms, and he was happiest when painting on location. His favourite medium was watercolours, but over time he used this less, in favour of oil acrylics, which he preferred to straight oils. His technique, derived from his signwriting days, often used only four colours, and the colour of the canvas, which allowed him to paint relatively fast, often finishing a painting in a matter of hours.
Mount Cook was a favourite subject for him, and the lounge bar and dining room at The Hermitage at that mountain still display his works.
By the 1990s Greathead was also making his own sculptured frames for his works, adding a 'third dimension' to the painting itself.
He also donated works to charity: 1000 limited edition prints of his Keas at dusk were donated to the Cancer Society in the 1980s, raising $200,000. In September 2008 he donated two paintings to an auction to raise money to upgrade the children's section of the Temuka cemetery.
Greathead retired to Blenheim in 1994, where he died 18 years later, survived by his three daughters, 10 grandchildren and 11 great-grandchildren.
References
Category:1921 births
Category:2012 deaths
Category:New Zealand artists
Category:People from Napier, New Zealand
Category:People from Kaikoura | wikipedia |
Game Tight Vol. 2: The Collaboration Album is a collaboration album by rapper JT the Bigga Figga. The album was released in 2003 for Get Low Recordz and was produced by JT the Bigga Figga, One Drop Scott, Rick Rock, Sean T, and Tone Capone.
Track listing
References
Category:JT the Bigga Figga albums
Category:2003 albums | wikipedia |
Schrödinger's equation for hydrogen atom (azimuthal part) [duplicate]
**This question already has an answer here**:
[Angular equation for Schrödinger's equation in 3D](/questions/514109/angular-equation-for-schr%c3%b6dingers-equation-in-3d)
(1 answer)
Closed 3 years ago.
Now, The azimuthal part of the Schrödinger's equation for a hydrogen atom (after separating variables) is:
$$ \frac{d^2 \Phi}{d \phi^2} + m^2 \Phi = 0$$
Which has solution $A e^{im\phi} + B e^{-im\phi}$, but I often see people assuming $B=0$, why?
I believe this question has already been answered [here](https://physics.stackexchange.com/questions/514109/angular-equation-for-schr%C3%B6dingers-equation-in-3d), but I will attempt to go through the superposition in more detail.
Firstly, note that for $m = 0$, $\Phi(\phi) = C \phi + D$, but we set $C = 0$ to ensure the wavefunction is single-valued (i.e. to ensure $\Phi(0) = \Phi(2 \pi z)$ for $z \in \mathbb{N}$). This factor of D will just be absorbed into the superposition coefficients for $m = 0$.
Secondly, note that the $\Theta(\theta)$ part of the solution makes use of the associated Legendre polynomials, which are insensitive to the sign of $m$ since the associated Legendre equations depend on $m^2$. Therefore, $\Theta\_{m,l}(\theta) = \Theta\_{-m,l}(\theta)$.
The general angular solution can be written as:
$$y\_l (\phi, \theta) = \sum\_{m = -\infty}^{\infty} \left(A\_m e^{i m \phi} + B\_m e^{- i m \phi} \right) \Theta\_{m,l}(\theta)$$
Rewriting the general solution,
$$\begin{align}
y\_l (\phi, \theta) &= \sum\_{m = 1}^{\infty} \left(A\_m e^{i m \phi} + B\_m e^{- i m \phi} \right) \Theta\_{m,l}(\theta) + \sum\_{m = -\infty}^{1} \left(A\_m e^{i m \phi} + B\_m e^{- i m \phi} \right) \Theta\_{m,l}(\theta) + (A\_0 + B\_0) \Theta\_{0,l}(\theta) \\ &= \sum\_{m = -\infty}^{1} \left(A\_m e^{i m \phi} + B\_m e^{- i m \phi} \right) \Theta\_{m,l}(\theta) + \sum\_{m' = 1}^{\infty} \left(A\_{-m'} e^{-i m' \phi} + B\_{-m'} e^{ i m' \phi} \right) \Theta\_{-m',l}(\theta) + (A\_0 + B\_0) \Theta\_{0,l}(\theta) \\ &= \sum\_{m = -\infty}^{1} \left(A\_m e^{i m \phi} + B\_m e^{- i m \phi} \right) \Theta\_{m,l}(\theta) + \sum\_{m = 1}^{\infty} \left(A\_{-m} e^{-i m \phi} + B\_{-m} e^{ i m \phi} \right) \Theta\_{-m,l}(\theta) + (A\_0 + B\_0) \Theta\_{0,l}(\theta) \tag{A}\\ &= \sum\_{m = 1}^{\infty} \left((A\_m + B\_{-m}) e^{i m \phi} + (B\_m + A\_{-m}) e^{- i m \phi} \right) \Theta\_{m,l}(\theta) + (A\_0 + B\_0) \Theta\_{0,l}(\theta) \tag{B}
\end{align}$$
Define $C\_m = A\_m + B\_{-m}$ so that:
$$\begin{align}
y\_l (\phi, \theta) &= \sum\_{m = 1}^{\infty} C\_m e^{im\phi} \Theta\_{m,l}(\theta) + \sum\_{m = 1}^{\infty} C\_{-m} e^{-im\phi} \Theta\_{m,l}(\theta) + (A\_0 + B\_0) \Theta\_{0,l}(\theta) \\ &= \sum\_{m = -\infty}^{\infty} C\_m e^{im\phi} \Theta\_{m,l}(\theta)
\end{align}$$
Therefore, it is sufficient to consider $C\_m e^{im\phi} \Theta\_{m,l}(\theta)$ as the separable solutions for the angular part of the TISE for the hydrogen atom (i.e. the simultaneous eigenstates of $L^2$ and $L\_z$).
**Edit: Further Comment**
In this analysis, we started with $B\_m \neq 0$, but showed we can regroup the coefficients in the sum to effectively end up with the new coefficients $A'\_m = C\_m$ and $B'\_m = 0$. This means that for all practical purposes, we could have just treated $B\_m = 0$ to begin with.
The confusion arises when one consider just one separable solution in isolation - but we're summing over all of them, so we're allowed to rewrite the summands in different ways if it still leaves the overall sum invariant.
---
* In step (A), I relabelled $m'$ to $m$ since these are just dummy indices.
* In step (B), I made use of $\Theta\_{m,l}(\theta) = \Theta\_{-m,l}(\theta)$
| stackexchange/physics |
Tilting of Earth rotational axis
In which way do the Earth's rotational axis tilted 23.5°.
[](https://i.stack.imgur.com/5OXF4.jpg)
see in the image we have been told that the axis of rotation of Earth is tilted 23.5° from the perpendicular to path.
But can anyone say in which direction the earth is tilted .AO or BO. Is
the axis of rotation tilted towards sun or away from sun.
And still it is confusing in solstices. Where the rotation axis of Earth at one solstice is towards the sun and at other solstice away from sun.
It's tilted with the N pole toward the sun at Summer Solstice,
and S pole toward the sun at Winter Solstice (assuming you are
in the northern hemisphere, and winter is in December).
The tilt is always 23.5 degrees, and it always points in the same direction (roughly to the Polaris star), but that means that it does not always point towards the sun or away from it. That depends on the time of year.
Let's say that in your drawing Polaris is "above" the earth orbit, and "left" from the center. Then the earth axis is tilt "to the left", matching your A direction.
At the "right" end of the orbit (as seen in your drawing), the axis points towards the sun, and that corresponds to June, meaning lots of sun (= summer) for the northern hemisphere.
Half a year later, in December, the earth is at the "left" end of its orbit (invisible part of your drawing), its axis still pointing to the left, which now means "away from the sun", resulting in less sunlight (= winter) for the northern hemisphere.
So, to literally answer your question:
Both A and B are correct, with A matching in June, and B matching in December (and looking into the solar system from the opposite direction).
The angle of tilt is measured between the axis of rotation and a line which is perpendicular to the plane of the orbit. The direction of tilt relative to the “fixed” stars changes very slowly (over thousands of years); a precession caused by a variable torque primarily from the moon. (It pulls harder on the closer side of the equatorial bulge.
| stackexchange/physics |
macular hole reopening after successful surgical repair is well documented in the literature , and it is commonly caused by cataract surgery , growth of an epiretinal membrane ( erm ) , and development of cystoid macular edema ( cme).1,2 however , there has been no documentation to our knowledge of traumatic reopening of a successfully repaired macular hole .
a 75-year - old caucasian female presented with a decreased vision in her left eye .
examination showed 20/400 vision , nuclear sclerotic cataract , and a full - thickness macular hole .
the macular hole was an evident on optical coherence tomography ( oct ) ( figure 1 ) .
the macular hole was repaired with pars plana vitrectomy , attempted internal limiting membrane ( ilm ) peeling without staining agent , perfluoropropane ( c3f8 ) gas , and 2 weeks of face down positioning .
the macular hole closed completely , which was shown on the postoperative oct done 8 weeks following surgery ( figure 2 ) .
the patient did well for 2 years until she presented after a fall onto her face and decreased vision in the left eye .
vision decreased to 20/400 and a full - thickness macular hole was again seen on examination and oct ( figure 3 ) .
six weeks later , repeated pars plana vitrectomy and ilm peeling were performed with brilliant blue stain , and the patient again had c3f8 gas and 2 weeks of face down positioning .
the macular hole was closed following the second surgery ( figure 4 ) , and the patient s vision improved to 20/100 6 weeks postoperatively .
there are three well - known factors that contribute to reopening of a surgically repaired macular hole : cataract surgery after the macular hole repair , growth of an erm , and development of cme.1,2 in addition , bartolini et al described a case of macular hole reopening after successful surgical repair 12 years later , which could have been caused by incomplete ilm removal.3 the incidence of macular hole reopening following successful surgical repair appears to be between 2% and 6.9%.1,46 however , there has been no documentation to our knowledge of reopening of a surgically repaired macular hole secondary to trauma . in our case ,
the reopening occurred 2 years following successful surgical repair of the macular hole and immediately following the trauma .
in addition to the trauma , there may also be an additive effect of incomplete peeling of the ilm during the first surgery due to the fact that no staining agent was used .
another compounding factor in the hole reopening could be the development of a small erm nasal to the macular hole .
our case highlights trauma as a possible contributing mechanism of macular hole reopening following the previous successful surgical repair .
ophthalmologists should be aware of the possibility of traumatic reopening of macular holes , which may help in preoperative patient education . | pubmed |
astronomy is facing the need for radical changes .
when dealing with surveys of up to @xmath3 sources , one could apply for telescope time and obtain an optical spectrum for each one of them to identify the whole sample .
nowadays , we have to deal with huge surveys ( e.g. , the sloan digital sky survey [ ] , the two micron all sky survey [ ] , the massive compact halo object [ ] survey ) , reaching ( and surpassing ) the 100 million objects . even at , say , 3,000 spectra at night , which is only feasible with the most efficient multi - object spectrographs and for relatively bright sources
, such surveys would require more than 100 years to be completely identified , a time which is clearly much longer than the life span of the average astronomer ! but
even taking a spectrum might not be enough to classify an object .
we are in fact reaching fainter and fainter sources , routinely beyond the typical identification limits of the largest telescopes available ( approximately 25 magnitude for 2 - 4 hour exposures ) , which makes `` classical '' identification problematic .
these very large surveys are also producing a huge amount of data : it would take more than two months to download at 1 mbytes / s ( a very good rate for most astronomical institutions ) the data release 3 ( ) sdss images , about a month for the catalogues .
the images would fill up @xmath4 1,300 dvds ( @xmath4 650 if using dual - layer technology ) .
and the final sdss will be about twice as large as the dr3 .
these data , once downloaded , need also to be analysed , which requires tools which may not be available locally and , given the complexity of astronomical data , are different for different energy ranges .
moreover , the breathtaking capabilities and ultra - high efficiency of new ground- and space - based observatories have led to a `` data explosion '' , with astronomers world - wide accumulating more than one terabyte of data per night ( judging from some of the talks at this conference , this is very likely to be an underestimate ) .
for example , the european southern observatory ( eso)/space telescope european coordinating facility ( st - ecf ) archive is predicted to increase its size by two orders of magnitude in the next eight years or so , reaching @xmath5 terabytes .
finally , one would like to be able to use all of these data , including multi - million - object catalogues , by putting this huge amount of information together in a coherent and relatively simple way , something which is impossible at present .
all these hard , unescapable facts call for innovative solutions . for example , the observing efficiency can be increased by a clever pre - selection of the targets , which will require some `` data - mining '' to characterise the sources properties before hand , so that less time is `` wasted '' on sources which are not of the type under investigation .
one can expand this concept even further and provide a `` statistical '' identification of astronomical sources by using all the available , multi - wavelength information without the need for a spectrum .
the data - download problem can be solved by doing the analysis where the data reside . and finally , easy and clever access to all astronomical data worldwide would certainly help in dealing with the data explosion and would allow astronomers to take advantage of it in the best of ways .
the name of the solution is the virtual observatory ( vo ) .
the vo is an innovative , evolving system , which will allow users to interrogate multiple data centres in a seamless and transparent way , to make the best use of astronomical data . within the vo ,
data analysis tools and models , appropriate to deal also with large data volumes , will be made more accessible .
new science will be enabled , by moving astronomy beyond `` classical '' identification with the characterisation of the properties of very faint sources by using all the available information .
all this will require good communication , that is the adoption of common standards and protocols between data providers , tool users and developers . this is being defined now using new international standards for data access and mining protocols under the auspices of the recently formed international virtual observatory alliance ( ) , a global collaboration of the world s astronomical communities .
one could think that the vo will only be useful to astronomers who deal with colossal surveys , huge teams and terabytes of data !
that is not the case , for the following reason .
the world wide web is equivalent to having all the documents of the world inside one s computer , as they are all reachable with a click of a mouse .
similarly , the vo will be like having all the astronomical data of the world inside one s desktop .
that will clearly benefit not only professional astronomers but also anybody interested in having a closer look at astronomical data . consider the following example : imagine one wants to find _ all _ the observations of a given source available in _ all _ astronomical archives in a given wavelength range .
one also needs to know which ones are in raw or processed format , one wants to retrieve them and , if raw , one wants also to have access to the tools to reduce them on - the - fly . at present , this is extremely time consuming , if at all possible , and would require , even to simply find out what is available , the use a variety of search interfaces , all different from one another and located at different sites .
the vo will make all this possible very easily .
the status of the vo in europe is very good . in addition to seven current national vo projects ,
the european funded collaborative astrophysical virtual observatory initiative ( ) is creating the foundations of a regional scale infrastructure by conducting a research and demonstration programme on the vo scientific requirements and necessary technologies .
the avo has been jointly funded by the european commission ( under the fifth framework programme [ fp5 ] ) with six european organisations participating in a three year phase - a work programme .
the partner organisations are eso in munich , the european space agency , astrogrid ( funded by pparc as part of the united kingdom s e - science programme ) , the cnrs - supported centre de donnees astronomiques de strasbourg ( cds ) and terapix astronomical data centre at the institut dastrophysique in paris , the university louis pasteur in strasbourg , and the jodrell bank observatory of the victoria university of manchester .
the avo is the definition and study phase leading towards the euro - vo - the development and deployment of a fully fledged operational vo for the european astronomical research community .
a science working group was also established to provide scientific advice to the project .
the avo project is driven by its strategy of regular scientific demonstrations of vo technology , held on an annual basis in coordination with the ivoa .
for this purpose progressively more complex avo demonstrators are being constructed .
the current one , a downloadable java application , is an evolution of aladin ( ) , developed at cds , and has become a set of various software components , provided by avo and international partners , which allows relatively easy access to remote data sets , manipulation of image and catalogue data , and remote calculations in a fashion similar to remote computing ( see fig .
[ fig1 ] ) .
the avo held its second demonstration , avo 1st science , on january 27 - 28 , 2004 at eso .
the demonstration was truly multi - wavelength , using heterogeneous and complex data covering the whole electromagnetic spectrum .
these included : merlin , vla ( radio ) , iso [ spectra and images ] and 2mass ( infrared ) , usno , eso 2.2m / wfi and vlt / fors [ spectra ] , and hst / acs ( optical ) , xmm and chandra ( x - ray ) data and catalogues .
two cases were dealt with : an extragalactic case on obscured quasars , centred around the great observatories origin deep survey ( goods ) public data , and a galactic scenario on the classification of young stellar objects .
the extragalactic case was so successful that it turned into the first published science result fully enabled via end - to - end use of vo tools and systems , the discovery of @xmath6 high - power , supermassive black holes in the centres of apparently normal looking galaxies .
how did we get a scientific paper out of a science demonstration ?
the extragalactic science case revolved around the two goods fields ( giavalisco et al .
2004a , ) , namely the hubble deep field - north ( hdf - n ) and the chandra deep field - south ( cdf - s ) , the most data - rich , deep survey areas on the sky .
our idea was to use the avo prototype to look for high - power , supermassive black holes in the centres of apparently normal looking galaxies .
black holes lurk at the centres of active galaxies ( agn ) surrounded by dust which is thought to be , on theoretical and observational grounds ( see , e.g. , urry & padovani 1995 ; jaffe et al .
2004 ) , distributed in a flattened configuration , torus - like .
when we look down the axis of the dust torus and have a clear view of the black hole and its surroundings these objects are called `` type 1 '' agn , and display the broad lines ( emitted by clouds moving very fast close to the black hole ) and strong uv emission typical of quasars . `` type 2 '' agn ,
on the other hand , lie with the dust torus edge - on as viewed from earth so our view of the black hole is totally blocked by the dust over a range of wavelengths from the near - infrared to soft x - rays .
the optical / uv spectrum of type 2 agn is characterized by emission lines much narrower than those of quasars , as they are emitted by clouds which are further away and therefore move more slowly . while many dust - obscured low - power black holes , the seyfert 2s ,
have been identified , until recently few of their high - power counterparts were known .
this was due to a simple selection effect : when the source is a low - power one and therefore , on average , closer to the observer , one can very often detect some features related to narrow emission lines on top of the emission from the host galaxy , which qualify it as a type 2 agn .
but when the source is a high - power one , a so - called qso 2 , and therefore , on average , further away from us , the source looks like a normal galaxy . until very recently , qso 2s were selected against by quasar surveys , most of which were tuned to find objects with very strong uv emission .
the situation has changed with the advent of chandra and xmm - newton , which are providing a sensitive window into the hard x - ray emission of agn .
the two key physical properties that we use to identify type 2 agn candidates are that they be obscured , and that they have sufficiently high power to be classed as an agn and not a starburst .
our approach was to look for sources where nuclear emission was coming out in the hard x - ray band , with evidence of absorption in the soft band , a signature of an obscured agn , and the optical flux was very faint , a sign of absorption .
one key feature was the use of a correlation discovered by fiore et al .
( 2003 ) between the x - ray - to - optical ratio and the x - ray power , which allowed us to select qso 2s even when the objects were so faint that no spectrum , and therefore no redshift , was available .
we selected absorbed sources by using the alexander et al .
( 2003 ) x - ray catalogues for the two goods fields , which provide counts in various x - ray bands .
we define the hardness ratio @xmath7 , where @xmath8 is the hard x - ray counts ( @xmath9 kev ) and @xmath10 is the soft x - ray counts ( @xmath11 kev ) .
szokoly et al .
( 2004 ) have shown that absorbed , type 2 agn are characterized by @xmath12 .
we adopt this criterion and identify those sources which have @xmath12 as absorbed sources .
we find 294 ( cdf - s : 104 , hdf - n : 190 ) such absorbed sources which represent @xmath13 of the x - ray sources in the alexander catalogues .
note that increasing redshift makes the sources softer ( e.g. , at @xmath14 the rest - frame @xmath15 kev band shifts to @xmath16 kev ) so our selection criterion will mistakenly discard some high - z type 2 sources , as pointed out by szokoly et al .
the number of type 2 candidates we find has therefore to be considered a lower limit .
the optical counterparts to the x - ray sources were selected by cross - matching the absorbed x - ray sources with the goods acs catalogues ( 29,599 sources in the cdf - s , 32,048 in the
hdf - n ) .
we used version v1.0 of the reduced , calibrated , stacked , and mosaiced images and catalogues as made available by the .
the goods catalogues contain sources that were detected in the @xmath17-band , with @xmath18 photometry in matched apertures ( giavalisco et al .
2004b ) .
we initially searched for optical sources that lay within a relatively large threshold radius of 3.5 ( corresponding to the maximal @xmath19 positional uncertainty of the x - ray positions ) around each x - ray source .
this was done using the cross match facility in the avo prototype tool using the `` best match '' mode . since the 3.5 radius is large relative to the median positional error , and given the optical source density the initial cross match inevitably includes a number of false and multiple matches . to limit our sample to good matches
, we use the criterion that the cross match distance be less than the combined optical and x - ray @xmath19 positional uncertainty for each individual match . applying this distance / error @xmath20 criterion we limit the number of matches to 168 ( cdf - s : 65 , hdf - n : 103 ) .
these matches are all within a much smaller radius than our initial 3.5 threshold , with most of the distance / error @xmath20 matches being within 1.25 ( and two matches at 1.4 and 1.5 ) .
the estimated number of false matches we expect to have is small , between 8 and 15% .
previously classified sources and their spectroscopic redshifts are available from szokoly et al .
( 2004 ) for the cdf - s and barger et al .
( 2003 ) for the hdf - n .
derivation of x - ray powers for these objects is straightforward km s@xmath21 mpc@xmath21 , @xmath22 , and @xmath23 . for the unclassified sources we estimated the x - ray power as follows : we first derived the @xmath24 flux ratio ( converting the acs @xmath25 magnitudes to the @xmath26 band ) , and then estimated the x - ray power from the correlation found by fiore et al .
( 2003 ) , namely @xmath27 ( fiore , p.c . ;
see their fig .
note that this correlation has an r.m.s .
of @xmath28 dex in x - ray power .
we stress that our estimated x - ray powers reach @xmath29 erg / s and therefore fall within the range of the fiore et al .
( 2003 ) correlation .
on the other hand it should be pointed out that our sources are much fainter than the objects which have been used to calibrate the fiore et al.s correlation . the work of szokoly et al .
( 2004 ) has shown that absorbed , type 2 agn are characterized by @xmath12 .
it is also well known that normal galaxies , irrespective of their morphology , have x - ray powers that reach , at most , @xmath30 erg / s ( e.g. , forman , jones & tucker 1994 ; cohen 2003 ) .
therefore , any x - ray source with @xmath12 and @xmath31 erg / s should be an obscured agn .
furthermore , following szokoly et al .
( 2004 ) , any such source having @xmath32 erg / s will qualify as a type 2 qso . out of the 546 x - ray sources in the goods fields , 203 are absorbed ( @xmath33 ) .
out of these we selected 68 type 2 agn candidates , 31 of which qualify as qso 2 ( estimated x - ray power @xmath34 erg / s ) .
we note that the distribution of estimated x - ray power covers the range @xmath35 erg / s and peaks around @xmath36 erg / s ( see fig .
[ fig2 ] ) .
the number of qso 2 candidates , therefore , is very sensitive to the dividing line between low- and high - luminosity agn , which is clearly arbitrary and cosmology dependent .
for example , if one defines as qso 2 all sources with @xmath37 erg / s , a value only a factor of 2 below the commonly used one and corresponding to the break in the agn x - ray luminosity function ( norman et al .
2002 ) , the number of such sources increases by @xmath38 .
we also note that , based on the r.m.s . around the fiore et al .
( 2003 ) correlation , the number of qso 2 candidates fluctuates in the @xmath39 region .
the number of type 2 agn , on the other hand , can only increase , as all our candidates have estimated @xmath40 .
our work brings to 40 the number of qso 2 in the goods fields , an improvement of a factor @xmath41 when compared to the only nine such sources previously known .
as expected , being still unidentified , our sources are very faint : their median acs @xmath25 magnitude is @xmath42 , which corresponds to @xmath43 ( compare this to the @xmath44 typical of the cdf - s sources with redshift determination ) .
the qso 2 candidates are even fainter , with median @xmath25 magnitude @xmath45 ( @xmath46 ) . therefore
, spectroscopical identification is not possible , for the large majority of objects , even with the largest telescopes currently available .
we have used our estimated x - ray powers together with the observed fluxes to derive redshifts for our type 2 candidates ( tests we have performed on the type 2 sources with spectroscopic redshifts show that this method , although very simple , is relatively robust ) .
our type 2 agn are expected to be at @xmath47 , while our qso 2 should be at @xmath48 . by using vo methods we are sampling a region of redshift - power space so far much harder to reach with classical methods .
for the first time , we can also assess how many qso 2 there are down to relatively faint x - ray fluxes .
we find a surface density @xmath49 deg@xmath50 for @xmath51 erg cm@xmath50 s@xmath21 , higher than previously estimated .
[ fig2 ] shows the x - ray power distribution for our new type 2 agn candidates ( dashed line ) , previously known type 2 agn ( solid line ) , and the combined sample ( dotted line ) .
it is interesting to note how the distributions are very different , with the already known type 2 agn peaking around @xmath53 erg / s and declining for luminosities above @xmath54 erg / s , while our new candidates are rising in this range and peak around @xmath55 erg / s . to be more quantitative ,
while only @xmath56 of already known type 2 agn have @xmath57 , @xmath58 of our candidates are above this value .
this difference is easily explained by our use of the x - ray - to - optical flux ratios to estimate x - ray powers and by the fact that our candidates are on average @xmath59 magnitudes fainter than previously known sources .
our method is then filling a gap in the luminosity distribution , which becomes almost constant in the range @xmath60 erg / s .
this also explains the fact that the number of qso 2 candidates we find is @xmath61 times larger than the previously known ones .
the identification of a population of high - power obscured black holes and the active galaxies in which they live has been a key goal for astronomers and will lead to greater understanding and a refinement of the cosmological models describing our universe .
the paper reporting these results has been recently published ( padovani et al .
2004 ) .
the avo prototype made it much easier to classify the sources we were interested in and to identify the previously known ones , as we could easily integrate all available information from images , spectra , and catalogues at once .
this is proof that vo tools have evolved beyond the demonstration level to become respectable research tools , as the vo is already enabling astronomers to reach into new areas of parameter space with relatively little effort .
the avo prototype can be downloaded from the .
we encourage astronomers to download the prototype , test it , and also use it for their own research . for any problems with the installation and any requests , questions , feedback , and
comments you might have please contact the avo team at [email protected] .
( please note that this is still a prototype : although some components are pretty robust some others are not . )
the avo is promoting science with vo tools through two further developments : a science reference mission and the next science demonstration .
the avo team , with input from the science working group , is putting together a science reference mission .
this will define the key scientific results that the full - fledged euro - vo should achieve when fully implemented and will consist of a number of science cases covering a broad range of astronomical topics , with related requirements , against which the success of the euro - vo will be measured . the next and last avo science demonstration is to be held in january 2005 at the european space astronomy centre ( esac ; formerly known as vilspa ) .
preparations are still on - going so the details are not fully worked out yet but it is firmly established that we will be dealing with two scenarios .
the first , on star formation histories in galaxies , will revolve around the european large - area iso survey ( elais ) , which covers five different areas of the sky over @xmath4 10 deg@xmath62 .
the second , on the transition from asymptotic giant branch to planetary nebulae , will be the strongest one on the science side and should produce a new list of stars in this very interesting transitional phase . on the technical side , the science demonstration will see the rollout of the first version of the euro - vo portal , through which european astronomers will gain secure access to a wide range of data access and manipulation capabilities .
also , we will demonstrate the use of distributed workflows , registry harvesting , and the wrapping of sophisticated astronomical applications as web services .
the avo demonstration will also mark the transition from the avo to the euro - vo .
funding for the technology part of the euro - vo , vo - tech , has been secured from the european community at a level of 6.6 million euros , which will translate into 12 full time equivalent ( ftes ) .
twelve more ftes will be provided by the partners , which include edinburgh , leicester , and cambridge in the uk , eso , cds , and inaf in italy .
the main results of this paper can be summarized as follows : * the virtual observatory is happening because it has to ! if it does not , we will not be able to cope with the huge amount of data astronomers are being flooded with .
* astronomy can and _ is being _ done with virtual observatory tools , which are now mature enough .
real science results are being produced and papers are being published . * the astrophysical virtual observatory , soon to be euro - vo , is committed to the pursuit of science with virtual observatory tools through scientific demonstrations , science papers , and a science reference mission .
the obscured quasar paper was done in collaboration with mark allen , piero rosati , and nic walton .
it is a pleasure to thank the avo team for their superb work , without which the paper would have not been possible , and the many people who have produced the data on which the paper is based , particularly the goods , cdf - s , penn state , and hellas teams .
alexander , d. m. et al .
2003 , , 126 , 539 barger , a. j. et al .
2003 , , 126 , 632 cohen , j. g. 2003 , , 598 , 288 fiore , f. et al .
2003 , , 409 , 79 forman , w. , jones , c. , & tucker , w. 1994 , , 429 , 77 giavalisco , m. et al .
2004a , , 600 , l93 giavalisco , m. et al .
2004b , in preparation jaffe , w. et al .
2004 , nature , 429 , 47 norman , c. et al .
2002 , , 571 , 218 padovani , p. , allen , m. g. , rosati , p. , & walton , n. a. 2004 , , 424 , 545 szokoly , g. p. et al .
2004 , , in press [ astro - ph/0312324 ] urry , c. m. , & padovani , p. 1995 , , 107 , 803 | arxiv |
Kiwi ingenuity - and a bit of masking tape - has saved a kiwi chick, after its egg was badly damaged, endangering its life.
The egg, with a large hole in its shell, was delivered to Kiwi Encounter at Rainbow Springs in Rotorua 14 days ago by a Department of Conservation worker.
Against all odds, it successfully hatched late last week, revealing a fluffy kiwi chick that has been named Fissure.
This egg was delivered to Kiwi Encounter at Rainbow Springs in Rotorua 14 days ago by a DOC worker. It had a large hole, which was patched using the shell of another chick's egg, and masking tape.
Rainbow Springs' kiwi husbandry manager Claire Travers said the shell was broken through to the egg's internal membrane, splitting it so the membrane had collapsed on top of the chick, which was very dangerous.
After cleaning up the egg and removing the broken shell pieces, Travers carefully placed the shell of another egg over the hole using masking tape to hold it in place.
"The shell is a vital structure as it maintains the correct moisture of the membrane, absorbing oxygen and expelling carbon dioxide.
"Without it, the egg is in danger of losing too much moisture," Travers said.
The egg was patched using the shell of another chick's egg, and masking tape.
"To be honest I didn't think the chick had any chance of surviving because the hole in the shell was so big.
"I was absolutely over the moon when it hatched. It really gave me a thrill that against all odds we had saved one of our iconic kiwi chicks.
"Saving the chick is a credit to the Kiwi Encounter team who pooled their expertise and experience to come up with a solution to help save it.
"The hatch itself was amazing with the part of the shell that was taped on to the egg actually mimicking the original shell and cracking in unison as if it was part of the existing egg," Travers said.
Fissure the kiwi hatched from a broken egg which was delivered to Kiwi Encounter at Rainbow Springs in Rotorua 14 days ago by a DoC worker. It had a large hole in its shell which was patched using the shell of another egg and masking tape.
The 2016/17 hatch season is well under way and 41 chicks have hatched at Kiwi Encounter with a further 20 in incubation.
This chick is from Paraninihi - a Maori trust block in north Taranaki near the coast.
Rainbow Springs' involvement in kiwi conservation began in 1995 with the arrival of its first egg, and the hatchery has grown over the years to become the largest kiwi hatching facility in New Zealand, incubating and hatching brown kiwi eggs from around the North Island.
Most kiwi chicks don't survive in the wild due to predators such as stoats, so DoC staff and independent kiwi organisations lift the partially incubated eggs from their burrows and deliver them to Kiwi Encounter to incubate and hatch.
Kiwi eggs take approximately 78 days to incubate, and slightly longer in the wild.
After hatching, the chicks are raised to a 'stoat-proof' weight of 1kg before being released back into the wild.
Kiwi Encounter is also involved in kiwi research.
The team are currently looking at making improvements to the artificial kiwi diet, lighting in nocturnal enclosures, the role of bacteria in egg shell contamination and coccidia (gut parasites) treatment trials. | slim_pajama |
ParkChirp
Pelican – Garage
Pricing and availability may change if you change parking dates and times.
Recalculating prices...
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1041 Collins Ave, Miami Beach, FL 33139, USA
For Pelican parking garage, the entrance and exit will be by Collins Avenue between 10th and 11th Street. If you will be coming from South Collins Avenue, the entrance is on the right hand side. If you will be coming from North Collins Avenue, the entrance is on the left hand side.
Facility Photos
Pelican parking garage entrance.
Street view of Pelican parking garage building.
Pelican parking garage entrance and exit lanes.
Pelican parking garage entry lane.
To redeem your parking pass, scan your barcode at the box with the red flashing light (Parkonect). When scanning, hold your barcode approximately 2 inches from the reader until the gate opens. Do not pull a ticket. When the gate opens, park anywhere that is not marked reserved. Upon exiting, scan your barcode again at the box with red flashing light. The gate will open and you are on your way!
EV Charging Available
License Plate Required
Mobile Pass Accepted
Self Park
Height Restriction: 6'4"
This facility does not allow in/out access.
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Density Matrix Characterization
I am working a two dimensional Hilbert space with basis {$|0\rangle, |1\rangle$} and I am trying to show that the density matrix is characterized by 3 real numbers and show that these three numbers are the expected values of the Pauli matrices.
I understand that a [density matrix](http://en.wikipedia.org/wiki/Density_matrix) is given by $M\_{ij} = \langle i|\rho|j\rangle$ where $|i\rangle$ is an orthonormal basis of $H$ and $\rho$ is the density operator. How do I go about showing this?
To give you a hint: Without losing generality you can use the given standard-basis. What is the dimension of the density matrix? How many complex numbers do you need to determine this matrix? Has the density matrix some special properties, you can use to get more information on these complex number and reduce them to three real numbers? What are the expectation values of the pauli matrices (as a function of these three real numbers)?
| stackexchange/physics |
telemonitoring to verify the proper functions of implantable cardioverter defibrillators ( icd ) with or without cardiac resynchronization therapy ( crt - d ) is becoming a standard means of ambulatory follow - up .
the continuous , wireless monitoring of important clinical variables and device functions , and immediate therapeutic responses , might improve the patient 's prognosis and quality of life ( qol ) and , by lowering the rates of hospitalizations , might represent a significant costs saving for the healthcare system .
it might also decrease the utilization of emergency services , or number of non - scheduled ambulatory visits and increase the productivity and efficiency of medical facilities . as several clinical trials have shown that primary prevention with icd and crt - d implants
increases the survival of patients suffering from heart failure , it is strongly recommended by the recently updated practice guidelines issued by the european society of cardiology .
consequently , the rate of device implantation and follow - ups in italy have grown significantly in recent years . in the current clinical practice for crt - d and icd recipients , regular follow - ups
are recommended every 3 or 6 months , although a large proportion of patients , particularly when suffering from heart failure , need additional visits for worsening of their health status .
therefore , ambulatory clinics are at high risk of becoming overloaded and unable to properly follow all patients , thus lowering the quality of healthcare and increasing the waiting time for services .
a solution to this problem is being proposed with the implementation of remote monitoring systems , which , besides limiting the number of scheduled follow - ups , might lower the number of emergency visits and hospitalizations by the early detection of arrhythmias and progression of heart failure , thus reducing healthcare costs for patients , caregivers , and hospitals , and alleviating the economic burden imposed on national healthcare systems .
in addition , an early reaction to clinical events might improve clinical outcomes and patient qol .
the merlin.net system ( st jude medical , sylmar , ca ) has been adopted by several medical institutions to enable the remote follow - up of devices and collect diagnostic and device status information via programmed remote transmissions . as the cost effectiveness of remote monitoring systems has not been widely studied , new evaluations of their economic value are needed .
tariff is designed to compare direct and indirect costs and benefits of on - site vs. remote follow - ups , including qol , hospitalizations , and ambulatory visits .
furthermore , the study intends to study the cost and the value of remote monitoring of healthcare services , to help the italian medical system make decisions regarding their reimbursement and supply to the hospitals .
the merlin.net pcn is a dedicated , virtual data collection centre , accessible via an internet site protected by a username and password .
the merlin.net transfers data collected either on - site or remotely , using the merlin@home transmitter , which communicates , on a daily basis and without patient interaction , with the implanted devices , notifying every pre - defined clinical and technical issue .
the data are automatically transmitted via wireless telemetry between merlin@home and the implanted devices , and sent to merlin.net via a standard landline or via the global system for mobile communication network .
the merlin.net website is similar to a mailbox interface , where the user can examine recent transmissions or direct alerts .
the data collected on merlin.net can also be exported to an electronic health record ( ehr ) , for a complete patient data management .
tariff is an observational , prospective , multicenter study designed to compare the costs and benefits of on - site vs. remote follow - ups .
this study is conducted at six italian medical centres and has been approved by the institutional ethics committees of each participating centre .
the enrolment of patients began in december 2009 and both enrolment phases will end before the end of 2011 .
the purposes of the study are to ( i ) measure the incremental economic value of remote monitoring of icd and crt - d for italian hospitals , third payers , and patients , and ( ii ) develop , from the hospital perspective , a cost - minimization and use analysis based on the qol associated with remote follow - up of icd and crt - d , using merlin@home and merlin.net , compared with standard , on - site patient care .
the primary endpoint of the study is to measure , under real - life circumstances , the incremental costs and benefits incurred by the italian healthcare system for the implementation of each method of follow - up .
the secondary study endpoint is to compare , from the hospital point of view , the incremental costs represented by each method of follow - up , including assessments of qol , using the eq-5d questionnaire .
the patients are enrolled within 28 weeks after device implant and followed for 12 months .
i , 100 consecutive patients are followed according to a standard on - site ambulatory follow - up at 3 , 6 , 9 , and 12 months after implantation of a device . in phase ii ,
the patients receive the transmitter programmed for remote transmissions at 3 , 6 , and 9 months after device implant . at 12 months of follow - up
the patients enrolled in phase ii are monitored daily remotely by programmable alerts throughout the 1-year study ; each time that the device 's parameters are out of the programmed range , an alert message is automatically sent to the clinic or to the physician in charge through e - mail or fax .
each patient is instructed to keep a diary during each 3 months period of follow - up to record information regarding interim hospitalizations , emergency department visits , adverse events , changes in medication regimens , eq-5d questionnaire , and visits with other healthcare professionals . in figure 1 the flow chart of the study is summarized .
patients who meet the following criteria are eligible to participate in the study : ( i ) men and non - pregnant women > 18 years of age ; ( ii ) implantation of an icd or crt - d for standard indications within 28 weeks ; ( iii ) willing and able to be followed by the same medical centre throughout the study ; and ( iv ) capable of understanding and completing the eq-5d questionnaire .
eligible patients who meet all the inclusion criteria are enrolled after they have signed a written , informed consent approved by the local ethics committee ( lec ) . during the enrollment visit ,
baseline data are collected , including demographics , medical history , estimation of new york heart association functional class , drug therapy , qol assessment , using the eq-5d questionnaire , economic costs incurred , and productivity loss for patients and caregivers . at each on - site ambulatory visit in phase i and remote follow - up visit in phase ii , the following data are collected : ( i ) changes in drug therapy ; ( ii ) interim medical history , medical tests , and examinations performed and any other clinical activity occurring in the last 3 months ; and ( iii ) qol assessment . at the final 1 year visit ,
all hospitalizations , unscheduled visits , and transmissions triggered by the patient or by the physician , and all adverse events are recorded on dedicated case report forms and referred to the lec as required .
all costs , clinical outcome data , and qol assessments recorded in both study phases are measured and compared .
if , globally , telemonitoring is found advantageous and less expensive for the patient than standard on - site , ambulatory follow - up , it is defined as the dominant method .
therefore , the incremental cost - effectiveness or cost utility ratio is calculated in order to estimate the incremental cost per effectiveness additional unit .
if the efficacy and clinical outcomes are similar with both methods , the analysis will be limited to a comparison of costs , in order to identify the least expensive treatments . besides clinical outcomes ,
the collection of resource utilization includes ( i ) hospitalizations ; ( ii ) emergency department , family physician , specialist , ambulatory department , and other healthcare professional visits ; ( iii ) medical tests and procedures , and surgical interventions ; and ( iv ) names and dosages of prescriptions and over - the - counter medications , as recorded in the patient expense log .
information regarding loss of productivity is estimated separately as days lost from ( i ) paid employment of the patient or the caregiver , ( ii ) homemaking activities ; and ( iii ) volunteer activities .
costs incurred for emergency department visits and hospitalizations are calculated by reviews of medical records .
productivity losses are estimated separately as days lost from paid employment for the patient or caregiver , days lost from homemaking activities , and days lost from volunteer activities .
sources of unit prices for this analysis : the professional fees are obtained from the national health service records or from a survey of local commercial providers .
costs of ambulatory and emergency department visits , laboratory tests and procedures , and hospitalization are obtained from the hospitals participating in the study .
costs of over - the - counter pharmaceuticals are obtained from the hospital databases and prescription costs from the patients during the follow - ups .
costs for analysing online data when remote monitoring system was used for follow - up are evaluated according to time spent by physicians and allied professionals involved in data analysis .
losses of productivity are calculated from patient interviews during the scheduled follow - up . among the large number of ( i ) drug and dosages combinations , ( ii ) tests and procedures , and ( iii ) hospitalizations recorded in the case report forms , the most frequent unit costs are presented .
a sample size of 200 patients ( 100 patients for each phase of the study ) , including an up to 15% dropout rate at 12 months of follow - up , was calculated from a review of several publications on the economics of telemonitoring in countries other than italy .
these assumptions were particularly considered in the reform study , which followed for 12 months , at 3 month intervals ( i ) a group with conventional ambulatory visits vs. ( ii ) a group followed by remote monitoring .
this german study found costs differences between the two follow - up methods , which were useful to calculate the sample size . with 94 patients included in the analysis ,
a single group t - test at a 5% two - sided significance level has an 80% power to detect an 10% difference between the two groups , with a common standard deviation ( sd ) assumed to be 400 . further assuming a 10% dropout rate , 100 patients for each phase in the study population are needed to reach an 80% power to detect a 10% difference between the two groups .
a 12-month follow - up was calculated to detect all the variables defined in the study objectives .
resource utilization data are presented as counts and percentages , and the continuous cost and utility variables are presented as mean sd . the differences in counts for resource utilization are compared , using the test . as the costs and qol estimates tend to be skewed , these variables are fitted , using gamma distributions and arithmetic means for across - groups comparisons .
cost - effectiveness acceptability curves are typically interpreted as the probability that one treatment is cost effective at a given willingness - to - pay threshold , based on stochastic uncertainty . as the curves are based on expectations , these results are not entered in a statistical analysis .
the estimated cost and outcome data for each patient are used to assess the stochastic uncertainty by estimating 1000 bootstrapped samples ( i.e. sampling with replacement ) . for a visual representation of this patient - level uncertainty ,
the cost - effectiveness acceptability curves are calculated , to show the probability of remote follow - ups to be more cost effective than conventional follow - ups , as a function of society 's willingness - to - pay for a qaly gained .
the merlin.net pcn is a dedicated , virtual data collection centre , accessible via an internet site protected by a username and password .
the merlin.net transfers data collected either on - site or remotely , using the merlin@home transmitter , which communicates , on a daily basis and without patient interaction , with the implanted devices , notifying every pre - defined clinical and technical issue .
the data are automatically transmitted via wireless telemetry between merlin@home and the implanted devices , and sent to merlin.net via a standard landline or via the global system for mobile communication network .
the merlin.net website is similar to a mailbox interface , where the user can examine recent transmissions or direct alerts .
the data collected on merlin.net can also be exported to an electronic health record ( ehr ) , for a complete patient data management .
tariff is an observational , prospective , multicenter study designed to compare the costs and benefits of on - site vs. remote follow - ups .
this study is conducted at six italian medical centres and has been approved by the institutional ethics committees of each participating centre .
the enrolment of patients began in december 2009 and both enrolment phases will end before the end of 2011 .
the purposes of the study are to ( i ) measure the incremental economic value of remote monitoring of icd and crt - d for italian hospitals , third payers , and patients , and ( ii ) develop , from the hospital perspective , a cost - minimization and use analysis based on the qol associated with remote follow - up of icd and crt - d , using merlin@home and merlin.net , compared with standard , on - site patient care .
the primary endpoint of the study is to measure , under real - life circumstances , the incremental costs and benefits incurred by the italian healthcare system for the implementation of each method of follow - up .
the secondary study endpoint is to compare , from the hospital point of view , the incremental costs represented by each method of follow - up , including assessments of qol , using the eq-5d questionnaire .
the patients are enrolled within 28 weeks after device implant and followed for 12 months .
i , 100 consecutive patients are followed according to a standard on - site ambulatory follow - up at 3 , 6 , 9 , and 12 months after implantation of a device . in phase ii ,
the patients receive the transmitter programmed for remote transmissions at 3 , 6 , and 9 months after device implant . at 12 months of follow - up
the patients enrolled in phase ii are monitored daily remotely by programmable alerts throughout the 1-year study ; each time that the device 's parameters are out of the programmed range , an alert message is automatically sent to the clinic or to the physician in charge through e - mail or fax .
each patient is instructed to keep a diary during each 3 months period of follow - up to record information regarding interim hospitalizations , emergency department visits , adverse events , changes in medication regimens , eq-5d questionnaire , and visits with other healthcare professionals . in figure 1 the flow chart of the study
patients who meet the following criteria are eligible to participate in the study : ( i ) men and non - pregnant women > 18 years of age ; ( ii ) implantation of an icd or crt - d for standard indications within 28 weeks ; ( iii ) willing and able to be followed by the same medical centre throughout the study ; and ( iv ) capable of understanding and completing the eq-5d questionnaire .
eligible patients who meet all the inclusion criteria are enrolled after they have signed a written , informed consent approved by the local ethics committee ( lec ) . during the enrollment visit ,
baseline data are collected , including demographics , medical history , estimation of new york heart association functional class , drug therapy , qol assessment , using the eq-5d questionnaire , economic costs incurred , and productivity loss for patients and caregivers . at each on - site ambulatory visit in phase i and remote follow - up visit in phase ii , the following data are collected : ( i ) changes in drug therapy ; ( ii ) interim medical history , medical tests , and examinations performed and any other clinical activity occurring in the last 3 months ; and ( iii ) qol assessment . at the final 1 year visit ,
all hospitalizations , unscheduled visits , and transmissions triggered by the patient or by the physician , and all adverse events are recorded on dedicated case report forms and referred to the lec as required .
all costs , clinical outcome data , and qol assessments recorded in both study phases are measured and compared .
if , globally , telemonitoring is found advantageous and less expensive for the patient than standard on - site , ambulatory follow - up , it is defined as the dominant method .
therefore , the incremental cost - effectiveness or cost utility ratio is calculated in order to estimate the incremental cost per effectiveness additional unit .
if the efficacy and clinical outcomes are similar with both methods , the analysis will be limited to a comparison of costs , in order to identify the least expensive treatments .
the collection of resource utilization includes ( i ) hospitalizations ; ( ii ) emergency department , family physician , specialist , ambulatory department , and other healthcare professional visits ; ( iii ) medical tests and procedures , and surgical interventions ; and ( iv ) names and dosages of prescriptions and over - the - counter medications , as recorded in the patient expense log .
information regarding loss of productivity is estimated separately as days lost from ( i ) paid employment of the patient or the caregiver , ( ii ) homemaking activities ; and ( iii ) volunteer activities .
costs incurred for emergency department visits and hospitalizations are calculated by reviews of medical records .
productivity losses are estimated separately as days lost from paid employment for the patient or caregiver , days lost from homemaking activities , and days lost from volunteer activities .
sources of unit prices for this analysis : the professional fees are obtained from the national health service records or from a survey of local commercial providers .
costs of ambulatory and emergency department visits , laboratory tests and procedures , and hospitalization are obtained from the hospitals participating in the study .
costs of over - the - counter pharmaceuticals are obtained from the hospital databases and prescription costs from the patients during the follow - ups .
costs for analysing online data when remote monitoring system was used for follow - up are evaluated according to time spent by physicians and allied professionals involved in data analysis .
losses of productivity are calculated from patient interviews during the scheduled follow - up . among the large number of ( i ) drug and dosages combinations , ( ii ) tests and procedures , and ( iii ) hospitalizations recorded in the case report forms , the most frequent unit costs are presented .
a sample size of 200 patients ( 100 patients for each phase of the study ) , including an up to 15% dropout rate at 12 months of follow - up , was calculated from a review of several publications on the economics of telemonitoring in countries other than italy .
these assumptions were particularly considered in the reform study , which followed for 12 months , at 3 month intervals ( i ) a group with conventional ambulatory visits vs. ( ii ) a group followed by remote monitoring .
this german study found costs differences between the two follow - up methods , which were useful to calculate the sample size . with 94 patients included in the analysis ,
a single group t - test at a 5% two - sided significance level has an 80% power to detect an 10% difference between the two groups , with a common standard deviation ( sd ) assumed to be 400 . further assuming a 10% dropout rate , 100 patients for each phase in the study population are needed to reach an 80% power to detect a 10% difference between the two groups .
a 12-month follow - up was calculated to detect all the variables defined in the study objectives .
resource utilization data are presented as counts and percentages , and the continuous cost and utility variables are presented as mean sd . the differences in counts for resource utilization are compared , using the test . as the costs and qol estimates tend to be skewed , these variables are fitted , using gamma distributions and arithmetic means for across - groups comparisons .
cost - effectiveness acceptability curves are typically interpreted as the probability that one treatment is cost effective at a given willingness - to - pay threshold , based on stochastic uncertainty . as
the curves are based on expectations , these results are not entered in a statistical analysis . the estimated cost and outcome data for each patient
are used to assess the stochastic uncertainty by estimating 1000 bootstrapped samples ( i.e. sampling with replacement ) . for a visual representation of this patient - level uncertainty ,
the cost - effectiveness acceptability curves are calculated , to show the probability of remote follow - ups to be more cost effective than conventional follow - ups , as a function of society 's willingness - to - pay for a qaly gained .
remote monitoring is becoming the standard means of following recipients of cardiac implantable electronic devices , and has been included in the international professional practice guidelines .
large randomized clinical trials have shown that the substitution of remote for on - site ambulatory follow - ups effectively lowers the healthcare source consumption without compromising patient safety .
furthermore , the reaction time to detected events can be significantly shortened by remote monitoring .
an early reaction to device malfunction or to adverse clinical events may have an effect on patient outcome . from this perspective , the merlin.net system is specifically designed to allow early interventions following daily alerts , previously programmed by physicians , according to the patient and device characteristics . the merlin.net site also represents a virtual data collection centre , easily and ubiquitously accessible via a simple internet connection , because this allows physicians to know important device diagnostic data and to react in case of alerts due to patient 's or device 's issues . the tariff study will be essential to ascertain the speed of physician 's reaction to direct incoming alerts , at a minimum cost and for a better patient 's outcome .
few data have been published regarding the cost - effectiveness of remote monitoring in standard clinical practice , and reimbursement continues to be an issue in several european countries , including italy .
furthermore , there is a need to accurately define the reimbursement value of remote follow - ups , as the periodic interrogations require time and dedicated personnel . in this respect ,
the failure to communicate the value of remote monitoring by industry , because of market competition and early marketing of the technology , is eroding the perceived value of innovation , thus limiting the availability of funding for innovative and valuable improvements .
the tariff observational study , based on the prospective comparison of two groups , will enable an assessment of the real - life added value of remote monitoring , considering also its value from the perspective of the different italian stakeholders for a broader adoption and for a better organization of the healthcare assistance .
future advances in remote care technologies allowing the monitoring of not only device function , but also the periodic evaluation of vital signs or specific disease indicators , such as fluid accumulation or left atrial pressure monitoring , will add further value to remote monitoring , more and more influencing the patient 's prognosis besides improving qol .
although the benefits conferred by remote monitoring have already been assessed on the basis of patient outcomes , its economic added value remains to be shown .
the tariff study , based on a cost - minimization analysis , directly comparing remote follow - up with standard ambulatory visits , will hopefully validate the cost effectiveness of the merlin.net technology , and define a proper reimbursement schedule applicable for the italian healthcare system .
funding to pay the open access publication charge was provided by st.jude medical italia , sponsor of the tariff registry .
funding to pay the open access publication charge was provided by st.jude medical italia , sponsor of the tariff registry . | pubmed |
Some question in flux which is produced by magnetic field
I was trying to solving [the problem](http://www.danfleisch.com/maxwell/chapter2/problem1/).
I know that total flux (which produced by magnetic field) of any system is $0$. Even flux in a closed surface is $0$ also. But flux in a non-closed surface isn't always $0$.
$$\phi=\int\_S ((5\hat i-3\hat j+4\hat k)\times10^{-9})\cdot(-\hat k)da$$
I have two question about the equation. Why they wrote $\times10^{-9}$? Did they write it cause they were defining only top or bottom of that cylinder.
Is it necessary to assume bottom as negative and top as positive. In simple algebra graph, we assume bottom as negative and top as positive. Can't I assume vice-versa here?
The given expression is for the flux out through the bottom surface where the outward area vector is in the negative (z) direction. The $10^{-9}$ indicates a field in nano-teslas (which was not given in the problem). The flux out through the top will be positive, through the bottom negative, and you do not need to calculate the sides because, as you noted, the total flux out through all the surfaces would be zero.
| stackexchange/physics |
Is the boundary of an atom well defined?
That question might seem weird, but that's what I have been imagining lately; going through Bohr's theory on the hydrogen atom. He clearly defines the radius of an orbit with an exact mathematical expression. But what do they mean when they say any atom (say $\ce{Na}$) has a radius $r$. Are we to consider atoms as solid, rigid spheres? If that's the case, what about water?
If all the atoms are defined as solid, rigid, spherical balls, how come an aggregation of so many solid objects be a liquid? How can it flow? So, in a nutshell what is the boundary of an atom made up of, or even this: does it have a defined boundary?
This troubles me a lot. I think maybe the modern atomic model has dealt with this problem. I haven't read it in detail, and I would be highly thankful to any references.
No, the boundary of an atom is not well defined. According Quantum mechanics the electron density around an atoms decreases exponentially, thus getting asymptotically close to zero.
Considering atoms as rigid spheres is only an approximation. The criteria used to decide on the actual value of the atomic radius is arbitrary. You can for example choose the expectation value $\langle\hat r\rangle$ of the electronic wavefunction. For the Hydrogren atom, this results in the bohr radius $a\_0$. But you might as well choose the maximum of the electron density ($\frac{3}{2}a\_0$ for $\ce{H}$), or something based on experiments.
Now the aggregate state is something completely different and not directly related to atomic radius and whether they are rigid sphere or not. Solid means the molecules/atoms of a substance are fixed in their positions. They can vibrate, but do not change their average position with respect to each other. In gases molecules may move freely. And a liquid is something in between, you have some order if you look at a small group of molecules, but not on a larger scale as for solids.
As was already mentioned, the boundary of an atom is everything but well-defined. Quantum mechanics tell us this very well: the probability of finding an electron at the distance $r$ from the nucleus is proportional to $\mathrm e^{-r}$, meaning that it will never hit zero.[1] The lack of a zero-point means that there is no cutoff after which we can clearly say the atom is over. Instead, when performing quantum calculations an arbitrary cutoff value is chosen. The boundary within which the probability of finding the electron is larger than the cutoff value is then plotted as the ‘extent of the orbital’.
However, even if atoms *were* rigid spheres that does not mean your macroscopic postulate (that rigid spheres cannot form a liquid) holds true because you are misestimating the difference between microscopic and macroscopic properties. I present you the following example:
We will both agree that sand is made up of rigid solid particles even if they are not perfect spheres. Yet, sand shows a few properties that almost make it look liquid if you look from far away. For example, it can ‘flow down’ a slope much in the same way as water could. And also if you try to pile it into a pyramid, it will flow outwards to a certain extent as water (or better: mercury) drops would. You might extend this analogy to marbles which are clearly spherical (usually). You cannot stack them on a blank surface as they will roll away much like you cannot stack water molecules because they will flow to the side.
The main difference between my macroscopic examples and actual molecules is the type and extent of attractive forces between them. While the rough texture of sand can be said to give it some kind of a surface tension (like water and mercury), the attractive forces between the particles are still low and the main force acting on them is gravity (of the Earth, not of other grains of sand). The same thing is true for the marbles example which even lack surface tension and are only attracted to the Earth by gravity. Actual molecules have much stronger intermolecular forces that dominate over the external gravity force source in the microscopic world. That contributes to the final edge of a difference between many grains of sand/many marbles and a sample of water.
All I have discussed above is, however, completely independent of the question whether the spheres that make up atoms are rigid and solid or not.
Seriously? Bohr's Atomic Model? It was known by 1920 that that model failed (badly) to explain observational data. That is, it hasn't been taken seriously for nearly 100 years. Perhaps you should invoke the 4 humors and reason from there. (The only atom the the theory did a pretty good job for is hydrogen. One down, 91 elements to go....) There are lots of different models which are useful for different purposes. One thing we know about all of them, is they're all wrong. So, since the "right" model isn't known, picking a "best" model requires you to know what your purpose is, what the context is. The issue is deciding which model is most useful, not which model is correct. That turns out to depend on context. What I was taught as an undergraduate chemistry major (almost 50 years ago) was that an electron bound in an atom (or molecule, or ion, or radical) is best thought of as a probability wave. This means that the location of the electron is "smeared out" in space and that for any distance, r, from the nucleus (center), there is a *non-zero* probability of the electron being at that distance. This means, to answer your question, that atoms do not have "hard surfaces". The reason why some Physical Chemistry textbooks still cover the Bohr Model is because it helps the student transition between the physics of everyday objects to the non-intuitive world of quantum mechanics. The best book for you depends on what your mathematical knowledge is, how much effort you want to spend, and how detailed you want to be. It is a mature science, and many popular books have been written about it. Concepts such as "radius" are mostly nonsensical at the quantum scale. For instance, the radius of an atom depends on how you measure it. Consider the simple case of shooting electrons at it. Then shooting protons at it. Then shooting neutrons at it. Then microwaves. Then (visible) light waves. Then x-rays. Each will give you a different radius. In some ways it is similar to the question of how long is a coastline. If you measure it with a 100 meter cable, you'll get one answer (ignoring differences in sea level, tides, wind, rain, etc.), if you measure it with a meter stick, you'll get a larger value. Measure it centimeter by centimeter, and it will be even larger, and just imagine if you could measure it atom-by-atom, it would be very difficult to determine where the liquid began and where the land ended. Coastline is a macroscopic concept, with little meaning at the micrometer scale (let alone the nanometer scale). Very much like your concept of radius. (Although to be fair, we "steal" the word and use it in various contexts which often have similarities to its macroscopic use.)
| stackexchange/chemistry |
The 201617 FA Women's Premier League Plate is the third running of the competition, which began in 2014. It is the secondary League Cup competition run by the FA Women's Premier League FA WPL, and is run in parallel with the league's primary League Cup competition, the Premier League Cup.
The teams that take part in the WPL plate are decided after the determining round of the WPL Cup. The winners of determining round matches continue in the WPL Cup, while the losers move into the WPL Plate.
All 72 Premier League clubs were included in the determining round draw, two of whom Forest Green Rovers and Nuneaton Town withdrew from the competition before playing a match, meaning 36 teams progressed in the Cup and 34 were entered in the Plate.
Reigning champions Coventry United, who beat Enfield Town 51 in the 201516 final, won their determining Round match this season, meaning that they did not defend their title.
Results
All results listed are published by The Football Association. Games are listed by round in chronological order, and then in alphabetical order of the home team where matches were played simultaneously.
The division each team play in is indicated in brackets after their name: S=Southern Division; N=Northern Division; SW1=South West Division One; SE1=South East Division One; M1=Midlands Division One; N1=Northern Division One.
First round
Due to there being 34 teams in the competition, two first round matches are required to eliminate two teams and allow a full single-elimination knockout tournament to take place.
Second round
Third round
Quarter-finals
Semi-finals
Final
References
Category:FA Women's National League Plate
Prem | wikipedia |
Subsets and Splits