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up to now the quark - level substructure of scalar mesons is still not well understood . especially , the slight scalars mesons , including @xmath17 and @xmath18 , which form an su(3 ) flavor nonet and are considered as either two quark states or tetraquak states ( di - quark and anti - diquark structure ) as originally advocated by jaffe @xcite .
certainly , there are other different su(3 ) scenarios about scalar mesons @xcite .
if one considers these light scalar mesons as two quark states , @xmath19 structure , there are experiments indicate that the heaviest one @xmath13 and the lightest one @xmath20 in this su(3 ) nonet must have a mixing @xmath21 . for the mixing angle @xmath4
, there are several different values from experimental measurements .
a mixing angle @xmath22 was determined from the decays @xmath23 , and @xmath24 or @xmath25 from the decays @xmath26 , while a range @xmath27 was given from the analysis of three body decay @xmath28 .
an analysis of @xmath3 mixing by using the light cone qcd sum rules @xcite , yielded @xmath29 and @xmath30 .
the value of @xmath4 @xmath31 or @xmath32 was obtained in the decays @xmath33 @xcite .
ochs @xcite found @xmath34 by averaging over several decay processes .
the authors of ref.@xcite provided a limit on the mixing angle @xmath35 at @xmath36 confidence . as we know , the mixing between @xmath37 is something like that in @xmath38 , but with much more uncertainties .
in order to explain the @xmath39 puzzle , some complex mixing mechanisms including gluon even @xmath40 meson in @xmath38 were also considered @xcite .
this led people to conjecture that @xmath13 and @xmath20 may not be simple quark - antiquark states , perhaps there exist more complicated structure except the @xmath37 mixing .
recently , the decays @xmath41 were measured by lhcb collaboration @xcite : ( b^0|d^0f_0(500))&=&(11.20.80.52.10.5)10 ^ -5 , + [ 1 ] ( b^0|d^0f_0(980))&=&(1.340.250.100.460.06)10 ^ -5 , + [ 2 ] ( b^0_s|d^0f_0(980))&=&(1.71.00.50.1)10 ^ -6 . where the first and the second uncertainties are statistical and experimental systematic errors , respectively , the third one is from the model - dependent error .
we see there exist larger statistical error in the @xmath42 decay and the model - dependent error in the fist two @xmath43 decays . by using these new data
, we will try to constrain the mixing angle between @xmath13 and @xmath44 through these @xmath0 decays in the perturbative qcd ( pqcd ) approach .
there was a work about constraining the mixing angle through @xmath45 decays @xcite , but two different approaches were used in the same decay channel : the factorizable contribution and vertex corrections are calculated in the qcd factorization ( qcdf ) approach , while the hard spectator scattering corrections are calculated in the pqcd approach .
so one may suspect its rationality and reliability in determining the mixing angle between @xmath37 .
the b meson decays with a d meson involved in the final states have been studied in pqcd approach , such as @xmath46 @xcite , here @xmath47 represent a pseudoscalar , vector and axial - vector meson , respectively .
most of the predictions can well explain the experimental data . while an explicit calculation for the branching ratio of the decay @xmath48 gives @xmath49 @xcite , which is quite different from the present experimental result .
so we would like to systematically study the decays @xmath50 in the pqcd approach , including the ckm suppressed decays @xmath51 . at last ,
the decays @xmath52 are also considered .
the layout of this paper is as follows . in sec.[proper ] , decay constants and light - cone distribution amplitudes of the relevant mesons are introduced . in sec.[results ] , we then analyze these decay channels using the pqcd approach .
the numerical results and the discussions are given in sec .
[ numer ] .
conclusions are presented in the final part .
for the wave function of the heavy @xmath0 meson , we take _ b_(s)(x , b)= ( p / _ b_(s ) + m_b_(s ) ) _ 5 _ b_(s ) ( x , b ) .
[ bmeson ] here only the contribution of the first lorentz structure @xmath53 is taken into account , since the contribution of the second lorentz structure @xmath54 is numerically small @xcite and can be neglected . for the distribution amplitude @xmath55 in eq.([bmeson ] ) , we adopt the following model : _ b_(s)(x , b)=n_b_(s)x^2(1-x)^2 , where @xmath56 is a free parameter and taken to be @xmath57 gev for @xmath58 in numerical calculations , and @xmath59 @xmath60 is the normalization factor for @xmath61 @xmath62 . for @xmath8 meson , the su(3 ) breaking effects
are taken into consideration .
as for the wave functions of the @xmath63 meson , we use the form derived in ref.@xcite e^ik0||c_(0)u_()||d^0&=&- [ ( p / _ d+m_d)_5]__d(x , b ) , + e^ik0||c_(0)u_()||d^*0&=&- [ ( p / _ d^*+m_d^ * ) / _ l]_^l_d^*(x , b ) , where @xmath64 is the longitudinal polarization vector . in this work only the longitudinal polarization component is used . here
we take the best - fitted form @xmath65 from b to charmed meson decays derived in @xcite as _ d(x , b)=6x(1-x)[1+c_d(1 - 2x ) ] . for the wave function @xmath66
, it has the similar expression as @xmath67 except with different parameters , and given as follows : @xmath68 mev , @xmath69 mev , and @xmath70 @xmath71 , @xmath72 @xmath73 @xcite . for the wave function @xmath74 , we take the same distribution amplitude with that of the pseudoscalar meson @xmath75 because of their small mass difference , except with different decay constants @xmath76 mev and @xmath77 mev @xcite .
since the neutral scalar meson @xmath13 can not be produced via the vector current , we have @xmath78 ( the abbreviation @xmath79 denotes the @xmath13 for simplicity ) . taking the @xmath37 mixing into account
, the scalar current @xmath80 can be written as : f_0^n|d|d|0=f_0^n|u|u|0=m_f_0f^n_f_0 , f_0^s|s|s|0=m_f_0f^s_f_0 , where @xmath81 represent for the quark flavor states for @xmath82 and @xmath83 components of @xmath79 meson , respectively . as the scalar decay constants @xmath84 and @xmath85 are very close@xcite
, we can assume @xmath86 and denote them as @xmath87 in the following .
the twist-2 and twist-3 lcdas for the different components of @xmath13 are defined by : f_0(p)||q(z)_l q(0)_j|0&=&^1_0dxe^ixpz\{p___f_0(x ) + m_f_0^s_f_0(x)+m_f_0(n__+n___1)^t_f_0(x)}_jl,[lcda ] where we assume @xmath88 and @xmath89 are the same and denote them as @xmath90 , @xmath91 and @xmath92 are light - like vectors : @xmath93 .
the normalization of the distribution amplitudes are related to the decay constants : ^1_0 dx_f_0(x)=^1_0 dx^t_f_0(x)=0,^1_0 dx^s_f_0(x)=. the twist-2 lcda @xmath94 can be expanded in terms of gegenbauer polynomials as : _
f_0(x)=|f_f_06x(1-x ) , with the decay constant @xmath95 gev @xcite .
it is noticed that all the even gegenbauer momentums vanish due to the charge conjugation invariance . as for the odd genbauer momentums ,
only the first term is kept and the value of the coefficient is taken as @xmath96 @xcite . for the twist-3 lcda , we also take the first term of the gegenbauer expansion , i.e. the asymptotic form , ^s_f_0(x)=|f_f_0 , ^t_f_0(x)=|f_f_0(1 - 2x ) . _
the weak effective hamiltonian @xmath97 for the charmed @xmath0 decays @xmath98 , is composed only by the tree operators and given by : h_eff = v^*_cbv_uq[c_1()o_1()+c_2()o_2 ( ) ] , where the tree operators are writen as : o_1=(|c_b_)_v - a(|d_u_)_v - a , o_2=(|c_b_)_v - a(|d_u_)_v - a , with @xmath63 represents @xmath99 .
these decays with larger ckm matrix elements , say the @xmath100 transition , @xmath101 are called ckm allowed decays .
another kind of decays @xmath102 with smaller ckm matrix elements ( in case of @xmath103 transition , @xmath104 ) are called ckm suppressed decays and the corresponding weak effective hamiltonian is given as : h_eff = v^*_ubv_cq[c_1()o_1()+c_2()o_2 ( ) ] .
here we take the decay @xmath105 as an example , whose leading - order feynman diagrams are shown in figure 1 .
= 18 cm the feynman diagrams on the first row are for the emission types , where figs.(a ) and ( b ) are the factorizable diagrams , figs.(c ) and ( d ) are the nonfactorizable ones , their amplitudes are written as : ^|d_bf_0&=&8c_fm^4_bf_d_0 ^ 1 d x_1 dx_2 _
0^ b_1 db_1 b_2 db_2 _ b(x_1,b_1 ) [ ( 1+x_2)_f_0(x_2)+r_f(1 - 2x_2 ) & & ( ^s_f_0(x_2)+^t_f_0(x_2 ) ) ] e_e(t_a)h_e(x_1,x_2(1-r^2_d),b_1,b_2)s_t(x_2 ) & & + 2r_f_f_s(x_2)e_e(t_b)h_e(x_2,x_1(1-r^2_d),b_2,b_1)s_t(x_1 ) ] , + ^|d_bf_0&=&32c_f m_b^4/_0 ^ 1 d x_1 dx_2 dx_3 _
0^ b_1 db_1 b_3 db_3_b(x_1,b_1)_d(x_3,b_3 ) & & \{.&&.e_en(t_c)h^c_en(x_1,x_2(1-r_d^2),x_3,b_1,b_3)+e_en(t_d)h^d_en(x_1,x_2(1-r_d^2),x_3,b_1,b_3 ) . & & . } , with the mass ratios @xmath106 and @xmath107 .
the evolution factors evolving the scale @xmath108 and the hard functions of the hard part of factorization amplitudes are listed as : e_e(t)&=&_s(t),[suda1 ] + e_en(t)&=&_s(t),[suda2 ] + h_e(x_1,x_2,b_1,b_2)&=&k_0(m_bb_1 ) , + h^j_en(x_1,x_2,x_3,b_1,b_3)&= & ( k_0(a_jm_bb_3 ) & a^2_j0 + h^(1)_0(m_bb_3 ) & a^2_j0 + ) , with the variables @xmath109 listed as : a^2_c&=&r_c^2-(1-x_1-x_3)(x_2(1-r^2_d)+r_d^2 ) , + a^2_d&=&(x_1-x_3)x_2(1-r^2_d ) . the hard scale @xmath108 and the expression of sudakov factor in each amplitude can be found in the appendix .
as we know , the double logarithms @xmath110 produced by the radiative corrections are not small expansion parameters when the end - point region is important . in order to improve the perturbative expansion , threshold resummation of these logarithms to all order
is needed , which leads to a quark jet function : s_t(x)=[x(1-x)]^c , with @xmath111 .
it is effective to smear the end point singularity with a momentum fraction @xmath112 .
this factor will also appear in the factorizable annihilation type amplitudes .
the amplitudes for the feynman diagrams on the second row can be obtained by the feynman rules and are given as : ^|d_ann&=&32c_f m_b^4/_0 ^ 1 d x_1 dx_2 dx_3_0^ b_1 db_1 b_3 db_3 _ b(x_1,b_1)_d(x_3,b_3 ) & & \{e_an(t_e)h^e_an(x_1,x_2,x_3,b_1,b_3).&&. + e_an(t_f)h^f_an(x_1,x_2,x_3,b_1,b_3 ) } , ^|d_ann&=&-8c_f f_bm_b^4_0 ^ 1 d x_2 dx_3 _ 0^ b_2 db_2 b_3 db_3 _
d(x_3,b_3)\{e_af(t_g)h_af(x_3,(1-x_2)(1-r_d^2),b_3,b_2).&&. + e_af(t_h)h_af(x_2,x_3(1-r_d^2),b_2,b_3)}. similarly , @xmath113 are the ( non)factorizable annihilation type amplitudes , where the evolution factors @xmath114 evolving the scale @xmath108 and the hard functions of the hard part of factorization amplitudes are listed as : e_an(t)&=&_s(t),[suda3 ] + e_af(t)&=&_s(t),[suda4 ] + h_an^j(x_1,x_2,x_3,b_1,b_3)&=&i ( k_0(l_jm_bb_1 ) & l^2_j0 + h^(1)_0(m_bb_1 ) & l^2_j0 + ) , + h_af(x_2,x_3,b_2,b_3)&=&(i)^2h^(1)_0(m_bb_2 ) & & , where the definitions of @xmath115 are written as : l^2_e&=&r_b^2-(1-x_3)(1-(1-x_2)(1-r^2_d)-x_1 ) , + l^2_f&=&x_3(x_1-(1-x_2)(1-r^2_d ) ) . the functions @xmath116 , which appear in the upper hard kernel @xmath117 are the ( modified ) bessel functions , which are obtained from the fourier transformations of the quark and gluon propagators . combining above amplitudes , one can easily to write down the total decay amplitudes of each considered channel ( b^0|d^0f_0(980))&=&v^*_cbv_ud(__f__^|d_bf_0a_2 + _ _ m__^|d_bf_0c_2+m^|d_annc_2+__f__^|d_anna_2 ) , + ( b^0d^0f_0(980))&=&v^*_ubv_cd(__f__^d_bf_0a_2 + _ _ m__^d_bf_0c_2+__m__^f_0_annc_2+__f__^f_0_anna_2 ) , + ( b^0_s|d^0f_0(980))&=&v^*_cbv_us(__f__^d_bf_0a_2 + _ _ m__^d_bf_0c_2+__m__^d_annc_2+__f__^d_anna_2 ) , + _ a_(b^0_sd^0f_0(980))&=&v^*_ubv_cs(__f__^d_bf_0a_2 + _ _ m__^d_bf_0c_2+__m__^f_0_annc_2+__f__^f_0_anna_2 ) , + ( b^+d^+f_0(980))&=&v^*_ubv_cd(__f__^d_bf_0a_1 + _ _ m__^d_bf_0c_2/3+__m__^f_0_annc_2/3+__f__^f_0_anna_1 ) , + ( b^+d^+_sf_0(980))&=&v^*_ubv_cs(__f__^d_bf_0a_1 + _ _ m__^d_bf_0c_2/3+__m__^f_0_annc_2/3+__f__^f_0_anna_1 ) , and likewise for the corresponding decays with the pseudoscalar meson @xmath63 replaced by the vector meson @xmath118 .
we use the following input parameters for numerical calculations @xcite : f_b&=&190 mev , f_b_s=230 mev , m_b=5.28 gev , m_b_s=5.37 gev , + _
b^&=&1.63810 ^ -12 s,_b^0=1.51910 ^ -12 s , _
b_s=1.51210 ^ -12 s , + m_d^0&=&1.869 gev , m_d_s^+=1.968 gev , m_d^*0=2.007 gev , m_d_s^*+=2.112 gev . for the ckm matrix elements ,
we adopt the wolfenstein parametrization and the updated values @xmath119 and @xmath120 @xcite . in the @xmath0-rest frame ,
the decay rates of @xmath121 can be written as : ( b_(s)d^(*)_(s)f_0(980))=(1-r^2_d^(*)_(s))a , where @xmath122 is the total decay amplitude of each considered decay , which has been given in last section . using the input parameters and the wave functions as specified in this section and sec.[proper ] , we give the dependencies of the branching ratios @xmath123 and @xmath124 on the mixing angle @xmath4 shown in fig.2 .
= 15.0 cm = 15.0 cm combining these two panels , one can find that the allowed mixing angle lies in the range @xmath125 at the large angle region .
it is not strange that , as mentioned before , the large mixing angle @xmath126 is also obtained in the analysis of @xmath127 decays @xcite . in the following
we mainly discuss the region with the mixing angle less than @xmath128 . for
the branching ratio of the decay @xmath129 , the experimental value @xmath130 with @xmath131 can give a stronger constrain on the mixing angle , and in the range of @xmath132 , the central theoretical values agree well with the data .
but if the theoretical uncertainties are included , the range will become wider .
although the branching ratio @xmath133 with large uncertainty can not give stringent constrain on the value of the mixing angle , we can get some hints from the data : if we take the mixing angle @xmath134 , that is , we consider that the scalar meson @xmath13 is composed entirely of two quark component @xmath14 , the corresponding branching ratio is about @xmath135 , which is a little lower than the experimental value .
if we consider the small mixing with @xmath136 , the branching ratio will get an enhancement for the interference between the two different kinds amplitudes from the different quark components , the maximal value for the branching ratio can be obtained at the mixing angle @xmath137 , and arrives at @xmath138 ( shown in the right panel of fig.2 ) .
but if we take such small mixing angle , say about @xmath139 , it will make the branching ratio of the decay @xmath129 undershoot the shaded band in the left panel of fig.2 , which represents the experimental allowed region .
while the mixing angle @xmath4 between @xmath13 and @xmath20 should not be too large , say larger than @xmath140 .
if so , the predicted branching ratios of both the decays @xmath141 and @xmath129 will deviate from the data even with the large errors taken into account .
so we get the conclusion that the two quark component should be dominant for b meson decays in dynamic mechanism .
furthermore , the @xmath14 component is more important than the @xmath142 component .
but it is not in conflict with the dominant four - quark structure in explaining the mass degeneracy of @xmath13 and @xmath18 , and the narrower decay width of @xmath13 than that of @xmath20 . in the following
, we will discuss the mixing angle by considering the ratio of branching fractions .
there are some advantages in considering the ratio , because one can eliminate the systematic errors on the experimental side , and avoid the hadronic uncertainties , such as the decay constants and the gegenbauer moments of the final states on the theoretical side . from the data
, one can find that the ratio of these two branching fractions @xmath143 .
unfortunately , here the uncertainty is mainly from the statistical error in the decay @xmath144 , so the errors of the ratio are not much improved compared to those of the branching ratio of each decay mode . certainly , here we consider a simple method , maybe there is a much better approach for the experimentalists to greatly reduce the errors from this ratio .
so we advice to accurately measure this ratio in experiment , because it is important to further restrict the mixing angle @xmath4 between @xmath13 and @xmath145 .
the ratio can change in a very large range with the mixing angle taking different values , especially for @xmath146 , the branching ratio of @xmath144 is very small and will be exactly equal to zero if the contribution from @xmath147 is turned off , while @xmath148 arrives its maximal value
. then it will be meaningless for the ratio , not mentioning the errors .
for the sake of comparison , we give two regions for the mixing angle shown in fig.3 .
if combining these four panels in fig.2 and fig.3 together , one will get two further shrunken mixing angle ranges @xmath149 and @xmath150 . in view of present large uncertainties from data and theory , it will be difficult to get an unitary value for the mixing angle .
but even if more precise data are available , we still can not get the unitary value .
this argument might be reasonable that there must be some influence from other components in @xmath13 , such as gluon , four quark component , and @xmath151 threshold effect , which we can not handle at present .
nevertheless , one can not deny that the two quark component in @xmath13 is dominant in b decay dynamic mechanism , and the @xmath14 component is more important than the @xmath142 component .
= 16.0 cm = 16.0 cm up to now we still do not analyze the decay @xmath152 , although the data of this channel is available .
there are many uncertainties from the decay constant and the light - cone distribution amplitudes ( lcdas ) of @xmath44 meson .
the authors of ref.@xcite assumed that @xmath44 has the similar decay constant and lcdas as those of @xmath13 , while the authors of ref.@xcite just took the same decay constant and lcdas with those of @xmath18 .
these two sets of parameters will generate very different results : if using the former , one will obtain small branching ratios which are far below the experimental lower limit in all the mixing angle region , but the predicted branching ratio will overlap with the data in some angle values by using the latter , which can be found in fig.4 .
it shows that the decay constant and lcdas of @xmath44 is more close to those of @xmath18 , so they should have the similar quark components and structure . from fig.4
, we find that there also exist two allowed mixing angle regions @xmath153 and @xmath154 , where the former region can overlap mostly with the allowed region @xmath155 obtained from the analysis of @xmath156 and @xmath157 decays .
while the two large angle regions have less coincidence , it seems that the small angle region is more favored than the large one .
= 18 cm .the cp - averaged branching ratios ( @xmath158 ) of @xmath159 obtained by taking the mixing angle @xmath160 and @xmath161 , respectively .
the first uncertainty comes from the @xmath162 for @xmath58 mesons , the second and the third uncertainties are from the decay constant @xmath163 gev and the gegenbauer moment @xmath96 of @xmath13 meson , respectively , and the last one comes from @xmath164 for @xmath75 meson . [ cols="^,^,^",options="header " , ] [ tab2 ]
in this paper , first we analyze the decays @xmath165 and @xmath166 carefully in the pqcd factorization approach and find two possible regions for the mixing angle @xmath4 , one is centered at @xmath5 and the other is near @xmath6 . if the data of the decay @xmath167 is also included , we find that the small angle region is more favored .
our analyses support that the two quark component in @xmath13 is dominant in b decay dynamic mechanism , and the @xmath14 component is more important than the @xmath142 component .
certainly other components , such as gluon , four quark component , and @xmath151 threshold effect may also give some more or less influences .
it is noticed that our picture is not in conflict with the popular explanation of dominant four - quark component in @xmath13 .
then we predict the branching ratios of other @xmath168 decay channels by fixing @xmath160 and @xmath161 , respectively and find that the branching ratios of @xmath8 decay modes are less sensitive to the mixing angle compared with those of @xmath169 decay modes .
especially , for the decay @xmath170 , its branching ratio changes in a small region between @xmath10 with the mixing angle @xmath4 running from @xmath11 to @xmath12 .
this work is partly supported by the national natural science foundation of china under grant no .
11347030 , by the program of science and technology innovation talents in universities of henan province 14hastit037 .
zhang is grateful to hai - yang cheng and hsiang - nan li for carefully reading the manuscript and very useful suggestions , wen - fei wang , henry t. wong , tzu - chiang yuan for helpful discussions .
he also thanks the institute of physics , academia sinica for their hospitalities during his visit when part of this work was done .
for the ckm suppressed decays , for example , @xmath171 , their feynman diagrams to leading order will be different from fig.1 , especially for the ( non-)factorizable annihilation diagrams , where the positions of @xmath63 and @xmath13 are exchanged compared with those of @xmath172 decay .
but the factorizable emission diagrams are the same with each other , so @xmath173 .
here we also list other amplitudes of these ckm suppressed decays : ^d_bf_0&=&32c_f m_b^4/_0 ^ 1 d x_1 dx_2 dx_3 _ 0^ b_1 db_1 b_3 db_3_b(x_1,b_1)_d(x_3,b_3 ) & & \{.&&.e_en(t_d)h^d_en(x_1,x_2(1-r_d^2),x_3,b_1,b_3)+e_en(t_c)h^c_en(x_1,x_2(1-r_d^2),x_2,b_1,b_3 ) . & & .
} , + ^f_0_ann&=&32c_f m_b^4/_0 ^ 1 d x_1 dx_2 dx_3_0^ b_1 db_1 b_3 db_3 _ b(x_1,b_1)_d(x_3,b_3 ) & & \{e_an(t_e)h^e_an(x_1,x_2,x_3,b_1,b_3).&&. + e_an(t_f)h^f_an(x_1,x_2,x_3,b_1,b_2 ) } , + ^f_0_ann&=&8c_f f_bm_b^4_0 ^ 1 d x_2 dx_3 _ 0^ b_2 db_2 b_2 db_2 _
d(x_3,b_3)\{e_af(t_g)h_af(x_3,(1-x_2)(1-r_d^2),b_3,b_2).&&. + e_af(t_h)h_af(x_2,x_3(1-r_d^2),b_2,b_3)}. here we do not show the amplitudes of the decays @xmath174 , because one can obtain them from those of the decays @xmath175 by the substitutions @xmath176 , where the terms including @xmath177 and @xmath178 were neglected .
it is similar for the decays involving @xmath179 meson .
t_a&=&(m_b,1/b_1,1/b_2 ) , + t_b&=&(m_b,1/b_1,1/b_2 ) , + t_c , d&=&(m_b , m_b,1/b_1,1/b_3 ) , + t_e , f&=&(m_b,,m_b,1/b_1,1/b_3 ) , + t_g&=&(m_b,1/b_2,1/b_3 ) , + t_h&=&t_g=(m_b,1/b_2,1/b_3 ) , + t_h&=&(m_b,1/b_2,1/b_3 ) . and
the @xmath180 functions in sudakov form factors in eq.([suda1 ] ) , eq.([suda2 ] ) , eq.([suda3 ] ) and eq.([suda4 ] ) are listed as s_b(t)&=&s(x_1,b_1)+2^t_1/b_1_q(_s(| ) ) , + s_d(t)&=&s(x_3,b_3)+2^t_1/b_3_q(_s(| ) ) , + s_f_0(t)&=&s(x_2,b_2)+s((1-x_2),b_2)+2^t_1/b_2_q(_s(| ) ) , where the quark anomalous dimension is @xmath181 , and the expression of the @xmath182 in one - loop running coupling coupling constant is used s(q , b)&=&()-(- ) + ( -1)&&- ( ) , with the variables are defined by @xmath183 , \hat{q}=\ln[1/(b\lambda)]$ ] and the coefficients @xmath184 and @xmath185 are _ 1&=&,a^(1)= , + a^(2)&=&- -n_f+_1(e^_e ) , where @xmath186 is the number of the quark flavors and @xmath187 the euler constant .
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pennington , phys.lett.b * 521 * , 15 ( 2001 ) .
hai - yang cheng and kwei - chou yang , , 114020 ( 2007 ) . | arxiv |
When can I use $\wedge$ instead of curl?
It seems in some circles the wedge product is used in preference to curl. I have a basic understanding of Green and Stokes' formula, I wish to use the $\wedge$ notation from now on.
Can someone tell me if this is commonly done, and if so what is the underlying assumption of the surface. If it is not too much to ask, can someone show me how to write say Maxwell's equations using $\wedge$ instead of Curl
The wedge product has its roots in exterior algebra. Exterior algebra lets you talk about objects like planes or volumes as algebraic elements of their own, separate from ordinary vectors, but still obeying the same notions of being "vectors" in their own vector spaces. The wedge product of two vectors is a bivector, and many concepts you may have been taught in vector calculus can be thought of in terms of bivectors instead. Normal vectors are just the unique vectors perpendicular to *bivectors* that are tangent to some surface instead. Rotations can be thought of as rotating *within* a bivector, instead of *around* a rotation axis (and incidentally, rotating within a bivector is a concept that still works in Minkowski space, unlike rotation axes).
Exterior algebra by itself is not enough, though: you need to have a way for vectors and bivectors to interact. There are a couple formalisms that give all the tools to do this:
1. Differential forms. Forms are very common and extensively used in high-level mathematics and for advanced electromagnetism and general relativity. Differential forms contributes the machinery to do *calculus* on bivectors and the like, using the "exterior derivative" $d$. It also has the concept of Hodge duality, with the Hodge star operator $\star$ that turns bivectors in 3d to their normal vectors and vice versa. This ultimately gives you the power to use forms effectively in metrical contexts: like special and general relativity.
2. Clifford algebra and geometric calculus. Clifford algebra is extensively used in quantum mechanics, through the so-called gamma or pauli matrices. The algebra of these objects, however, is worthy of study independent of the idea that these are matrices using matrix multiplication. In this mindset, you can use clifford algebra for run-of-the-mill 3d vector geometry and calculus. Clifford algebra introduces a "geometric product" of vectors instead, which incorporates both the metric and the exterior algebra into one nifty operation. Many of the core concepts are the same as with differential forms, but the notation is often a little closer to traditional vector calculus in look.
You should use wedge products anytime you're not in 3d space, as the cross product is only used in 3d or 7d and not an immediately generalizable concept.
A traditional differential forms writing of Maxwell's equations might be like this:
$$\star d (\star E) = \rho, \quad dE = -\partial\_t B, \quad dB = 0, \quad \star d (\star B) = j + \partial\_t E$$
This form takes $B$ as a 2-form (a bi-covector), but it's not particularly common, as forms are more often used in the context of spacetime, where $E$ is also a 2-form and the two fields come together in the Faraday 2-form $F$. Maxwell's equation in vacuum then take on the simpler form
$$d(\star F) = J, \quad dF = 0$$
In geometric calculus, the derivative operator $\nabla$ has the capability to do both divergences and curls in one operation, so the last equation is typically written
$$\nabla F = \nabla \cdot F + \nabla \wedge F = J + 0 = J$$
The relationship between wedges and the cross product, is as follows: In differential forms,
$$a \times b = \star (a \wedge b)$$
While in clifford algebra, we typically keep explicit the unit trivector $i$:
$$a \times b = i^{-1} (a \wedge b)$$
Canonically, the [wedge product](http://mathworld.wolfram.com/WedgeProduct.html) is distinct from the [cross product](http://mathworld.wolfram.com/CrossProduct.html) and should not be confused, however in three dimensions they are inextricably linked.
The wedge product (or outer product) comes from [exterior algebra](http://en.wikipedia.org/wiki/Exterior_algebra), first due to [Grassmann](http://en.wikipedia.org/wiki/Hermann_Grassmann) who generalized vector products to arbitrary dimensions. This would later be extended by [Clifford](http://en.wikipedia.org/wiki/William_Kingdon_Clifford) into the [Clifford Algebra](http://en.wikipedia.org/wiki/William_Kingdon_Clifford), which would unite the inner and outer products for arbitrary dimensions.
The cross product itself would come from a term in the [quaterion](http://en.wikipedia.org/wiki/Quaternion)'s first described by [Hamilton](http://en.wikipedia.org/wiki/William_Rowan_Hamilton). It only exists in three dimensions, and is defined as
$$ \vec c = \vec a \times \vec b $$
$$ c\_i = \epsilon\_{ijk} a\_j b\_k $$
Where $\epsilon$ is the [Levi-Cevita symbol](http://en.wikipedia.org/wiki/Levi-Civita_symbol), a completely anti-symmetric "tensor"
$$ \epsilon\_{ijk} = \begin{cases} 1 & \text{$ijk$ an even permutation of 123} \\ -1 & \text{$ijk$ an odd permutation of 123} \\ 0 & \text{otherwise} \end{cases} $$
This defines a vector that is perpendicular to the other two vectors. And there we can immediately see the problem. In dimensions higher than 3 there is no longer a unique direction perpendicular to two vectors, there is an entire subspace.
To get around this difficulty, Grassmann had to change the geometric interpretation of the vector product. His wedge product (or outer product) takes two vectors and returns an object that represents the oriented, scaled plane that the two vectors span, and axiomatically is defined to be antisymmetric.
$$ \vec a \wedge \vec b = - \vec b \wedge \vec a $$
*From [wikimedia](http://en.wikipedia.org/wiki/Exterior_algebra#mediaviewer/File:Exterior_calc_cross_product.svg)*
This can naturally be extended to further geometric objects by wedging by still further vectors to build up a fully complete algebra.
Now we can write the correspondence between the cross product and the wedge product:
$$ \vec a \times \vec b = \star ( \vec a \wedge \vec b) $$
This is pretty unsatisfactory as an equation, for I've hidden all of the relevant bits into a new symbol: ($\star$), which represents the [Hodge dual](http://en.wikipedia.org/wiki/Hodge_dual). You see, one of the consequences of this geometric algebra of Clifford is that you can only wedge things against each other so far, eventually you run out of *space* to wedge against. Additionally, the dimensionality of any particular rank of objects in this algebra happen to correspond to rows of Pascal's triangle. In particular, in three dimensions we have:
$$ 1 \quad 3 \quad 3 \quad 1 $$
Which is to say, we have 1 linearly independent scalar, 3 independent vectors, 3 independent planes and only 1 independent volume element. For four dimensions you would have
$$ 1 \quad 4 \quad 6 \quad 4 \quad 1 $$
1 scalar, 4 vectors, 6 plane elements, 4 independent (3D) volumes and only 1 4D volume. It is always true that these sequences are symmetric about the middle. This allows us to define an operator: ($\star$) the hodge dual, that maps from an object on the left half of one of these sequences to the right half and vice versa. In particular, this allows us to associate any plane in 3D with a corresponding vector. This is entirely natural, we do this all of the time in 3D, the natural vector associated with a plane is just the vector perpendicular to the plane. In 4D, every vector is associated with a 3D volume element and vice versa.
At this point, we notice that 3 dimensions is quite special. The natural vector product ($\wedge$) takes two vectors and creates a plane element, but in 3D we can always uniquely assign a vector to this (orientated) plane, this associated vector is the cross product. The wedge of two vectors in any higher dimension cannot be uniquely associated with a vector, as I have hopefully made clear.
It all seems nice a tidy, but the fact that the vector generated by the cross product isn't the *natural* result of vector multiplication leaves a sort of smudge on the vectors created by cross products: they transform differently under reflections. This creates the whole confusion over [pseudovectors](http://en.wikipedia.org/wiki/Pseudovector). The product of vectors is *naturally* a plane, and planes don't switch sign under reflection, while vectors do. For more details see this [answer by ACuriousMind](https://physics.stackexchange.com/a/130105/51994) to another question.
| stackexchange/physics |
Samurai Shodown Anthology サムライスピリッツ 六番勝負 Samurai Supirittsu Rokuban Shobu, lit. Samurai Spirits: The Sixth Match is a game compilation released by SNK Playmore on Wii, PlayStation 2, and PlayStation Portable. It was re-released as a downloadable game on the PlayStation Store for PSP on October 1, 2009. This release does not include Samurai Shodown V Special, which added significant changes to the first version of the game.
Games included
Samurai Shodown
Samurai Shodown II
Samurai Shodown III
Samurai Shodown IV
Samurai Shodown V
Samurai Shodown VI
References
External links
Category:2008 video games
Category:Samurai Shodown video games
Category:SNK Playmore games
Category:PlayStation 2 games
Category:Wii games
Category:PlayStation Portable games
Category:SNK game compilations
Category:Video games developed in the United States | wikipedia |
Górowo is a village in the administrative district of Gmina Kozłowo, within Nidzica County, Warmian-Masurian Voivodeship, in northern Poland. It lies approximately east of Kozłowo, south of Nidzica, and south of the regional capital Olsztyn.
The village has a population of 80.
References
Category:Villages in Nidzica County | wikipedia |
fast radio bursts ( frbs ) are mysterious astronomical radio transients with short intrinsic durations ( @xmath7 ) , large dispersion measures ( @xmath8 ) , and high galactic latitudes @xcite .
recently , thanks to the precise localization and multi - wavelength follow - up observations of the repeating source frb 121102 @xcite , the distance scale of frbs has been finally settled to the cosmological range . so far , even though only frb 121102 has a measured redshift @xmath5 @xcite , the large dm excess of other frbs with respect to the galactic value and their high galactic latitudes suggest that most , if not all , frbs should have a cosmological origin .
the host galaxies of frbs carry important information regarding the progenitor of frbs . for frb 121102 ,
optical imaging and spectroscopy indicate a dwarf galaxy with a mass of @xmath9 as the host galaxy .
the @xmath10 flux of the host galaxy suggests a star formation rate of @xmath11 @xcite .
no information about the host galaxies of other frbs is available .
one possible way to derive frb host galaxy information is to extract the host galaxy dm from data .
@xcite proposed a method to derive @xmath4 using the measured dm and @xmath12 of a sample of frbs .
however , the @xmath12 values of most frbs are not obtained so far . in this paper , we further develop a method to apply dm and flux of frbs to infer @xmath4 .
this method is applied to the current frb sample with 18 sources . through a markov chain monte carlo ( mcmc )
simulation , we derive a relatively large mean host galaxy dm , @xmath0 , for frbs .
we also provide two supporting evidence for a large value of @xmath4 : millisecond - duration of scattering tails for some frbs and @xmath13 for frb 121102 .
for an frb , the observed dispersion measure has three contributions ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , i.e. @xmath14 which are from the milk way , the frb host galaxy ( which itself includes the contributions from the interstellar medium ( ism ) in the host galaxy and a near - source plasma ) , and the igm , respectively . according to the galactic pulsar data
, @xmath15 can be well constrained @xcite , which is a strong function of the galactic latitude @xmath16 , e.g. @xmath17 for @xmath18 and @xmath19 for @xmath20 .
since @xmath15 can be well extracted for a localized frb , one can define the extragalactic ( or excess ) dispersion measure of an frb as @xmath21 which can be treated as an observed quantity .
the properties of frb host galaxies may be assumed to have no significant evolution with redshift , i.e. @xmath22 , where @xmath0 is the average value of the rest - frame host galaxy dm within a certain redshift of distance bin . due to cosmological time dilation ,
the observed host dm value reads @xmath23 @xcite .
considering the local inhomogeneity of the igm , we define a mean dm of the igm as @xcite @xmath24,\nonumber\\ \label{dm } \label{dmigm}\end{aligned}\ ] ] where @xmath25 , @xmath26 and @xmath27 are the hydrogen and helium mass fractions normalized to 3/4 and 1/4 , respectively , and @xmath28 and @xmath29 are the ionization fractions for hydrogen and helium , respectively . for @xmath30 , @xmath31 , due to full ionization of both hydrogen and helium @xcite .
therefore , one has @xmath32 .
we adopt the flat @xmath33 parameters recently derived from the _ plank _ data : @xmath34 , and @xmath35 @xcite . for the fraction of baryon mass in the intergalactic medium ,
we adopt @xmath36 @xcite . for an frb with an intrinsic frequency - dependent luminosity @xmath37 ,
the observed flux is given by @xmath38 .
the luminosity distance of the frb may be given by @xmath39 where @xmath40 is the isotropic intrinsic luminosity , and @xmath41 is the characteristic frequency of frbs - correction is needed to derive a more rigorous @xmath42 .
however , the frb spectral shape is not well constrained .
since the frb emission seems to peak around 1 ghz and since the frb redshift is not very high , our approximate treatment is justified . ] . for a flat universe
, one has @xmath43 . \label{dl}\end{aligned}\ ] ] for @xmath44 , according to eq.([dm])-eq.([dl ] ) , we can obtain approximately @xmath45 , where @xmath46 .
therefore , one has the @xmath47 relation : @xmath48 as shown in eq.([dmf ] ) , @xmath49 for @xmath50 , and @xmath51 for @xmath52 , where @xmath53
. one can numerically solve eq.([dm])-eq.([dl ] ) , and use the observed @xmath47 relation to fit the current sample of 18 frbs .
we take the frb data from the _ frb catalogue _ of @xcite . for the repeating frb , frb 121102 , we take the brightest pulse as its peak flux .
we apply the mcmc method to extract @xmath0 from the observed @xmath47 relation .
the likelihood for the fitting parameters is determined by the @xmath54 statistics , i.e. @xmath55 where @xmath56 represents the sequence of an frb in the sample , @xmath57 represents the error of @xmath58 , and @xmath59 is the system error , and @xmath60 is a fitting parameter reflecting the uncertainty of the model . we minimize @xmath54 and convert it into a probability density function .
we can then obtain the probability distribution of the fitting parameters using the software _ _
emcee__. the analysis results are shown in figure [ fig1 ] .
we have @xmath61 , @xmath62 and @xmath63 .
our results show that frbs may have a large host galaxy dm , although with large dispersion . on the other hand ,
the luminosity distribution is quite narrow , which would suggest a possible common origin of the observed frbs .
interestingly , we note that the fitting intrinsic luminosity @xmath64 is closed to the characteristic luminosity of the magnetar giant flares , e.g. @xmath65 . on the other hand , it is possible that frbs may have a wide luminosity function , with the fainter ones not detectable with current telescopes .
our derived relatively large value of @xmath0 is supported by two other independent pieces of evidence .
first , for galactic pulsars , the scattering time @xmath66 for @xmath67 ( e.g. * ? ? ?
* ) . however , some frbs with @xmath68 have measured scattering time of a few millisecond @xcite , suggesting that scattering happens outside the milky way . the scattering contribution from the igm
is calculated to be negligibly small , so that most the scattering would occur in the frb host galaxy @xcite .
observations show that a larger scattering tail correspond to a larger dm , e.g. @xmath69 for galactic pulsars
@xcite , a fact understandable and required by turbulence theories @xcite . if one assumes that the frbs hosts have a similar relation , for the millisecond scattering time , one would require @xmath70 .
this is consistent with our derived results .
second , the host galaxy dm frb 121102 can be precisely derived .
frb 121102 was localized to a @xmath71 arcsecond precision by @xcite .
the observed dispersion measure is @xmath72 . according the location of frb 121102
, @xcite identified an extended source coincident with the burst , which is a host galaxy at @xmath5 .
adopting the _ plank _ cosmological parameters and @xmath73 , one derive @xmath74 .
the mw contribution is @xmath75 in the direction @xcite .
so one can derive @xmath76 and @xmath77 for frb 121102 .
such a value is also consistent with our fitting results .
the above results suggest that the frb host galaxies have a relatively large value of dm . there could be two possible contributions to such a large dm : the ism in the host galaxy and the near - source plasma . for the case of a host ism
, one immediate inference is that the type of the host galaxies of most frbs would not be mw - like disk galaxies .
the reason is that for disk galaxies , frbs would be most likely emitted from galactic high latitudes , which gives rise to negligible dm .
indeed , the host galaxy of frb 121102 was identified as a dwarf galaxy @xcite , which is consistent with our expectation .
however , our inferred value is still somewhat larger than the simulated host galaxy dm for various types of galaxies @xcite , suggesting that a near - source plasma may be needed . for the case of a near - source plasma
, we consider the contributions from a snr , pwn , or hii region .
first , in a thin shell approximation , the dm value through a young snr may be estimated by ( see also * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) @xmath78 where @xmath79 , @xmath80 and @xmath81 are the snr mass , radius and thickness , respectively , and @xmath82 is the mean molecular weight .
note that the snr dispersion measure does not depend on @xmath81 of the thin shell .
the dm variation of the snr during an observation time @xmath83 is given by @xmath84 where @xmath85 is the characterized snr velocity .
the age of the snr may be estimated as @xmath86 . in principle , it is possible to expect that the host dm is dominated by a supernova ejecta . however , there are two caveats for this possibility : 1 .
the thin shell model predicts an observable dm variation over the decade - long time scale , which is inconsistent with the non - variation dm of the repeating frbs during the approximately four - year period of observations ; 2 . for an age - independent event rate (
the time delay between sn and frb is uniformly distributed for frbs ) , the cumulative distribution of dms of frbs should satisfies @xmath87 if the observed dm is dominated by the snrs associated with the frbs .
however , the statistical results of the observed frbs obviously deviate from this relation @xcite .
next , we consider the dm contribution from a pwn . some authors suggested an association of frbs with young pulsars @xcite , while some others suggested an association of frbs with magnetar giant flares @xcite . while these models are greatly constrained by available observations @xcite
, we nonetheless consider the dm contribution from a pulsar / magnetar wind .
the classical goldreich - julian number density is given by @xcite @xmath88 where @xmath89 is the polar - cap magnetic field strength , and @xmath90 is the rotation period .
a relativistic electron - positron pair plasma is expected to stream out from the magnetosphere .
the dm of the pulsar / magnetar wind may be estimated using the pair flux near the light cylinder ( e.g. * ? ? ?
* ) @xmath91 where @xmath92 is the radius of the light cylinder , @xmath93 is multiplicity parameter , @xmath94 is relativistic wind lorentz factor at the light cylinder , and @xmath95 is the pulsar / magnetar spin - down luminosity . the pulsar / magnetar wind can provide a significant contribution to dm if @xmath96 is large enough .
recently , @xcite proposed a unified interpretation of frbs in the so - called `` cosmic comb '' model , which invokes the interaction between an astrophysical plasma stream and a foreground regular pulsar . since cosmic combs more easily happen in slow ( @xmath97 ) and low - field ( @xmath98 ) pulsars , the dm contribution from the near - source plasma is @xmath99 .
therefore , in the cosmic comb model , the large host galaxy dm might result from the host galaxy ism or the near - source plasma of the stream source in front of the pulsar towards earth . at last
, we consider the dm contribution from a hii region in the host galaxy , assuming that an frb is embedded in a strmgren sphere .
the dm contributed by a strmgren sphere may be estimated as @xmath100 where @xmath101 is the gas number density in the hii region , @xmath102 is the rate of ionizing photons from a star , @xmath103 is the recombination rate , and @xmath104 is the strmgren radius .
we assume that the there is an o5 star in hii region , so that @xmath105 for @xmath106 , and the strmgren radius is @xmath107 .
we note that the strmgren radius is much larger than the projected size of @xmath108 of frb 121102 radio persistent emission source @xcite . in summary
, we show that the current frb observations imply large host galaxy dm values , e.g. , @xmath109 .
such a large dm may be contributed by the host ism or a near - source plasma .
such a result poses requirements to frb progenitor models . in the total host galaxy
dm , the contribution from the near - source plasma also plays an essential role to identify the progenitor systems of frbs .
the various models have a wide dm distribution . for models invoking young energetic pulsars and magnetars ( e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) or collapse of new - born supra - massive neutron star ( e.g. * ? ? ?
* ; * ? ? ?
* ) , a near - source snr or pwn may give an important contribution to the observed dm . also irregular star - forming galaxies
( e.g. the host galaxy of frb 121102 ) do not have a disk - like structure , and may provide a relatively large host dm . for the models invoking compact object mergers ( e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) , the contribution from a near - source plasma may not be important .
these systems may also have a large offset from the host galaxy .
however , elliptical or early - type host galaxies that harbor these events may also provide large free electron column needed to account for the large @xmath4 inferred from the data .
we thank zi - gao dai , yan huang , tian - qi huang and su yao for helpful discussions .
this work is partially supported by the initiative postdocs supporting program ( no .
bx201600003 ) , the national basic research program ( 973 program ) of china ( no .
2014cb845800 ) , the national natural science found ( no.11273005 ) and project funded by china postdoctoral science foundation ( no .
2016m600851 ) .
yuan - pei yang is supported by a kiaa - cas fellowship . | arxiv |
Is sodium doublet caused by Zeeman effect inside atom?
My understanding is that electron and nucleus spin are interacting, creating a magnetic field which is causing Zeeman effect and essentially splitting optical lines emmited by sodium and these lines can be further split by introducing external magnetic field again causing Zeeman effect. Anyone willing to confirm/correct? Thanks!
You're mostly correct. The sodium doublet is part of the *fine structure* of the atomic spectrum. This difference is caused by [spin-orbit interaction](https://en.wikipedia.org/wiki/Spin%E2%80%93orbit_interaction), which says that the energy of an electron is affected by the alignment between its spin angular momentum $\vec{S}$ and its orbital angular momentum $\vec{L}$.
Spin-orbit interaction can in some sense be thought of as an "internal Zeeman effect". Classically, any electron moving in an *electric* field will "see" a *magnetic* field in its own rest frame. Since the electron is orbiting the atom, it "sees" a magnetic field due to the nucleus in its own rest frame. It is the interaction between this "rest frame magnetic field" and the electron's magnetic dipole moment (proportional to $\vec{S}$) that causes the energy splitting.
However, you also say that
>
> My understanding is that electron and **nucleus spin** are interacting, creating a magnetic field...
>
>
>
The interactions between the electron's magnetic field (both due to its motion and its spin) and the nucleus's magnetic dipole moment (also proportional to the nuclear spin) give rise to the *hyperfine* structure of the atomic spectrum. As the name implies, these energy splittings are generally much, much smaller than the splittings of the fine structure.
| stackexchange/physics |
(Picsart Editing Tutorial) Well, I hope you enjoy it down here I leave the Images you need! Remember to update your PicsArt since I use the latest version!
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In This photo editing, we have changed the background and added a different background with the help of eraser tool that is present in the tool option of PicsArt. and added some light png smoke etc to give this photo cool look if you want to watch the tutorial click on the watch us on YouTube button.
However, you can Follow these easy step-by-step instructions or watch our video tutorials to learn how to edit photos, use advanced photo editing tools and much more with PicsArt.
Just Watch This Video Carefully And Follow Step By Step.
If you like this article don't forget to share and connect with us on Twitter and Facebook. | slim_pajama |
RLW is the abbreviation for two different rugby league magazines, one in the UK and the other in Australia:
Rugby League Week, an Australian publication
Rugby League World, a British publication
In science and engineering
Regularized long-wave equation, a model for surface gravity waves which are long and propagate unidirectionally | wikipedia |
HMS Herring was a Royal Navy Ballahoo-class schooner of four 12-pounder carronades and a crew of 20. The prime contractor for the vessel was Goodrich & Co., in Bermuda, and she was launched in 1804. She spent most of her career in North American waters though she did spend two years sailing between Britain and Spain before returning to North America where she foundered in 1813.
Service
She was commissioned under Lieutenant Isaac Morrison for the Leeward Islands or Newfoundland, and in fact served on the Newfoundland Station. In 1804 she was temporarily under Lieutenant John G. M'B. McKillop. He wrote the following letter:
His Maj. Schooner Herring, Bermuda October 1804
Sir,
I have the honor to acquaint your excellency that since my letter of the19 ..... the Herring and Pilchard have been launched, the former coppered and the inside work nearly compleat, the latter not yet coppered. The ship with spars for the several vessels arrived the day before yesterday which will enable the above vessels to be completed and ready for sea by the last of this month. The Capelin and Mackeral will not be launched until the middle of next month and I fear will not be ready to proceed to Newfoundland this winter. There being no iron ballast sent out for the schooners is of great inconvenience and the Navy Board have positively forbid any being purchased. The schooners being very buoyant obliges us to fill the hold with stone and carry all the water and provisions between decks so that the men have very little room. They are fine vessels of the kind and have the appearance of fast sailors. I beg leave to observe to your excellency that there being no establishment for the supply of necessaries, we are supplying them on the most reasonable terms possible and mean to forward the vouchers to the victualling board. The Officers and men are all in perfect health. I have the honor to remain &&&
John McKillop Lieut.
To: His Excellency Sir Erasmus Gower.
In 1805 Herring was again under the command of Morrison, on the Newfoundland station. Between 1806 and 1809, she was under the command of Morrison, then McKillop, and then by 1807 Lieutenant Walter J. Sprott. In 1808 she was under the command of Samuel W. Sprott, and in that year and the next she sailed twice for the Bay of Exploits in two unsuccessful attempts to make contact with the Beothuk people.
Herring then came under the command of Lieutenant Strong, who sailed her for Portugal on 5 March 1810. Herring underwent repairs at Portsmouth from 2 November until 16 January 1811. She spent that year and early 1812 sailing between Lisbon or Cadiz and Falmouth.
In 1812 Lieutenant John Murray took command, sailing her for North America on 3 July. On 15 February 1813 the American schooner Rachel arrived at Portsmouth. She was a prize to Herring.
Fate
Herring was lost in July 1813, presumed foundered with all hands while on the Halifax station. As a result of an administrative error Herring remained on the Navy List until 7 December 1817.
Citations
References
Gossett, William Patrick 1986 The lost ships of the Royal Navy, 1793-1900. London:Mansell.
Hepper, David J. 1994 British Warship Losses in the Age of Sail, 1650-1859. Rotherfield: Jean Boudriot.
Marshall, Ingeborg 1998 History and ethnography of the beothuk. Montreal: Mcgill-Queens Univ Press.
Category:1804 ships
Category:Ballahoo-class schooners
Category:Maritime incidents in 1813
Category:War of 1812 ships of the United Kingdom
Category:Ships built in Bermuda | wikipedia |
Effect of temperature change in an equilibrium reaction
Talking about an exothermic reaction in equilibrium it is said that heat is on the product side, so according to Le Chatelier principle, the reaction should move backward to counteract the increase in the number of products.
But it is also stated that in an exothermic reaction when the temperature increases, the value of equilibrium constant decreases, which means the product is less than reactant, then shouldn't the reaction move in the forward direction?
Please help me with wherever I'm going wrong.
As per Le Chatelier's principle, when the temperature is increased, for an exothermic reaction , the reaction shifts in the backward direction. This is clear from the van't Hoff's equation:
$$ \log\left( \frac{K'\_\mathrm{p}}{K\_\mathrm{p}}\right) = \frac{\Delta H^0}{2.303R}\left(\frac{1}{T\_1} - \frac{1}{T\_2}\right)$$
where $T\_1$ corresponds to $K\_p$ and $T\_2$ corresponds to $K'\_p$ . Also $T\_2 > T\_1$.
This is because $K'\_\mathrm{p}$ becomes less than $K\_\mathrm{p}$. Hence the reaction goes in the reverse direction.
| stackexchange/chemistry |
the patient was a previously healthy 8-year - old male with reported history of fever for 2 days prior to hospitalization .
clonic seizures progressed over the course of hours to refractory status epilepticus . on the suspicion that he was having viral encephalitis ,
a lumbar puncture was performed on the day of admission , which showed slightly elevated cerebrospinal fluid protein of 48.3 mg / dl ( normal 15 - 45 mg / dl ) without pleocytosis .
a meningoencephalitis panel was positive only for recent or current infection with influenza a / b by antibody enzyme immunoassay .
other routine laboratory testing on admission was normal other than elevations in aspartate transaminase of 406 iu / l ( normal 10 - 40 iu / l ) and alanine transaminase of 324 iu / l ( normal 7 - 56
the patient was intubated at the time of admission , and pentobarbital and midazolam drips were used to induce electroencephalography suppression , leading to hypotension requiring pressor support . a brain magnetic resonance imaging ( mri ) done at this stage of his illness
was read as normal , other than gadolinium enhancement of the meninges , consistent with meningoencephalitis . despite being on high doses of several antiepileptic drugs ,
his hemodynamic instability progressively worsened to the point of cardiovascular collapse , and he was placed on extracorporeal membrane oxygenation .
he was being treated with broad - spectrum antibiotics for intermittent fevers , a positive sputum culture for pseudomonas , and a posterior scalp ulceration , and there was clinical suspicion for sepsis .
when the patient developed dilated pupils and hypertension , computed tomography ( ct ) and mri scans of the head were performed , and extensive bilateral brain lesions were seen . given the refractory nature of his seizures and the severity of his brain damage , the family and medical care team agreed on a decision to withdraw care .
the ct head with and without contrast ( hospital day 15 ) showed extensive focal and confluent areas of low density in the cerebellum and right cerebral hemisphere , including the right basal ganglia ( figure 1 ) .
magnetic resonance imaging brain without contrast ( hospital day 36 ) showed diffuse areas of edema and microhemorrhages involving bilateral cerebellar hemispheres , bilateral occipital lobes , right cerebral white matter , right basal ganglia , and left sylvian region .
the findings were nonspecific but suggested possible hypoxia with subsequent hemorrhagic transformation or disseminated intravascular coagulation ( dic ) ; the asymmetric distribution , white matter , and cerebellar involvement were not typical for hypoxic ischemic injury , which primarily affects the cerebral cortex and deep gray matter structures . the predominant white matter and
cerebellar distribution also suggested a possible metabolic abnormality related to the underlying infection , encephalitis , or autoimmune - mediated reaction ( figure 2 ) .
magnetic resonance spectroscopy ( hospital day 36 ) showed markedly low n - acetylaspartate diffusely and a large lactate peak in the mid - occipital gray matter , consistent with hypoxic
noncontrast head computed tomography ( ct ) images . a , extensive white matter hypodensity in the right centrum semiovale ( black arrows ) .
b , hypodensity in the right caudate head and anterior lentiform nucleus ( white arrows ) and cerebral white matter ( black arrows ) .
a , t2-weighted axial image showing heterogeneous signal in the right centrum semiovale ( black arrows ) .
b , t2-weighted axial image showing patchy t2 hyperintensity in the right basal ganglia ( white arrows ) and bilateral posterior thalami ( black arrows ) .
c , t2-weighted axial image shows bilateral cerebellar patchy t2 hyperintensity ( black arrows ) .
d , t1-weighted axial image showing faint hyperintensity in the right basal ganglia ( white arrows ) and posterior left thalamus ( black arrow ) consistent with hemorrhage .
e and f , susceptibility weighted images showing scattered hypointensities in the right cerebral hemisphere and bilateral cerebellar hemispheres , right greater than left ( black arrows ) , consistent with petechial hemorrhages . on gross examination ( figure 3 ) , the brain hemispheres were symmetrical without external or parenchymal hemorrhage or petechiae the small hemorrhagic lesions noted earlier in the disease course on neuroimaging were not detected and had likely resolved .
the leptomeninges were thin and free of exudate , and the cerebral vasculature , including the venous sinuses , was unremarkable and without thrombosis .
sectioning revealed a 2.5-cm - diameter area of yellow necrosis that extended through the right cerebral hemisphere in an almost continuous lesion approximately 13 cm in length , extending rostrocaudally toward the occipital region .
it mostly involved the white matter and extended into the right basal ganglia , obliterating the centrum semiovale . similar but smaller lesions
sections of the brain showing ( a ) right frontoparietal white matter necrosis ; ( b ) bilateral cerebellar white matter necrosis ; and ( c ) right basal ganglia and thalamus with areas of necrosis .
microscopic findings of circumscribed , firm , necrotic areas in the right centrum semiovale , basal ganglia , parietal white matter , and cerebellum showed diffuse glassy or
mummified necrosis with prominent central neovascularization and perivascular rosette - like infiltrates of plump macrophages ( figure 4a c ) .
there were prominent perivascular dystrophic calcifications ( figure 4d ) arranged peculiarly in linear rows .
very little chronic inflammatory response was seen , and essentially no acute inflammation was present .
there was no evidence of demyelination or inflammation in perivascular areas or elsewhere in the better preserved white matter .
sections of hippocampi showed decreased numbers of neurons in the cornu amonis 1 ( ca1 ) and proximal ca2 areas with residual neurons displaying changes ranging from ischemia to individual cell necrosis ( figure 5a ) . the purkinje cell layer within the cerebellum was almost completely attenuated ( figure 5b ) .
no microorganisms , including fungal elements , were identified on periodic acid - schiff ( pas ) , grocott 's methenamine silver ( gms ) , or gram stain in the areas of necrosis .
microscopic images showing ( a ) abrupt necrosis ( n , bottom left ) in the white matter ( w , middle ) and uninvolved cortical gray matter ( g , top right ; hematoxylin eosin stain 40 ) ; ( b ) smooth opaque , mummified central necrosis without cavitation and preserved vasculature ( hematoxylin eosin stain 100 ) ; ( c ) necrosis with peripheral macrophage clustering in an angiocentric fashion ( hematoxylin eosin stain 100 ) ; ( d ) perivascular calcification linear rows ( hematoxylin eosin stain 100 ) .
microscopic images showing ( a ) hippocampus massive neuronal loss within the ca1 and proximal ca2 regions ( arrow approximately at the ca2/3 interface with neuronal losses and reactive vascular prominence to the right and viable ca3 neurons to the left of arrow ; hematoxylin eosin stain 20 [ inset 40 ] ) ; ( b ) cerebellum selective , extensive purkinje cell loss ( hematoxylin eosin stain 100 ; m , molecular layer ; p , purkinje cell layer ; g , [ internal ] granule cell layer ) ; ( c ) spinal cord with myelin pallor , vacuolation , and fiber loss in the lateral corticospinal tract ( hematoxylin eosin stain 100 ) ; ( d ) skeletal muscle with extensive atrophy ( hematoxylin eosin stain 100 ) .
the multifocal abnormalities were consistent with a form of acute necrotizing encephalopathy , but the pattern of white matter necrosis in the right cerebral hemisphere and cerebellum was not typical , there being only subtle thalamic changes .
changes in the descending corticospinal tracts , suggesting degenerative axonal pathology ( figure 5c ) , and sections of the psoas muscle showed diffuse patchy atrophy with a few admixed hypertrophic fibers ( figure 5d ) .
type ii atrophy is favored due to the lack of fiber grouping , but an element of denervation effect can not be excluded , as cryopreserved skeletal muscle was not available for histochemical ( enzymatic ) confirmation .
other systemic autopsy findings of significance included a resolving pneumonia with focal pulmonary hemorrhage , bilateral pleural effusions , renal and hepatosplenic enlargements , and thymic atrophy .
the patient was a previously healthy 8-year - old male with reported history of fever for 2 days prior to hospitalization .
clonic seizures progressed over the course of hours to refractory status epilepticus . on the suspicion that he was having viral encephalitis ,
a lumbar puncture was performed on the day of admission , which showed slightly elevated cerebrospinal fluid protein of 48.3 mg / dl ( normal 15 - 45 mg / dl ) without pleocytosis .
a meningoencephalitis panel was positive only for recent or current infection with influenza a / b by antibody enzyme immunoassay .
other routine laboratory testing on admission was normal other than elevations in aspartate transaminase of 406 iu / l ( normal 10 - 40 iu / l ) and alanine transaminase of 324 iu / l ( normal 7 - 56
the patient was intubated at the time of admission , and pentobarbital and midazolam drips were used to induce electroencephalography suppression , leading to hypotension requiring pressor support . a brain magnetic resonance imaging ( mri ) done at this stage of his illness
was read as normal , other than gadolinium enhancement of the meninges , consistent with meningoencephalitis . despite being on high doses of several antiepileptic drugs ,
his hemodynamic instability progressively worsened to the point of cardiovascular collapse , and he was placed on extracorporeal membrane oxygenation .
he was being treated with broad - spectrum antibiotics for intermittent fevers , a positive sputum culture for pseudomonas , and a posterior scalp ulceration , and there was clinical suspicion for sepsis .
when the patient developed dilated pupils and hypertension , computed tomography ( ct ) and mri scans of the head were performed , and extensive bilateral brain lesions were seen . given the refractory nature of his seizures and the severity of his brain damage , the family and medical care team agreed on a decision to withdraw care .
the ct head with and without contrast ( hospital day 15 ) showed extensive focal and confluent areas of low density in the cerebellum and right cerebral hemisphere , including the right basal ganglia ( figure 1 ) .
magnetic resonance imaging brain without contrast ( hospital day 36 ) showed diffuse areas of edema and microhemorrhages involving bilateral cerebellar hemispheres , bilateral occipital lobes , right cerebral white matter , right basal ganglia , and left sylvian region .
the findings were nonspecific but suggested possible hypoxia with subsequent hemorrhagic transformation or disseminated intravascular coagulation ( dic ) ; the asymmetric distribution , white matter , and cerebellar involvement were not typical for hypoxic
the predominant white matter and cerebellar distribution also suggested a possible metabolic abnormality related to the underlying infection , encephalitis , or autoimmune - mediated reaction ( figure 2 ) .
magnetic resonance spectroscopy ( hospital day 36 ) showed markedly low n - acetylaspartate diffusely and a large lactate peak in the mid - occipital gray matter , consistent with hypoxic
noncontrast head computed tomography ( ct ) images . a , extensive white matter hypodensity in the right centrum semiovale ( black arrows ) .
b , hypodensity in the right caudate head and anterior lentiform nucleus ( white arrows ) and cerebral white matter ( black arrows ) .
brain magnetic resonance imaging ( mri ) . a , t2-weighted axial image showing heterogeneous signal in the right centrum semiovale ( black arrows ) .
b , t2-weighted axial image showing patchy t2 hyperintensity in the right basal ganglia ( white arrows ) and bilateral posterior thalami ( black arrows ) .
c , t2-weighted axial image shows bilateral cerebellar patchy t2 hyperintensity ( black arrows ) .
d , t1-weighted axial image showing faint hyperintensity in the right basal ganglia ( white arrows ) and posterior left thalamus ( black arrow ) consistent with hemorrhage .
e and f , susceptibility weighted images showing scattered hypointensities in the right cerebral hemisphere and bilateral cerebellar hemispheres , right greater than left ( black arrows ) , consistent with petechial hemorrhages .
on gross examination ( figure 3 ) , the brain hemispheres were symmetrical without external or parenchymal hemorrhage or petechiae the small hemorrhagic lesions noted earlier in the disease course on neuroimaging were not detected and had likely resolved .
the leptomeninges were thin and free of exudate , and the cerebral vasculature , including the venous sinuses , was unremarkable and without thrombosis .
sectioning revealed a 2.5-cm - diameter area of yellow necrosis that extended through the right cerebral hemisphere in an almost continuous lesion approximately 13 cm in length , extending rostrocaudally toward the occipital region .
it mostly involved the white matter and extended into the right basal ganglia , obliterating the centrum semiovale .
similar but smaller lesions were seen in the right temporal region and right inferior cerebellar white matter .
sections of the brain showing ( a ) right frontoparietal white matter necrosis ; ( b ) bilateral cerebellar white matter necrosis ; and ( c ) right basal ganglia and thalamus with areas of necrosis .
microscopic findings of circumscribed , firm , necrotic areas in the right centrum semiovale , basal ganglia , parietal white matter , and cerebellum showed diffuse
mummified necrosis with prominent central neovascularization and perivascular rosette - like infiltrates of plump macrophages ( figure 4a c ) .
there were prominent perivascular dystrophic calcifications ( figure 4d ) arranged peculiarly in linear rows .
very little chronic inflammatory response was seen , and essentially no acute inflammation was present .
there was no evidence of demyelination or inflammation in perivascular areas or elsewhere in the better preserved white matter .
sections of hippocampi showed decreased numbers of neurons in the cornu amonis 1 ( ca1 ) and proximal ca2 areas with residual neurons displaying changes ranging from ischemia to individual cell necrosis ( figure 5a ) . the purkinje cell layer within the cerebellum was almost completely attenuated ( figure 5b ) .
no microorganisms , including fungal elements , were identified on periodic acid - schiff ( pas ) , grocott 's methenamine silver ( gms ) , or gram stain in the areas of necrosis .
microscopic images showing ( a ) abrupt necrosis ( n , bottom left ) in the white matter ( w , middle ) and uninvolved cortical gray matter ( g , top right ; hematoxylin eosin stain 40 ) ; ( b ) smooth opaque , mummified central necrosis without cavitation and preserved vasculature ( hematoxylin eosin stain 100 ) ; ( c ) necrosis with peripheral macrophage clustering in an angiocentric fashion ( hematoxylin eosin stain 100 ) ; ( d ) perivascular calcification linear rows ( hematoxylin eosin stain 100 ) .
microscopic images showing ( a ) hippocampus massive neuronal loss within the ca1 and proximal ca2 regions ( arrow approximately at the ca2/3 interface with neuronal losses and reactive vascular prominence to the right and viable ca3 neurons to the left of arrow ; hematoxylin eosin stain 20 [ inset 40 ] ) ; ( b ) cerebellum selective , extensive purkinje cell loss ( hematoxylin eosin stain 100 ; m , molecular layer ; p , purkinje cell layer ; g , [ internal ] granule cell layer ) ; ( c ) spinal cord with myelin pallor , vacuolation , and fiber loss in the lateral corticospinal tract ( hematoxylin eosin stain 100 ) ; ( d ) skeletal muscle with extensive atrophy ( hematoxylin eosin stain 100 ) .
the multifocal abnormalities were consistent with a form of acute necrotizing encephalopathy , but the pattern of white matter necrosis in the right cerebral hemisphere and cerebellum was not typical , there being only subtle thalamic changes .
changes in the descending corticospinal tracts , suggesting degenerative axonal pathology ( figure 5c ) , and sections of the psoas muscle showed diffuse patchy atrophy with a few admixed hypertrophic fibers ( figure 5d ) .
type ii atrophy is favored due to the lack of fiber grouping , but an element of denervation effect can not be excluded , as cryopreserved skeletal muscle was not available for histochemical ( enzymatic ) confirmation .
other systemic autopsy findings of significance included a resolving pneumonia with focal pulmonary hemorrhage , bilateral pleural effusions , renal and hepatosplenic enlargements , and thymic atrophy .
the authors have presented a unique case of acute postviral encephalopathy with correlative radiologic and autopsy findings , with a view to alerting the medical community of this fatal and somewhat infrequent condition .
the conclusion is that an atypical form of acute necrotizing encephalopathy would best explain this presentation , although the authors recognize that more such cases need to be studied before precise terminology is agreed upon .
classic acute necrotizing encephalopathy was first described in 1995 in cases from japan , where its incidence and mortality appear to remain much higher than elsewhere , including the united states .
patients with acute necrotizing encephalopathy present with acute and rapid neurologic deterioration and often intractable seizures preceded by febrile illness .
the mortality of acute necrotizing encephalopathy has been as high as 30% in some case series , with severe neurodevelopmental morbidity in most survivors , although some less severe cases have also been described .
recently , acute necrotizing encephalopathy has been most commonly associated with the influenza a ( h1n1 and h3n2 ) outbreaks , but it has also been linked to a variety of viral infections , such as herpes virus , varicella zoster , enterovirus , rotavirus , and parainfluenza .
brain imaging and pathological findings are most commonly characterized by bilateral thalamic necrosis and petechial hemorrhage , with variable areas of cerebral and cerebellar white matter edema and congestion , but the literature lacks detailed autopsy studies that address radiologic and neuropathologic correlates of acute postviral encephalopathies in diverse clinical and geographic settings , and this is one of the reasons for documenting this child s brain and systemic findings .
the authors report a case of fatal acute postviral encephalopathy in an 8-year - old male with influenza infection .
his imaging and pathological findings are somewhat atypical , with asymmetric prominent necrotic lesions in the cerebral white matter and basal ganglia as well as bilateral cerebellar white matter and only mild involvement of the thalami .
although some of the smaller cortical and subcortical lesions can represent the findings of superimposed hypoxic injury ( which was also correlated by magnetic resonance spectroscopy ) , the large , noncavitating , white matter lesions were believed to be areas of necrosis , consistent with a form of acute necrotizing encephalopathy .
there was no evidence of demyelination or inflammation in perivascular areas , or elsewhere in the better preserved parts of white matter , to suggest evolving acute disseminated encephalomyelitis - like changes nor was there evidence of the cavitary lesions typically seen with ischemic infarcts .
mild ischemic overlay may have been present , given the clinical course , and is difficult to exclude , but it is noteworthy that the systemic autopsy findings did not reveal significant ischemic injury in other organ systems ( as has been reported in some instances of acute necrotizing encephalopathy ) . the patient s prolonged refractory status epilepticus , respiratory failure , and cardiovascular collapse likely contributed to vasculopathy and hypoxemia .
this can help to explain the atypical pathological findings in this case , which share some features of hypoxic ischemic encephalopathy .
the changes seen in the spinal cord and skeletal muscle may or may not be related to the encephalopathy , and this will ultimately be established through more detailed reporting from other cases . from a clinical viewpoint ,
our patient is slightly older than average but within the range of reported ages for acute necrotizing encephalopathy .
our patient s initial blood tests did reveal transaminitis prior to his hemodynamic collapse , and this hepatic dysfunction is a finding that has been reported to be variably present in acute necrotizing encephalopathy . also typical for the diagnosis of acute necrotizing encephalopathy
brain barrier secondary to accumulation of cytokines has been proposed as the underlying pathogenesis of acute necrotizing encephalopathy and is likely related to the accompanying vasculitis and hypoxic injury . in addition , the effects of cytokines and macrophage activation causing widespread endothelial damage can also contribute to the systemic response often associated with acute necrotizing encephalopathy , including cardiovascular collapse and respiratory and renal failure .
recent studies have established a genetic link between acute necrotizing encephalopathy and an autosomal - dominant mutation of the gene for the protein ran - binding protein 2 .
a few familial cases have been described , in which multiple siblings with this mutation have developed acute necrotizing encephalopathy following a nonspecific viral illness .
patients with the genetic susceptibility have also been shown to have atypical , recurrent acute necrotizing encephalopathy .
familial cases appear to have a somewhat milder disease course , but this may be due in part to early diagnosis and aggressive treatment .
so far , early therapeutic intervention with high - dose intravenous corticosteroids and intravenous immunoglobulin has been associated with better outcomes compared to supportive therapy alone in patients with acute necrotizing encephalopathy .
more recently , brain cooling therapy has also been used with the suggestion of positive results , as it is now considered one of the treatment methods in acute encephalopathy . however , in most nonfamilial cases , the diagnosis of acute necrotizing encephalopathy is made only late in the disease course , after extensive brain injury is apparent on imaging studies and when a good response to the treatment is less likely .
the typical imaging findings of acute necrotizing encephalopathy , bilateral thalamic lesions with microhemorrhages and edema , are the most likely sign to prompt consideration of the diagnosis .
our case had an atypical distribution of lesions , with primarily cerebral and cerebellar white matter necrosis and only mild thalamic involvement , confirmed by autopsy findings .
the totality of the imaging findings , medical history , clinical presentation , and pathology encouraged the authors to favor an atypical form of acute necrotizing encephalopathy as the possible diagnosis , although the authors recognize that other differentials may also be in consideration . in conclusion
, typical acute necrotizing encephalopathy still remains a rare but extremely serious complication of acute viral illness in children that is likely more common in certain geographic areas and in genetically susceptible individuals .
however , atypical forms , such as the case presented earlier , do exist , and their presentation and outcome can vary , depending on the clinical circumstances .
whether such acute postviral encephalopathies are best categorized as acute necrotizing encephalopathy or a form of hypoxic ischemic encephalopathy , the authors would like to emphasize that early recognition of the clinical syndrome , its neurologic effects , and potentially fatal complications are critical to save lives .
the authors hope that awareness of such atypical presentations will encourage clinicians , radiologists , and pathologists to document more cases of postviral encephalopathies . as more cases are investigated and reported , the authors can hope to see improvements in earlier diagnosis , further elucidation of the pathogenesis , and better treatment outcomes . | pubmed |
Is the reaction of calcium carbide with water a Brønsted-Lowry acid-base reaction or Lewis acid-base reaction?
Consider the following reaction:
$$\ce{CaC2 + 2H2O -> Ca(OH)2 + 2C\_{2}H\_{2}}$$
If it can be considered as an acid-base reaction, is it a Brønsted-Lowry (B.L.) reaction or a Lewis reaction?
If it is B.L., of course it is also Lewis; but I cannot understand if it can be B.L. in this case, since 2 protons are actually passed to the double carbon atom, but there is also the $\ce{Ca}$.
We may regard the calcium hydroxide and calcium carbide as essentially ionic except for the covalent bonding within the anions. So there is no Lewis reaction involving the calcium.
That leaves the proton transfer, which can be described fully by the B-L theory. You actually have two reactions, successively forming $\ce{C2H-}$ and then $\ce{C2H2}$.
| stackexchange/chemistry |
MINIMUM AND AVERAGE SALARY IN IRELAND
Ireland is a very beautiful country, located in the north-western part of Europe, next to Great Britain. It occupies the most part of the island of the same name, borders with Northern Ireland and is washed by the Atlantic Ocean from the west, north, and south. It is a very developed and rich state with a high standard of living and strong economy.
The population of Ireland is only 5 million people. The unemployment does not exceed 4-6%, and among young people it reaches 13%. There are 67.7 thousand men and 67.4 thousand women unemployed in the country. The most popular professions are programmers, doctors, financiers and business analysts. Next, find out what the salary in Ireland in 2022.
Minimum salary in Ireland
The minimum income that Irish workers can count on is regulated by Ireland's national Minimum Wage Act of 2000. In certain sectors, rates are regulated by special agreements.
According to the Irish Department of Employment and Social Security, the official minimum wage in Ireland from 1 January 2022 is 10.50 euros per hour. However, for young professionals hourly rates are calculated as a percentage of the base amount:
up to 18 years – 7.35 euros (70%)
18 years – 8.40 euros (80%)
If an employer in Ireland provides food and accommodation to an employee, the following amounts may be included in the calculation of the minimum wage: 0.94 euros per hour (meals) and 24.81 euros per week/3.55 euros per day (accommodation).
Average salary in Ireland
According to the official data of the Irish Central Statistical Office, the average salary in Ireland in 2022 is 864.51 euros per week, which is 2% more compared to the same period last year (847.21 euros). The hourly rate is 26.22 euros. Before paying taxes the Irish earn 3,745 euros per month, and after all deductions remains 2,885 euros.
The highest average weekly earnings in Ireland are in the information and communications sector (1,371.23 euros), as well as finance, insurance and real estate transactions (1,216.69 euros). The lowest income is generated by accommodation and food services (397.42 euros) and by the arts, entertainment and recreation (588.14 euros).
Average wages in Ireland in the public sector showed an increase of 1.1% to €1,032.65 per week. In the private sector the growth was 2.7% - up to 813.84 euros. Overall, Irish workers' earnings increased 17% over 5 years, from €717.52 in Q4 2016 to €864.51 in 2022.
AVERAGE SALARY IN IRELAND BY SECTOR OF ECONOMY
Sector of economy Euro per week
Information and communication 1,371.23
Finance, insurance and real estate 1,216.69
Professional, scientific and technical activities 1,075.93
Public administration and defence 1,017.79
Manufacturing 989.93
Education 932.69
Construction 901.97
Transportation and storage 830.15
Human health and social work 805.27
Administrative and support services 701.90
Wholesale and retail trade 653.98
Art, entertainment, recreation and other services 588.14
Accommodation and food service 397.42
Favorable economic situation in Ireland, including high salaries, is largely due to the influx of skilled labor migrants. For example, according to local authorities, only in the field of information technology in recent years, about half of new jobs were occupied by foreign specialists. Moreover, work in Ireland attracts not only applicants from Central and Eastern Europe, but also from many EU countries, including Italy, Spain and Croatia.
wagecentre.com | slim_pajama |
Why the explosives get formed? [closed]
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In many reactions mechanisms, we study things like *'it forms explosive mixture and should be discarded off immediately'*.
Now my question is 'If those compounds are that much unstable that it will explode, why they form at the first place?' For example, if an explosive is getting formed, atoms might have assembled together and its energy will be increasing. But if that much energy is stored that it will explode, why it gets stored then?
Think of chemical changes as a **heavy** ball rolling down a hill. In some cases, there's a divot near the top of the hill, and the ball gets trapped (a metastable state). However, just beyond that divot is a **steep** drop-off.
As long as the ball stays in the depression (i.e., there's insufficient energy to activate it), all well and good. For example, the substance [2-methyl-1,3,5-trinitrobenzene](https://en.wikipedia.org/wiki/TNT) is easily produced by the (step-wise) nitration of toluene. This product is *quite* stable under most conditions; in fact, it took 28 years from Wilbrand's synthesis in 1868 until Häußermann found it explosive!
Once the activation energy is reached, and the ball rolls downhill, it shakes the ground (i.e., causing vibration, and releasing heat), freeing enough energy to activate others that are trapped -- a *[chain reaction](https://en.wikipedia.org/wiki/Chain_reaction)*.
The only fly in the ointment is quantum mechanics. Depending how deep the activation well, occasionally, the ball can tunnel out of the divot. *Bang!* with no obvious activation. For example, [nitrogen triiodide](https://en.wikipedia.org/wiki/Nitrogen_triiodide) has a remarkably low activation energy, causing [rapid unscheduled disassembly](https://knowyourmeme.com/memes/rapid-unscheduled-disassembly) of the sample and related equipment while drying.
| stackexchange/chemistry |
the diagnosis of mci due to ad ( the symptomatic predementia phase of ad ) has been recently proposed by the national institute on aging and the alzheimer 's association .
diagnostic criteria include concern regarding a change in cognition , impairment in one or more cognitive domains , preservation of independence in functional abilities , and not demented . within the generally accepted framework
clinical studies of prodromal stages to ad tend to focus on persons with amnestic mci ( amci ) . both the alzheimer 's disease neuroimaging initiative ( adni ) and
the mayo clinic cohorts typify this population . in the mayo clinical study of aging ,
persons in the age range of 7089 years are enrolled , with 2/3 of the mci group being amci .
adni enrolls participants between ages 55 and 90 , and mean age for the mci group is 74.7 years .
researchers from the mayo clinic proposed quantitative criteria for identifying mci as a prodromal stage to alzheimer 's disease in 1999 .
they stressed the importance of memory impairment and proposed quantitative criteria specifying the level of memory deficit relative to global cognitive functioning . in adni
, mci is defined as a clinical dementia rating of 0.5 , and performance on the free recall measure of a neuropsychological memory test ( logical memory ii ) is below a given threshold .
since the vast majority of the subjects characterized as amci will develop ad , amci may be defined as a prodromal condition of ad .
the pathophysiological basis and prognosis of nonamnestic mci remains unclear , and the group is probably heterogenous [ 6 , 7 ] , including patients with frontotemporal dementia , parkinson 's disease , dementia with lewy bodies , vascular dementia , and neuropsychiatric conditions ( depression ) .
change in the frontostriatal network supporting executive functions may occur as a part of healthy aging [ 13 , 14 ] .
thus , an mci subgroup with isolated executive difficulties may be an extreme group of normal aging .
the objective of this paper is to review executive / attentional impairment as an important aspect of mci or pre - mci in terms of symptom manifestation and importance for disease progression .
we will focus on recent research on mri and genetic markers that may serve to further understanding of the pathophysiological processes underlying executive mci ( emci ) and its relation to ad .
attention and executive impairment are frequent and disabling symptoms in mci when measured with neuropsychological tests ranging from simple processing speed tasks to tasks of complex problem solving .
the distinction between clinical tests of attention and test of executive function is a fuzzy one and they are here treated as on the same continuum .
there is no consensus on how executive function should be tested in clinical studies , and studies that take into consideration developments in cognitive psychology find high frequency of executive impairment in both amnestic and nonamnestic mci , with some subfunctions more affected than others .
alzheimer 's disease ( ad ) is the most common cause of dementia and accounts for approximately 6070% of all dementia cases , and deficits of episodic memory are a cognitive hallmark of the disease .
executive dysfunction is evident in the prodromal stage of ad [ 2022 ] and appears predominantly in tasks requiring cognitive flexibility , inhibition , and self - monitoring .
there is evidence that the commonly reported impaired ability to perform two tasks simultaneously in ad reflects a specific deficit in dividing attention , rather than the result of a more general processing speed deficit . according to the model of cognitive decline leading to ad presented by perry and colleagues ,
executive problems appear after memory problems in time , but before typical parietal lobe symptoms ( aphasia , visuospatial deficits ) .
when executive dysfunction is present , it has a clear negative influence on ability to manage activities of daily living and may thus add to the risk of conversion from mci to ad .
predictive accuracy for conversion from mci to ad for one set of cognitive variables ( composed of episodic memory and processing speed measures ) has been found to be as high as 0.86 ( sensitivity , 0.76 ; specificity , 0.90 ) .
. found that a test of executive function and assessment of baseline functional capacity predicted conversion from mci to ad after 2 years better than biomarkers ( mr and csf ) .
both amci and attention / executive mci subtypes have been regarded as important predementia subtypes , at risk for ad .
while amci is usually defined as a prodromal , at - risk condition of ad , isolated executive dysfunction can be a prodromal stage for several neurodegenerative diseases . in cases of predementia ad
, it is not clear if amci and emci may be two different categories / subtypes of ad or represent different phases of ad development .
if attention / executive mci is not a distinct ad subtype , but an earlier stage of ad than amci , then amci should be expected to have executive / attentional deficits in addition to memory impairment .
it has been reported that attention and executive functions may be impaired in the incipient stages of ad and may contribute to the observed memory deficit .
it has been argued that even patients defined as pure amci on screening tests may have executive impairment , when a comprehensive neuropsychological examination of executive cognition is performed .
the existence of nonamnestic attention / executive mci has been recorded in several mci studies [ 29 , 3237 ] , where a comprehensive neuropsychological test battery has been utilized for classification purposes .
the prevalence of attention / executive mci will vary widely in different samples based on recruitment criteria and assessment methods but has been reported as from 3 to 15% . in the sample studied by us attention / executive mci without amnestic deficit constitutes about 30% of the total mci group , which on the whole is 1015 years younger than the adni study group . in a study of johnson and colleagues ,
of the 12 executive mci patients who progressed clinically after two years , 2 converted to probable dementia with lewy bodies , 10 retained the clinical diagnosis of mci , and none reverted to normal .
patients with single domain executive mci who progressed quickly over two years had more temporal lobe atrophy on mri and slightly lower scores for visual memory recall when compared to the stable executive mci patients , possibly suggesting that converters may be at their later stages of clinical progression .
the executive mci patients who progressed reported fewer dysexecutive symptoms than nonprogressors , while there were no differences in informant - rated dysexecutive symptoms and baseline performance on all four executive tests .
nine subjects with pure attention / executive mci were identified in the longitudinal study of whitwell and colleagues . in this study , almost 70% of mci patients within an attention / executive subgroup progressed to dementia in the period of four years , suggesting that the group is at high risk of developing dementia .
three patients converted to dementia with lewy bodies and three patients converted to ad dementia .
the prognosis for other patients with isolated attention / executive dysfunction in the study of whitwell and colleagues is not clear , but they may also convert to other dementias or remain stable over many years . by using similar criteria for classification of subjects as those used in the study of whitwell and colleagues ,
the attention and executive functions depend on distributed networks , encompassing both frontal and parietal associative cortices , as well as subcortical structures and white matter ( wm ) pathways .
the executive functions control and monitor task performance and depend critically on the frontal lobes .
three fronto - subcortical circuits ( originating in the prefrontal cortex ) have been identified as responsible for executive control functions , that is , the dorsolateral prefrontal cortex ( working memory ) , the lateral orbital cortex ( inhibition ) , and the anterior cingulate cortex ( response conflict ) [ 41 , 42 ] .
findings from functional imaging indicate that during prodromal ad , the brain network involving the dorsolateral prefrontal cortex and the anterior cingulate , is affected .
while amci is characterized by medial temporal lobe affection , atrophy in the basal forebrain has been found to be characteristic for the mci groups with isolated attention / executive deficits [ 29 , 33 ] .
some studies have reported an association between prefrontal cortical changes and attention / executive impairment in mci [ 29 , 34 , 46 ] .
significant cortical atrophy in frontal regions has been found in predementia ad . it has been argued that prefrontal damage , in combination with cingulate damage , has predictive value for the conversion from mci to ad .
another recent study indicates that white matter ( wm ) pathology in ad is distributed in all lobes of the brain but it is most prominent in the frontal wm .
in addition to frontal wm changes , mci patients may have wm changes in both anterior and posterior cingulate regions .
the anterior cingulate region is regarded as belonging to a network responsible for executive control function while the posterior cingulate belongs to a memory network .
thus , it has been hypothesized that the caudal portion of the anterior cingulate plays a major role in executive function abilities , primarily through its reciprocal connections with the prefrontal cortex [ 53 , 54 ] . in our recent study on attention / executive mci ,
we have demonstrated consistent relationships between neuropsychological function and the microstructural properties of the wm brain pathways measured by diffusion tensor imaging ( dti ) , as well as cortical - morphometric parameters .
executive impairment in mci patients with unaffected memory performance has been associated with reduced wm tract integrity ( increased radial diffusion ( dr ) and mean diffusivity ( md ) ) in frontal and cingulate regions and cortical thinning in caudal middle frontal region .
we have found that wm dr / md increases in frontal , cingulate , and entorhinal regions in patients with attention / executive mci , but cortical thickness was not different from controls in any of the studied regions .
the findings may thus indicate that the relative importance of grey matter versus wm changes may differ at different stages of predementia cognitive impairment [ 55 , 56 ] .
frontal and temporal wm diffusivity changes have been previously described in amci patients . by using dti to characterize executive networks in mci , we found wm dr / md changes in both the anterior and posterior cingulate regions in emci suggesting that both regions may contribute to attention / executive impairment in mci .
the cingulate cortex projects into the striatum , and both the anterior and posterior cingulate cortices receive mediodorsal thalamic afferents , which are part of fronto - subcortical circuits , involved in executive function . some attention / executive subfunctions correlated significantly with imaging findings in frontal and cingulate regions in the emci group , but no significant correlations were found in the controls . in attention
/ executive mci , response inhibition was associated with wm dr / md underlying the superior frontal cortex , and response inhibition / switching was associated with wm dr / md underlying the superior frontal , rostral middle frontal , lateral / medial orbitofrontal , and retrosplenial cortices .
test scores for attention and divided attention were associated with the cortical thinning of the caudal middle frontal region .
the study results thus support the results from previous mci studies , where associations between prefrontal changes and attention / executive impairment have been reported [ 29 , 34 , 46 ] . in addition , the results confirm that cingulate changes are associated with executive impairment in mci .
in one recent study , mci patients with isolated executive dysfunction had cerebral hypoperfusion in bilateral middle frontal cortex , bilateral posterior cingulated , and the left precuneus relative to controls .
relative to amci patients , emci patients had hypoperfusion in the left middle frontal cortex , left posterior cingulate , and the left precuneus , supporting the existence of pathophysiologically distinct mci subgroups . in the study of pa and colleagues , executive nonamnestic mci subgroup had significantly less grey matter in the left dorsolateral prefrontal cortex compared with control subjects .
the emci subgroup had less volume in the caudate nucleus compared with amci group , but the differences for prefrontal cortex in emci versus amci were not significant , which could be due to some reduction of prefrontal cortex volume in amci as well .
in contrast , the amci patients had less volume in the right inferior parietal cortex , typical for ad , than emci
. these neuroimaging findings also suggest that some of the emci patients may represent a distinct subgroup of mci .
we have found increased entorhinal wm dr and md in both patients with memory impairment and those with attention / executive dysfunction without objective memory impairment [ 37 , 58 ] , suggesting a common affection of regions known to show changes in early ad .
attention / executive mci may be an earlier stage of ad than amci and the patients with nonamnestic attention / executive impairment may develop memory problems later .
it is also possible that patients with attention / executive mci may progress to non - ad dementias or ad with disproportionate neuropathology in the frontal cortex .
to study very early development of ad , neurobiological markers of high risk in asymptomatic individuals may be used . sperling et al . use the term ad - p to denote pathophysiological factors that are significant for the development of clinical ad ( ad - c ) , but each factor in isolation does not cause ad - c .
amyloid accumulation may be measured with positron emission tomography ( pet ) or with cerebrospinal fluid ( csf ) analyses , but both are invasive and costly procedures that are not suitable for screening .
genetic risk can be assessed relatively simply , and followup studies of healthy at risk populations are not prohibitively expensive although they have ethical problems .
apolipoprotein e ( apoe ) and e4 allele carrier status confer a significant increase in risk of developing ad .
recent studies of relative risk based on large samples argue that the impact of apoe e4 on ad risk is similar to that of major genes in mendelian diseases and comparable to genetic risk of breast cancer .
amyloid load in cognitively normal persons above age 60 correlates positively with apoe e4 . in mci patients
pib - positive pet scans are more frequent in apoe e4 carriers . in patients with ad , progression of cerebral amyloid load is associated with e4 gene dose .
there is thus evidence that a major genetic risk factor for ad is associated with preclinical accumulation of beta amyloid , the most significant pathophysiological causal factor for developing ad .
greenwood et al . have argued that in view of the complexity of apoe mechanisms affecting cognition , it would be misleading to view all cognitive effects of e4 as evidence of incipient ad , and they argue that in normal aging there is an accumulating effect of inefficient neural repair mechanisms associated with the e4 allele .
these changes make the brain more vulnerable to pathological processes , including accumulation of amyloid beta 42 in ad , but do not cause this process to occur in all e4 carriers .
severe cholinergic changes are found in advanced ad , with loss of cholinergic neurons and receptors [ 66 , 67 ] .
the authors propose that the loss of this apparent compensatory response may mark the conversion of mci to diagnosable ad .
recent evidence indicates that complex interactions between apoe e4 and cholinergic genes ( buche ) affect the conversion rate of mci to ad and that the level of beta amyloid accumulation in the brain is related to both apoe and cholinergic activity [ 70 , 71 ] .
thus we see evidence of a negative interaction between apoe , beta amyloid accumulation , and cholinergic dysfunction .
there have been numerous studies of cognitive symptoms associated with apoe e4 carrier status in nondemented persons .
used a meta analysis of more than 2000 participants and found significant positive effect size for memory and global intellectual function .
the effect sizes are moderate , and the studies are influenced by choice of methods , especially in nonmemory cognitive domains .
parasuraman and collaborators have taken a cognitive neuroscience approach to study effects of genes involved in risk of ad ( apoe ) or mechanisms involved in cognitive deficit in ad ( cholinergic genes
they concluded that intact focusing and impaired disengagement of visuospatial attention may be linked to dysfunction in early ad of corticocortical networks linking the posterior parietal and frontal lobes .
greenwood et al . found that healthy middle - aged adults without dementia who carry the apoe e4 allele show deficits in spatial attention and working memory that are qualitatively similar to those seen in clinically diagnosed ad patients .
greenwood et al . used an experimental paradigm measuring working memory for dot locations in a spatial array and found that accuracy was reduced in healthy e4 homozygotes , of mean age 5760 .
reinvang et al . found that e4 carriers performed worse on letter - number span , another working memory task , and in addition on the stroop color - word interference task .
wishart et al . studied cortical activation pattern in a working memory task and the e4 group showed greater activity during working memory in the medial frontal and parietal regions bilaterally and in the right dorsolateral prefrontal cortex .
there were no regions in which the e3 group showed greater activation than the e4 group . by measuring event - related potentials ( erps ) while mci patients 5076 years of age worked on an experimental attention task ( auditory three - stimulus oddball ) .
reinvang et al . performed an event related potential ( erp ) study with mci patients and found attenuated n1 and n2 amplitudes in e4 carriers . in a follow up study with only normal controls covering the same age range working on the same auditory oddball task ,
furthermore , n2 latency was longer for e4 carriers , and this latency predicted memory decline 3.5 years later , suggesting that attention - related functions may presage memory decline in those with elevated risk for ad .
the later component p3 has been shown to be associated with apoe in healthy controls .
irimajiri et al . found reduced amplitude among healthy female e4 carriers in auditory task , and espeseth et al
together , these findings indicate a potential clinical significance of individual differences in the attention - related erp components n1 , n2 , and p3 .
these findings of apoe - related changes in attention are associated with apoe - related differences in brain structure .
found that healthy e4 carriers had thicker cortices than noncarriers in regions of the brain known to be involved in attentional function .
however , an age by apoe interaction showed that this effect was specific for the middle - aged participants .
the crosssectional data indicated that there might be an accelerated thinning of the cortex for e4 carriers , suggesting that the thicker cortex among the middle - aged might be associated with a dysfunctional process .
espeseth et al . showed that cortical thickness in regions with significant carrier versus noncarrier diffrerences was negatively correlated with p3a amplitudes , suggesting that the increase in cortical thickness was indeed dysfunctional .
[ 84 , 85 ] who showed that while symptomatic psen1 mutation carriers had widespread cortical thinning compared to healthy controls , asymptomatic mutation carriers had thicker cortices , suggesting that high risk for ad may be associated with a temporary thickening of the cortex .
cognitive functions are sensitive to interaction of apoe with other factors , including interaction with other genes .
have argued that interaction ( epistasis ) of apoe and chrna4 , a nicotinic receptor gene , influences function in the domains of attention and executive function .
chrna4 has been shown to be related to attentional function in several studies [ 8693 ] .
the search for cognitive markers of very early ad , possibly predating amnestic mci , should therefore take account of the cognitive neuroscience literature on the role of cholinergic systems in attention and executive function .
furthermore , tasks from cognitive neuroscience research that have proven to be related to specific cortical - subcortical activation patterns or neurotransmitter systems may in general be more sensitive to subtle cognitive changes than tests derived from clinical studies of advanced pathology .
problems of attention and executive function are common in mci , and in patients with amci they are the most important additional symptom domain in multidomain amci .
it is generally believed that in this group , executive deficit appears after memory impairment in the sequence of cognitive decline leading to full blown dementia .
executive mci may occur without memory impairment , and there is evidence that although etiology is heterogenous , a significant proportion of these patients develop ad . how large this group is in mci samples varies and is dependent on several factors .
the strong focus on memory problems as key symptom in early ad , and the wide normal variation in attention and executive function in aging , may indicate a high threshold for these patients to seek medical service .
our own data indicate that in a relatively young mci population investigated with comprehensive neuropsychological testing , emci is a common variant .
attentional and executive dysfunctions may remain undetected even though a thorough neuropsychological examination is performed .
difficulties in dividing attention and manipulating remembered information may be reflected in everyday tasks , such as packing a bag , keeping track of conversations , or walking whilst talking .
patients with executive mci may show increased behavioral symptoms on questionnaires that specifically measure executive behaviors compared with amci and control subjects .
knowing that decreased awareness of cognitive symptoms has been reported in some patients with mci and executive mci , it may be helpful to ask other informants to rate executive symptoms of the patient .
current conceptions of early mr changes emphasize hippocampal and cortical atrophy as the significant pathological event , closely linked with emergence of memory impairment [ 59 , 96 ] .
mr analysis yields sensitive measures of a range of pathognomonic events , and recent publications from our group and others indicate that reduced quality of the connectivity of brain networks may compromise cognitive function .
this is true , both for the memory network of the brain , including posterior cingulate , and additionally for frontal networks .
our studies and those of others indicate that in identifying the brain changes underlying emci one should emphasize fiber integrity as measures with dti as well as frontal lobe cortical thinning . in their report on the status of preclinical markers , ad sperling and collaborators use the concept of alzheimer 's disease - pathophysiological process ( ad - p ) to denote different processes that may contribute to development of clinical alzheimer 's disease ( ad - c ) .
furthermore they point to studies combining biomarkers ( of ad - p ) with measures sensitive to very subtle cognitive decline as clearly needed .
large - scale longitudinal studies of biomarker - positive populations raise enormous problems in terms of ethics , costs , and logistics .
we suggest that healthy apoe e4 carriers are a realistic and highly relevant study group .
subclinical genetic effects on mr - morphometry , dti , and default mode have been shown .
experimental cognitive studies have identified specific attention and executive subfunctions as sensitive to apoe allele variation .
the paradigms need to be further developed and standardized for use in clinical / epidemiological studies .
this development could be modeled on the effort to standardize cognitive neuroscience paradigms for application in schizophrenia research .
a great advantage is that they are suited for computerized administration and scoring , so that one may foresee study participants in a longitudinal study logging on to the internet and complete a set of standard tasks at regular intervals . | pubmed |
Sir John Dalrymple of Cousland, 4th Baronet FRSE FSAScot 1726 26 February 1810 was a Scottish advocate, judge, chemist and author. He is best known for his Memoirs of Great Britain and Ireland from the dissolution of the last parliament of Charles II until the sea battle of La Hogue, first published in 1771. A new edition of 1790 carried on to the capture of the French and Spanish navies at Vigo. The Dalrymples formed a dynasty among the legal profession in Scotland. Although a central figure in the Scottish Enlightenment and a friend of persons like David Hume and Adam Smith, Dalrymple's writings were rather unappreciated and he has been described as an irritating member of the Edinburgh literati.
Life
Sir John was the son of Sir William Dalrymple of Cranstoun, 3rd Baronet 17041771 and a cousin of William Dalrymple-Crichton, 4th Earl of Stair. His mother was Agnes Crawford died 1755. He was educated at Edinburgh and Cambridge universities, Dalrymple was admitted to the Faculty of Advocates in 1748. He served as Solicitor to the Board of Excise, and as a Baron of the Exchequer 17761807.
On Thomas Hamilton's death in 1779, Sir John inherited Oxenfoord, and began laying out the gardens. He published his Essays on Different Natural Situations of Gardens in 1774, which became an influential book at the time.
In 1783 Dalrymple was a co-founder of the Royal Society of Edinburgh. In later life his Edinburgh house was at 15 Buccleuch Place, just south of George Square.
Sir John Dalrymple died on 26 February 1810.
Family
In 1760 Dalrymple married his cousin, Elizabeth Hamilton MacGill, daughter and heiress of Thomas Hamilton of Fala, who himself had inherited Oxenfoord Castle, property of the Viscounts of Oxfuird. This led him to adopt her name upon her inheritance. They had thirteen children only five of whom still lived at the time of his death.
Memoirs of Great Britain and Ireland
David Hume, in the course of writing his History of England, requested that Dalrymple search the French state archives. Dalrymple discovered that the Secret Treaty of Dover did indeed contain a provision that Charles II convert to Roman Catholicism, and that there was a secret agreement between Charles and Louis XIV made in March 1681. He also uncovered King William's Chest at Kensington Palace, which contained the original Invitation to William from the Immortal Seven. When Dalrymple, a devoted Whig, saw that he had discovered the original, he was filled with emotion: Immortal Seven! whose memories Britain can never sufficiently revere. He published this in the first volume of his Memoirs in 1771. However, when he returned to the French archives for the second volume published in 1773, he found in the French Ambassador's despatches evidence that the legendary Whig martyr Algernon Sidney had accepted money from Louis XIV in 1678 and that William Russell, Lord Russell had negotiated with him. Dalrymple wrote: When I found Lord Russell intriguing with the Court of Versailles, and Algernon Sidney taking money from it, I felt very near the same shock as if I had seen a son turn his back in the day of battle.
When the first volume of Dalrymple's Memoirs appeared in 1771, Hume criticised it: There is not a new circumstance of the least importance from the beginning to the end of the work. He said of the controversy surrounding the revelations on Russell and Sidney:
It is amusing to observe the general, and I may say national rage, excited by the late discovery of this secret negotiation [with the French Court]; chiefly on account of Algernon Sidney, whom the blind prejudices of party had exalted into a hero. His ingratitude and breach of faith in applying for the King's pardon, and immediately on his return entering into cabals for rebellion, form a conduct much more criminal than the taking of French gold. Yet the former circumstance was always known, and always disregarded. But everything connected with France is supposed in England to be polluted beyond all possibility of expiation. Even Lord Russell, whose conduct in this negotiation was only factious, and that in an ordinary degree, is imagined to be dishonoured by the same discovery.
In a discussion with James Boswell, Samuel Johnson said of the discoveries on Russell and Sidney:
JOHNSON. Why, Sir, every body who had just notions of government thought them rascals before. It is well that all mankind now see them to be rascals. BOSWELL. But, Sir, may not those discoveries be true without their being rascals? JOHNSON. Consider, Sir; would any of them have been willing to have had it known that they intrigued with France? Depend upon it, Sir, he who does what he is afraid should be known, has something rotten about him. This Dalrymple seems to be an honest fellow; for he tells equally what makes against both sides. But nothing can be poorer than his mode of writing: it is the mere bouncing of a school-boy. Great He! but greater She! and such stuff.
Maurice Ashley wrote that the publication of the Memoirs was a striking change in the historiography of the revolution as he had access to important papers. J. P. Kenyon has said that the careful and accurate transcripts [Dalrymple] published... [of] key documents have been a boon to other historians right down to the present day.
Other publications
Essay Towards a General History of Feudal Property in Great Britain 1757
Consideration Upon the Policy of Entails in Great Britain 1764
Notes
References
Nicholas Phillipson, 'Dalrymple, Sir John, of Cousland , fourth baronet 17261810', Oxford Dictionary of National Biography, Oxford University Press, Sept 2004; online edn, Jan 2008, accessed 7 June 2009.
Category:1726 births
Category:1810 deaths
Category:Scottish historians
Category:Scottish knights
Category:Members of the Faculty of Advocates
Category:Alumni of the University of Edinburgh
Category:Alumni of Trinity Hall, Cambridge
Category:Scottish antiquarians
Category:Scottish chemists
Category:Scottish essayists
Category:Founder Fellows of the Royal Society of Edinburgh
Category:Barons of the Court of Exchequer Scotland
Category:Fellows of the Society of Antiquaries of Scotland | wikipedia |
motion along curved trajectories is always associated with a normal force which according to kinematics is given by , @xmath0 where @xmath1 is the speed and @xmath2 the radius of curvature of the track .
if the only physical force is the constraint ( or reaction ) force from the track , constant normal force simply requires @xmath3 .
in most cases , however , the problem of interest involves a conservative force , usually gravity , and a normal ( constraint ) force . in these cases
the problem is conservative since the normal force does not do work , by definition .
one application is to roller coasters and these have recently been discussed in the pedagogical literature , see pendrill @xcite and mller @xcite . in simple mechanical problems given to students the shape of the track
is often taken to be circular but in practice this leads to unpleasantly large time variation of the normal force . in practice
therefore more complicated shapes are used , in particular the clothoid since the curvature ( @xmath4 ) of this curve varies linearly with arc length @xcite .
students that wish to understand the physics behind amusement park experiences in greater detail must therefore be prepared to study curves more advanced than the circle . here
we will derive the shape of the tracks that produce a constant normal force .
pendrill @xcite formulates the problem but does not solve it .
auelmann @xcite has studied the effect of adding a normal force of constant magnitude to the central gravitational force of the kepler problem .
he showed that this problem is integrable and derived some general results . adding a normal force in space
requires the firing of rockets perpendicular to the velocity . the much more natural problem of a constant gravitational force , a good approximation in amusement parks , with the normal force coming from a smooth track , also turns out to be integrable , as we will show in this article .
gonzlez - villaneuva _ et al . _
@xcite found that the trajectories of the kepler problem are arcs of circles in velocity space .
as it turns out the trajectories of our problem are circles in acceleration space .
integrating once we thus find that the trajectories in velocity space correspond to the conic section solutions of the kepler problem .
the shape of the tracks that lead to a normal force of constant magnitude @xmath5 are then obtained by one further integration .
we write the equation of motion , @xmath6 where @xmath7 , and @xmath8 is the angle between the velocity vector and the @xmath9-axis .
we use polar coordinates in velocity space and put @xmath10 .
clearly the vector @xmath11 is perpendicular to the velocity @xmath12 and thus normal to the trajectory .
we note that ( [ eq.of.mot.vec ] ) means that the tip of @xmath13 is on a circle of radius @xmath5 centered on the tip of the gravitational force vector @xmath14 .
the two cartesian components of this vector equation are , @xmath15 we introduce the following dimensionless variables , @xmath16 and put , @xmath17 using this the equations of motion are , @xmath18 we denote the dimensionless speed by @xmath19 so that , @xmath20 transforming eqs .
( [ eq.of.mot.dimless.xy ] ) to velocity space polar coordinates @xmath21 gives , @xmath22 which means that , @xmath23 add the first of these multiplied with @xmath24 to the second multiplied with @xmath25 to get , @xmath26=0 .\ ] ] using the second of the eqs .
( [ eq.of.mot.dimless.rtheta ] ) then shows that , @xmath27={{\rm d}}(r^2\dot{\theta})=0 .\ ] ] evidently , @xmath28 is a conserved quantity ( constant of the motion ) .
one recognizes this as a quantity that corresponds to conserved angular momentum ( or sectorial velocity ) in velocity space .
obviously there is another conserved quantity for this problem : the energy @xmath29 without loss of generality we can assume initial conditions such that @xmath30 .
we then have , @xmath31 we thus have a two dimensional problem with two conserved quantities and this means that we have an integrable problem .
from eq . ( [ eq.conserv.ang.mom.vel ] ) we find that , @xmath32 @xmath19 and @xmath8 being polar coordinates for the velocity vector .
this is easily recognized as the expression for a conic section ( see _ e.g. _ goldstein @xcite ) where @xmath33 corresponds to the eccentricity , and where the origin corresponds to one of the foci .
we have arrived at the conclusion that the velocity space trajectory , the hodograph , of a constant normal force trajectory is a conic section , _
i.e. _ an ellipse , a parabola , or a hyperbola .
we note that , only in the elliptic case , when the eccentricity @xmath34 will the speed , @xmath35 , be finite for all angles . for @xmath36 , the parabolic case
, the speed goes to infinity for @xmath37 .
when @xmath38 the speed goes to infinity along the asymptotes @xmath39 .
since this two dimensional problem has two constants of the motion it is fully integrable . here
we use this to calculate the trajectories for the various cases that arise .
we chose initial conditions so that , at time @xmath40 , we have , @xmath41 , and @xmath42 .
according to ( [ eq.y.r.rel ] ) we then also have @xmath43 .
the simplest case is the trivial case of @xmath44 , or @xmath45 . from ( [ eq.conserv.ang.mom.vel ] )
we then have that @xmath46
so @xmath8 is constant @xmath47 .
then @xmath48 and we have , @xmath49 using that @xmath50 , where @xmath51 is arc length , we find , @xmath52 the second of these follow from time integration of @xmath53 , and the second from ( [ eq.y.r.rel ] ) .
these results can also be written , @xmath54 so we are dealing with a straight line of slope @xmath55 . if @xmath56 , then @xmath57 according to eq .
( [ eq.conserv.ang.mom.vel ] ) . using this and the second of eqs .
( [ eq.of.mot.dimless.rtheta ] ) one finds that @xmath58 and hence that , @xmath59 the second of these is obtained by noting that @xmath60 , and the third follows from @xmath61 . finding the functions @xmath62 thus requires the following integrals to be done : @xmath63 @xmath64 @xmath65 a complete expression for the trajectory
is obtained by noting that the function @xmath66 is given by , @xmath67 according to eqs .
( [ eq.y.r.rel ] ) and ( [ eq.r.as.qoutient.init.cond ] ) .
when doing the integrals ( [ eq.t.integral ] ) - ( [ eq.x.integral ] ) it is convenient to distinguish the following cases : @xmath68 the explicit results are given in appendix a. it turns out that the complicated expressions obtained by direct integration using the variable @xmath8 become much simpler if one introduces a suitably chosen new integration variable . in the kepler problem this new variable is called the eccentric anomaly @xcite . for case 1 we chose , @xmath69 so that , @xmath70 , is in the same range as @xmath8 .
one then finds that _ e.g. _
@xmath71 , as given in eqs .
( [ eqs.dtsx ] ) , becomes , @xmath72 also the other integrals simplify considerably . for case 1
we then get the following explicit results for the trajectory as a function of the parameter @xmath73 , @xmath74 , \\
x(\psi,\lambda)&=&\frac{(\lambda-1)^2}{2(\lambda^2 - 1)^{5/2 } } \left\ { 3\lambda\psi+\left[2(\lambda^2 + 1)+\lambda\cos\psi\right]\sin\psi \right\ } , \\
y(\psi,\lambda)&=&-\frac{(\lambda-1)^2}{2(\lambda^2 - 1)^2 } \left(\lambda+\cos\psi\right)^2 , \end{aligned}\ ] ] from eqs .
( [ eq.t.integral ] ) - ( [ eq.y.integral ] ) .
one notes that one can allow @xmath73 to take values from @xmath75 to @xmath76 here .
plot of case 1 trajectories for @xmath77 ( red curve with two loops ) and for @xmath78 ( green curve with four loops ) . as in all our plots
the @xmath9-axis is horizontal and the @xmath79-axis vertically upwards . ]
two such curves are plotted in fig .
[ fig.trajcase1 ] .
one notes the limit @xmath80 which corresponds to a straight horizontal line . for this case
therefore @xmath81 . in the limit
@xmath82 the curve approaches a circle .
let us get some explicit numbers out . using the factors given in eq .
( [ eq.dim.less.var ] ) , @xmath83 being the speed at the bottom of the loop , we now find that the time @xmath84 that it takes to traverse a complete period is given by , @xmath85 = \frac{v_0}{g } \frac{2\lambda\pi}{\sqrt{\lambda^2 - 1}(\lambda+1)}\ ] ] where the function @xmath86 is given by eq .
( [ eq.t1 ] ) above .
similarly the total length @xmath87 of one period of the track is given by , @xmath88 = \frac{v_0 ^ 2}{g } \frac{(2\lambda^2 + 1)\pi}{\sqrt{\lambda^2 - 1}(\lambda+1)^2},\ ] ] the horizontal width @xmath89 is , @xmath90 = \frac{v_0 ^ 2}{g } \frac{3\lambda\pi}{\sqrt{\lambda^2 - 1}(\lambda+1)^2},\ ] ] and the vertical height @xmath91 is , @xmath92 = \frac{v_0 ^ 2}{g } \frac{2\lambda}{(\lambda+1)^2}.\ ] ] we also find from ( [ eq.r.as.qoutient.init.cond ] ) that @xmath93 , so the speed @xmath94 at the top of the loop ( @xmath95 ) is given by , @xmath96 let us take the speed at the bottom of the track to be @xmath97 m/s ( this corresponds to 72 km / h ) and use @xmath98m / s@xmath99 .
one then finds that , for @xmath100 , _ i.e. _ normal force @xmath101 , @xmath102s , @xmath103 m , @xmath104 m , @xmath105 m , and @xmath106 m/s . for @xmath78
this becomes @xmath107s , @xmath108 m , @xmath109 m , @xmath110 m , and @xmath111 m/s .
finally we note that case 2 , the other elliptic case with @xmath112 , simply gives similar displaced trajectories compared to case 1 .
for case 2 the top of a loop will be at , @xmath113 , as in figs .
[ fig.trajcase3 ] and [ fig.trajcase5 ] below .
we therefore proceed directly to the remaining cases .
for all the cases with @xmath114 the trajectory in velocity space goes to infinity .
these tracks can therefore not constitute a real roller coaster with constant normal force in themselves .
however as parts of more complicated tracks , spliced together with clothoids , they might be of interest . for case 3 , the parabolic case
, we have @xmath115 and @xmath116 , so that @xmath117 .
the variable that simplifies the integrations turns out to be , @xmath118 with range @xmath119 . from eqs .
( [ eq.t.integral ] ) - ( [ eq.y.integral ] ) one finds , @xmath120 for this track , in terms of the parameter @xmath121 .
[ fig.trajcase3 ] shows the shape of this one - loop track .
plot of the unique case 3 trajectory with normal force equal to gravity ( @xmath115 ) . ]
we now come to the two hyperbolic cases . for case 4 we have @xmath122 and @xmath123 so @xmath124 . let , @xmath125 with range @xmath126
. then , @xmath127 , \\ x(\chi,\lambda)&=&-\frac{(\lambda-1)^2}{2(1-\lambda^2)^{5/2 } } \left\ { 3\lambda\chi+\left[2(\lambda^2 + 1)+\lambda\cosh\chi\right ] \sinh\chi\right\ } , \\
y(\chi,\lambda)&=&-\frac{(\lambda-1)^2}{2(1-\lambda^2)^2 } \left(\lambda+\cosh\chi\right)^2 .\end{aligned}\ ] ] the shape of some of these tracks are shown in fig .
[ fig.trajcase4 ] .
one notes that in the limiting case of @xmath128 this trajectory becomes , @xmath129 the parabola that is the ballistic trajectory of free fall .
plot of a case 4 trajectories . the lowest ( innermost )
red curve is the parabola of free fall corresponding to @xmath130 . above that one
the curves correspond to @xmath131 ( green ) , @xmath132 ( brown ) , @xmath133 ( blue ) and finally the horizontal straight line ( violet ) corresponds to @xmath134 . ]
one may also note that the limit @xmath135 when taken in the @xmath136-dependent parts of @xmath137 and @xmath138 make these identical : @xmath139 .
this means that the curve becomes a straight horizontal line .
finally we have case 5 . here
@xmath122 and @xmath116 so @xmath140 .
let , @xmath141 with range @xmath142 .
then @xmath143 , \\ x(\eta,\lambda)&=&\frac{(\lambda+1)^2}{2(1-\lambda^2)^{5/2 } } \left\ { 3\lambda\eta-\right [ 2(\lambda^2 + 1)-\lambda\cosh\eta\left ] \sinh\eta \right\ } , \\ y(\eta,\lambda)&=&-\frac{(\lambda+1)^2}{2(1-\lambda^2)^2 } \left(\lambda-\cosh\eta\right)^2 .\end{aligned}\ ] ] for @xmath130 this curve also becomes a the ballistic parabola . for positive values of @xmath144
this trajectory has a loop and it is shown in fig .
[ fig.trajcase5 ] for some @xmath144-values .
plot of a case 5 trajectories .
the outermost red curve is the parabola corresponding to @xmath145 . inside the parabola
there are curves corresponding to the @xmath144-values @xmath146 ( green ) , @xmath147 ( brown ) , and @xmath148 ( blue ) .
the limit @xmath134 is in fig .
[ fig.trajcase3 ] . ]
we have presented explicit solutions for the problem of which smooth tracks produce a normal force of constant magnitude on a particle that slides along the track under the influence of a constant gravitational field in a vertical plane .
the obvious application is to the design of roller coasters . as we hope to have shown , the problem in itself has many interesting and surprising features .
one of them is the relation to the kepler problem of planetary motion .
students can learn various classical techniques of analysis by studying this problem .
one notes that a direct numerical approach can not reveal the fact that there are five ( or four , depending on the point of view ) qualitatively different regions of parameter values , nor the qualitative features of the corresponding solutions and their limiting behavior .
explicit results for the integrals in eqs .
( [ eq.t.integral ] ) - ( [ eq.x.integral ] ) , without the constants factors @xmath149 , with @xmath150 or 2 , in front , _
i.e._@xmath151 @xmath152 @xmath153 are given here .
for each of the three integrals there are five cases ( [ case1])-([case5 ] ) and @xmath154 represents the case number .
one finds : @xmath155\\ \nonumber t_2(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)}\left [ -\frac{2\lambda}{\sqrt{\lambda^2 - 1}}\arctan\left ( \sqrt{\frac{\lambda-1}{\lambda+1}}\frac{\sin\theta}{1-\cos\theta } \right)+\frac{\sin\theta } { \left(\lambda-\cos\theta\right)}\right]\\ \nonumber t_3(\theta)&=&-\frac{1}{3 } \frac{\left(2-\cos\theta\right)\sin\theta } { \left(1-\cos\theta\right)^2}\\ \nonumber t_4(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)}\left [ -\frac{2\lambda}{\sqrt{1-\lambda^2}}\operatorname{arctanh}\left ( \sqrt{\frac{1+\lambda}{1-\lambda}}\frac{\sin\theta}{1+\cos\theta } \right)+\frac{\sin\theta } { \left(\lambda-\cos\theta\right)}\right]\\ \nonumber t_5(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)}\left [ -\frac{2\lambda}{\sqrt{1-\lambda^2}}\operatorname{arctanh}\left ( \sqrt{\frac{1-\lambda}{1+\lambda}}\frac{\sin\theta}{1-\cos\theta } \right)+\frac{\sin\theta } { \left(\lambda-\cos\theta\right)}\right]\end{aligned}\ ] ] @xmath156\\ \nonumber s_2(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)^2}\left [ -\frac{2\lambda^2 + 1}{\sqrt{\lambda^2 - 1}}\arctan\left ( \sqrt{\frac{\lambda-1}{\lambda+1}}\frac{\sin\theta}{1-\cos\theta } \right)+\frac{\left(4\lambda^2 - 3\lambda\cos\theta-1\right)\sin\theta } { 2\left(\lambda-\cos\theta\right)^2}\right]\\ \nonumber s_3(\theta)&=&-\frac{1}{15 } \frac{\left(2\cos\theta^2 - 6\cos\theta+7\right)\sin\theta } { \left(1-\cos\theta\right)^3}\\ \nonumber s_4(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)^2}\left [ -\frac{2\lambda^2 + 1}{\sqrt{1-\lambda^2}}\operatorname{arctanh}\left ( \sqrt{\frac{1+\lambda}{1-\lambda}}\frac{\sin\theta}{1+\cos\theta } \right)+\frac{\left(4\lambda^2 - 3\lambda\cos\theta-1\right)\sin\theta } { 2\left(\lambda-\cos\theta\right)^2}\right]\\ \nonumber s_5(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)^2}\left [ -\frac{2\lambda^2 + 1}{\sqrt{1-\lambda^2}}\operatorname{arctanh}\left ( \sqrt{\frac{1-\lambda}{1+\lambda}}\frac{\sin\theta}{1-\cos\theta } \right)+\frac{\left(4\lambda^2 - 3\lambda\cos\theta-1\right)\sin\theta } { 2\left(\lambda-\cos\theta\right)^2}\right]\end{aligned}\ ] ] @xmath157\\ \nonumber x_2(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)^2}\left [ -\frac{3\lambda}{\sqrt{\lambda^2 - 1}}\arctan\left ( \sqrt{\frac{\lambda-1}{\lambda+1}}\frac{\sin\theta}{1-\cos\theta } \right)+\frac{\left((2\lambda^2 + 1)\lambda- ( \lambda^2 + 2)\cos\theta\right)\sin\theta } { 2\left(\lambda-\cos\theta\right)^2}\right]\\ \nonumber x_3(\theta)&=&\frac{1}{5 } \frac{\left(\cos\theta^2 - 3\cos\theta+1\right)\sin\theta } { \left(1-\cos\theta\right)^3}\\ \nonumber x_4(\theta,\lambda)&=&\frac{1}{(\lambda^2 - 1)^2}\left [ -\frac{3\lambda}{\sqrt{1-\lambda^2}}\operatorname{arctanh}\left ( \sqrt{\frac{1+\lambda}{1-\lambda}}\frac{\sin\theta}{1+\cos\theta } \right)+\frac{\left((2\lambda^2
+ 1)\lambda- ( \lambda^2 + 2)\cos\theta\right)\sin\theta } { 2\left(\lambda-\cos\theta\right)^2}\right]\\ \nonumber x_5(\theta,\lambda)&=&\frac{1}{(\lambda^2
- 1)^2}\left [ -\frac{3\lambda}{\sqrt{1-\lambda^2}}\operatorname{arctanh}\left ( \sqrt{\frac{1-\lambda}{1+\lambda}}\frac{\sin\theta}{1-\cos\theta } \right)+\frac{\left((2\lambda^2 + 1)\lambda- ( \lambda^2 + 2)\cos\theta\right)\sin\theta } { 2\left(\lambda-\cos\theta\right)^2}\right]\end{aligned}\ ] ] these complicated expressions simplify considerably after transformation to new integration variables corresponding to eccentric anomalies as discussed above . | arxiv |
What is the difference between the photoelectric effect and secondary emission?
What is the difference between [photoelectric effect](http://en.wikipedia.org/wiki/Photoelectric_effect) and [secondary emission](http://en.wikipedia.org/wiki/Secondary_emission) in [photo multiplier tubes](http://en.wikipedia.org/wiki/Photomultiplier)?
In other words, why the difference between the energy of the incident photon and the work function of the material (in photoelectric effect) turns into kinetic energy to the released electron, while this is not the case in secondary emission ?
The difference you are looking for is in the particle energy. The photon energy for visible light is about $3\,\mathrm{eV}$ (electron-volt), just enough to kick *one* electron from photocathode. In the photomultiplier, this electron is accelerated towards dynodes with high voltage. If it is $1000\,\mathrm{V}$, then the electron gains kinetic energy of $1000\,\mathrm{eV}$, thus being able to release much more secondary electrons on impact.
| stackexchange/physics |
neuroinflammation plays a prominent role in the progression of alzheimer 's disease [ ad , ] .
brain regions , particularly those involved in learning and memory , which demonstrate the greatest degree of microglia cell activation early in the disease ultimately show the highest rate of atrophy and pathology .
neurons within the entorhinal cortex ( ec ) and hippocampus degenerate in ad and are particularly vulnerable to the consequences of chronic neuroinflammation and aging [ 6 - 9 ] .
although the mechanism underlying the degeneration of these cells is unknown , excitotoxicity via the stimulation of glutamate receptors may play an important role [ 10 - 15 ] .
glutamate n - methyl - d - aspartate ( nmda ) receptors are highly concentrated in the hippocampus and ec and their activation has a dual role in normal neuroplasticity as well as neurodegeneration .
the number of nmda receptors within the hippocampus , ec and basal forebrain substantia innominata declined following an acute neuroinflammatory challenge produced by an injection of lipopolysaccharide ( lps ) into the cisterna magna .
therefore , neurons that express nmda receptors within these brain regions might be at increased risk in the presence of chronic neuroinflammation similar to that present in the brains of ad patients .
brain inflammation leads to increased extracellular levels of glutamate that may induce increased calcium entry through the nmda receptors and the degeneration or dysfunction of nmda receptive neurons .
activated glia may also potentiate nmda - mediated toxicity via the production and release of nitric oxide or interleukin-1 , suggesting that neuroinflammation may exacerbate excitotoxicity in neurons .
we have developed a model of chronic brain inflammation using a slow lps infusion into the 4ventricle of rats that reproduces many of the behavioral , electrophysiological , neurochemical and neuropathological changes associated with ad , including the presence of activated microglia within the hippocampus and ec , impaired long term potentiation in the dentate gyrus , impaired learning and memory , and a significant loss of ca3 hippocampal pyramidal cells and entorhinal pyramidal neurons in layers ii & iii [ 6 - 9,25 - 27 ] .
similarly , the long term infusion of lps into the basal forebrain was associated with the selective degeneration of cholinergic basal forebrain neurons . a critical role for stimulation of the nmda receptors
is supported by the finding that the neurodegenerative consequences of chronic neuroinflammation upon basal forebrain cholinergic neurons can be reversed by treatment with the nmda receptor antagonist memantine .
the current study demonstrates that chronic neuroinflammation is associated with the loss of nmda receptors within the hippocampus and ec .
because nmda receptors contain the obligatory nr1 subunit , receptor localization was determined using a monoclonal antibody that recognizes all variants of the nr1 subunit . a quantitative verification of the loss of these receptor sites
twenty - two young ( 3 months old ) male f-344 rats ( harlan sprague - dawley , indianapolis , in ) were singly housed in plexiglas cages with free access to food and water .
the rats were maintained on a 12/12-h light - dark cycle in a temperature - controlled room ( 22c ) with lights off at 0800 .
all rats were given health checks , handled upon arrival and allowed at least one week to adapt to their new environment prior to surgery .
each rat was anesthetized with isoflurane gas and placed in a stereotaxic instrument with the incisor bar set 3.0 mm below the ear bars .
the scalp was incised and retracted and a hole was made at the appropriate location in the skull with a dental drill .
coordinates for the 4ventricle infusions were as follows : 2.5 mm posterior to lambda , on the mid - line , and 7.0 mm ventral to the dura .
an osmotic minipump ( alzet , palo alto , ca , model 2004 , to deliver 250 l / h ) was attached via a catheter to a chronic indwelling cannula that had been positioned stereotaxically so that the tip extended to the coordinates given above . each minipump was prepared to inject either the vehicle artificial cerebrospinal fluid ( acsf ) or 250 g lps / h ( prepared in acsf ) .
the composition of the acsf ( in mmol / l ) was 140 nacl ; 3.0 kcl ; 2.5 cacl2 ; 1.2 na2hpo4 , ph 7.4 .
the following post - operative care was provided to all rats : betadine was applied to the exposed skull and scalp prior to closure to limit local infection and 5 ml of sterile isotonic saline were injected subcutaneously to prevent dehydration during recovery .
the rats were closely monitored during recovery and kept in an incubator ( ohio medical products , madison , wi ) at temperatures ranging from 3033c .
twenty - nine days after surgery rats from each group were anesthetized and were either transcardially perfused with cold saline containing 1 u / ml heparin , followed by 4% paraformaldehyde in 0.1 m sodium phosphate buffer , ph 7.4 , or sacrificed by decapitation , the brains frozen ( -70c ) and used for the fluorescence labeling studies .
the perfused brains were post - fixed one hour in the same fixative and then stored ( 4c ) in phosphate buffered saline , ph 7.4 .
free - floating , serial coronal sections ( 40 m ) were taken by vibratome from perfused tissues for staining with standard avidin / biotin peroxidase methods .
the frozen brains were arranged into a block of gelatin as a group of three brains representing rats from both groups in order to reduce variability in the immunostaining between slides .
the blocks were then sectioned ( 20 m ) using a cryostat and prepared for fluorescence labeling .
the monoclonal antibody ox-6 ( final dilution 1:400 , chemicon , san diego , usa ) was used to visualize activated microglia cells .
this antibody is directed against class ii major histocompatibility complex ( mhc ii ) antigen .
since nmda receptors contain the obligatory nr1 subunit , in order to label all nmda receptors with equal probability , we used a monoclonal antibody anti - nr1 subunit specific , nmdar1 ( chemicon , final dilution 1:250 ) .
after quenching endogenous peroxidase activity and blocking nonspecific binding , the sections were incubated ( 4c ) either overnight ( for ox-6 ) or 3 days ( for nmdar1 ) with primary antibodies directed against the specific epitopes ( mch ii and r1 , respectively ) .
thereafter , the sections were incubated for 2 h ( 22c ) with the secondary monoclonal antibody , rat adsorbed biotinylated horse anti - mouse immunoglobulin g ( final dilution 1:200 , vector , burlingame , usa ) , sections were than incubated for 1 h ( 22c ) with avidin - biotinylated horseradish peroxydase ( vectastain , elite abc kit , vector ) . after washing again in pbs
sections were mounted on gelatin - chrome - alum - coated glass slides , air - dried and coverslipped with cytoseal ( allan scientific , kalamazoo , mi ) mounting medium .
immunofluorescence was visualized with fluorescent substrates ( fitc , fluorescein , perkin - elmer , boston , ma ) and all nuclei were counterstained with topro3 ( 1:1,000 in tbs , molecular probes ) .
a z - section image series were acquired using a confocal microscope ( carl zeiss , model 510nlo - meta , thornwood , ny ) with a 25 water immersion objective .
the entire left hippocampus from the brain of four rats infused with acsf and four infused with lps for four weeks was isolated and stored ( -70c ) until assayed for nmda receptors using [ h]mk-801 according to a modified method previously described .
crude membrane fractions were prepared by initial homogenization in 20 volumes of 0.32 m sucrose containing 1.0 mm egta and centrifuged at 1000 g for 10 min at 4c .
the resulting pellet was resuspended in 20 volumes of 1.0 mm egta and centrifuged ( 40,000 g , 40 min , 4c ) .
the pellet was resuspended in 50 mm tris - acetate buffer ( ph 7.4 ) and centrifuged ( 47,900 g , 10 min , 4c ) .
this final sequence was repeated three times to remove any endogenous components of the tissue that might interfere with binding .
the tissues were stored frozen overnight and then centrifuged again ( 47,900 g , 10 min , 4c ) .
due to the small size of the samples and the desire to avoid pooling tissues only single - point determinations were made .
the assays were conducted in an incubation volume of 500 l containing [ h]mk-801 ( 1.0 m ) and 100150 g of membrane protein at 25c for 60 min in the presence of 100 m glycine and 50 m spermidine .
incubation was terminated by dilution with 4 ml of ice - cold 50 mm tris - acetate buffer , ph 7.4 , followed immediately by rapid filtration through whatman gf / b glass fiber filters on a cell harvester ( brandel , model phd 2000 , gaithersburg , md ) . the filters were rinsed three times with 4 ml of buffer .
all filters were presoaked in 0.3% polyethylenimine ( ph 7.0 ) for at least 2 h at 25c .
twenty - two young ( 3 months old ) male f-344 rats ( harlan sprague - dawley , indianapolis , in ) were singly housed in plexiglas cages with free access to food and water .
the rats were maintained on a 12/12-h light - dark cycle in a temperature - controlled room ( 22c ) with lights off at 0800 .
all rats were given health checks , handled upon arrival and allowed at least one week to adapt to their new environment prior to surgery .
standard procedures were used for the surgery . each rat was anesthetized with isoflurane gas and placed in a stereotaxic instrument with the incisor bar set 3.0 mm below the ear bars . the scalp was incised and retracted and a hole was made at the appropriate location in the skull with a dental drill .
coordinates for the 4ventricle infusions were as follows : 2.5 mm posterior to lambda , on the mid - line , and 7.0 mm ventral to the dura . an osmotic minipump ( alzet , palo alto , ca , model 2004 , to deliver 250 l / h ) was attached via a catheter to a chronic indwelling cannula that had been positioned stereotaxically so that the tip extended to the coordinates given above .
each minipump was prepared to inject either the vehicle artificial cerebrospinal fluid ( acsf ) or 250 g lps / h ( prepared in acsf ) .
the composition of the acsf ( in mmol / l ) was 140 nacl ; 3.0 kcl ; 2.5 cacl2 ; 1.2 na2hpo4 , ph 7.4 .
the following post - operative care was provided to all rats : betadine was applied to the exposed skull and scalp prior to closure to limit local infection and 5 ml of sterile isotonic saline were injected subcutaneously to prevent dehydration during recovery .
the rats were closely monitored during recovery and kept in an incubator ( ohio medical products , madison , wi ) at temperatures ranging from 3033c .
twenty - nine days after surgery rats from each group were anesthetized and were either transcardially perfused with cold saline containing 1 u / ml heparin , followed by 4% paraformaldehyde in 0.1 m sodium phosphate buffer , ph 7.4 , or sacrificed by decapitation , the brains frozen ( -70c ) and used for the fluorescence labeling studies .
the perfused brains were post - fixed one hour in the same fixative and then stored ( 4c ) in phosphate buffered saline , ph 7.4 .
free - floating , serial coronal sections ( 40 m ) were taken by vibratome from perfused tissues for staining with standard avidin / biotin peroxidase methods .
the frozen brains were arranged into a block of gelatin as a group of three brains representing rats from both groups in order to reduce variability in the immunostaining between slides .
the blocks were then sectioned ( 20 m ) using a cryostat and prepared for fluorescence labeling .
the monoclonal antibody ox-6 ( final dilution 1:400 , chemicon , san diego , usa ) was used to visualize activated microglia cells .
this antibody is directed against class ii major histocompatibility complex ( mhc ii ) antigen .
since nmda receptors contain the obligatory nr1 subunit , in order to label all nmda receptors with equal probability , we used a monoclonal antibody anti - nr1 subunit specific , nmdar1 ( chemicon , final dilution 1:250 ) .
after quenching endogenous peroxidase activity and blocking nonspecific binding , the sections were incubated ( 4c ) either overnight ( for ox-6 ) or 3 days ( for nmdar1 ) with primary antibodies directed against the specific epitopes ( mch ii and r1 , respectively ) .
thereafter , the sections were incubated for 2 h ( 22c ) with the secondary monoclonal antibody , rat adsorbed biotinylated horse anti - mouse immunoglobulin g ( final dilution 1:200 , vector , burlingame , usa ) , sections were than incubated for 1 h ( 22c ) with avidin - biotinylated horseradish peroxydase ( vectastain , elite abc kit , vector ) .
after washing again in pbs , the sections were incubated with 0.05% 3,3'-diaminobenzidine tetrahydrochloride ( vector ) as chromogen .
sections were mounted on gelatin - chrome - alum - coated glass slides , air - dried and coverslipped with cytoseal ( allan scientific , kalamazoo , mi ) mounting medium .
immunofluorescence was visualized with fluorescent substrates ( fitc , fluorescein , perkin - elmer , boston , ma ) and all nuclei were counterstained with topro3 ( 1:1,000 in tbs , molecular probes ) .
a z - section image series were acquired using a confocal microscope ( carl zeiss , model 510nlo - meta , thornwood , ny ) with a 25 water immersion objective .
the entire left hippocampus from the brain of four rats infused with acsf and four infused with lps for four weeks was isolated and stored ( -70c ) until assayed for nmda receptors using [ h]mk-801 according to a modified method previously described .
crude membrane fractions were prepared by initial homogenization in 20 volumes of 0.32 m sucrose containing 1.0 mm egta and centrifuged at 1000 g for 10 min at 4c .
the resulting pellet was resuspended in 20 volumes of 1.0 mm egta and centrifuged ( 40,000 g , 40 min , 4c ) .
the pellet was resuspended in 50 mm tris - acetate buffer ( ph 7.4 ) and centrifuged ( 47,900 g , 10 min , 4c ) .
this final sequence was repeated three times to remove any endogenous components of the tissue that might interfere with binding .
the tissues were stored frozen overnight and then centrifuged again ( 47,900 g , 10 min , 4c ) .
the final pellet was resuspended in 15 volumes ( to achieve approx . 0.4 mg / ml protein ) of 50 mm tris acetate buffer .
due to the small size of the samples and the desire to avoid pooling tissues only single - point determinations were made .
the assays were conducted in an incubation volume of 500 l containing [ h]mk-801 ( 1.0 m ) and 100150 g of membrane protein at 25c for 60 min in the presence of 100 m glycine and 50 m spermidine .
incubation was terminated by dilution with 4 ml of ice - cold 50 mm tris - acetate buffer , ph 7.4 , followed immediately by rapid filtration through whatman gf / b glass fiber filters on a cell harvester ( brandel , model phd 2000 , gaithersburg , md ) .
all filters were presoaked in 0.3% polyethylenimine ( ph 7.0 ) for at least 2 h at 25c .
overall , chronic infusion of lps was well tolerated by all rats . initially after surgery , all lps - treated rats lost only a few grams of weight . within a few days , however , most rats had regained weight and continued to gain weight normally for the duration of the study . lps
infused rats had numerous , highly activated microglia cells ( ox-6 positive ) distributed throughout the hippocampus and ec ( see figure 1 ) .
rats infused with acsf showed only a few mildly activated microglia scattered throughout the brain ( figure 1a ) , similar to our previous reports .
activated microglia were widely scattered throughout the hippocampus ( figure 1b ) and were characterized by a contraction of their highly ramified processes that appeared bushy in morphology ( figure 1c,1d ) .
confocal microscope images of activated microglial cells mhc ii ( green ox-6 positive ) in the dentate gyrus .
rats infused with acsf ( a ) had only a few activated microglia scattered throughout the brain . chronic infusion of lps into the 4ventricle produced high activated microglia distributed throughout the hippocampus ( b ) .
higher magnifications of an activated microglia ( c , d ) show the characteristic contracted and ramified processes with bushy morphology .
scale bars : ( a - b ) 100 m ; ( c ) 25 m ; ( d ) 2.5 m .
rats infused with acsf showed numerous nmdar1 immunoreactive large neurons throughout the hippocampus and ec that had intense dark staining within the cytoplasm of the cell bodies that extended into the dendrites .
chronic infusion of lps for four weeks reduced the number of nmdar1-immunoreactive cells within the hilar region of the dentate gyrus as well as in area ca3 , as compared to the staining in these hippocampal regions of rats infused with acsf ( see figure 2 ) .
chronic infusion of lps had a lesser effect upon nmdar1 immunoreactivity within cells in the ec ( figure 3 ) .
confocal microscopic images of nmdar1 receptors within the hippocampus . in rats infused with acsf ( a , b , c )
, fluorescence labeling showed large nmdar1-positive neurons ( red ) in dentate gyrus ( a ) , hilar region ( b ) and ca3 area ( c ) .
scale bars : ( a ) 100 m ; ( b , c ) 25 m .
immunohistochemistry of nmdar1-positive neurons revealed dark staining in the cytoplasm that extended along the dendrites in cells within the dentate gyrus ( g ) , hilar region ( h ) , and ca3 ( i ) .
scale bars : ( g ) 100 m ; ( h , i ) 25 m .
confocal microscopic images showed reduced nmdar1 staining within the hippocampus of lps infused rats : dentate gyrus ( d ) , hilar region ( e ) and ca3 area ( f ) .
immunohistochemistry of nmdar1-positive neurons revealed fewer cells expressing nmdar1 receptors with a lower degree of immunoreactivity throughout the dentate gyrus ( j ) , hilar region ( k ) and ca3 ( l ) .
scale bars : ( j ) 100 m , ( k , l ) 25 m .
highly activated microglial cells ( b ) that are typical of lps infused rats were completely absent in the brains of rats infused with acsf ( a ) .
nmdar1-immunoreactive cells within the entorhinal cortex of rats infused with acsf ( c ) were characterized by darkly stained cell bodies and dendritic arbors .
scale bars : ( a , b ) 100 m ; ( c , d ) 25 m .
rats chronically infused with lps had significantly ( t = 10.8 , df = 6 , p < 0.001 ) fewer [ h]mk-801 binding sites in the hippocampus compared to the acsf infused animals ( see figure 4 ) .
nmda receptor number declined significantly ( p < 0.001 vs. csf ) in the hippocampus following chronic neuroinflammation produced by infusion of lps into the 4ventricle .
lps infused rats had numerous , highly activated microglia cells ( ox-6 positive ) distributed throughout the hippocampus and ec ( see figure 1 ) .
rats infused with acsf showed only a few mildly activated microglia scattered throughout the brain ( figure 1a ) , similar to our previous reports .
activated microglia were widely scattered throughout the hippocampus ( figure 1b ) and were characterized by a contraction of their highly ramified processes that appeared bushy in morphology ( figure 1c,1d ) .
confocal microscope images of activated microglial cells mhc ii ( green ox-6 positive ) in the dentate gyrus .
rats infused with acsf ( a ) had only a few activated microglia scattered throughout the brain .
chronic infusion of lps into the 4ventricle produced high activated microglia distributed throughout the hippocampus ( b ) .
higher magnifications of an activated microglia ( c , d ) show the characteristic contracted and ramified processes with bushy morphology .
scale bars : ( a - b ) 100 m ; ( c ) 25 m ; ( d ) 2.5 m .
rats infused with acsf showed numerous nmdar1 immunoreactive large neurons throughout the hippocampus and ec that had intense dark staining within the cytoplasm of the cell bodies that extended into the dendrites .
chronic infusion of lps for four weeks reduced the number of nmdar1-immunoreactive cells within the hilar region of the dentate gyrus as well as in area ca3 , as compared to the staining in these hippocampal regions of rats infused with acsf ( see figure 2 )
. chronic infusion of lps had a lesser effect upon nmdar1 immunoreactivity within cells in the ec ( figure 3 ) .
confocal microscopic images of nmdar1 receptors within the hippocampus . in rats infused with acsf ( a , b , c )
, fluorescence labeling showed large nmdar1-positive neurons ( red ) in dentate gyrus ( a ) , hilar region ( b ) and ca3 area ( c ) .
scale bars : ( a ) 100 m ; ( b , c ) 25 m .
immunohistochemistry of nmdar1-positive neurons revealed dark staining in the cytoplasm that extended along the dendrites in cells within the dentate gyrus ( g ) , hilar region ( h ) , and ca3 ( i ) .
scale bars : ( g ) 100 m ; ( h , i ) 25 m .
confocal microscopic images showed reduced nmdar1 staining within the hippocampus of lps infused rats : dentate gyrus ( d ) , hilar region ( e ) and ca3 area ( f ) .
immunohistochemistry of nmdar1-positive neurons revealed fewer cells expressing nmdar1 receptors with a lower degree of immunoreactivity throughout the dentate gyrus ( j ) , hilar region ( k ) and ca3 ( l ) .
scale bars : ( j ) 100 m , ( k , l ) 25 m .
highly activated microglial cells ( b ) that are typical of lps infused rats were completely absent in the brains of rats infused with acsf ( a ) .
nmdar1-immunoreactive cells within the entorhinal cortex of rats infused with acsf ( c ) were characterized by darkly stained cell bodies and dendritic arbors .
scale bars : ( a , b ) 100 m ; ( c , d ) 25 m .
rats chronically infused with lps had significantly ( t = 10.8 , df = 6 , p < 0.001 ) fewer [ h]mk-801 binding sites in the hippocampus compared to the acsf infused animals ( see figure 4 ) .
nmda receptor number declined significantly ( p < 0.001 vs. csf ) in the hippocampus following chronic neuroinflammation produced by infusion of lps into the 4ventricle .
chronic neuroinflammation in young rats produced by infusion of lps into the 4ventricle for 28 days was associated with an increased number of highly activated microglia cells throughout the temporal lobe and greatly decreased immunolabelling of nmdar1 receptors within the pyramidal layer of the ca3 and hilar regions of the dendate gyrus and to a somewhat less degree within the ec .
the loss of immunostaining may reflect either diminished receptor protein concentration or an inflammation - induced conformational change in the protein structure such that the antibody no longer recognized its antigenic binding site .
we have previously shown using electron microscopy that chronic neuroinflammation in the hippocampus is associated with numerous changes in the intracellular components involved in the protein synthesis ; in contrast , no significant changes were associated with the mitochondria or lysosomes .
the decline in immunoreactive receptor sites was paralleled by a decline in the number of [ h]mk-801 binding sites within the hippocampus , which is consistent with a previous report on the effects of acute exposure to lps upon nmda receptor density within this brain region .
taken together , these findings are consistent with the hypothesis that selected vulnerable cells degenerated as a consequence of the chronic neuroinflammatory processes . we have previously shown that neurons in the ec degenerated in a model of chronic neuroinflammation similar to that used in the present study .
we speculate that the loss of entorhinal afferents might underlie a component of the decline in nmda r1 immunoreactivity within the hippocampus given that the ec provides the main glutamatergic afferents to the hippocampus via the perforant pathway and this is usually the first region to undergo degenerative changes in ad . because so little
is known regarding the consequences of long term neuroinflammation produced in this model , it is impossible to be certain whether the loss of nmda glutamate receptors that we report is selective for this brain region or this particular receptor .
we have previously only documented the loss of pyramidal neurons using this model although we are currently pursuing this question . in the current model of chronic brain inflammation
we have hypothesized the following sequence of events leading to the degeneration of nmda - expressing neurons .
the infusion of lps leads to the release of inflammatory cytokines by activated astrocytes and microglia ; these cytokines stimulate the production of other inflammatory mediators such as prostaglandins ; prostaglandins would induce the release of glutamate from astrocytes leading to increased levels of extracellular glutamate and the stimulation of glutamate receptors , the depolarization - dependent unblocking of nmda receptors by mg , and the entry of toxic amounts of cainto neurons and the subsequent generation of toxic levels of nitric oxide and initiate a cascade of reactive oxygen intermediates .
prostaglandins and various cytokines may also indirectly elevate the extracellular concentration of glutamate by inhibiting its reuptake by astrocytes ; in addition , blockade of the uptake of glutamate by astrocytes results in significant neurodegeneration .
we have hypothesized that a similar cascade of biochemical events , possibly initiated by the loss of forebrain norepinephrine , may occur associated with normal aging .
consistent with this hypothesis and the results of the current study is a recent report that chronic administration of an anti - inflammatory drug could attenuate the age - related loss of hippocampal nmdar1 receptors .
taken together , our hypothesis and the results of our current study suggest that neurons expressing nmda receptors would be vulnerable to degeneration in the presence of chronic neuroinflammation . due to the widespread presence of inflammation in vulnerable brain regions ,
a similar series of biochemical processes might contribute to the cognitive deficits observed in patients with ad [ 1 - 3 ] or associated with normal aging .
ad : alzheimer 's disease ; acsf : artificial cerebrospinal fluid ; ec : entorhinal cortex ; nmda : n - methyl - d - aspartate ; lps : lipopolysaccharide ; mhc ii : class ii major histocompatibility complex ;
sr and glw participated in the design of the study and preparation of the manuscript .
supported by the u.s . public health service , ag10546 and an alzheimer 's association , iirg-01 - 2654 , award to glw , and a human frontiers science program award to vra , lft 000112 - 2002-c . | pubmed |
Like many ice beers, crisp, no aftertaste. Similiar in taste to Molson Ice, but IMHO a little better. Not as tasty as Blue, but after a sixer of this, who the hell cares?! Kris has his "Get drunk beer." Now I have mine.
If you find yourself drinking this, drink it quick before it gets warm. If that happens, you may as well dump it out and lick the bottle cap, it has the same taste. But then you won't be ingesting the 5.6% alcohol which I think is why those guys just out of high school like to split a two-four of this when they're drinking in their parent's garage. Or the fact that it's cheap. They must be immune to the gut rot I got from drinking this stuff too. Or maybe you forget about that when your head is thumping. Either way, this is a get drunk beer. Not as vile as "Maximum Ice" and if you drink it cold it's tolerable (watery). I'd hate to experience what this tastes like out of a can. | slim_pajama |
Thermochemistry: forms of energy & pressure
I've been in a few classes now that teach about energy, and I feel they're always so bad. There is always such a rush to start using equations to get problems solved, and I often feel I don't have an intuitive grasp on energy at all. I guess this question is also about pressure.
Questions:
1. Does pressure decrease with time? If pressure is caused by the force of gas molecules hitting the inside surface of a container, don't they transfer energy and eventually slow down enough to totally reduce pressure?
2. Along the same lines, energy can be released or absorbed by a reaction as work or heat. If the only change that happens is through work (in something that is totally insulated - where gas is formed and pressure is created), after the pressure is created, doesn't it require continuous energy to maintain pressure against a constant force of 1 atm (or whatever it is)? Heat dissipates to all things, and that makes sense as everything gets colder in time. The same does not seem true for pressure.
Thanks in advance.
Noobsauce
>
> 1.Does pressure decrease with time?
>
>
>
The ideal gas law tells us that
$$PV=nRT$$
or
$$\mathrm{P=\frac{[nRT]}{[V]}}$$
If the temperature, number of moles or volume does not change, then the pressure will not change.
>
> If pressure is caused by the force of gas molecules hitting the inside
> surface of a container, don't they transfer energy and eventually slow
> down enough to totally reduce pressure?
>
>
>
Yes, that's correct. **If energy is transferred out of the system**, then the temperature will fall and the pressure will decrease. But if everything is already at the same temperature, there will be no energy flow in or out and the pressure will remain constant.
>
> after the pressure is created, doesn't it require continuous energy to
> maintain pressure against a constant force
>
>
>
No, there is no requirement that energy must be supplied to maintain the pressure. Again, if the gas, the vessel and the surroundings are all at the same temperature the pressure will not change. However, if the entire system is not at thermal equilibrium, then heat will flow so as to put things at equilibrium and the temperature will change.
>
> Does pressure decrease with time? If pressure is caused by the force of gas molecules hitting the inside surface of a container, don't they transfer energy and eventually slow down enough to totally reduce pressure?
>
>
>
No. As you know, an aerosol can remains pressurised indefinitely until it is used. The molecules do not slow down if no energy transfer occurs, because there are no smaller bodies to transfer their energy to.
At the start of a game of snooker/pool/billiards (whatever you play in your part of the world) the balls are arranged in a triangle at the bottom of the table. You place the white ball at the top of the table and hit it into the other balls. When the collision occurs, the white ball shares its energy (normally unevenly) with the other balls. What we see is an *increase in disorder.* Even if we neglect friction, once this has occured it is very unlikely (impossible even) that all the other balls would stop and the white ball would have all the energy again. The way the energy of the white ball is spread between the other balls is a macroscopic display of how kinetic energy is dissipated by friction.
You will learn later on that while energy must be conserved, disorder in a *closed* system can only stay the same or increase; it can never decrease. Disorder is quantified by *entropy* but the quantification is beyond the scope of your question.
The balls on the table will soon stop moving, due to friction. What happen is that the kinetic energy is shared around in a more disordered way amongst the molecules of the balls and table. The energy is still there (the balls and table are very very slightly warmer) but it is now distributed in random movements of the molecules so that the balls are no longer moving.
Once it gets to this level, the molecules just keep vibrating (or in the case of a gas, colliding.) There is no friction in these interactions, because there is nothing smaller than a molecule for energy to be dissipated into.
*(well actually there is one thing: the molecules could shake themselves free of the solid they are in and become a liquid, shake themselves free of the liquid they are in and become a gas, or even shake themselves apart and become smaller molecules or atoms. But breaking these bonds or interactions can only occur with additional heat absorption, or by cooling of the material.)*
>
> after the pressure is created, doesn't it require continuous energy to maintain pressure against a constant force of 1 atm (or whatever it is)?
>
>
>
"work" (which is a transfer of mechanical energy) only occurs when something is moved against a force. For example, when you put your finger over the end of a bicycle pump and squeeze the plunger, your squeezing arm does work. If you release the plunger, it moves outward again, releasing the stored energy.
The fact that you find it difficult to maintain the force on the plunger indefinitely does not mean that any work is being done. Your body is not designed to maintain a force with perfect efficiency; energy is expended within your body to maintain that muscle contracted. But if you had a latch on the bicycle pump, you could close that and maintain the pressure indefinitely.
Similarly, when you lie down on an airbed, you increase the pressure inside it. You have no expenditure of energy while you are lying on the bed, yet you maintain the pressure. Similarly the aerosol can maintains its internal pressure with no expenditure of energy.
| stackexchange/chemistry |
Why the metric tensor?
Inspired by my previous question [Variation of gamma and Christoffel](https://physics.stackexchange.com/questions/412615/variation-of-gamma-and-christoffel) (mostly from AccidentalFourierTransform's comment), I was wondering why the metric tensor is used in physics to define a spacetime as opposed to any other tensor. It makes sense that the metric defines a notion of distance and corresponds to the generalization of the newtonian potential so in that sense it is fundamental.
Along those lines however, it seems more fundamental/easier to construct physics based on the tetrads $e^{a}\_\mu$ instead. According to [this](https://arxiv.org/pdf/1106.2037.pdf) paper variations with respect to the tetrad generalizes the Einstein equations (eq 122) and also has the stress-energy tensor proportional to the tetrad (eq 127). What makes the metric particularly "privileged" as to be the basis of GR (at least in elementary presentations)?
You have correctly identified that the metric $g\_{\mu\nu}$ is not the only exclusive field to characterise gravitation. In particular, as you mentioned, the vielbein $e^a\_\mu$ can be used. It is particularly useful to work with the vielbein when computing curvatures by hand, using Cartan's equation.
This is because we can usually read off connections from $\mathrm de + \omega \wedge e = 0^\dagger$ and compute the curvature tensor from the standard relation,
$$R = \mathrm d \omega + \omega \wedge \omega.$$
When it comes to supergravity, the vielbein is crucial. The Einstein supergravity multiplet consists of the components, $e^a\_\mu$, $\Psi\_{\mu\alpha}, \bar\Psi^{\dot\alpha}\_\mu, A\_\mu,B,\bar B$.
Furthermore, for a general supermanifold, it is quite common to work with the supervielbein, which consists of,
$$E\_A = (E\_\mu,E\_\alpha,\bar E^{\dot\alpha})$$
such that for a point $p\in\mathbb R^{p|q}$, $\{E\_A |\_p\}$ is a standard basis for $T\_p(\mathbb R^{p|q})$.
---
$\dagger$ In index notation, $\mathrm de^a + \omega^a\_b \wedge e^b = 0$ is a linear system of equations to solve for $\omega^a\_b$, where we have abbreviated $e^a = e^a\_\mu \mathrm dx^\mu$ and $\omega^a\_b = \omega^a\_{b\mu}\mathrm dx^\mu$.
| stackexchange/physics |
the description of correlated quantum many - body systems far from equilibrium remains one of the challenging problems in modern statistical mechanics , quantum field theory , nuclear , atomic , molecular and condensed matter physics.@xcite most of theoretical approaches are based on keldysh nonequilibrium green s functions ( negf ) which enables perturbative treatment of nonequilibrium many - body systems.@xcite negf also allows systematic summation of specific classes of nonequilibrium diagrams , for example , random phase approximation@xcite or gw theory.@xcite nonperturbative methods , such as , numerical renormalization group theory , are also available but often restricted to the oversimplified model systems.@xcite in this paper we propose a new theoretical method nonequilibrium configuration interaction ( neci ) , which provides a nonperturbative treatment and , in principle , is able to achieve the exact solution of the nonequilibrium problem by representing the density matrix as a linear combination of nonequilibrium quasiparticle excitations above the vacuum state .
let us briefly explain the main ideas of our approach .
we start from the superoperator representation of the master equation for the density matrix .
a summary of the superoperator formalism relevant to this work is provided in appendix a , while a detailed discussion can be found elsewhere @xcite . in this representation nonequilibrium dynamics of many - body system
is given by the schrdinger - like equation @xmath0 where @xmath1 is the vector in liouville - fock space , which corresponds to the density matrix , and @xmath2 is the liouville superoperator ( liouvillian ) . in this paper
, we focus on the nonequilibrium steady - state density matrix , which is a solution of the equation @xmath3 once the equation is solved , the average of any physical operator @xmath4 can be computed according to @xmath5={\ensuremath{\langle{i|\hat a|\rho}\rangle}}.\ ] ] here , @xmath6 is the bra - vector in the liouville - fock space which corresponds to the unit operator @xmath7 , and the superoperator @xmath8 is related to an operator @xmath4 according to definition .
thus , our goal is to find the liouville - fock space vector which satisfies condition .
by the application of wick theorem in liouville - fock space@xcite the liouvillian can be brought to the normal ordered form .
the diagonalization of the quadratic part in terms of nonequilibrium quasiparticles , i.e. in terms of normal modes of the uncorrelated part of the liouvillian , yields:@xcite @xmath9 where @xmath10 and @xmath11 are creation and annihilation superoperators for nonequilibrium quasiparticles .
the liouvillian describes a system of nonequilibrium quasiparticles with complex spectrum @xmath12 and the quasiparticle - quasiparticle interaction @xmath13.@xcite following the ideas of equilibrium configuration interaction method,@xcite in order to describe many - body correlations we need to specify a reference state with respect to which the correlations are defined .
we choose the reference state as a vacuum for nonequilibrium quasiparticles , i.e. , @xmath14 .
then the exact nonequilibrium density matrix can be represented a linear combination of the vacuum , two nonequilibrium quasiparticle excitations , four nonequilibrium quasiparticle excitations and so on .
therefore , neci expansion for the correlated exact density matrix has the following form @xmath15 where @xmath16 contains a sum of the multi - quasiparticle creation superoperators which generate @xmath17-quasiparticle excitations above the reference state @xmath18 , i.e. , @xmath19 , @xmath20 , etc .
the relative weights ( amplitudes ) of multi - quasiparticle excitations can be found by demanding that the density matrix satisfies the steady - state condition ( [ lrho0 ] ) , i.e. @xmath21 this equation is equivalent to the system of inhomogeneous linear equations for the amplitudes of the density matrix expansion . to compute the average of a single - particle operator ( current , population , etc . )
we need to know two - quasiparticle amplitudes . however , some truncation are to be made in the density matrix expansion for practical purposes .
this results in an approximate solution of equation . in this paper
, we develop this approach on the specific example of electron transport through a quantum system ( central region ) with electron - phonon interaction . but
the method can be easily extended to an arbitrary correlated central region .
the remainder of the paper is organized as follows . in sec . 2
, we introduce the lindblad master equation for an embedded system and its superoperator representation .
section 3 presents the nonequilibrium configuration interaction method .
we discuss two different truncated expansions for the density matrix and apply the theory to calculate the steady - state current . in this section
, we also proof that neci method is current conserving .
the numerical neci calculations of the steady - state current and comparison with other approaches are presented in sec .
conclusions are given in sec .
appendix a contains a summary of the superoperator formalism .
finally , in appendix b we provide details about negf calculations within the first born approximation and the second - order perturbation theory .
we use natural units throughout the paper : @xmath22 , where @xmath23 is the electron charge .
as shown in figure [ system ] , we consider a paradigmatic model of nonequilibrium many - body theory : the interacting quantum system ( central region ) connected to two noninteracting electrodes , left ( @xmath2 ) and right ( @xmath24 ) , maintained with different chemical potentials , @xmath25 and @xmath26 , and the same temperature @xmath27 .
to be specific , we focus on the electron transport problem through one electronic single - particle level with energy @xmath28 coupled linearly to a vibrational mode ( phonon ) of frequency @xmath29 ( the so called local holstein model ) .
thus , the central region hamiltonian is @xmath30 where @xmath31 ( @xmath32 ) and @xmath33 are electron and phonon creation ( annihilation ) operators , respectively .
the left and right electrodes are modeled as semi - infinite tide - binding chains of atoms characterized by the hopping matrix element @xmath34 and the on - site energy @xmath35 ( @xmath36 ) .
the coupling between the cental region and the end site of @xmath37 electrode is given by the matrix element @xmath38 .
is connected to the dissipator and the central region . ]
we replace the infinite system by a finite one using open boundary conditions . to this end
each electrode is partitioned into two parts : the macroscopically large reservoir and the finite buffer zone between the central region and the reservoir . in doing so
, the hamiltonian of the whole system takes the form @xmath39 in the energy representation the reservoir and the buffer zone hamiltonians are diagonal @xmath40 where @xmath41 denote the continuum single - particle spectra of the left ( @xmath42 ) and right ( @xmath43 ) reservoir states , while the buffer zones have discrete energy spectrum @xmath44 .
the buffer - reservoir and central region - buffer couplings have the standard tunneling form : @xmath45 @xmath46 projecting out the reservoir degrees of freedom from the liouville - von neumann equation for the total density matrix , we obtain lindblad master equation for the reduced density matrix of the embedded system ( central region + finite buffer zones ) @xcite @xmath47 + i{\pi}\rho(t).\end{aligned}\ ] ] here , @xmath48 is the hamiltonian of the embedded system which includes the lamb shift of the buffer zone single - particle levels @xmath49 and @xmath50 is the non - hermitian dissipator given by the standard lindblad form @xmath51 the operators @xmath52 and @xmath53 are referred to as the lindblad operators , which represent the buffer - reservoir interaction .
they have the following form : @xmath54 with @xmath55 , @xmath56 . here
@xmath57^{-1}$ ] _ _ _ _ and @xmath58 ( @xmath59 ) is the imaginary ( real ) part of the self - energy arising from the buffer - reservoir interaction @xmath60 .
the lindblad master equation describes the time evolution of an open embedded quantum system preserving hermiticity , normalization , and positivity of the nonequilibrium density matrix .
open boundary conditions are taken into account by the non - hermitian dissipative part , @xmath61 , which represents the influence of the reservoir on the buffer zone .
the applied bias potential enters into the master equation via fermionic occupation numbers @xmath62 which depend on the temperature and the chemical potential in the left and right electrodes .
we have recently demonstrated that this embedding procedure makes the master equation ( [ lindblad ] ) exact in the steady - state regime , if the buffer zones are large enough to cure the deficiencies of born - markov approximation for treating the buffer - reservoir interface.@xcite we use a superoperator formalism and convert the lindblad master equation to the non - hermitian schredinger - like equation for the nonequilibrium density matrix.@xcite within the superoperator formalism the density matrix is considered as a vector in the liouville - fock space and all other operators as superoperators . in appendix
a we present a brief summary of the formalism and demonstrate how to convert the lindblad master equation into a superoperator form .
the resulting equation is @xmath63 here , the superoperators @xmath64 and @xmath65 are obtained from the hamiltonian by replacing ordinary creation and annihilation operators @xmath66 with non - tilde , @xmath67 , and tilde , @xmath68 , superoperators , respectively ( note that we include the lamb shift into @xmath69 ) .
the dissipators are given by @xmath70 the liouville superoperator @xmath2 is non - hermitian because of @xmath71 .
some other important properties of @xmath2 are discussed in appendix a. in particular , the relation @xmath72 holds , where the liouville - fock space bra - vector @xmath6 corresponds to the unit operator @xmath7 .
we focus our attention on asymptotic ( @xmath73 ) nonequilibrium steady - state situation , where the density matrix @xmath74 does not depend on time .
therefore the problem is reduced to the problem of finding the right zero - eigenvalue eigenvector of the non - hermitian finite - dimensional liouville superoperator @xmath75 knowing the solution of , we can compute the steady - state current into the central region from @xmath37 buffer zone as @xmath76 where @xmath77 is the current superoperator . in the next section
we discuss the development of neci method to solve equation .
we also present the application of neci to compute the steady - state current through the central region .
in the beginning of the section , we make the important remark on the notation use in the rest of the paper : only creation / annihilation superoperators written with letters @xmath78 ( such as for example @xmath79 and @xmath80 ) are related to each other by the hermitian conjugation ; all other creation @xmath81 and annihilation @xmath82 superoperators ( as well as their tilde - conjugated partners ) are `` canonically conjugated '' to each other , i.e. , for example , @xmath83 does not mean @xmath84 although @xmath85 ( @xmath86 - bosons / fermions ) .
let us introduce nonequilibrium quasiparticle creation and annihilation superoperators , which are the basic building blocks for the neci method .
we start by decomposing the liouvillian as @xmath87 where @xmath88 is the liouvillian for noninteracting electrons and phonons , @xmath89 while @xmath90 represents the interaction between them @xmath91 hereinafter , the notation t.c stands for tilde conjugated superoperators ( see the tilde - conjugation rules in appendix a ) .
nonequilibrium quasiparticles are defined by diagonalizing the electronic part of @xmath92 : @xmath93 where @xmath94 . using the equation of motion method we find non - unitary ( but canonical )
bogoliubov transformation which diagonalizes
@xmath95 : @xmath96 where @xmath97 amplitudes @xmath98 , @xmath99 are the solution of the following systems of equations @xmath100 and @xmath101 with @xmath102 . by solving the eigenvalue problem
we also obtain the quasiparticle spectrum @xmath103 , @xmath104 . taking into account property , we see that @xmath6 is a vacuum state for @xmath105 and @xmath106 superoperators , @xmath107 although superoperators @xmath105 and @xmath108 ( @xmath106 and @xmath109 ) are not hermitian conjugate to each other , they obey the fermionic anticommutation relations .
particularly , from @xmath110 it follows that @xmath98 amplitudes are normalized according to @xmath111 other useful relations between amplitudes @xmath112 can derived by making use the transformation inverse to ( see relations ( a4 ) in our previous paper @xcite ) and computing the anticommutators .
for example @xmath113 to compute the steady - state curent we need to express the current superoperator @xmath114 in terms of quasiparticle superoperators . by doing so and taking into account property ,
we obtain the following expression for the steady - state current @xmath115 where @xmath116 is the two - quasiparticle amplitude . note , that this is an _ exact _ expression for the steady - state current .
the only problem is to find the unknown @xmath117 . in the absence of electron - phonon interaction ,
i.e. , when the nonequilibrium density matrix does not contain quasiparticle excitations , the current through the central region is given by the first terms in . in what follows
we will refer to this current as a free - field current @xmath118 .
the correction to the free - field current , @xmath119 , is given by the second term involving @xmath117 .
in @xcite , it was shown how to compute @xmath117 making use of the perturbation theory . in the following subsections
we demonstrate how to find @xmath117 within the neci approach using different reference states for the density matrix expansion , namely , free - field and coherent reference states .
we define the free - field reference state as the steady - state density matrix in the absence of electron - phonon interaction , i.e. , @xmath120 and @xmath121 the density matrix @xmath122 is a vacuum state for nonequilibrium quasiparticles , i.e. , @xmath123 to determine @xmath124 we take into account the possibility that the phonon subsystem can contain a certain number of thermally excited vibrational quanta .
let @xmath125 be the number of thermally excited phonons , i.e. , @xmath126 it is convenient to perform a non - unitary canonical transformation and introduce new phonon operators @xmath127 and their tilde conjugated partners @xmath128 such that @xmath129 is the vacuum state for @xmath130 superoperators , @xmath131 while @xmath6 is the vacuum for @xmath132 superoperators ( see property in appendix ) .
now , the free - field liouvillian takes the form @xmath133 and the vacuum state @xmath18 for annihilation superoperators @xmath134 is the free - field reference state obeying condition .
the free - field density matrix @xmath135 is normalized according to @xmath136 . due to the electron - phonon interaction
the exact steady - state density matrix contains multi - quasiparticle and multi - phonon excitations above the free - field density matrix .
we are looking for the exact steady - state density matrix in the form @xmath137 where the operator @xmath138 is given by the infinite power series of creation superoperators @xmath139 defined this way , the density matrix is normalized according to @xmath140 , as @xmath6 is a vacuum for quasiparticle and phonon creation superoperators . since the density matrix is tilde - invariant ( see the definition in appendix a ) , the superoperator @xmath138 obeys the property @xmath141 , i.e. it remains the same if we complex conjugate all @xmath142 and replace the non - tilde superoperators by the tilde ones and vice versa .
we demand that the steady - state density matrix obeys the equation @xmath143 , therefore @xmath144\bigr\}{\ensuremath{\,|{\rho^{(0 ) } } \rangle}}= -l'{\ensuremath{\,|{\rho^{(0 ) } } \rangle}}.\ ] ] this superoperator equation is equivalent to the infinite inhomogeneous system of linear equations for @xmath142 amplitudes in the expansion for nonequilibrium density matrix ( [ s_ci_full ] ) .
any truncation in the expansion leads to approximate solution of equation . here , we consider the simplest form of @xmath138 which allows us to calculate the correction for the free - field current .
namely , @xmath145 where @xmath146 and @xmath147 is a real number .
inclusion of @xmath147 and @xmath148 terms into the density matrix expansion is necessary , since @xmath149 , @xmath150 configurations and their tilde - conjugate contribute to the right - hand side of ( see the expression for @xmath90 below ) .
if we neglect them , we observe a homogeneous linear system having a trivial solution . in this sense , these terms are correlations inducing terms . in order to find equations for the amplitudes @xmath151 we first express @xmath90 in terms of nonequilibrium quasiparticle superoperators : @xmath152\hat c^\dag_m \hat c_n -\mathrm{t.c.}\bigr\ } \notag\\ -&i\kappa\sum_{mn}\bigl[l^{(4)}_{mn}\hat\gamma^\dag - ( l^{(4)}_{nm})^*\widetilde\gamma^\dag+ l^{(5)}_{mn}(\gamma+\widetilde\gamma)\bigr]\hat c^\dag_m\widetilde c^\dag_n \notag\\ -&i\kappa\sum_{mn}l^{(6)}_{mn}(\hat\gamma^\dag-\widetilde\gamma^\dag)\hat c_m\widetilde c_n+ \kappa n^{(0)}(\hat\gamma^\dag-\widetilde\gamma^\dag).\end{aligned}\ ] ] here the coefficients @xmath153 are
@xmath154\psi_n , \notag\\ l^{(2)}_{mn}&=\bigl[\varphi_m+n_\omega\psi_m\bigr]\psi_n,~~l^{(3)}_{mn}=\psi_m\psi_n , \notag\\ l^{(4)}_{mn}&=\bigl[(\psi_m-\varphi_m)\varphi_n^*+n_\omega(\psi_m\varphi^*_n-\varphi_m\psi_n^*)\bigr ] \notag\\ l^{(5)}_{mn}&=\psi_m\varphi_n^*-\varphi_m\psi^*_n,~~l^{(6)}_{mn}=\psi_m\psi_n^*,\end{aligned}\ ] ] and @xmath155 is the free - field population of the electron level .
note , that after normal ordering @xmath90 does not involve terms containing annihilation superoperators only .
therefore , the condition @xmath72 is fulfilled . substituting @xmath138 given by into and demanding equation to be fulfilled up to terms
included into @xmath138 we derive the system of linear equations for unknown amplitudes : @xmath156 \notag\\ & - \kappa\sum_i ( l^{(3)}_{ni})^*[z_{m i } + z^*_{im } ] - 2\kappa l^{(5)}_{mn } w = 0 \notag\\ z_{mn}(\omega_m & - \omega_n^ * + \omega_0 ) + \kappa n^{(0 ) } f_{mn } \notag\\ & + \kappa \sum_i [ l^{(1)}_{mi } f_{in } - ( l^{(2)}_{ni})^ * f_{mi } ] = \kappa l^{(4)}_{mn } \notag \\
w\omega_0 - & \kappa\sum_{mn } l^{(6)}_{mn}f_{mn } = -\kappa n^{(0)}. \end{aligned}\ ] ] it should be pointed out that the first and the last equations above are exact in the sense that the inclusion of other terms into @xmath138 does not modify these equations .
within neci method we have some flexibility in the choice of the reference state .
ideally , we would like to put as much correlations as possible into the reference state while maintaining the possibility to define it as a vacuum for some quasiparticle annihilation operators .
we note that @xmath90 given by contains the term @xmath157 which is linear in phonon superoperators .
it gives us an idea to eliminate this term by the non - unitary canonical transformation @xmath158 and @xmath159 , @xmath160 .
the vacuum of the `` shifted ''
phonon operators is the coherent state @xmath161 normalized according to @xmath162 .
let us consider this coherent state as a reference state for the configuration interaction expansion , i.e. @xmath163 where @xmath138 is given by @xmath164 to distinguish from the neci expansion on the free - field reference state , we denote the present method as neci@xmath165 .
the advantage of neci@xmath165 approach is that it effectively includes multi - phonon excitation and de - excitation processes via the exponent in the coherent reference state . to fulfill the condition @xmath166
, the superoperator @xmath138 must obey the equation @xmath167\bigr\}{\ensuremath{\,|{\rho^ { ( * ) } } \rangle}}= -l'{\ensuremath{\,|{\rho^ { ( * ) } } \rangle}},\ ] ] where @xmath168 and @xmath169 -il^{(5)}_{mn}c^\dag_m\widetilde c^\dag_n\bigr\ } \notag \\ + & \kappa\sum_{mn}\bigl\{\bigl[l^{(1)}_{mn}\xi^\dag+l^{(2)}_{mn}\widetilde \xi^\dag + l^{(3)}_{mn}(\xi+\widetilde\xi)\bigr]c^\dag_m c_n -\mathrm{t.c.}\bigr\ } \notag\\ -&i\kappa\sum_{mn}\bigl[l^{(4)}_{mn}\xi^\dag - ( l^{(4)}_{nm})^*\widetilde\xi^\dag+ l^{(5)}_{mn}(\xi+\widetilde\xi)\bigr]c^\dag_m\widetilde c^\dag_n \notag\\ -&i\kappa\sum_{mn}l^{(6)}_{mn}(\xi^\dag-\widetilde\xi^\dag)c_m\widetilde c_n.\end{aligned}\ ] ] if all terms are included into the density matrix expansion , the two methods , neci and neci@xmath165 , coincide because both are formally exact .
however , when we truncate the expansion for the density matrixes , neci and neci@xmath165 give different results .
likewise to neci , we take the operator @xmath138 in the form @xmath170 demanding that equation is fulfilled up to terms included into @xmath138 we obtain the following system of equations @xmath171 \notag\\ & + \kappa\sum_i l^{(3)}_{mi}[z_{i n}+ z_{n i}^ * ] - \kappa\sum_i ( l^{(3)}_{ni})^*[z_{m i } + z^*_{im } ] \notag\\ & - 2\kappa l^{(5)}_{mn } w = -\frac{2\kappa^2 n^{(0)}}{\omega_0}l^{(5)}_{mn } \notag\\ z_{mn}&(\omega_m - \omega_n^ * + \omega_0 ) -
\frac{2\kappa^2 n^{(0)}}{\omega_0}\sum_i [ l^{(3)}_{mi}z_{in } - ( l^{(3)}_{ni})^*z_{mi } ] \notag\\ & + \kappa \sum_i [ l^{(1)}_{mi } f_{in } - ( l^{(2)}_{ni})^ * f_{mi } ] + \frac{2\kappa^2 n^{(0)}}{\omega_0 } l^{(5)}_{mn}w = \kappa l^{(4)}_{mn } \notag \\
w&\omega_0 -\kappa \sum_{mn } l^{(6)}_{mn}f_{mn } = 0 .
\end{aligned}\ ] ] solving this system we compute the two - quasiparticle amplitudes @xmath117 and , hence , obtain the neci@xmath165 correction to the free - field current . here
again , the first and the last equations are exact , i.e. , additions of new terms to @xmath138 does not modify these equations .
the truncation of the density matrix expansion introduces approximations into the theory .
it is important to ensure that observables computed with the truncated density matrix still satisfy conservation laws dictated by the symmetries of the underlying hamiltonian.@xcite in the nonequilibrium case it is particularly important to demonstrate that the proposed configuration interaction theory preserves the particle number continuity equation in all orders of configurations included into the density matrix . to this end
, we are going to prove that there is no artificial current leakage from the system introduced by the approximations and the current which enters the system from the left reservoir is exactly the same as the current which leaves the system to the right reservoir : @xmath172 let us first prove the current conservation in the free - field approximation .
indeed , the following equality is true @xmath173 here , we have used relations as well as the first equations in and .
the solution of system ( or ) provides us the two - quasiparticle amplitudes @xmath117 and the neci ( neci@xmath165 ) correction @xmath119 to the free - field current ( see equation ) . with the help of the first equation in and using the property @xmath174
we find @xmath175 expressing @xmath176 from the first _
exact _ equation in ( or ) and taking into account the explicit expressions for @xmath177 , @xmath178 we find that @xmath179 .
note that this result does not depend on the particular choice of @xmath138 , i.e. it is valid for any truncated neci ( or neci@xmath165 ) expansion .
thus , the presented configuration interaction theory is current - conserving in all orders of nonequilibrium quasiparticle configurations included into the density matrix expansion .
in our numerical calculations we assume that the applied voltage @xmath180 symmetrically shifts the on - site energies , i.e. , @xmath181 .
additionally , we assume that the electrodes are half filled , i.e. , the corresponding left and right chemical potentials are positioned at @xmath182 .
we choose the following parameters of the electrodes : @xmath183 , @xmath184 and the temperature is @xmath185 . since the on - site energies @xmath186 are affected by the applied voltage the left and right electrodes are nonidentical . in the subsequent discussion we set the applied voltage @xmath187 . for the buffer zones we take a finite chain of @xmath188 atoms from each electrode .
therefore the energy spectrum of each buffer zone is given by @xmath189 and the tunneling matrix elements in are @xmath190 the parameter @xmath191 in lindblad operators is taken to be equal the distance between neighbor energy levels in the buffer zones , i.e. , @xmath192 . in our calculations
we include @xmath193 sites into each buffer zone .
this size of the buffer zone has been proven to give the exact results for the steady state density matrix of the system .
@xcite let us say some words concerning numerical solution of the systems of equations and . to be specific we consider the system obtained within neci theory ( for the neci@xmath165 system we have used the same solution method ) .
the dimension of the system is of the order of @xmath194 , where @xmath195 .
although the systems is sparse , it contains about @xmath196 nonzero matrix elements . assuming that each complex number requires 16 bytes of computer memory
, we find that for @xmath193 the total system matrix needs about 700 gigabyte for storage .
a required memory size can be reduced drastically if we contract the indices by introducing the following linear combinations @xmath197 and their complex conjugate .
note , that the correction to the free - field current can be written as @xmath198 then , it is possible to rewrite the system as a system for @xmath199 , @xmath200 and their complex conjugate .
the obtained system contains @xmath201 equations and the total number of nonzero elements is about @xmath202 . to solve the system we have used standard routines from intel mkl fortran library . in figure [ fig2 ]
we compare the second - order perturbation theory ( sopt ) and first born approximation ( 1ba ) results for the electron current with the results obtained within neci and neci@xmath165 method for different values of the central region parameters .
the currents are shown as functions of the level energy , @xmath28 , i.e. , for different transport regimes ( resonant / off - resonant ) .
since the first born approximation does not guarantee the current conservation , we plot the 1ba current from the left electrode to the central region as well as the 1ba current from the central region to the right electrode .
the details of sopt and 1ba calculations using nonequilibrium green s functions are presented in appendix b. we first consider the case when @xmath203 , i.e. , there is no equilibrium thermally excited vibrational quanta . as evident from the figure in this case the first born approximation does not violate the current conservation significantly since the left and right currents are close to each other . we see that for a weak coupling ( @xmath204 ) all approaches predict a similar @xmath28 dependency of the current , which reaches a maximum value at @xmath205 .
the peak value of the sopt and 1ba currents slightly exceeds the neci and neci@xmath165 ones .
when we increase the electron - phonon coupling ( @xmath206 ) both sopt and neci currents become unphysical negative in the off - resonant regime when the electronic level @xmath28 is below the electrode chemical potentials . in the resonant regime sopt and neci currents significantly overestimate the results of other approaches .
in addition , comparing neci@xmath165-based calculations with other calculations , we can see that neci@xmath165 approach gives the current peak position at @xmath205 .
if we now consider the case of larger phonon energy ( @xmath207 ) we notice that negative sopt and neci currents in the off - resonant regime disappear and all approaches again demonstrate a similar @xmath28 dependency of the current .
now we consider results obtained for nonzero number of thermally excited equilibrium vibrational quanta .
namely , we assume that @xmath208 . in this case
the first born approximation clearly reveals its current nonconserving nature .
this is illustrated in the lower panels of figure [ fig2 ] where we can see that the left and right 1ba currents can be very different from each other .
nevertheless , in the weak electron - phonon coupling regime ( @xmath204 ) , all approached predict qualitatively similar dependence of the current upon the electronic level @xmath28 . comparing the result for @xmath204 , @xmath208 with those for @xmath209 , @xmath203 we notice that inclusion of thermally excited equilibrium vibrational quanta into consideration produces slightly broadened current peak with a reduced amplitude . when the coupling constant increases ( @xmath206 ) sopt and neci approaches again show unphysical negative current in the off - resonant regime when @xmath28 is below the electrode chemical potentials .
moreover , for @xmath206 the electron - phonon coupling splits the neci@xmath165 current peak , while neci approach gives only one peak . for a larger phonon energy , @xmath210 ,
neci@xmath165 predicts three pronounced peaks , while neci gives only two peaks .
in addition , sopt and 1ba show unphysically negative current for certain values of @xmath28 . from the above consideretion
it is evident that the configuration interaction method built on the coherent reference state is preferable when the electron - phonon coupling is large or when there are thermally excited vibrational quanta in the system .
this result is not surprising since , contrary to neci , neci@xmath165 method accounts for multi - photon excitations and de - excitation processes which are important in these regimes .
we developed nonequilibrium configuration interaction method , which formally gives the exact solution of out - of - equilibrium correlated many - body problem .
our approach is based on a superoperator representation of the lindblad master equation for the reduced density matrix of the embedded quantum system .
it was shown that the steady - state density matrix can be decomposed in liouville - fock space in terms of nonequilibrium multi - quasiparticle excitations above the reference vacuum state .
the amplitudes of these excitations provide a measure of the many - body nonequilibrium correlations .
the theory was applied to study the inelastic electron transport through the system with electron - phonon interaction . to compute the current we used truncated expansion of the steady - state density matrix .
two different reference states were considered : free - field vacuum and coherent state .
it was proved that both approximations are current conserving in all orders of the density matrix expansion .
the current through the system was computed for different model parameters and compared with the second - order perturbation theory and the first born approximation results .
it was shown that the configuration interaction method based on the coherent reference state is superior to the other approaches when the electron - phonon coupling is large or when there are thermally excited vibrational quanta in the system .
the method can be readily extended to dynamical nonequilibrium case by making the amplitudes in the density matrix expansion time - dependent functions .
here we briefly review the formalism of superoperators acting in the liouville - fock space , while the detailed discussion is given in @xcite .
we suppose that the fock space of the system under consideration is spanned by the complete orthonormal set of basis vectors @xmath211 which are eigenvectors of the particle number operator : @xmath212 the operators in the fock space form themselves a linear vector space called the liouville - fock space .
the set of vectors @xmath213 constitutes a orthonormal basis in the liouville - fock space .
thus , every fock space operator @xmath214 can be considered as a liouville - fock space ket - vector @xmath215 .
the adjoint operator @xmath216 is represented by the bra - vector @xmath217 . the scalar product in the liouville - fock space is defined as @xmath218 . in particular , the scalar product of a vector @xmath219 with @xmath6 is equivalent to the trace operation in the fock space , @xmath220 .
now we introduce creation and annihilation superoperators .
fermion creation and annihilation superoperators are defined as @xmath221 where @xmath222 . for bosonic creation and annihilation superoperators
we drop the phase factor @xmath223 .
so defined superoperators satisfy the same ( anti)commutation relations as their fock space counterparts . additionally , the basis vectors of the liouville - fock space are super - particle number eigenvectors , i.e. , @xmath224 for an operator @xmath225 we formally define two superoperators @xmath226 and refer to them as non - tilde and tilde superoperators , respectively .
the connection between non - tilde and tilde superoperators is given by the `` tilde conjugation rules '' @xmath227 with the help of superoperators an arbitrary liouville - fock space vector can be represented as @xmath228 hereinafter , the phase @xmath229 if @xmath4 is a fermionic operator and @xmath230 if @xmath4 is a bosonic operator .
we also define a liouville - fock space vector tilde conjugated to a given one , @xmath231 . therefore ,
if @xmath4 is a hermitian bosonic operator then @xmath219 is tilde - invariant , i.e. , @xmath232 .
the examples of tilde - invariant vectors are @xmath233 and the density matrix @xmath234 . considering the adjoint of and assuming that @xmath235 we find @xmath236 this gives us the idea introduce superoperator @xmath237 and its tilde conjugate , @xmath238 , which annihilate the bra - vector @xmath6 . for the product of operators
the following relation is valid @xmath239 where @xmath240 if both @xmath241 and @xmath242 are fermionic and @xmath243 otherwise . with the help of relations the average of an operator @xmath4 in the state with the density matrix @xmath244
can be calculated as the matrix element of the corresponding superoperator @xmath8 sandwiched between @xmath6 and @xmath245 : @xmath246 let us now consider the lindblad master equation
. in the liouville - fock space this equation takes the form @xmath247 applying raltions , i.e. , taking into account that @xmath248 , @xmath249 , @xmath250 , etc .
, we can rewrite this equation in the schrdineger - like form .
the time evolution of the density matrix is governed by the non - hermitian liouville superoperator @xmath2 .
two important properties of @xmath2 should be noted : 1 . since
the density matrix is tilde invariant , then @xmath251 ; 2 .
taking the time derivative of @xmath252 we find @xmath253 , i.e. , @xmath6 is the left zero - eigenvalue eigenvector of @xmath2 .
in this appendix we briefly describe the details of transport calculations based on nonequilibrium green s functions relevant to our discussion . we first define four kind of interacting green s functions : @xmath254 and @xmath255 .
the retarded and advanced green s functions are given as the solutions of dyson s equation @xmath256 where @xmath257^{-1}$ ] is the noninteracting retarded green s function .
the lesser and greater green s functions satisfy the keldysh equation @xmath258 the interaction self - energies @xmath259 account for the electron - phonon coupling in the central region , while the electrode self - energies , @xmath260 , describe the effects of the coupling between the central region and the electrodes @xmath261\bigl(f_\alpha(\omega)-1\bigr ) , \notag \\
\sigma^{>}_{\alpha}(\omega ) & = + 2i\mathrm{im}[\sigma^r_\alpha(\omega)]f_\alpha(\omega).\end{aligned}\ ] ] here , @xmath262 is the fermi - dirac distribution function with chemical potential @xmath263 and temperature @xmath27 .
once the full interacting green s functions are defined , we can write explicit expressions for physical quantities of interest . for the net electric current passing through the @xmath37 electrode to the central region
we adopt the meir - wingreeen transport formula @xcite @xmath264 and for the electron level nonequilibrium population we use @xmath265 neglecting the electron - phonon interaction , i.e. , assuming @xmath266 , we obtain the free - field current , @xmath267 , and electron populations , @xmath268 . the exact electron - phonon interaction self - energies @xmath269 in green s functions ( [ lesser_gf ] ) and ( [ retarded_gf ] ) contain all possible diagrams that satisfy feynman rules . in this work , we calculate @xmath269 from the lowest order self - energy diagrams referred to as the hartree and fock diagrams , @xmath270 .
this approach is known as the first born approximation ( 1ba ) . using the standard rules of feynman s diagrams and the langreth theorem for analytical continuation we find the hartree and fock self - energies @xmath271\bigr\}.\end{aligned}\ ] ] with the usual definition for the bare phonon green s functions @xmath272 \notag\\ d^{r}_0(\omega ) & = \frac{1}{\omega - \omega_0 + i0^+ } - \frac{1}{\omega + \omega_0 + i0^+ } , \end{aligned}\ ] ] where @xmath125 is the equilibrium occupation number of the phonon mode with frequency @xmath29 .
we see that @xmath273 because @xmath274 unless @xmath275 . since @xmath276 , we have @xmath277 .
substituting self - energies into dyson equation and keldysh equation we find the lesser and greater green s functions within the first born approximation .
although the 1ba does not generally guarantee current conservation , computationally it is not as demanding as the self - consistent born approximation when the full interacting green s functions are used in the definition of the self - energies . in the case of weak electron - phonon coupling
the second - order perturbation theory ( sopt ) may be a good approximation . in this approximation
the lesser and greater green s functions obtained within 1ba are expanded with respect to electron - phonon coupling up to @xmath278 terms @xmath279.\end{aligned}\ ] ] substituting this expression into we evaluate the current within the second - order perturbation theory .
it should be noted that this approximation satisfies the current conservation condition . in the end of this appendix we present explicit expression for the electrode retarded self - energy . for the semi - infinite one - dimensional chain with on - site energy @xmath35 and hopping parameter
@xmath34 coupled to the central region with hoping matrix element @xmath38 , the retarded self - energy @xmath280 can be written in an analytical form as @xmath281 where @xmath282 , @xmath283 .
10 catalin d. spataru , mark s. hybertsen , steven g. louie , and andrew j. millis .
gw approach to anderson model out of equilibrium : coulomb blockade and false hysteresis in the @xmath284 characteristics .
, 79(15):155110 , apr 2009 .
r. b. saptsov and m. r. wegewijs .
fermionic superoperators for zero - temperature nonlinear transport : real - time perturbation theory and renormalization group for anderson quantum dots . , 86:235432 , dec 2012 . | arxiv |
aerobic ammonia oxidation , the first and rate - limiting step in nitrification , is the only biological process converting reduced to oxidized inorganic nitrogen species on earth . for over 100 years ,
this process was thought to be mediated by autotrophic beta - proteobacteria and gamma - proteobacteria ( aob ) occasionally supported by heterotrophic nitrifiers in soil environments .
however , in situ measurements of nitrification in marine and terrestrial environments showed that ammonia oxidation often proceeds at substrate concentrations significantly below the growth threshold of cultured aob ( e.g. ) indicating the presence of unknown nitrifiers .
the recent discovery of homologs of ammonia monooxygenase genes in archaea [ 57 ] and the cultivation of autotrophic ammonia - oxidizing archaea ( aoa ) [ 811 ] revealed that an additional group of microorganisms is able to catalyze this process .
the widespread distribution of putative archaeal ammonia monooxygenase ( amo ) genes and their numerical dominance over their bacterial counterparts in most marine and terrestrial environments suggested that aoa play a major role in global nitrification [ 1215 ] , but our understanding of their evolutionary history and metabolic repertoire is still in its infancy .
in 1992 , jed fuhrman 's team and ed delong reported the discovery of a novel clade of archaeal 16s rrna sequences from ocean surface waters , which formed a mesophilic sister group to the hyperthermohilic crenarchaeota .
when it became apparent that this novel group contained aoa , these organisms were consequently also referred to as mesophilic crenarchaeota .
this perception was questioned by phylogenetic analysis of the first available genome sequence of a putative aoa , the sponge symbiont candidatus cenarchaeum symbiosum .
when brochier - armanet and colleagues analyzed a concatenated data set of 53 ribosomal proteins common to archaea and eukarya , they made the surprising observation that c. symbiosum branched off before the separation of crenarchaeota and euryarchaeota .
based on this phylogenetic analysis , on gene presence / absence data , and on the diversity and wide distribution of aoa , they proposed that that these organisms belong to the phylum thaumarchaeota .
recently , this analysis was extended to the ammonia - oxidizing candidatus nitrosopumilus maritimus , a marine group i.1a representative , and candidatus nitrososphaera gargensis , a soil group i.1b representative enriched from a hot spring . in this study ,
phylogenetic analysis of concatenated ribosomal proteins ( figure 1a ) and several other marker genes as well as presence / absence patterns of information processing machineries in archaea strongly supported the assignment of aoa to the deep - branching phylum thaumarchaeota .
consistent with this finding , comparative genomics revealed that 6 conserved signature indels and > 250 proteins are unique to the thaumarchaeota c. symbiosum and n. pumilus and are not found in crenarchaeota .
additional support for the phylum thaumarchaeota stems from comparative analysis of fosmid clones obtained from different deep - sea locations . among 200 phylogenetic trees of protein families present in thaumarchaeotal fosmids from these sites , thaumarchaeota sequences branched as separate cluster distinct from hyperthermophilic crenarchaeota and euryarchaeota in 162 phylogenetic trees .
independent from genomic data , the presence of the lipid crenarchaeol in all analyzed aoa [ 9,2224 ] is consistent with a separate placement of these organisms in the archaeal tree as this lipid has so far not been found in any other bacterium or archaeon .
thus , it seems likely that this membrane lipid , which may now be more appropriately termed thaumarchaeol , is an invention of an early thaumarchaote and represents a signature lipid for this phylum . revisiting
the phylogenetic placement of thaumarchaeota in 16s rrna - based trees also reveals a clear separation from crenarchaeota and euryarchaeota ( figure 1b ) . a number of environmentally retrieved clone groups consisting of the sagmgc-1 group ( subsurface mine ) , group i.1c ( acidic soils ) , aloha group ( open ocean ) , psl12 group ( hot spring ) , and the hwcgiii / nitrosocaldus group ( hot springs / hydrothermal vents )
since this cluster is supported by all treeing methods and has a bootstrap value of 100% ( figure 1b ) , its representatives very likely all belong to the phylum thaumarchaeota and at least some of them might be aoa . supporting this hypothesis ,
a good correlation between copy numbers of archaeal amoa ( coding for the -subunit of ammonia monooxygenase ) and 16s rrna genes of the aloha group has been observed in the north pacific .
it will be fascinating to see whether all thaumarchaeota have the capability to perform ammonia oxidation or whether certain members use a different energy metabolism .
just recently two giant thaumarchaeota , candidatus giganthauma karukerense and candidatus giganthauma insulaporcus , were characterized by molecular methods but all attempts to amplify archaeal amoa genes failed . however ,
this could also be caused by primer bias as has been previously recognized for archaeal amoa - targeted surveys in deep ocean waters .
currently , the mcg ( miscellaneous crenarchaeotic group ) , mbgb ( marine benthic group b ) , and hwcgi ( hot water crenarchaeotic group i ) clusters have no clear affiliation to any of the established archaeal phyla and show an unstable branching order when 16s rrna - based trees inferred with different treeing methods are compared ( figure 1b ) .
little is known about these organisms but recently the first genome of a representative of the hwcgi cluster , that of candidatus caldiarchaeum subterraneum , was found to be distinct from other archaeal phyla including genes encoding a ubiquitin - like protein modifier system that was so far only found in eukaryotes . as a consequence , the lineage
however , a comparative genome analysis by brochier - armanet and colleagues revealed some typical thaumarchaeal features in c. subterraneum and thus places it at the base of thaumarchaeota in protein trees ( for details see brochier - armanet et al .
, this issue ) . with the availability of more genomes within this and related lineages , comparative genomics will show whether
aigarchaeota represent a new archaeal phylum or will be classified as deep - branching members of the crenarchaeota or thaumarchaeota .
the phylogenetic structure of aoa can also be analyzed by the functional marker gene amoa , which is found in all ammonia - oxidizing microorganisms .
the presence of aoa within group i.1a and group i.1b thaumarchaeota as well as within the thaumarchaeota - group hwcgiii / nitrosocaldus is mirrored in the respective amoa phylogeny ( figure 1b ) .
in addition , a fourth amoa - cluster with no established link to a thaumarchaeotal lineage in the 16s rrna - based tree became apparent during the accumulation of environmental amoa sequences within the last few years .
since amoa sequences from a wide range of habitats ( including various marine , terrestrial , and hot water environments ) are affiliated with this lineage , we have named it the ubiquitous cluster. it is tempting to speculate that this cluster represents so - far unrecognized aoa within the sagmgc-1 , group i.1c , aloha , or psl12 cluster .
almost every study that investigates ammonia - oxidizing thaumarchaeota uses the amoa gene to explore their diversity and abundance with the implicit assumption that all amoa - carrying archaea are oxidizing ammonia .
however , of the > 10,000 deposited archaeal amoa sequences , thus far only four have been directly linked to archaeal strains for which experimental evidence of ammonia oxidation exists [ 811 ] .
although phylogenetically closely related enzymes often perform the same function , it deserves consideration that the family of copper - containing membrane - bound monooxgenases ( cummo ) , to which archaeal ammonia monooxygenases belong , has a wide substrate range .
in addition to ammonia [ ammonia monooxygenase ( amo ) in -proteobacteria , -proteobacteria , and thaumarchaeota ] , this includes methane [ particulate methane monooxygenase ( pmmo ) in -proteobacteria , -proteobacteria , verucomicrobia , and candidatus methylomirabilis oxyfera ] , and short - chained alkanes [ particulate butane monooxygenase ( pbmo ) in the gram - positive nocardioides strain cf8 ] .
in addition , non - specific substrate catabolism such as oxidation of chlorinated ethenes and aromatic hydrocarbons has been observed with some members of this enzyme family , clearly indicating substrate promiscuity .
therefore , it has been suggested that not necessarily the type of cummo but rather the downstream enzyme machinery defines the energy metabolism of a microorganism . for example , the -proteobacterium aob nitrosococcus oceani can oxidize methane but lacks all subsequent enzymes to gain energy by methane oxidation .
likewise , co - oxidation of ammonia by methane oxidizing bacteria does not support their growth .
furthermore , it is interesting to note that -proteobacterial amos are more closely related to -proteobacterial pmmos than to -proteobacterial amos and have a near equal substrate specificity for ammonia and methane .
consequently , the mere presence of an amoa - like gene , transcript , or protein is insufficient to infer that the respective organism is oxidizing ammonia .
currently , it is not clear whether aoa are strict autotrophs or also assimilate organic substrates . for n. maritimus , autotrophy has been shown and for n. gargensis co2-fixation has been experimentally demonstrated .
incorporation of labeled bicarbonate into lipids , proteins , and cells of marine thaumarchaeota are consistent with autotrophy , which is enabled by a modified 3-hydroxypropionate/4-hydroxybutyrate ( hp / hb ) cycle for co2-fixation as found in known aoa genomes and in marine thaumarchaeal fosmids . however ,
analysis of the c. symbiosum and n. maritimus genomes as well as of thaumarchaeal fosmids from bathypelagic plankton also has revealed the presence of a tca cycle ( possibly incomplete ) and of potential transporters for organic substances such as amino acids , oligopeptides , and glycerol .
thus , mixotrophic or even heterotrophic growth of marine thaumarchaeota as supported by other isotope labeling studies and natural distribution of radiocarbon in archaeal membrane lipids can to date not be excluded .
furthermore , it has been suggested that parts of the hp / hb cycle can serve to co - assimilate organic compounds including , for example , 3-hydroxypropionate , an intermediate in the metabolism of the ubiquitous marine osmoprotectant dimethylsulphoniopropionate . for soil environments ,
co2-stable isotope probing revealed ammonia oxidizing activity of members of group i.1a as well as i.1b thaumarchaeota indicating an autotrophic or mixotrophic lifestyle .
two of these studies found label incorporation into genes or transcripts of the 4-hydroxybutyryl - coa - dehydratase or acetyl - coa - propionyl - coa - carboxylase , respectively , with both enzymes being involved in the co2-fixing hp / hb cycle .
however , growth of soil aoa with no concomitant incorporation of co2 has been also observed when nitrification was inhibited indicating that at least some soil aoa can grow heterotrophically . for comparison , heterotrophic growth of crenarchaeota that possess the hp / hb cycle
is known for sulfolobus solfataricus and metallosphaera sedula with the latter being able to switch between an autotrophic and heterotrophic lifestyle .
the question under which conditions aoa or aob dominate ammonia oxidation is currently attracting a lot of attention . for ammonia oxidation by the group i.1a
thaumarchaeote n. maritimus , an extremely low substrate threshold ( < 10 nm total nh4 + nh3 , representing the detection limit of the used method ) and apparent km - value ( 133 nm ) were determined with the latter being very similar to in situ nitrification measurements made in oligotrophic oceans .
adaptation to low ammonium concentrations has also been reported for the thermophilic group i.1b thaumarchaeote n. gargensis , indicating a widespread distribution of oligotrophic ammonia oxidation within the thaumarchaeota . in comparison ,
minimum total ammonium concentrations required for growth of cultured aob are 100-fold higher ( > 1 m near neutral ph ) with km - values ranging from 46 to 1780 m total ammonium .
thus , a dominating activity of aoa in the large water bodies of oligotrophic oceans is highly likely with aob being restricted to organic - matter rich particles and coastal environments with higher nutrient loads .
measured apparent km - values for soils range from 2 to 42 m total ammonium and may therefore be influenced by both aoa and aob . in general , activity of soil aoa
was seen when total ammonia concentrations were below 15 g nh4-n ( g dw .
soil ) whereas aob responded to high ammonia concentrations [ > 100 g nh4-n ( g dw .
in addition , the form of supplied nitrogen might also play a critical role : aoa activity was seen when n was supplied as mineralized organic n derived from composted manure or soil organic matter and aob - dominated activity was seen with ammonia from inorganic fertilizer ( reviewed in ) . based on genome analyses of n. maritimus and c. symbiosum and due to the fact that aoa do not contain a homologue of the bacterial hydroxylamine oxidoreductase ,
a mechanism for ammonia oxidation distinctly different from that of aob has been proposed . here
, ammonia is not oxidized via hydroxylamine ( nh2oh ) as in aob but rather via nitroxyl ( hno ) to nitrite , which possibly involves only 0.5 o2 per nh3 oxidized ( proposed by martin klotz ( louisville ) ) .
this hypothesized lower oxygen demand could explain why aoa are found not only in fully areated soils and oxic marine waters but also in suboxic marine waters , sediments , and oxygen - depleted hot springs . in oxygen gradients of marine sediments and in the stratified water body of the black sea different aoa ecotypes
aoa can also be found over a wide range of ph , temperature , salinity , and phosphate concentrations with some aoa being adapted to sulfidic environments , which extends the potential range of aoa niche differentiation to a multitude of environmental factors ( reviewed in ) .
until recently , methanogenic euryarchaeota were the only known archaea of global relevance for element cycling .
this perception changed with the discovery of ammonia - oxidizing archaea , which belong to the newly recognized archaeal phylum thaumarchaeota and contribute significantly to the global n - cycle and c - cycle .
their shear abundance in the ocean ( up to 20% of all bacteria and archaea ) and extremely low substrate threshold for total ammonium provide compelling evidence for their role as dominant ammonia oxidizers in the open ocean , where they also contribute to primary production by their autotrophic ( or possibly partly mixotrophic ) lifestyle . the dominance of aoa over aob in many terrestrial environments can not be so easily explained .
low km - values of unfertilized soils for ammonia oxidation might point to a contribution of certain aoa ecotypes to nitrification , especially under low ammonia availability . on the other hand ,
it is well possible that some soil thaumarchaeotes use other substrates than ammonia for energy generation and are heterotrophs or that they switch to ammonia oxidation only under certain environmental conditions .
further dissection of the ecological interplay of aoa groups among themselves and with aob is urgently required and might reveal that aoa exhibit a similar type of niche partitioning as found for different nitrite oxidizers . here ,
prefer low nutrient and microoxic sites , with different nitrospira lineages adapted to different nitrite concentrations .
papers of particular interest , published within the period of review , have been highlighted as: of special interest of outstanding interest of special interest of outstanding interest | pubmed |
How will the compression ratio increase thermal effeciency of otto cycle while Win is higher?
Why the ideal otto cycle thermal effeciency increase with compression ratio although that will increase work input? While the temperature difference in the combustion chamber could be low,the overall effect is decrease in nth otto. Regardless of the compression ratio.
the reason that efficiency increases with compression ratio is it raises the temperature at which the heat is added to the working fluid. The work input is recovered during the expansion phase of the cycle- it is not lost.
| stackexchange/physics |
some decades ago regge and wheeler began a pioneering study of a small perturbation in the background of a black hole in order to get information of the stability of this object @xcite , a problem that was continued by zerilli @xcite .
the oscillations found in these studies are not normal modes due to the emission of gravitational waves ; thus , their frequencies are complex and , as a result , the oscillations are damped .
the terminology quasinormal mode ( qnm ) and quasinormal frequency ( qnf ) , aiming to name these new modes and their frequencies , was first pointed out by vishveshwara @xcite and press @xcite . although initially studied in black hole backgrounds , the concept of qnm applies to a much broader class of systems .
the qnms of black holes were first numerically calculated by chandrasekhar and detweiler @xcite showing that the amplitude is dominated by a ringing characteristic signal at intermediate times .
the qnms are independent of the particular initial perturbation that excited them . the frequencies and damping times of the oscillations depend only on the parameters of the black hole and are , therefore , the `` footprints '' of this structure .
soon , the connection of qnms to astrophysics was established by noting that their existence can lead to the detection of black holes through the observation of the gravitational wave spectrum .
the interest in qnms has motivated the development of numerical and analytical techniques for their computation ( see @xcite for a review ) .
also , the study of the quasinormal spectrum gives information about the stability aspects of black hole solutions using probe classical matter fields ( scalar , electromagnetic , spinorial ) evolving in the geometry without backreacting on the spacetime background .
much has been done in that direction , not only in four dimensions @xcite@xcite , but also in two @xcite , and in more than four @xcite . aside from the study of the stability of the solutions , the qnfs are important in the context of the gauge - gravity correspondence , whose most celebrated example is the duality between the type iia - b string theory in @xmath1 spacetime and the four - dimensional supersymmetric yang - mills theory @xcite .
such a correspondence can be generalized for those cases in which there is an event horizon in the gravity side . in this case
the hawking temperature of the black hole is related to the temperature of a thermal field theory defined at the anti - de sitter ( ads ) boundary .
also , as a consequence of the correspondence , the quasinormal spectrum corresponds to the poles of thermal green functions @xcite , more precisely , the inverse of the imaginary part of the fundamental quasinormal frequency can be interpreted as the dual field theory relaxation time @xcite . another interesting application of qnms appears in the context of black hole thermodynamics .
some decades ago bekenstein @xcite suggested that the horizon area of a black hole must be quantized , so that the area spectrum has the form @xmath2 , with @xmath3 a dimensionless constant to be determined .
the first proposal to calculate this constant through qnms was made by hod @xcite .
accordingly , the real part of the asymptotic quasinormal mode can be seen as a transition frequency in the semiclassical limit , and its quantum emission causes a change in the mass of the black hole , which is related to the area . in this way , the constant @xmath3 for a schwarzschild black hole was determined as @xmath4 .
later , kunstatter @xcite repeated the calculation quantizing the adiabatic invariant @xmath5 via the bohr - sommerfeld quantization and using the real part of the qnf as the vibrational frequency .
the result was exactly the same as hod s .
however , recently maggiore @xcite pointed out that qnms should be described as damped harmonic oscillators , thus , the imaginary part of the qnf should not be neglected , and the proper physical frequency is the module of the entire qnf . moreover , when considering the quantization of the adiabatic invariant , the frequency to be considered is that corresponding to a transition between two neighboring quantum levels . with this identification ,
the constant @xmath3 for a schwarzschild black hole becomes @xmath6 , a result that coincides with the value calculated by other methods @xcite .
the consequences of hod s and maggiore s proposals were promptly studied in several spacetimes @xcite . in this paper , we are interested in the study of the stability of the @xmath0 , three - dimensional lifshitz black hole found in the context of the so - called new massive gravity ( nmg ) @xcite . moreover , as an application of our qnm results we aim to calculate the area spectrum of this black hole .
nmg is a novel parity - preserving , unitary @xcite , power - counting super - renormalizable @xcite , three - dimensional model describing the propagation of a massive positive - energy graviton with two polarization states of helicity @xmath7 in a minkowski vacuum , whose linearized version is equivalent to the pauli - fierz theory for a massive spin-2 field in three dimensions .
the action of nmg consists of a `` wrong sign '' einstein - hilbert term plus a quadratic curvature term given by a precise combination of the ricci tensor and the curvature scalar , which introduces a mass parameter @xcite . as with other massive gravity theories ,
nmg also admits black hole - type solutions with several asymptotics and additional parameters @xcite .
even though this last feature could challenge the usual einstein - hilbert gravity , it is seen that the definition of mass in this new type of black holes is a conserved charge computed from a combination of the black hole parameters , which satisfies the first law of thermodynamics .
a study of qnms in these static new type of black holes has been performed in @xcite .
the black holes we take into account for our study are asymptotically lifshitz , _
i.e. _ , they exhibit the anisotropic scale invariance , @xmath8 , @xmath9 , where @xmath10 is the dynamical critical exponent .
specifically , we deal with the solutions found for the particular case of @xmath0 and a precise value of the mass parameter @xcite .
the general class of these solutions are important in the context of gauge - gravity duality @xcite and were also investigated in other background theories @xcite .
no stability study of black holes with lifshitz asymptotics in three dimensions in the scenario of nmg has been performed yet .
we aim to give some contribution to this issue by considering the qnf of scalar and spinorial matter fields in the probe limit , _ i.e _ , there are no backreaction effects upon the asymptotically lifshitz black hole metric .
spinor fields have been extensively studied in general relativity @xcite@xcite , and their quasinormal frequencies have also been considered @xcite@xcite@xcite .
the paper is organized as follows . in section 2
we introduce the lifshitz black holes and discuss their causal structure .
sections 3 and 4 are dedicated to the study of stability under scalar and spinorial perturbations with special emphasis on the massless spinor for the latter . in section 5
we present the numerical analysis for both kinds of perturbations showing the qnms and the corresponding qnfs computed in each case .
section 6 is devoted to the calculation of the area spectrum of these black holes as an application of our quasinormal spectrum .
finally , we discuss our results and conclude in section 7 .
in this section we review the black hole solutions we will consider within this paper , and we comment some of their features .
the nmg theory @xcite is defined by the @xmath11-dimensional action , @xmath12\,,\ ] ] where @xmath13 is the so - called `` relative '' mass parameter , and @xmath14 is the three - dimensional cosmological constant . defining the dimensionless parameters , @xmath15 and @xmath16
, it is found that the theory exhibits special properties at the points @xmath17 .
when looking for black hole solutions with lifshitz asymptotics , it is precisely at the point @xmath18 , @xmath19 , with lifshitz scaling @xmath0 , where the field equations turn out to be solved by @xcite @xmath20 where @xmath21 and @xmath22 with @xmath23 an integration constant and @xmath24 .
also , the nmg admits as a solution , the well - known baados - teitelboim - zanelli ( btz ) black hole with the dynamical critical exponent @xmath25 . as we shall see below in more detail
, this metric ( [ metric ] ) exhibits a regular single event horizon located at @xmath26 and a spacetime singularity at @xmath27 .
besides , the surface @xmath28 acts as a one - way membrane for physical objects as we can see from the norm of a vector @xmath29 normal to a given surface @xmath30 .
since @xmath30 has to be null in order to be a one - way membrane , the norm of @xmath29 must be null as well , _
i.e. _ , @xmath31 , which occurs at @xmath28 . from the behavior of the kretschmann invariant for the metric ( [ metric ] ) , @xmath32\,,\ ] ] we see that , for @xmath33 @xmath34 and for @xmath35 @xmath36 thus , the black hole solution has a genuine spacetime singularity at the origin @xmath27 and an event horizon at @xmath28 . nevertheless , to see if the singularity is timelike , spacelike , or null we have to construct the penrose - carter diagram .
first of all , we must remove the coordinate singularity at @xmath28 . rewriting the metric in terms of null
coordinates @xmath37 @xmath38 where @xmath39 is the tortoise coordinate shown in the next section , we get @xmath40 which is manifestly regular at @xmath28 .
finally , to construct the penrose - carter diagram ( fig.[penrose ] ) we use the following set of null coordinates @xmath41 with @xmath42 and @xmath43 .
is light - like and covered by a regular event horizon @xmath44.,height=302 ] from this diagram we see that the spacetime singularity is located at @xmath27 , as previously observed from the behavior of the kretschmann invariant .
moreover , it is light - like and covered by a regular event horizon at @xmath28 .
in this section , we analyze the behavior of a scalar field perturbation in the background of a three - dimensional lifshitz black hole .
the scalar field obeys the klein - gordon equation , @xmath45 where @xmath13 is the mass of the field @xmath46 . performing the decomposition @xmath47
the klein - gordon equation takes the form , @xmath48 even though this equation has an analytical solution , as we will see in what follows , it is also useful to check the numerical results . with this goal
we further decompose @xmath49 , where the _ tortoise _ coordinate @xmath39 is given by @xmath50 \,.\ ] ] in this way the klein - gordon equation reduces to @xmath51 where @xmath52 is the scalar effective potential given by @xmath53 now let us come back to the issue of finding an exact solution for eq.([kg3 ] ) .
we set the time dependence of the field @xmath54 as @xmath55 and redefine the radial coordinate as @xmath56 .
thus , eq.([kg3 ] ) turns out to be @xmath57 r=0 \,,\ ] ] whose solution is given in terms of heun confluent functions , @xmath58 where @xmath59 and @xmath60 are integration constants , while @xmath61 , and @xmath62 .
imposing the dirichlet condition at infinity we set @xmath63 . in order to apply the boundary condition of in - going waves at the horizon we use the following connection formula @xcite , @xmath64 this formula connects a solution around the singular regular point @xmath65 to the corresponding solution about the singular regular point @xmath25 of the confluent heun equation given by @xmath66 h ' + ( dz-\epsilon ) h=0\,.\ ] ]
the parameters @xmath67 and @xmath30 are obtained from @xmath68 and @xmath69 is related to @xmath70 as @xmath71 thus , near @xmath72 eq.([solr ] ) can be written as @xmath73 with @xmath74 as constants .
as we are looking for quasinormal frequencies with negative imaginary parts , which give stable solutions , we find that for @xmath75 we need @xmath76 .
thus , the quasinormal frequencies are @xmath77\,,\ ] ] where @xmath78 is a positive integer .
the imaginary part of the fundamental frequency ( @xmath79 ) is negative provided that @xmath80 while the asymptotic frequency ( @xmath81 ) is given by @xmath82 thus , since the imaginary part of the quasinormal frequencies is negative provided that the parameters respect the relation ( [ condition ] ) , we can conclude that the model is stable under scalar perturbations .
in this section , we are going to consider a spinorial field as a perturbation in the spacetime given by the three - dimensional lifshitz black hole .
we analyze the covariant dirac equation for a two component spinor field @xmath83 with mass @xmath84 .
this equation is given by @xmath85 where greek indices refer to spacetime coordinates @xmath86 , and the latin indices enclosed in parentheses describe the flat tangent space in which the triad basis @xmath87 is defined .
the spinor covariant derivative @xmath88 is given by @xmath89\,,\ ] ] where @xmath90 is the spin connection , which can be written in terms of the triad @xmath87 as @xmath91 where @xmath92 are the metric connections .
the @xmath93 denotes the usual flat gamma matrices , which can be taken in terms of the pauli ones . in this work
we take @xmath94 , @xmath95 , and @xmath96 .
we can write the triad basis @xmath87 for the metric ( [ metric ] ) as follows : @xmath97 and the metric connections , @xmath98,\hspace{0.3cm}\gamma^{1}_{\phantom{1}11}=\frac{d}{dr}\left[\ln\left(\frac{r^{2}}{\delta}\right)^{1/2}\right],\hspace{0.3 cm } \gamma^{1}_{\phantom{1}00}=\frac{\delta}{2r^2}\frac{d}{dr}\left[\frac{a(r)\delta}{r^{2}}\right],\hspace{0.3cm}\gamma^{1}_{\phantom{1}22}=-\frac{\delta}{r},\hspace{0.3cm}\gamma^{2}_{\phantom{2}12}=\frac{1}{r}\,.\ ] ] using these quantities it is straightforward to write down the expressions for spin connection components . in the present case , we have only two nonvanishing components , @xmath99 at this point we are able to write the dirac equation for the two component spinor @xmath100 which turns to be the set of coupled differential equations @xmath101\psi_{2}-\mu_{s}\psi_{1}=0\,,\label{dirac1 } \\ -\frac{ir}{\sqrt{a(r)\delta}}\partial_{t}\psi_{1}+\frac{i\sqrt{\delta}}{r}\partial_{r}\psi_{1}-\frac{i}{r}\partial_{\phi}\psi_{2}+\frac{i}{4}\left[\frac{a(r)'\delta}{a(r)r}+\frac{\delta'}{r\sqrt{\delta}}\right]\psi_{1}-\mu_{s}\psi_{2}=0\,.\label{diracb}\end{aligned}\ ] ] in order to simplify our problem , we redefine @xmath102 and @xmath103 as @xmath104^{1/4}e^{-i\omega t+im\phi}\phi_{+}(r),\nonumber \\ \psi_{2}&=&\left[a(r)\delta\right]^{1/4}e^{-i\omega t+im\phi}\phi_{-}(r)\,,\end{aligned}\ ] ] and the tortoise coordinate as in the scalar case ( [ tortoise ] ) , @xmath105 thus , we can rewrite eqs.([dirac1 ] ) and ( [ diracb ] ) as @xmath106 where @xmath107 . and @xmath108 for different values of black hole mass @xmath23.,width=264,height=340 ] furthermore
, we define a new function @xmath109 , a new rescaling for the spinorial components @xmath110 , and a new _ tortoise _
coordinate @xmath111 through the expressions , @xmath112 in this way eqs.([dirac2 ] ) and ( [ dirac2b ] ) become @xmath113 where @xmath114 is the so - called superpotential , @xmath115 notice that when @xmath116 , eq.([superpotential ] ) reduces to the btz superpotential @xcite . finally , letting @xmath117 we have @xmath118 where @xmath119 are the superpartner potentials , @xmath120 which in the case of a massless spinor ( @xmath121 ) reduces to @xmath122
in this section , we numerically solve eqs.([schrod - sc ] ) and ( [ dirac - final ] ) , which correspond to the scalar and massless spinorial perturbations , respectively .
although in the scalar case we found an analytical solution and the corresponding qnf , our motivation to perform the numerical analysis is to verify the applicability of certain numerical methods in asymptotically lifshitz spacetimes . in particular , it would be interesting to check if the horowitz - hubeny method @xcite works well when finding the qnf . using the finite difference method ,
we define @xmath123 , @xmath124 , and rewrite eqs.([schrod - sc ] ) and ( [ dirac - final ] ) as @xmath125 which can be rearranged as @xmath126 the initial conditions @xmath127 and @xmath128 define the values of @xmath129 for @xmath130 and @xmath108 and we use eq .
( [ diffin_rearranged ] ) to obtain the values of @xmath129 for @xmath131 .
at @xmath132 we impose dirichlet boundary conditions since @xmath133 tends to infinity as @xmath134 tends to zero .
the numerical solution is stable if @xmath135 where @xmath136 is the largest value of @xmath137 in our domain .
this condition is verified in all cases studied here .
now we are going to analyze the potential for the scalar case . by rewriting eq.([sc - pot ] ) in terms of a new variable @xmath138 , we obtain @xmath139\,,\ ] ] where @xmath140 .
the parable in brackets tends to infinity as long as @xmath141 , which is consistent with the breitenlohner - freedman - type bound for the present case .
the roots of this polynomial potential are given by @xmath142\,.\end{aligned}\ ] ] and @xmath108 varying the azimuthal parameter @xmath143 .,width=264,height=340 ] if @xmath144 , we see that @xmath145 .
thus , going back to the original variable @xmath146 , the roots of the potential are @xmath27 with double multiplicity , @xmath147 and @xmath148 ( @xmath149 and @xmath150 are excluded as @xmath151 ) .
then , since @xmath152 is the biggest root and @xmath52 tends to @xmath153 when @xmath146 tends to @xmath153 , the potential is positive - definite in the region @xmath154 .
therefore , the quasinormal modes for @xmath144 are necessarily stable @xcite . the numerical results regarding the decay of the scalar field are shown in figs.[escalar_varm]-[escalar_vark ] , and the comparison between the numerical and analytical results is displayed in fig.[comparacao ] .
our results reinforce the conclusion already found analytically ; the @xmath0 lifshitz black hole is stable under scalar perturbations .
moreover , according to fig.[comparacao ] , the numerical results have a very good agreement with the analytical calculation .
figure [ comparacao ] shows that the horowitz - hubeny method gives unreliable results . in @xcite
, it is argued that the frequencies do not converge as required by the method , and that may be explained by ill - conditioned polynomials .
however , in this work , the frequencies converge , but they do not agree with the analytic expression and with the results from finite difference method . in @xcite ,
the authors find cases where this method does not work either , and they do so by comparing the results with other methods . for instance , they find that the method is unreliable for dimensions bigger than 6 . even in the original work @xcite the method is unreliable for small black holes , and there is no clear explanation for this limitation . in our case
the asymptotic behavior of the black hole under study might play an important role in the convergence of the method .
nevertheless , a general criteria for the convergence of the horowitz - hubeny method remains an open question .
in the case of the massless spinorial perturbation the superpartner potentials ( [ potential - weyl ] ) can be written as @xmath155\,,\ ] ] and their derivative turns to be @xmath156\right\ } \,.\ ] ] we can see that outside the event horizon @xmath157 is positive - definite if @xmath158 , and @xmath159 if @xmath160 . whereas @xmath161 is positive - definite if @xmath160 , and @xmath162 if @xmath158 .
moreover , we notice that if @xmath163 , we have a free - particle case .
the decaying behavior of the massless spinor is given in figs.[espinorm10]-[espinorm15 ] .
thus , we conclude that the @xmath0 lifshitz black hole is stable under massless spinorial perturbations . and black hole mass @xmath164 for different values of the azimuthal parameter @xmath13.,width=264,height=340 ] and black hole mass @xmath165 for different values of the azimuthal parameter @xmath13.,width=264,height=340 ]
one of the applications of our results for the quasinormal frequencies is the relation they have with the area spectrum of a black hole . according to maggiore @xcite ,
the proper physical frequency of the damped harmonic oscillator equivalent to the black hole quasinormal mode is given by @xmath166 where @xmath167 and @xmath168 stand for the real and imaginary part of the asymptotic qnf , respectively .
thus , using ( [ asymptotic ] ) we have @xmath169 according to myung _
et al . _
@xcite , the arnowitt - deser - misner ( adm ) mass of the lifshitz black hole we are studying is given by @xmath170 applying maggiore s method , we calculate the adiabatic invariant @xmath171 as @xmath172 where @xmath173 is the change of proper frequency between two neighboring modes , _
i.e. _ , @xmath174 thus , @xmath175 which is quantized via bohr - sommerfeld quantization in the semiclassical limit . recalling that the horizon area of the black hole is given by @xmath176 , with @xmath177 , and using ( [ invariant ] ) , we arrive at the result , @xmath178 with @xmath179 an integer number .
therefore , we see that the horizon area for the @xmath0 lifshitz black hole is quantized and equally spaced .
this result would not be expected for a theory containing higher order curvature corrections since , in general , black hole solutions in such theories do not have a proportional relation between their entropy and area , and consequently , both of them ( if any ) should not be quantized with an equally spaced spectrum for large quantum numbers @xcite .
however , it was already demonstrated that the @xmath0 , three - dimensional lifshitz black hole has an entropy proportional to its horizon area @xcite .
thus , our result ( [ areasp ] ) also states that the entropy should be quantized with a spectrum evenly spaced .
nevertheless , we should stress that a generalization of this result for lifshitz black holes should wait for the calculation of the area spectra of other black holes of such a type . solely these studies can give a definite answer on this subject .
we have studied the stability of the three - dimensional lifshitz black hole under scalar and spinorial perturbations in the probe limit through the computation of quasinormal modes . in addition , we have found the event horizon area quantization as an application of the results for quasinormal modes using maggiore s prescription . regarding the stability ,
we have not found unstable quasinormal modes in the range of parameters that we have considered ; all the frequencies have a negative imaginary part indicating that the modes are damped and thus , the perturbations decay , leaving the system stable against this particular sort of probe fields . in the case of a scalar probe field
, such results totally agree with the analytical expressions for the quasinormal frequencies ; they show a very large imaginary part and a very small real part .
these modes are almost purely imaginary .
we have implemented two different numerical methods in order to obtain the quasinormal frequencies and modes : the finite difference and the horowitz - hubeny methods .
the former allows us to obtain the temporal behavior of the fields showing all the stages of the decay , while the latter gives only the frequencies values .
as explained in section [ numerical ] , the horowitz - hubeny method failed in the calculation of the scalar frequencies as it can be observed in fig.[comparacao ] . on the contrary , the finite difference method has a very good agreement with the analytical expression ( [ freq_analitico ] ) .
apart from the numerical factor , the asymptotic scalar frequency found in the present work is the same as the one calculated in the hydrodynamic limit of the scalar perturbations in the context of gauge - gravity duality@xcite . regarding the spinorial perturbation ,
our numerical results show that the probe massless spinor decays and , thus , the @xmath0 lifshitz black hole is stable also under spinorial perturbations . as a by - product we also obtained the area spectrum of this black hole by means of the application of maggiore s method using our results for the scalar asymptotic quasinormal frequencies .
equation ( [ areasp ] ) shows that the horizon area is quantized and equally spaced .
furthermore , in light of the conclusions shown in @xcite , the corresponding entropy should also have an evenly spaced spectrum . finally ,
although we have demonstrated the stability of the @xmath0 , three - dimensional lifshitz black hole under scalar and spinor perturbations , we should stress that the definite answer on stability should come from the gravitational perturbations , in particular , from the tensor part of the metric perturbation .
it is well known that einstein gravity in three dimensions has no propagating degrees of freedom , however , the massive versions of the theory , _ e.g. _ , nmg , allow the propagation of gravitational waves .
albeit this subject deserves further study , the calculation of metric perturbations is a formidable task that is out of the scope of the present paper . the analysis is not dead easy because the perturbation equation is a fourth order differential equation .
thus , some other techniques need to be used together with the traditional qnm analysis @xcite .
this study will be discussed elsewhere .
we thank e. abdalla and a. m. da silva for enlightening discussions and remarks .
we also thank e. papantonopoulos and g. giribet for reading the manuscript and pointing out useful suggestions , and j. oliva for interesting comments .
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neutrino flavor transformations are determined by the elements of the pmns matrix @xcite and the differences between the squares of neutrino mass eigenvalues .
pmns matrix represents the mixture between flavor and mass eigenstates of neutrinos and is conventionally decomposed as shown in ( [ pmns ] ) .
neutrino oscillation experiments can yield the best estimations for some of those parameters , which has been demonstrated by sno @xcite and kamland @xcite .
@xmath0 \nonumber \\ & = & \left [ \begin{array}{ccc } 1 & 0 & 0 \\ 0 & c_{2 3 } & s_{2 3 } \\ 0 & -s_{2 3 } & c_{2 3 } \end{array } \right ] \left [ \begin{array}{ccc } c_{1 3 } & 0 & s_{1 3}e^{-i\delta } \\ 0 & 1 & 0 \\ -s_{1 3}e^{i\delta } & 0 & c_{1 3 } \end{array } \right ] \nonumber \\ & \times & \left [ \begin{array}{ccc } c_{1 2 } & s_{1 2 } & 0 \\ -s_{1 2 } & c_{1 2 } & 0 \\ 0 & 0 & 1 \end{array } \right ] \left [ \begin{array}{ccc } e^{i\alpha_1/2 } & 0 & 0
\\ 0 & e^{i\alpha_2/2 } & 0 \\ 0 & 0 & 1 \label{pmns } \end{array } \right],\end{aligned}\ ] ] where @xmath1 , @xmath2 , @xmath3 is the phase factor ( non - zero if neutrino oscillation violates cp symmetry ) . @xmath4 and @xmath5 majorana phase factors ( non - zero only if neutrinos are majorana particles ) , to which neutrino oscillation experiments are not sensitive . besides the pmns matrix , neutrino oscillations depend on mass eigenvalues or , more precisely , on the difference between the squared mass eigenvalues .
if there are three neutrino mass eigenvalues , then there are only two independent differences , the third being either a sum or a difference of the other two .
neutrinos studied in experiments are produced in certain flavor eigenstates with known abundances of each of them or , as an important special case , in only one flavor eigenstate .
for example , neutrinos are generated in the atmosphere with the known @xmath6 ratio of about two for low energies ; solar neutrinos and reactor antineutrinos are , initially , all @xmath7 and @xmath8 , respectively .
detector sensitivity is , generally , flavor dependent .
in particular , the inverse beta decay , the primary method for detecting reactor antineutrinos since the very beginning of neutrino experiments @xcite , involves electron antineutrinos only . therefore , the number of detected neutrino events can be different from the no - oscillation expectation .
the deficit of observed neutrinos compared to no - oscillation prediction was first detected in a solar neutrino experiment @xcite .
however the rate information alone could not provide sufficient evidence to ascribe conclusively the phenomenon of neutrino `` disappearance '' to flavor oscillations . the energy dependence of neutrino oscillations not only changes the neutrino event rate but also distorts the observed neutrino energy spectrum .
the spectrum distortion provides more information about the pnms matrix components and neutrino mass eigenstates than rate studies alone can .
the inverse beta decay method offers excellent energy sensitivity , which is very valuable for the oscillation studes .
recoil smearing present in this reaction is small compared to detector energy resolution , the latter being the main limiting factor in the accuracy of @xmath8 energy measurement .
other advantages include a relatively large cross section of the reaction and , most importantly , very powerful background suppression due to the characteristic double - coincidence signature . the limitations of this method are the @xmath8 energy threshold of about 1.8 mev and weak directionality .
the success of a neutrino oscillation experiment depends not only on the characteristics of the detector and on the neutrino source but also on the proper choice of the distance between the two ( the baseline ) .
there is no single baseline optimal for all neutrino oscillation studies .
for example , the average baseline of kamland experiment , about 180 km , is fairly good for @xmath9 and especially for @xmath10 but not for @xmath11 , @xmath12 and @xmath13 .
moreover , such parameters as detector resolution , the amount , the nature of the background and the a - priori information about its properties can affect the optimal baseline value . a tunable baseline experiment , which implies movable detector or source , may have a big advantage here .
these considerations , along with the interest in studying terrestrial antineutrinos , led to the idea of a big kamland - like underwater detector @xcite .
the potential of such a detector for neutrino oscillation parameter measurements was the primary motivation for the study presented here .
however , the scope of the actual study is much wider and not limited to the hanohano project .
the results are in fact applicable to any similar medium - baselined experiment .
for baselines associated with current and near - future reactor based neutrino experiments ( up to hundreds of kilometers ) , the matter effects @xcite critical in solar neutrino studies are not significant , so the vacuum oscillation approximation can be used . as was mentioned above
, the inverse beta decay detection is sensitive to electron antineutrinos only .
reactors produce exclusively electron antineutrinos as well , so the observable effect is the apparent `` disappearance '' of a fraction of reactor - produced electron antineutrinos .
the @xmath8 `` survival '' probability is given by the formula @xcite : @xmath14 where @xmath15 . note that `` atmospheric '' mixing angle @xmath16 does not affect the @xmath7 survival and hence not measurable in electron neutrino disappearance experiments .
here , @xmath17 is the `` baseline '' , the distance between the @xmath8 source and the detector .
given the evidence from solar neutrino experiments @xcite that @xmath18 , and the knowledge that @xmath19 from superk @xcite , k2k @xcite , minos @xcite on the one hand and kamland @xcite on the other , only two neutrino hierarchies out of possible six are allowed with currently available data .
they are commonly referred to as `` normal hierarchy , nh '' ( @xmath20 ) and `` inverted hierarchy , ih '' ( @xmath21 ) ( fig . [ hierarchies ] ) .
the former implies that @xmath22 , the latter that @xmath23 , so the sufficiently precise measurement of the those squared mass differences should be enough to establish the neutrino mass hierarchy .
the measurement of @xmath12 , @xmath13 and the mass hierarchy with this approach is possible , in theory , only if @xmath11 is finite and , in practice , if this mixing angle is large enough .
moreover , if the `` solar '' mixing is maximum ( @xmath24 ) , the @xmath12 and @xmath13 become mutually indistinguishable , thus still ruling out the mass hierarchy study , although their values may still be determined without knowing `` which is which '' .
this maximum mixing is strongly disfavored by kamland @xcite and essentially excluded by solar eperiments @xcite .
unfortunately , the same can not be said about the @xmath11 since only the upper limit for this value exists today and there is no experimental evidence that it is not zero .
if it is , then future @xmath8 vacuum oscillation experiments are limited to probing @xmath9 and @xmath10 along with setting still better upper limits on the @xmath11 itself .
that said , global analysis shows a slight preference for non - zero @xmath11 @xcite .
a typical reactor @xmath8 spectrum @xcite multiplied by the inverse beta decay cross section @xcite is shown in figure [ raw ] , dotted .
the antineutrinos are generated in @xmath25 decays of short living fission products of initial fissionable fuel isotopes : @xmath26 , @xmath27 , @xmath28 , @xmath29 . for this study
, the ratio of the isotopes is taken the same as in @xcite .
such a spectrum can be observed at very short - baselined experiments ( baseline @xmath30 1 km ) , where oscillation effects are negligible . at much longer baselines ( 30 km and above ) , the `` solar '' oscillations governed by @xmath9 and @xmath10 lead to an energy - dependent deficit of the observed @xmath8 events .
the effect of those oscillations alone is the `` coarse '' oscillatory pattern of event deficit over the spectrum ( figure [ raw ] , dashed ) with a high amplitude ( determined by @xmath31 ) and a relatively low frequency ( determined by @xmath10 ) .
the amplitude of oscillations driven by the squared mass differences @xmath12 and @xmath13 is proportional to @xmath32 and much smaller than that of `` solar '' oscillations for any currently allowed value of this mixing angle . because @xmath12 and @xmath13 are known to be larger than @xmath10 , the frequency of those sub - dominant oscillations is higher .
a typical @xmath8 energy spectrum expected for a non - zero @xmath11 is shown in figure [ raw ] , solid .
the spectrum analysis approach has already been successfully used by kamland to set by now the best limits on @xmath10 and to confirm sno and superk values for @xmath9 . the idea to measure the remaining three of the five oscillation parameters by precision measurement of the sub - dominant oscillation pattern in a reactor @xmath8 disappearance experiment has been already suggested and thoroughly examined @xcite . in this paper , we examine the capacity of an intermeidate baseline ( 30 - 90 km ) reactor @xmath8 experiment for measuring @xmath9 , @xmath11 , @xmath10 , @xmath12 , @xmath13 and neutrino mass hierarchy .
although this study has been motivated by the project of a big underwater detector hanohano ( @xcite ) , we make no assertions specific for that particular choice .
a special emphasis is placed on the systematic uncertainties and technical limitations present in any real experiment . in our study of the sensitivity to each of the oscillation parameters we take into account the impact of those uncertainties , as well as some detector parameters and the baselines on the resulting performance to formulate in a quantitative way the requirements to which such an experiment must conform .
in this study , we consider the measurement of all the oscillation parameters to which such @xmath8 disappearance experiments are sensitive : @xmath9 , @xmath11 , @xmath10 , @xmath12 , @xmath13 .
three types of detector - related systematic uncertainties are considered which are present to some extent in any experiment and are capable of a non - trivial impact on the sensitivity to the target parameters .
although the success of the borexino experiment @xcite suggests that careful detector design can make the inverse - beta based @xmath8 detection almost background - free , geologically produced antineutrinos @xcite will technically remain a background source for a reactor @xmath8 study in the lower energy region .
what makes this background especially significant is the lack of exact information about its overall intensity and the relative amounts of antineutrinos produced in the `` uranium - radium '' and `` thorium '' decay series .
this amounts to two more systematic uncertainties which have to be left unconstrained within geologically feasible models .
the following detector - related uncertainties were accounted for : * the uncertainty in the predicted event rate .
it is sensitive to the number of target protons ( due to fiducial volume estimation error and uncertainty of the scintillator composition ) , the efficiency of coincidence selection cuts , and live time estimation error . for current similar experiments
, this error tends to be on the order of 1 to 5% .
below we refer to this as `` efficiency '' error .
* the uncertainty in the detector energy resolution estimation .
although often ignored in current experiments , it can have a considerable effect on the measurement of the @xmath11 mixing angle from medium baselines .
numerically , it can be quite big ( about 10% ) depending on the detector calibration options . * the `` linear '' energy scale uncertainty .
this is the uncertainty in the average number of photoelectrons produced by an 1 mev event .
the amount of this uncertainty depends on the detector calibration as well .
normally it can be made quite small ( around 1% ) but its impact on the resulting accuracy of the parameter estimation may still be noticeable .
the energy scale in scintillator - based detectors is in fact substantially non - linear , this non - linearity always producing additional systematic uncertainties which are often rather tricky to parametrize .
however the study of this error is very detector - specific , requires extensive monte - carlo simulations with real calibration data feedback and considering it at this stage would be too speculative . although , kamland internal studies indicate that the nonlinear energy scale uncertainty is less of an issue than the linear one which we can take into account now , hanohano or any other future experiment will have to revisit this issue , once the real experimental feedback from the detector becomes available . the geo - neutrinos yield two more systematic uncertainties : * total detectable terrestrial antineutrino flux , conventionally expressed in terrestrial neutrino units ( tnu ) defined as the number of inverse - beta decay interactions per @xmath33 free protons per year . *
the ratio of @xmath8 originating from the @xmath27 decay chain to those coming from the @xmath34 decay chain .
although geological models do provide some guidelines for the expected geo - neutrino flux and kamland was able to produce the first experimental measurement of the flux , these data are of little use for the purpose of future experiments , including hanohano , because the geo - neutrino estimation precision needed to produce an appreciable advantage over the `` agnostic '' approach is about one order of magnitude higher than available now .
since we ve included background and systematics in the analysis , the direct likelihood approach has been chosen over the combination of the matched digital filter and the fourier transform of the spectrum employed in the earlier publications dedicated to or motivated by hanohano project @xcite .
this approach facilitates the accommodation of the systematic uncertainties and the background .
the likelihood method used here is the unbinned statistical analysis similar to the one employed by kamland experiment @xcite . instead of the real experimental data , a series of `` experiments '' can be simulated as sequences of `` events '' with energies distributed according to the spectra distorted by different oscillation parameters ( including the background ) .
the potential sensitivity is essentially the ability of the data analysis to distinguish between different hypotheses about the oscillation parameter sets .
this study is based on the `` rate+shape '' likelihood function defined for a real or simulated experiment as : @xmath35 where @xmath36 are the event energies , n the number of observed events , @xmath37 the expected number of events ( given the set of parameters @xmath38 ) , @xmath39 @xmath8 energy spectrum normalized to @xmath40 ( after the distortion by the set of parameters @xmath41 ) .
note that while both @xmath42 and @xmath43 are denoted as vectors , these vectors are in different spaces .
the @xmath42 has as many dimensions as the sum of the number of @xmath8 and background events in the experiment , and is fixed for a given experiment .
the @xmath43 lies in the parameter space , its dimensionality being the number of unknown parameters to be fitted , and is variable .
the best fit is obtained by varying the parameter vector @xmath41 to achieve the maximum value of @xmath44 or its logarithm , the latter often being more convenient to calculate and handle .
after the best fit point @xmath45 has been found , the general prescription to evaluate the sensitivity to some individual parameter @xmath46 is the following : * make a small increment ( or decrement ) @xmath47 to the @xmath46 from the `` best fit '' point @xmath48 : @xmath49 . *
find a new point of maximum likelihood by varying all the parameters @xmath41 except for @xmath46 which is kept fixed at @xmath50 .
the new maximum @xmath51 over the subspace constrained by the requirement @xmath52 is not higher than the global maximum @xmath53 .
* repeat the above steps with varying @xmath47 until the condition @xmath54 is met for both positive and negative increments of @xmath47 .
the corresponding points @xmath55 and @xmath56 will limit the confidence range for the k - th parameter .
the value @xmath57 depends on the confidence level for which the range is to be determined . for an individual parameter variation and the confidence level equal to @xmath58 , @xmath59 . in general , for a cl of @xmath60 , @xmath61 .
when instead of a one - dimensional confidence range , a multidimensional confidence region in the parameter subspace is required , the values @xmath57 will be different but the general procedure will not change .
the same is true for the case of discriminating two discrete hypotheses , e.g. between the normal and the inverted neutrino mass hierarchies .
more detailed information on the likelihood analysis can be found in @xcite . for a simulated experiment
, the experimental points @xmath62 do not exist in the first place and are generated according to some reasonable choice of parameters @xmath41 . except for this initial stage ,
the rest of the analysis is the same as described above .
if the initial choice of the parameters to simulate the events is not too far off , this procedure will yield an accurate prediction for the sensitivity of the actual experiment .
systematic uncertainties are introduced by adding `` hidden '' parameters to the parameter space and allowing them to vary during the search for the maximum likelihood as well .
when some information about these values is available a `` penalty '' term is subtracted from @xmath63 to account for the fact that big deviations from the central values of those hidden parameters are unlikely .
if the parameters of uncertainty are normally distributed around their central value and if all systematic uncertainty parameters are uncorrelated , the `` penalty '' term takes on the form : @xmath64 where @xmath65 is the number of systematic uncertainty parameters , @xmath66 is the index of the parameter corresponding to the @xmath67-th uncertainty , @xmath68 is the deviation of the @xmath66-th parameter from its most probable value , and @xmath69 is the value of systematic error ascribed to the @xmath67-th uncertainty .
when some uncertainties are correlated , the penalty term becomes a more general positive definite quadratic form but for our current study that is not the case .
the full equation for the likelihood logarithm with systematic uncertainties takes on the form : @xmath70 in this work , we used the total of nine continuous parameters .
these are four neutrino oscillation parameters : @xmath71 , @xmath72 , @xmath10 , @xmath12 .
note that for each of the two mass hierarchies , @xmath13 is determined by the two other squared mass differences and has not to be introduced into the parameter space .
five parameters were dedicated to systematic uncertainties : two geo - neutrino parameters and three detector - associated systematic errors as described in the previous section .
the geo - neutrino parameters are left unconstrained , which is equivalent to infinite @xmath73 in ( [ penalty - term ] ) .
the default values for the systematic errors in `` efficiency '' , energy resolution estimation and energy scale were taken to be 2% , 8% and 1% , respectively , which is reasonably conservative for experiments of this kind .
additionally , two extreme cases were analyzed : the most `` optimistic '' one with the corresponding parameters fixed at zero deviations as if they were known exactly , and the most `` pessimistic '' one with those three uncertainties left unconstrained as well as geo - neutrino parameters .
although practically impossible , these limiting cases indicate how much sensitivity can be gained by improving the systematics and , conversely , how much would be lost if the systematic errors of the real experiment happen to be worse than expected .
the `` solar '' mixing angle has been fairly well constrained by sno @xcite and kamland @xcite .
our computations suggest that there is still an opportunity for a significant improvement , though .
this measurement is moderately sensitive to detector - based systematic uncertainties but the terrestrial antineutrino background is much more troublesome ( fig [ ss12 ] ) .
these background decrease the sensitivity by about a factor of two and drives the optimum baseline for this parameter to about 60 km , which conflicts with the goal of measuring @xmath11 and @xmath12 in the same experiment as well . constraining the geo - neutrino flux would change the situation , but currently there seems to be no way of doing that . the geo - neutrino flux measurements made by kamland @xcite are not nearly precise enough to improve the situation noticeably and , besides , not directly applicable to a future experiment located elsewhere , especially in the ocean . even with that background and the associated uncertainty , the sensitivity of the medium - baseline experiment is noteworthy . for a 10 kt detector at 50 km from a 6 gwt nuclear plant ,
an exposure of 300 gigawatt - kiloton - years ( 5 years ) is required to achieve the one - sigma confidence range of 0.01 in @xmath74 , which is about 5 times better than the current best estimation . at 60 km
, the same precision can be achieved with just above one - third of this exposure .
although higher energy resolution is always better , the @xmath9 study does not exhibit appreciable dependence on this parameter and @xmath75}$ ] is almost as good as @xmath76}$ ] .
of the detector - associated systematics , the most significant is the `` efficiency '' uncertainty .
the measurement of this parameter by kamland is more difficult to improve on .
for example , the target sensitivity for hanohano is @xmath77 , which would be about three times better than the current best estimation . as our calculations suggest ,
this can be achieved in 300 gigawatt - kiloton - years at the 60 km baseline or in 450 gigawatt - kiloton years from 50 km .
still longer baselines offer better sensitivity for this particular study ( fig [ dms12 ] ) but would be clearly sub - optimal for all other oscillation parameters .
the part ( b ) of the plot shows the dramatic effect of terrestrial neutrino background and , particularly , the uncertainty of this background . without geo - neutinos , the same detector would be four times more efficient at 60 km and seven times at 50 km . the fact that geo - neutrinos drive the optimum baseline towards longer distance may seem somewhat counter - intuitive .
the shorter the baseline , the higher the reactor @xmath8 rate , so the relative fraction of terrestrial @xmath8 background is smaller and should have a smaller effect .
however , at shorter baselines , the reactor @xmath8 deficit due to oscillations appears mostly in the lower - energy zone where it is harder to separate from the variation in the terrestrial neutrino background . like the @xmath9 measurement
, this study is not demanding of detector energy resolution and not particularly sensitive to detector - associated systematics .
this is a very important oscillation parameter not only because of its theoretical significance but also because its value defines the amplitude of the sub - dominant high - frequency oscillations governed by @xmath78 and @xmath79 .
only if @xmath11 is not zero ( and not too small ) is it possible to measure those mass squared differences in @xmath8 disappearance experiments .
currently , only an upper bound for this angle is known ( from the chooz experiment @xcite ) : @xmath80 .
several experiments are proposed or already under construction to set better limits and the hanohano detector can contribute to those efforts .
the sensitivity profiles ( figure [ ss13 ] ) show that medium baselines ( above 30 km ) are not optimal for this study and much shorter ones are better from the statistical standpoint
. however even at 50 km the absolute sensitivity can be quite impressive with a big detector . except for the longest baselines ( 60 km and above ) which are clearly sub - optimal
, this study is not severly affected by the geo - neutrino background and its uncertainties .
the systematics of the detector itself , however , play a more important role here . at 50 km ,
the main systematic error is the uncertainty of energy resolution estimation , followed by the `` efficiency '' error . at shorter baselines the `` efficiency '' uncertainty dominates .
although the medium baselines have a strong statistical disadvantage for @xmath11 measurement , they also have the compelling feature that systematic uncertainties do not ruin the measurement . unlike the shorter baseline experiments where
relatively more information is obtained through the neutrino event rate , the spectrum shape distortion characteristic of medium baseline is not so easy to imitate by any of the detector systematic errors .
this means that , in the long run when even better accuracy for @xmath11 is required , medium baseline experiments may prove to be more robust .
figure [ ss13r ] exhibits another important feature of this measurement : its energy resolution dependence . although not as critical as for the hierarchy study ( below ) , the effect of detector energy resolution is quite noticeable . compromising this parameter to @xmath75}$ ] from the @xmath76}$ ] ( as projected for hanohano )
will cost about 2.5 times the exposure .
unlike all previously considered parameters where the potential sensitivity of an experiment could be predicted more or less accurately based just on the @xmath8 exposure , this measurement depends on the value of @xmath11 which is still unknown .
any quantitative sensitivity prediction makes sense only with some particular value of @xmath11 in mind .
the larger the mixing angle , the easier it is to determine @xmath12 , @xmath13 and neutrino mass hierarchy .
it has been found that the sensitivity scales approximately as the square of @xmath32 . in other words , getting the same sensitivity in @xmath12 , @xmath13 and neutrino mass hierarchy if @xmath81 will take four times the exposure required if @xmath82 . in this paper we carried out calculations for two scenarios : @xmath83 , and @xmath84 .
another ambiguity associated with the study of @xmath12 and @xmath13 follows from the closely related question of neutrino mass hierarchy .
depending on the actual value of the mixing angle @xmath11 , the neutrino mass hierarchy may turn out unfeasible to establish at an adequate cl . at the same time , within each of the two possible hierarchies , stringent limits on both @xmath12 and @xmath13 may still be set with reasonable exposures .
since the ambiguity is at worst only a two - fold one , it makes sense to estimate the `` known - hierarchy '' sensitivity to either @xmath12 or @xmath13 .
figure [ dms13 - 50 ] and [ dms13 - 25 ] show that shorter baselines are better for this study , although this trend is not as pronounced as with @xmath11 measurement and actually reverses below 25 km .
it is clear that @xmath12 study is not systematics - constrained , including the systematics from geo - neutrinos . on the other hand ,
the dependence on energy resolution for this measurement is even stronger than that for @xmath11 ( figure [ dms13r-50 ] and [ dms13r-25 ] ) .
like the @xmath12/@xmath13 measurement , the hierarchy study depends on the actual value of @xmath11 .
our calculations suggest that for any @xmath11 it takes more statistics to make a high confidence level conclusion about the hierarchy than to measure @xmath12 and @xmath13 to an accuracy of @xmath85 .
this makes reliable hierarchy determination with a 10 kt detector feasible only if the mixing angle turns out to be quite high ( @xmath86 ) .
the sensitivity dependence on this value is approximately quadratic in the exposure as well .
the baseline profile of the sensitivity to the hierarchy is shown in figure [ hier ] .
after taking into account the geo - neutrino background and the uncertainties the optimum baseline remains in the same range as was found earlier with less comprehensive models @xcite 50 km or slightly more . of the systematic errors ,
the most damaging is the geo - neutrino flux uncertainty , although its effect is not as decisive as for the solar parameter studies .
the hierarchy study proves to be the most demanding of the detector energy resolution ( figure [ hier - r ] ) . even within the best values for that parameter of the detector achievable today the sensitivity dependence on
the energy resolution enters its asymptotic 4-th power curve .
in particular , this implies that between two detectors of the same photocathode area but different volumes , the bigger detector will offer _ inferior _ sensitivity : all other parameters being equal , a smaller relative photocathode coverage will lead to lower resolution which will prevail over the higher reactor @xmath8 statistics .
theoretically , the mass hierarchy study is secondary to the measurement of @xmath12 and @xmath13 and is determined immediately after those mass differences are found .
the analysis of the oscillated @xmath8 energy spectrum yields all mass differences ( provided , @xmath87 and @xmath88 ) . in practice , however , the squared mass differences can be measured with limited accuracy only and at a limited cl
. this may not be sufficient to determine the hierarchy .
moreover , it has been found that for any combination of @xmath89 and @xmath90 there exists another one ( denoted below as @xmath91 and @xmath92 ) that delivers a similar oscillation pattern despite comprising the oppositie mass hierarchy .
the similarity is never perfect and , given enough statistics , it is always possible to distinguish between the two spectra but it may take much more exposure to discriminate between those `` conjugate '' opposite hierarchy solutions than to constrain the squared mass differences within one of the solutions with a remarkable precision . in figure [ likedef ] ,
the curves provide the measure of relative `` unlikeliness '' of an alternative hypothesis , assuming normal hierarchy and @xmath93 , for which the experiment was simulated .
zero @xmath94 means an indistinguishable hypothesis , the higher its value , the less statistics is needed to discriminate the hypothesis .
solid lines show the normal hierarchy and dotted lines show the inverted one .
the dashed vertical lines through the centers of the dotted curves point to the @xmath95 which combined with the inverted hierarchy provide the closest similarity to the simulated physical spectrum .
comparison of figure [ likedef](a ) and figure [ likedef](b ) explains why the 60 km baseline offers better hierarchy discrimination than 40 km , although the latter yields significantly better sensitivity to @xmath12/@xmath13 within each of the two hierarchies : the vertex of the quasi - parabolic dotted curve is located higher for 60 km .
the `` conjugate '' @xmath95 for a given real @xmath95 is not the same for different baselines , which implies that two measurements at different baselines may offer improved efficiency . for instance , the allowable values of @xmath95 to which the 60 km baselined measurement is least sensitive are much better excluded at 40 km and vice versa . in case of a land - based detection , a multiple - detector configuration can be considered .
hanohano , additionally , can use the advantage of its movability and make two consecutive exposures instead of one twice as long . indeed , as the comparison between figure [ likedef](c ) and figure [ likedef](d ) shows , the combination of 60 and 40 km baselined observations should provide a better hierarchy resolution than one twice as long at the practically optimal 50 km .
although the advantage is marginal , we considered only a two - baseline combination with equal exposures .
a more systematic optimization with different exposures and possibly more than just two baselines should offer further gains .
with a single detector and a 300 kiloton - gigawatt - year exposure and a 5 - 6 gw thermal power @xmath8 source , both @xmath10 and @xmath9 are expected to be measured with the accuracy of 1% , a three to five time improvement on the current best limits @xcite .
an experiment with a more powerful reactor @xmath8 source but the same exposure due to a smaller detector size or a shorter livetime will have a slight advantage because of the relatively smaller geo - neutrino effect .
detector - associated systematic uncertainties do not appear to be a significant limiting factor in the resulting accuracy .
these studies are not particularly sensitive to the detector resolution and @xmath96}$ ] would be quite sufficient .
however the expected sensitivity , especially that for @xmath10 , will be severely handicapped by the presence of geo - neutrinos and in particular by the lack of accurate estimation for the intensity of this background source , effectively turning its value into yet another systematic uncertainty the dominating one for this study .
this is not a `` hard '' limitation since geo - neutrinos , having a different spectrum , can not mimic the reactor @xmath8 oscillaton pattern , but rather an efficiency impairment .
the study of the @xmath11 mixing angle is different , in that the medium baselines that this study deals with are not optimal . on a per - event basis ,
the baseline dependence of sensitivity is rather flat , but short baselines gives quadratically higher event rate and hence lower statistical error . on the other hand , longer baselines offer more robustness with respect to the `` efficiency '' systematic uncertainty . given the careful design of hanohano or any similar ( considering the size and the baseline ) detector and its accurate calibration , it is still possible to reach an accuracy of better than 0.02 in @xmath97 evaluation , which is competitive with the dedicated experiments like double chooz and daya bay .
the sensitivity to this mixing angle does not exhibit strong dependence on its own real value .
in other words , setting the upper limit of 0.02 for @xmath32 if the angle happens to be zero takes about as much exposure as setting the range between 0.03 and 0.07 if the value is really 0.05 .
the measurement of @xmath12 and @xmath13 and the closely related question of neutrino mass hierarchy are common in their dependence on the actual value of @xmath11 . if the angle turns out to be big enough ( within currently allowed values )
, then some spectacular results are possible .
if it is zero or very small , nothing interesting can be measured with either haonhano or any other similar experiment .
the necessary exposure is approximately inversely quadratic to the value of @xmath32 in both cases , although the hierarchy measurement generally requires much more statistics . for a moderately optimistic scenario in which @xmath98 , hanohano or a similar experiment can yield a very good estimation for the values of the squared mass differences but
reliable mass hierarchy separation may call for prohibitively long exposures .
another feature that these measurements have in common is the requirement for the excellent energy resolution . generally , assuming either normal or inverted hierarchy , the problem of @xmath12 and @xmath13 becomes simpler , less demanding of the energy resolution and with higher chance of success for unfavorably small values of @xmath11
. even if the hierarchy question is not conclusively answered at that stage , the squared mass differences can still be measured , even though the remaining hierarchy ambiguity will split the allowable solutions into two groups .
in such a case , the result of the @xmath12 and @xmath13 study will have the form : @xmath99 @xmath100 for normal hierarchy , and @xmath101 @xmath102 for inverted hierarchy , with one solution somewhat more favored over the other ( i.e. should the hierarchy discrimination be achieved to marginal confidence levels ) . here
@xmath103 and @xmath104 are best fit values for the @xmath12 for the normal and inverted scenarios , respectively , the @xmath10 is expected to be found from the same experiment with superior accuracy and @xmath105 and @xmath106 are the error bars for both the @xmath12 and @xmath13 in the normal and inverted hierarchy , respectively .
as was proposed in @xcite and discussed in numerous later publications , neutrinos may have non - standard interactions which could affect the flavor content at the source and also the flavor content detected . for our case at hand , it means that the observed mixing angles @xmath9 and @xmath11 in general will differ from the `` true '' mixing angles .
for example , the measured @xmath11 can be larger than the true @xmath11 @xcite .
since the survival probability ( [ 3flavor ] ) depends on the effective @xmath11 , the nsi have no adverse effect on the determination of @xmath12 , @xmath107 and the neutrino mass hierarchy .
in fact an effective @xmath11 larger than the real one will be advantageous for these studies . at the same time
, the effective @xmath11 measured at different baselines are going to be different , should these interactions take place . this way , medium baseline experiments targeting @xmath11 will become complementary to the short baseline ones in testing new physics .
* medium - baselined @xmath8 oscillation experiments are not systematics - constrained .
this follows from the shapes of oscillated spectra .
in particular , physically feasible systematic errors do not tend to imitate the spectral distortions characteristic of the neutrino oscillations .
* there is no single baseline optimal for all oscillation studies .
the difference in sensitivity profiles is big enough to give an advantage to multiple detector or / and movable detector configurations . even in individual studies
where a pronounced baseline optimum exists , a multiple baseline configuration can outperform a single baseline configuration , as has been shown for the neutrino mass hierarchy discrimination case .
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the purpose of this study was to find out the supplemental value of topiramate , after miniplate fixation of infraorbital nerve results from compression of the nerve due to entrapments , as it leaves the infra orbital foramen .
the surgical management of infra orbital nerve injury requires decompression of nerve by reduction of zygomatic complex fracture and sometimes mobilization of nerve , surrounding soft - tissue and help in early recovery of sensory function .
smith - swintosky claimed that topiramate help in nerve regrowth and enhanced the recovery of facial nerve function after injury when administered orally at therapeutically relevant doses , and significantly increased neurite outgrowth in cell cultures derived from fetal rat cortical and hippocampal tissues .
sakavicious reported a 64.4% incidence of infra orbital nerve injury of zygomatic - complex fracture .
schilli reported that in 95% cases of zygomatic complex fractures , the fracture lines involve the infra orbital foramen and may cause some degree of sensory disturbances .
the main pharmacological action of this compound has been identified and responsible for its anticonvulsant action as it reduces the duration and frequency of action potentials within spontaneous epileptiform bursts of neuronal firing it has neuroprotective activity reported in rodent models of cerebral ischemia brain injury , stroke , epilepsy , etc .
, it can be prescribed in dosages 50 - 400 mg daily in divided dosages .
dosages can be increased by 25 - 50 mg / day each subsequent week as tolerated .
peak plasma concentration can be achieved in 2 h following a single 400 mg oral dose .
symptoms of nerve injury may be varied from paresthesia , numbness at the site of the nose , upper lip .
several methods of sensory testing have been applied , i.e. , gross mapping of altered areas of sensation . the conventional mechanical tests including two - point discrimination light - touch pinprick and sharp - blunt discrimination .
few studies have suggested that the treatment of isolated zygomatic complex fracture with open reduction and mini plate fixation , yields better recovery of sensory function .
undisplaced zygomatic complex fracture can be treated conservative method successfully generally open reduction and miniplate fixation gives better results than transosseous wiring or conservative methods .
gabapentin single or combination , topiramate and carbmezepine have also been used in post traumatic neuropathic pain .
various studies have been reported about the beneficial effects of this antiepileptic drug in post - traumatic nerve injury without affecting the final size of the traumatic lesion .
two cases were slected in this study , who were reported after 2 - 3 weeks of injury .
chief complaints of the patients were altered sensation in the distribution of infraorbital nerve . on clinical examination step deformity and tenderness was present at the infra orbital margin and frontozygomatic region .
infra orbital nerve paresthesia was tested with two - point discrimination test and cotton wick test . on percussion
conventional x - rays ( occipetomental and submento vertex view of the skull were advised to rule out the involvement / entrapment of infra orbital nerve .
the surgical decompression of the nerve was achieved by fracture reduction and single miniplate fixation was done at fronto zygomatic region .
the initial dose of topiramate was 25 mg / day administrated for the 1 week at night and the dosages had to be increased to 50 mg / day in the 2 week .
postoperatively patients were assessed clinically and radio logically , the patients were recalled after 7 days to check up and suture removal .
dose were increased to 50 mg twice daily and further dose titration advised as to increase by 25 mg twice daily and minimum dose was maintained .
a minimum of 6 months follow - up was chosen in both the patients . , the patients were responding well with complete functional recovery and remission of symptoms .
antiepileptic drug like topiramate was supplemented post miniplate fixation in infra orbital nerve injury cases for early nerve recovery as reported in the literature .
. reported , study of the 30 subjects in highly significant beneficial effect on nerve function , champy , et al .
, stated that reduction and fixation are important factors in the recovery from sensory disturbances of the nerve . above mentioned studies of the miniplate fixation at fronto zygomatic region
patients were supplemented with topiramate 25 mg to 50 mg twice daily , which helped in early recovery of sensory nerve function .
drug supplementation showed early improvement in nerve function as reported , but takes the longer period for complete recovery .
this may be explained on the basis that a surgical exploration / reduction of fracture fragments prevents further damage to the nerve and drug therapy helps in nerve regeneration as reported by many studies .
from our study , we recommend an open reduction with miniplate fixation at fronto zygomatic region supplemented with topiramate in therapeutic dosages provided early recovery of sensory function of infra orbital nerve . | pubmed |
Auchnagatt railway station was a railway station in Auchnagatt, Aberdeenshire. Before its closure, services ran to Fraserburgh, Peterhead and Aberdeen.
History
The station was opened by the Formartine and Buchan Railway, then part of the Great North of Scotland Railway. It became part of the London and North Eastern Railway during the Grouping of 1923, and then passed on to the Scottish Region of British Railways during the nationalisation of 1948. It was then closed to passengers by the British Railways Board in 1965 under the Beeching Axe.
The site today
The station is still fairly intact beside the lifted railway.
References
Station on navigable O.S. map
RAILSCOT on Formartine and Buchan Railway
Category:Disused railway stations in Aberdeenshire
Category:Railway stations opened in 1861
Category:Railway stations closed in 1965
Category:Beeching closures in Scotland
Category:Former Great North of Scotland Railway stations
Category:1861 establishments in Scotland
Category:1965 disestablishments in Scotland | wikipedia |
Which elements tend to form the most phases?
Some combinations of two elements have very complicated binary phase diagrams across the weight% horizontal axis. Others are rather simple. Is this a function of only one or both of the elements involved? I would think both. However, surely there are some elements that tend to form more phases than others. Has this tendency to form more phases (or less) been quantified for the various elements? If no, is it quantifiable?
Obviously elements form only a given number of known allotropes. However, it is not known if the number of known allotropes is exhaustive. Therefore the number of pseudomorphs in a binary phase diagram seems like a more thorough method of investigating an element's "binding flexibility."
Much empirical data is needed to either produce or validate phase diagrams. Any phase diagram would likely need to be of practical consequence to justify spending the energy and resources to produce it.
An example of a binary mixture with practical consequence would be a metal oxide formed during corrosion. The many forms of iron and oxide are well studied since iron is commonly used to construct tools.
In 2015 a group claimed to use the computer code CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) to discover a new phase of beryllium. Beryllium is used in aerospace and the construction of nuclear reactors, so the expenditure of effort was justifiable.
*So to answer the sub-questions:*
*Is this a function of **only** one or both of the elements involved?*
Practically .. No. In the case of iron oxide in an aqueous solution, multiple iron oxide phases can form at the same temperature and pressure if the pH of the solution or the redox potential value of the solution were changed.
*Has this tendency to form more phases (or less) been quantified for the various elements?* - Yes, phases of practical consequence have been quantified at great effort; however, discoveries of new phases are likely to continue.
It is possible to estimate the existence of new phases using computer algorithms; however, these phases must be experimentally validated. A computer algorithm could be constructed around pseudomorphs; however, if a new phase were discovered it would need practical validation by experimentation.
"Which elements form the most phases?" is an impossible question to give and absolute answer as we are limited to certain pressures and temperatures with which to experiment. The way experimentation is done is likely to bias any verifiable answer toward more practical materials.
| stackexchange/chemistry |
The 1958 NBA draft was the 12th annual draft of the National Basketball Association NBA. The draft was held on April 22, 1958, before the 195859 season. In this draft, eight NBA teams took turns selecting amateur U.S. college basketball players. In each round, the teams select in reverse order of their winloss record in the previous season. The draft consisted of 17 rounds comprising 88 players selected.
Draft selections and draftee career notes
Elgin Baylor from Seattle University was selected first overall by the Minneapolis Lakers. Baylor went on to win the Rookie of the Year Award in his first season. Guy Rodgers from Temple University was selected before the draft as Philadelphia Warriors' territorial pick. Three players from this draft, Elgin Baylor, Guy Rodgers and Hal Greer, have been inducted to the Basketball Hall of Fame. Frank Howard from Ohio State University was selected in the third round by the Philadelphia Warriors, but he opted for a professional baseball career and eventually playing 16 successful seasons in the Major League Baseball MLB.
Key
Draft
Other picks
The following list includes other draft picks who have appeared in at least one NBA game.
Trades
Prior to the draft, the New York Knicks acquired the Detroit Pistons' first-round pick, which was used to select Mike Farmer, from the Pistons in exchange for Dick McGuire.
References
General
Specific
External links
NBA.com
NBA.com: NBA Draft History
Draft
Category:National Basketball Association draft
Category:National Basketball Association lists | wikipedia |
Inspiring Speakers and Marshmallow Challenge
20 October 2021 | Author: Christopher Yau, Director, HDRUK-Turing Wellcome PhD Programme in Health Data Science
In his first blog post, PhD Programme Director Chris Yau reports that Health Data Research UK's 2020 and 2021 student cohorts have finally been able to meet in person. Their long-awaited induction session involved everything from The Marshmallow Challenge to talks from leaders in health data science.
Christopher Yau
[email protected]
This October Health Data Research UK (HDR UK) were finally able to welcome our 2020 and 2021 PhD Programme cohorts in person for the first time at our induction event. Our 16 PhD students, from six UK universities, assembled for the first time for two days of long overdue cohort building activities.
On Day One, I was joined by Talent and Training Director Sarah Cadman, and we kicked off with my personal introduction to HDR UK, our ethos, and the importance of the PhD programme in our overall mission. I emphasised that each of our students represents a massive investment by Wellcome and HDR UK and that they would have our fullest support throughout their studies to maximise the impact of their research. I particularly mentioned the unique flexibility they possess within our programme to shape their own training and development and not be bound by a pre-determined syllabus.
I led the students in a group exercise to consider why they thought HDR UK had selected them, reminded them of their interview process and asked them to consider what qualities HDR UK had been looking for and why they had succeeded. I then informed the students that the exercise was not merely for reflection but a precursor to asking them to join in the recruitment process that has recently open for our third cohort. At HDR UK we really want our students to not only be participants in the programme but also to be leaders who can influence and improve the programme for subsequent cohorts.
The students then took on an entirely different type of activity: The Marshmallow Challenge. Armed with nothing more than a few paper straws, paper card, scissors and some Sellotape, each team of four students was asked to construct the tallest freestanding structure that could hold a marshmallow at its top. This challenge really brought out the competitive spirit in our students and a mixture of solutions arose from the truly outstanding to the not-quite-so upstanding (quite literally!). Ultimately the team of Claire Coffey, Breeshey Roskams-Heiter, Tianxiao Wang and Xiyun Jiang emerged victorious with their splendid blue structure reaching the room ceiling.
There was no let up after the excitement of the marshmallows. A short coffee break and the students were back at it with an exercise I call "Round Robin Teaching". Students are asked to teach a concept to a partner in five minutes. The recipient then teaches someone else what they just learnt and this person must then teach what they have learnt back to the person from whom the concept originated to see how much information and insight has been preserved. I was genuinely impressed with the enthusiasm shown by the students who all made a serious attempt to teach and learn over very short time scales. This exercise is designed to mimic scientific interactions between supervisors, their students, and external collaborators where information can get lost in translation particularly in interdisciplinary partnerships.
PhD Students in London. October 2021.
Day One ended with a keynote talk from returning former HDR UK Training Director Professor Peter Diggle. I was delighted that Peter was able to join us and give a tour de force of his professional career from his early days as a boy living in the shadow of the Sellafield nuclear plant through his studies with the great statistician, Julian Besag, and work that took him to all corners of the world including Sweden, CSIRO (Australia), and Johns Hopkins (USA) before arriving back in the UK in Lancaster. Peter outlined the foundations of statistical modelling and inference upon which his work is built and which is the bedrock of our PhD programme as well. Though retired from his role as Director, Peter will always remain a close friend to the programme.
Associate Director Max Little – the new "fun one"
At dinner, I was delighted to announce the appointment of our new Associate Director, Max Little from the University of Birmingham. Max had undergone a rigorous selection process at HDR UK in which a committee of our PhD students had been selected to evaluate all our candidates for their technical, teaching and communication skills. We place tremendous faith and trust in the ability of our students to take on professional tasks within the programme to extend their experience and to give them a genuine role in the operation of the programme.
Sadly, Max's appointment marks my retirement as the Programme Director who is the "fun one", which will now be Max's role, as I move to being the "serious and responsible one".
Max will formally start his position shortly and I and the rest of HDR UK look forward to working with him in the coming years.
The following day kicked off with students being asked to consider the nine principles that collectively form the Bradford Hill framework for establishing evidence of a causal relationship between a presumed cause and an observed effect in public health research. While formal methodology is appropriate for the mathematically well-versed and statistically trained, the purpose of this exercise was to make students consider the qualitative aspects of real-world policy and decision making, and the communication skills they will need to develop to enable an effective conversation with stakeholders in different sectors and disciplines.
Our current PhD cohorts
The group then split into two groups with Professor Peter Bannister (VP Life Sciences, Ada Health) and his team of Academy of Medical Sciences FLIER colleagues: Dr Rebecca Sims, Professor Marc Vendrell and Professor Richard Mellanby introducing the 2020 Cohort to the Leadership course. Peter began by outlining the multi-part, multi-year leadership programme that will span the next three years of their PhD involving a cross-sector range of academic, industry and NHS leaders. Rebecca, Marc and Richard then introduced different leadership styles and both personal and more academic perspectives on leadership. This introduction was a prelude to the start of a year-long project for the 2020 cohort where they will seek to learn and apply their emerging leadership skills supported by Peter and colleagues.
Professor Marc Vendrell (University of Edinburgh) talking about Leadership
While our students are at an early stage in their careers, we are deliberately encouraging and developing leadership skills early. Unlike a university which graduates hundreds of PhDs every year, at HDR UK we only have 16. Every student is therefore unique and special to us and we will use our national platform to its fullest effect to support each and every one of them to become future leaders in health data science.
Meanwhile, in the other room, Max and UCL University Lead, Ioanna Manolopoulou led the 2021 cohort in a series of data science exercises building on his work in wearables and Parkinson's disease. Students were asked to consider the wider issues in tackling data science problems, which extend beyond simply the algorithms and data, but issues such as replicability, reproducibility, ethics, project management and infrastructure. Students were shown that technical expertise developed as part of a PhD only comprises one component of the technology development pipeline and that the health innovation pathway involves many more activities and stakeholders.
Sadly, after two action-packed days, it was time for our students to return to their homes and the care of their universities. However, we look forward to them returning for a busy series of immersion weeks, courses and seminars that HDR UK have programmed for them throughout the academic year. I could not be more excited about what comes next for these students.
Special thanks to our Talent and Training programme and various members of the HDR UK Central team for supporting us in planning delivering this event.
Talent, Training
Researcher Roadshow – Exploring Health Data Science
Increase your understanding of roles of health data scientists and value of health data science.
Health Data Research UK wins prestigious diversity and inclusion award
Earlier in November, Health Data Research UK was awarded first place in the Best diversity and inclusion category 2023 by CorpComms Magazine for their Black Internship Programme campaign.
HDR UK Master's Programme Trains 300 Students
We have worked with leading universities across the UK to establish a variety of specialist master's courses that have prepared hundreds of talented people for careers in health data science | slim_pajama |
stable heavy isotopes above iron ( @xmath526 ) can be classified into three categories , @xmath6- , @xmath7- and @xmath2-nuclei corresponding to the topology of the nuclide chart .
the @xmath6-nuclei are located along the valley of stability while the @xmath7- and @xmath2-nuclei can be found on the neutron rich and proton rich side of the valley , respectively .
the names refer to the production process synthesizing the corresponding isotopes .
the @xmath6-process isotopes are produced by the s ( slow ) neutron capture process in stellar helium and carbon burning environments with steady neutron production through the @xmath8c , @xmath9o , and @xmath10ne(@xmath3,n ) reactions .
the @xmath6-process sites have been identified as low mass agb stars ( @xmath11 @xmath12 5 @xmath13 ) for the main @xmath6-process @xcite and massive red giant stars ( @xmath11 @xmath14 6 @xmath13 ) for the weak @xmath6-process @xcite . on the other hand ,
the @xmath7-isotopes are produced by the @xmath7 ( rapid ) neutron capture process which takes place in explosive stellar environments providing a high neutron flux .
the @xmath7-process site is still under debate but the presently favored candidates are type - ii supernovae @xcite and merging neutron stars @xcite . for the production of a number of isotopes located along the valley of stability
both the @xmath6 and @xmath7 processes have their contributions .
the @xmath2-nuclei , however , can not be produced by neutron capture reactions . their production mechanism ,
the @xmath2-process , has been identified as a sequence of photodisintegration processes in a high @xmath15-flux scenario @xcite .
the initial abundance distribution of @xmath6- and @xmath7-nuclei at the @xmath2-process site is converted by subsequent ( @xmath15,n ) reactions toward the neutron - deficient region .
as the neutron threshold increases , competing ( @xmath16 ) and ( @xmath17 ) photodisintegration processes branch the reaction flow towards lower mass regions @xcite .
the final @xmath2-nuclei abundance distribution depends critically on the seed abundance distribution as well as on the reaction flow which is determined by the associated reaction rates and reaction branchings .
a recent detailed overview of the @xmath2-process and a discussion about possible @xmath2-process sites can be found in @xcite .
the modeling of @xmath2-process nucleosynthesis requires a large network of thousands of nuclear reactions involving stable and unstable nuclei .
the relevant astrophysical reaction rates which are derived from the reaction cross sections are necessary input to this reaction network .
their knowledge is essential for @xmath2-process calculations . in some cases ,
the cross section of @xmath15-induced reactions can be measured directly by photodissociation experiments @xcite ; however , in such an experiment the target nucleus is always in its ground state while in stellar environments thermally populated excited states also contribute to the reaction rate .
thus theoretical considerations can not be avoided @xcite .
alternatively , the @xmath15-induced reaction cross sections can be calculated through `` detailed balance '' from the cross section of the inverse capture reactions .
while there are extensive compilations of neutron capture data along the line of stability above the iron region ( e.g. @xcite ) , there are only very few charged - particle cross sections determined experimentally ( despite substantial experimental efforts in recent years ) .
therefore , the @xmath2-process rates involving charged particles are still based mainly on theoretical cross sections obtained from hauser - feshbach statistical model calculations .
it is particularly important to study the charged particle photodissociation processes [ ( @xmath16 ) , ( @xmath15,p ) ] since those determine the reaction flow towards the lower mass range . because of the large number of experimentally unaccessed or unaccessible nuclei in astrophysical reaction networks , statistical model codes in astrophysics focus on the prediction of reaction rates from microscopic input or global parameterizations .
contrary to standard hauser - feshbach calculations applied in other areas of nuclear physics , they deliberately refrain from using local fine - tuning by utilization of local nuclear properties .
it is assumed that such models allow better predictions for nuclei further off stability .
the trade - off is in a possible loss of accuracy locally while the average deviation over a larger range of nuclei remains low .
nevertheless , also such models have to be tested against local data in order to arrive at further improvements .
there is an increasing number of ( p,@xmath15 ) reactions relevant for the @xmath2-process which have been measured in recent years @xcite .
generally , the statistical models are able to reproduce this experimental data to better than a factor of two and the predictions are not very dependent on the input parameters ( e.g. optical potentials ) . however , for ( @xmath18 ) reactions only few cases have been measured @xcite or are under study @xcite .
the experimental results show substantial discrepancies compared to the model predictions .
it has been suggested that these discrepancies are related to insufficiencies in the @xmath3-optical potential .
it is therefore important to measure ( @xmath18 ) cross sections at sub - coulomb energies and compare the results with the model calculations to identify the source of the observed discrepancies . in the present work
the @xmath3-capture cross section of @xmath0cd is measured .
this reaction is particularly important since it focuses on the study of photodisintegration of a @xmath19sn nucleus with @xmath20=50 closed proton shell . near closed shells
the level density is reduced and the statistical model may not be fully applicable .
the @xmath0cd(@xmath1sn reaction is therefore a prime example to test the validity of the hauser - feshbach approach in this mass region .
in addition , while for higher @xmath20 nuclei along the @xmath2-process path the alpha threshold is negative , for @xmath19sn the @xmath3-threshold turns positive @xmath21=1.136 mev and increases towards lower @xmath20 .
this means that ( @xmath16 ) photodissociation into the alpha channel for even - even nuclei below @xmath20=50 is reduced and the reaction flow may become diverted towards the line of stability by competing ( @xmath17 ) reactions @xcite .
( the experimantal study of the ( p,@xmath15 ) reactions on @xmath0cd and @xmath22cd is in progress .
preliminary results are already available @xcite ) . for nuclei between @xmath23=50 and @xmath20=50 both proton and @xmath3-photodissociation channels need to be studied in detail to see how the reaction flow develops in this low mass range of the @xmath2-process .
this in particular will address the question of feeding the @xmath24mo and @xmath25ru @xmath2-nuclei which remain underproduced in present @xmath2-process nucleosynthesis simulations @xcite .
the primary aim of the present study is to extend the existing experimental database relevant to the @xmath2-process by measuring the cross section of the @xmath0cd(@xmath1sn reaction .
based on the hauser feshbach predictions for the reaction rate , the @xmath2-process branching point at which the ( @xmath16 ) and ( @xmath15,p ) reactions become competitive with the ( @xmath15,n ) process along the @xmath20=50 isotopic chain ( sn isotopes ) is located at mass number region 110 - 112 @xcite ( see fig.[fig_flow ] ) . the ( @xmath16 ) and subsequent ( @xmath15,p ) reactions on @xmath19sn and @xmath26sn lead to the production of the @xmath2-nuclei @xmath0cd and @xmath22cd ,
respectively ( @xmath22cd has a slight contribution from the @xmath6-process as well ) .
the precise knowledge of these reaction rates is essential to the reliable prediction of the @xmath0cd and @xmath22cd abundances in @xmath2-process modeling . in the present work
the @xmath0cd(@xmath1sn cross section is determined and the results are compared with the prediction of statistical model calculations performed with the non - smoker code @xcite using different input parameters such as optical model potentials and nuclear level densities . in addition , the cross sections of the @xmath0cd(@xmath3,n)@xmath4sn reaction and the @xmath0cd(@xmath3,p)@xmath4 in reaction below the ( @xmath3,n ) threshold have been measured and are compared with the non - smoker predictions .
the peak of the gamow window for the @xmath0cd(@xmath1sn reaction at a @xmath2-process temperature of @xmath27=3.0 is located at 7.21 mev , its width is about 4 mev .
the lowest energy reached in our experiments was @xmath28=7.56mev ( well within the gamow window ) .
the measurements extended up to e@xmath29=12.06mev to probe the reliability of the hauser - feshbach predictions over a wider energy range .
the reaction products of all three investigated reactions : @xmath0cd(@xmath1sn , @xmath0cd(@xmath3,n)@xmath4sn and @xmath0cd(@xmath3,p)@xmath4 in are radioactive .
this makes it possible to determine the cross sections using the activation technique .
the induced activity in a @xmath0cd target after bombarding with an @xmath3 beam can be measured off - line , and the above reaction cross sections can be deduced from the measured @xmath15-activity .
the reaction product of @xmath0cd(@xmath3,p)@xmath4 in is the same as the daughter of @xmath4sn from the @xmath0cd(@xmath3,n)@xmath4sn reaction .
moreover , above the ( @xmath3,n ) threshold ( e@xmath30=10.53mev ) , the ( @xmath3,n ) channel becomes stronger than the ( @xmath3,p ) .
hence the @xmath0cd(@xmath3,p)@xmath4 in cross section is determined only below the ( @xmath3,n ) threshold ( see sec .
[ sec_results ] ) . the relevant part of the chart of nuclides can be seen in fig.[fig_decay ] where the alpha - induced reactions and the decay of the reaction products are shown .
the decay parameters used for the analysis are summarized in table[decaypar ] .
ccccc & & & & + @xmath19sn & 4.173 @xmath31 0.023 & 280.5 & 97 & @xcite + & ( [email protected] ) & & & @xcite + + @xmath4sn & 18.0 @xmath31 0.2 min .
& 1099.2 & 30.1 @xmath31 3.0 & @xcite + & & 1321.3 & 11.9 @xmath31 1.4 & + & & & & + @xmath4 in & 4.167 @xmath31 0.018 & 203.5 & 73.5 @xmath31 0.5 & @xcite + [ decaypar ]
in order to increase the reliability of the experimental results and to find any hidden systematic error , the experiments have been carried out independently in atomki , debrecen , hungary and at the university of notre dame , indiana , usa . in the following sections the experimental set - ups used in the two laboratories are discussed .
the targets were prepared by evaporating highly enriched ( 96.47% ) @xmath0cd onto thin ( d=3@xmath32 m ) al foil .
the cd powder was evaporated from a mo crucible heated by electron bombardment .
the al foil was placed 5 cm above the crucible in a holder defining a circular spot with a diameter of 12 mm on the foil for cd deposition .
this procedure made it possible to determine the target thickness by weighing .
the weight of the al foil was measured before and after the evaporation with a precision better than 5@xmath32 g and from the difference the @xmath0cd number density could be determined . altogether
5 enriched targets were prepared with thicknesses varying between 100 and 600@xmath32g/@xmath33 .
the thickness of the al foil ensures that the heavy reaction products are stopped in the backing . at the highest @xmath3-bombarding energy of 12.5mev
the energy of the @xmath19sn recoil is 450kev and hence its range in al is roughly 0.17@xmath32 m , much smaller than the foil thickness .
the activations have been performed at the mgc cyclotron at atomki .
the energy range from e@xmath34=8.5 to 12.5mev was covered in 10 steps .
the schematic view of the target chamber can be seen in fig .
[ chamber ] .
after the last beam defining aperture , the whole chamber served as a faraday - cup to collect the accumulated charge .
a secondary electron suppression voltage of @xmath35 v was applied at the entrance of the chamber .
each irradiation lasted about 10 hours and the beam current was restricted to 500ena in order to avoid target deterioration .
the current was kept as stable as possible but to follow the changes the current integrator counts were recorded in multichannel scaling mode , stepping the channel in every minute .
this recorded current integrator spectrum was then used for the analysis solving the differential equation of the population and decay of the reaction products numerically .
a surface barrier detector was built into the chamber at @xmath36=150@xmath37 relative to the beam direction to detect the backscattered @xmath3 particles and to monitor the target stability this way .
the rbs spectra were taken continuously and the number of counts in the cd peak was checked regularly during the irradiation . having
the beam current restricted to 500ena , no target deterioration was found within the precision of the rbs measurement i.e. of the order of 1% . weighing the target foils after irradiation also confirmed this .
the beam stop was placed 10 cm behind the target from where no backscattered particles could reach the surface barrier detector .
the beam stop was directly water cooled . because of an energy gap of the cyclotron , it is not possible to accelerate @xmath3-beam in the energy range between e@xmath34=9 and 10.8mev ( with the exception of a narrow allowed window around 10mev where limited @xmath3-current is possible ) .
therefore the energy points of e@xmath34=9.5 and 10.33mev have been measured with higher energy beam and energy degrader foils . for energy degrader al foil with 8.8@xmath32 m
thickness was used .
the thickness was determined with measuring the energy loss of @xmath3-particles from an @xmath3-source when passing through the foil .
the 10.33mev energy was reached from the beam energy of 11.2mev using one layer of degrader foil while for the 9.5mev point two layers of degrader foil and 11.3mev beam was used . in order to test the reliability of the degrader foil method , the reaction cross section at 11.6mev was measured directly as well as using 12.4mev beam and one degrader foil .
the two measurement gave the same result ( see sec .
[ sec_results ] ) .
the highest energy point ( e@xmath29=12.06mev ) has also been measured using a cd target with natural isotopic composition .
the results with enriched and natural targets are the same within the error ( sec .
[ sec_results ] ) .
the @xmath15 radiation following the @xmath38-decay of the produced sn and in isotopes was measured with a hpge detector of 40% relative efficiency .
the target was mounted in a holder at a distance of 10 cm from the end of the detector cap .
the whole system was shielded by 10 cm thick lead against laboratory background .
the @xmath15-spectra were taken for at least 10 hours and stored regularly in order to follow the decay of the different reaction products .
the absolute efficiency of the detector was measured with calibrated @xmath39ba , @xmath40co and @xmath41eu sources in the same geometry used for the measurement . at e@xmath42=280.5kev the photopeak efficiency is ( [email protected])% .
[ gammaspec ] shows an off - line @xmath15-spectrum taken after irradiation with 12 mev @xmath3-s in the first 1h counting interval .
the @xmath15 lines used for the analysis are indicated by arrows .
taking into account the detector efficiency and the relative intensity of the emitted @xmath15-rays , coincidence summing effects for all three reactions were well below 1% and were neglected .
@xmath0cd targets used at notre dame were prepared by rolling with nominal thicknesses of 2.3 mg/@xmath33 and a @xmath0cd enrichment of 86.4 % .
the foils were mounted on ta frames with hole diameters of 12.5 mm .
the actual thickness was determined prior to the activations by rutherford backscattering ( rbs ) to 2.1 @xmath31 0.2 mg/@xmath33 .
the targets were also monitored by rbs during the activations ( see below ) and the thicknesses were again verified after the conclusion of the experiment .
tests with natural targets showed no deterioration of the targets when the @xmath3-beam currents were limited to @xmath43 300ena . because the notre dame experiment was designed to extend the atomki data to lower beam energies , the targets were not backed by a thin al layer to avoid the short lived @xmath15-activity associated with the al activation .
for this reason no waiting time was required between the end of the activation and the counting ; however , this allows a small fraction of the heavy recoils to escape from the target . at beam energies of @xmath4310
mev the target layer from which recoils can escape is @xmath430.06 mg/@xmath33 or less than 3 @xmath44 of the target thickness .
in addition , the cross section drops significantly across the target thickness ( factor of @xmath45 5 ) leading to an overall loss of activity of @xmath430.6 % .
the activations at notre dame were carried out with the fn tandem van de graaff accelerator at beam energies between 7.0 and 12.0 mev .
however , no data could be obtained below 8 mev because of strong compton background caused by a @xmath15-line ( e@xmath42=373 kev ) from the @xmath46ca(@xmath3,p)@xmath47sc reaction .
@xmath46ca is a common contaminant which has a coulomb barrier substantially lower than @xmath0cd and the half - life of @xmath47sc is similar to that of @xmath19 in .
the cross section for this reaction only changes little over the investigated energy range ( see e.g. @xcite ) while the @xmath0cd + @xmath3 cross sections drop exponentially with beam energy .
the experimental setup of the target chamber was similar to atomki .
a collimator with a diameter of 5 mm defined the beam spot .
the isolated target chamber served as faraday cup and a suppression voltage of 300 v was applied to an isolated cathode between collimator and chamber .
in addition , a si detector was placed at 135@xmath37 with respect to the beam direction to monitor the target stability .
the target was placed in a brass holder which was air cooled and the beam was stopped in a thick carbon foil located directly behind the target .
the digitized charge and the energy signal of the si detector were recorded event - by - event together with the time of the event .
each activation lasted 8 hours ( approximately 2 half - lives ) and the beam current was kept below 300ena ( see above ) .
the resulting @xmath15-activity was measured with a pair of ge clover detectors which were mounted face to face .
the detectors were shielded by 5 cm of pb against the room background and the distance between the detectors was 5 mm .
the activated targets were mounted in a holder which placed them at the center of the detection system .
the holder was made out of plastic and filled out the whole space between the clover detectors except for the space needed by the target .
each clover detector consists of 4 individual crystals with a relative efficiency of 20% .
the energies of the crystals were recorded event - by - event together with the time of the event .
in addition a pulser signal was fed into the test input of one of the ge preamplifiers .
this allowed to reconstruct the dead time as a function of time .
each of the crystals were treated as an independent ge detector to reduce the problem of pile - up and summing losses .
the absolute and relative @xmath15-efficiencies of the detectors were determined using calibrated @xmath48mn , @xmath40co , and @xmath39ba sources as well as an uncalibrated @xmath41eu source .
the activity of the @xmath41eu source was determined relative to the @xmath48mn and @xmath40co sources .
the efficiency was determined by two independent methods . in the standard method the known decay branchings and activities of the sources
were used to determine the efficiency . however , because of the high counting efficiency of the detector system , summing correction has to be applied for the multiple line sources .
these were taken from ref @xcite .
the second method makes use of the high counting efficiency and granularity of the detection system .
choosing selected @xmath15-transitions which are in sequence the detector efficiency can be determined independent of the source strength from ratios of single- and coincidence events . in this method ,
the problem of summing correction is either absent or greatly removed .
both methods agreed within the uncertainties .
the off - line detection system has a peak peak efficiency of ( [email protected])% for a @xmath15-energy of 280.5 kev .
lr@@xmath31lr@@xmath31 lr@@xmath31l e@xmath49 & & & + [ mev ] & & & + + 8.500 & 8.123 & 0.029 & 0.85 & 0.37 & 180 & 78 + 9.008 & 8.632 & 0.026 & 4.87 & 0.55 & 155 & 18 + 11.300 & 9.108 & 0.049 & 22.8 & 2.9 & 143 & 18 + 10.000 & 9.599 & 0.030 & 79.1 & 8.2 & 105 & 11 + 11.200 & 9.909 & 0.036 & 147 & 15 & 78.4 & 8.1 + 10.800 & 10.371 & 0.033 & 234 & 24 & 34.3 & 3.5 + 11.200 & 10.775 & 0.033 & 298 & 31 & 15.1 & 1.6 + 11.600 & 11.167 & 0.034 & 507 & 53 & 9.8 & 1.0 + 12.400 & 11.167 & 0.037 & 471 & 49 & 9.08 & 0.94 + 11.998 & 11.544 & 0.035 & 601 & 62 & 4.78 & 0.50 + 12.523 & 12.050 & 0.036 & 1270 & 150 & 3.28 & 0.39 + 12.523 & 12.057 & 0.036 & 1280 & 133 & 3.26 & 0.34 + + 8.000 & 7.566 & 0.010 & 0.078 & 0.014 & 164 & 29 + 8.500 & 8.040 & 0.010 & 0.480 & 0.048 & 141 & 14 + 9.000 & 8.513 & 0.011 & 2.59 & 0.26 & 126 & 13 + 9.500 & 8.992 & 0.012 & 11.8 & 1.2 & 108 & 11 + 10.000 & 9.466 & 0.012 & 46.4 & 4.6 & 92.7 & 9.3 + 10.000 & 9.470 & 0.012 & 48.3 & 4.8 & 95.3 & 9.5 + 10.000 & 9.599 & 0.012 & 75.1 & 5.4 & 99.9 & 7.7 + 11.000 & 10.429 & 0.014 & 244 & 124 & 30.6 & 3.6 + 11.500 & 10.909 & 0.014 & 434 & 43 & 15.8 & 1.6 + 12.000 & 11.385 & 0.015 & 596 & 61 & 6.85 & 0.70 + [ tab_ag ] .experimental cross section and @xmath50 factor of the @xmath0cd(@xmath3,n)@xmath4sn reaction [ cols= " < , > , < , > , < , > , < " , ] [ tab_an ] lr@@xmath31lr@@xmath31 lr@@xmath31l e@xmath49 & & & + [ mev ] & & & + + 10.000 & 9.599 & 0.030 & 6.0 & 0.8 & 8.0 & 1.1 + 11.200 & 9.909 & 0.036 & 39.6 & 4.2 & 21.1 & 2.2 + + 9.500 & 8.992 & 0.012 & 0.24 & 0.04 & 2.23 & 0.35 + 10.000 & 9.470 & 0.012 & 2.76 & 0.28 & 5.45 & 0.55 + 10.000 & 9.599 & 0.01 & 5.70 & 0.67 & 7.58 & 0.89 + [ tab_ap ] the cross sections and @xmath50 factors for the reactions @xmath0cd(@xmath1sn , @xmath0cd(@xmath3,n)@xmath4sn and @xmath0cd(@xmath3,p)@xmath4 in are listed in tables [ tab_ag]-[tab_ap ] , respectively . the second column shows the effective center - of - mass energies which accounts for the decrease of the cross section over the target thickness . for the atomki measurement ,
the quoted errors of the energies include the energy loss in the targets calculated with the srim code @xcite , the energy stability of the cyclotron and the energy straggling in the degrader foil where it was applied .
for the notre dame results , the energy error is determined by the uncertainty in the calculation of the effective energy .
the results obtained in atomki and in notre dame are listed separately . for the @xmath0cd(@xmath3,n)@xmath4sn reaction
no results from the notre dame experiment are listed .
the complex @xmath15-decay scheme @xcite as well lack of any dominant @xmath15-line and the close geometry of the notre dame counting system require significant summing corrections leading to large uncertainties .
for this reason we abstain from quoting any notre dame results for this reaction .
both sets of data are in excellent agreement ( see tables [ tab_ag ] and [ tab_ap ] ) . to test for systematic uncertainties ,
the @xmath0cd(@xmath1sn cross section was measured at notre dame at the same beam energy ( 10 mev ) using the same target as in atomki .
the values are in excellent agreement ( see table [ tab_ag ] ) .
the error of the cross section ( @xmath50 factor ) values is the quadratic sum of the following partial errors : efficiency of the detector system ( @xmath517%(atomki ) , @xmath512.3%(notre dame ) ) , number of target atoms ( @xmath516%,@xmath519% ) , current measurement ( 3%,@xmath513% ) , uncertainty of the level parameters found in literature ( @xmath5212% ) , counting statistics ( 0.1 to 40% ) .
one possible uncertainty is the decay branching ratio of @xmath19sn .
the compilation @xcite lists a 100 % @xmath15-branching ratio to the 345 kev level in @xmath19 in .
however , this value is based only on an unpublished phd thesis from 1956 @xcite .
the resulting log ft value of 3.24 is unusually small when compared with other @xmath38-transitions between @xmath53(1@xmath54 ) and @xmath55(1g@xmath56 ) in this mass region and some of the decay branches might not have been observed @xcite .
calculation of the @xmath0cd(@xmath1sn cross section from the mother ( @xmath19sn ) and from the daughter ( @xmath19 in ) activities provide an indirect way to determine this decay branching ratio .
this has been done for several activations at atomki and the resulting cross sections are always in good agreement within the errors .
the weighted average of the ratios of the two cross sections from the two analyses is [email protected] .
this confirms the decay branching of 100 % for the @xmath19sn @xmath38-decay .
while the @xmath0cd(@xmath1sn reaction has been successfully observed for all measured energies , @xmath0cd(@xmath3,n)@xmath4sn cross sections can only be measured in the upper half of the investigated energy region where the ( @xmath3,n ) channel is open . because of the problems described in sec .
[ invesreac ] , the @xmath0cd(@xmath3,p)@xmath4 in cross section has been determined only below the @xmath0cd(@xmath3,n)@xmath4sn threshold . moreover , at the three lowest measured energies the @xmath0cd(@xmath3,p)@xmath4 in cross section is so low that no cross section value could have been derived .
therefore , the @xmath0cd(@xmath3,p)@xmath4 in cross section has been measured only at 4 energies .
figures [ ag_fig ] and [ anp_fig ] show a comparison of the experimental results to the hauser - feshbach statistical model cross sections @xcite obtained with the standard settings of the non - smoker .
there is excellent agreement for the ( @xmath3,n ) reaction .
the predicted cross sections are too low in the case of the ( @xmath3,p ) reaction . finally , the calculation yields cross sections which are too high by an almost constant factor of about 2.2 compared to the atomki data in the case of the ( @xmath3,@xmath15 ) reaction . while being at the same level of disagreement with the ( @xmath3,@xmath15 ) notre dame data above 9 mev , the notre dame data for the three lowest energies seem to indicate a different energy dependence than the theoretical one .
there is a factor of 5 disagreement between theory and experiment at the lowest measured energy of 7.566 mev .
since not only the capture reaction was measured but also the neutron and proton emission channels , interesting conclusions on the impacts of different inputs can be drawn . usually , it is assumed that the @xmath15 widths determine the cross sections in capture reactions because they are smaller than the particle widths .
inspection of the computed widths ( directly derived from the calculated transmission coefficients ; see @xcite for further details ) shows that this is not the case here . due to the small @xmath57 value and the high coulomb barrier the @xmath3 widths are smaller or comparable . only at the upper limit of the range of measured energies
the cross section also becomes sensitive to the @xmath15 width .
this is shown in fig .
[ sensi_fig ] where the sensitivity of the cross section ( ranging between 0 for no sensitivity to 1 for full sensitivity ) to variations in the @xmath3 and @xmath15 widths , respectively , is plotted .
a similar comparison was performed for the other measured channels .
our ( @xmath3,n ) cross sections are sensitive to the @xmath3 width and weakly dependent on the neutron width ( except close to the threshold where the neutron width becomes smaller than the @xmath3 width ) .
the @xmath0cd(@xmath3,p ) reaction is equally sensitive to @xmath3 and proton widths .
all channels are quite independent of the nuclear level density because transitions to the low - lying states dominate and a number of these are explicitly included in the calculation ( see @xcite for a list of included states ) .
the standard predictions make use of the @xmath3+nucleus optical potential by @xcite .
although this potential can reproduce scattering data over a large range of masses , it has been found to be problematic in describing @xmath3 capture and emission at low energies ( see , e.g. , @xcite ) . in figs .
[ potentials_ag_fig ] and [ potentials_anp_fig ] cross sections obtained with two different ( more recent ) @xmath3+nucleus potentials are shown . using the potential of @xcite , which was fitted on scattering data across a wide range of energies and masses , we obtain values not much different from those resulting from the use of the standard potential . using the potential of @xcite , which was fitted to ( n,@xmath3 ) and ( @xmath3,@xmath15 ) reaction data around @xmath58 ,
the capture cross sections are reduced by more than a factor of two and thus better agreement is found for the ( @xmath3,@xmath15 ) reaction .
however , due to the sensitivity of the ( @xmath3,p ) and ( @xmath3,n ) channels to the optical @xmath3 potential , their cross sections are also reduced which removes the previously good agreement with the ( @xmath3,n ) data and worsens the case of the ( @xmath3,p ) reaction .
it is interesting to note that recently the authors of ref . @xcite
have pointed out a possible difference between optical potentials derived from scattering data and such derived from reaction data .
they conclude that optical potentials derived from scattering may have to be modified before applying them to reactions @xcite .
figure [ sensi_fig ] clearly shows the high sensitivity of the capture reaction to the @xmath3 potential .
this leads to the conclusion that indeed the @xmath3 potential is the source of the disagreement with the experiment and that the capture reaction is best described with the potential of @xcite , even though it appears to have a similar energy dependence as the standard potential and thus may still overestimate the cross sections at energies below the measured ones . fixing the @xmath3 potential through the ( @xmath3,@xmath15 ) reaction
, one could assume that the disagreement between calculation and data for the ( @xmath3,p ) channel has to arise from the proton optical potential .
this conclusion appears puzzling when finally comparing with the ( @xmath3,n ) reaction .
for the latter we found only weak sensitivity to the neutron widths and compensating for the disagreement by changing the neutron width would require large modifications of the neutron optical potential .
since good agreement was found for neutron capture in this mass region @xcite , it seems far - fetched to allow such a large modification .
a possible explanation might be the fact that both ( @xmath3,p ) and ( @xmath3,n ) have a large negative @xmath57 value and that therefore only few , low - energy neutron and proton transitions contribute
. these will be very sensitive to the level scheme of low - lying levels .
the spin assignments to these levels still bear considerable uncertainty even in the latest compilation @xcite and the level schemes might still not be complete .
this could explain why the neutron and proton emission channels are underestimated in the calculation .
the standard statistical model rates of @xcite , utilizing the potential of @xcite , are widely used in stellar models .
for instance , with those rates the production of @xmath2-nuclei in the @xmath2-process in massive stars was studied in @xcite .
details on the branchings in the @xmath2-process path for the usual temperature range @xmath59 can be found in @xcite . in table
i of ref .
@xcite , it can immediately be seen what changes are brought about by switching from the @xmath3 potential of @xcite to the potential of @xcite which better describes our capture data . the branching at @xmath60 remains unchanged ( a ( @xmath15,p ) branching at @xmath19sn ) because photon - induced proton emission is by far faster than @xmath3 emission . at @xmath61 , proton and @xmath3
emission start to compete when using the standard rates .
however , with the lower rates obtained with the potential of @xcite , @xmath3 emission is still suppressed and proton emission is dominating . at @xmath62
the standard rates predict a ( @xmath15,@xmath3 ) branching already at @xmath26sn . with the new potential
the branching is shifted back to @xmath19sn and becomes a combined ( @xmath15,p)+(@xmath15,@xmath3 ) branching .
considering that the energy dependence at low energies may not be well reproduced and that the actual cross section may be even lower , as indicated by the trend seen in the low energy notre dame data , it is conceivable that the @xmath3 branching at @xmath62 is even further suppressed and may become negligible compared to the @xmath19sn(@xmath15,p ) branching .
the modification of the branching in the sn chain by itself will not lead to large changes in the description of the @xmath2-process .
however , our results show that the treatment of the optical @xmath3 potential at astrophysically relevant energies will have to be improved . they also seem to suggest that the branchings obtained with rate set c of @xcite may be more accurate than those obtained with the standard rate set a concerning the @xmath3 branchings .
the cross sections of three @xmath3-induced reactions on @xmath0cd have been measured using the activation technique .
the @xmath0cd(@xmath1sn cross section was determined in the energy range between e@xmath29=7.56 and 12.06mev . within this energy range , the particle emitting @xmath0cd(@xmath3,n)@xmath4sn and @xmath0cd(@xmath3,p)@xmath4 in cross sections have been measured above and below the ( @xmath3,n ) threshold , respectively .
for all three investigated reactions , the experimental results were compared with the cross sections calculated using the non - smoker statistical model code .
the standard settings of the non - smoker code provided an excellent prediction for the ( @xmath3,n ) cross section while the calculated cross sections were too low and too high for the ( @xmath3,p ) and ( @xmath18 ) channels , respectively .
the sensitivity of the predictions to the input parameters was also examined .
it was found that good agreement with the experiment can be obtained for the ( @xmath18 ) channel by modifying the @xmath3 optical potential . the same potential , however , simultaneously results in a worse reproduction of the experimental results in the ( @xmath3,n ) and ( @xmath3,p ) channels .
the calculations for these channels , in turn , appear to have problems in other nuclear properties , the proton and neutron optical potentials or , most likely , the uncertain spin and parity assignments of excited states in the exit channels . the value of the ( @xmath3,@xmath15 ) reaction cross section and rate influences the branching points in the @xmath2 process path .
the impact of the new experimental cross section , which is lower than previously predicted , has been examined for the sn isotopic chain .
the result underlines the importance of the experimental investigation of @xmath3-induced reactions in the mass and energy region relevant to the astrophysical @xmath2 process .
we like to thank j. greene from argonne national laboratory for the preparation of the targets used at notre dame . the assistance of c. ugalde , e. strandberg , a. couture , j. couture , and e. stech during the course of the experiment is highly appreciated .
this work was supported by otka ( grant nos .
t042733 , t049245 , f043408 and d048283 ) , by the nsf - grant phy01 - 40324 , mta - otka - nsf grant 93/049901 , the swiss nsf ( grants 2024 - 067428.01 , 2000 - 105328 ) , the scientific and technical research council of turkey ( tubitak ) - grant tbag - u/111 ( 104t2467 ) , and through the joint institute of nuclear astrophysics ( www.jinaweb.org ) nsf - pfc grant phy02 - 16783 . gy .
gy . and zs . f. acknowledge support from the bolyai grant .
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apart from providing independent supporting evidence of the big bang , the detection and subsequent study of cosmological chemical evolution provides the empirical details of galaxy formation and evolution .
how primordial and processed gas is consumed by star formation , the dominant feedback processes and merging scenarios , may all contribute to the overall evolution of chemical abundances .
one high - precision probe of this evolution is the spectroscopic study of damped lyman-@xmath0 systems ( dlas ) : absorbers with neutral hydrogen column densities @xmath2 .
although these observations demonstrate that dlas arise along lines of sight through distant galaxies , they do not directly disclose details such as the galaxy s morphology , luminosity , mass or age .
there exists substantial evidence that dlas arise in a variety of galaxy types . at low-@xmath3 ( @xmath4 ) ,
kinematic and hi 21-cm absorption studies ( e.g. @xcite ; @xcite ) suggest a significant contribution from spiral galaxies , a view supported at high-@xmath3 by kinematic modelling and abundance studies @xcite .
however , direct imaging at low-@xmath3 ( e.g. * ? ? ?
* ) reveals that dla hosts are a mix of irregulars , spirals and low surface - brightness galaxies ( lsbs ) .
a recent @xmath5 hi 21-cm emission study @xcite supports this .
@xcite argue that the number of dlas per redshift interval and the @xmath6 distribution imply that dlas at @xmath7 are a mix of spirals and lsbs whereas , at higher @xmath3 , they are more likely to be dwarfs .
this is supported by fitting of chemical evolution models to dla metal abundances ( e.g. * ? ? ?
* ) and by recent 21-cm absorption searches at high redshift @xcite .
though further work is clearly needed , the direct and indirect evidence for a ` mixed bag ' of dla hosts is already compelling .
evidence for an increase in dla metallicities , [ m / h ] , with cosmic time has emerged only gradually @xcite , the latter reference using over 100 dlas to provide the strongest statistical evidence so far .
such large samples are required due to the huge scatter ( @xmath8 ) in [ m / h ] at a given epoch ( see fig .
[ fig:1 ] ) , a diversity expected given the variety of dla hosts discussed above .
however , the diversity in [ m / h ] could also significantly _ bias _ any estimate of chemical evolution , as could several observational selection effects ( e.g. * ? ? ? * ) . in @xcite
we suggest that by selecting those dlas in which h@xmath1 absorption is detected , one may reduce or possibly avoid some of the biases besetting the general dla population .
there are currently 9 confirmed h@xmath1-bearing dlas ( see below ) and , typically , h@xmath1 is detected in only a few velocity components .
these h@xmath1-bearing components seem distinct from the others , showing lower temperatures and higher dust depletion factors [ m / fe ] @xcite .
therefore , h@xmath1-bearing dlas might be a less biased tracer of chemical evolution than the general dla population since they may allow one to focus on a narrower range of physical conditions throughout cosmic time .
, dust - depletion [ m / fe ] , and molecular fraction ( @xmath9 ) evolution for confirmed ( filled circles ) and tentative ( hollow circle ) h@xmath1 detections compared with values from the @xcite dlas ( small diamonds ) .
the values adopted are discussed in the text .
linear fits to the h@xmath1-bearing dlas ( long dashes ) and general dlas ( short dashes ) were obtained by quadrature addition of a constant to the individual error bars such that @xmath10 . due to its much lower @xmath11 and potentially high photo - dissociation rate @xcite ,
we do not include 0515@xmath124414 in these fits ( but see table [ tab:1]).,scaledwidth=70.0% ] h@xmath1 is detected in dlas via the lyman and werner - band uv absorption lines which generally lie in the hi lyman-@xmath0 forest .
a compilation of results from h@xmath1 searches in dlas is given in table 8 of ( * ? ? ?
* , hereafter l03 ) , for which 7 dlas have confirmed h@xmath1 detections and metallicity measurements : 0013@xmath12004 ( @xmath13 ) , 0347@xmath123819 , 0405@xmath12443 ( @xmath14 ) , 0528@xmath122505 , 0551@xmath12366 , 1232@xmath15082 and 1444@xmath15014 .
the dla towards 0013@xmath12004 @xcite comprises several absorbing components , of which 2 are dominant ( their components @xmath16 and @xmath17 ) : @xmath6 is measured at the mean redshift and we use the mean @xmath18h@xmath19 with error given by the range of @xmath18h@xmath19 in l03 . for the dla towards
1232@xmath15082 we use the @xmath18h@xmath19 value and error from @xcite .
we include two further dlas : ( i ) the recent detection towards 0515@xmath124414 @xcite and ( ii ) 0000@xmath122620 , regarded as only a tentative detection by l03 .
however , the h@xmath1 identification has been carefully scrutinised by @xcite and relies on two h@xmath1 absorption features , the l(4 - 0)r1 and w(2 - 0)q(1 ) lines , the former appearing relatively clean from lyman-@xmath0 forest blending .
a tentative detection of h@xmath1 in 0841@xmath151256 has also been reported @xcite , though confirmation requires future data and analyses .
lcccccc & & & + sample & @xmath20 & @xmath21 & @xmath20 & @xmath21 & @xmath22 & @xmath23 + + exc .
0515 & 0.08 & @xmath24 & 0.14 & @xmath25 & 2.2 & 0.28 + inc .
0515 & 0.04 & @xmath26 & 0.03 & @xmath27 & 1.9 & 0.33 + + exc .
0515 & 0.05 & @xmath28 & 0.24 & @xmath29 & 1.7 & 0.47 + inc .
0515 & 0.06 & @xmath30 & 0.25 & @xmath31 & 1.0 & 0.95 + + exc .
0515 & 0.04 & @xmath32 & & & & + inc .
0515 & 0.06 & @xmath33 & & & & + [ tab:1 ] in fig .
[ fig:1 ] we plot against @xmath11 the metallicity [ m / h ] , dust - depletion factor [ m / fe ] and molecular fraction @xmath34 $ ] for the 9 h@xmath1-bearing dlas , comparing the former two quantities with dlas in @xcite with zn , si , s or o metallicity over the relevant redshift range .
[ m / h ] for the h@xmath1-bearing dlas is [ zn / h ] , except for 0347@xmath123819 and 1232@xmath15082 where it is [ s / h ] and [ si / h ] . for 0515@xmath124414 , [ zn / fe ]
is from @xcite . the main results from fig .
[ fig:1 ] are summarized by the statistics in table [ tab:1 ] : ( i ) [ m / h ] , [ m / fe ] and @xmath9 for the h@xmath1-bearing dlas are anti - correlated with @xmath11 at the 95% confidence level ( i.e. more significant than for the general dla population ) , ( ii ) [ m / h ] shows a steeper evolution with @xmath11 and a smaller scatter about the slope than the general dla population , ( iii ) [ m / fe ] in h@xmath1-bearing dlas shows strong evolution with @xmath11 while the general dlas show no evidence for evolution , and ( iv ) @xmath9 ranges over @xmath35 and shows a very steep evolution with @xmath11 .
the new results ( i)(iii ) support our hypothesis that h@xmath1-bearing dlas form a chemically distinct sub - class and may trace chemical evolution more reliably .
the @xmath9@xmath11 correlation was studied by l03 and is discussed further below .
the [ m / h]s and @xmath9s in fig .
[ fig:1 ] are measured using the total @xmath6 across the dla profile and are not specific to the h@xmath1-bearing components .
[ m / fe ] is generally found to be uniform across most dla profiles @xcite , indicating that [ m / h ] should be uniform .
however , the h@xmath1-bearing components typically have much higher [ m / fe ] values than other components in the same dla ( e.g. l03 and 0347@xmath12383 s [ si / fe ] profile in @xcite ) .
these components usually dominate the non - refractory metal - line profiles and so , although [ m / h ] and @xmath9 will be systematically underestimated , the effect will not be large .
the fitted slopes in fig .
[ fig:1 ] are likely to be reasonably robust against this effect , but a larger sample and more detailed study is clearly required . what observational selection effects and biases could contribute to the steep @xmath9@xmath11 evolution ?
firstly , the sample is inhomogeneous since the spectra do not all have similar s / n and since the h@xmath1 detection methods and criteria were not uniform .
indeed , the weak h@xmath1 lines detected towards 0000@xmath122620 are at the typical non - detection level ( see fig . 16 in l03 ) .
the @xmath9@xmath11 correlation is therefore only tentative .
secondly , the h@xmath1 detection limit will alter with @xmath3 : equivalent widths increase but lyman-@xmath0 forest blending worsens with increasing @xmath3 .
though this is an unlikely culprit for the @xmath35 evolution observed , precise quantification of these competing effects requires numerical simulations .
dlas containing large amounts of dust could suppress detection of their background quasars and may therefore be ` missing ' from our sample @xcite .
however , since [ m / h ] , [ m / fe ] and @xmath9 are positively correlated with each other ( e.g. l03 ) , this effect is likely to suppress , rather than create , the correlations in fig .
[ fig:1 ] .
a recent survey for dlas towards radio - selected quasars @xcite also indicates that the number of such ` missing ' quasars is likely to be small .
selecting those dlas which exhibit h@xmath1 absorption may focus on systems with a narrower range of physical conditions than the dla population as a whole .
tentative support for this conjecture lies in the steeper , tighter [ m / h]@xmath11 anti - correlation observed for the h@xmath1 systems studied here .
@xcite recently presented detailed chemical evolution models which give a slope for the [ m / h]@xmath11 relation of @xmath36 .
they correct this result for various observational biases to match the shallower slope observed for the general dla population .
however , the steep [ m / h]@xmath11 slope observed for h@xmath1-bearing systems could be less affected by these biases and may avoid those introduced by sampling many different ism gas phases .
it might therefore be more comparable to the uncorrected slopes in the models .
h@xmath1-selected dlas are therefore a candidate for a less biased probe of chemical evolution .
that there exists such a large range ( @xmath37 ) in the values of @xmath9 in fig .
[ fig:1 ] may not be surprising : @xcite describes a @xmath38}=-1 $ ] photo - ionization model for clouds in local hydrostatic equilibrium . for a representative incident uv background flux and dust - to - metals ratio , the molecular fraction in this model shows a sudden increase of @xmath39 for only a small increase in the total hydrogen density .
therefore , the very steep @xmath9@xmath11 correlation could be achieved with a modest increase in dust content at lower redshifts , consistent with the observed [ m / fe]@xmath11 anti - correlation .
l03 also discuss how @xmath9 might be very sensitive to local physical conditions .
for example , within the schaye model , one expects an anti - correlation between @xmath9 and the intensity of the uv background .
however , the behaviour of the uv background flux with redshift over the range @xmath403 is still a matter of considerable uncertainty .
the strong decrease in @xmath9 at high redshift may also be consistent with recent hi 21-cm absorption measurements in dlas @xcite , where a generally higher spin / excitation temperature is found at @xmath41 .
with an increased sample size and more detailed analyses , the @xmath9@xmath11 anti - correlation , if real , may provide complementary constraints on these problems . , a. c. , mathlin , g. p. , churches , d. k. , & edmunds , m. g. 2000 , in esa sp , vol .
445 , star formation from the small to the large scale , ed .
f. favata , a. kaas , & a. wilson ( noordwijk , the netherlands : european space agency ) , 21 , s. a. , molaro , p. , centuri ' on , m. , dodorico , s. , bonifacio , p. , & vladilo , g. 2001 , in deep fields , ed .
s. cristiani , a. renzini , & r. williams , eso astrophysics symposia series ( berlin , germany : springer ) , 334 | arxiv |
in recent years , accumulating evidence supports the hypothesis that agn reflects an important stage of galaxy formation .
observations reveals the fact that agn activity and star formation frequently occur together ( e.g. , cid fernandes et al .
2001 ; kauffmann et al . 2003
; see reviews in gonzalez delgado 2002 ) .
an important clue of co - evolution of agn and starburst is the fundamental , tight relationship between mass of supermassive black hole ( smbh ) and the velocity dispersion of bulge where the smbh resides in ( e.g. , magorrian et al .
1998 ; gebhardt et al .
2000 ; tremaine et al .
2002 , greene & ho 2006 ) . by analyzing the spectra of narrow - line agns from sloan digital sky survey ( sdss , york et al .
2000 ) , heckman et al .
( 2004 ) found that most of accretion - driven growth of smbh takes place in the galaxy with relatively young stellar population .
recently , as essential relationships relating to agn s activity , the eigenvector 1 space ( boroson & green 1992 , hereafter bg92 ) was found to be related with ages of the stellar populations as assessed by infrared color @xmath7(60,25 ) ( wang et al . 2006 ) .
it is then natural to ask a question `` what is a young agn ? '' .
mathur ( 2000 ) argued that narrow - line seyfert 1 galaxy ( nls1 ) with high eddington ratio and small black hole mass might be a young agn .
if so , the co - evolution of agn and starburst implies that nls1s are expected to be associated with relatively young stellar populations . to understand the elusive agn - starburst connection
, we need to carefully examine the properties of agn s host galaxy
. however , optical spectroscopic study is possible for only a few type i agns because the strong nuclear emission usually masks the relatively faint stellar components . by fitting deep off - nuclear optical spectra canalizo & stockton ( 2001 ) and nolan et al .
( 2001 ) determined the ages of circumnuclear stellar populations for a few ir and optical - selected qsos respectively . in the happy case ,
brotherton et al .
( 1999 ) discovered a spectacular `` post - starburst quasar '' unj1025 - 0040 with a @xmath3400 myr old stellar population .
wang et al . ( 2004 ) identified sdssj022119.84 + 005628.4 as a nls1 ( [email protected] ) whose spectrum displays a clear balmer jump .
however , the authors did not perform further stellar population analysis . in this paper
, we perform a detailed examination of the physical properties of post - starburst agn sdssj085338.27 + 033246.1 and discuss its implications on study of agn s evolution .
the optical spectrum is extracted from sdss data release 4 ( adelman - mccarthy et al . 2006 ) .
its appropriate spectrum allows us to separate it into a young stellar population and a typical nls1 spectrum .
in addition , the emission line profiles allows us to determine the location on the line ratio diagnostic diagrams .
we begin with a brief description of the data reduction in 2 .
the results and implications are presented in 3 .
the cosmological parameters : @xmath9 , @xmath10 , and @xmath11 are adopted for calculations .
we extract the optical spectrum of sdssj085338.27 + 033246.1 when we carry out a systematic search for broad line agns from the objects listed in the catalogues released by kauffmann et al .
( 2003 ) and heckman et al .
totally hundreds of such objects are extracted from the parent sample .
the details of the search and properties of the sub - sample will be presented in subsequent papers . among these objects sdssj085338.27 + 033246.1 has unique properties with strong enough typical agn spectrum superposed on a spectrum of a - type star .
it is coincident that we find the object has been identified as a member of a sample of 74 post - starburst broad line agns by zhou et al .
( 2005 ) when our paper is being prepared .
the observed spectrum is smoothed with a boxcar of 3 pixels ( @xmath35 ) to enhance s / n ratio and precision of the spectra measurements .
standard iraf procedures are adopted to reduce the raw data , including galactic extinction correction ( with @xmath12 from nasa / ipac extragalactic database ( ned ) and assuming @xmath13 ) and de - redshift to rest frame with @xmath14 .
the total light spectrum at rest frame is displayed in figure 1 ( the second line from top to bottom ) .
the spectrum clearly shows a prominent balmer jump at blue even diluted by an agn continuum and high order balmer series . in the next step
, the principal component analysis ( pca ) method is developed to remove the stellar light from the observed spectrum ( e.g. , li et al . 2005 ; hao et al 2005 ) .
we build a library of stellar absorption spectra by applying pca technique on standard ssp models developed by bruzual & charlot ( 2003 , hereafter bc03 ) .
the first seven eigenspectra are used to model the starlight component by their linear combination . in order to appropriate model the starlight component ,
our template contains the seven eigenspectra , a power - law continuum , a feii complex of agn ( adopted from bg92 ) and a galactic extinction curve ( cardelli et al .
1989 ) . in order to avoid the distortion of low s / n
, a @xmath15 minimizing is performed over the rest wavelength range from @xmath163700 to @xmath166800 , except for the regions around the strong emission lines .
the removal of the stellar component is illustrated in figure 1 as well .
also plotted are the modeled feii blends and emission - line spectrum of the agn .
the flux of the feii blends measured between rest frame wavelength @xmath164434 and @xmath164684 is @xmath17 .
the detailed comparison between the observed and modeled spectrum at blue is shown in the insert plot a. it is clear that the modeled spectrum reproduces the observed absorption features rather well .
the agn emission lines are modeled by specfit task as described in wang et al .
( 2005 , 2006 ) .
briefly , each narrow line ( e.g. , h@xmath7 , h@xmath18 , [ nii ] ) is modeled by a gaussian component
. the intensity ratio of [ nii ] doublets is forced to equal to the theoretical prediction .
the spectra modeling is schemed in the insert plot b and c for h@xmath18 and h@xmath7 region , respectively .
the upper limit of [ oiii]@xmath165007 flux @xmath19 } ) < 1.2\times10^{-16}\ \rm{ergs\ s^{-1}\ cm^{-2}}$ ] is estimated by integration rather than fit because the feature is very faint .
in addition to these lines , the spectrum displays a broad emission feature at about 5880 . based on its asymmetric profile
, we identified this feature as hei@xmath165876 contaminated by broad naid@xmath205890 , 5896 emission .
we find ew(hei+naid)@xmath21 and ( hei+naid)/h@xmath22 .
the naid emission was detected in a few agns ( e.g. , veron - cetty et al .
2004 ; veron - cetty et al . 2006 and references therein , thompson 1991 ) .
the calculations indicated that the existence of large naid emission ( naid / h@xmath7=0.01 - 0.05 ) is related to models with high density ( @xmath23 ) and large column density ( @xmath24 ) ( thompson 1991 ) .
the measured line properties are summarized in table 1 .
the propagation of error is included in the uncertainties shown in parentheses .
all the uncertainties given in columns ( 2 ) and ( 3 ) are caused by profile modeling .
according to its spectra properties , we classify sdssj085338.27 + 033246.1 as a nls1 both because of the extremely faint [ oiii ] emission ( [ oiii]/[email protected] ) and because of the relatively narrow h@xmath18 broad component ( fwhm(h@xmath26)=@xmath27 ) .
moreover , the measured rfe is as large as @xmath28 , which is typical of nls1s .
we further calculate its black hole virial mass and eddington ratio in terms of the h@xmath7 broad component according to the equations in greene & ho ( 2005 ) : @xmath29 @xmath30 the intrinsic luminosity @xmath31 is used for calculations because of the large intrinsic extinction @xmath32 .
the extinction is calculated from the line ratio h@xmath33/h@xmath34 , assuming a galactic extinction curve and @xmath13 ( osterbrock 1989 ) . the inferred virial mass and eddington ratio is @xmath2 and @xmath1 , respectively .
it is clear that all these properties ( i.e. , small black hole mass , large rfe value and large eddington ratio ) indicate the object should be potentially classified as a nls1 . the radio radiation at 1.4ghz of the object was detected by nvss ( condon et al .
1998 ) and first survey ( becker et al . 1995 ) .
the map of the first survey shows an unresolved source with a flux @xmath34.04mjy and position @xmath35 , @xmath36 ( j2000 ) .
the discrepancy in position given by the optical and radio surveys is much less than 1 ( @xmath30.3 ) .
we determined the extinction - corrected continuum flux that is contributed by agn at rest wavelength @xmath37 to be @xmath38mjy . if the radio emission is mainly due to agn , the inferred radio loudness @xmath39 defined as @xmath40 ( kellermann et al .
1989 ) is @xmath41=1.40 corresponding to @xmath42=1.12 for 5ghz radio flux assuming a spectral shape @xmath43 from optical to radio band . ] . adopting the division @xmath44 between radio loud and quiet agn , sdssj085338.27 + 033246.1
is an object with intermediately strong radio emission .
we further calculate its radio luminosity @xmath45 .
this luminosity has same order of magnitude of the most radio - luminous starburst ( @xmath46 , smith et al .
it has long been known that the decimeter radio luminosity emitted from star - forming galaxy traces supernova rate of massive enough stars ( i.e. , @xmath47 ) .
the lifetime of these massive supernova progenitors is @xmath48yr .
the radio supernova itself and its remnant has lifetime @xmath49yr and @xmath50yr , respectively .
the average sfr over the past @xmath51yr therefore relates with the radio emission attributed to supernova as ( condon 1992 ) @xmath52 for the object , the estimated average sfr is @xmath53 ( see sect . 3.2 for details ) . using a salpeter imf ( salpeter 1955 )
, this corresponds to a @xmath54 .
the inferred luminosity is therefore @xmath55 and is about one order lower than the total radio luminosity .
the `` a - type star '' spectrum indicates the age of the stellar population is no more than a few@xmath56 yrs . to interpret the spectrum of the young stellar population , we extract a series of spectra of ssp models of bc03 with a solar metallicity and with a chabrier initial mass function .
the extracted spectra are matched with the observed spectrum one by one within the wavelength range 3500 - 5000 .
the spectrum red of @xmath165000 is not used because this part is obviously contaminated by an old population .
figure 2 illustrates the best match between the observed spectrum and a 0.1gyr old ssp model .
the model predicted mass of the starburst is @xmath57 .
this simple ssp model shows a past average sfr @xmath58 .
however , recent studies suggested that the agn and starburst activity perhaps not co - evolve simultaneously .
schmitt ( 2001 ) suggested that the starbursts may predominate over agns in their earlier phase .
yan et al .
( 2005 ) recently suggested that most of sdss post - starburst galaxies hold somewhat agn like activities .
the post - starburst is the phase in which the galaxy already ceased star formation at some recent epoch .
the derived @xmath59gyr post - starburst in sdssj085338.27 + 033246.1 is somewhat similar with the @xmath60gyr post - starburst that was obtained by brotherton et al .
( 1999 ) in unj1025 - 0040 .
[ oii]@xmath163727 line is widely used as an empirical indicator of ongoing sfr ( @xmath61yr ) for emission line galaxy surveys ( e.g. , gallagher et al .
1989 ; kennicutt 1992 ; hippelein et al .
its practicability led to several calibrations and a great deal discussions ( e.g. , kewley et al .
2004 ; kennicutt 1998 ; yan et al .
the extinction - corrected flux of [ oii]@xmath62 doublets is @xmath63 ( with its observed flux shown in table 1 ) , which yields a ratio @xmath64([oii]/[oiii])@xmath650.55 . adopting the ratio @xmath64([oiii]/h@xmath66)@xmath67 - 0.65
, the object is consequently located in the region that represents star formation ( kim et al .
2006 and references therein ) .
it means that the [ oii ] emission ought to be almost entirely attributed to star formation ( see below ) .
we use the calibration @xmath68,42}}}{16.73 - 1.75[\log(\mathrm{o / h})+12]}m_{\odot}\rm{yr^{-1}}\ ] ] ( kewley et al . 2004 ) to estimate the sfr , where @xmath69,42}$ ] is the luminosity of [ oii ] emission in units of @xmath70 .
the sfr is inferred to be round about 3.0 @xmath71 by adopting the assumption used in ho ( 2005 ) , i.e. , the metallicity is twice of solar corresponding to @xmath72 . here , we obtain a residual but quenched ongoing sfr as obtained in the optically selected qsos by ho ( 2005 ) .
the distance - independent birthrate parameter @xmath73 is defined as the ratio of the current sfr to the average past one ( kennicutt et al .
1994 ) . as a particular case ,
the object has extremely small value of @xmath74 , i.e. , has present sfr significantly lower than the past .
the traditional bpt diagram ( baldwin et al . 1981 ) is a powerful tool for diagnosing the origin of emission of narrow lines for emission - line galaxies .
the location of the object in the bpt diagram in which the line ratio [ oiii]/h@xmath18 is plotted against [ nii]/h@xmath7 is marked by solid square in figure 3 ( left panel ) .
the solid and dashed line shows the demarcation line between agn and starburst galaxy defined by kewley et al .
( 2004 ) and kauffmann et al .
( 2003 ) , respectively .
the figure shows clearly that the position of the object is marginally above the threshold used to define representative hii region .
the similar plot is shown in figure 3 ( right panel ) but for [ oiii]/h@xmath18 v.s . ( [ sii]@xmath166719 + 6731)/h@xmath7 . in this case , the position of the object falls into the region that represents starburst and is far below the demarcation line .
the combination of these two diagnosis suggests the observed narrow emission lines are mainly produced by star - formation .
what is the distribution in the bpt diagram for post - starburst agns is a further interesting question . here
it is interesting to give more discussions on the elusive agn - starburst connection .
wang et al . ( 2006 ) recently indicated that the well - documented e1 sequence most likely represents an evolutionary track of agn .
the track further implies that agn with high eddington ratio evolves to one with low eddington ratio .
this result also naturally implies that nls1s that occupy one extreme end of e1 should be associated with relatively young stellar populations .
apart from the evidence mentioned above , for the ir - selected qsos , canalizo & stockton ( 2001 ) found the ages of circumnuclear stellar populations range from current star formation to @xmath75myr old .
subsequent spectroscopy studies indicated that about 70%-100% ir - selected qsos are extremely or intermediately strong feii emitters ( e.g. , lipari et al .
2003 ; zheng et al .
moreover , zhou et al .
( 2005 ) found that more than half of the post - starburst type i agn fulfill the criterion for nls1 .
all these evidence appear to reveal that a young agn is most likely a strong feii emitter with relatively narrow h@xmath18 profile .
in contrast , old stellar populations ( @xmath76gyr ) are found to dominate the off - nuclear ( @xmath77 ) stellar population for optical - selected qsos ( nolan et al .
2001 and references there in ) .
these accumulating clues lead us to propose a possible evolutionary scenario that links both agn and starburst phenomena
. the massive starburst might be dominant in the earlier evolutionary phase .
then the starburst passively evolves to a - type stars when the plenty gas falls into the center of a galaxy under the gravitational attraction of smbh . at one stage about @xmath78yr after the beginning of the starburst , the smbh begin to accrete matter with small black hole mass and high eddington ratio .
the feedback of the agn suppresses circumnuclear star formation at the same time ( e.g. , kim et al .
the black hole mass grow substantially in the formed bulge in this short phase ( e.g. mathur et al .
2001 ; mathur & grupe 2005 ) .
the duration of the phase is commonly estimated as @xmath79-folding time scale @xmath80yr ( salpeter 1964 ) , where @xmath81 is the radiative efficiency .
the differential growth of agn and starburst allows the nls1s below the @xmath82 relation for inactive galaxies to approach normal @xmath82 relation ( mathur & grupe 2005 ; mathur et al .
2001 ; wandel 2002 ; bian & zhao 2004 ) .
the agn then shines with decreasing accretion rate and insignificantly increasing black hole mass because of the consumption of the gas .
the scenario implies that the agn and host co - evolve marginally around the common @xmath82 relation .
the luminous agn phase persists for typical agn lifetime which is usually believed to be @xmath83 yr with however large uncertainties ( see reviews in matini 2004 ) . during this phase , the young stellar population continuously ages and
its importance gradually fades .
the underlying old stellar population ( a few gyr ) finally becomes dominant in the emission of host of an old agn .
in fact , in addition to the old stellar populations , relatively old post - starbursts ( 0.1 - 2gyr ) are frequently detected in off - nuclear regions of a few powerful radio - loud agns ( e.g. tadhunter et al .
2005 and references therein ) .
after the luminous phase , agn then passively evolves to a stage with low luminosity , or low radiative efficiency . in summary
, this scenario could be described as following path : starburst @xmath84 nls1+post - starburst @xmath84 luminous agn with decreased eddington ratio+old stellar population @xmath84 less luminous agn .
we believe future studies of agn+post - starburst composite objects such as sdssj085338.27 + 033246.1 are important for developing a rational scenario to interpret the agn - starburst connection .
the physical properties of post - starburst agn sdssj085338.27 + 033246.1 are derived by analyzing its optical spectrum .
it allows us to obtain results as following .
the object can be identified as a nls1 ( ( [ oiii]/h@xmath85 , @xmath86 and [email protected] ) associated with a post - starburst stellar population as identified from the size of the balmer jump .
a simple ssp model indicates the starburst with a mass @xmath87 possibly took place @xmath88 yr ago .
the [ oii ] inferred sfr is as small as @xmath33.0@xmath89 which is much smaller than the past average one @xmath6 .
its locations in the bpt diagrams show the hii region significantly contributes to the emission of the narrow lines .
we further discuss its implications on the elusive agn - starburst connection .
we would like to thank the anonymous referee for very useful comments and important suggestions .
we thank d. w. xu , c. n. hao , j. s. deng and c. cao for valuable discussions .
we are grateful to todd a. boroson and richard f. green for providing us the feii template .
this work was supported by the national science foundation of china ( grant 105030005 and 10473013 ) .
this research has made use of the nasa / ipac extragalactic database , which is operated by jpl , caltech , under contact with the nasa .
the sdss archive data is created and distributed by the alfred p. sloan foundation .
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, 2006 , astro - ph/0602239 wandel , a. , 2002 , , 565 , 762 wang , j. , wei , j. y. , & he , x. t. , 2004 , chjaa , 4 , 415 wang , j. , wei , j. y. , & he , x. t. , 2005 , , 436 , 417 wang , j. , wei , j. y. , & he , x. t. , 2006 , , 638 , 106 yan , r. b. , newman , j. a. , faber , a. m. , et al .
2006 , astro - ph/0512446 york , d. g. , et al .
2000 , , 120 , 1579 zheng , x. z. , xia , x. y. , mao , s. , wu , h. , deng , z. g. , 2002 , , 124 , 18 zhou , h. y. , wang , t. g. , dong , x. b. , wang , j. , lu , h. , 2005 , mem , s. a. it 76 , 93 cccc line identification & flux ratio & fwhm + & & ( @xmath90 ) + h@xmath66 & 1.0 & @xmath91 + h@xmath26 & @xmath92 & @xmath93 + @xmath94\lambda$]5007 & @xmath95 & + h@xmath33 & @xmath96 & @xmath97 + h@xmath98 & @xmath99 & @xmath100 + @xmath101\lambda6583 $ ] & @xmath102 & @xmath103 + feii 4570 & @xmath104 & + @xmath105\lambda$]3727 & @xmath106 & + @xmath107\lambda$]6716 & @xmath108 & @xmath109 + @xmath107\lambda$]6731 & @xmath110 & + hei+naid & @xmath111 & + | arxiv |
How Is Digital Transformation Changing Marketing?
Digital Marketing Digital Transformation Corporate
Author Clodagh O'Brien
Topic Digital Marketing
Digital Transformation: 5 Examples of Organizations that Excel Digital Marketing Digital Skills Digital Transformation Industry
Is the Future of Digital Transformation Cognitive? Digital Transformation Industry Corporate
What are the Benefits of Digital Transformation? Digital Skills Digital Transformation Industry Corporate
The rise of the internet and the proliferation of digital, not just as a technology, but as a media format, have had some profound and unexpected effects on 21st-century life. While everyone expected that digital technology would make things faster what few people correctly predicted was the social impact that digital media, combined with online connectivity, would have.
When it comes to marketing, going digital has had massive consequences. Now properties of digital media such as more accurate metrics, combined with interactivity, have created whole new marketing opportunities.
So, there's no doubt that digital technology can play a powerful role as a marketing tool. But what about the digital transformation itself? What is this doing to change the way that marketing works?
Int his article, we dig deep to take a closer look at the implications.
The Unavoidable Change
While the term "digital transformation" may sound like a nebulous concept, the actual results are pretty easy to understand. We have been experiencing them for years and are now seeing an accelerated pace of changes that have come before.
When people in professional industries talk about digital transformation they're talking about how digital technology is understood, and then applied and integrated into our everyday work tasks, whether that is at daily, individual employee level or the broader sense of entire business operations.
At an individual level, digital transformation might be something as efficient as electronic health records in the medical or wellness industries. The transition to digital records makes this data more accessible, faster to process, and increases the likelihood of health professionals being able to make more informed decisions.
On an industry scale, the digital transformation has already shown what it can do for businesses like Amazon and Uber. These businesses have taken traditional business concepts, like retail sales and transit, and then applied innovative digital technologies that have left the competition behind as they surged ahead.
In general, however, digital transformation is usually looked at as a whole for how it is affecting business. In the area of marketing, specifically, it can bring about some exciting and profitable changes for those with vision.
The Digital Funnel
One of the first places where digital transformation influences marketing is the funnel, a traditional concept that marketers use to map out the actions potential customers make, taking a multi-stage journey that finally results in committing to an actual purchase.
Before the advent of digital technologies, the marketing funnel was straightforward and, in some ways, inviolable. The five stages include:
Awareness – the stage where consumers first realize that you offer a product or service they may be looking for.
Interest – when a shopper does further research to see whether your business meets their needs.
Consideration – they are now taking a serious interest.
Intent – when they start building towards a decision in a business's favor because they feel they need to product or service.
Decision – a consumer is converted into a customer after making a purchase.
At nearly every state, in a pre-digital marketing world, a business could only create marketing materials and then hope for the best. An intervention was only possible if an informed sales person was there to engage with a potential customer directly.
Due to digital transformation, these steps now gives a business a much greater amount of control in the process giving marketers two invaluable new tools: multi-stage interactivity and analytics.
Personalization Is Possible
One of the most effective ways that the digital transformation has changed the way digital marketing works is the way it can now personalize content to individual customers.
Due to the combination of metrics and interactivity, it's now possible to track the actions and behavior of consumers at an individual level, then take that data to provide a personalized marketing response.
Keeping track of a customer purchase, and then suggesting similar products—or in some cases, 'refills' for consumable items—is just the tip of the iceberg. Now, with the metrics from social media platforms like Facebook, it's possible to track the interests of individual customers, make recommendations, and even send personalized emails based on that consumer behavior before they convert.
Marketing experts no longer need to guess at where consumer interest may lie when consumer interest is being tracked on social media.
Data Is King in Digitization
The single, biggest 'blind spot' in marketing prior to digital transformation was the lack of high quality, actionable data for marketing experts to make decisions. Once a poster for a subway station was created, or a commercial for television was produced, there was no accurate way to engage the effectiveness of that marketing content. How many people saw that subway poster? How many people watched the commercial on television, let alone went out and bought the product strictly because of it?
Analytics was a game changer for marketing and digital transformation continues to emphasize just how useful it is going to be in all future marketing efforts. For example, a video on YouTube, Facebook, Instagram, and other social media platforms can tells a marketing team exactly how many people watched the video. Moreover, if those people click on the "Call To Action" button taking a viewer to a website it's easy to measure how effective the video is in converting people. More granular information is available, such as which social media platforms people watched the video on, where these people live, or what time of day the video garnered the most views and click-throughs.
In other words, digital transformation now gives marketing experts much more precise user data and metrics, allowing them to tweak and optimize marketing plans. Knowing what doesn't work or what does and just how well makes it possible to be far more agile, responsive, and targeted.
Interactivity is Changing Marketing
Digital transformation has had a huge, unprecedented impact on interactivity. Unlike traditional media, such as film, television, and music, digital media is interactive giving people more choice over what they consume, how they consume it, and who they share it with.
For instance, websites can now give people options on what information they want to view and the order in which they want to consume it. Social media allows people to interact with company accounts, asking questions and getting responses back in return. Consumers can even give feedback for content they read or view with heart, thumbs-up, and favorite buttons or leave comments.
The exchange that can happen on social media, and even directly on ads, changes everything. With live ads, like live streams, consumers can be on social media and watch an influencer discuss a product. Now, instead of just watching a social influencer, viewers can interact by making comments, giving suggestions, and even getting responses back during that live stream. There is a level of engagement and interaction in 2019 that simply wasn't possible before digital transformation, and it changes the scope and nature of how marketers can approach their targets.
Automation Increases Proactivity
Timing can be critical when it comes to influencing a purchasing decision. A consumer may be 'on the fence' about making a purchase, even getting so far as to take the preliminary steps to make a purchase, only to stop right at the shopping cart phase, before committing to an actual purchase.
Automation combined with metrics means that consumer behavior is being tracked, it can be addressed without necessarily requiring a human to supervise the activity and be lucky enough to catch it and react to it in time. Digital transformation now means that when certain data or actions are recognized, the software can act upon those conditions to send emails or personalized responses quickly, without needing to notify a human agent to act on a time sensitive issue.
This type of automation is now increasing as chatbots even take on the role of basic customer service support for simple tasks, improving marketing response and productivity.
Digital transformation can potentially affect a huge spectrum of business operational and marketing activities. They key is to understand what's involved, learn from digital leaders across sectors and ensure your company has the technology, processes and talent in-house to progress and thrive.
Clodagh O'Brien
Senior Content Specialist
The What, Why & How of Digital Transformation Digital Transformation Industry
20 Things Leaders Need to Know to Master Digital Transformation (infographic) Digital Transformation Industry | slim_pajama |
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Andreas Tietze Memorial Fellowship
Andreas Tietze Fellows
Dr. Mustafa Kemal Baran
Project Title: Archaeology in Times of War and Peace: Austrian Excavations in Ephesus (1914-1954)
Fellowship Period: March-June 2023
Mustafa Kemal Baran completed his Ph.D. in the Department of Archaeology and History of Art at Koç University. His dissertation, "Between Place, Local Communities, and Labour: Archaeological Heritage and Memory in Turkey" explored the history and politics of archaeological practice and heritage based on a theoretical framework framed by memory studies. He currently works as a postdoctoral research fellow at the Center for Late Antique and Byzantine Studies (GABAM) at Koç University. He previously held Ertegun Graduate Scholarship in the Humanities at the University of Oxford, the Berlin State Museums International Scholarship, the SALT Research Award, and the Princeton University Library Research Fellowship. His interdisciplinary research is grounded in cultural heritage studies, archaeology, and architectural history, specifically focusing on the history and politics of archaeological practice in Turkey.
Baran's project investigates the history and politics of archaeological practice in Turkey during and between two world wars. Focusing on the social history of the excavations directed by the Austrian Archaeological Institute in Ephesus during this period, his research will produce a case study that contributes to a better understanding of the history of archaeological practice in Turkey, where issues and debates related to preservation and stewardship of cultural heritage and archaeological practice that persist to this day. Moving beyond the role of political ideologies in archaeology, the project intends to conceptualize a history of archaeology that goes into a personal level which will include narratives and roles of local communities that lived near the ancient sites and the landscape of labour in archaeological fieldwork.
Dr. Ezgi Sarıtaş
Project Title: A Transgender History of Movement and Translation between Vienna and Istanbul
Fellowship Period: June-September 2023
Ezgi Sarıtaş received her Ph.D. in Gender Studies from Ankara University. Her dissertation, which focused on the heteronormalization of love and eroticism in the nineteenth and early twentieth centuries, was published as a book in Turkish in 2020 under the title Cinsel Normalliğin Kuruluşu (Construction of Sexual Normality). She works as a research assistant at Ankara University, where she teaches courses on gender and sexuality and the history of the Ottoman Empire and the Turkish Republic. She is a former visiting scholar at the University of Michigan, Ann Arbor, a former postdoctoral fellow of Europe in the Middle East - The Middle East in Europe program in Berlin (EUME), and a visiting scholar at Humboldt-Universität zu Berlin. During her research, she received support from the Scientific and Technological Research Council of Turkey (TÜBITAK) and the Gerda Henkel Foundation. Her research focuses on sexual modernities in the Ottoman Empire and the early Turkish Republic, as well as the women's rights and feminist movements in modern Turkey. She collaborates with various civil society organizations, groups, and journals in Turkey, engaged in feminist and queer activism and research.
Sarıtaş's research under the Andreas Tietze Memorial Fellowship titled "A Transgender History of Movement and Translation between Vienna and Istanbul," aims to examine the production and translation of scientific knowledge about sexuality in the interplay between the movement of people and the translation of ideas and concepts by juxtaposing personal narratives and medical discourses. Prominent Turkish neuropsychiatrist Mazhar Osman used the story and photographs of a transfeminine person, Larein, who had fled Nazi Vienna for Istanbul, when he introduced the category of transvestite and translated it into Turkish in the 1940s. When Magnus Hirschfeld coined the sexological category of transvestite in 1910, the imperial knowledge of non-Western transgenderism was central to his work. By translating and introducing the category of transvestite into Turkish via a Western subject, Mazhar Osman reversed the division of labor in imperial knowledge production; but his attitude toward Lareine, marked by transphobia and national pride, made this reversal anything but radical.
Her research will examine how historical subjects like Lareine and Mazhar Osman contributed to and negotiated the transnational circulation of medico-legal categories of gender and sexuality. Educational trips of Ottoman Turkish neuropsychiatrists to German-speaking countries played a role in translating scientific knowledge about sexuality into Turkish. During her stay in Vienna, Sarıtaş aims to decipher the international subcultural, nightlife and scientific networks that may have helped Lareine, and perhaps others with non-normative genders and sexualities, travel to Turkey before and during the war. Existing scholarship has examined how non-normative gender and sexual subjectivities along with scientists and medical professionals played a role in the development of modern sexual taxonomies. By focusing on Lareine's story, the research will make a contribution to this body of scholarship by examining how both groups of people have contributed to a transnational formation of sexual modernity through their travels across the borders that set up the dichotomy between the West and the Orient. The research shows that the translation of modern medical and scientific knowledge about sexuality was not a simple transmission of regulative taxonomies but a complex, multilayered process in which the journeys of concepts intermingled with those of people, shaped by imperial circuits of scientific knowledge production as well as wars, crises, tourism, and entertainment.
Dr. Onur İnal
Spitalgasse 2, Court 4 (Campus)
[email protected] | slim_pajama |
The Public Administration Campus PAC जन प्रशासन क्याम्पस is the constituent campus of Tribhuvan University TU. It was the only one campus for public administration studies in Nepal for long time, now joined by two other colleges. It is currently located at Balkhu, Kathmandu. The campus operates under Central Department of Public Administration CDPA.
History
Initially, public administration education was started with one-year diploma in public administration for HMG Second Class Gazetted Officers under Center for Economic Development and Administration CEDA of the Tribhuvan University. Later in 1976, Public Administration Campus PAC - a full-fledged constituent campus of the Tribhuvan University was established. PAC was assumed the sole responsibility for education for public administration and undertook Diploma in Public Administration DPA Program until 1979. The mission quickly evolved to include offering master's degree in Public Administration in 1979. To upgrade and get more independent status, the Tribhuvan University has created [Central Department of Public Administration CDPA] in 1986. Since then PAC/CDPA has been imparting education, training and conducting research in the area of public affairs management.
Courses
Public Administration Campus previously offered Diploma in Public Administration DPA course. It was later on upgraded to Master in Public Administration MPA. Now with the need of mid level administrators, it has started offering Bachelor in public Administration BPA course. Following are currently offered courses through this campus.
Bachelor in Public Administration BPA
Master in Public Administration MPA
Bachelor in Public Administration Campus BPA
Bachelor in Public Administration BPA course is a 4-year, 8-semester program. It is aimed towards producing mid level administrators in the public sector of the country. It was started on 2070 BS. This program is currently available at only one place - Public Administration Campus, in the country.
Master in Public Administration MPA
Master in Public Administration MPA is a 2-year course aimed at producing high level administrative manpower for public sector of the country. It was upgraded from DPA program, previously offered by this campus. MPA program is currently offered by Public Administration Campus and Mahendra Morang Campus Biratnagar.
The objective of the master's degree programme in Public Administration MPA is to produce high-level human resources in order to serve public affairs management of the government, non-government, public enterprises and private sectors. The programme focuses on areas of specialization such as Development Administration, Human Resource Development, Public Finance, and Law and Order Administration. After successful completion of the programme, a student will be able to function as an administrator/manager in government, non-government, public enterprises and private sectors. The MPA programme specifically aims to:
Curricular Structure
The curriculum for MPA degree comprises four separate and distinct course components as follows :
Core Courses
Core courses integrate all functional areas and provide the students with an appreciation of the diversity and interrelationship of Public Administration, Development Administration, Public Policy Analysis, Public Financial Administration, Public Personnel Administration and Organizational Behaviour.
Analytical and Professional Core Courses
Analytical courses are designed to enable the students to develop the skill of identifying and analyzing the problems. It includes subjects - Research Methods in Public Administration, Public Enterprise Management and Social Responsibility, International Administration and Contemporary Issues in Public Affairs Management.
Specialization Courses
Specialization in any one of the areas, Development Administration, Human Resource Development, Public Finance and Law and Order Administration areas enables the student to develop their expertise in the functional area.
Thesis Writing
Thesis writing is an optional subject. While completing the specialization areas elective courses, students are required to take either four courses of 50 marks each or thesis writing of 100 marks with any two courses of 50 marks each from the same specialized area. The thesis has to be written within the specialisation area opted by the students.
Course Composition
The duration of MPA Program is of two year four Semester. The student require to study following core and compulsory as well as choose one area of Specializatiom course. There will be core course, specialization course.
First Semester
{| class=wikitable sortable
|-
! Subject !! Nature of Course !! Credit
|-
| MPA 501 Fundamental of Public Administration || Core ||3
|-
| MPA 502 Development Management || Core ||3
|-
| MPA 503 Public Sector Human Resource Management || Core ||3
|-
| MPA 504 Public Finance || Core ||3
|-
| MPA 505 Local Self-Government|| Core ||3
|-}
Second Year
PA 600 Public Policy Analysis 100
PA 610 Public Enterprise Management and Social Responsibility 100
PA 620 International Administration 50
PA 630 Contemporary Issues in Public Affairs Management 50
Specialization Areas Elective Courses
Courses equivalent 200 marks to be selected from any one of the following areas.
Development Administration Area
DA 621 Rural Development 50
DA 622 Urban Development 50
DA 623 Development Planning 50
DA 624 Project Management 50
Human Resources Development Area
HR 631 Personnel Administration in Nepal 50
HR 632 Comparative Personnel Administration of SAARC Countries 50
HR 633 Labour Policy and Administration in Nepal 50
HR 634 Human Resources Development 50
Public Finance Area
PF 641 Budgeting 50
PF 642 Accounting system in Nepal 50
PF 643 Auditing system in Nepal 50
PF 644 Tax Administration in Nepal 50
Law and Order Administration Area
PO 651 Public Security and Development 50
PO 652 Police Administration 50
PO 653 Security Management 50
PO 654 District Administration and Law Enforcement 50
Thesis Writing
TH 655 Thesis 100
References
Category:Tribhuvan University | wikipedia |
data provided by the world health organization show that during the last decade , cardiovascular disease became the main cause of death worldwide , accounting for 17.3 million deaths per year.1 during 19902001 , cardiovascular mortality increased from 26% to 28% in developed and developing countries.1 the highest rates of mortality due to cardiovascular diseases , representing approximately 58% , are recorded in eastern european countries , whereas the lowest ( 10% ) are to be found in the african territories ( saharan africa).1 however , in financially strong countries , the percentages reach 38%.1 all in all , the incidence of most cardiac diseases increases with the process of aging . in romania , although there are important limitations regarding the data - collection system , we can identify a clear tendency of increasing mortality due to ischemic heart disease and stroke .
in the 1990s , there was a sudden increase in the prevalence of ischemic heart disease , with a subsequent increasing tendency . according to the latest american heart association statistics , published in january 2013 , romania holds fourth place in the world in terms of mortality due to ischemic heart disease and stroke in men , after the russian federation , lithuania , and bulgaria , and third place in women , after the russian federation and bulgaria.2 while in 1970
, 7.33% of the cardiovascular deaths were due to myocardial infarction , the proportion amounted to 13.5% in 1998.3 in this context , this study aims at determining how the main cardiovascular risk factors and ischemic heart disease evolved in the course of 1 year in a group of subjects over 65 years of age in an urban community of romania .
we conducted a retrospective study based on medical records issued by general practitioners , aimed at achieving an epidemiological survey of cardiovascular risk factors and cardiac diseases in subjects over 65 years old by highlighting sex differences .
the study population was followed prospectively during 1 year ( 20072008 ) in order to determine the changes that occur in cardiovascular risk profile and cardiovascular disease .
we studied 515 patients ( 264 women and 251 men ) over 65 years of age , evaluated for the presence of cardiovascular risk factors and ischemic heart disease .
fifty - three patients were lost to follow - up ( deceased or with unavailable personal data ) , and only 462 patients underwent the second assessment ( 235 women , 227 men ) . during the initial evaluation and 1 year after that ,
the following parameters were determined : anthropometric measurements , blood pressure , smoking status , lipid profile ( total cholesterol , triglycerides , high - density lipid [ hdl]-cholesterol , low - density lipid [ ldl]-cholesterol ) , fasting plasma glucose , and the presence of ischemic heart disease .
blood glucose was measured by the glucose oxidase method , while serum lipids , total cholesterol , triglycerides , and hdl - cholesterol were measured by using commercially available kits .
ldl - cholesterol was estimated using friedewald s formula . according to current european society of cardiology guidelines ,
hypertension was classified as : mild hypertension 140/90159/99 mmhg , moderate hypertension 160/100179/109 mmhg , and severe hypertension > 180/110 mmhg.4 data on hypertension were collected from the medical records kept by the patients family physicians .
uncomplicated hypertension was registered as a cardiovascular risk factor , not as cardiovascular disease . by using the criteria set out in the national cholesterol education program adult treatment panel iii approach to dyslipidemias , total cholesterol levels over 200 mg / dl , ldl - cholesterol levels over 100 mg / dl , triglyceride plasma concentrations exceeding 150 mg / dl , and hdl - cholesterol levels less than 46 mg / dl in women and 40 mg / dl in men were considered pathological.5 patients
were classified according to their body mass index ( bmi ) as normal weight ( bmi 25 kg / m ) , overweight ( bmi between 25 kg / m and 29.9 kg / m ) and obese ( bmi > 30 kg / m).4 statistical analysis was performed using spss for windows ( version 16.0 ; ibm corporation , armonk , ny , usa ) and medcalc ( version 10.3.0.0 ; medcalc software , ostend , belgium ) software programs .
analysis of the differences between qualitative variables was performed using the test . the kolmogorov
the normality condition was met by bmi and serum lipids ( total cholesterol and ldl - cholesterol ) , but not for glycemia , hdl - cholesterol , or triglycerides ( so we had to use the mann
there were no differences between the first and second assessments concerning the incidence of smoking ( 12.3% versus ( vs ) 12.5% ) , obesity ( 25% vs 26% ) , diabetes mellitus ( 19% vs 22.9% ) , or hypertension ( 88.2% vs 92.2% ) .
regarding the presence of dyslipidemia , we found a marked decrease in its prevalence ( 40.6% vs 30.3% , p<0.001 ) .
as shown in table 1 and figure 1 , there were no differences between the two medical assessments regarding the plasma mean levels of triglycerides , hdl - cholesterol , and ldl - cholesterol .
however , there was a significant decrease in total cholesterol levels , but also an increase in plasma glucose concentrations ( table 1 ) .
although at the initial medical evaluation there were significant sex differences in the incidence of smoking , obesity , dyslipidemia , and hypertension , at 1-year follow - up most of them had disappeared ( only those concerning smoking and dyslipidemia stayed unchanged ) ( table 2 ) . during the first assessment
, there was a significant difference in all plasma lipid - fraction values between women and men , in contrast to the second evaluation , when these differences were present only in terms of hdl - cholesterol and total cholesterol levels ( table 3 ) . a higher incidence of ischemic heart disease ( 51.65% vs 63% ) was noticed during the second evaluation , even though the occurrence of silent ischemic heart disease decreased from 3.9% to 0.2% ( p=0.0002 ) , which emphasizes the fact that the increase was due to stable angina pectoris , old myocardial infarction , or other causes of ischemic heart disease ( arrhythmias or heart failure ) , regardless of sex ( table 4 ) .
the incidence of ischemic heart disease was considerably higher in elderly women than in men , with an increase from 55.7% to 65.1% in women and from 47.4% to 60.8% in men , which revealed a similar growth for both sexes , the ratio differences between men and women being significantly similar .
myocardial infarction amounted to 9.5% in 2008 , similar to the values recorded in 2007 ( 8.7% , not significant ) .
there were no significant differences between the initial evaluation and 1 year later , irrespective of sex ( women 5.7% vs 6% in 2008 , men 12% vs 13.2% in 2008 ) .
differences regarding stable angina remained unchanged between the two assessments , in both women ( 24.7% in 2008 vs 21.2% in 2007 ) and men ( 12.8% in 2008 and 12.7% in 2007 ) .
stable angina occurred more often in women , whereas old myocardial infarction was predominant in men during both evaluations .
in addition , there were no significant changes in the incidence of heart failure and rhythm disorders between the two assessments ( 10.48% vs 13.2% and 23.1% vs 26% , respectively ) .
as for cardioprotective medication , 65% of the patients received aspirin , 71.9% beta - blockers , and 74.9% angiotensin - converting enzyme inhibitors ; 48.8% were given statins .
patients over 75 years of age received less medication than those under 75 years : 32% versus 54.2% , respectively ( p=0.009 ) .
according to the interheart study , traditional cardiovascular risk factors account for most of myocardial infarction risk worldwide in both sexes , ages and in all regions.6 in eastern europe , the most frequent modifiable cardiovascular risk factors are smoking , obesity , hypertension , and hypercholesterolemia ( serum cholesterol levels over 200 mg / dl ) .
the present study showed that the main investigated cardiovascular risk factors ( arterial hypertension , diabetes mellitus , smoking , obesity ) had the same incidence 1 year after the initial assessment .
there are insufficient data on the incidence of cardio vascular risk factors in general and the main heart diseases in romania , especially as after the 1990s there was a heart disease boom following the transition from communism to a so - called liberalization .
the rise is constant , with no perceptible tendencies of improvement , which could be explained by a drastic lifestyle change , chiefly the prevalence of smoking and fast - food diets .
hypertension is one of the major cardiovascular risk factors found in romania , with a constantly growing incidence . in 2006 ,
the occurrence of hypertension was reported to be 40% , and by 2012 it remained unchanged , increasing with age.7,8 the incidence of hypertension was very high in the study group of elderly subjects : 88% in 2007 and 92.2% in 2008 . among the countries of eastern
europe , croatia has the highest ratio of hypertensive men ( 50% ) and bosnia - herzegovina has the highest number of hypertensive women ( 45%).1 romanian epidemiological data show that the incidence of smoking decreased from 29.7% to 22% between 2003 and 2011.9 presently , 35.2% of romanian men and 15.3% of romanian women are smokers.9 in our study , the prevalence of smoking was more than double in men than in women , both during 2007 and 2008 . in eastern europe ,
the highest incidence of smoking in men was reported in ukraine ( 62% ) and in women in serbia ( 27%).1 the prevalence of diabetes mellitus increased insignificantly from 19% to 22.9% .
women displayed similar ratios during both years ( 21.2% vs 23.8% ) , whereas men presented a significantly higher incidence ( from 16.7% to 22% ) . in 2007 , 40.6% of the subjects displayed dyslipidemia , whereas dyslipidemia was found only in 30.3% of the patients in 2008 , the decrease being similar in women and men ( from 48.5% to 36.6% in women , and from 32.3% to 23.8% in men ) . significantly lower levels were recorded for hypercholesterolemia .
the incidence of hypercholesterolemia in romania amounted to nearly 63% , but only 16% of the subjects were therapeutically controlled ( values < 175 mg / dl).1 hypercholesterolemia affects almost 39% of the world population , with more than half this incidence from developing countries . in eastern europe , the highest occurrences of unaware hypercholesterolemia can be found in bulgaria ( 72% ) , latvia ( 70% ) and croatia ( 70%).10 among romanian subjects over 30 years old , cholesterol levels vary between 192 and 216 mg / dl in men and between 189 and 217 mg / dl in women.1 in our group of elderly romanian subjects , the lower lipid - fraction levels could be due to both primary and secondary cardiovascular prevention measures and also to the intensive treatment with statins recommended by physicians or even requested by patients who were informed about the role of high lipid - fraction levels in the development of cardiovascular diseases . according to the data provided by the euroaspire ( european heart survey on secondary and primary prevention of coronary heart disease ) iii study,10 the statin administration ratio was lower than the all lipid - lowering drugs ( 88.8% ) administration ratio in europe . in spite of the lower ratio of statin prescription , our study recorded a significant decline in the incidence of dyslipidemia in general and average cholesterol level in particular .
the respective changes can be ascribed to the fact that the initial assessment of risk factors had alerted the patients to the presence of dyslipidemia ( side by side with the presence of other risk factors ) , which triggered lifestyle adjustments .
the ratios remained almost identical in men and women during both years ( women , 29.5% in 2007 , 29.6% in 2008 ; men [ insignificant difference ] , 20.3% in 2007 , 20.6% in 2008 ) .
the incidence of obesity is also growing in romania in both women ( 8% [ 35.9% overweight ] ) and men ( 7.6% [ 49.9% overweight]).11 an alarming increase in obesity was recorded among children and teenagers.11 in europe , the highest rates of obesity in men and women are to be noticed in croatia ( 22% ) and turkey ( 30% ) , respectively.1,12 special attention needs to be paid to the evolution of cardiovascular risk factors and sex - related differences . in our study , the incidence of hypertension was basically identical in both years : 88.2% in 2007 and 92.2% in 2008 .
women had higher blood pressure values than men in both years , but a high incidence was found in both sexes .
the incidence of hypertension increased with age for both sexes , with a more noticeable increase in women between 45 and 54 years old . in subjects
younger than 35 years , hypertension was clearly more common in men than in women.13 however , regardless of age , the presence of hypertension in women is associated with a three- to fivefold higher risk of coronary heart disease.14,15 our study showed that in elderly subjects , all lipid fractions levels were higher in women than in men , regardless of the assessment moment . before menopause ,
total cholesterol and ldl - cholesterol were generally lower in women , whereas hdl - cholesterol was higher than in men.16 whereas after the age of 50 years , ldl - cholesterol levels remained relatively the same in men , in menopausal women there was a significant increase in ldl - cholesterol levels , reaching maximum values between the ages of 55 and 65 years.16 thus , after the age of 65 years , the incidence of dyslipidemia was about twice as high in women.17 menopause also influenced hdl - cholesterol levels , which decreased gradually during the last 2 years preceding menopause and after , especially the hdl2 fraction , which has an important cardioprotective role.16,18 cardiovascular protection dropped with the decrease in hdl levels .
therefore , low hdl values may be considered major factors for an increased cardiovascular risk in postmenopausal women . however , in our study , hdl - cholesterol levels were higher in women in both years .
triglyceride levels also increased after menopause.19 our research showed that the incidence of obesity was higher in elderly women than in men , especially in the first year of observation .
women seemed more likely to display cardiovascular risk factors than men , especially obesity in adolescence , pregnancy , and menopause.16 the increasing occurrence of ischemic heart disease can be attributed to the 1-year aging process of the subjects enrolled in the study . in addition
, another explanation could be the fact that the patients who underwent the initial assessment of cardiovascular risk factors were informed about the presence of cardiovascular risk factors and cardiovascular disease .
therefore , the patients probably sought medical advice more often during the following year , so additional cardiovascular diseases perhaps present at the initial assessment but undetected by regular screening tests might have been diagnosed .
ischemic heart disease occurs about 10 years later in women than in men.20,21 in general , the form of ischemic heart disease prevailing in women is angina pectoris , whereas myocardial infarction occurs more often in men , previous assertions being in agreement with our findings.17,22 it is important to emphasize that in the present study , the data were collected from medical records kept by general practitioners , so none of the subjects displayed acute coronary syndromes at the moment of assessment .
the highest incidence of st - segment elevation acute coronary syndromes occurs in young men ( under 55 years ) , the ratio decreasing with age.21 nearly half of the male patients with ischemic heart disease younger than 65 years came with clinical symptoms of an st - segment elevation acute coronary syndrome , whereas only 40% of the women did.21 in patients over 65 years of age , the differences between men and women were less significant.21 in women , unstable angina is responsible for most cases of acute coronary syndromes,21,23 especially before the age of 65 years . after the age of 65 years , women present in equal proportions st - segment elevation and non - st - segment elevation acute coronary syndromes.13 in the present study , although the main risk factors , chiefly obesity and dyslipidemia , decreased during 1 year , the incidence of ischemic heart disease increased .
the data prove that over 65 years of age , cardiovascular pathology ceases to be sex - related .
the increase in the incidence of cardiovascular diseases could be chiefly ascribed to the 1-year aging of the study patients , and secondly to the fact that the initial assessment of the risk factors alerted the patients to their presence and the possibility of cardiovascular diseases , so that more cardiovascular diseases possibly present at initial examination but undetected by regular screening were diagnosed . finally , we believe that the results of the present paper present significant data on the incidence of cardiovascular risk factors in a population over 65 years of age of a city that is an academic center , supposedly with highly proficient medical specialists . in conclusion , the data supplied by our study show that in subjects over 65 years old , cardiovascular disease prevails in women , with some particular characteristics that should be taken into account , and that cardiovascular risk factors need to be addressed and influenced .
however , one should not expect a major decrease or improvement in the cardiovascular risk factors during such a short period ; positive results will probably be achieved through long - term interventions . | pubmed |
an interest of physicists in complex potentials @xmath8 with the generalized symmetry property v(x ) = rev(-x ) ,
v(x ) = -imv(-x ) [ pts ] dates back to the perturbative study of imaginary cubic anharmonic oscillators v(x ) = x^2 + ix^3 [ ixnatri ] by caliceti et al @xcite . in the early nineties ,
an increase of this interest @xcite was inspired by the role of the imaginary cubic anharmonicity in field theory where eq .
( [ pts ] ) mimics the fundamental parity times time - reversal (= @xmath1 ) symmetry of phenomenological lagrangians @xcite . under certain circumstances ,
the @xmath1 symmetric and hermitian models can even prove mathematically equivalent @xcite . in the late nineties , bender and
boettcher @xcite analysed the one - parametric family of the power - law @xmath9 models v(x ) = x^2 ( ix)^[ixnadelta ] by the quasi - classical and purely numerical means . on this basis
they conjectured that all the @xmath10 bound - state energies @xmath11 form a real and discrete , smooth continuation of the well known harmonic - oscillator @xmath12 spectrum .
an extension of this study inspired them later to apply the conjecture ( formulated , originally , by bessis at @xmath13 @xcite ) to a still broader class of interactions . within the resulting generalized "
( so called @xmath1 symmetric ) quantum mechanics @xcite , there appears a growing number of interesting studies , promoting the ideas of supersymmetry @xcite , exact semiclassical techniques @xcite , functional analysis @xcite and perturbation theory @xcite .
all of them provide a consistent picture of a theory with certain ( not quite well understood ) limitations . even in the above guiding " example ( [ ixnadelta ] ) the @xmath1 symmetry breaks down spontaneously at @xmath14 @xcite .
phenomenological appeal of the @xmath1 symmetric modifications need not even stop before the sacred " quantum electrodynamics @xcite .
still , the formalism abounds in open questions and its mathematical foundations are mostly conjectures .
this is the reason why the attention quickly spreads from the phenomenologically oriented eq .
( [ ixnadelta ] ) to its exactly solvable alternatives . in this direction , the partially solvable extension of the @xmath15 quartic case @xcite and the discovery of the exact solvability of the certain version of the @xmath16 limiting case
@xcite were the first and encouraging successes .
they were followed by the @xmath1 symmetric regularization of the more - dimensional harmonic oscillator @xcite and by the formulation and solution of many further shape - invariant models @xcite-@xcite .
once we move beyond the domain of analytic potentials , numerical studies provide significantly less encouraging results @xcite .
this is the reason why the most elementary " square well v(x ) = 0 , x ( -1,1 ) + imv(x ) = z , x ( -1,0 ) + imv(x ) = -z , x ( 0,1 ) [ sqw ] has always been @xmath1 symmetrized just in the ( various , non - equivalent ) @xmath16 limits of eq .
( [ ixnadelta ] ) @xcite .
presumably , the reason for absence of the forgotten " @xmath1 symmetric square well ( [ sqw ] ) in the literature lies in an ambiguity of its continuation beyond the discontinuities at @xmath17 .
we are going to treat this problem simply by imposing the dirichlet boundary conditions on our ( complex ) wave functions , ( 1 ) = 0 .
[ bc ] having made the latter decision the explicit computations are really elementary .
their essence lies in the easy construction of the general right and left solutions _
+ = c_+ e^x + d_+ e^-x + _ - = c_- e^^x + d_- e^-^x [ gens ] with the complex @xmath18 and its conjugate @xmath19 .
we re - parametrize the ( by assumption , real ) energies @xmath20 and the measure of non - hermiticity @xmath21 .
this gives the complex exponents @xmath22 since @xmath23 is also complex ( and constant for all @xmath24 ) .
our solutions ( [ gens ] ) are made explicit , for every real @xmath25 and @xmath26 , when we use the inverse formulae t=(e+)^1/2 , s=(e+)^-1/2 . in the light of the @xmath1 symmetry of our hamiltonian @xmath27 ,
the product @xmath28 will satisfy the same schrdinger equation as @xmath29 .
hence , in the origin , we are permitted to normalize our bound states in a @xmath1 symmetric way , _ + ( 0)=_-(0)=1 , _ x_+(0)=_x_-(0)=ia .
these conditions contain a free real parameter @xmath30 and are equivalent to the matching of wave functions , c _ = 1 - d _ , + ( 1 - 2d_+ ) = ^(1 - 2d_-)=ia .
this implies that we know all the coefficients in eq .
( [ gens ] ) , d_+= - i , d_-= - i. it is easy to satisfy the external boundary conditions ( [ bc ] ) and reduce them to the elementary prescription ia=- .
[ bcexpl ] in terms of the real parameters @xmath31 and @xmath32 this represents a system of two algebraic equations , a=- + t s = s t + . [ graph ] its first part defines the ( necessarily , real ) value of @xmath33 .
a re - arrangement of the second algebraic equation is elementary and gives the rule -2t2
[ hical ] as long as both its sides depend on the mere absolute values of the respective variables @xmath32 and @xmath31 , we may pick up @xmath34 , insert the definition of @xmath35 and solve this equation numerically .
by construction , the spectrum of the real energies @xmath36 is defined in terms of the roots @xmath37 of eq .
( [ hical ] ) , @xmath38 , @xmath39 , @xmath40 .
after we re - scale @xmath41 , we immediately see that in the limit @xmath2 this spectrum degenerates to the known hermitian one , with @xmath42 etc . from our equation ( [ hical ] ) it is obvious that at the very small @xmath26 ( and , hence , @xmath43 ) , the change of the above roots @xmath44 ( and , of course , energies ) remains very small as well . at the larger ( and ,
say , positive ) @xmath26 , the analysis of our quantization condition ( [ hical ] ) becomes significantly simplified by the re - scalings @xmath45 and @xmath46 such that , say , @xmath47 .
both these steps represent a one - to - one mapping exhibiting the strict leading - order quasi - linearity @xmath48 achieved at both ends of our half - axis , i.e. , for @xmath49 as well as for @xmath50 .
moreover , this introduces just a minimal deformation of the scale of the coordinate @xmath31 ( practically invisible on a picture ) and replaces equation ( [ hical ] ) by a new one , -tt = 4 ^ 2 s. [ hicalbe ] this new relation is explicitly solvable .
the resulting analytic and @xmath51independent formula @xmath52 defines a curve in our new @xmath53 plane .
its @xmath54 part is displayed in figure 1 . in order to determine the separate roots @xmath44 ( and , hence , the spectrum of energies ) ,
it remains for us to recollect the @xmath51dependent , hyperbolic constraint @xmath35 .
after we translate its form in our new variables , @xmath55 , we discover that it has a monotonous , hyperbolic shape which depends on @xmath26 .
figure 1 offers a few samples .
we may conclude that each point of the intersection of our two curves @xmath56 and @xmath57 determines a @xmath51dependent root @xmath58 and , hence , a real energy .
the @xmath51 dependence of the roots @xmath59 is , in general , smooth .
a non - perturbative effect is only encountered at certain critical values @xmath60 . in the vicinity of these points , the two leftmost roots @xmath61 , @xmath62 merge in a single , doubly degenerate real root @xmath63 .
figure 1 gives two examples and shows that even the smallest one of these critical values is already quite large ( @xmath64 ) .
below this bound we may summarize that * our complexified square well generates the infinite set of real energies ; * the roots @xmath44 which define these energies are almost equidistant , especially at the higher @xmath65 ; * as expected , the standard square - well - type behaviour of the spectrum is reproduced at the small @xmath26 and for the highly excited states . in the strongly non - hermitian domain ,
the lowest doublets of states subsequently disappear .
presumably , their energies dissolve in conjugate pairs in complex plane .
the @xmath1 symmetry of their wave functions breaks down .
the related solutions become unphysical " and have to be omitted in a way paralleling the similar disappearance of states " at @xmath66 in the model ( [ ixnadelta ] ) of ref .
the resulting sudden upward jump of the ground - state energy definitely enters the list of paradoxes , emerging in the other exactly solvable models .
their present list already involves the unavoided level crossings in the harmonic and coulomb oscillators @xcite , the anomalously large excitations in the @xmath1 symmetrized but bounded rosen - morse field @xcite , some unexpected manifestations of the strong singularities in the psch - teller and eckart models @xcite , and a spontaneous re - ordering of levels in the morse asymmetric well @xcite . in this context , the role of the complexified square well is as exceptional as in the hermitian limit .
we may expect that its generalizations with more points of discontinuity will remain tractable analytically .
this could be of a significant help , say , within perturbation theory @xcite .
in the more pragmatic numerical setting , one should recollect that the so called prfer transformation @xcite ( i.e. , nothing but a square - well - inspired use of the _ locally _ exponential solutions ) found a firm place in the standard computer software @xcite .
last but not least , one has to keep in mind that in the hermitian quantum mechanics the use of the locally constant forces could also clarify the various manifestations of the pertaining sturm liouville theory @xcite .
an appropriate @xmath1 symmetrization of this theory is expected to be quite a difficult task @xcite .
in such a direction , also the knowledge of our present solutions could mediate a further progress , hopefully , in the near future .
partially supported by the ga as grant nr . a 104 8004 . | arxiv |
binary neutron stars ( bnss ) are the leading candidates for the central engine of short gamma - ray bursts ( sgrbs ; @xcite ) .
they are also one of the most powerful sources of gravitational waves ( gws ) , and advanced interferometric detectors are expected to observe these sources at rates of @xmath4 events per year @xcite .
fully general - relativistic simulations have shown how such mergers can lead to the formation of hypermassive neutron stars ( hmnss ) , i.e. , of nss with masses larger than the maximum mass that can be supported by uniform rotation .
due to loss of angular momentum via gw emission and magnetic fields , the hmns eventually collapses in less than @xmath5 to a black hole ( bh ) surrounded by an accretion disk @xcite .
when magnetic fields are present , they can provide a mechanism to extract energy from the bh and disk , and power collimated relativistic jets @xcite .
a source of uncertainty in bns simulations is due to the lack of detailed knowledge of the equation of state ( eos ) of nss ( see @xcite for a recent discussion of eoss ) .
current observations have shown that nss with masses of @xmath6 exist @xcite , and therefore the ns eos must support a mass at least as large as that .
this opens the interesting possibility that the merger of bnss could produce not only hmnss , but also nss which are stable against gravitational collapse .
this possibility has interesting applications for observations of sgrbs @xcite , as well as for the possible emission of long periodic gw signals @xcite and their electromagnetic counterparts @xcite .
in particular , @xcite found that several of the sgrbs that show a plateau phase in the x - ray lightcurve may be explained with the formation of a stable magnetar after the bns merger .
x - ray lightcurves indeed suggest a long - lived central engine @xcite , which is hard to explain if all the bns mergers produce an hmns which collapses to a bh in less than @xmath7 ; the remnant torus is also expected to be completely accreted on the same timescale @xcite , unless magnetic or gravitational instabilities set in @xcite .
the formation of a stable magnetar could also explain the extended emission observed in several sgrbs @xcite . in this letter
we investigate , for the first time and in fully general - relativistic mhd , the regime in which bnss may lead to the formation of a stable ns . by considering models with and without magnetic fields , and by performing the longest ( to date ) general relativistic simulations of magnetized bns mergers , we show that stable magnetized nss can indeed be formed for some range of masses , and we discuss the implications of these new results for the electromagnetic signals that they may emit .
note that the formation of a stable magnetar is a non - trivial outcome ; in fact , even if the total mass of a bns system is below the maximum mass , collapse to bh may still happen if the central density of the merger product is above a certain value ( depending on the eos ) .
nss with masses below the maximum mass can indeed collapse to bhs ( e.g. , model d0 in @xcite ) , and the stability properties of nss are defined by both their masses and central densities @xcite . in this letter , together with presenting the first simulation of the formation of a stable ns from a binary merger , we also discuss the ns final spin , the formation of a disk , magnetic field amplification , the gw signal , and possible electromagnetic counterparts .
lcccccccc & @xmath8 & @xmath9 & @xmath10 & @xmath11 & @xmath12 & @xmath13 & @xmath14 & @xmath15 + b0 & @xmath16 & @xmath17 & @xmath18 & @xmath19 & @xmath20 & @xmath21 & @xmath22 & @xmath23 + b12 & @xmath16 & @xmath17 & @xmath18 & @xmath19 & @xmath20 & @xmath21 & @xmath22 & @xmath24 + section [ methods ] details our numerical methods and the initial models .
section [ dynamics ] describes evolution and dynamics of these systems , while in section [ gws ] we discuss their gravitational and electromagnetic signals .
section [ conclusions ] summarizes our main results . for convenience ,
we use a system of units in which @xmath25 , unless explicitly stated otherwise .
the simulations presented here were performed using the publicly available einstein toolkit @xcite , coupled with our fully general relativistic mhd code ` whisky ` @xcite .
details about the numerical methods can be found in @xcite , except that in our work the spacetime evolution is obtained using the ` mclachlan ` code @xcite , and ` whisky ` now implements the modified lorenz gauge to evolve the vector potential and the magnetic field @xcite .
the simulations presented here use adaptive mesh refinement with six refinement levels ; the finest grid covers completely each of the nss during the inspiral and merger , while the coarsest grid extends up to @xmath26 .
our fiducial runs have a resolution of @xmath27 on the finest grid , but convergence tests have been performed using both a coarser ( @xmath28 ) and a finer resolution ( @xmath29 ) .
the initial data were produced using the publicly available code lorene @xcite .
the initial solutions for the binaries were obtained assuming a quasi - circular orbit , an irrotational fluid - velocity field , and a conformally - flat spatial metric .
the matter is modeled using a polytropic eos @xmath30 , where @xmath31 is the pressure , @xmath32 the rest - mass density , @xmath33 and @xmath34 , in which case the maximum gravitational mass is @xmath35 for a non - rotating ns , and @xmath36 for a uniformly maximally - rotating star , in agreement with recent observations of ns masses @xcite .
an ideal - fluid eos with @xmath34 is used during the evolution in order to allow for shock heating during merger .
this eos has been chosen since it fits very well the shen nuclear eos @xcite at high densities @xcite , and hence it provides a more accurate description of the evolution of the plasma in the high - density regions than the simpler @xmath37 polytrope used in our previous simulations @xcite . in this work
we consider an equal - mass system both with and without a magnetic field , and with a total gravitational mass @xmath38 . when a magnetic field is present , its initial configuration is purely poloidal and aligned with the angular momentum of the binary as in @xcite .
details about the initial configurations are provided in table [ table1 ] .
we first evolved the unmagnetized case ( model b0 ) with three different resolutions : @xmath39 ( low ) , @xmath40 ( medium ) , and @xmath41 ( high ) . in all cases , the binary inspirals for five orbits before merging .
the main aspects of the dynamics are illustrated in figure [ figure1 ] , where we show the rest - mass density on the equatorial plane for the high resolution case .
one important point to note is that , as observed in previous simulations of bns mergers , the compact object that is formed after the inspiral is differentially rotating .
however , while in previous simulations it was an hmns , in the current simulations the ns is well below that limit ( @xmath36 for our eos ) , and hence it does not collapse to bh . at the end of our simulation ,
the differentially - rotating ns has a mass @xmath42 and is surrounded by a disk of @xmath3 . [
cols="^,^ " , ] other numerical simulations of magnetized hmnss have further demonstrated the possibility of producing outflows with energy of @xmath43 for magnetic fields of @xmath44 @xcite . as already discussed before ,
such magnetic fields can be naturally formed in our scenario via kh and mri instabilities . according to @xcite
, a magnetic field of @xmath45 could give rise to an electromagnetic emission observable in the radio band and hence provide an interesting electromagnetic counterpart to the gw signal even if a sgrb is not observed .
we have presented the first general relativistic magnetohydrodynamic simulations that show the possible formation of a stable magnetar .
the ns formed after the merger is found to be differentially rotating and ultraspinning . since our computational resources are not enough to fully resolve the mri , the magnetic field is amplified by about two orders of magnitude , but further amplification is possible and indeed observed in two and three - dimensional simulations of differentially rotating nss @xcite . moreover
, long term evolution of such models has shown that the magnetic field can impact the angular velocity profile of the ns leading to the formation of an uniformly rotating ns surrounded by an accretion disk and with a collimated magnetic field @xcite .
while it will be difficult to differentiate the gw signal between the magnetized and the unmagnetized scenarios , strong electromagnetic counterparts that would be suppressed in collapsing nss could be easily produced and observed in radio @xcite , optical @xcite , x - rays @xcite , and gamma - rays @xcite . while our simulations focused on equal - mass systems , the same scenario may be produced after the merger of unequal - mass bnss . in this case ,
matter ejected during the inspiral due to the tidal disruption of the less massive components , may later fall back on the magnetar and trigger its collapse to bh @xcite .
more detailed observations of the early afterglow phase , as expected with the planned future mission _ loft _ @xcite , will be especially useful in discriminating among various formation scenarios .
last , simultaneous detections of gws and sgrbs will fully unveil the mechanism behind the central engine and help constrain its properties @xcite .
we thank brian metzger , christian ott , antonia rowlinson , luigi stella , eleonora troja , bing zhang and an anonymous referee for useful comments .
b.g . and r.p .
acknowledge support from nsf grant no .
ast 1009396 and nasa grant no .
nnx12ao67 g .
this work used xsede ( allocation tg - phy110027 ) which is supported by nsf grant no . oci-1053575 . | arxiv |
What happens when we bring an electron and a proton together?
I have a couple of conceptual questions that I have always been asking myself.
Suppose we have an electron and a proton at very large distance apart, with nothing in their way. They would feel each the other particle's field - however weak - and start accelerating towards each other.
Now:
1) Do they collide and bounce off? (conserving momentum)
2) Does the electron get through the proton, i.e. between its quarks?
3) Do both charges give off Brehmsstrahlung radiation while moving towards each other?
Different scenario:
Suppose I can control the two particles, and I bring them very close to each other (but they are not moving so quickly as before, so they have almost no momentum).
Then I let them go:
1) Would an atom be spontaneously formed?
2) If anything else happens: what kind of assumptions do we make before solving the TISE for an Hydrogen atom? Does the fact that the electron is bound enter in it?
This is to say: is quantum mechanics (thus solving the Schrödinger equation) the answer to all my questions here?
Part 1: Conceptual/physical intuition
=====================================
Since there is an electrostatic attraction between the 2 particles, then when
they are apart they are at a higher potential energy then when they are
together.
Here's an analogy:
Physically, this situation is like having a ball at the top of a hill
overlooking a valley or well. The ball will roll down the hill and that
potential energy is converted into kinetic energy. When the ball reaches the
bottom of the valley it will start climbing back out of the well and turn that
kinetic energy back into potential, so if the ball starts at rest it only gets
back to being as high as it started. However in the real world there is
friction that will steal some of this kinetic energy and so the ball will roll
back and forth, but eventually come to rest at the bottom of the hill.
For the electron an proton you'll see something similar. The 2 particles will
accelerate towards each other, pass/scatter off each other (and then repeat) and will slowly lose
energy to "friction" i.e. to radiation.
Part 2: Specific questions
==========================
>
> 1. Do they collide and bounce off? (conserving momentum)
> 2. Does the electron get through the proton, i.e. between its quarks?
>
>
>
The collision between the two particles is perfectly elastic. In addition the
energies (~13eV) are so small relative to the strong force holding together the
proton that quarks are not involved in any way, and the scattering is described
by [Rutherford
scattering](http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/elescat.html).
>
> 3. Do both charges give off Brehmsstrahlung radiation while moving towards each other?
>
>
>
The 2 particles will radiate and lose their kinetic energies. The term
Brehmsstrahlung is generally reserved for much higher particle energies (>keV), and much larger accelerations.
>
> Suppose I can control the two particles, and I bring them very close to each
> other (but they are not moving so quickly as before, so they have almost no
> momentum). Then I let them go:
>
>
> 1. Would an atom be spontaneously formed?
>
>
>
You can immediately describe the 2 particles by their center of mass
description (an atom) plus their individual attributes (i.e. what the particles
are doing within the atom). Assuming the 2 particles start off at rest, then
they are in a bound state already because they can't escape each other (go off
to infinite separation) due to lack of energy.
However the atom will not be in it's ground state until it has decayed into the
lowest level via spontaneous emission of radiation.
>
> 2. If anything else happens: what kind of assumptions do we make before
> solving the TISE for an Hydrogen atom? Does the fact that the electron is
> bound enter in it? This is to say: is quantum mechanics (thus solving the
> Schrödinger equation) the answer to all my questions here?
>
>
>
The TISE of the atom itself will give you energy levels etc, but you will not
get spontaneous emission into the ground state unless you put it in by hand
(and it would not be time independent anymore) or also quantize the EM vacuum
(which is how you derive SE). So trying to solve it would be like solving the ball moving on the hill while ignoring friction, it will just oscillate at constant energy forever.
Check this link [here.](http://coldfusionnow.org/electron-capture-by-a-proton-where-would-the-energy-come-from/) This is a quote from the website:
>
> When an electron falls from infinity towards a proton it acquires 13.6 electron Volts of energy to reach the ground state “orbital” around the proton. I have always wondered why it does not go all the way. Apparently, its Debroglie wavelength has to fit” around the “orbit radius” for it to occupy a stable state.
> Perhaps another explanation is that an electron can only arrive in an atom and occupy an orbital by dissipating its arrival energy in the form of a photon.
>
>
>
I believe they would emit Bremsstrahlung as there is acceleration involved, but the electron will still end up gaining 13.6 eV of energy anyway.
In the second case, the electron is inside a potential well, and will stay confined, thus creating an atom. Solving the TISE is very useful in this case.
To provide a graphic version of Punk\_Physicist's answer, we have the Feynman diagram for that particular interaction:
This diagram evolves in time from bottom to top, ie take a piece of paper, and run it upwards along the diagram to see how the system evolves. We have an electron and a proton coming towards each other, then we see them interact by releasing a $ \gamma $ particle, ie a photon--electromagnetic braking radiation (See [Bremsstrahlung](https://en.wikipedia.org/wiki/Bremsstrahlung)). The energy of this photon is of course the kinetic energy lost by the electron passing by the proton. The closer they pass, the higher the potential, the greater the loss in $ E\_k $ of the electron.
In nuclear fussion electrons and protons can fuse to form neutrons with the release of photons.
To rephrase: an electron approaches an cation.
Most likely result: a photon is emitted and the electron is captured.
Added: The way I see it: an ion and an electron at a large distance apart. This would probably be an electron in a very high orbital of the ion. As the electron approaches, all the natural forces affect the electron and the electron slows down when it approaches the nucleus. This would equate to dropping down orbitals which would release a photon.
| stackexchange/physics |
Determine the oxidation number of sulfur in SF6
I've just started learning about redox chemistry and oxidation numbers. I can work out most of the oxidation number questions, but I don't know how to determine the oxidation number of sulfur in $\ce{SF6}$. This is not an ionic compound, and doesn't contain $\ce{H}$ or $\ce{O}$, so it seems as if I have no starting point.
If you could, please answer the question and provide a simple explanation.
In the case of $\ce{SF6}$, sulfur would have the oxidation number of +6 because the charge being applied to the fluorine is +6. Similarly fluorine would consequently have an oxidation number of -1 since $$6x + 6 = 0 \Rightarrow x = -1$$
(the right-hand side is equal to zero since that happens to be the net charge on the overall chemical formula).
Being the most electronegative element in periodic table (placed in right-upper corner) fluorine always has negative oxidation state in compounds besides $\ce{F2}$ and due to the fact the fluorine is a halogen (group $17$) the only negative oxidation state is $-1$.
So fluorine in $\ce{SF6}$ has an oxidation state $-1$. Then we can calculate o. s. for sulfur:
$x + 6×(-1) = 0$
$x = +6$
So sulfur in this compound has an o. s. of $+6.$
| stackexchange/chemistry |
the experimental discovery of the higgs boson is crucial for the understanding of the mechanism of electroweak symmetry breaking .
the search for higgs particles is one of the main goals for the lep2 and tevatron experiments and is one of the major motivations for the future large hadron collider ( lhc ) and linear @xmath0 collider ( lc ) .
once the higgs boson is discovered , it will be of primary importance to determine in a model independent way its tree - level and one - loop induced couplings , spin , parity , @xmath1-nature , and its total width . in this respect the @xmath2 compton collider @xcite option of the lc offers a unique opportunity to produce both standard model ( sm ) higgs boson and neutral higgs states @xmath3 , @xmath4 , @xmath5 of the minimal supersymmetric standard model ( mssm ) or general two higgs doublet model ( 2hdm ) @xcite as @xmath6-channel resonance decaying into @xmath7 , @xmath8 , @xmath9 or @xmath10 : @xmath11 the ability to control the polarizations of back - scattered photons @xcite provides a powerful means for exploring the @xmath1 properties of any single neutral higgs boson that can be produced with reasonable rate at the photon linear collider @xcite .
@xmath1-even higgs @xmath12 bosons @xmath13 , @xmath14 couple to the combination @xmath15 while a @xmath1-odd @xmath16 higgs boson @xmath17 couples to @xmath18\cdot\vec{k_\gamma}= \frac{\omega_\g}{2}i\lambda_1 ( 1+\lambda_1\lambda_2 ) , \label{pseudoscalar}\ ] ] where @xmath19 and @xmath20 are photon polarization vectors and helicities .
the first of these structures couples to linearly polarized photons with the maximal strength if the polarizations are parallel , the letter if the polarizations are perpendicular . moreover , if the higgs boson is a mixture of @xmath1-even and @xmath1-odd states , as can occur _
e.g. _ in a general 2hdm with @xmath1-violating neutral sector , the interference of these two terms gives rise to @xmath1-violating asymmetries @xcite .
since mssm higgs particles @xmath13 , @xmath14 , @xmath17 decay predominantly into @xmath7 or @xmath10 quark pairs depending on the mass of the higgs boson , the heavy quark pair background in @xmath2 collisions has been studied in great detail .
one - loop qcd corrections were calculated for the photon helicity states corresponding to projection of total angular momentum on beam axes @xmath21 and @xmath22 @xcite .
virtual one - loop qcd corrections for @xmath21 were found to be especially large due to the double - logarithmic enhancement factor , so that the corrections are comparable or even larger than the born contribution for the two - jet final topologies @xcite . in order to solve this theoretical problem leading qcd corrections for @xmath21
have been calculated at the two - loop level @xcite and recently these leading double - logarithmic qcd corrections were resummed to all orders @xcite .
the account of non - sudakov form factor to higher orders makes the @xmath21 cross section well defined and positive definite in all regions of the phase space @xcite .
all these studies of the influence of qcd corrections on heavy quark production in @xmath2 collisions were concentrated on circularly polarized initial photons . however , for the direct measurements of the parity of states of higgs bosons , ( [ scalar]-[pseudoscalar ] ) , linear polarization of photon beams is needed @xcite . in the present paper
we consider the qcd corrections to heavy quark - antiquark pair production in photon - photon collision for the general case of initial photon polarizations .
we mainly concentrate on qcd corrections for linearly polarized photon - photon collisions .
the production cross sections and spin asymmetries for @xmath10-pair production are calculated for linearly polarized photon collisions .
the measurement of spin asymmetries is necessary to determine the @xmath1 parity of the higgs boson . in the scattering of linearly polarized photon off circularly polarized ones at one - loop level _ azimuthal _
asymmetries arise in the production of heavy fermion pairs .
this is a pure quantum effect which does not exist at the born level .
these type of asymmetries are suppressed by factor @xmath23 , @xmath6 is the c.m.s energy of colliding photons , and are sizeable only for @xmath10-pair production .
the paper is organized as follows . in the next section we recall the basic definitions and consider the born cross section of heavy quark - antiquark pair production in polarized photon collisions .
calculations of virtual corrections are presented in section 3 .
the real gluon emission part is discussed in section 4 .
the numerical results for top - antitop pair production cross sections and expected asymmetries for linearly polarized photon beams are discussed in section 5 .
the cross section of heavy quark - antiquark pair production in polarized photon - photon collision @xmath24 can be written in the most general form using the stokes parameters which describe the polarizations of initial photons .
the covariant density matrix of polarized photon with arbitrary polarization can be written in the following form @xmath25 here @xmath26 are three stokes parameters describing polarization of the photon with momentum @xmath27 and @xmath28 and @xmath29 denote ort vectors in @xmath30 and @xmath31 directions . the momenta of the particles involved in the reaction in the c.m.s . of the initial photons
are given by @xmath32 where @xmath33 is the photon beam energy and @xmath34 is the quark ( antiquark ) velocity . with this definitions ,
the born cross section of heavy quark pair production in photon - photon collisions has the form @xmath35 where @xmath36 and @xmath6 , @xmath37 and @xmath38 are mandelstam variables for the process under consideration , @xmath39 in the above formulae instead of the original stokes parameters their combinations are used .
the expressions of the cross sections are shorter and more convenient for integration if one includes the dependence on the azimuthal angle in the stokes parameters , @xmath40 .
they can be expressed by original stokes parameters through the equations : @xmath41 here @xmath42 is the azimuthal angle .
parameters @xmath40 describe photon polarization with respect to unit vectors @xmath43 , @xmath44 , where @xmath43 lies in the reaction plane and @xmath44 is orthogonal to the reaction plane .
the first order qcd corrections to the cross section are determined by the interference between the tree level and one - loop diagrams . at the one - loop level
no three - gluon vertex enters and the calculation is analogous to calculations of qed corrections to compton scattering for finite electron mass ( see _ e.g. _ @xcite ) .
the calculations of virtual corrections were done by using the symbolic manipulation program form @xcite . to regularise the infrared singularities we introduced an infinitesimal mass of the gluon @xmath45 . in the basis of the stokes parameters the one - loop corrections have the form @xmath46 in addition to the born level expression , eq .
2 , there is the new term proportional to the non - diagonal product @xmath47 , which corresponds to the scattering of linearly polarized photon on the circularly polarized one .
the functions @xmath48 can be expressed through scalar one - loop integrals @xmath49 , @xmath50 and @xmath51 .
@xmath52 @xmath53 @xmath54 @xmath55 @xmath56 @xmath57 here @xmath58 , @xmath59 , and @xmath60 .
the definitions and expressions for the scalar integrals are given in the appendix a of @xcite .
it is worth mentioning that all functions @xmath48 are expressed through four- and three - point functions and ultraviolet finite combinations of two - point functions .
the contribution of the real gluon emission to the total cross section is separated in two parts , soft gluon emission which cancels out the infrared divergences of virtual corrections and hard gluon emission .
the cross section of the soft gluon emission can be reproduced in a factorized form as a product of born level cross section and the infrared divergent factor : @xmath61 where @xmath62\ln{\frac{2k_c}{\lambda } } \nonumber\\ & & + \frac{1}{2\beta}\biggl(1-\frac{2m_q^2}{s}\biggr ) \biggl[{\rm sp}\biggl(\frac{-2\beta}{1-\beta}\biggr)-{\rm sp}\biggl(\frac{2\beta}{1+\beta}\biggr)\biggr ] \nonumber\\ & & + \frac{1}{2\beta}\ln{\frac{1+\beta}{1-\beta}}\biggr\},\end{aligned}\ ] ] here @xmath63 is the soft photon energy cut and the velocity @xmath64 is defined in section 2 .
the dependence on the gluon mass @xmath45 is exactly canceled while adding soft gluon emission part and virtual corrections for any sets of stokes parameters . as can be seen from eqs .
( [ born ] ) and ( [ virt ] ) the term proportional to the product @xmath65 appears only in the virtual part and therefore should be infrared finite , although one - loop scalar functions @xmath66 , @xmath67 and @xmath68 do contain infrared logarithms . one can easily check that infrared divergent contributions from these scalar functions cancel each other in the @xmath69-term of eq .
the hard gluon emission part is also calculated using form program .
the expressions for the squared matrix elements are lengthy and we do not reproduce them in the paper . the integration over three - particle phase space is done by using monte - carlo integration routine vegas @xcite . after adding the soft and hard gluon emission cross sections the final numerical results do not depend on the imposed energy cut of emitted gluon , @xmath63 .
special care is taken to handle sharp peaks of the cross section while the gluon is soft or is emitted along the quark or antiquark three momenta ( see detailed discussion in @xcite ) .
these peaks correspond to the infrared and collinear singularities in the case of massless fermions and in our case become essential when mass of quark is small compared to the c.m.s .
energies of photons . to arrange the infrared and collinear singularities along the integration axis we take the gluon energy , denominator of the quark propagator , polar angles of quark and antiquark and azimuthal angle of reaction as integration variables .
integration over azimuthal angle is necessary in the case of linearly polarized photons , as in this case the cross section does depend on the @xmath42 angle .
the infrared singularity lies on the axis of integration over gluon energy , whereas collinear singularities are located along the axis of quark propagator .
there are also additional peaks when quark or antiquark are produced at zero angle with respect to the beam direction .
such singularities are treated by integration over the polar angles of quark and antiquark .
as was mentioned above , the helicity cross sections @xmath70 , @xmath71 for the heavy quark pair production in the circularly polarized photon - photon collisions were considered in @xcite . in this paper
we mainly present numerical results for the production of heavy quark - antiquark pair for the linearly polarized photons .
we consider two cases of linear polarizations of initial photons , when @xmath72 and @xmath73 , where @xmath74 is the angle between the directions of polarization vectors of the photons . the @xmath75 correspond to the collision of linearly polarized photons with parallel and perpendicular polarizations , respectively .
for the measurements of the higgs boson parity it is necessary to consider collisions of linearly polarized photons in order to measure the polarization asymmetry @xcite @xmath76 l7.cm in fact if inclusive two - jet final states are studied then after averaging over azimuthal angles and spins of the final particles only three independent cross sections remain for arbitrary polarization states of initial photons .
these independent cross sections can be taken as @xmath77 , @xmath78 and @xmath79 @xcite .
for the study of the higgs boson signal in photon - photon collisions @xcite it was essential that the background from @xmath80 quark production is suppressed by a factor of @xmath81 for @xmath21 at the born level .
however at the next - to - leading order the cross section of the @xmath82 production for @xmath21 is not suppressed any more .
therefore experimental cuts selecting only two - jet final states were important to suppress the @xmath82 background @xcite . in this section
we show , that the difference of @xmath79 is suppressed by a factor of @xmath23 even at the next - to - leading order .
the cross section for heavy quark pair production can be cast in the form @xcite : @xmath83 . @xmath84 for different polarization states of the photons as a function of dimensionless parameter @xmath85 . [
cols="^,^,^,^,^,^,^",options="header " , ] where the functions @xmath86 depend on the dimensionless variable @xmath87 only .
the numerical values of the functions @xmath88 are presented in the figure 1 and table i. because of the sommerfeld rescattering correction , the function @xmath89 is nonzero at the threshold , as one can see from the table i. in the both cases , @xmath72 and @xmath90 , the functions corresponding to qcd corrections are positive and rising at high energies . taking the average of values of these two functions one obtains the corresponding function for the unpolarized cross section .
our results are in agreement with previous calculations of qcd corrections for heavy quark - antiquark production in unpolarized photon - photon collisions @xcite . as in the case of born level functions @xmath91 and @xmath92 , in the asymptotic regime the difference between @xmath93 and @xmath89 vanishes and each of the function tends to the unpolarized one , @xmath94 .
such an asymptotic behavior of the corrections can be understood considering the helicity amplitudes for massless quarks .
the difference of the cross sections with parallel and orthogonal polarized photons can be expressed via the interference term of the following helicity amplitudes @xmath95 l7.cm here
the sum over the helicities of the final state particles @xmath96is implied .
the born amplitude of the @xmath97 pair production in the photon - photon collisions is known to vanish like @xmath23 for equal photon helicities and massless quarks @xcite .
therefore first two terms in the eq .
19 vanish in the high energy limit .
in addition , helicity amplitudes for the process of massless @xmath97 pair production with the additional gluon emission @xmath98 identically vanish for photon and gluon helicities @xmath99 and arbitrary quark helicities @xcite . consequently , in the third term of the eq
. 19 amplitudes @xmath100 and @xmath101 are nonzero only in the case when emitted gluons have different polarizations .
therefore there is no interferention between corresponding amplitudes and third term of eq .
19 term also vanishes at high energies . as result , the difference of the cross sections for @xmath102-pair production , @xmath103 is suppressed by a factor of @xmath104 . for @xmath7 production
the relative difference of the cross section for parallel and orthogonal polarized photons is less than @xmath105 for @xmath106 gev , i.e. in the whole range of the plc energies . on the other hand , for top - antitop production
there is no strong suppression of @xmath107 by the mass of quark at energies @xmath108 gev .
the production cross sections for @xmath10-pair production are illustrated in the figure 2 for different helicity states of initial photons .
the usual cut for suppression the higgs background is imposed , @xmath109 .
the solid lines correspond to the born level cross sections and the dashed lines to the qcd corrected ones .
as one can see from figure 2 the corrections are large near the threshold and decrease very rapidly with increasing the photon - photon c.m.s energy , @xmath110 . in the figure 3a
the difference of two cross sections , @xmath111 , is shown .
the correction to the @xmath107 are rather large near the threshold , up to @xmath112 gev , and decreases rapidly . however , the asymmetry , @xmath113 gets only small corrections in the whole range of energies .
the _ azimuthal _ asymmetry of heavy quark pair production is the specific effect which occurs only at one - loop level . the relevant term in eq . 8
proportional to imaginary unit @xmath114 corresponds to the scattering when one photon is polarized linearly and the other circularly , @xmath115 and @xmath116 or other way round ( all other stokes parameters are zero ) .
this term gives the contributions with opposite signs to the cross section being integrated in two different ranges of azimuthal angle , @xmath117 and @xmath118 .
the value @xmath119 corresponds to the direction of polarization vector of linearly polarized photon .
it is obvious that the total contribution of @xmath69-term to the cross section is zero .
we define the _ azimuthal _ asymmetry of @xmath102-pair production in the linearly polarized photon scattering off circularly polarized one in the following way @xmath120 this asymmetry can be sizeable only for top - antitop production at plc energies , while for the @xmath7-pair production _ azimuthal _
asymmetries are also suppressed by factor @xmath121 .
the expectations for the @xmath10-pair production asymmetry are shown in figure 3 .
the effect is @xmath122 at energies of the plc .
in the presented paper we derived the compact expressions for the @xmath123-corrections to the squared matrix element @xmath124 for the general case of initial photon polarizations .
the total cross sections up to the order @xmath125 are calculated , which are given by the sum of the tree level cross section , contribution of the interference term between the qcd one - loop @xmath123-correction and tree level amplitude and tree level cross sections of quark pair production accompanied by the real gluon emission .
the numerical results are obtained for heavy quark pair production cross sections in the case of linearly polarized photon collisions .
the difference of the cross sections of heavy quark pair production for parallel and perpendicular polarized photon collisions is suppressed by factor @xmath23 .
we show that the qcd correction for the @xmath7 production asymmetry is less than @xmath105 in the whole energy range of the plc and practically does not change the background for the measurement of @xmath1 parity of higgs boson . at the same time
, there is no such suppression for top - antitop production due to the large mass of top quark .
the relevant cross sections for @xmath126-pair productions are calculated .
the qcd corrections are large near the threshold and decrease rapidly with increasing the c.m.s energy of colliding photons . * * i.f .
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What is the citric acid concentration, [HCit], in the lemon juice?
>
> The pH of lemon juice is about 2.1. What is the citric acid concentration, [HCit], in the lemon juice?
>
>
>
I am given that $HCit \leftarrow \rightarrow H^+ + Cit^-$ and that $K\_a = 8.4 \times 10^{-4}$.
$K\_a = \frac{[H+][Cit]}{[HCit]} = 8.4 \times 10^{-4}$, and $[H+]$ is $10^{-2.1}$. However, without knowing $[Cit]$, how can I get [HCit]? Any help would really be appreciated!
For any mono-protic acid, when the acid dissociates in water, every H+ created will create one CB-.
>
> H-Cit <--> H+ + Cit-
>
>
>
For each 1 H-Cit. 1 H+ and 1 Cit- is produced upon dissociation.
Therefore, the [H+] = [Cit-]
For a Ka expression, set these two [] equal to each other, and the expression for [H+]\*[Cit-] = x^2
Use this to determine the amount of [Cit-] created when you create x amount of [H+].
| stackexchange/chemistry |
Question about relative speeds on a different "scales of perception"
I was kind of puzzled yesterday when thinking about this.
1. If we observe an object moving away from us with 10m/s we would say the object is moving away from us really slowly
2. But if we (humans, making an observation) would be the size of a proton, previously mentioned 10m/s would appear enormously faster than in the first case
What puzzles me is this. If we say two protons move away one of another with relative speed 0.999c, then those (second case) two-man-protons would say the relative speed between them is much greater than 0.999c.
Does this make any sense?
If I understand you correctly, your two points about apparent slowness of speeds is related to scale, and disappears when you quantify it using a common unit.
ie: We think of 10m/s as relatively slow because the average human is 1.8 metres in height, and we can imagine that 10 metres per second, or 36 kilometer/hour as an achievable speed using a machine (car).
If we were the size of a proton, obviously, 36 km/h would appear to be quite fast. It's quite fast even if we were the size of ants.
But in physics, we quantify everything. To human of our size, AND to a human the size of a proton, we will have to agree on scales and units, and thus the speed in itself will not change due to the size consideration alone.
As for you final scenario: the relative speed in both cases is 0.999c, and c would be the same unit for both parties, so the relative speed is the same.
On the other hand, if we used the height of human and diameter of proton(assuming hard spherical shape for simplicity) covered in a second as the unit in each case respectively, then we would have a different numerical value as the units are different. If the numerical values were the same, then the speeds would actually be different because the units are different.
The important thing is that *all* speeds seem to change:
If you would look at the universe, in this case the two protons, from the perception of a man shrunk to the size of a proton, not only would the particles appear much faster, but so would the speed of light.
So if you shrunk yourself to a trillionth of what you are now, one proton would have a diameter of 40 centimeters, or 15.7 inches, *relative to you*. The speed of light, then, would also a billion times greater, again, relative to you. In 'absolute' terms, i.e. relative something that did not change its size, nothing would change.
In your terms, the speed of the protons would go from 0.999c to 999,000,000,000c but the speed of light would have gone up, too: from c to 1,000,000,000,000c. Now if you look at the numbers, you can see that the ratio staid the same: 0.999.
Hope I could help.
Sincerely
Marrus with a Q
No this doesn't make sense.
Your argument number $2$ is wrong because if we(humans making the observation) shrink to the size of proton then we would use metre scales of size of order of our(human's) size whose one unit would be much smaller than 1 metre. The magnitude of the measurement made by this small scale would be larger in numbers but then to compare this measurement with $c$ we would have to convert the units of our measurement to the units in which $c$ is measured .
More precisely let $v$ be the velocity of that object then the ratio $\dfrac{v}{c}$ will be less than unity if $v$ and $c$ are measured in same units.
| stackexchange/physics |
power law scaling consists of universal properties that characterize collective phenomena that emerge from complex systems composed of many interacting units .
power law scaling has been observed not only in physical systems , but also in economic and financial systems [ 1 - 22 ] .
the discovery of this scaling behavior in economic and financial systems has shed new light on economics , and , in recent years , has led to the establishment of a new scientific field bridging economics and physics .
market economy land is one of the most important assets in capitalism .
the movement of land prices has a strong influence on the economic behavior of individuals and firms [ 23,24 ] . over the past few decades
, a considerable number of studies have been conducted on the scaling behavior in economic systems .
nevertheless , no studies have ever tried to study the scaling behavior in a land market . here ,
we introduce power law statistics in the distributions of land prices and of the relative price , as a new example of power law scaling in economic systems .
in most other countries , land price is a residual of property price , calculated by the income approach : net income divided by yield , minus building cost .
however , in japan , property price , including that for income producing properties , usually comprises land price plus building price , which are calculated separately .
land prices are normally determined by market comparisons utilizing land price indices prepared by the government ; such as the assessed value of land by ministry of land , infrastructure and transport , whilst building prices are normally determined in the market through the cost approach .
the assessed value of land is a price of a centare of a place as of january 1 , evaluated by two real estate valuers [ 25 ] .
the investigation is undertaken throughout the land once a year .
we analyze a database of the assessed value of land covering the 6-year period between 1995 - 2000 .
the data for each of the 6 annual intervals contains the land prices in approximately 30,000 points .
we first study the probability distribution of land price . in fig.1
, we plot the cumulative probability distribution of land price ( s ) of 30,600 points in the year 1998 , which is the log - log plot of the cumulative probability as a function of land price .
the ordinate shows the cumulative probability in a log scale , that is , the probability of finding land of a price equal to , or higher than , x. it is apparent that this plot tends towards becoming a linear function in the high price range .
we find that the tail of the cumulative probability distribution of the land price is described by a power law distribution , @xmath0 the solid line in fig .
1 represents this function . in the range of land prices
higher than @xmath1 yen , the probability distribution follows a power low with exponent @xmath2 @xmath3 , as determined by ordinary least squares ( ols ) regression in log - log coordinates . here , @xmath4 denotes the coefficient of determination .
the distribution fits the power law ( 1 ) very accurately in the high price range but it gradually deviates from ( 1 ) as the price becomes lower . as a further test of the strength of this result
, i repeated the same analyses for the data of land prices for each of the periods between 1995 - 2000 .
the power law exponents were in the range of @xmath5 .
the results are represented in table 1 .
overall , the power law distribution of land prices is very strong .
.power law exponents @xmath6 for the cumulative probability distribution of japan s land prices .
the results are obtained by using ols regression on data .
s.e . denotes standard errors , and r2 the coefficient of determination . [
cols="^,^,^,^,^",options="header " , ] to quantify the fact that the standard deviations of the relative prices vary by the price - ranges , we next calculated the standard deviation @xmath7 of the relative prices as a function of a price .
3b shows how the standard deviation of the relative price increases linearly with the logarithm of price . using the ordinary least squares method on the data , the standard deviation @xmath7
is estimated as @xmath8 with @xmath9 and @xmath10 @xmath11 .
the reason why the price fluctuations depend on the price level is probably as follows .
the land prices in urban areas are on average higher than in rural areas , and , furthermore , trades take place more actively in urban areas than in rural ones , so that the price fluctuations are generally higher in urban areas than in rural areas . as a consequence ,
the price fluctuations in the high price - range are higher than the price fluctuations in the low price - range . finally , we standardized the relative prices in order to find a form of the probability distribution of the relative prices that does not depend on the price - range .
we standardized the relative price that comes into each price - range by dividing by the estimated standard deviation given a price - range . in fig .
3c , we plot the logarithm of the probability density @xmath12 as a function of the logarithm of the standardized relative price @xmath13 , where @xmath14 denotes the mean . after standardizing ,
the resulting empirical probability distributions appear identical for the observations drawn from different points grouped by the price - range .
we found that the conditional probability distributions could be expressed by power law distributions @xmath15 using the ordinary least squares regression method in fig .
3c , we obtained estimates for the asymptotic slope @xmath16 where @xmath17 . to test if these results for the conditional probability distributions held for the data of the other years , we analyzed the data of each year of the 6-year period between 1995 - 2000 .
similar quantitative behavior was found for the conditional probability distributions .
we have shown that the prices and the relative prices of land are very well described by the power law distributions .
our empirical results give the conditions that any empirically accurate theories of land market have to satisfy .
since no model so far has successfully satisfied the statistical properties demonstrated in this paper , the next step is to model the behavior in land markets . in modeling land markets
, we should notice that land markets are complex systems compromised of many interacting agents . in land markets ,
participants meet randomly and negotiated trade takes place when an agent willing to buy land meets an agent willing to sell land .
the price formation in land markets is generated through this random matching process .
thus , it is likely that the methods of statistical physics developed to study complex systems , from which power law scaling emerges , will be useful to describe behavior in land markets .
a further important point to note is that land are a very important real asset , and the movement of land price strongly affect decision - making by consumers and firms [ 23 , 24 ] .
therefore , the investigation of the relationship between land prices and other economic variables such as consumption and investment will lead us further into a new understanding of the dynamics of the macro - economy , which is a complex system that is composed of many interacting subsystems , each with a complex internal structure comprising many interacting agents .
i am indebted to michiyo kaizoji for her assistance in collecting the data , to yoshi fujiwara and takuya yamano for his helpful suggestions .
this research was supported in part by a grant from the land institute of japan . v. plerou et .
al . , similarities between the growth dynamics of university research and of competitive economic activities , nature 400 , 29 433 - 437 ( 1999 ) .
r. l. axtell , zipf distribution of u.s .
firm sizes , science 293 , 1818 - 1820 ( 2001 ) . points .
the horizontal axis denotes the relative price change which is defined as the logarithm of the relative price , @xmath20 .
the relative prices asymptotically follow a power law .
the solid line is the regression fit in a log - log plot .
the lines have the slopes with @xmath21 for the lower tail and @xmath22 for the upper tail.,width=491 ] of the relative prices @xmath23 from 1997 to 1998 .
data contains the relative land prices at 29843 points in japan .
different symbols refer to different price - ranges , @xmath24 , @xmath25 ( circles ) , @xmath26 ( squares ) and @xmath27 ( triangles ) .
the solid lines are the ols regression lines through the data for each of the three price - ranges in the log - log plots.,width=491 ] | arxiv |
Sailor Moon Fridge Monster
Fridge Monster By: Ari-chan Rated: G
Notes and Disclaimers: All right.. this one is really strange, and I really don't think it's all that good. It's another one that I wrote in about five minutes only this one didn't come out as good. Oh well.. please just read it and review ... or send me an e-mail at [email protected].
All characters belong to Naoko-sama.. Jello belongs to whoever makes it, I can't think of who.
Haruka poked the blob carefully, it jiggled and the blonde jumped back. "Michiru," she said in a shaky voice. "Can you come here a minute? There's a monster in our fridge!"
Hearing the word monster Michiru quickly transformed into Sailor Neptune and rushed into the kitchen.
"What is it?"
"I'm not sure. Come take a look." Neptune bent down so she could see the green thing that stared back at her. "Do you know what it is?"
Neptune shook her head. "We better be careful, lets take it to Setsuna."
"I'm not going to touch it, it could be ... alive." The blonde shuddered. "It might have teeth too."
"What are you two doing?" The two women stood up and Haruka hit her head on the door of the fridge.
"Shimmata!"
"Setsuna it's a good thing you're here. We found this weird thing ... it's green and jiggles. We can't seem to figure it out. We thought maybe you could help."
"Of course." The green haired woman walked over to the fridge and took out the platter that the "monster" sat on. She looked at Neptune then to Haruka then started laughing.
"What's so funny?" Haruka crossed her arms upset at her friend for laughing when such a serious thing was happening.
"It's just jello."
"Jello?" Neptune and her lover said at the same time.
Setsuna nodded. "Jello. Hotaru made it the other day. I thought you knew."
"Is it edible?" Haruka asked.
"Yes,.."
"Then I'm going to eat it for scaring me."
"It scared you?" The senshi of time asked amused.
"Well, er no.. not really. It scared me 'cause it scared Michiru and when she's scared so am I...." The blonde coughed, and her two friends just nodded. Suddenly Haruka jumped. "Shimmata! It moved!"
End file.
| fanfiction |
Rockefeller Group Sells New Industrial Building to KKR for $43.5 Million | KKR & Co. Inc.
IRVINE, Calif., Jan. 30, 2019 /PRNewswire/ -- Rockefeller Group, a leading real estate developer, owner and operator, announced today that it has sold a recently completed 406,650-square-foot industrial distribution building to KKR for $43.5 million. The building, located at Optimus Logistics Center in Perris, Calif., a 1.45 million-square-foot industrial complex, is the second building to be completed and sold at the project, following the September 2018 sale of a 1.04 million-square-foot distribution building to Ferguson Enterprises.
"The sale of the last building at Optimus marks an important milestone for Rockefeller Group in the Inland Empire," said James V. Camp, Senior Vice President and Regional Development Officer for Rockefeller Group's West Region. "In less than two years, we were able to develop 1.45 million square feet of industrial space on a speculative basis along the I-215 freeway and complete the business plan by selling both buildings shortly after completion of construction. This success confirms that the I-215 corridor has become a destination for companies who need to distribute throughout the Western United States and also signifies the appetite by investors who see the area's growth potential."
Rockefeller Group completed construction of Optimus Logistics Center, which is a joint venture of Rockefeller Group and MBK Real Estate (MBK), in September 2018.
"We are excited to add Optimus Logistics Center to our industrial portfolio," said Roger Morales, Head of Real Estate Acquisitions in the Americas at KKR. "This is our first acquisition in the Inland Empire and we are confident that this investment will be attractive to potential tenants. Rockefeller Group has built an excellent asset."
"Throughout the escrow process on this sale, there was strong lease activity on this building given the site's direct access to I-215 and proximity to I-10 as well as the growing demand for industrial space by e-commerce companies," said Marc Berg, Vice President and Regional Director for Rockefeller Group's West Region. "We had been negotiating with several tenants prior to closing escrow with KKR and are confident that they will be successful in finding a tenant for the building in the near term."
Along with the completion of Optimus Logistics Center, Rockefeller Group completed 425,500 square feet of distribution space consisting of two buildings at Tri-City Industrial Complex in San Bernardino, whereby one of those buildings (Building #2 at 81,286 square feet) sold to 4F Capital in September 2018.
"Rockefeller Group is committed to developing industrial distribution and e-commerce facilities in the Inland Empire given the current demand for space in the region," said Camp. "In 2019, the Inland Empire is expected to see continued strong absorption, stable vacancy rates and growing rents. As a result, we will continue our development activities in the Inland Empire and other markets in the Western United States."
Mike McCrary, Peter McWilliams, Sharon Wortmann and Scott Coyle of JLL represented Rockefeller Group and KKR for the sale at Optimus.
Rockefeller Group is a leading real estate developer, owner and operator, known since the development of Rockefeller Center for pioneering large-scale urban mixed-use development. For nearly nine decades the company has been trusted for its financial strength, stability and vision, and today remains committed to the selective development of innovative, high-quality office, industrial, residential and mixed-use properties in urban centers and strategic distribution markets. Visit RockefellerGroup.com. | slim_pajama |
Nucleophilic addition of grignard reagent
[](https://i.stack.imgur.com/UfYnn.jpg)
Here why isn't the phenyl group attacking the carbonyl carbon? Isn't the first step in addition of grignard reagent the attack by the carbanion on the carbonyl carbon ?
The attacking of the Grignard reagent in these kinds of **$\alpha$-$\beta$ unsaturated carbonyl compounds** depends on two factors mainly.
$1$) ***Hardness of the acid centre***
$2$) ***Steric repulsion between the surrounding groups and incoming nucleophile***.
When the attacking nucleophiles are Grignard reagents,as per your equation, they are generally hard bases.**According to Pearson's HSAB Theory, Hard bases prefer to bind to the Hard acid centre and soft bases prefer to bind to the soft acid centre**. In your compound i.e in *$\alpha$-$\beta$ unsaturated carbonyl compounds, the carbonyl carbon centre is the Harder acid centre, whereas the $\ce{C=C}$ double bond centre is the softer acid centre*.So, **Grignard reagents try to first bind with the carbonyl carbons unless there is no other destabilising factor.**
The second governing factor is the steric crowding, which can sometimes make the attacking nucleophile attach to the least sterically crowded region even though it is violating HSAB theory. So, the addition compound actually depends on these two competititive factors.
Now, in your given compound the attacking nucleophile is $\ce{PhMgBr}$.It is undoubtedly *Hard Base*. But if it were to bind to the carbonyl carbon i.e. $\ce{C=O}$ double bond, there will be huge repulsion between the lone pair of oxygen and $\pi$-electron cloud of Phenyl ring which actually makes the previously stated second factor to dominate. So, due to this huge steric repulsion, The attacking nucleophile has to attack the *less sterically crowded*(Note: **The repulsion is also there at the double bonded carbon centre , but repulsion between methyl groups and phenyl rings are only due to inefficient spatial orientation which is definitely smaller than inter electronic strong columbic repulsion forces in close vicinity in the case of $\ce{C=O}$**) *softer basic* $\ce{C=C}$ centre which infact gives the product.
| stackexchange/chemistry |
the internal structure of the hadron has continually been a very important and interesting subject in the research field of high - energy physics . from the perspective of the experiment , in terms of the measurements of decay rate or cross section
, one can realize the internal structure ; on the other hand , from the viewpoint of theory , the internal structure is displayed from the distribution amplitude or the form factor .
no matter whether decay or collision happens in the hadron , the strong interaction plays an important role . until now
, the most successful theory for describing the strong interaction is quantum chromodynamics ( qcd ) .
however , it is still difficult to carry out accurate calculations based on qcd ; the main key lies in the strong coupling constant , especially in the low - energy region , close to unity .
such large value makes the perturbative calculation an arduous process .
there were several nonperturbative approaches inspired by qcd which could obtain some properties of the hadron and recently , based on the correspondence of string theory in anti - de sitter ( ads ) space and conformal field theory ( cft ) in physical space - time @xcite , a semiclassical approximation to qcd , light - front holography ( lfh ) , was successfully developed for describing the phenomenology of hadronic properties @xcite .
lfh provides mapping of the string modes in ads fifth dimension @xmath4 to the light - front wave function in the impact variable @xmath5 , which measures the separation of the constituents inside a hadron .
the mapping is proceeded by matching certain matrix elements presented within the string theory in ads space and the light - front theory in minkowski space .
this approach , known as bottom - up , allows to built models that have been successful in various qcd applications , such as hadronic scattering processes @xcite , hadronic spectrum @xcite , hadronic couplings and chiral symmetry breaking @xcite , and quark potentials @xcite .
it is well known that the main feature of qcd as the fundamental theory of the strong interaction lies in its nonperturbative behavior .
the picture of nonperturbative qcd leads to quark confinement and chiral symmetry breaking , which are believed to be the two essential mechanisms for forming hadron formation from qcd . undoubtedly , the complicated and nontrivial vacuum is not only the most important object to be understood for the nonperturbative aspect of qcd , but also a starting point for the construction of hadronic wave functions .
furthermore , in the light- front ( lf ) coordinates , the nontrivial vacuum is connected to the particles with zero - longitudinal momentum ( the so - called zero - mode particles ) and the infrared divergences from the small longitudinal momentum @xcite .
in fact , the lf infrared divergences are to be expected as the sources of chiral symmetry breaking @xcite . however , the understanding and application of the true qcd vacuum are still very limited in the lf framework .
thus , here we study the relevant subjects in the lf framework with a trivial vacuum .
an alternate approach which can reveal the phenomena of chiral symmetry breaking was proposed by the authors of ref .
@xcite , who chose the field content of the five - dimensional theory to holographically reproduce the dynamics of chiral symmetry breaking in qcd .
while this holographic model depends on only three free parameters , it agrees surprisingly well with the seven observables of the light meson . for compatibility with qcd
, the conformal invariance must be broken and the confinement in the infrared region must be introduced .
there are two types of the modified ads geometry which can achieve this results , as in the literature .
one is the hard - wall " ( hw ) model @xcite where partons are free inside the hadron and a hard cutoff is applied as the boundary . unlike the standard bag model @xcite , these boundary conditions are imposed on the impact variable @xmath5 , not on the bag of the radius .
the other is the soft - wall " ( sw ) model @xcite which has no sharp boundaries and employs a background dilaton field in the ads space as a smooth cutoff .
a problem with the hw model is that the dependence of hadron masses on the higher orbital angular momenta is linear , which is different from the quadratic behavior or the so - called regge trajectory " .
conversely , the sw model was initiated for solving the problem of the hadronic mass spectrum .
each of these two models has certain advantages which are explained the above references . in this work ,
we study the wave functions of light and heavy mesons and make the comparisons of the asymptotic behaviors of the electromagnetic ( em ) form factor , the distribution amplitudes , and the @xmath3-moments in both the hw and sw holographic models .
the case of the massless constituents is first considered , and a generalization regarding the behavior of the massive quarks @xcite follows .
there are two points worth mentioning : first , for the hw model , we use the parameter @xmath6 instead of @xmath7 to represent the size of the meson in both cases of the massless and massive constituents .
second , for the sw model , although both dilaton field profiles @xmath8 have been used in the literature @xcite to reproduce the behavior of regge trajectories for higher spin states , and the authors of ref .
@xcite related these solutions by a canonical transformation , the main motivation for using the dilaton field profiles @xmath9 is its seemingly better confinement properties @xcite .
however , as shown in refs .
@xcite , on one hand , the dilaton exponential @xmath10 leads to the existence of a spurious massless scalar mode in the model ; on the other hand , the desired confinement properties can be realized in the model with the dilaton exponential @xmath11 .
thus , here we apply the latter one to both the hadronic field and the bulk - to - boundary propagator .
the remained of this paper is organized as follows .
section ii reviews the extraction of wave functions by the holographic mapping of the light - front formulism to ads string mode . in sec .
iii , we compare both models in regard to the massless and massive constituents . in sec .
iv , we fit the dilaton scale parameter and the radius of bag with the decay constants of the distinct mesons and estimate the distribution amplitudes .
the first four @xmath3-moments in both models are compared with those of the other theoretical calculations .
conclusions are presented in sec .
v. other useful derivations for the discussion are given in the appendices .
the action for a spin-@xmath12 field @xmath13 in ads@xmath14 space - time in presence of a dilaton background field @xmath15 is given by @xcite s_=d^4 x d ze^-(z)(_n_j^n_j-^2_j(z)^2_j ) , [ action ] where @xmath16 is a dressed " five - dimensional mass because of the interaction of @xmath15 with @xmath13 .
the mass @xmath17 is related to the conformal dimension @xmath18 by @xmath19 and the coupling @xmath20 will be fixed later .
in addition , @xmath21det@xmath22 , @xmath23 is the metric tensor with @xmath24 , and the ads metric is defined as ds^2=g_mndx^mdx^n= ( _ dx^dx^-dz^2 ) , with @xmath25 the horizon radius and @xmath26diag@xmath27 .
@xmath13 is a rank tensor field @xmath28 which is totally symmetrical in all of its indices .
factoring out the plane wave along the poincar@xmath29 coordinates @xmath30 , we get : _
p(x , z)_j = e^-ipx(z)_j,[phi ] with four - momentum @xmath31 and invariant hadronic mass @xmath32 , and taking the variation of ( [ action ] ) , the ads wave equation for the spin-@xmath12 field is : ( z)_j=^2 ( z)_j.[eqphi ] we may assume that the hadron field @xmath33 minimally couples to a massless vector field @xmath34 with the action @xcite : s_a = d^4xdze^-(z)[-f_mnf^mn+i g_5a^m_p^*(x , z)_j _ m_p(x , z)_j],[la ] where @xmath35 and @xmath36 is a five - dimensional effective coupling constant . in the ads space , the propagation of an em probe can polarize along minkowski coordinates as : a_(x , z)=_e^-iqxv(q^2,z),a_z=0,[a ] where @xmath37 and @xmath38 is the bulk - to - boundary propagator with @xmath39 , since we are normalizing the bulk solutions to the total charge operator , and a boundary limit of the external current @xmath40 . taking the variation of the first term in eq .
( [ la ] ) , the ads wave equation for the external current is : v(q^2,z)=0 .
[ eqv ] the lorentz - invariant hamiltonian equation for a relativistic bound - state hadron is given by p_p^|(p)=^2 |(p ) , where @xmath31 is the four - momentum in four - dimensional minkowski space .
in the lf qcd , the hadron four - momentum @xmath31 can be expressed as : @xmath41 with @xmath42 and @xmath43 .
the hadronic state , which is an eigenstate of @xmath44 , @xmath45 and the total longitudinal spin @xmath46 , is normalized as @xmath47 in terms of the lf relative momentum variables @xmath48 and @xmath49 , the on - shell partonic momentum @xmath50 can be expressed as p^+_i = x_i p^+,*p*_i = x_i * p*_+*k*_i , and the hadronic state is expanded as |(p^+ , * p * _ , j_z)&= & _ n,_i^n_i=1 ( 16 ^ 3)(1-^n_j=1x_j)^2(^n_j=1**k**_j ) + & & _ n(x_i,*k*_i,_i)|n;p_i,_i , [ expandh ] where the delta functions are required from the momentum conservation , @xmath51 is the multiparticle fock eigenstates with @xmath52 the number of patrons in a given fock state , and @xmath53 is the projection of the constituent s spin along @xmath4 direction . the lf wave function @xmath54 complies with the angular momentum sum rules @xcite @xmath55 and is normalized as _ n,_i^n_i=1 ( 16 ^ 3)(1-^n_j=1x_j)^2(^n_j=1**k * * _ j)|_n(x_i,*k*_i,_i)|^2=1 , which is derived from ( [ norm ] ) . in the lf framework ,
a lot of physical quantities relate to the lf wave function . here
we show some of them which are of concern .
first , the decay constant of a pseudoscalar meson @xmath56 is given by : 0|j^+_w|m(p^+,*p*_)=ip^+f_m,[fm ] where @xmath57 is the flavor changing weak current which is evaluated at fixed light - cone time @xmath58 .
only the valence quarks contribute to the decay ; thus , we expand the initial state in eq .
( [ fm ] ) into the fock component and find f_m=2_| q q(x,*k*_).[fmexpand ] equation ( [ fmexpand ] ) enables the straight evaluation of the decay constant in terms of the lf wave function @xmath59 .
next , the distribution amplitude @xmath60 , which is the amplitude for finding constituents with longitudinal momentum fraction @xmath61 in the meson and collinear up to the scale @xmath62 , is defined as @xcite : ( x , q)^q^2 _
m(x,*k*_).[distribution ] the meson state @xmath63 , which is expanded into fock states , will approximate @xmath64 when @xmath65 is large . therefore , we can also calculate @xmath66 by the wave function @xmath67 .
in addition , an approach to parameterize distribution amplitude is to calculate the so - called @xmath3-moments : ^n = , [ ximoment ] where @xmath68 .
finally , the em form factor of a meson is defined as : m(p)|j^+(0)|m(p)=(p+p)^+f(q^2),[em ] where @xmath69 , @xmath70 , and @xmath71 . using the expanded state eq .
( [ expandh ] ) and the normalization condition eq .
( [ norm ] ) , the em form factor of a meson can be expressed as @xcite : f(q^2 ) & & dx ( x , * q * _ ) , + & = & _ i e_i ^*_|qq(x , |*k*_)_|qq(x,*k * _ ) , [ fq2 ] where @xmath72 is an effective single - particle density and @xmath73 .
equation ( [ fq2 ] ) reveals that the current matrix element in eq.([em ] ) can be represented as overlaps of the lf wave functions . for the holographic mapping of the light - front wave function to ads string mode , it is convenient to define the transverse center of momentum of a hadron @xmath74 as : * r*_=dy^- d^2**y**_t^++ * y * _ , where @xmath75 is the energy momentum tensor
. then the partonic transverse position @xmath76 and the internal coordinates @xmath77 , which conjugate to the relative momentum variable @xmath49 , have the following relations : x_i * r*_i = x_i * r*_+ * b*_i , ^n_i=1 * b*_i=0 , * r*_=^n_i=1 x_i * r*_i .
the light - front wave function @xmath78 can be expressed by the internal coordinates @xmath77 as : _ n(x_i,*k * _ i)=(4)^(n-1)/2^n-1_i=1d^2*b*_i ( i^n-1_i=1**b**_i**k * * _ i)_n(x_i,*b*_i),[fourier ] where @xmath79 is the light - front wave function in the coordinate space and is normalized as : _
n^n_i=1dx_id^2*b*_i |_n(x_i,*b*_i)|^2=1 .
then , we can substitute eq .
( [ fourier ] ) into eq .
( [ fq2 ] ) and integrate over @xmath80 phase space .
the em form factor of a meson @xmath81 can be obtained as : f(q^2)=dx d^2**b**_(i**q**_(1-x ) * b*_)|_|q q(x,*b*_)|^2 .
we can also express @xmath81 in terms of an effective single - particle transverse distribution @xmath82 @xcite : f(q^2)=dx d^2 * c*_(-i*c * _ * q*_)(x,*c*_),[fc ] where @xmath83 is the @xmath61-weighted transverse position coordinate of the spectator quark , and ( x , * c*_)&= & ( i**c**_*q*_)(x,*q * _ ) + & = & d^2 * b*_^2((1-x)*b*_-*c*_)| _ |qq(x,*b*_)|^2.[rholf ] if we integrate eq .
( [ fc ] ) over angles , the form factor can be obtained as @xcite : f(q^2)=2dxdj_0(q ) ( x , ) , [ fzeta ] where @xmath84 and @xmath85 is the bessel function of the first kind . on the other hand , if we consider a pseudoscalar meson coupled to an external em field in ads space , the second term of eq .
( [ la ] ) can be related to a hadron matrix element as @xcite : & & d^4xdze^-(z)a^m_p^*(x , z)_j _ m_p(x , z)_j + & & ~(2)^4 ^ 4(p-p - q ) _
m(p,j)|j^|m(p , j ) .
[ correspond ] substituting eqs .
( [ phi ] ) and ( [ a ] ) to the left hand side of eq .
( [ correspond ] ) and extracting a delta function from momentum conservation at the vertex , the form factor can be obtained as : f(q^2)=r^3e^(z)(z)v(q^2,z)(z ) , [ fz ] and be treated as the overlap in the fifth dimension coordinate @xmath4 of the normalizable modes which correspond to the incoming and outgoing mesons , @xmath86 and @xmath87 , with the non - normalizable mode , @xmath38 , which deal to the external source . comparing eq .
( [ fz ] ) with eq .
( [ fzeta ] ) and identifying the holographic variable @xmath4 with the transverse lf variable @xmath5 , the holographic mapping of the light - front wave function to ads string mode can be accomplished .
next , two kinds of dilaton background fields were considered and their respective wave functions extracted . the simplest dilaton background field is none ; that is , @xmath88 .
thus , the ads wave equation , eq .
( [ eqv ] ) , for the external current is reduced as : [ z^2 ^ 2_z - z _ z - z^2q^2]v_(q^2,z)=0 , and its solution with the boundary condition is : v_(q^2,z)=z q k_1(z q),[vsolution ] where @xmath89 is the modified bessel functions of the second kind .
in addition , an integral is done @xcite as : ^1_0 dx j_0(q ) = q k_1(q ) .
[ j0k1 ] substituting eqs .
( [ vsolution ] ) and ( [ j0k1 ] ) to eqs .
( [ fz ] ) and ( [ fzeta ] ) , respectively , and comparing the latter two equations , the relation between the lf wave function and the ads string mode is obtained as : |_|qq(x,)|^2=x(1-x ) , [ hardrelation ] where @xmath90 and eq .
( [ rholf ] ) are applied . on the other hand , for the meson field , eq . ( [ eqphi ] )
is reduced as : _ ( z)=^2_(z).[mesonh ] by substituting @xmath91 , an effective schrodinger equation is obtained as : _ ( ) = ^2_(),[phieq ] where the conformal dimension @xmath92 and @xmath93 are used . however , for the known confinement inside a hadron , a baglike model @xcite is considered where partons are free inside the meson and are forbidden outside the meson .
an additional hard - well potential is needed : @xmath94 if @xmath95 and @xmath96 if @xmath97 , where @xmath6 is the size of hadron . then , the solution to eq .
( [ phieq ] ) is @xmath98 with a boundary condition @xmath99 and a normalization condition @xmath100 . as for the meson field , the solution to eq .
( [ mesonh ] ) is : _ (
z)= j_l(z ) .[phih ] from eq .
( [ hardrelation ] ) , the lf wave function in the hw model in the limit of massless constituents is : _
l , n(x,*b*_)= j_l(|**b**_| _ l , n ) ( * b*_^2 ) , + [ hardb ] where @xmath101 is the root of the bessel function , @xmath102 , and @xmath103 is the step function .
another background field which introduced an infrared soft cutoff is a dilaton @xmath104 .
this time eq .
( [ eqv ] ) is reduced as : [ z^2 ^ 2_z-(1 + 2 ^2 z^2 ) z _ z - z^2q^2]v_(q^2,z)=0 , and the solution with the boundary condition is : v_(q^2,z)=(1+)u(,0,^2z^2 ) , [ softv ] where @xmath105 is the gamma function and @xmath106 is the confluent hypergeometric function . in the large @xmath65 limit ,
that is , @xmath107 , the solution is reduced as @xcite : v_(q^2,z)z q k_1(z q)=v_(q^2,z).[lq ] thus , in the large @xmath62 limit , the relation between the lf wave function and the ads string mode is obtained as : |_|qq(x,)|^2=x(1-x)e^-^2z^2 .
[ softrelation ] for this background field , eq . ( [ eqphi ] ) is reduced as : ( z)=^2(z ) , and an effective schrodinger equation can be obtained as : _ ( ) = ^2 _ ( ) , [ phieqsoft ] where @xmath108 . the normalized solution to eq .
( [ phieqsoft ] ) is : _
( ) = ^l+1^l+1/2e^-^2 ^ 2/2l^l_n(^2 ^ 2 ) , with ^2=4 ^2(n+ ) , and the meson field is : _
( z)=^l+1l^l_n(^2z^2).[softphi ] in order to obtain a massless pion and a linear regge trajectories : @xmath109 at large @xmath12 , the value @xmath110 is fixed .
thus , from eq .
( [ softrelation ] ) , the lf wave function in the soft - wall model in the limits of massless constituents is : _ l(x,*b*_)=[x ( 1-x)]^(l+1)/2| * b*_|^l e^-^2x ( 1-x)*b*_^2/2l^l_n(^2x ( 1-x)**b**^2_),[softb ] with ^2=4 ^2(n+ ) .
in this section , we make the comparisons between the hw and sw models for some hadron properties . for the em form factor of the charged pion , we take @xmath111 and substitute eqs .
( [ vsolution ] ) , ( [ phih ] ) and ( [ softv ] ) , ( [ softphi ] ) into eq .
( [ fz ] ) : f^_(q^2)&=&2 dz j_0 ^ 2()z q k_1(z q ) , + f^_(q^2)&=&2 dz z^2 ( l_0 ^ 0(^2 z^2))^2(1 + ) u(,0,^2z^2),[fpian ] which correspond to the hw and sw models , respectively . for the hw model ,
the analytical result is not easily obtained . as for the sw model ,
the em form factor is @xcite : f^_(q^2)=.[softfpi ] however , if we check the asymptotic behavior in the large @xmath62 limit , the results are f_(q^2)-|^q u_0 . where @xmath112 for the hw(sw ) model .
thus : q^2f^_(q^2)|_q^2=4()^2 , q^2f^_(q^2)|_q^2=4 ^ 2 .
they are derived in appendix a and , of course , the latter is easily checked according to eq .
( [ softfpi ] ) . in other words , if we set a parametric relation : = , [ kappalambda ] the asymptotic behaviors of @xmath113 for both models are the same . in addition , the mean square radius of the meson @xmath114 is determined from the slope of @xmath115 at @xmath116 : r^2_p=-6|_q^2=0 .
thus , from eq .
( [ softfpi ] ) , the mean square radius of the pion in the sw model is r^2_^=.[msrpi ] for the hw model , although the value of @xmath117 diverges logarithmically , as mentioned in ref .
@xcite , this problem in defining mean square radius of the pion does not appear if one uses neumann boundary conditions , and @xmath118 .
thus , the inverse relation between @xmath0 and @xmath6 is still satisfied .
one may speculate whether or not there are other similarities between these two models .
thus , we consider @xmath119 , which are the normalized solutions of the effective schrodinger equation and are derived from the meson field , for @xmath120 .
if the parametric relation ( [ kappalambda ] ) is used , we have : ^n=0_()=_n=0^c_n ^n_(),[expand ] where @xmath121 . it should be noted that @xmath122 is independent of the parameters @xmath0 and @xmath6 , which is described in appendix b. qualitatively , the coefficient @xmath123 tells us how much " @xmath124 is contained in @xmath125 .
we easily find @xmath126 .
in other words , the former is dominated within the latter .
it is convenient to study other hadron properties in the momentum space .
the lf wave function of the hw model for @xmath127 can be obtained from eqs .
( [ fourier ] ) and ( [ hardb ] ) as : _ ( x,*k*_)=j_0(),[wfh ] where @xmath128 . the distribution amplitude and decay constantcan be obtained from eqs .
( [ distribution ] ) and ( [ fmexpand ] ) , respectively : _ ( x)=,f_= , [ masslessh ] and the @xmath3-moments can be obtained by eq .
( [ ximoment ] ) : ^n _ = .
we see that the @xmath3-moments is zero when @xmath129 is odd . in other words ,
the distribution amplitude is symmetric for @xmath130 or @xmath131 .
this is apparent because of @xmath132 .
on the other hand , also for @xmath120 , the lf wave function of the sw model in momentum space can be obtained from eqs .
( [ fourier ] ) and ( [ softb ] ) as : ^n_(x,*k*_)=e^- l^0_n ( ) , [ wfs ] and the distribution amplitude and decay constant for @xmath133 can be obtained as : _ ( x)=,f_= .[masslesss ] equations ( [ masslessh ] ) and ( [ masslesss ] ) are consistent with the result of ref .
@xcite where they used a derivation : @xmath134 as @xmath135 .
the @xmath3-moments of this distribution amplitude , because of the same dependence as that of the hard - wall model : @xmath136 , is @xmath137 .
in fact , if we again set the parametric relation in eq .
( [ kappalambda ] ) , then : _ ( x)=_(x),f_=f_. [ hsequal ] as for the similarity between @xmath138 and @xmath139 , we can follow the similar argument for @xmath119 in appendix b : introducing a new variable @xmath140 , and rewriting the lf wave functions of the two models as _(*k*_)=j_0 ( ) , and _(*k*_)=e^- , where @xmath141 and both new functions satisfy the normalization condition : @xmath142 .
we may consider a complete set : @xmath143 which is the solution of the schrdinger equation for a two - dimension harmonic oscillator : ^_n(*k*_)=e^-l^0_n(k^2 ) . here
the function @xmath144 , which is the ground state " for this two - dimension harmonic oscillator , and the function @xmath145 can be written as a linear combination of @xmath146 : @xmath147 .
we can easily check that @xmath148 , @xmath149 , and @xmath150 .
the coefficients @xmath151 also satisfy the relation : _ ( * k*_)=_n c_n^n_(*k*_).[hsrelation ]
this means that the sw wave function is dominated within the hw one for @xmath127 .
we can realize this situation in terms of sketching @xmath152 and @xmath145 in fig .
[ fig : c00 ] . and @xmath145 , respectively.,width=384 ] if the integration of @xmath80 for both sides of eq .
( [ hsrelation ] ) is taken , we obtain = _
n c_n , where ^n_(*k*_)= , is independent of @xmath52 .
thus , using the parametric relation eq .
( [ kappalambda ] ) , we have another constraint of @xmath151 : ^_0 c_n=1.[cnp ] the convergence of @xmath153 is slower than that of @xmath154 because the sign of @xmath151 may be positive or negative . a simple generalization of the lf wave function for massive quarks follows from the assumption that the momentum space lf wave function is a function of the invariant off - energy shell quantity @xcite : ^2-=+m_0 ^ 2 . in other words , one may make the following replacement : m^2_0=+m^2_12 , m^2_12=+ , [ m12 ] where @xmath155 is the current mass of quark . for the sw model , this replacement is equivalent to a change of the kinetic term in the effective schrodinger equation eq .
( [ phieqsoft ] ) @xcite : --+m^2_12.[add ] the alterant masses of the light and heavy mesons were obtained by combining eqs .
( [ phieqsoft ] ) and ( [ add ] ) and solving them : m^2_n_j=4 ^ 2(n+)+n ^1_0 dx m^2_12 e^- , where @xmath129 is the normalization constant fixed from the integral @xmath156 .
here we generalize this replacement to the hw and sw models .
thus , the lf wave functions of these two models for @xmath133 can be replaced as : _ ( x,*k*_,m_i ) & ~&j_0(m_0 l ) , + _
( x,*k*_,m_i)&~&e^- .
[ wfm2 ] if the distribution amplitude for massive quarks is considered , we find that they are just the integrations of the massless lf wave function with an infrared cutoff : _ ( x , m_i)^_- _ ( x , * k*_,m_i)~^__(x,*k * _ ) , where @xmath157 .
for the sw model , we obtain _ ( x , m_i)~e^ , which is consistent with the result of @xcite . as for the hw model
, we may use eq .
( [ hsrelation ] ) to obtain : _ ( x , m_i)~_n c_n^_^n_(x,*k * _ ) .
thus , the distribution amplitude for the hw model is _ ( x , m_i)&~&e^.[phih - s ] because of the constant term of @xmath158 , for all @xmath52 s , being equal to @xmath159 , we substitute eq .
( [ cnp ] ) into eq .
( [ phih - s ] ) and obtain : _ ( x , m_i)&~&_(x , m_i).[comparephi ] thus , the difference between @xmath160 and @xmath161 is displayed as a function of @xmath162 .
if the ratio @xmath163 , that is , the meson is composed of the light quarks , the predictive distribution amplitudes from the hw and sw models are nearly the same .
in contrast , if @xmath164 , the parameter relation @xmath165 may be unable to be satisfied and the distribution amplitudes will be quite different .
we will display these comparisons in the next section .
in addition , for the sw model , if we consider the heavy and light quarkonium states , the scalings of the leptonic decay constants are : f_qq~ , f_qq~-(a_1+a_2 ) , which is described in appendix c. the latter is consistent with the case of the massless quark in eq .
( [ masslesss ] ) : @xmath166 . on the other hand ,
if we take the heavy quark limit @xmath167 , the scaling of the leptonic decay constants of heavy - light mesons is : f_qq~ , which is described in appendix d. this result is in agreement with the heavy quark effective theory ( hqet ) : f_~1/m_q^1/2,[hqet ] if @xmath168 .
these results reveal that the dilaton scale parameter @xmath0 seems to vary with the quark mass ; this inference is in accordance with the conclusion in section iii .
@xcite , even though they fixed @xmath0 and varied an additional parameter @xmath169 with the distinct mesons .
for the pion , whose constituent quarks approximate masslessness , the numerical results of the em form factor for the hw and sw models are obtained by eq .
( [ fpian ] ) and the parameters @xmath170 fm , @xmath171 gev , which fit the decay constant of pion @xmath172 mev @xcite , and shown in fig .
[ fig : fpi ] . as a function of @xmath65 .
the solid and dotted lines correspond to the sw and hw models , respectively .
data are taken from @xcite ( triangles ) , @xcite ( circles ) , and @xcite ( boxes ) for large @xmath62 transfers .
the long dashed line is the limiting behavior @xmath173.,width=384 ] we find that the difference between the two lines is large for the region @xmath174 , while for the others , it is relatively small . the long dashed line in fig .
[ fig : fpi ] is the limiting behavior @xmath173 for both models .
in addition , the line for the sw model is a little different from that in fig . 2 of @xcite because for the latter , the parameter @xmath175 gev is obtained by fitting the data for the form factor .
however , for the parameter @xmath171 gev , the mean square radius of pion @xmath176 , which is small compared with the pdg value @xmath177 @xcite . for the other light and heavy mesons , we apply the values of current quark mass as @xmath178 mev , @xmath179 mev , @xmath180 mev , @xmath181 gev , and @xmath182 gev @xcite . as for the dilaton scale parameter @xmath0
, we try to let it change with the decay constant of the different mesons . here
we use the following values : @xmath183 mev , @xmath184 mev , @xmath185 mev , @xmath186 mev , @xmath187 mev @xcite , @xmath188 mev @xcite , @xmath189 mev , and @xmath190 mev @xcite . from the above input values ,
the parameters @xmath0 and @xmath6 can be fixed as shown in table [ kappa_l ] .
.[kappa_l ] parameters @xmath0 and @xmath6 for the various mesons [ cols="^,^,^,^,^,^,^,^,^,^",options="header " , ]
we have compared two types of wave functions for pseudoscalar mesons in the light - front framework , obtained by the ads / cft correspondence within the hard - wall and soft - wall holographic models . in the case of massless constituents , we find that the asymptotic behaviors of @xmath191 , the distribution amplitudes , and the decay constants for both models are the same if a parametric relation , @xmath165 , is set . furthermore , in terms of the normalized wave functions of the sw model as a complete set , the ground state of the sw wave function dominates within that of the hw one . on the other hand , by introducing a quark mass dependence , the differences of the distribution amplitudes between the two models are obvious , and the above parametric relation is no longer satisfied if the decay constants of the various mesons are regarded as inputs .
in addition , for the sw model , the dependences of the decay constants of meson on the dilaton scale parameter differ : @xmath192 , @xmath193 , and @xmath1 .
the last one , if @xmath2 , is consistent with hqet : @xmath194 .
thus , we fit the values of @xmath0 and @xmath6 with the decay constants of the distinct mesons and find that the ratios of parameters are consistent with the prediction of hqet and with the ratios of the mean square radius for the light mesons . finally , we plot the distribution amplitudes of mesons for the two models and compare the first four @xmath3-moments of our estimations with those of the other theoretical calculations .
* acknowledgements * + this work was supported in part by the national science council of the republic of china under grant no nsc-99 - 2112-m-017 - 002-my3 .
from eq . ( [ fz ] )
, we have the em form factor of pion as : f_(q^2)=r^3^u_0e^(z)(z)v(q^2,z)(z),[a1 ] where @xmath112 , @xmath195 , and @xmath196 for the hw ( sw ) model .
recalling eq .
( [ lq ] ) , that is , @xmath197 in the large @xmath62 limit , we rewrite eq .
( [ a1 ] ) as : f_(q^2)=^q u_0(z q)^2k_1(z q)d(z q),[a2 ] the integral eq .
( [ a2 ] ) can be taken the integration by parts , and the result is : f_(q^2)= , + [ a3 ] where @xmath198 , @xmath199 , and @xmath200 is the generalized form of meijer g function .
we plot the curve of this meijer g function in fig .
[ fig : g ] and find it approaches @xmath159 and @xmath201 in the large @xmath62 limit and @xmath202 , respectively .
thus , the first .
the dotted line equals 1.,width=384 ] term of eq .
( [ a3 ] ) vanishes because @xmath203 for both two models , and the second term approximately equals a constant when the large @xmath62 limit is taken : f_(q^2)| _ q ( -)^q u_0(z ) d(zq)= -|^q u_0 . substituting the relevant functions and numbers , we find : q^2f^_(q^2)|_q^2=4()^2 , q^2f^_(q^2)|_q^2=4 ^ 2
the solutions of the effective schrodinger equations , eqs .
( [ phieq ] ) and ( [ phieqsoft ] ) , for @xmath120 are : ^n_()= j_0 ( ) , and ^n_()=e^-^2 ^ 2/2l^0_n(^2 ^ 2 ) , where @xmath204 is satisfied . if eq .
( [ kappalambda ] ) is substituted to eq .
( [ expand ] ) , we have : c_n=^1/j_1(_0,1)_0 d j_0(_0,1j_1(_0,1))e^-^2 ^ 2/2l^0_n ( ^2 ^ 2 ) .
[ dot ] we may introduce a variable @xmath205 , then @xmath119 can be rewritten as ^n_()&=&j_0(_0,n+1j_1(_0,n+1 ) ) , + ^n_()&=&e^-/2l^0_n ( ) , which satisfy the normalization condition @xmath206 .
it is well known that the associated laguerre polynomials @xmath207 have an orthogonality : ^_0 e^-l^0_n()l^0_m()d=_m , n .
thus , @xmath208 is a complete set and eq .
( [ dot ] ) can be rewritten as : c_n=^1/j_1(_0,1)^2_0 d j_0(_0,1j_1(_0,1))e^-/2l^0_n ( ) .
[ dotr ] it is obvious that @xmath122 is only dependent of @xmath209 and is independent of the parameters @xmath0 and @xmath6 .
in considering the heavy quarkonium , the lf wave function for the sw model is : _
( x,*k*_,m_i)=n_qq , where @xmath212 is the normalization constant and n_qq=^-1/2 . if we change the variable @xmath213 , the normalization constant is replaced as : n_qq=^-1/2=^-1/2 . the distribution amplitude and the decay constant
can be evaluated as : _ ( x , m_q)=^-1/2 e^- , and f_qq=^-1/2 , [ fqq ] where @xmath214 and @xmath215 is the complementary error function . performing an expansion in powers of @xmath216 for eq .
( [ fqq ] ) , we obtain : f_qq= + ( ) . taking the heavy quark limit
, we have the scaling : @xmath193 . for the light quarkonium , we perform an expansion in powers of @xmath217 for eq .
( [ fqq ] ) and obtain : f_qq= -(3 + 2 + 2 + ) r^2+(r^3 ) , where @xmath218 is the euler s constant and @xmath219 $ ] is the digamma function .
in considering the heavy - light meson , the lf wave function for the sw model is : _
( x,*k*_,m_i)=n_qq , where @xmath221 is the normalization constant and n_qq=\{^1_0 dx } ^-1/2 . taking the limit @xmath222 and ignoring the light quark mass , we obtain : n_qq\{e^--}^-1/2 , where @xmath223 $ ] is the incomplete gamma function .
thus , the distribution amplitude and the decay constant can be evaluated as : _ ( x , m_q)=e^- , and f_qq,[fqq ] we perform an expansion in powers of @xmath216 for eq .
( [ fqq ] ) and obtain : f_qq2 + ( ) . taking the heavy quark limit , we have the scaling : @xmath224 .
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the three data components of the analysis are age- and sex - specific mortality rates , age- and sex - specific population estimates by weight status , and age- and sex - specific diabetes incidence rates .
mortality rates were calculated based on number of deaths by sex and age from the national vital statistics system ( 9 ) .
population estimates , including information on age , sex , height , weight , and diabetes , were drawn from the national health interview survey ( nhis ) , an ongoing nationally representative cross - sectional survey of the civilian noninstitutionalized population .
the nhis uses multistage probability sampling to select respondents and collects self - reported health information , with marginal response rates of 70% for the adult sample interviews ( 10 ) .
population estimates and number of diabetes cases were classified by age ( 10-year intervals ) , sex , and bmi levels ( normal / underweight , < 25 kg / m ; overweight , 25 to < 30 kg / m ; and obese , 30 kg / m ) .
incident cases of diabetes were identified based on reported age at diagnosis of diabetes that is , being told by a doctor or health care professional that they had diabetes and age at time of interview .
diabetes incidence rates were derived by dividing the estimated number of people in a given age - sex group reporting that they were diagnosed during the year before the survey by the total population in each age - sex group .
individuals diagnosed with diabetes > 1 year before were no longer at risk for developing diabetes and so were not included in the numerator or denominator for rates .
analyses included 143,765 adults in 19801989 and 150,718 adults in 20002004 , of whom 507 and 1,366 , respectively , reported being diagnosed in the previous year .
we estimated the number of years an individual can expect to live without diabetes given their age , sex , and bmi status while also accounting for mortality risks using multiple - decrement life table techniques ( 12,13 ) .
diabetes - free life expectancy must be lower than total life expectancy , as an individual faces the competing risk of diabetes and death , both of which end diabetes - free life .
to determine the contribution of each age and bmi group to changes in total diabetes - free life expectancy between 19801989 and 20002004 , we used a discrete - time decomposition method by arriaga ( 14 ) .
the method calculates the total effect of a change in life expectancy above age x between two points in time as the sum of the direct effect of a change in rates above age x and the sum of the change in life expectancies contributed by the additional person - years lived above age x as a result of the improvements in rates between the two periods .
an extension of the method allows us to decompose changes in life expectancy by type of decrement , with the decrements in this analysis being diabetes incidence and death .
the contribution of each of these two types of decrements to the total decrement at each age is calculated from the proportion of the differences in total decrements it represents between two points in time .
thus , the difference in diabetes - free life expectancy at a given age between two periods is the result of differences in diabetes incidence and mortality rates above that age ( 14,15 ) .
in addition to examining the competing risks of diabetes and all - cause mortality in the entire population , we also performed these calculations for each bmi group separately .
this allowed for a better understanding of the effects of secular changes in weight on diabetes incidence overall and among people of different weights , showing the number of years that a person in each bmi category can expect to live without diabetes . using similar life table techniques ( 12,13 )
, we also estimated the proportion of the population that will eventually be diagnosed with diabetes given their weight status and the current diabetes and mortality rates in the u.s . because data on age at diagnosis were not available for people younger than age 18 and older than age 79 in some nhis waves , analyses were restricted to ages 18 to 79 years .
this approach implies that incidence rates at younger ages are negligible or that the calculations are conditional on not having been diagnosed before age 18 .
we tested this assumption by reallocating in our estimates observed mortality according to risk ratios by bmi group reported in the literature ( 16,17,18 ) .
we tested the possibility that changes in diagnosis detection rather than incidence are driving the results .
the results are robust to each of these sensitivity tests ( supplementary table 1 ) .
the bmi - specific calculations do not model the transition of individuals between bmi categories . to relax this assumption , we estimated diabetes - free life expectancy for each bmi group at ages 18 , 40 , and 60 years , which shows how the changing weight composition of the population at each age may affect diabetes - free life expectancy in bmi groups .
on the basis of nhis data and vital statistics , we calculated that life expectancy at birth in the u.s
. in 19801989 was 70.6 years for men and 77.4 years for women , and it had increased to 74.3 years for men and 79.0 years for women by 20002004 .
remaining life expectancy at age 18 also increased by 3.1 years for men and 1.1 years for women ( supplementary table 1 ) .
in contrast , diabetes - free life expectancy at age 18 decreased by 1.4 years among men ( from 50.2 to 48.8 years ) and 1.7 years among women ( from 54.2 to 52.5 years ) ( table 1 and supplementary fig .
1 ) . these reductions in diabetes - free life expectancy in the context of otherwise increasing life expectancy in the u.s . indicate declines in the proportion of the lifetime spent without diabetes .
the proportion of the lifetime spent without diabetes fell from 0.93 to 0.85 for men and from 0.90 to 0.85 for women between 19801989 and 20002004 .
years of diabetes - free life expectancy by age and bmi levels , 19801989 vs. 20002004 , u.s .
data are from national vital statistics system of the national center for health statistics , centers for disease control and prevention , and single - year data are from the nhis . the role of diabetes incidence in these reductions in diabetes - free life expectancy
can be better appreciated by standardizing mortality levels : if mortality rates had remained the same between 19801989 and 20002004 instead of improving by 2.4 years for men and 0.8 years for women , diabetes - free life expectancy would have fallen even more by 3.8 years for men and 2.5 years for women ( not shown ) .
in fact , mortality rates decreased , so reductions in diabetes - free life expectancy result solely from increases in diabetes incidence or diagnoses rather than from increases in mortality . while overall diabetes - free life expectancy decreased between the 1980s and the 2000s , there are substantial differences between bmi groups . diabetes - free life expectancy at age 18 among normal / underweight individuals increased from 51.6 to 53.5 for men and from 57.3 to 59.0 for women , as shown in table 1 .
the diabetes - free life expectancy of overweight individuals was slightly lower than those of normal / underweight individuals at both time periods .
however , the diabetes - free life expectancy of overweight individuals also increased , from 50.4 to 51.4 for men and from 52.2 to 54.9 for women .
obese individuals had by far the lowest expected diabetes - free lifetimes in both time periods .
furthermore , this was the only group to experience decreases in diabetes - free life expectancy between the 1980s and the 2000s , and these decreases were large : 5.6 years for men and 2.5 years for women .
thus , all of the observed reductions in diabetes - free life expectancy at the population level were actually due to increases in diabetes only among obese individuals , a situation that also holds for diabetes - free life expectancy at ages 40 and 60 .
in fact , when we decomposed the contributions of each bmi group to changes in the u.s .
population overall , we found that improvements in the other weight groups countered these reductions in diabetes - free life expectancy without completely offsetting them .
, obese 18-year - old men and women could expect to live 13.7 and 19.1 fewer years without diabetes than normal and underweight 18-year - old men and women , respectively .
these numbers represent increases in the difference in diabetes - free life expectancy between obese and normal / underweight individuals of 7.5 years for men and 4.2 years for women compared with the 1980s .
our decomposition of the contribution of each age group to changes in diabetes - free life expectancy shows that losses in years of life without diabetes occurred generally at younger ages for men than for women ( fig .
normal and underweight women saw improvements at all ages , with the greatest improvements at ages 18 to 39 ; overweight women also experienced improvements at most ages . on the other hand
, obese women saw reductions in diabetes - free life expectancy at all ages > 30 .
for men , the gains in diabetes - free life expectancy among normal / underweight and overweight men were less even , with some losses in the 3rd decade of life .
obese men in all age groups experienced decreases in diabetes - free life expectancy , with the greatest losses among men younger than age 50 .
contribution of age groups to changes in diabetes - free life expectancy between 19801989 and 20002004 in the u.s .
the proportion of 18-year - olds who would develop diabetes increased greatly between 19801989 and 20002004 ( fig .
23.3% of 18-year - old women and 17.8% of 18-year - old men would eventually have diabetes given the current mortality and diabetes incidence rates . in the 2000s
, this proportion had increased to just over one - third of the population , specifically 33.8% of women and 34.7% of men , suggesting closing gender gaps in diabetes incidence .
proportion of 18-year - olds in the u.s . who will develop diabetes , by sex , bmi , and period .
normal / underweight , overweight , and obese individuals experienced different changes in lifetime risk of diabetes .
for women , in the 1980s , 12 , 31 , and 53% of normal / underweight , overweight , and obese 18-year - olds , respectively , could expect to be diagnosed with diabetes . by 20002004 ,
these risks did not change for normal / underweight and overweight women but did increase for obese women to 66% . during the 1980s , normal / underweight men had similar risks of developing diabetes in their lifetimes to those faced by women ( 12% ) . however , heavier men were at considerably lower risk than women : 17% for overweight and 37% for obese . by the 2000s , the proportion of men who would develop diabetes in their lifetime increased for all weight groups to 16 , 27 , and 63% for normal / underweight , overweight , and obese men , respectively .
the calculations above assume that there were no differences in mortality by diabetes or weight status .
allowing for differential mortality between bmi groups and by diabetes status does not change the finding that diabetes - free life expectancy decreased and that this decrease resulted from increasing diabetes incidence among obese individuals ( supplementary table 1 and supplementary fig .
1 ) . it could be that fewer obese individuals with diabetes were undiagnosed in the 2000s than in the 1980s , meaning that diabetes incidence would appear to be higher even if there were no change in incidence .
previous research has shown that the proportion of diagnosed cases has increased significantly only for those with bmis > 35 ( 19 ) .
the resulting diabetes - free life expectancy at age 18 is 3 years lower than implied by diagnosed incidence rates , falling in the 2000s to 46.0 years for men and 49.4 years for women .
accounting for changes in undiagnosed diabetes does not fully explain the decreases in incidence among normal / underweight and overweight men and women ( with the possible exception of overweight men ) , nor does it explain the increases in diabetes incidence among the obese population .
thus , even if diabetes detection has improved disproportionately in obese patients , obese individuals still bear the burden of decreases in diabetes - free life expectancy that occurred during the past 20 years .
on the basis of nhis data and vital statistics , we calculated that life expectancy at birth in the u.s
. in 19801989 was 70.6 years for men and 77.4 years for women , and it had increased to 74.3 years for men and 79.0 years for women by 20002004 .
remaining life expectancy at age 18 also increased by 3.1 years for men and 1.1 years for women ( supplementary table 1 ) .
in contrast , diabetes - free life expectancy at age 18 decreased by 1.4 years among men ( from 50.2 to 48.8 years ) and 1.7 years among women ( from 54.2 to 52.5 years ) ( table 1 and supplementary fig .
1 ) . these reductions in diabetes - free life expectancy in the context of otherwise increasing life expectancy in the u.s . indicate declines in the proportion of the lifetime spent without diabetes .
the proportion of the lifetime spent without diabetes fell from 0.93 to 0.85 for men and from 0.90 to 0.85 for women between 19801989 and 20002004 .
years of diabetes - free life expectancy by age and bmi levels , 19801989 vs. 20002004 , u.s .
data are from national vital statistics system of the national center for health statistics , centers for disease control and prevention , and single - year data are from the nhis . the role of diabetes incidence in these reductions in diabetes - free life expectancy
can be better appreciated by standardizing mortality levels : if mortality rates had remained the same between 19801989 and 20002004 instead of improving by 2.4 years for men and 0.8 years for women , diabetes - free life expectancy would have fallen even more by 3.8 years for men and 2.5 years for women ( not shown ) .
in fact , mortality rates decreased , so reductions in diabetes - free life expectancy result solely from increases in diabetes incidence or diagnoses rather than from increases in mortality . while overall diabetes - free life expectancy decreased between the 1980s and the 2000s , there are substantial differences between bmi groups . diabetes - free life expectancy at age 18 among normal / underweight individuals increased from 51.6 to 53.5 for men and from 57.3 to 59.0 for women , as shown in table 1 .
the diabetes - free life expectancy of overweight individuals was slightly lower than those of normal / underweight individuals at both time periods .
however , the diabetes - free life expectancy of overweight individuals also increased , from 50.4 to 51.4 for men and from 52.2 to 54.9 for women .
obese individuals had by far the lowest expected diabetes - free lifetimes in both time periods .
furthermore , this was the only group to experience decreases in diabetes - free life expectancy between the 1980s and the 2000s , and these decreases were large : 5.6 years for men and 2.5 years for women .
thus , all of the observed reductions in diabetes - free life expectancy at the population level were actually due to increases in diabetes only among obese individuals , a situation that also holds for diabetes - free life expectancy at ages 40 and 60 .
in fact , when we decomposed the contributions of each bmi group to changes in the u.s .
population overall , we found that improvements in the other weight groups countered these reductions in diabetes - free life expectancy without completely offsetting them .
, obese 18-year - old men and women could expect to live 13.7 and 19.1 fewer years without diabetes than normal and underweight 18-year - old men and women , respectively .
these numbers represent increases in the difference in diabetes - free life expectancy between obese and normal / underweight individuals of 7.5 years for men and 4.2 years for women compared with the 1980s .
our decomposition of the contribution of each age group to changes in diabetes - free life expectancy shows that losses in years of life without diabetes occurred generally at younger ages for men than for women ( fig .
normal and underweight women saw improvements at all ages , with the greatest improvements at ages 18 to 39 ; overweight women also experienced improvements at most ages . on the other hand
, obese women saw reductions in diabetes - free life expectancy at all ages > 30 .
for men , the gains in diabetes - free life expectancy among normal / underweight and overweight men were less even , with some losses in the 3rd decade of life .
obese men in all age groups experienced decreases in diabetes - free life expectancy , with the greatest losses among men younger than age 50 .
contribution of age groups to changes in diabetes - free life expectancy between 19801989 and 20002004 in the u.s .
the proportion of 18-year - olds who would develop diabetes increased greatly between 19801989 and 20002004 ( fig .
23.3% of 18-year - old women and 17.8% of 18-year - old men would eventually have diabetes given the current mortality and diabetes incidence rates . in the 2000s , this proportion had increased to just over one - third of the population , specifically 33.8% of women and 34.7% of men , suggesting closing gender gaps in diabetes incidence .
proportion of 18-year - olds in the u.s . who will develop diabetes , by sex , bmi , and period .
normal / underweight , overweight , and obese individuals experienced different changes in lifetime risk of diabetes .
for women , in the 1980s , 12 , 31 , and 53% of normal / underweight , overweight , and obese 18-year - olds , respectively , could expect to be diagnosed with diabetes . by 20002004 ,
these risks did not change for normal / underweight and overweight women but did increase for obese women to 66% . during the 1980s , normal / underweight men had similar risks of developing diabetes in their lifetimes to those faced by women ( 12% ) .
however , heavier men were at considerably lower risk than women : 17% for overweight and 37% for obese . by the 2000s , the proportion of men who would develop diabetes in their lifetime increased for all weight groups to 16 , 27 , and 63% for normal / underweight , overweight , and obese men , respectively .
the calculations above assume that there were no differences in mortality by diabetes or weight status . in robustness check ,
we incorporated risk ratios from the literature into our estimates . allowing for differential mortality between bmi groups and by diabetes status does not change the finding that diabetes - free life expectancy decreased and that this decrease resulted from increasing diabetes incidence among obese individuals ( supplementary table 1 and supplementary fig .
1 ) . it could be that fewer obese individuals with diabetes were undiagnosed in the 2000s than in the 1980s , meaning that diabetes incidence would appear to be higher even if there were no change in incidence .
previous research has shown that the proportion of diagnosed cases has increased significantly only for those with bmis > 35 ( 19 ) .
the resulting diabetes - free life expectancy at age 18 is 3 years lower than implied by diagnosed incidence rates , falling in the 2000s to 46.0 years for men and 49.4 years for women .
accounting for changes in undiagnosed diabetes does not fully explain the decreases in incidence among normal / underweight and overweight men and women ( with the possible exception of overweight men ) , nor does it explain the increases in diabetes incidence among the obese population .
thus , even if diabetes detection has improved disproportionately in obese patients , obese individuals still bear the burden of decreases in diabetes - free life expectancy that occurred during the past 20 years .
in this study , we used demographic techniques and large national datasets to examine changes in diabetes - free life expectancy between 19801989 and 20002004 for adult men and women in the u.s . and to examine the changing role of body mass for diabetes risks .
these methods offer the advantage of allowing us to examine the changing incidence of diabetes while holding the improvements in mortality during the period constant .
they also allow us to estimate the contributions of changing diabetes incidence rates for different levels of body weight to overall diabetes - free life expectancy , which makes it possible to better understand the observed changes in overall diabetes risks and the differing risks in the population .
we found that the proportion of 18-year - olds who would develop diabetes in their lifetimes increased by almost 50% among women and almost doubled among men between the 1980s and the 2000s . while life expectancy for men and women in the u.s .
increased , diabetes - free life expectancy at age 18 decreased by 1.7 years for women and 1.4 years for men , indicating declines in the proportion of the lifetime spent without diabetes .
this pattern points to the emergence of a prolonged period of morbidity rather than longer healthy life spans , but only among obese individuals .
, obese 18-year - old men and women could expect to live 13.7 and 19.1 fewer years without diabetes , respectively , compared with normal / underweight 18-year - old men and women .
increases in diabetes incidence among obese people led to reductions in diabetes - free life expectancy so large that the overall diabetes - free life expectancy of the adult u.s
. population decreased in spite of improvements in diabetes - free life expectancy among nonobese individuals , who represent the majority of the population .
in the main models , we standardized mortality across bmi groups to isolate the effect of changes in diabetes incidence .
the approach allowed us to determine that changes in diabetes incidence rather than mortality were responsible for the decrease in diabetes - free life expectancy .
it also allowed us to identify the ages at which the greatest changes in diabetes incidence occurred .
sensitivity analyses show that our results are robust to adjusting mortality rates by diabetes and weight status to the rate ratios reported in the literature .
since our estimates did not directly model transitions between bmi groups , we have not shown the effect of gaining or losing weight on the expected life span without diabetes , as was also the case for previous studies ( 20 ) .
the measures yield cumulative estimates of diabetes - free life expectancy for people starting at a given bmi level at age 18 .
because the bmi composition of cohorts tends to change over time , with people gaining weight as they age , we also relaxed this assumption to account for weight increases by estimating diabetes - free life expectancy for each bmi group at age 40 and 60 .
shifts in the bmi composition of the population likely have reinforced changes in diabetes risks within bmi categories ; that is , as the proportion of the population who is obese has increased , higher incidence rates of diabetes seen among heavier individuals affect a larger proportion of the population , leading to increases in diabetes cases .
there are several possible explanations for our finding that the decreases in diabetes - free life expectancy have been borne almost exclusively by the obese population .
one explanation is that rates of diabetes detection have changed , specifically among obese individuals .
robustness checks indicate that changes in undiagnosed diabetes in obese patients relative to others explain part but not all of the reductions in diabetes - free life experienced by this group .
another reason may be changes in weight distributions within bmi groups , because our analyses indicate that weight increases were greatest among obese men and women : the average obese american was > 3.4% heavier in the 2000s than in the 1980s . since diabetes risk increases with bmi ( 2,3 ) , that the average obese person was heavier in the 2000s explains some of the increases in diabetes risk .
another consideration could be changes in the racial composition within each bmi category , since previous studies showed that the prevalence of diabetes has increased more among non - hispanic blacks and hispanics relative to non - hispanic whites in the normal and overweight categories but less in the obese category ( 21 ) .
nhis data show that the change in racial composition of bmi groups was lowest among obese individuals , leading to a relatively higher proportion of whites in the obese category .
thus , the racial distribution in the bmi categories is not likely to explain the observed trends .
another possible explanation is that diabetes risks are higher with younger age of obesity onset ; indeed , the prevalence of obesity has tripled among children since the 1970s ( 22 ) .
our estimates are not conditional on bmi level before the age to which they pertain , so earlier onset of obesity could explain some of the increases in diabetes risk for obese individuals .
a limitation of this study is our reliance on self - reported data on diabetes diagnosis , weight , and height , which have been shown to be biased ( 23 ) and may be systematically different by sex , ethnicity , and age ( 24 ) .
in addition , nhis data are collected via rigorous in - person interviews , and the differences in reported and measured bmi are not large and do not affect health risk estimates , including those associated with diabetes ( 24 ) .
furthermore , in spite of this limitation , the nhis is the only dataset with sufficient sample size to conduct this analysis . since 34% of the u.s .
adult population is obese ( 25 ) , these findings entail that more than one - third of americans can expect to develop diabetes , even if they reached adulthood without diabetes ; this proportion stands at approximately two - thirds of obese men and women .
these estimates suggest a large future increase in the prevalence of diabetes and its complications , especially among obese individuals .
our results suggest that in the face of budgetary or logistic constraints , new efforts to prevent diabetes can have the greatest impact among obese individuals , because those who are not obese generally have experienced decreases in risks during the past 2 decades with current prevention efforts .
this study highlights the growing prevalence of diabetes , implying greater future health care demand at younger ages and for longer life spans .
this will necessitate medical and public health professionals with training in diabetes management and facilities well equipped for the management of diabetes and treatment of comorbidities among obese individuals .
the many dimensions of changing population and individual health must be well understood and tracked with methods such as those demonstrated in this study to improve health care planning and health . | pubmed |
power outages , internet congestion , traffic jams , and many other problems of social and economical interest are ultimately limited by the physical assignment of resources in infrastructure networks . the recent realization that numerous such systems can be modeled within the common framework of complex networks @xcite has stimulated several theoretical studies on network resilience @xcite . however , despite much advance @xcite , the relation between the large - scale allocation and actual usage of resources in distributed infrastructure systems is a question that goes beyond previous complex network research . here we propose to cast this question as a statistical physics problem by exploring that the dynamics of many such systems can be modeled as a network transport process .
for example , website browsing and e - mail communication are based on packet transport through the internet ; movement of people and goods is heavily based on road , rail , and air transportation networks ; public utility services depend on the transport of energy , water and gas through supply networks . in these examples ,
the transport of packets , passengers , and physical quantities creates traffic loads that must be handled by nodes and links of the underlying networks .
because the capacities of nodes and links are limited by cost and availability of resources , the proper allocation of capacities is an essential condition for the robust and cost - effective operation of infrastructure networks . in this paper
, we investigate this question by focusing on the relationship between _ capacity _ and _ load _ from the perspective of a decentralized optimization between _ robustness _ and _
cost_. by analyzing four types of infrastructure networks , the air transportation , highway , power - grid and internet router network , we find empirically that the capacity load relation is mainly determined by the relative importance given to the cost : if robustness is much more important than cost , the capacity @xmath0 approaches the _ line of maximum robustness _
@xmath1 , where @xmath2 is the maximum available capacity , irrespective of the load ; if cost is a strongly limiting factor , the capacity approaches the _ line of maximum efficiency _
@xmath3 , for all values of the load @xmath4 .
the real systems analyzed fall in between these two extremes and exhibit an unanticipated nonlinear behavior , which , as shown schematically in , is very different from the constant @xcite , random @xcite , and linear @xcite assignments of capacities considered in previous models .
we study this nonlinearity using the concept of _ unoccupied capacity _ , the difference between the capacity and the time - averaged load .
it follows , surprisingly , that the percentage of unoccupied capacity is smaller for network elements with larger capacities . interpreting this as a result of a decentralized evolution in which capacities and loads are allocated or reallocated in response to increasing load demand @xcite
, we demonstrate the observed behavior using a traffic model devised to minimize the probability of overloads in a scenario of fluctuating traffic and limited availability of resources .
our model shows that the reduction of the unoccupied capacity is a consequence of the reduction of the traffic fluctuations on highly loaded elements , but it also shows that the probability of overloads can be larger on elements with _ larger _ capacities .
we consider four different types of real - world infrastructure networks : _ air transportation network _ , using seat occupation data of aircraft operating between @xmath5 us and foreign airports available at the bureau of transportation statistics database ( http://www.bts.gov ) ; _ highway network _ , using traffic data of the state of colorado for @xmath6 highway segments available at the colorado department of transportation database ( http://www.dot.state.co.us ) ; _ power - grid network _ , using available data for @xmath7 transmission lines of the electric reliability council of texas ( http://www.ercot.com ) ; _ internet router network _ , using packet traffic data measured by the multi router traffic grapher ( http://oss.oetiker.ch/mrtg/ ) on @xmath8 routers of the abilene backbone , mit and princeton university
. shows the relation between the time - averaged load and capacity of the network elements in a log - binned scale .
the air transportation network [ ( a ) ] is very close to the line of maximum efficiency @xmath3 , indicating effective allocation of resources , which is likely to be a consequence of the high costs of air transportation combined with flexibility to adjust seat availability to demand .
the highway network shows less efficient behavior in the region of small loads [ ( b ) ] , a feature that may provide alternative routes for congested traffic . a similar pattern is observed in the power - grid network [ ( c ) ] although , compared to the highway network , the power grid has larger unoccupied capacities for the heavily loaded components of the network .
these unoccupied capacities can be useful for the dispatch of power generation to adjust to specific market , weather , and demand conditions .
the internet router network [ ( d ) ] shows weaker dependence of the capacity on the load than those found in the other networks , which is probably due to the discreteness of the commercially available router bandwidths , the fast growing bandwidth demand , and the tendency to simultaneously upgrade groups of routers regardless of their individual loads .
therefore , while the capacity load relation depends on the specific network , the pattern of this dependence can be understood in connection with a trade - off between the robustness and the cost of capacities in the construction and maintenance of the system . for quantitative characterization
, we define the _ efficiency coefficient _ @xmath9 of a network as the ratio between the total load and total capacity , @xmath10 where the sums are taken over all components of the system .
this quantity provides a measure of the importance of the cost .
as the cost becomes more important , the capacity is expected to approach the load in order to prevent overallocation of resources , which increases @xmath9 ; when the robustness is more important , the capacity is expected to be much larger than the load , which decreases @xmath9 .
we find that the efficiency coefficient is @xmath11 for the air transportation network , @xmath12 for the highway network , @xmath13 for the power - grid network , and @xmath14 for the internet router network .
therefore , one can argue that cost is increasingly deprioritized over robustness as one goes from the air transportation to the highway , power - grid and internet router network .
in particular , the average unused capacity reaches @xmath15 in the internet router network as opposed to @xmath16 in the air transportation system . in interpreting these results
one should notice that the capacities of the air transportation network can be easily downgraded while the same does not hold true for the other networks .
power transmission lines , highways , and internet hardware involve permanent allocation of physical capacities that can not be dynamically adjusted or redistributed across the system .
the presence of network elements ( nodes and links ) with finite minimum physical capacities is likely to be a contributing factor for the plateaus observed in the region of small loads [ ( b)-(d ) ] .
we now analyze our empirical findings using a model based on the optimization of capacities at the level of individual network elements . we define a simple objective function @xmath17 for node @xmath18 , which incorporates competing robustness ( @xmath19 ) and cost @xmath20 functions , and where @xmath21 $ ] represents the importance of the cost .
given functions @xmath19 and @xmath22 , the minimization of @xmath23 will lead to an optimized capacity @xmath24 for node @xmath18 subjected to the time - averaged load @xmath25 , which defines a capacity load relation @xmath26 . to formulate this model ,
we consider a time - dependent transport process in which traffic moves from source to destination along predetermined paths .
this process includes as a special case the directed flow model where traffic moves along the shortest paths @xcite , and it leads to a general yet mathematically treatable model that is not dependent on the details of the network structure and routing scheme . within this model ,
we identify the time fluctuation of traffic as the main perturbation that can cause accidental overloading failures . defining the robustness function @xmath19 as the overloading probability @xmath27 , the objective function can be written as @xmath28 where , for concreteness
, we have chosen the cost @xmath22 to be a linear function of the capacity . to determine the overloading probability
, we calculate the load @xmath29 on node @xmath18 at time @xmath30 , where @xmath31 is the amount of the traffic towards node @xmath32 originating from node @xmath33 at time @xmath34 . here
, @xmath35 is @xmath36 if @xmath18 lies on the path from @xmath33 to @xmath32 and @xmath37 otherwise .
if we take a time window @xmath38 much larger than the autocorrelation time of @xmath39 s , we can rewrite the time - averaged load @xmath25 as @xmath40 where @xmath41 is used for ensemble averages . then , given the distribution of @xmath39 , and thereby the load distribution @xmath42 , we can write the overloading probability @xmath27 as @xmath43 = \int^\infty_{c_i } p_i(l_i ) dl_i\ ] ] for given capacity @xmath24 such that @xmath44 .
the capacity @xmath0 is assumed to be physically upper - bounded by @xmath2 and lower - bounded by @xmath4 . for the explicit calculation of the capacity load relation , we consider uncorrelated and synchronized traffic fluctuations .
we consider both types of fluctuations since random internal fluctuations can be strongly modulated by external driving forces @xcite . in the internet backbone , for example , it has been observed that the traffic dynamics is well - characterized by a poisson process for millisecond time scales , while long - range correlations appear for longer time scales @xcite . in the systems we consider ,
synchronized fluctuations can be generally triggered by exogenous factors , such as weather and seasonal conditions or collective human behavior . * uncorrelated fluctuations .
* we consider fluctuations in which the traffic @xmath39 is completely uncorrelated with the traffic between different source - destination nodes . in this regime
, the quantity @xmath39 can be regarded as an independent identically distributed random variable @xmath45 following a probability distribution @xmath46 . assuming that @xmath46 has finite moments , including average @xmath47 and variance @xmath48
, we apply the central limit theorem to obtain a gaussian distribution of loads , @xmath49,\ ] ] with average @xmath50 and variance @xmath51 . the relation @xmath52 , a corollary of eq .
( [ eq : pdf_uncorrel ] ) , is in agreement with the empirical results of previous studies @xcite .
now , using eq .
( [ eq : pdf_uncorrel ] ) in the minimization of @xmath23 in eq .
( [ eq : objfn ] ) , we obtain the capacity load relation as @xmath53 with @xmath54 where @xmath55 , parameter @xmath56 denotes @xmath57 , and @xmath58 satisfies @xmath59 . * synchronized fluctuations .
* since the modulation of traffic that we describe by synchronized fluctuations occurs in a longer time scale @xcite , we neglect the travel time @xmath60 to express @xmath61 and the synchronized traffic load as @xmath62 . assuming statistical independence of @xmath63 in different modulation periods
, we use the peak value @xmath45 of @xmath63 in each modulation period as a reference for capacity determination .
given the distribution @xmath46 , we can write the overloading probability @xmath27 as @xmath64 and determine @xmath26 by minimizing @xmath23 . the resulting optimized capacity is @xmath53 , with @xmath65 where @xmath66 and @xmath67 is obtained by inverting @xmath68 . for @xmath68 having more than one solution ,
we conventionally select @xmath69 that gives the largest capacity .
because we have defined @xmath45 as the maximum traffic amount of many individual traffic events in a modulation period , extreme value distributions can be used as an input for @xmath46 .
here we numerically calculate @xmath26 for the gumbel distribution @xmath70 $ ] and the frchet distribution @xmath71 $ ] , where all parameters are positive , referred to as the first and second asymptotes in the extreme value statistics literature @xcite .
these two asymptotes correspond to exponential and power - law initial distributions , respectively .
the third asymptote is for bounded initial distributions and gives similar results when the bound of the traffic @xmath63 becomes large
. shows our model predictions for uncorrelated and synchronized fluctuations . in both regimes
we find that the allocation of capacities exhibits characteristics in common with the empirical data .
in particular , the calculated @xmath26 shows the common trend that a larger relative deviation from the line @xmath3 , representing a larger unoccupied portion of the capacity , is found in the region of smaller @xmath4 .
these results are determined by general statistical properties of the traffic and do not depend on the details of the network structure and dynamics .
this generality represents an advantage over previous models based on betweenness centrality because the latter is only weakly correlated with the actual flows in the networks and can not be used to predict @xmath26 .
note that betweenness centrality only accounts for the shortest paths , while @xmath72 in eq .
( [ eq:3 ] ) accounts both for paths that are not necessarily the shortest and for non - uniform distributions of the size " @xmath39 of the individual traffic events .
the observed nonlinearity in the capacity load relation suggests that infrastructure systems have evolved under the pressure to minimize local failures rather than global failures .
previous work @xcite has established that the incidence of large cascading failures can be reduced by shedding loads on low - load nodes , despite the fact that this causes a concurrent increase in the incidence of small failures . in the present model
this would correspond to a higher probability of overloads for network elements subjected to smaller loads , which is the _ opposite _ of the trend observed in this study . indeed , as a result of the optimization of capacities , the overloading probability @xmath73 is an increasing function of @xmath4 and differs , in particular , from capacity allocations that assume the same overloading probability for all the nodes .
the predicted vulnerability to large - scale failures is consistent with the absence of global optimization given that real infrastructure networks evolve in a decentralized way . in the case of the power grid , for example , it has been proposed @xcite that the evolution of the system is driven by the opposing forces of slow load increase and corresponding system upgrades , keeping the system in a dynamic equilibrium that balances the probability of outages .
it is likely that a similar self - organization mechanism is at work in infrastructure systems in general , which would further expand the concept of network self - organization @xcite within transportation problems . while providing additional rationale for the decentralized optimization incorporated in our model
, this view emphasizes that in infrastructure systems local robustness is prioritized at the expense of global robustness .
these results are expected to enable researchers to build models to study network evolution and the impact of disturbances in complex communication and transportation systems .
this work was supported by nsf grant dms-0709212 .
newman mej , barabsi a - l and watts dj ( eds ) 2006 _ the structure and dynamics of networks _ ( princeton : princeton university press ) | arxiv |
exactly soluble lattice - statistical models attract scientific interest as they offer a valuable insight into diverse aspects of cooperative phenomena @xcite . the mapping technique based on generalized algebraic transformations @xcite belongs to the simplest mathematical methods , which allow to obtain the exact solution for various statistical models . recently
, this approach has been applied to an interesting diamond - chain model of interacting spin - electron system @xcite .
this motivated us to start studying a similar spin - electron system on doubly decorated two - dimensional ( 2d ) lattices in order to provide a deeper insight into how the mobile electrons influence their magnetic properties @xcite .
the investigated model system might provide guidance on a magnetic behavior of magnetic metals such as srco@xmath0o@xmath1 @xcite , which contain both localized spins and itinerant electrons .
consider a hybrid lattice - statistical model of interacting spin - electron system on doubly decorated 2d lattices ( see fig . 1 in ref .
@xcite ) , which have one localized ising spin at each nodal lattice site and two delocalized mobile electrons at each couple of decorating sites .
the total hamiltonian of the model can be written as a sum over bond hamintonians @xmath2 , where each bond hamiltonian @xmath3 involves all interaction terms of @xmath4th couple of delocalized electrons @xmath5 here , @xmath6 and @xmath7 ( @xmath8 ) represent usual creation and annihilation fermionic operators , respectively , @xmath9 and @xmath10 is the standard spin-1/2 operator .
the hopping parameter @xmath11 takes into account kinetic energy of mobile electrons , @xmath12 describes the ising interaction between the itinerant electrons and their nearest ising neighbors and @xmath13 denotes the on - site coulomb repulsion . following the rigorous approach developed in ref .
@xcite , one obtains a simple universal equality @xmath14 which establishes an exact mapping relationship between the partition function @xmath15 of the interacting spin - electron system on the doubly decorated 2d lattice and the partition function @xmath16 of the spin-1/2 ising model on the corresponding undecorated lattice of @xmath17 vertices with the coordination number @xmath18 and the effective temperature - dependent nearest - neighbor interaction @xmath19 .
note that the relation ( [ 2.02 ] ) allows direct calculation of all relevant physical quantities to be useful for understanding of magnetic behavior of the considered system .
now , let us proceed to a discussion of the most interesting numerical results obtained for the interacting spin - electron model on doubly decorated 2d lattices with the on - site coulomb repulsion . before doing this
, however , it is noteworthy that the special case of this hybrid system without the on - site repulsion term has already been examined in detail by present authors in the earlier paper @xcite . the exact results for this particular model revealed that the ground state of the system consists of an interesting four - sublattice quantum antiferromagnetic phase @xmath20 .
@xmath20 is characterized by a perfect nel order of the ising spins situated at the nodal lattice sites and the quantum entanglement of four microstates @xmath21 , @xmath22 , @xmath23 , and @xmath24 of itinerant electrons delocalized over decorating lattice sites ( see fig .
[ fig1 ] ) , whose probability amplitudes depend on a mutual ratio between the hopping term @xmath11 and the ising interaction @xmath12 . with this background ,
the purpose of the present work is to shed light on how the on - site coulomb repulsion @xmath25 affects the spontaneous long - range order to emerge in @xmath20 . for simplicity
, we will further assume the ferromagnetic ising interaction @xmath26 , because the sign change @xmath27 brings just a trivial change in the mutual orientation of the nodal ising spins with respect to their nearest - neighbor electrons .
the deeper insight into the effect of the on - site coulomb repulsion on a probability distribution of four entangled microstates in @xmath20 may be gained from fig .
[ fig2 ] , which shows the abundance probabilities of relevant microstates as functions of @xmath28 for the fixed @xmath29 . as one
can clearly see from this figure , the abundance probability @xmath30 of the majority microstate @xmath21 monotonically increases upon strengthening the on - site repulsion at the expense of the abundance probabilities @xmath31 , @xmath32 , @xmath33 of minority microstates , until they asymptotically reach the values @xmath34 and @xmath35 , respectively , in the limit @xmath36 .
consequently , one may conclude that in the limit of infinitely strong on - site repulsion each decorating lattice site is occupied by just one mobile electron , which prefers the ferromagnetic alignment with respect to its nearest ising neighbor . providing that within the second - order perturbation theory the kinetic term @xmath11 at half - filling is equivalent to the af heisenberg interaction between spins
, one may conclude that for sufficiently strong repulsion , the ground state of the interacting spin - electron system is identical with the one of the spin-1/2 ising - heisenberg antiferromagnet defined on the same doubly decorated lattice @xcite . in fig .
[ fig3 ] , we depict the critical temperature of the spin - electron model on doubly decorated square lattice as a function of the the on - site coulomb repulsion for several values of the kinetic term .
as one can see , the critical temperature monotonically decreases upon strengthening the coulomb repulsion for sufficiently small hopping terms @xmath38 , while for stronger kinetic terms @xmath39 it exhibits a more striking dependence with a pronounced maximum due to a mutual competition between the sufficiently strong hopping term @xmath37 and the coulomb term @xmath28 .
in conclusion , the effect of on - site coulomb repulsion on the ground - state properties and critical behavior of the interacting spin - electron system on doubly decorated 2d lattices have been examined using the generalized decoration - iteration transformation .
the obtained exact results clearly show that the dependence of critical temperature on a strength of the on - site coulomb repulsion basically depends on whether the kinetic term is greater than or less than the boundary value @xmath40
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a total of 26 lean ( bmi 18.524.9 kg / m ) and 40 obese ( 30.344.2 kg / m ) sedentary ( < 1 h of exercise per week ) subjects participated in this study .
lean and obese subjects underwent a two - stage hecp in conjunction with stable isotopically labeled tracer infusions as part of previous studies ( 6,7 ) and for this study .
all subjects completed a comprehensive medical evaluation , which included a history and physical examination , blood tests , and a 2-h oral glucose tolerance test .
no subject had impaired fasting glucose or diabetes or took medications that can affect glucose or lipid metabolism .
all subjects gave their written informed consent before participating in this study , which was approved by the human research protection office of washington university school of medicine in st .
body fat mass and fat - free mass ( ffm ) were determined by using dual - energy x - ray absorptiometry ( delphi - w densitometer ; hologic , waltham , ma ) .
subjects were admitted to the clinical research unit at washington university school of medicine in the evening before the hecp . between 1800 and 2000 h , subjects consumed a standard meal , containing 1215 kcal / kg ffm comprising 55% carbohydrate , 30% fat , and 15% protein .
subjects then fasted until completion of the hecp the next day . at 0500 h the next morning ,
one catheter was inserted into a forearm vein to infuse stable isotopically labeled tracers ( cambridge isotope laboratories , andover , ma ) , dextrose , and insulin , and a second catheter was inserted into a radial artery in the contralateral hand to obtain blood samples .
when radial artery cannulation was not possible , a catheter was inserted into a hand vein , which was heated to 55c with a thermostatically controlled box , to obtain arterialized blood samples . a primed , continuous infusion of [ 6,6-h2]glucose ( priming dose 22.5 mol
kg , infusion rate 0.25 mol kg min ) was started at 0600 h , followed at 0800 h by a continuous infusion of [ 2,2-h2]palmitate ( 0.035 mol kg min ) or [ u - c]palmitate ( 0.006 mol kg ffm min ) , and in obese subjects only , a primed , continuous infusion of [ 1,1,2,3,3-h5]glycerol ( priming dose 1.2 mol
after 3.5 h of [ 6,6-h2]glucose infusion ( basal period ) , a two - stage hecp was started and continued for 6.5 h. either [ 2,2-h2]palmitate or [ u - c]palmitate tracer infusion could be used to evaluate palmitate kinetics , because both tracers result in the same palmitate ra values ( b.w.p .
, unpublished observation ) . in all 26 lean subjects and in 14 obese subjects ,
insulin was infused at a rate of 7 mu m body surface area ( bsa ) min ( initiated with a priming dose of 28 mu m bsa min for 5 min and then 14 mu m bsa min for 5 min ) for 180 min during stage 1 . in the remaining 26 obese subjects , insulin was infused at a rate of 20 mu m bsa min ( initiated with a priming dose of 80 mu m bsa min for 5 min and then 40 mu m bsa min for 5 min ) during stage 1 . in all 66 subjects , insulin was infused at a rate of 50 mu m bsa min ( initiated with a priming dose of 200 mu m bsa min for 5 min and then 100 mu m bsa min for 5 min ) and continued for 210 min during stage 2 .
these three different insulin infusion rates allowed assessments of adipose tissue and liver insulin sensitivities ( low - dose and medium - dose insulin infusion rates during stage 1 to suppress adipose tissue lipolysis and hepatic glucose production submaximally ) and skeletal muscle insulin sensitivity ( high - dose insulin infusion to stimulate muscle glucose uptake during stage 2 ) ( 3 ) .
euglycemia ( 5.5 mmol / l ) was maintained by infusing 20% dextrose enriched to 2.5% with [ 6,6-h2]glucose at variable rates .
the glucose , glycerol , and palmitate tracer infusion rates were decreased by 50% during stage 1 of the clamp procedure and by additional increments of 50% ( glucose ) and 75% ( glycerol and palmitate ) during stage 2 to account for the expected declines in hepatic glucose production and lipolytic rates .
plasma glucose concentration was measured with an automated glucose analyzer ( yellow spring instruments co. , yellow springs , oh ) .
plasma insulin and c - peptide concentrations were measured with a chemiluminescent immunoassay ( immulite 1000 ; diagnostic products corporation , los angeles , ca ) .
plasma ffa concentrations were determined by gas chromatography , and plasma glucose , palmitate , and glycerol tracer - to - tracee ratios in plasma were determined by using electron impact ionization gas chromatography
triglyceride and cholesterol concentrations in plasma were measured enzymatically by using a hitachi 917 autoanalyzer ( hitachi , tokyo , japan ) ; ldl cholesterol was calculated by using the friedewald equation ( 8) .
isotopic steady - state conditions were achieved during the final 30 min of the basal period and stages 1 and 2 of the clamp procedure .
steele s equation for steady - state conditions was therefore used to calculate substrate kinetics ( 9 ) .
glucose rd from plasma was equal to endogenous glucose ra plus the rate of exogenously infused dextrose and glucose tracer .
palmitate and glycerol kinetics were expressed in micromoles per kilogram of fat mass per minute to provide an index of adipose tissue lipolytic activity in relation to the amount of endogenous fat stores and in micromoles per kilogram of ffm per minute to provide an index of ffa availability for lean tissues that use fatty acids for fuel .
portal vein and hepatic sinusoidal insulin concentrations in obese subjects were estimated from the measured arterial insulin and c - peptide concentrations according to the method of staehr et al .
statistical analyses were performed with spss for windows ( version 17.0 ; spss , chicago , il ) .
results are reported as means sem ( normally distributed data sets ) or medians and interquartile ranges ( skewed data sets ) .
accordingly , the student t test for independent samples or the mann - whitney u test were applied as appropriate to compare differences in subject characteristics and multiorgan insulin sensitivity between lean ( n = 26 ) and obese ( n = 14 ) subjects who received the same insulin infusion rates during the hecp ( i.e. , low- and high - dose infusions ) .
the paired student t test or the wilcoxon signed rank test were used to evaluate the effect of insulin infusion on substrate kinetics within lean ( n = 26 ) and obese ( n = 14 for low - dose infusion [ 7 mu m bsa min ] , n = 26 for medium - dose infusion [ 20 mu m bsa min ] , and n = 40 for high - dose infusion [ 50 mu m bsa min ] ) groups .
body fat mass and fat - free mass ( ffm ) were determined by using dual - energy x - ray absorptiometry ( delphi - w densitometer ; hologic , waltham , ma ) .
subjects were admitted to the clinical research unit at washington university school of medicine in the evening before the hecp . between 1800 and 2000 h , subjects consumed a standard meal , containing 1215 kcal / kg ffm comprising 55% carbohydrate , 30% fat , and 15% protein .
subjects then fasted until completion of the hecp the next day . at 0500 h the next morning ,
one catheter was inserted into a forearm vein to infuse stable isotopically labeled tracers ( cambridge isotope laboratories , andover , ma ) , dextrose , and insulin , and a second catheter was inserted into a radial artery in the contralateral hand to obtain blood samples .
when radial artery cannulation was not possible , a catheter was inserted into a hand vein , which was heated to 55c with a thermostatically controlled box , to obtain arterialized blood samples . a primed , continuous infusion of [ 6,6-h2]glucose ( priming dose 22.5 mol
kg , infusion rate 0.25 mol kg min ) was started at 0600 h , followed at 0800 h by a continuous infusion of [ 2,2-h2]palmitate ( 0.035 mol kg min ) or [ u - c]palmitate ( 0.006 mol kg ffm
min ) , and in obese subjects only , a primed , continuous infusion of [ 1,1,2,3,3-h5]glycerol ( priming dose 1.2 mol
after 3.5 h of [ 6,6-h2]glucose infusion ( basal period ) , a two - stage hecp was started and continued for 6.5 h. either [ 2,2-h2]palmitate or [ u - c]palmitate tracer infusion could be used to evaluate palmitate kinetics , because both tracers result in the same palmitate ra values ( b.w.p .
, unpublished observation ) . in all 26 lean subjects and in 14 obese subjects ,
insulin was infused at a rate of 7 mu m body surface area ( bsa ) min ( initiated with a priming dose of 28 mu m bsa min for 5 min and then 14 mu m bsa min for 5 min ) for 180 min during stage 1 . in the remaining 26 obese subjects , insulin was infused at a rate of 20 mu m bsa min ( initiated with a priming dose of 80 mu m bsa min for 5 min and then 40 mu m bsa min for 5 min ) during stage 1 . in all 66 subjects ,
insulin was infused at a rate of 50 mu m bsa min ( initiated with a priming dose of 200 mu m bsa min for 5 min and then 100 mu m bsa min for 5 min ) and continued for 210 min during stage 2 .
these three different insulin infusion rates allowed assessments of adipose tissue and liver insulin sensitivities ( low - dose and medium - dose insulin infusion rates during stage 1 to suppress adipose tissue lipolysis and hepatic glucose production submaximally ) and skeletal muscle insulin sensitivity ( high - dose insulin infusion to stimulate muscle glucose uptake during stage 2 ) ( 3 ) .
euglycemia ( 5.5 mmol / l ) was maintained by infusing 20% dextrose enriched to 2.5% with [ 6,6-h2]glucose at variable rates .
the glucose , glycerol , and palmitate tracer infusion rates were decreased by 50% during stage 1 of the clamp procedure and by additional increments of 50% ( glucose ) and 75% ( glycerol and palmitate ) during stage 2 to account for the expected declines in hepatic glucose production and lipolytic rates .
plasma glucose concentration was measured with an automated glucose analyzer ( yellow spring instruments co. , yellow springs , oh ) .
plasma insulin and c - peptide concentrations were measured with a chemiluminescent immunoassay ( immulite 1000 ; diagnostic products corporation , los angeles , ca ) .
plasma ffa concentrations were determined by gas chromatography , and plasma glucose , palmitate , and glycerol tracer - to - tracee ratios in plasma were determined by using electron impact ionization gas chromatography
triglyceride and cholesterol concentrations in plasma were measured enzymatically by using a hitachi 917 autoanalyzer ( hitachi , tokyo , japan ) ; ldl cholesterol was calculated by using the friedewald equation ( 8) .
isotopic steady - state conditions were achieved during the final 30 min of the basal period and stages 1 and 2 of the clamp procedure .
steele s equation for steady - state conditions was therefore used to calculate substrate kinetics ( 9 ) .
glucose rd from plasma was equal to endogenous glucose ra plus the rate of exogenously infused dextrose and glucose tracer .
palmitate and glycerol kinetics were expressed in micromoles per kilogram of fat mass per minute to provide an index of adipose tissue lipolytic activity in relation to the amount of endogenous fat stores and in micromoles per kilogram of ffm per minute to provide an index of ffa availability for lean tissues that use fatty acids for fuel .
portal vein and hepatic sinusoidal insulin concentrations in obese subjects were estimated from the measured arterial insulin and c - peptide concentrations according to the method of staehr et al .
isotopic steady - state conditions were achieved during the final 30 min of the basal period and stages 1 and 2 of the clamp procedure .
steele s equation for steady - state conditions was therefore used to calculate substrate kinetics ( 9 ) .
glucose rd from plasma was equal to endogenous glucose ra plus the rate of exogenously infused dextrose and glucose tracer .
palmitate and glycerol kinetics were expressed in micromoles per kilogram of fat mass per minute to provide an index of adipose tissue lipolytic activity in relation to the amount of endogenous fat stores and in micromoles per kilogram of ffm per minute to provide an index of ffa availability for lean tissues that use fatty acids for fuel .
portal vein and hepatic sinusoidal insulin concentrations in obese subjects were estimated from the measured arterial insulin and c - peptide concentrations according to the method of staehr et al .
statistical analyses were performed with spss for windows ( version 17.0 ; spss , chicago , il ) .
results are reported as means sem ( normally distributed data sets ) or medians and interquartile ranges ( skewed data sets ) .
accordingly , the student t test for independent samples or the mann - whitney u test were applied as appropriate to compare differences in subject characteristics and multiorgan insulin sensitivity between lean ( n = 26 ) and obese ( n = 14 ) subjects who received the same insulin infusion rates during the hecp ( i.e. , low- and high - dose infusions ) .
the paired student t test or the wilcoxon signed rank test were used to evaluate the effect of insulin infusion on substrate kinetics within lean ( n = 26 ) and obese ( n = 14 for low - dose infusion [ 7 mu m bsa min ] , n = 26 for medium - dose infusion [ 20 mu m bsa min ] , and n = 40 for high - dose infusion [ 50 mu m bsa min ] ) groups .
the characteristics of the study subjects are shown in table 1 . although mean basal plasma glucose concentrations were not significantly different between lean and obese subjects , mean plasma insulin concentration was threefold higher in the obese group than in the lean group .
mean plasma triglyceride concentration was greater in obese than lean subjects , and hdl cholesterol concentration was lower ; however , ldl cholesterol concentration did not differ between lean and obese subjects .
characteristics of the study subjects three distinct systemic plasma insulin ( spi ) concentrations , which spanned the physiological range , were achieved during the hecp in obese subjects .
insulin infusion of 7 , 20 , and 50 mu m bsa min resulted in significantly different ( p < 0.01 ) spi concentrations of 151 13 , 295 19 , and 595 8
nmol / l . neither the low - dose infusion ( 7 mu m bsa min ) nor the medium - dose infusion ( 20 mu m bsa min ) resulted in significant changes in c - peptide concentrations from baseline ( 0.89 0.07 and 0.76 0.08
plasma c - peptide concentration , however , decreased from baseline during high - dose insulin infusion to 0.58 0.04 nmol / l ( p < 0.01 ) .
portal and hepatic sinusoidal insulin concentrations were estimated in obese subjects and were greater than spi concentration during basal conditions and at all insulin infusion rates . during the basal stage ,
pmol / l , respectively , values that increased with each progressive increase in insulin infusion rate ( p 0.01 ) to 288 29 , 416 33 , and 809 43 pmol / l , respectively in the portal vein and 261 26 , 392 31 , and 766 39 pmol / l , respectively in the hepatic sinusoids .
the portal venous - to - peripheral insulin concentration gradient was assumed to be 2.4 pmol / l in the postabsorptive state ( 10 ) and decreased to 1.85 0.5 , 1.38 0.15 , and 1.35 0.2
pmol / l during low- , medium- , and high - dose insulin infusions , respectively ( p 0.01 vs. basal for all insulin infusion values ) .
1a and b ) ; however , the relative suppression of glycerol ra was much less than the relative suppression of palmitate ra at all insulin infusion rates ( fig .
the ratio of palmitate ra to glycerol ra thus decreased progressively as plasma insulin concentration increased from a basal value of 0.53 0.02 to 0.22 0.01 mol during the high - dose insulin infusion ( p 0.01 ) .
palmitate ra ( a ) , glycerol ra ( b ) , glucose ra ( c ) , and glucose rd ( d ) at baseline ( white bars ) and during low - dose ( speckled bars ) , medium - dose ( hatched bars ) , and high - dose ( black bars ) insulin infusions in obese subjects .
values are means sem . * p < 0.01 significantly different from baseline . p < 0.01 significantly different from lower insulin dose . fm , fat mass . suppressions of glycerol ra ( white bars ) , palmitate ra ( hatched bars ) , and glucose ra ( black bars ) during low - dose , medium - dose , and high - dose insulin infusions in obese subjects .
values are means sem . * p < 0.01 significantly different from glycerol suppression . p < 0.01 significantly different from palmitate suppression .
the relative suppression of glucose ra increased from 69 2% during low - dose insulin infusion to 90 2% during high - dose insulin infusion ( p < 0.01 ) ( fig .
the relative suppression of glucose ra was significantly greater than the relative suppression of palmitate ra and glycerol ra at all insulin infusion rates ( p < 0.01 ) ( fig .
2 ) . the change in glucose rd during insulin infusion increased progressively with increasing insulin infusion rates ( fig .
the relative stimulation of glucose rd ( 24 5% ) was lower than the relative suppression of glucose ra ( 69 2% ) during low - dose insulin infusion ( p < 0.01 ) ( fig .
glucose rd increased more than threefold relative to baseline during high - dose insulin infusion ( fig .
multiorgan insulin sensitivity was compared in lean ( n = 26 ) and obese ( n = 14 ) subjects who received the same insulin infusion rates during the hecp ( i.e. , 7 mu m bsa min and 50 mu m bsa min , respectively ) . in the lean group , insulin infused at 7
( low dose ) and 50 ( high dose ) mu m bsa min resulted in significantly different ( p 0.01 ) spi concentrations of 70 7 and 399 25 pmol / l , respectively . during low - dose insulin infusion ,
the spi concentration in lean subjects was 50% lower than the corresponding spi concentration in obese subjects ( p < 0.01 ) . during high - dose insulin infusion
basal glucose ra and rd , expressed as per kilogram of ffm , were greater in lean ( 16.3 0.5 and 16.6 0.5 mol kg ffm min , respectively ) than obese ( 12.7 0.5 and 13.1 0.5 mol
kg ffm min , respectively ) subjects ( p < 0.001 ) , whereas palmitate ra , expressed as per kilogram of ffm , was significantly higher in obese ( 2.1 0.2 mol kg ffm
min ) than lean subjects ( 1.7 0.1 mol kg ffm min ; p < 0.05 ) .
the suppressions of palmitate ra and glucose ra were greater in lean than obese subjects when plasma insulin concentrations were in the low physiological range but were the same in both groups when insulin concentrations were in the high physiological range ( fig .
3 ) . in contrast , the stimulation of glucose rd during insulin infusion was greater in lean than obese subjects across the entire physiological range of plasma insulin concentrations ( fig .
3 ) . correlation between systemic plasma insulin concentration and substrate kinetics in lean ( ; n = 26 ) and obese ( ; n = 14 ) subjects .
a : glucose ra ( r = 1 and r = 0.968 , respectively ) .
b : palmitate ra ( r = 0.9486 and r = 0.988 , respectively ) .
c : glucose rd ( r = 0.957 and r = 0.932 , respectively ) . values are medians and interquartile ranges .
the characteristics of the study subjects are shown in table 1 . although mean basal plasma glucose concentrations were not significantly different between lean and obese subjects , mean plasma insulin concentration was threefold higher in the obese group than in the lean group .
mean plasma triglyceride concentration was greater in obese than lean subjects , and hdl cholesterol concentration was lower ; however , ldl cholesterol concentration did not differ between lean and obese subjects .
three distinct systemic plasma insulin ( spi ) concentrations , which spanned the physiological range , were achieved during the hecp in obese subjects .
insulin infusion of 7 , 20 , and 50 mu m bsa min resulted in significantly different ( p < 0.01 ) spi concentrations of 151 13 , 295 19 , and 595 8 pmol / l , respectively .
nmol / l . neither the low - dose infusion ( 7 mu m bsa min ) nor the medium - dose infusion ( 20 mu m bsa min ) resulted in significant changes in c - peptide concentrations from baseline ( 0.89 0.07 and 0.76 0.08
plasma c - peptide concentration , however , decreased from baseline during high - dose insulin infusion to 0.58 0.04 nmol / l ( p < 0.01 ) .
portal and hepatic sinusoidal insulin concentrations were estimated in obese subjects and were greater than spi concentration during basal conditions and at all insulin infusion rates . during the basal stage , portal and hepatic sinusoidal insulin concentrations were 215 18 and 190 16
pmol / l , respectively , values that increased with each progressive increase in insulin infusion rate ( p 0.01 ) to 288 29 , 416 33 , and 809 43 pmol / l , respectively in the portal vein and 261 26 , 392 31 , and 766 39 pmol / l , respectively in the hepatic sinusoids .
the portal venous - to - peripheral insulin concentration gradient was assumed to be 2.4 pmol / l in the postabsorptive state ( 10 ) and decreased to 1.85 0.5 , 1.38 0.15 , and 1.35 0.2 pmol / l during low- , medium- , and high - dose insulin infusions , respectively ( p 0.01 vs. basal for all insulin infusion values ) .
1a and b ) ; however , the relative suppression of glycerol ra was much less than the relative suppression of palmitate ra at all insulin infusion rates ( fig .
the ratio of palmitate ra to glycerol ra thus decreased progressively as plasma insulin concentration increased from a basal value of 0.53 0.02 to 0.22 0.01 mol during the high - dose insulin infusion ( p 0.01 ) .
palmitate ra ( a ) , glycerol ra ( b ) , glucose ra ( c ) , and glucose rd ( d ) at baseline ( white bars ) and during low - dose ( speckled bars ) , medium - dose ( hatched bars ) , and high - dose ( black bars ) insulin infusions in obese subjects .
values are means sem . * p < 0.01 significantly different from baseline . p < 0.01 significantly different from lower insulin dose . fm , fat mass . suppressions of glycerol ra ( white bars ) , palmitate ra ( hatched bars ) , and glucose ra ( black bars ) during low - dose , medium - dose , and high - dose insulin infusions in obese subjects .
values are means sem . * p < 0.01 significantly different from glycerol suppression . p < 0.01 significantly different from palmitate suppression .
the relative suppression of glucose ra increased from 69 2% during low - dose insulin infusion to 90 2% during high - dose insulin infusion ( p < 0.01 ) ( fig .
the relative suppression of glucose ra was significantly greater than the relative suppression of palmitate ra and glycerol ra at all insulin infusion rates ( p < 0.01 ) ( fig .
2 ) . the change in glucose rd during insulin infusion increased progressively with increasing insulin infusion rates ( fig .
the relative stimulation of glucose rd ( 24 5% ) was lower than the relative suppression of glucose ra ( 69 2% ) during low - dose insulin infusion ( p < 0.01 ) ( fig .
glucose rd increased more than threefold relative to baseline during high - dose insulin infusion ( fig .
1a and b ) ; however , the relative suppression of glycerol ra was much less than the relative suppression of palmitate ra at all insulin infusion rates ( fig .
the ratio of palmitate ra to glycerol ra thus decreased progressively as plasma insulin concentration increased from a basal value of 0.53 0.02 to 0.22 0.01 mol during the high - dose insulin infusion ( p 0.01 ) .
palmitate ra ( a ) , glycerol ra ( b ) , glucose ra ( c ) , and glucose rd ( d ) at baseline ( white bars ) and during low - dose ( speckled bars ) , medium - dose ( hatched bars ) , and high - dose ( black bars ) insulin infusions in obese subjects .
values are means sem . * p < 0.01 significantly different from baseline . p < 0.01 significantly different from lower insulin dose . fm , fat mass . suppressions of glycerol ra ( white bars ) , palmitate ra ( hatched bars ) , and glucose ra ( black bars ) during low - dose , medium - dose , and high - dose insulin infusions in obese subjects .
* p < 0.01 significantly different from glycerol suppression . p < 0.01 significantly different from palmitate suppression .
the relative suppression of glucose ra increased from 69 2% during low - dose insulin infusion to 90 2% during high - dose insulin infusion ( p < 0.01 ) ( fig .
the relative suppression of glucose ra was significantly greater than the relative suppression of palmitate ra and glycerol ra at all insulin infusion rates ( p < 0.01 ) ( fig .
2 ) . the change in glucose rd during insulin infusion increased progressively with increasing insulin infusion rates ( fig .
the relative stimulation of glucose rd ( 24 5% ) was lower than the relative suppression of glucose ra ( 69 2% ) during low - dose insulin infusion ( p < 0.01 ) ( fig .
glucose rd increased more than threefold relative to baseline during high - dose insulin infusion ( fig .
multiorgan insulin sensitivity was compared in lean ( n = 26 ) and obese ( n = 14 ) subjects who received the same insulin infusion rates during the hecp ( i.e. , 7 mu m bsa min and 50 mu m bsa min , respectively ) . in the lean group , insulin infused at 7 ( low dose ) and 50 ( high dose ) mu m bsa
min resulted in significantly different ( p 0.01 ) spi concentrations of 70 7 and 399 25 pmol / l , respectively . during low - dose insulin infusion ,
the spi concentration in lean subjects was 50% lower than the corresponding spi concentration in obese subjects ( p < 0.01 ) . during high - dose insulin infusion
basal glucose ra and rd , expressed as per kilogram of ffm , were greater in lean ( 16.3 0.5 and 16.6 0.5 mol kg ffm min , respectively ) than obese ( 12.7 0.5 and 13.1 0.5 mol
kg ffm min , respectively ) subjects ( p < 0.001 ) , whereas palmitate ra , expressed as per kilogram of ffm , was significantly higher in obese ( 2.1 0.2 mol kg ffm
min ) than lean subjects ( 1.7 0.1 mol kg ffm min ; p < 0.05 ) .
the suppressions of palmitate ra and glucose ra were greater in lean than obese subjects when plasma insulin concentrations were in the low physiological range but were the same in both groups when insulin concentrations were in the high physiological range ( fig .
, the stimulation of glucose rd during insulin infusion was greater in lean than obese subjects across the entire physiological range of plasma insulin concentrations ( fig .
3 ) . correlation between systemic plasma insulin concentration and substrate kinetics in lean ( ; n = 26 ) and obese ( ; n = 14 ) subjects . a : glucose ra ( r = 1 and r = 0.968 , respectively ) .
b : palmitate ra ( r = 0.9486 and r = 0.988 , respectively ) .
c : glucose rd ( r = 0.957 and r = 0.932 , respectively ) . values are medians and interquartile ranges .
insulin resistance in liver ( suppression of glucose production ) , muscle ( stimulation of glucose uptake ) , and adipose tissue ( suppression of lipolysis ) is involved in the pathogenesis of many of the metabolic complications associated with obesity , including diabetes , dyslipidemia , nonalcoholic liver disease , and the metabolic syndrome .
we evaluated insulin sensitivity during basal postabsorptive conditions and across a physiological range of plasma insulin concentrations designed to simulate those observed during postprandial conditions in lean and obese subjects who had normal oral glucose tolerance .
our data demonstrate that egp and adipose tissue lipolytic rate are much more sensitive to insulin infusion than muscle glucose uptake ; glucose production and lipolytic rate were nearly completely suppressed in both lean and obese subjects at plasma insulin concentrations that only minimally stimulated muscle glucose uptake .
although obese subjects demonstrated multiorgan insulin resistance relative to lean subjects , higher basal postabsorptive and higher simulated postprandial plasma insulin concentrations in the obese group were able to overcome the impairment in liver and adipose tissue insulin sensitivity so that glucose and ffa ra into plasma during basal conditions and high - dose insulin infusion were similar between the groups .
in contrast , insulin - stimulated muscle glucose uptake was 40% higher in lean than obese subjects during high - dose insulin infusion , despite higher insulin concentrations in the obese group .
these results suggest that hyperinsulinemia can compensate for both liver and adipose tissue insulin resistance , but not skeletal muscle insulin resistance , in obese people who have normal glucose tolerance .
impaired insulin - stimulated skeletal muscle glucose uptake , rather than suppression of hepatic glucose production or lipolysis of adipose tissue triglycerides , should therefore be considered the major manifestation of insulin resistance in obese people .
we studied a group of lean subjects to serve as a comparison group for our obese subjects . although relative to the lean group the obese group demonstrated evidence of insulin - resistant liver and skeletal muscle glucose metabolism and adipose tissue fatty acid metabolism during the hecp , basal glucose concentration was not significantly different between the two groups .
the normalization of basal glucose metabolism was presumably caused by a threefold greater plasma insulin concentration in the obese than lean subjects , which compensated for the defect in insulin action .
thus , even though our obese subjects had normal fasting plasma glucose and oral glucose tolerance test results , they had evidence of multiorgan insulin resistance when challenged by an insulin infusion .
although approximately one third of obese people are considered to be metabolically normal ( 11,12 ) , it is likely that most of these individuals are insulin resistant with respect to glucose and fatty acid metabolism and therefore at increased risk for diabetes and coronary heart disease ( 1315 ) .
our data demonstrate that physiological hyperinsulinemia causes a greater suppression of egp than glycerol ra and palmitate ra ( fig .
this observation is consistent with the results from the only previous study of which we are aware that evaluated the effect of insulin on egp and adipose tissue lipolytic activity ( assessed by glycerol kinetics ) simultaneously in the same subjects ( 16 ) ; however , even though hyperinsulinemia caused greater maximal suppression of egp than glycerol ra , the half - maximal suppression of glycerol ra occurred at a lower plasma insulin concentration than that required for half - maximal suppression of egp .
evaluation of hepatic insulin sensitivity with respect to glucose metabolism by using the hecp is complex , however , because of the dual blood supply to the liver and the effects of insulin on other organ systems that can affect glucose production .
normally , insulin is secreted from pancreatic -cells into the portal vein and metabolized by the liver before entering the systemic circulation . during basal conditions ,
infusing insulin through a peripheral vein during the hecp decreases the gradient between portal and systemic insulin concentrations , so that the relationship between insulin delivered to the liver and insulin delivered to other organs changes with increasing insulin infusion . furthermore , the extrahepatic effects of systemic insulin can decrease hepatic glucose production by suppressing adipose tissue lipolysis and circulating ffa ( 17 ) , stimulating hypothalamic pathways ( 18 ) , and inhibiting pancreatic glucagon secretion ( 19 ) .
in addition , systemic insulin decreases egp by the kidney ( 20 ) , which can account for 25% of egp during basal conditions ( 21 ) .
infusions of palmitate and glycerol tracers are often used to evaluate adipose tissue lipolytic rate , because hydrolysis of 1 mol adipose tissue triglyceride releases 3 mol ffa and 1 mol glycerol into the bloodstream ( 22 ) .
we found that the suppression of palmitate ra was always greater than the suppression of glycerol ra during all rates of insulin infusion , indicating that there must be sources of glycerol release into plasma that are not suppressed by insulin .
palmitate released into plasma is derived primarily from lipolysis of adipose tissue triglycerides ( 23 ) ; however , plasma glycerol is derived from lipolysis of adipose tissue triglycerides , lipoprotein lipase mediated lipolysis of circulating vldl triglyceride , with spillover of glycerol into the bloodstream ( 24 ) , and glycerol released from lipolysis of intramyocellular triglycerides ( 25 ) .
an increase in circulating insulin inhibits adipose tissue lipolysis and glycerol released from adipose tissue but stimulates adipose tissue lipoprotein lipase activity ( 26 ) and does not affect glycerol release from skeletal muscle ( 27 ) .
in addition , it is possible that increasing plasma insulin concentration stimulates re - esterification of ffa within adipocytes , preventing their release into the circulation ( 28 ) . thus , palmitate ra provides an index of adipose tissue lipolytic rate and ffa availability , whereas glycerol ra provides an index of whole - body lipolytic activity .
although our groups were not ideally matched with respect to age , it is unlikely that the age differences confounded our results or conclusions .
both lean and obese subjects were middle - aged , and our obese subjects were slightly younger than our lean subjects .
therefore , the difference in age between groups could not have contributed to the insulin resistance observed in our obese subjects compared with our lean group , because insulin sensitivity declines with aging ( 29,30 ) . in summary ,
even obese people who have normal oral glucose tolerance exhibit multiorgan insulin resistance relative to lean subjects . a small increase in plasma insulin concentration
suppresses glucose production and lipolytic rates , whereas stimulation of muscle glucose uptake is minimal until high physiological plasma concentrations of insulin are reached .
this stepwise , integrated organ response to increasing insulin concentrations ( and glucose availability ) helps maintain euglycemia and ensure that adequate glucose is delivered to the brain while preventing unnecessary mobilization of endogenous energy stores when there is a small increase in glucose availability ; however , it prevents potentially toxic hyperglycemia when glucose availability and plasma insulin concentrations are high .
the hyperinsulinemia associated with obesity helps normalize egp and lipolytic rate but is not adequate to compensate for the defect in insulin - mediated skeletal muscle glucose uptake . | pubmed |
Nalle may refer to:
People
Given name:
Nalle Finnish bear Finnish nickname for persons named Björn Swedish bear
Nalle Wahlroos, Björn Wahlroos
Nalle Westerlund, Björn Westerlund
Nalle Hukkataival, 1986 Finnish professional climber
Nalle Karlsson, Swedish songwriter,
Nalle Colt, Swedish guitarist
Nalle Knutsson, 1943-2012, Swedish musician
Surname:
David Nalle 1924-2013 American diplomat, writer
Claudionei Nalle Jr 1972 Brazilian Professor
Other
Uppo-Nalle, bear and series of Finnish children's novels by the Finnish author Elina Karjalainen
Nalle band
Nalle-Sisu, marketing name for Sisu KB-24 and KB-124 lorries
See also
O Nanna Nalle 2000 Kannada movie | wikipedia |
Holiday '80 is an EP released by the original line-up of the British synthpop band The Human League. The EP was issued in the UK by Virgin Records in April 1980, a month before the release of the band's second album Travelogue. The EP peaked at no. 56 in the UK Singles Chart in May 1980, but was later reissued and returned to the chart, peaking at no. 46 in February 1982.
The recordings were produced with John Leckie, who had also been working with new wave bands such as Simple Minds and XTC. The principal song on the EP was Marianne, however Virgin felt the band's preferred version of the track was not strong enough and refused to release it. The EP also featured a new, more elaborate recording of the band's debut single Being Boiled, which would subsequently be included on the Travelogue album. The last track was a medley consisting of a cover of Gary Glitter's Rock and Roll titled Rock 'n' Roll in the track listings seguéing into the Iggy Pop track Nightclubbing. The Japanese release also features the song Toyota City, which also appears on Travelogue.
The track Dancevision is a short instrumental track originally recorded by Ian Craig Marsh and Martyn Ware under the name of The Future, of which Adi Newton had also been a part. Newton released a longer version of Dancevision in 2015 as part of his career spanning Horology 2 compilation, which also included several other tracks recorded as The Future. The 2002 CD release The Golden Hour of The Future did not include Dancevision.
The UK release of Holiday '80 was as a double 7 containing four tracks and two single 7 versions both containing three tracks each, all with the same catalogue number, and a 12 EP containing four tracks. The Japanese release was a 12 with different tracks to the UK 12.
The band performed Rock 'n' Roll on Top of the Pops on 8 May 1980, even though the EP had not entered the Top 40. Although the EP would chart no higher than 56 after their appearance, the band garnered mainstream attention and their album Travelogue would enter the UK Top 20, peaking at no. 16, following the performance. This would be the band's only Top of the Pops appearance featuring the original line-up of Oakey, Ware, Marsh and Wright. The performance was officially issued for the first time on the DVD of the 2016 anthology by The Human League A Very British Synthesizer
Band The anthology CD also features Nightclubbing as a standalone song without being immediately preceded by Rock 'n' Roll.
Track listing
UK 2×7 Gatefold Virgin SV-105
Marianne Marsh/Oakey/Ware 3:17
Dancevision Marsh/Ware 2:21 [performed by The Future]
Being Boiled Album Version Marsh/Oakey/Ware 4:22
Rock n Roll / Nightclubbing Gary Glitter, Mike Leander Jim Osterberg, David Bowie 6:22
UK 12 Virgin SV-105-12
Marianne Marsh/Oakey/Ware 3:17
Being Boiled Album Version Marsh/Oakey/Ware 4:22
Dancevision Marsh/Ware 2:21 [performed by The Future]
Rock n Roll / Nightclubbing Glitter, Leander Osterberg, Bowie 6:22
UK 7 Holiday '80: Being Boiled Virgin SV-105
Being Boiled Oakey 4:10
Marianne Oakey 3:14
Dancevision Marsh/Ware 2:15
UK 7 Holiday '80: Rock 'n' Roll Virgin SV-105
Rock 'n' Roll Glitter, Leander 3:15
Being Boiled Oakey 4:10
Dancevision Marsh/Ware 2:15
Japanese 12 Virgin VIP-5906
Marianne Marsh/Oakey/Ware 3:17
Dancevision Marsh/Ware 2:21 [performed by The Future]
Toyota City Marsh/Ware 3:22
Rock n Roll / Nightclubbing Glitter, Leander Osterberg, Bowie 6:22
Being Boiled Album Version Marsh/Oakey/Ware 4:22
Charts
References
External links
http://www.the-black-hit-of-space.dk/holiday_80.htm
Category:1980 EPs
Category:Albums produced by John Leckie
Category:The Human League EPs
Category:Virgin Records EPs | wikipedia |
Where do the chloride ions go during saponification precipitation?
During saponification hydroxide ions from the lye join to the triglyceride to form glycerol, and the sodium bonds with the fatty acids making the soap molecules. However, it is sometimes the case that $NaCl$ is needed at this point to precipitate out the soap. The sodium ions are used in this precipitation. But, what happens to the excess chloride ions?
Adding a concentrated $\ce{NaCl}$ solution to a soap solution produces the precipitation of sodium alkanoates (indeed it is a mixture of alkanoates and alkenoates). This is a consequence of the law of mass action. The ions $\ce{Cl-}$ and $\ce{Na+}$ added in this operation remain in solution. The only products to precipitate are the sodium alkanoates which were present in the solution before adding $\ce{NaCl}$
| stackexchange/chemistry |
Mass Effect 1. Prologue
**Whoa! A new story for a new group of people. That's surprising, as I usually stick to writing for Azumanga. But having just beat Mass Effect 3, I decided it was finally time to do an ME fanfic. After all, I've wanted to do so since I first joined FFN. But I wanted to wait until the main trilogy was over. By the way, this story WILL contain spoilers from the ending, just so ya know :D**
***Spoiler Alert* This story is set after ME3. The ending is as so: Ultimate Paragon Shepard, Love with Tali, Everyone on your teams who can live lives (Ashley alive), Destroy Ending... *Spoiler Alert***
**Anyway, this prologue might be a bit boring. It's really just supposed to set up the link between cannon ME, and this story. Everything Mass Effect belongs to EA, Bioware, and all of the other owners respectively. No copyright infringment is meant by this story. Happy Reading :)**
* * *
**Mass Effect: Generation**
**Prologue:**
"Shepard? ...Shepard?" Admiral Hackett called out as he looked around the wreckage of what used to be the Citadel. It'd been a few hours since the Reaper Invasion was quelled, and the Alliance forces that were left wanted to know that their savior was still alive. Hackett bounced around the low-gravity wreckage, looking every which way for signs of life. His team had spread out across the area, searching just as diligently.
It was strange that nobody had ever found this room in the Citadel before. But it was even stranger that it had held up to the forces of the Crucible being fired. Every other section of the Citadel had taken quite a bit of damage, and this particular area had taken the brunt of the impact. Hackett made his way up to the terminal in the center of the room. The holo-display was flashing red, as it flickered, sparks emanating from the console itself. He took a closer look to find the answers to his current query; to why this section of the Citadel was still mostly intact.
On the display, three words continued to flash... "Fail-Safes Initiated". Hackett touched the nearest button on the display, which brought up another section of information. He started reading, trying to understand what kept this section of the Citadel safe. Apparently, 'the creators' had implemented several defense protocols and such to prevent damage from any nearby battles, during the harvesting periods of each cycle. Hackett didn't really have a clue who these 'creators' were, but it wasn't like it mattered anymore anyway. The Reapers were gone, and current objective was finding Shepard.
All this meant was that it was possible for Shepard to have made it. Hackett backed out to the original display, and was about to continue his search, when something caught his attention. Down near the bottom of the display were a few more words he hadn't noticed before.
"Lower level: 52% damage. No damage to organic-sustaining systems. Keeper #325 dispatched for repairs," Hackett read under his breath, before continuing to the line below. "Upper level: 37% damage. Major damage to oxygen systems. Approximately twenty minutes until reserves are depleted. No Keepers dispatched for repairs – unsafe environment for organics."
Hackett paused for a second, closing his eyes. "Upper level?" he whispered, glancing around toward the extremely high ceiling. He suddenly spotted a large door at the very top, that seemed to be connected to another room. Hackett looked back toward the console, and glanced around frantically for some sort of button that could help him. There didn't seem to be anything, and the aging man began to get a little frustrated. With a small growl, he pounded his fist on the large console.
A rather surprising rumble emanated from the ground below him, and the section of floor he was on began to rise toward the ceiling. As he got closer, the doors above opened up, and a warning sounded about the room. "Alert! Upper level not safe for organic life! Eighteen minutes until oxygen levels are depleted!"
The warning continued, but the elevator didn't stop rising. Finally, Hackett was in the upper level. He could already feel that the air here was much thinner than in the room below. The elevator dropped back down right as he stepped off, and the doors separating the two rooms sealed, possibly trapping him there. But Hackett didn't really care at this point. His age-old instincts told him that Shepard was around here somewhere. He had to find Shepard first... then he could figure out how to escape.
The lighting in the room flickered rapidly, and debris cluttered the floor, making it difficult to move. Much of the room was made up of windows out to space. But many panels covered now them from the outside, almost like an exo-skeleton, shielding the room from harm. Hackett struggled to search quickly, as the warning continued on. "Fifteen minutes until oxygen levels are depleted!" The lights in the massive room finally failed, and he was left with only the light of the sun that shown through the few broken safety panels over the windows.
Hackett glanced around the room quickly, trying not to panic. He only had about ten minutes left, but it was so hard to see that -if he didn't find Shepard soon- he probably wouldn't. Without warning, something moved sharply under some rubble nearby, and Hackett new he'd succeeded. Rushing to move the rubble, he unearthed a battered and beaten Shepard. The Admiral was ready to make a quip about Shepard being impossible to kill, just like a cockroach. But unfortunately, the Commander was as unconscious as could be, so he would have to save the jokes for later.
Hackett checked in with his team, and told them he'd found the package. He directed them toward the console in the center of the room, and asked the team technician to figure out how to bring the elevator back up to them. Within two minutes, he'd succeeded, and both Hackett and the beaten Shepard were on their way to safety.
* * *
Joker sat solemnly in his seat at the front of the Normandy. Some of the crew were speaking excitedly about how they'd faced the Reapers and won. Others were wondering what happened to Shepard and those down on Earth, and whether the galactic races would be able to stay as peaceful as they were right before the final battle. Still others were trying to figure out exactly what the Normandy's crew was going to do from here, since the Mass Relays had all been damaged by the Crucible.
But at the moment, Joker didn't feel like joining them. EDI had once told him that she felt he hid his problems behind a wall of humor. Every time something came up that he didn't want to talk about, he would make a joke to deflect the conversation altogether. Usually, she was right. He hated to admit it -to the point of making a joke when she brought it up- but that's exactly what he did. But right now, he was even beyond that.
"Joker... are you okay?" a soft female voice questioned from behind, though he didn't need to face her to know that it was Liara. He simply stared down at his pilot console, which wasn't working at the moment. "Would you like to talk about it?" she continued on, but still Joker stayed silent.
"Listen, I understand that losing EDI must've been hard for you. But I'm sure-" Liara began, before several panels around them re-lit in a torrent of orange glows.
"Looks like we've already gotten the Normandy's systems up and running again," Engineer Adams' voice sounded over the intercom system. "A quick diagnostics check, and we can take flight again."
Joker prayed that EDI would greet him once more now that the systems were up, though he knew such a thing was impossible. He'd seen the Reapers all shut down simultaneously as they escaped the Crucible's blast. He heard the radio chatter about the Geth forces stopping in their tracks on Earth, and how their ships never left the system; almost as if they'd all simply passed on in that very moment. He'd seen EDI...
He knew that, whatever Shepard had done, it'd destroyed the programming in any and all AI's. It'd killed all synthetics. There really wasn't any hope for EDI to be alive. Joker watched as the Normandy's systems booted up fully, and his display changed to its normal setup. Up in the corner, a red light sat blinking from the display. He reluctantly raised his arm up, and pressed the small button, opening another display window. Joker glanced at what it said, and sat up rather quickly, surprising Liara a bit.
"Call coming in from Admiral Hackett!" he shouted, turning to face Liara. But she was already on her way toward the Quantum-Entanglement communications room.
"Liara T'Soni," Hackett started, not at all surprised to be talking to the Asari rather than one of the other crew members. "It's good to see that you all made it out safely."
"Yes, sir. Joker's piloting skills, bravery, and quick thinking lead us through the Relay just in time. Everything here is fine," she explained quickly, wanting to hear the news on the other end.
"And where exactly is 'here'?" Hackett questioned casually.
"For better or for worse, Joker sent the Normandy to the place where all of this began," Garrus announced, as he walked up next to Liara. "We're on Eden Prime, sir. Let's just hope that another galactic catastrophe isn't awaiting us once we get the ships engines running correctly, and can make it to the nearest colony."
Hackett chuckled a bit, before continuing on. "So, I'm guessing you're all anxious to hear how it is on our end," he asked rhetorically, to thirsting eyes. "Well, Earth will survive, as will what seems to be about fifty percent of the fleets we brought out for the final assault. We don't yet know enough from the other sectors of space, but you'll be updated when we get news. That may not be what you were hoping to hear, but it's better than the alternative."
"As for the Citadel," he continued "it seems the Keepers are already starting up repairs. Once we can get our bearings, we're going to begin helping them. In the meantime, each of the different galactic ground forces used in the final push will be staying on Earth. We actually found several extremely useful notes on the Mass Relays, hidden within the plans for the Crucible. So once we can make contact with each star system, we'll be sending the information to them, and we can rebuild the galactic network much quicker than anticipated. I've actually already sent the info to the Normandy, for you to make use of."
"We'll get right on that!" Liara's small voice chimed rather energetically, as if she finally believed things were truly looking up; for the first time in years.
"Well, I'd better get back to work," Hackett began, before being interrupted.
"Uh, wait, sir," Garrus shot quickly, stopping the old man in his tracks. "Any news on Shepard? Did he make it?"
Hackett began to laugh rather heartily, placing his hand over his face in shame. "I can't believe I almost forgot the most important bit of information I needed to relay to you all. I really hope this is the last war during my lifetime, because my mind clearly isn't what it needs to be for this sort of thing anymore."
"Shepard's going to be fine, though he'll probably need quite a bit of work before he's up and moving. Since Cerberus put him back together using synthetic parts and computer systems, he needs to basically be rebooted, and some of the computers need to be replaced. Otherwise, he'll be alive, though not exactly coherent. Luckily, we've already got Miranda on it, as well as a few of the people from the original team that put Humpty-Dumpty back together in the first place. Good thing Shepard helped those Cerberus defectors when he had the chance, or he might have died. As it is, he's going to be fine... Hackett out," the Admiral finished, leaving them with the note he knew they were hoping to hear.
* * *
***Some Time Later***
Shepard sat down under the nearby tree, wiping the sweat from his brow and breathing deeply with relief. Seconds later, Tali followed suit, smiling at him through her helmet though she knew he couldn't see it. The both of them simply stared at the work they had done; some of the first work toward rebuilding Rannoch. The Quarians finally had their home back, after such a long time away.
"It's just like you, Shepard," Tali remarked mysteriously, still staring off into the distance, where thousands of other Quarians continued building the new capital city; Normandy.
"What is?" he questioned back, grabbing her hand with a grin.
"You've only been in full health for a couple of days, and already you're working to fix the universe and all of it's problems. Nobody expects you to help out. After all, you're the reason we even have the chance to rebuild after the Reaper Invasion, and most feel that's enough. You're going to be legendary as it is Shepard, but still you continue."
"I'm just doing what needs to be done," Shepard modestly explained in return.
"But that's more than most can say when things get difficult," Tali retorted, pausing for a second. "Thank you Shepard..."
Shepard waited in silence. Though he couldn't see Tali's face, he could tell that she had more to say. "You left your home planet to help me rebuild my own. You've left everything to make sure that I'm taken care of. You-" Tali started to confess, before Shepard stopped her.
"Tali... I'm not only doing this for you. I'm doing this for _us_. Earth is in capable hands. They don't need me there. I came here to be with you, so that we can start a new life for the Quarian race. _This_ -Rannoch- is my home now; it's our home," he told her warmly.
Comforting silence ensued between the two of them for a few minutes, before they decided it was time to get back to work. Shepard got to his feet, before holding out a hand for Tali. The Quarian girl gracefully stood up and embraced him tightly. As she did so, Shepard caught a glimpse of a small Quarian child peeking out from behind another nearby tree. Shepard gently broke off the hug, and began walking slowly toward the young child, Tali following curiously in tow.
As the two of them neared, the child -who was now clearly a boy- hid himself nervously behind the trunk of the tree. Shepard slowly bent down and gave the boy a calming look. "Are you lost?" Shepard questioned curiously, though the the boy just looked away in a nervous silence. Tali proceeded to sit down across from the young one, and placed her hand on his shoulder.
"What's your name?" she asked politely, getting the boy to actually glance her way. He stayed quiet for nearly ten or so seconds before whispering a response.
"Richka'Orion nar Neema. I'm six years old."
"Well that answers my next question," Tali giggled. "Where are your parents?"
Almost immediately the boy shut himself back down, looking down at his hands without uttering a single word. "They're... gone," a strong male voice echoed from behind them. Tali looked up to see a rather large Quarian standing above them, looking stalwart and confident in stance. "We found him alone two days after the war got over with, hiding in the storage area of the Neema. We'd just made it back to Rannoch after our quick escape through the Relay, and were ready getting ready to start re-colonization efforts. I saw him trying to find his way into one of the ventilation ducts."
At this statement, Shepard was barraged with images of the small Earth child from the day of the initial Reaper attack. This boy seemed so similar, that even Shepard had to admit, it was a bit frightening.
"When I finally got him to trust me, we started looking around for his parents. Only after I'd given up did he finally speak to me. He told me that we weren't going to find them; that the 'big metal monsters' had taken them away. It seems they had been two of the six unfortunate souls that were killed when the Neema took damage... from the one and only Reaper attack that had actually made contact with it."
Tali looked down at the child in sadness. Even though the war was over, it seemed its impact wasn't fully understood. It was hard to fathom being so young, and having something so terrible utterly rip your simple and happy life to shreds. "So... what's going to happen to him?" Shepard questioned, a rather fierce and determined look in his eye.
"Once things are a little more stable, I'm going to try and find an actual family that can adopt him. Until then, I'll be taking care of him."
Shepard placed his hand on the opposite shoulder from where Tali's hand still sat, and looked the boy in the eyes. "Would you like to be a part of our family, Richka? I'm sure Tali here would be happy if you joined us, and I know I would."
Richka once again waited in silence, looking slowly from Shepard to Tali. Finally, he gave a small nod, and tightly hugged Shepard around the neck. "It's going to be alright Richka. We'll take good care of you," Shepard muttered in a comforting tone, as he closed his eyes and thought back to the boy from Earth one last time...
* * *
**Well, that's the prologue. A little sappy, and a little... exaggerated in some ways. But this is really just a bridge to the story beyond, and doesn't have a whole lot to do with it. Please, please, please review if you would be so kind. Anyway, Hope You Liked :)**
2. Mercenary Work
**Welcome to the first chapter. Since I don't usually do heavy gunplay action in my stories, this was kind of fun. I think it turned out pretty good overall, and it does a great job of characterizing and revealing the required information on a sub-level that isn't quite so straightforward as telling you outright would be. Anyway, I'll let you get to it. All things Mass Effect belong to their respective owners. Happy Reading :)**
* * *
**Chapter One: Mercenary Work**
Shots continued to whiz by at a near-constant rate, each of them flying by so quickly that they left a trail of rippled heat behind. A rather strong looking Quarian woman stayed well behind the wall for cover, knowing that it wouldn't take too many shots to rip through her kinetic barrier, along with any flesh that was in the way. She was waiting patiently for her chance to strike, and knew that it was coming up soon.
"Two minutes in and I'm already being shot at. Can I _ever_ get a break?" she wondered aloud, making sure that her weapon was ready, and the safety was off. In that moment, she was glad she'd decided to spend the money on upgrading to the new M-14 Locust SSO sub-machine gun. It was the newest model just put into production by Kassa Fabrication a few months before. Unlike the previous Locust -the M-12- it was capable of much longer ranged accuracy, thanks to an extended barrel, and mass effect 'simulated rifling' which would spin the projectile much like that of a human weapon from the days before their exploits beyond the Sol Relay.
But lucky for her, she'd also sprung for a little black market upgrade, hence the SSO in its name. The acronym stood for 'single-shot option'. When activated, a rather sophisticated computer system in the firearm allowed her to switch to a single-shot firing system. The mass effect propulsion system in the gun was then allowed the ability to focus on firing each projectile at a much higher speed, rather than firing them at a higher rate as per usual. Add in that it was much less taxing on the heavy duty thermal clip system -which in a sub-machine gun expects rapid fire bursts- and the user virtually never had to watch the heat their weapon is producing.
"I hope you're ready," the Quarian girl grinned in a mischievous manner, before diving from cover the very instant that the shots being fired at her ceased. The world seemed to slow down to a crawl, as she lined up a shot and fired. A sharp snapping sound, accompanied by an airy whirr emanated from her weapon. The projectile flew from the gun at breakneck speed, before ripping through the shields of her enemy, shattering his helmet visor and his skull, and finally imbedding itself in the wall ten feet further back. The Quarian could almost see the blank look on his face before it was torn apart; the look of someone who had clearly underestimated his opponent.
Everything sped back up to normal pace as she landed on her side, before using the momentum to role herself back to her feet behind another piece of cover. The grin that had graced her lips a few moments ago once again appeared, no more shots being fired from the opposite end of the room. The point of her rather risky attack wasn't to kill that single enemy... it was about instilling an intense fear in his colleagues. She wanted to shake them up; to prevent them from fighting her with a proper mindset. And frankly, that wasn't exactly difficult to do with this group of amateurs. She knew _much_ more about them than they did her.
They were all part of a pro-human organization that was once called Cerberus, but had since gone through a metamorphosis into a sort of elitist cult, long before she was even born. They now called themselves the Alliance for Rule over Extrinsic Species'... or Ares. Named after the ancient Human Greek god of war, bloodlust, and violence, they tended to be extremely hostile toward any non-human species.
As was obvious, they were a rather radical human interests group geared toward proving the superiority of the Human race. But in order to bypass the grim fate of Cerberus, they felt it was necessary to keep their membership exclusive to families who hadn't branched out to living anywhere but Earth and the various human-run bases in the Sol system. It was as pure as pure could be from a technical standpoint, but it didn't stop them from being what most considered to be cruel and disgusting extremists. And this 'purity' also didn't help them train their combatants any better than any other wannabe organization. They were basically just civilians who had one-track minds, anger problems, and a gun in their hands; not exactly something to be afraid of.
"Davidson? Davidson?" the Quarian heard one of the Ares soldiers yell, as she counted down the steps that would ensue within the coming seconds. "Damn you, you bitch! You'll pay for that!"
Shots fired, as a male voice could be heard shouting profanities. The gun continued to fire for several seconds until suddenly it stopped, and all that could be heard was the angry neanderthal. The Quarian nodded slightly in acknowledgment, as the voice then died down, clearly in a state of confusion.
"Three, two, one," she whispered, whipping the top half of her body from cover. Within the next moment, she'd made yet another masterful move toward completing her mission. The soldier who'd went berserk had forgotten to limit the amount of shots fired in that short period of time. She could tell from the sound of his gun, that he was using an Elkoss M-9 Avenger. That was the gun every noob without any real experience or cash bought, so she had a lot of experience with being shot at by this gun.
The M-9 had the ability to produce approximately thirty-five shots before you needed to replace the thermal clip, otherwise it would overheat and jam. The second the gun and profanities stopped firing in her direction, she had known that was her cue to make a move. She sent just one more shot downrange, and it made contact with his helmet as with the first soldier. She hid back behind her cover before hearing the sound of a full suit of armor collapsing to the floor.
She could hear sounds of distress and confusion coming from the final soldier standing between her and her objective, and knew it was all over. The last Ares soldier steeled his will, and sprinted toward the Quarian's position. She might have been thrown off by such a tactic, if she hadn't glanced at the weapon in his hands last time she peeked out from her position. As it stood, she knew he was using a shotgun. His rage and hatred had boiled over, leaving his fear to drown in the wake of blind vengeance.
The footsteps quickly closed in, and the Quarian waited until it was time to strike. As her opponent made his way around the cover from the side she'd last attacked from, she rolled around the opposite corner. She slipped her melee weapon from the sheath at her lower back, and got the jump on him. By the time he knew what had happened and turned to face her, she'd shoved him against the nearby wall, and had the sixteen inch blade at his neck.
The shock caused him to drop his gun, which made a loud clang as it hit the ground. Through his visor, she could see the fear in his young eyes, as he gave up all hope of living. She could see him reliving what little life he'd experienced, all in that very instant. The beautiful blade -based on an ancient Quarian weapon using modern technology- ever so slightly touched the neck of his armor. As if it was red-hot, it began to melt through the material, inching the man ever closer to his death.
"P-p-please!" he cried, breathing sharply, clearly about to break out in tears.
The Quarian halted her blade, refusing to show any emotion toward him; though it wasn't like he could see her expression behind her helmet anyway. As if thinking long and hard about his fate, she stayed completely still for nearly a minute. By the time she opened her mouth, the Ares soldier was openly sobbing, having resigned himself to an early grave.
"Never..." the Quarian began in a hiss. "...come...back..."
She dropped the blade down to her waist, and sheathed it, before continuing to her destination. She knew enough about her opponent by now to know that she could turn her back to him. He was gone; long gone. And he would probably live out the rest of his days as a nomad, deathly afraid that she would show up one night to finish the job.
As the Quarian listened to the clambering of a once-soldier escaping from the scene of the most pivotal moment in his life, she casually walked on toward the final room in the Ares base. Her client had luckily enough researched the base beforehand. He knew exactly how many people were to be guarding it, and where they would be stationed. He knew the floorplan and everything, relaying the information to her; leaving nothing to surprise her as she made her way to the 'hit'.
She finally made it to the very back room, where the commander of this Ares squad was stationed. He had clearly been alerted to her presence, as the door was locked and shut down from the inside. Anyone else would have had a hell of a time trying to get in without a custom made omni-tool blade, but not her. Unsheathing her own custom weapon, she thrust it into the door, as if it was butter. With a strong yank, she forced it downward in a vertical fashion, cutting through the electronics inside the barrier that stalled her progress.
Sparks flew from the giant gash and the door struggled open. The same could be said about the man inside the room, as he fumbled with his assault rifle, not at all expecting the Quarian to make it in the room so easily. By the time he had his gun raised, she had lifted her own weapon, and took a shot. The assault rifle in her enemy's hands flew up into the air, now in several pieces. She holstered her weapon once more, the whole spectacle happening in stride.
The man suddenly grunted loudly, and made for her, fists raised. He swung his left arm vertically toward her face, as his omni-tool spawned a blade. The Quarian simply side-stepped the attack, and grabbed his arm at the elbow. Spinning gracefully, she wrapped herself toward his body, and slammed her arm into his face, knocking him back.
Gaining composure as quickly as possible, he lunged for her as if to attempt to strangle her. But the Quarian simply swept her foot across the floor, their ankles embracing each other and flooring the shocked man. He rolled over as fast as he could, and scrambled away across the floor, until his back hit the wall.
"This is why you wretched alien _freaks_ need to be enslaved! All you do is kill, and it's always a human who's the victim! We humans are the good guys here, and the great Commander Shepard proved that in the war with the Reapers; only when lead by a human does anyone have the strength to save the galaxy from alien threats!"
As she stood a few feet away from her assassination contract, the Quarian breathed slowly and steadily, not yet making a move to end his pitiful existence. She slowly reached up toward her helmet, and pressed a small button on the side. The visor quickly rose up into the top section of the helmet, revealing the Quarian face underneath. She took a deep breath, a fierce scowl that could level a mountain embracing her face. Dark brown hair fell from her head, and caressed her soft cheeks. Her ghost-blue eyes pierced the air, as well as the soul of the frightened human that cowered just feet from her.
"Do I look that alien to you? Do I look like a heartless monster bent on destroying Humanity? I am Demesii'Orion nar Normandy, and in seconds I will be _your_ killer, and _only_ yours," the Quarian growled, before adding one last sentence in a rather cheeky tone. "But you can call me Dem."
"You're a filthy fork-fingered whore of an alien who only knows of murder! I hope you rot in Hell!" the man interrupted. "If Shepard were still alive today, he would see the point of Ares! If he were alive, he'd kn-"
"Save the speech for some other fool. If my grandfather -Commander Shepard- were here today, he'd be standing in _my_ position, gun pointed at your head, ready to end the life of another psychotic zealot who just happened to mess with the wrong person."
"What did I ever do to _you_? How in the world did I 'mess with' you?" the man screamed.
"Don't get me wrong; I hate what you are _and_ what you stand for. But you did nothing to cause friction with me. You're too pathetic of a man for that," Demesii began explaining slowly and quietly.
"T-then why did you come here if this isn't some sort of alien vendetta of yours?" the man questioned venomously.
Demesii raised her M-14 Locust in silence, until it was aimed directly between the eyes of the man. "A Human... A Human named Victor Halstrom sent me... you messed with _him_..."
"Vic?" the man gasped in amazement before a loud bang echoed around the room, and his entire body went limp.
* * *
**There you go. I hope you're genuinely excited for new chapters, because they should be coming really soon. Please take the time to review if you would. You can only make this story better by doing so... well unless you only want to flame me. Hope You Liked :)**
End file.
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an important group of critically ill patients in intensive care units ( icus ) are those exhibiting a systemic inflammatory response caused by extreme stimulation of the immune system .
etiologic factors include micro - organisms ( sepsis ) and noninfectious insults such as trauma , burns , major surgery , ischemia / reperfusion , and pancreatitis ( i.e. systemic inflammatory response syndrome [ sirs ] ) .
immunopathogenetic mechanisms play an important role in the course and progression of both sepsis and sirs .
sepsis is frequently an important factor in the mortality of patients in icus . from a clinical point of view , differentiating between an infectious and a noninfectious etiology in patients with clinical symptoms of sepsis is very difficult .
the limiting factor is the lack of specificity in differentiating between underlying causes of inflammation .
one of the parameters currently employed to establish whether sepsis is present is c - reactive protein ( crp ) . during the past few years several new parameters have been introduced , including procalcitonin and lipopolysaccharide - binding protein ( lbp ) .
two classes of acute phase proteins may be distinguished on the basis of their synthesis .
class 1 , induced by il-1 in synergy with il-6 , includes crp and mbp .
class 2 , induced by il-6 alone , includes antiproteases , 2-macroglobulin , and fibrinogen [ 5 - 8 ] . in 1986 ,
it is a 58 kda protein that is synthesized in the liver , and it potently enhances the sensitivity of monocytes and granulocytes to lipopolysaccharide ( lps ) by facilitating binding of lps to the cd14 cell membrane molecule .
the mature cd14 protein is a myeloid marker antigen that is expressed on the surface of myeloid cells .
cd14 is also found circulating free in plasma , where it is referred to as soluble cd14 ; the latter form of cd14 mediates lps activation of cd14-negative cells , such as endothelial and epithelial cells .
lbp catalyzes movement of lps monomers from lps aggregates to high - density lipoprotein particles , leading to neutralization of lps .
lbp takes part in the transport of other phospholipids by acting as a lipid exchange protein . under physiologic circumstances ,
lbp binds gram - negative bacteria via the lipid a part of lps , which mediates its binding to the cd14 cellular receptor molecule presented by monocytes and macrophages .
the outcome is the production of proinflammatory cytokines ( i.e. il-1 and tumor necrosis factor- ) . under normal circumstances
serum levels of lpb vary in the range 515 g / ml , but levels increase several fold during the acute phase response .
after the relationship between lps and sepsis was unraveled , the diagnostic and/or prognostic value of lbp levels in patients with sirs and sepsis were investigated .
previous studies have shown elevated lbp levels in patients with gram - negative sepsis , and elevated lbp levels in patients with sirs and in patients with sepsis and septic shock .
the primary objective of the present study was to determine whether lbp can distinguish between infectious and noninfectious etiologies of sirs .
secondary objectives were to assess the relationships between lbp levels and procalcitonin , crp , and clinical , microbiologic , and prognostic parameters in sepsis .
sixty - eight patients ( age range 1868 years , median 48 years ; 42 men , 26 women ) , who fulfilled the diagnostic criteria for sirs ( 40 patients ) , sepsis ( 19 patients ) or septic shock ( 9 patients ) , were consecutively enrolled between february 2000 and november 2001 .
the diagnostic criteria for sirs were temperature greater than 38c or less than 36c ; heart rate greater than 90 beats / minute ; respiratory rate greater than 20 breaths/ minute or arterial carbon dioxide tension greater than 32 mmhg ; and white blood cell count greater than 12 10/l or less than 4 10/l , or the presence of 10% immature forms .
sepsis was confirmed by the isolation of an organism considered to be of pathogenic significance from an otherwise sterile site ( blood , peritoneal cavity , or lung via bronchial lavage ) or by the isolation of an organism of recognized pathogenic potential from an intravascular catheter removed for infection related reasons .
all patients were screened on a daily basis for the presence of pathogenic organisms by blood and urine culture and , where indicated , by biopsy or aspiration of potentially infected sites .
septic shock was defined as sepsis with hypotension resistant to fluid resuscitation and evidence of organ hypoperfusion or dysfunction . specifically ,
the criteria for septic shock were hypotension ( defined as systolic pressure < 90 mmhg or reduced by more than 40 mmhg from baseline ) and all of the following criteria : temperature greater than 38c or less than 36c ; heart rate greater than 90 beats / minute ; respiratory rate greater than 30 breaths / min or hyperventilation with arterial carbon dioxide tension under 32 mmhg ; white blood cell count greater than 12 10/l or less than 4 10/l ; or the presence of more than 10% immature cells .
blood samples were obtained from patients within 24 hours of meeting the criteria for sirs , sepsis , or septic shock .
patients with sepsis and septic shock were given antibiotic therapy adjusted in accordance with culture results .
the study was approved by the ethics committees of the participating hospitals , and written consent was obtained from all patients or their relatives .
the following data were compiled for each patient : demographic data ; acute physiology and chronic health evaluation ii score ; diagnosis of sirs , sepsis , or septic shock ; the presence of gram - negative or gram - positive infection ; and outcome ( mortality ) .
blood was obtained in vacutainers ( becton dickinson , heidelberg , germany ) containing 15% edta for blood counts , and 30 u lithium heparin for bilirubin , crp , alkaline phosphatase , and other routine biochemical measurements . for lbp and procalcitonin ,
serum was prepared , following coagulation in vacutainer tubes , by centrifugation at 2000 g at room temperature for 20 min .
the serum levels of lbp were measured by means of a commercial chemiluminiscence method ( immulite dpc ; biermann , bad nauhe , germany ) .
twenty - three healthy adult volunteers ( age range 1848 years ) , who exhibited no signs of inflammatory or gastrointestinal disease , served as control individuals .
procalcitonin was measured by immunoluminometric assay ( lumitest pct ; brahms diagnostica gmbh , berlin , germany ) .
we analyzed the levels from study entry , which was defined as the first 24 hours in which sirs , sepsis , and septic shock criteria were met .
twenty - three patients were assessed repeatedly ( 12 patients with sepsis , six patients with sirs , and five patients with septic shock ) at 3- to 5-day intervals for the next 30 days or until death . in the remaining patients , who either died or were transferred to other departments ,
the levels of serum proteins were compared with levels in healthy volunteers , sirs patients , and patients with sepsis and septic shock ; they were also compared between survivors and non - survivors .
the results are expressed as either a mean and standard deviation , or as a median with range . significance testing of between group differences was performed using the student 's t - test and mann whitney test .
changes in serum concentrations of lbp , procalcitonin , and crp over time were compared using the kruskal
the following data were compiled for each patient : demographic data ; acute physiology and chronic health evaluation ii score ; diagnosis of sirs , sepsis , or septic shock ; the presence of gram - negative or gram - positive infection ; and outcome ( mortality ) .
blood was obtained in vacutainers ( becton dickinson , heidelberg , germany ) containing 15% edta for blood counts , and 30 u lithium heparin for bilirubin , crp , alkaline phosphatase , and other routine biochemical measurements . for lbp and procalcitonin ,
serum was prepared , following coagulation in vacutainer tubes , by centrifugation at 2000 g at room temperature for 20 min .
the serum levels of lbp were measured by means of a commercial chemiluminiscence method ( immulite dpc ; biermann , bad nauhe , germany ) .
twenty - three healthy adult volunteers ( age range 1848 years ) , who exhibited no signs of inflammatory or gastrointestinal disease , served as control individuals .
procalcitonin was measured by immunoluminometric assay ( lumitest pct ; brahms diagnostica gmbh , berlin , germany ) .
we analyzed the levels from study entry , which was defined as the first 24 hours in which sirs , sepsis , and septic shock criteria were met .
twenty - three patients were assessed repeatedly ( 12 patients with sepsis , six patients with sirs , and five patients with septic shock ) at 3- to 5-day intervals for the next 30 days or until death . in the remaining patients , who either died or were transferred to other departments , only the baseline investigations were performed . altogether
the levels of serum proteins were compared with levels in healthy volunteers , sirs patients , and patients with sepsis and septic shock ; they were also compared between survivors and non - survivors .
the results are expressed as either a mean and standard deviation , or as a median with range .
significance testing of between group differences was performed using the student 's t - test and mann whitney test .
changes in serum concentrations of lbp , procalcitonin , and crp over time were compared using the kruskal
sixty - eight patients consecutively admitted to the interdisciplinary icu were enrolled in the study upon meeting criteria for sirs , sepsis , or septic shock .
in addition , 23 adult healthy volunteers ( age range 1848 years ) served as control individuals .
the observed mortality in patients with sirs was 15% ( 6/40 ) , that in patients with sepsis was 57.9% ( 11/19 ) , and that in patients with septic shock was 89% ( 8/9 ) .
pneumonia was the leading cause of sepsis ( 57% ) , and refractory septic shock and multiple organ dysfunction syndrome were the immediate causes of death . during hospitalization ,
eight patients with sirs developed sepsis , and in four patients sepsis changed to septic shock .
the mean serum concentration of lbp in all groups of patients was significantly greater than in control individuals ( p < 0.0001 ) ; in ascending order , the levels were 30.6 g / ml in patients with sirs , 37.1 g / ml in those with sepsis , and 59.7 g / ml in those with septic shock .
the difference between levels in patients with sirs and those with septic shock was statistically significant ( p < 0.01 ) .
the specificity and sensitivity of serum lbp concentration in differentiating between patients with sirs and those with sepsis / septic shock ( with cutoff set at 29.8 g / ml ) were poor , at 50% and 74.2% , respectively .
serum lbp at study entry did not differ between patients with gram - negative ( 43.1 21.3 g / ml ) and gram - positive infections ( 45.2 19.8 g / ml ) .
there was no significant difference between serum lbp in survivors and nonsurvivors in the group of patients with sirs , or in the group of patients with sepsis and septic shock ( p = 0.69 and p = 0.61 , respectively ) .
there was no correlation between serum lbp and clinical status according to acute physiology and chronic health evaluation ii ( spearman 's rho 0.199 ; p = 0.278 ) .
lbp serum levels did not differ between patients with positive and those with negative blood cultures ( 42.1 21.4 g / ml versus 39.5 18.1 g / ml ) .
lbp levels were not associated with hepatic dysfunction , as defined by bilirubinemia > 50 mol / l ( spearman 's rho = -0.125 ; p = 0.36 ) .
the mean serum concentrations of lbp , crp and procalcitonin are listed in table 2 .
there was only a weak correlation between lbp and crp in the group of patients with sepsis and septic shock , and in survivors ( table 3 ) .
the higher levels seen at the first examination decreased thereafter and were lowest at the last examination , despite the temporary increase seen in some patients who did not survive sepsis ( fig .
the difference between the first and last examination was statistically significant ( in survivors , median 25.4 g / ml versus 11.9 g / ml [ p = 0.009 ] ; in nonsurvivors , median 41.8 g / ml versus 26.4 g / ml [ p = 0.010 ] ; fig .
lbp levels at the last examination were significantly different between survivors and nonsurvivors ( p = 0.014 ) .
the mean serum concentration of lbp in all groups of patients was significantly greater than in control individuals ( p < 0.0001 ) ; in ascending order , the levels were 30.6 g / ml in patients with sirs , 37.1 g / ml in those with sepsis , and 59.7 g / ml in those with septic shock . the difference between levels in patients with sirs and those with septic shock was statistically significant ( p < 0.01 ) .
the specificity and sensitivity of serum lbp concentration in differentiating between patients with sirs and those with sepsis / septic shock ( with cutoff set at 29.8 g / ml ) were poor , at 50% and 74.2% , respectively .
serum lbp at study entry did not differ between patients with gram - negative ( 43.1 21.3 g / ml ) and gram - positive infections ( 45.2 19.8 g / ml ) .
there was no significant difference between serum lbp in survivors and nonsurvivors in the group of patients with sirs , or in the group of patients with sepsis and septic shock ( p = 0.69 and p = 0.61 , respectively ) .
there was no correlation between serum lbp and clinical status according to acute physiology and chronic health evaluation ii ( spearman 's rho 0.199 ; p = 0.278 ) .
lbp serum levels did not differ between patients with positive and those with negative blood cultures ( 42.1 21.4 g / ml versus 39.5 18.1 g / ml ) .
lbp levels were not associated with hepatic dysfunction , as defined by bilirubinemia > 50 mol / l ( spearman 's rho = -0.125 ; p = 0.36 ) .
the mean serum concentrations of lbp , crp and procalcitonin are listed in table 2 .
there was only a weak correlation between lbp and crp in the group of patients with sepsis and septic shock , and in survivors ( table 3 ) .
the higher levels seen at the first examination decreased thereafter and were lowest at the last examination , despite the temporary increase seen in some patients who did not survive sepsis ( fig .
the difference between the first and last examination was statistically significant ( in survivors , median 25.4 g / ml versus 11.9 g / ml [ p = 0.009 ] ; in nonsurvivors , median 41.8 g / ml versus 26.4 g / ml [ p = 0.010 ] ; fig .
lbp levels at the last examination were significantly different between survivors and nonsurvivors ( p = 0.014 ) .
the present study showed that serum lbp levels in patients with sirs , sepsis , or septic shock were higher than those in healthy volunteers .
we found no difference in lbp levels at study entry between patients with sirs of noninfectious etiology and patients with sepsis ; neither did we find any difference in lbp levels between surviving and nonsurviving patients with sirs , or any significant difference in the group of patients with sepsis or septic shock .
however , during the follow up of these patients , the nonsurviving septic patients had higher lbp levels than did the surviving patients , which is in accordance with the findings reported by carroll and coworkers and by schumann and coworkers but not with those reported by opal and coworkers . in a surveillance study of several hundred patients , carroll and coworkers demonstrated a wide range of inflammatory diseases or conditions in which the levels of lbp were elevated ( i.e. sepsis , meningococcemia , abdominal infection , and inflammatory bowel disease ) and unchanged ( i.e. systemic lupus erythematosus , rheumatoid arthritis , and acute graft versus host disease ) .
that study also showed that elevated levels of lbp ( > 46 g / ml ) at study entry in patients with suspected gram - negative sepsis were associated with significantly greater mortality .
severity of disease would be expected to occur in conjunction with increased endotoxin in the systemic circulation .
endotoxemia may originate from regional hypoperfusion and mucosal ischemia , which was suggested to promote translocation of endotoxin to the systemic circulation . in the present study
we did not perform measurements of endotoxin and so we are unable to assess its correlation with lbp levels .
opal and coworkers also did not find any such correlation , but they reported significantly lower serum lbp levels in nonsurvivors than in survivors within 24 hours of onset of sepsis .
they hypothesized that synthesis of lbp fails in the presence of rapidly progressive septic shock .
carroll and coworkers reported data from additional clinical trials suggesting that lbp is elevated in patients with hemorrhagic trauma or cystic fibrosis , as well as in patients with partial hepatectomy , and concluded that these patients were systemically exposed to bacteria and endotoxin . in the present study we did not find any relationship between lbp and hepatic function , as indicated by bilirubinemia .
similar to froon and coworkers , we observed no difference between lbp levels in patients with gram - negative and those with gram - positive infections .
the dynamics of lbp levels in surviving and nonsurviving patients with sepsis were interesting . in both groups of patients ,
the higher lbp levels seen at the first examination decreased thereafter and were lowest at the last examination .
this can not be explained by hepatic failure because in the survivors hepatic function recovered , but the phenomenon could be due to anergy or tolerance to a long - lasting insult , in this case endotoxin or infection .
we found initial lbp levels to have low specificity and sensitivity in distinguishing between sepsis and sirs .
this conclusion is consistent with earlier reports that lbp is a marker of overall inflammation ( i.e. sirs or multiple organ dysfunction syndrome ) .
it is possible that patients with sepsis were erroneously classified as having sirs because of limitations in currently used diagnostic methods .
we found no correlation between lbp and procalcitonin or crp in any diagnostic group of patients , and neither were the lbp serum levels correlated with illness severity scores .
in conclusion , lbp is a nonspecific marker of the acute phase response and can not be used as a diagnostic tool for differentiating between infectious and noninfectious etiologies of sirs .
this conclusion is supported by our observation of similar lbp serum levels in patients with sirs and in those with sepsis .
the dynamics of lbp levels ( followed in 17 patients ) suggest that the lbp levels in septic patients decrease over the course or at the end of the disease
lbp is a nonspecific marker of the acute phase response lbp is not a suitable parameter for differentiating between infectious and noninfectious etiologies of sirs
crp = c - reactive protein ; icu = intensive care unit ; il = interleukin ; lbp = lipopolysaccharide - binding protein ; lps = lipopolysaccharide ; sirs = systemic inflammatory response syndrome .
time course of lipopolysaccharide - binding protein ( lbp ) levels in surviving and nonsurviving patients with sepsis and septic shock . shown
are data from patients available for follow up , who were assessed repeatedly at 3- to 5-day intervals for 30 days or until death .
serum lipopolysaccharide - binding protein ( lbp ) at the first and last examinations in patients with sepsis and septic shock .
there was a statistically significant difference between first and last examination in the group of patients who survived ( p = 0.009 ) and in those who did not ( p = 0.010 ) .
demographic characteristics of patients apache = acute physiology and chronic health evaluation ; sirs = systemic inflammatory response syndrome .
serum lipopolysacharide - binding protein , procalcitonin , and c - reactive protein at study entry ( baseline measurement ) data are expressed as median ( range ) .
crp , c - reactive protein ; lbp , lipopolysacharide - binding protein ; pct , procalcitonin ; sirs = systemic inflammatory response syndrome .
correlations of lipopolysaccharide - binding protein ( lbp ) with procalcitonin , and of lbp with c - reactive protein at study entry ( baseline measurement ) shown are pearson 's correlation coefficients along with corresponding p values . | pubmed |
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globular clusters can provide simultaneous estimates of velocity , metallicity and age : a powerful trio with which to study the history of a galaxy .
they are particularly helpful to complement integrated light studies , which average over all stellar populations along a line of sight . in this paper
we discuss the kinematics of old clusters projected on the inner 10 kpc of m31 .
roughly one third of our sample of over 300 old clusters in m31 ( presented in caldwell et al . 2009 and 2010 ,
papers 1 & 2 hereafter ) are located within 3 kpc of its center . because of our careful treatment of the effect of field star contamination from the bright bulge and inner disk region in our fibers , our dataset is particularly well suited for study of the central regions of m31
. early work on bulge kinematics @xcite showed that bulges resemble low - luminosity ellipticals in being kinematically hot with a high degree of rotational support ( @xmath0 ) .
later studies , however , showed that bulges are more complex and that an important distinction must be made between classical bulges which are kinematically hot and formed rapidly from mergers and collapses and bulges formed via secular evolution of disks , which have a lower sersic index ( kormendy & kennicutt 2004 ) . in this second category athanassoula ( 2005 ) distinguished the boxy / peanut bulges which are parts of bars seen edge - on and the disk - like bulges , which have a disk shape .
boxy / peanut bulges can be distinguished in near - edge - on galaxies from photometry or via kinematics ( eg * ? ? ?
* ; * ? ? ?
evidence from isophotal twists and kinematics was used to argue that m31 might have a triaxial bulge or a bar ( lindblad 1956 , stark 1977 , stark & binney 1994 ) .
more recently , athanassoula & beaton ( 2006 ) and beaton et al .
( 2007 ) , using deep 2mass observations , considerably strengthened the case for a bar and suggested that m31 also has a centrally concentrated classical bulge , which dominates the light in the inner 200 pc .
we note here that this is a considerably smaller and less dominant classical bulge than the one suggested by previous authors : @xcite found an effective radius of 3.5 kpc , and @xcite derived an effective radius of 2 kpc and found that the bulge contributed 40% of the light of the galaxy .
our globular cluster kinematical data allow us to further explore this shift in our view of m31 s bulge , since we have [ fe / h ] and velocity measurements for 98 old clusters projected within 3 kpc of m31 s center .
we assume a distance of 770 kpc throughout @xcite and a pa of 37.7 degrees .
the xy coordinate system we use in this paper has units of kpc , with positive x along the major axis towards the ne .
paper 2 presented [ fe / h ] , age and velocity measurements based on high s / n hectospec @xcite spectra ( a median s / n of 75 per @xmath1 ) for over 300 m31 clusters with ages greater than 6 gyr .
( in fact the great majority of these clusters have ages greater than 10 gyr . ) here we discuss the old clusters from this paper which are within 2 kpc of m31 s major axis .
repeat hectospec observations showed a median velocity error of 6 km s@xmath2 .
our study contains 17 entirely new cluster velocities and is the first fiber study to use offset exposures near each cluster in the bright inner regions to correct for the contamination from field stars there .
@xcite showed that ignoring this effect can lead to velocity errors of more than 100 km s@xmath2 . in the small number of cases where our velocities differed significantly from the hectochelle velocities of strader and caldwell ( 2010 , in preparation ) , we have used the more accurate hectochelle data .
our [ fe / h ] values are in good agreement with the recent results of @xcite and @xcite and the hst color - magnitude derived values .
we found that the old cluster metallicity distribution was neither unimodal nor simply bimodal , showing a median [ fe / h ] around 1.0 and possible peaks at [ fe / h ] = 0.3 , 0.8 and 1.4 .
previous work on m31 globulars suggested a larger systemic rotation for the metal - richer clusters ( eg * ? ? ?
* ; * ? ? ?
since all but one of the clusters with @xmath3 are projected on the inner disk ( less than 1.5 kpc from the major axis ) we first explore connections between the metal - rich clusters and m31 s disk . in the milky way ,
the metal - rich globular clusters are likely associated with its inner disk : @xcite connected these clusters with the thick disk , @xcite with the bulge . since
more recent work has shown that the milky way bulge is dominated by a bar @xcite , the most metal - rich globulars in the milky way are all likely to be connected to its disk in some way : either as a bar distortion or a thicker component .
to compare our old clusters with m31 s disk , we use the fibers which were designed to measure the contamination from m31 s disk and bulge : each fiber s measured velocity will be the _ mean _ velocity of all the stars along that line of sight .
figure [ hilofekin ] compares cluster velocities ( with different colors for clusters with different metallicities : red for most metal rich through blue for the most metal poor ) with these mean velocity estimates , shown in black .
the top panel shows clusters with @xmath4 ; the bottom panel shows more metal poor clusters .
the difference between their kinematic behavior is stunning .
0.6 ) and the lower panel the more metal - poor clusters which dominate m31 s old clusters . in both panels ,
black symbols show the _ mean _ velocity of stars at that position , integrated along the line of sight .
open symbols denote ages less than 10 gyr , closed symbols greater than 10 gyr ( note that we are unable to measure ages for clusters with less than 1.0 , and we use closed symbols for these clusters ) .
the vertical grey lines show the end of the thick bar ( dashed lines ) and the thin bar ( solid ) , from @xcite and @xcite , and the solid black line is the rotation curve from @xcite .
note that measurements of the dimensions of the thin and particularly the thick bar are approximate only .
[ hilofekin ] ] metal poor clusters ( lower panel ) show little sign of rotation and occupy the four quadrants of the plot similarly . on the other hand ,
the metal - rich clusters ( upper panel ) show a distinct and quite cold kinematical signature .
there are almost no clusters in the forbidden quadrants ( occupancy here corresponds to rotation in the opposite direction to the disk ) and most of those more than 2 kpc from the center ( ie @xmath5 ) have velocities which closely follow the disk velocity at that position . however , in the inner 2 kpc the signature differs from the usual one for a disk composed of stars on near - circular orbits . although all except one cluster occupy the same quadrant as the disk , thus respecting the same direction of rotation , their velocities can deviate from the local mean velocity of the integrated light by up to 350 km s@xmath2 ( recall that m31 s rotation velocity is 250 km s@xmath2 ) .
we note that very high velocities are also observed in the hi gas in this region @xcite . in the following section we will describe expectations for the kinematics of thin disk , bar and classical bulge objects , and
show that this signature is expected for bar orbits .
thin disks in galaxies have `` cold '' kinematics dominated by rotation and show a low velocity dispersion .
we showed in paper 1 ( see figure 13 ) that the young m31 clusters ( with ages less than 2 gyr ) have such kinematics : the young clusters all follow the same narrow locus in position vs velocity .
we also showed ( see figure 12 ) the mean velocity field across the face of the disk , obtained from our `` sky '' fibers .
the mean velocity changes smoothly and slowly as we look from the receding side of the disk through the center to the approaching side , as expected for a thin disk .
it is particularly simple to follow the kinematic signature of a cold , thin disk by examining velocities of objects seen close to the major axis . in a galaxy close to edge - on such as m31 ,
such a star in a circular orbit will have all its velocity in the line of sight , giving a clean measure of @xmath6 , the azimuthal component , from the line - of - sight velocity . for disk stars observed at larger distances from the major axis , less of their azimuthal velocity
will be projected onto the line of sight and so the change in mean velocity from one side of the disk to the other will be smaller .
most orbits in bars follow the two main families of closed periodic orbits @xcite : the orbits , which are aligned along the long axis of the bar ( close to the major axis in m31 , see beaton et al ( 2007 ) ) and orbits which are aligned along its short axis ( close to m31 s minor axis ) . for orbits , velocities can reach very high values close to the center of the galaxy .
this is due to the fact that they are observed near - end - on , so that the line - of - sight component is nearly along the orbit at its pericenter @xcite .
figure [ x1x2orbits ] ( from * ? ? ?
* ) illustrates the spatial and velocity signatures of and orbits .
it can be seen that in this example , the orbits reach velocities much higher than the circular velocity .
( a similar position - velocity diagram for a m31-like system can be seen in the middle top panel of figure 11 of * ? ? ?
lastly , we would expect any classical bulge component to show @xmath0 : some rotational support but a roughly equivalent amount of random motion .
@xcite fitted the m31 bulge using an oblate rotator model with major - axis velocity of around 90 km s@xmath2 and velocity dispersion of 130 km s@xmath2 at 1.5 kpc from the center .
we saw in figure [ hilofekin ] that the kinematics of old m31 clusters with @xmath7 in its innermost region show the distinctive behavior of objects on orbits in m31 s bar .
this is in very good agreement with orbital structure in bars since the orbits are always confined to the innermost regions , in the region interior to the inner lindblad resonance ( ilr ) .
most of the rest of the metal - rich clusters have orbits consistent with disk objects .
we see little or no indication in the kinematics in the upper panel of figure [ hilofekin ] for a kinematically hot population such as the classical bulge of @xcite . however , we note again that the classical bulge identified by @xcite was quite small , only dominating the inner 200 pc .
we have only one cluster within 200 pc of m31 s center in our sample , so we can not probe the kinematics of this region in m31 . only in the lower panel , with the more metal - poor clusters ,
do we see a signature like that of a kinematically hot classical bulge : there are roughly equal numbers of clusters in each quadrant , and we see that the velocity dispersion rises sharply close to the center , as we would expect for a centrally concentrated classical bulge .
however , as we shall show below , the starlight in this region is dominated by old metal - rich stars of near solar abundance , so these metal - poor clusters are not tracing the dominant component here . to summarize : we see strong evidence from the kinematics of the metal - rich old clusters ( [ fe / h]@xmath80.6 ) for both disk and bar kinematics .
a number of the clusters within 2 kpc of the center of m31 show the kinematic signature of orbits in a barred potential .
the rest of these clusters ( plus the other metal - rich clusters within 2 kpc of the major axis ) show the cold kinematics of the disk .
these kinematics strongly confirm the result of @xcite and @xcite that m31 has a bar whose inner parts constitute the boxy bulge which dominates its light in the inner few kpc . to our knowledge , this is the first clear detection of globular clusters with bar kinematics in any galaxy .
however , there is one massive cluster ( the arches cluster ) in the milky way which has a large space velocity ( 232 km s@xmath2 ) and is currently at a projected distance of only 26 pc from the galactic center @xcite .
these authors note that the cluster could be on a transitional trajectory between and orbits in the milky way s barred potential , and may have been formed in a starburst triggered when a massive molecular cloud `` collided on the boundary between and orbits in the inner bar '' .
we now consider the relationship between field stars and globular clusters in the inner regions of m31 .
@xcite studied the integrated light of m31 s bulge , in a circular aperture of diameter 250 pc .
they found a mean metallicity of + 0.2 dex , and a mean age of around 6 gyr .
more recently , @xcite have made a detailed study of the m31 bulge region using a number of long - slit exposures with the het .
they find a mean metallicity around solar , and an age of around 12 gyr in the inner 1 - 2 kpc .
( note that they do see a metallicity gradient , reaching up to [ z / h]=+0.4 , over the inner 200 pc , the region dominated by the classical bulge . )
@xcite used hst / wfpc2 observations to produce a color - magnitude diagram for m31 s bulge at 1.6 kpc from its center , and inferred a metallicity distribution which peaked near solar .
@xcite summarized near ir color - magnitude diagrams from high spatial resolution studies of m31 to find that the stellar population in the inner few kpc was dominated by old , nearly solar - metallicity stars .
interestingly , by comparing fields in the bulge with an inner disk field , they found no evidence for an age difference between bulge and disk .
this is unsurprising if m31 s bulge is dominated by a bar , since bar stars are merely inner disk stars which have become part of the bar pattern .
the mean metallicity of the integrated light from field stars thus exceeds the mean metallicity of the globulars in the inner few kpc ; it is closer to the mean of those with [ fe / h]@xmath80.6 , which show either disk or bar kinematics .
( it has been suggested before that globular clusters are formed less efficiently in metal - rich populations : @xcite calculate that the efficiencies differ by more than a factor of 10 in the milky way , by comparing metal - rich globular clusters to the bulge luminosity and metal - poor numbers to the halo luminosity .
this number will not be changed radically if we substitute the thick disk luminosity for the bulge luminosity in this calculation . )
thus a simple picture can explain the existence of the metal - rich globular clusters in m31 : they merely participated in the early formation of the inner disk and the onset of the bar instability .
we have discussed accurate kinematical data for old m31 clusters in its inner regions within 2 kpc of its major axis .
the majority of the metal - rich clusters ( those with [ fe / h ] greater than 0.6 ) show disk kinematics , and many of the clusters within the innermost bar region have the signature of the family .
this clearly shows the existence of an ilr and , to our knowledge , this is the first time it has been clearly shown using stellar kinematics . in the only other known example
, @xcite showed this using gas kinematics in the strongly barred galaxy ngc 1365 .
our result also gives an estimate of the ilr location , which provides useful constraints for future dynamical studies of m31 since it could be used to set limits to the bar pattern speed .
these metal - rich clusters share the population properties ( metallicity and age ) of the integrated light in the inner few kpc , which has been studied both via spectroscopy and via deep color - magnitude diagrams from hst and adaptive optics imaging .
by contrast , clusters with less than 0.6 within 2 kpc of the major axis show little rotational support and a velocity dispersion which increases as radial distance to the center decreases
. our data do not probe the small region ( 200 pc ) occupied by m31 s classical bulge in the description of @xcite , so we can not comment on its kinematics .
however , we caution against simply interpreting a high velocity dispersion in m31 s inner few kpc as a bulge velocity dispersion and then using it to constrain m31 s black hole mass ( as done most recently by * ? ? ?
* ) : the contribution of the bar , which dominates the light there , needs to be assessed .
hlm thanks the nsf for support under grant ast-0607518 , ajr for grants ast-0808099 and ast-0909237 , and ea the anr for anr-06-blan-0172 .
rps is supported by gemini observatory , which is operated by aura , inc , on behalf of the international gemini partnership of argentina , australia , brazil , canada , chile , the united kingdom and the united states of america .
we also thank john wiley and sons for permission to reproduce figure 2 .
barmby , p. , huchra , j. p. , brodie , j. p. , forbes , d. a. , schroder , l. l. , & grillmair , c. j. 2000 , , 119 , 727 beasley , m. a. , brodie , j. p. , strader , j. , forbes , d. a. , proctor , r. n. , barmby , p. , & huchra , j. p. 2005
, , 129 , 1412 beaton , r. l. , et al .
2007 , , 658 , l91 binney , j. , gerhard , o. e. , stark , a. a. , bally , j. , & uchida , k. i. 1991 , , 252 , 210 binney , j. , gerhard , o. , & spergel , d. 1997 , , 288 , 365 binney , j. and tremaine , s. 2008 , galactic dynamics , princeton university press , princeton nj .
brinks , e. , & shane , w. w. 1984 , , 55 , 179 bureau , m. , & athanassoula , e. 1999 , , 522 , 686 bureau , m. , & athanassoula , e. , 2005 , apj , 626 , 159 caldwell , n. , harding , p. , morrison , h. , rose , j. a. , schiavon , r. , & kriessler , j. 2009 , , 137 , 94 caldwell , n. , schiavon , r. , morrison , h. , rose , j. and harding , p. 2010
, submitted to aj .
colucci , j. e. , bernstein , r. a. , cameron , s. , mcwilliam , a. , & cohen , j. g. 2009 , , 704 , 385 saglia , r. p. , et al .
2010 , , 509 , a61 sarajedini , a. , & jablonka , p. 2005
, , 130 , 1627 stark , a. a. 1977 , , 213 , 368 stark , a. a. , & binney , j. 1994 , , 426 , l31 stolte , a. , ghez , a. m. , morris , m. , lu , j. r. , brandner , w. , & matthews , k. 2008 , , 675 , 1278 strader , j. , brodie , j. p. , cenarro , a. j. , beasley , m. a. , & forbes , d. a. 2005 , , 130 , 1315 | arxiv |
How to read Robin-Day Classification?
I am currently preparing for an exam and am stuck now with the Robin-Day classification. We had these three diagrams and also the explanations how the systems differ but we never talked about what the diagrams are supposed to show or how we have to read them.
The paper suggests that λ here is not (as one might suggest) the wavelenght required to excite an electron but the so called Marcus-reorganization energy and h(ab) is here the electronic coupling.
I understand that you have to treat the system a bit more complicated because you have a system that exchanges electrons without the formation or cleavage of bonds or any major geometric change. And there is also the concept of conductor and non conductive if we see class III compounds as being fully delocalized.
But why does the class I non conducting intervalence compound have these two energy curves, the class II a double well. I suppose because there is no λ in class three that, as there is no localization of the corresponding electrons, this reorganization is not important there. Still I'd be interested in how to actually understand the diagrams and what I can take from them.
[](https://i.stack.imgur.com/6Fth3.jpg)
Theses are potential energy diagrams, representing the 'stable' forms of both the reactant and the product of IVCT (and their immediate relationship with ligands and surrounding solvent). This is most easily seen in the class I case, where the curves are not merged at all, and instead represent the species as distinct (and the reaction unable to proceed). The reason the curves appear to merge is because the class II and class III cases are where electron transfer is able to occur, and thus the reactant has a reaction path with which to proceed to the product.
There are in fact two reaction paths that a class II mixed-valence species can proceed to the product, one being optical (which is the IVCT transition, caused by absorption of light), and the other being thermal. The optical pathway occurs upon absorption of light at the bottom of the leftmost potential well, where it is excited to the top left of the upmost curve. This corresponds to lambda, which confusingly represents the *energy* of this optical transition (E=hv=\lambda). The position that the ion is now at on the potential energy curve is representative of a state where the electron has been exchanged, but the molecule is yet to rearrange bond lengths, and the surrounding solvent has not rearranged to accomodate the new distribution of charge. The molecule then relaxes down the adiabatic potential energy curve (not shown here, some diagrams have the same structure as class I in dotted lines, these lines being the adiabatic energy curves), to the rightmost potential energy well, where the molecule has completely rearranged the surrounding solvent and changed bond lengths to accomodate the new charge distribution. The thermal process is less relevant, except to note that the hump in the class II diagram is the thermal activation barrier, where an activation energy equivalent to or greater than this barrier is required for the reaction to proceed via this pathway.
A class III ion is one where there is full mixing of the two potential energy curves, such that they become the structure you see above. Clearly here there is no thermal activation barrier, as there is no hump, and the optical transition energy is actually equivalent to or smaller than 2Hab (twice the coupling constant). The result of the now missing thermal activation barrier is that the ion can freely transition between both states, equilibrating between them, resulting in partially charged ions, and a very delocalised system. Note that optical transitions still occur in class III ions, and are typically more intense than transitions in class II ions. There is just no good way of displaying where the transition occurs as it is in the same position as the 2Hab gap.
I realise this thread was created long ago, so this response likely won't be useful to the original poster, but hopefully anyone else who is interested will have a greater appreciation of how these diagrams work.
I strongly recommend reading this paper <https://onlinelibrary.wiley.com/doi/10.1002/9780470166314.ch1> if you can get access to it. It is by far the most understandable of all the papers on the subject, and very comprehensive.
| stackexchange/chemistry |
Albert Gillman IIII, M.D., F.A.C.S.
As part of the DMH Medical Group, our well-rounded team of experienced specialists are backed by the state-of-the-art technology and resources offered at Decatur Memorial Hospital.
Call us for answers to your digestive questions. | slim_pajama |
One Piece 1. Zoro
The Curse of the Traveling Hiccups!
Written by: Okami
**Authors Note**: I'm at work one day when I suddenly start hiccupping with no idea how they got started. Well, as I go on through my day I think about how funny it would be if the Straw Hat Pirates developed hiccups. And…well…here it is! I tried to keep the characters in character as much as possible. Oh! Also, I do not own One Piece. (Drat!) Enjoy!
The enemy inched closer, swords poised and ready. He could tell they were hesitating to make the first move; he cracked a smirk. Sometimes it really paid to have the title of pirate hunter and be thought of as a demon. Three swords drawn, bandana tied atop his head, and his shadowed eyes glaring down his opponents, he was a force to be reckoned with. Crossing his arms over his chest, he prepared his attack.
"Oni—" His opened mouth paused when his stomach tensed and the strangest sound erupted from his throat.
"—Giri!" Quickly ignoring whatever had happened, he finished his attack and swept through the pirate crew with no problem. He allowed a smile of satisfaction to cross his lips as he began sheathing his swords.
Hiccup
Zoro's hand slipped when his body once again tensed involuntarily, slicing his finger in the process. He hissed and quickly sheathed his katanas, sticking his finger his mouth after the fact. What was going on? Why was his stomach having spasms? Well, at least all the other annoying pirates had been kicked off so he didn't have to deal with those guys anymore. Damn them all for disturbing his nap with their pitiful excuse for a raid. His mouth opened for a yawn but what escaped his lips was anything but what it was supposed to be. It sounded more like someone had just hit him in the gut with a two ton hammer. This gained him surprised looks from his crew mates.
"Wh—hiccup—at?" he growled. Zoro could feel his face flush when he hiccupped in the middle of the word. He had tried to make it sound intimidating but the effect was lost amidst the roar of laughter. The swordsman would have opened his mouth once more but another stomach spasm silenced the words before they could form. Being too tired from lack of sleep, he made his way over to his previous napping place. He'd deal with them later. He would have enjoyed the leisurely doze had his body not jerked every time he hiccupped, followed soon after by snickers from his comrades.
Zoro cast the sharpshooter and captain one last death glare before closing his eyes again. It took him awhile but he finally dozed off and slept peacefully. He didn't know how long he had been asleep but a rather familiar sound roused him from his slumber.
Hiccup
After a moment's pause the green haired man realized he wasn't the one that had hiccupped. "Ah ha!" he exclaimed, sitting bolt upright. "Pay back's a bitch!"
**Authors Note**: Who will be next to experience the wrath of the hiccups! MUHAHAHA!
2. Sanji
**Author's Note**: I don't own One Piece. Drat!
He couldn't help but laugh at the swordsman's discomfort. To watch the burly man jerk occasionally as he tried to sleep was just too funny not to watch. It was even funnier to hear him try and spout out threats while hiccupping in the middle of a word. It made his day!
Sanji chuckled to himself again as he entered the kitchen. It was almost lunch time aboard the Going Merry and he had a special treat in mind for a certain red head. He could almost picture her beautiful face as she tasted the delicious delicacy: a bright smile, sparkly eyes, and that beautiful song of a laugh. Hearts formed in the cook's eyes as he felt his pulse race, nostrils flaring in pleasure. He didn't need a recipe for his masterpiece so he set right to work. He opened one of the drawers and reached for a knife.
Hiccup
His hand slipped and nearly had a close encounter with the sharp objects. He couldn't help but groan inwardly at the set back. Sucking in a deep breath and holding it tight, he continued with the task at hand. The vegetables were rinsed, washed, and then rinsed again before they were ready to be sliced and diced. As he chopped, the knife moving fast along the food, he took in a sudden breath through his nose. A bubble of the air caught in his throat and he choked, momentarily taking his mind away from his previous task. The knife came down quickly and missed his fingers by a hair's breath.
Hiccup
Damn these hiccups! That was a close call…too close. Sanji downed a glass of water like a shot, hopping that would take care of the problem. Well, at least the vegetables were finished. Now on to the rice.
Everything was moving smoothly with the occasional hiccup here and there. They were becoming quite the problem as some were even disturbing his ability to function, jerking his body with every spasm of his diaphragm. He slid the vegetables into the rice and stirred them all together in his frying pot. The cook lifted the pot to flip its contents when another spasm attacked. His hand jerked and the mixture spilled out of the pan and right onto the stove top. The hot irons spit and sizzled in fury as they burned the food to a crisp.
"Sh—hiccup—it!" he cursed loudly. Luckily, the majority of the food had remained in the pot. But that was going to be a major pain to clean up.
It took much care to finish the rest of the meal. He used extra caution when fixing the meat, not wanting to ruin that in anyway as he knew his captain would probably have his head. Not that Luffy really cared if the meat was cooked or not, as long as it was there he would eat it. Well, the meal was prepared and ready to go. Sanji balanced the plates on his arms and head and began the trek to the aft deck. It was such a beautiful day so they all decided to eat outside. He had just turned the corner and was in full view of the crew when it happened.
Hiccup
Sanji's whole body jerked when another hiccup reared its ugly head. His balance had the best of the Straw Hat pirates, but even he has his moments of miscalculation. In that moment of over correction, the plates of food went crashing down, on top of him and all over the deck.
"Ahh! Meat!" Luffy cried, dashing to the rescue of his precious food.
"Ah ha!" Zoro's voice exclaimed from behind.
Sanji's face was beet red with embarrassment as he stood there, rice clinging to his suit like large lint balls, noodles dangling in his blonde locks, and meat splattered across his shoes. He could stand the laughter from his fellow men, but what hurt the most was hearing his love's laughter and know it was directed at him.
"Sanji-kun," he heard Nami say between fits of laughter. "You're so cute!"
The cook instantly forgot his embarrassment and floated over to her, heart-shaped eyes pounding hard. She pushed him away quickly and told him to take a shower, the other boys would clean up the mess. He agreed instantly, she was always right, and hurried away to get clean. Of course, he promised to make her something extra special once he was finished.
Sanji towel dried his hair as stepped out on to the deck, taking in a deep breath. Now that he was squeaky clean he could prepare that treat for his Nami-san.
Hiccup
The sound stopped him in his tracks and he looked around. It hadn't come from him…so who was it this time?
**Author's Note**: Who is next indeed. Evil laughter You read my mind lightpaladin! I had planned on doing Sanji next anyway. I'm not sure who I will torture in the next chapter though…I have an idea but I'm not sure.
3. Nami
**Author's Note**: I don't own One Piece. Drat!
Nami groaned inwardly and looked skyward as if to ask, 'What did I ever do to you!' She knew something strange would happen today but nothing like this. The brilliant red-orange sunrise told of dangers lying in wait. It couldn't have been the marines that chased them during breakfast, or the nameless pirates that attacked before lunch. No, it had to be this. She breathed in a deep sigh only to have that too interrupted.
Hiccup
"Damn it Sanji-kun look what you did! You gave me the hiccups!" She knew it really wasn't the cook's fault she had the hiccups, but someone was to blame and he had been the last one to have them.
The blonde cook stared at her from the main deck, his fresh cigarette dangling from his open lips. He looked about ready to cry.
"Oh my dearest Nami-swan! I feel so ashamed to have given you these dreaded hiccups! I don't deserve to be in the presence of your beauty."
"Then why don't you just jump overboard," a deep voice grunted.
The navigator was surprised when Sanji didn't respond with a quick remark like she had thought. Instead, he seemed to be pondering the idea seriously.
"It's all right, Sanji—hiccup—kun. I'm sure they'll go away in a little bit," she said reassuringly. A smile crept across her face. "I am a bit hungry…."
The cook was in the kitchen in a flash, whipping up something extra special just for her.
Nami sighed again to herself as another hiccup erupted from her lips. A steely glare silenced the snickers from certain members of the crew. Noticing the sky was particularly calm, she took the opportunity to continue work on her world map. She spread her paper, maps, ink, pens, and other various instruments needed for mapmaking and set to work.
Hiccup
"Ahh! Not again!" The navigator slammed her hands down on the table in frustration and glared down at the ruined map. This particular map had been especially hard due to the strange mountain formations, various elevations, and unique shoreline. But, she was determined and had nearly finished when they hit.
Hiccup
Those damned hiccups! Her usually steady hand slipped, making a nice sloppy line across the paper. This was the third time on this one map! It was infuriating beyond belief. She reached over to return her feather pen to its ink pot when—
Hiccup
The ink split all over the table and onto the floor, covering all the papers in a film of black liquid. Nami quickly tried to salvage as much as of the parchment as possible. Her attempts only managed to smear the liquid more, even splattering it across her clothes.
"Ah man! These were new!" She cursed silently as she looked down at herself.
Hiccup
The navigator growled to herself. This was getting old—fast. She slammed her hands down on the table again, letting out a groan. Unfortunately for her, the wood was slick from the ink and her hands slipped forward. Nami face faulted onto the table and froze, not believing what had just happened. Just outside the door she heard the voice of one of the many people she did not want to deal with right now.
"Nami-swan!" Sanji opened the door to the galley and stepped in, balancing a tray with what looked like ice-cream in one hand. His mouth opened to continue his praising but the words caught in his throat at the sight before him.
"Sanji—hiccup—kun," Nami growled dangerously. She rose from the table, her front pitch black, and glared at him from behind her dripping bangs. "Not—hiccup—now!" The cook fled from the room and just barely managed to avoid being struck in the head by a flying ink pot.
Nearly two hours later, the navigator emerged from her study. With clean clothes and freshly finished maps hanging to dry, she felt pretty good.
Hiccup
She tensed inwardly until realization hit her. _ That wasn't me! _ she thought happily. Nami looked around, eyes wide. _ Who had them this time! _
**Author's Note**: Evil laughter I already know who I'm doing next. Can you guess who it is?
End file.
| fanfiction |
the origin of the classical lagrange and markov spectra lies in number theory .
more precisely , given an irrational number @xmath12 , let @xmath13 be its best constant of diophantine approximation .
the set @xmath14 consisting of all finite best constants of diophantine approximations is the so - called _
lagrange spectrum_. similarly , the _ markov spectrum _
@xmath15 consists of the reciprocal of the minimal values over non - trivial integer vectors @xmath16 of indefinite binary quadratic forms @xmath17 with unit discriminant .
these spectra are closely related : it is know that the lagrange and markov spectra are closed subsets of @xmath18 such that @xmath19 .
the reader can find more informations about the structure of these sets on the classical book @xcite of cusick and flahive , but let us just mention that : * hurwitz theorem says that @xmath20 ; * markov showed that @xmath21 where @xmath22 is an explicit , @xmath23 , @xmath24 , etc .
] increasing sequence of quadratic surds converging to @xmath25 ; * hall showed that @xmath26 contains a half - line and freiman determined the biggest half - line contained in @xmath26 ( namely , @xmath27 where @xmath28 ) ; * moreira @xcite proved that the hausdorff dimension of @xmath29 varies continuously with @xmath10 , and , moreover , the sets @xmath29 and @xmath30 have the same hausdorff dimension for all @xmath10 . for our purposes , it is worth to point out that the lagrange and markov spectra have the following _ dynamical _ interpretation , see @xcite for instance . ] in terms of the continued fraction algorithm .
denote by @xmath31 $ ] the continued fraction @xmath32 .
let @xmath33 the space of bi - infinite sequences of positive integers , @xmath34 be the shift dynamics @xmath35 , and let @xmath36 be the function @xmath37 + [ 0 , a_{-1 } , a_{-2},\dots]\ ] ] then , @xmath38 in the sequel , we consider the natural generalization of this dynamical version of the classical lagrange and markov spectra in the context of horseshoes of smooth diffeomorphisms of compact surfaces . in this setting , our main result ( cf . theorem [ t.a ] below ) will be a dynamical analog of the results of @xcite ( quoted above ) on the continuity of hausdorff dimension across lagrange and markov spectra .
let @xmath1 be a surface and consider @xmath39 a @xmath40-diffeomorphism possessing a horseshoe @xmath8
. given @xmath41 a @xmath42-function , @xmath43 , and @xmath10 , we define the _ dynamical markov , resp .
lagrange , spectrum _
@xmath6 , resp .
@xmath5 as @xmath44 where @xmath45 [ r.l < m ] an elementary compactness argument ( cf .
remark in section 3 of @xcite ) shows that @xmath46 whenever @xmath47 is a compact @xmath4-invariant subset . in this paper
, we will be interested in the fractal geometry ( hausdorff dimension ) of the sets @xmath11 and @xmath9 as @xmath10 varies .
for this reason , we will also study the fractal geometry of @xmath48 for @xmath10 .
more precisely , we will consider the following setting ( and we refer to palis - takens book @xcite for more details ) .
let us fix a geometrical markov partition @xmath49 with sufficiently small diameter consisting of rectangles @xmath50 delimited by compact pieces @xmath51 , resp .
@xmath52 , of stable , resp .
unstable , manifolds of certain points of @xmath8 .
we define the subset @xmath53 of admissible transitions as the subset of pairs @xmath54 such that @xmath55 . in this way , the dynamics of @xmath4 on @xmath8 is topologically conjugated to a markov shift @xmath56 of finite type associated to @xmath57 . next , we recall that the stable and unstable manifolds of @xmath8 can be extended to locally invariant @xmath58-foliations in a neighborhood of @xmath8 for some @xmath59 .
therefore , we can use these foliations to define projections @xmath60 and @xmath61 of the rectangles into the connected components @xmath62 and @xmath63 of the stable and unstable boundaries of @xmath64 where @xmath65 and @xmath66 are fixed arbitrarily . using these projections
, we have the stable and unstable cantor sets @xmath67 associated to @xmath8 . the stable and unstable cantor sets @xmath68 and @xmath69 are @xmath58-dynamically defined / @xmath58-regular cantor sets , i.e. , the @xmath58-maps @xmath70 for @xmath71 and @xmath72 for @xmath73 are expanding of type @xmath74 defining @xmath68 and @xmath69 in the sense that * the domains of @xmath75 and @xmath76 are disjoint unions @xmath77 and @xmath78 where @xmath79 , resp .
@xmath80 , are compact subintervals of @xmath81 , resp . @xmath82 ; * for each @xmath83 , the restrictions @xmath84 and @xmath85 are @xmath58 diffeomorphisms onto @xmath86 and @xmath82 with @xmath87 , resp .
@xmath88 , for all @xmath89 , resp .
@xmath80 ( for appropriate choices of the parametrization of @xmath51 and @xmath52 ) ; * @xmath68 , resp .
@xmath69 , are the maximal invariant sets associated to @xmath75 , resp .
@xmath76 , that is , @xmath90 moreover , we will think the intervals @xmath91 , resp .
@xmath92 , @xmath93 inside an abstract line so that it makes sense to say that the interval @xmath91 , resp .
@xmath92 , is located to the left or to the right of the interval @xmath94 , resp .
@xmath95 , for @xmath96 ( see @xcite ) . the stable and unstable cantor sets @xmath68 and @xmath69 are closely related to the geometry of the horseshoe @xmath8 : for instance
, it is well - known that @xmath97 where @xmath98 stands for the hausdorff dimension , and , furthermore , @xmath99 when @xmath4 is conservative , i.e. , @xmath4 preserves a smooth area form @xmath100 .
partly motivated by this fact , we will study the subsets @xmath101 introduced above through its projections @xmath102 on the stable and unstable cantor sets of @xmath8 . using the notations of the previous subsection , our main result is the following .
let @xmath0 be a smooth conservative diffeomorphism of a surface @xmath1 possessing a horseshoe @xmath2 with hausdorff dimension @xmath103 .
denote by @xmath104 a small @xmath105 neighborhood of @xmath0 in the space @xmath106 of smooth conservative diffeomorphisms of @xmath1 such that @xmath2 admits a continuation @xmath8 for every @xmath107 .
[ t.a ] if @xmath104 is sufficiently small , then there exists a baire residual subset @xmath108 with the following property . for every @xmath109
, there exists a @xmath42-open and dense subset @xmath110 such that the functions @xmath111 are continuous and @xmath112 whenever @xmath113 .
[ r.ta ] our proof of theorem [ t.a ] shows that @xmath114 , resp .
@xmath115 , coincide with the box counting dimension of @xmath116 , resp . @xmath117 .
in plain terms , our strategy of proof of theorem [ t.a ] is very similar to @xcite : we want to approximate from inside @xmath117 and @xmath116 by dynamically defined cantor sets , resp .
@xmath101 by subhorseshoes of @xmath8 without losing too much hausdorff dimension in such a way that the values of @xmath7 on these approximating objects are controlled from above .
recall that the geometrical description of @xmath8 in terms of the markov partition @xmath49 has a combinatorial counterpart in terms of the markov shift @xmath118 .
in particular , we have a homeomorphism @xmath119 conjugating @xmath4 to the shift map @xmath120 and , moreover , we can use @xmath121 to transfer the function @xmath7 from @xmath8 to a function ( still denoted @xmath7 ) on @xmath122 . in this
setting , @xmath123 where @xmath124 given an admissible finite sequence @xmath125 ( i.e. , @xmath126 for all @xmath127 ) , we define @xmath128 similarly , given an admissible finite sequence @xmath125 , we define @xmath129 here , @xmath130 denotes the _ transpose _ of @xmath131 .
we say that the _ unstable size _
@xmath132 of @xmath131 is the lenght @xmath133 of the interval @xmath134 and the _ unstable scale _ of @xmath131 is @xmath135 .
similarly , the _ stable size _ @xmath136 is @xmath137 and the _ stable scale _ of @xmath131 is @xmath138 .
[ r.bounded-distortion ] in our context of @xmath58-dynamically defined cantor sets , we can relate the unstable and stable sizes of @xmath131 to its length as a word in the alphabet @xmath139 via the so - called _ bounded distortion property _ saying that there exists a constant @xmath140 such that : @xmath141 we refer the reader to @xcite for more details .
[ r.stable-unstable-sizes ] in our context of horseshoes of conservative @xmath40 surface diffeomorphisms , there exists a constant @xmath142 such that the stable and unstable sizes of any word @xmath131 in the alphabet @xmath139 satisfy @xmath143 [ l.nu-submultiplicative ] for each @xmath10 , the sequences @xmath151 , @xmath144 , and @xmath152 , @xmath144 , are essentially submultiplicative in the sense that there exists a constant @xmath153 such that @xmath154 and @xmath155 for all @xmath156 . since the expanding map @xmath76 defining the cantor set @xmath69 is @xmath58 , the usual bounded distortion property ( cf .
remark [ r.bounded-distortion ] ) ensures the existence of a constant @xmath159 such that the sizes of the intervals @xmath160 behave essentially submultiplicatively under admissible concatenations of words , i.e. , @xmath161 for all @xmath131 , @xmath162 , @xmath163 finite words such that the concatenation @xmath164 is admissible .
therefore , by taking @xmath177 it follows that we can cover @xmath171 with @xmath178 intervals @xmath173 whose scales satisfy @xmath179 whenever @xmath174 , @xmath175 , @xmath180 and @xmath164 is admissible .
hence , we conclude that @xmath181 for all @xmath156 . by contradiction , suppose that this is not the case .
then , there exists @xmath194 such that @xmath195 for all @xmath192 . by corollary [ c.du-definition ] , this implies that @xmath196 for all @xmath192 and @xmath197 . for this sake ,
let us fix a smooth system of coordinates @xmath215 on the initial markov partition @xmath49 so that , given @xmath216 and @xmath59 , the function @xmath217 for @xmath218 can be extended ( via an adequate partition of unity ) to a @xmath219-@xmath42-perturbation of @xmath7 whenever @xmath220 has norm @xmath221 . for each @xmath225 ,
let us consider the set @xmath226 of admissible finite words of the form @xmath227 , @xmath228 , such that the rectangle @xmath229 has diameter @xmath230 but the rectangles @xmath231 and @xmath232 have diameters @xmath233 .
next , let us take @xmath242 such that @xmath243 for all @xmath244 .
also , since @xmath7 is @xmath40 , there exists a constant @xmath245 such that @xmath246 for all @xmath247 .
moreover , by lemma [ l.lipschitz-directions ] , there exists a constant @xmath248 such that @xmath249 and @xmath250 where @xmath251 and @xmath252 ( resp . )
are unitary vectors in @xmath253 and @xmath254 ( resp . ) . in this
setting , for each rectangle @xmath255 , @xmath256 , such that @xmath257 is perpendicular to @xmath258 , @xmath259 , for some @xmath260 , we write @xmath261 we control this quantity as follows . since @xmath255 has diameter @xmath230 , we see from our previous discussion that @xmath262 @xmath263 in particular , it follows that @xmath264 for @xmath223 .
therefore , since the function @xmath265 satisfies @xmath266 , the proof of the proposition is complete once we show that there exists @xmath220 such that @xmath267 and @xmath268 .
as it turns out , this fact is not hard to check : by our previous discussion , for all @xmath237 , the lebesgue measure of @xmath269 is @xmath270 because , for each @xmath256 , the lebesgue measure of @xmath271 is @xmath272 , and the cardinality of @xmath226 is @xmath273 . by definition of @xmath206
, we can refine the initial markov partition @xmath49 ( if necessary ) so that the restriction of @xmath7 to each of the intervals @xmath63 , @xmath93 , is monotone ( i.e. , strictly increasing or decreasing ) , and , furthermore , for some constant @xmath275 , the following estimates hold : @xmath276 , @xmath277 and @xmath278 , @xmath279 are admissible . moreover , we observe that , since @xmath7 is lipschitz ( actually @xmath280 ) , there exists @xmath281 such that one also has the following estimates : @xmath282 , @xmath277 and @xmath278 , @xmath279 are admissible .
[ p.ta ] let @xmath8 be a horseshoe of a conservative @xmath40-diffeomorphism @xmath4 of a surface @xmath1 .
let @xmath274 with @xmath204 as defined in subsection [ ss.r - construction ] , and let us fix @xmath10 with @xmath283 , resp .
. then , for each @xmath285 , there exists @xmath225 and a complete subshift @xmath286 , resp .
@xmath287 , associated to a finite set @xmath288 , resp .
@xmath289 , of finite sequences @xmath290 , resp .
@xmath291 such that @xmath292 and @xmath293 resp .
@xmath294 where @xmath295 , resp .
@xmath296 , is the subset of @xmath69 , resp .
@xmath68 , consisting of points whose trajectory under @xmath76 , resp .
@xmath75 , follows an itinerary obtained from the concatenation of words in the alphabet @xmath297 , and @xmath298 is the alphabet whose words are the transposes of the words of the alphabet @xmath297 .
our plan towards the proof of proposition [ p.ta ] is to extract from @xmath309 a rich alphabet @xmath310 inducing a complete shift @xmath311 for some @xmath225 . in this direction
, the following notion plays a key role : [ d.good-position ] given @xmath312 with @xmath313 for all @xmath314 , we say that @xmath315 is a _
right - good position _ of @xmath162 if there are two elements @xmath316 of @xmath309 such that @xmath317 , i.e. , the interval @xmath318 is located between @xmath319 and @xmath320 .
similarly , we say that @xmath321 is a _ left - good position _ of @xmath162 if there are two elements @xmath322 of @xmath309 such that @xmath323 , i.e. , the interval @xmath324 is located between @xmath325 and @xmath326 .
let us begin by estimating the cardinality of @xmath309 .
recall that the sizes of the intervals @xmath134 behave essentially submultiplicatively due the bounded distortion property of @xmath76 ( cf .
remark [ r.bounded-distortion ] ) so that , for some constant @xmath329 , one has @xmath330 for any @xmath331 , and , thus , @xmath332 is a covering of @xmath171 by intervals of sizes @xmath333 . in particular , we have a natural surjective map @xmath334 given by @xmath335 where @xmath336 now , let us estimate the cardinality of the subset of @xmath309 consisting of words @xmath162 such that at least @xmath343 positions are not right - good .
first , we notice that there are at most @xmath344 choices for the set of @xmath345 right - bad ( i.e. , not right - good ) positions . secondly ,
once this set of right - bad positions is fixed : * if @xmath346 is a right - bad position and @xmath347 were already chosen , then we see that there are at most two possibilities for @xmath348 ( namely , the choices leading to the leftmost and rightmost subintervals of @xmath349 of the form @xmath350 intersecting @xmath171 ) ; * if @xmath346 is not a right - bad position , then there are at most @xmath351 choices of @xmath352 .
in particular , once a set of @xmath345 right - bad positions is fixed , the quantity of words in @xmath309 with this set of @xmath353 right - bad positions is at most @xmath354 therefore , the quantity of words in @xmath309 with at least @xmath343 right - bad positions is @xmath355 analogously , the quantity of words in @xmath309 with at least @xmath343 left - bad positions is also @xmath356 . by definition of @xmath357 , it follows that @xmath358 since @xmath359 ( by ) and @xmath360 ( from our choices of @xmath361 large , @xmath351 and @xmath362 ) , we deduce that @xmath363 this completes the proof of the lemma .
* the number of possibilities for @xmath383 is at most @xmath384 and * for each fixed @xmath383 , the number of possibilities for @xmath385 is at most @xmath386 ( because @xmath387 and @xmath388 for @xmath389 ) .
hence , we can choose @xmath390 with @xmath391 for @xmath389 , and some words @xmath392 such that the set @xmath370 has cardinality @xmath393 since @xmath394 ( cf .
lemma [ l.most-good ] ) and @xmath395 ,
the proof of the lemma is complete . our third combinatorial lemma states that it is possible to cut excellent words in the subset @xmath396 provided by lemma [ l.excellent-words ] at certain good positions in such a way that one obtains a finite set @xmath397 with non - neglectible cardinality .
[ l.nice-cuts-of-excellent-words ] in the context of lemma [ l.excellent-words ] , given @xmath398 , let @xmath399 be the projection @xmath400 obtained by cutting a word @xmath401 at the positions @xmath402 and @xmath403 and discarding the words @xmath352 with @xmath404 and @xmath405 . we affirm that the cardinality of the set @xmath415 of excluded indices is @xmath416
indeed , suppose by contradiction that @xmath417 .
by definition , @xmath415 is the union of the finite family of intervals @xmath414 $ ] with @xmath412 .
now , it is not hard to see that , given any finite family of intervals @xmath418 , there exists a subfamily @xmath419 of _ disjoint _ intervals whose sum of lengths @xmath420 is at least _
half _ of the measure of @xmath421 applying this fact to the family of intervals defining @xmath415 , it follows that we can select a subfamily @xmath422 of pairs @xmath411 such that @xmath423 leading to disjoint intervals @xmath414 $ ] whose sum of lengths @xmath424 since @xmath425 , @xmath426 , were constructed so that @xmath367 ( cf .
lemma [ l.excellent-words ] ) and we are assuming ( by contradiction ) that @xmath417 , we deduce from the previous estimate that @xmath427 on the other hand , since @xmath412 for @xmath428 , we get that @xmath429 \,\forall\,(p , q)\in\mathcal{p}\}}\ ] ] because there are at most @xmath351 choices for @xmath313 for indices @xmath430 $ ] , @xmath314 . by plugging into the previous estimate
, we would obtain that @xmath431 however , by lemma [ l.excellent-words ] , we also have @xmath432 , so that @xmath433 a contradiction with our choice of @xmath434 .
once we know that the subset @xmath415 of excluded indices in @xmath413 has cardinality @xmath435 , we conclude that there are at least @xmath436 non - excluded indices .
since for each @xmath426 there are at most @xmath351 possibilities for @xmath437 , we deduce that there are two non - excluded indices @xmath406 such that @xmath407 and @xmath438 . by definition of non - excluded index , @xmath439 satisfies the conclusions of the lemma .
recall from remark [ r.symmetry-du-ds ] that our task is reduced to show that the complete shift @xmath441 associated to @xmath397 generates a cantor set @xmath442 with hausdorff dimension @xmath443 and @xmath444 for some @xmath225 .
note that @xmath445 is a @xmath58-dynamically defined cantor set associated to certain iterates of @xmath76 defined on the intervals @xmath134 , @xmath447 . in this situation , it is known from the usual bounded distortion property ( cf .
remark [ r.bounded-distortion ] ) that the hausdorff dimension and box counting dimensions of @xmath448 coincide and they satisfy @xmath449 since @xmath450 ( cf .
lemma [ l.nice-cuts-of-excellent-words ] ) and , for some constant @xmath140 , one has @xmath451 ( by the usual bounded distortion property cf .
remark [ r.bounded-distortion ] ) for each @xmath447 , we deduce from the previous estimate that @xmath452 now , recall that @xmath453 satisfy so that @xmath454 .
hence , by plugging this into the previous inequality ( and by recalling that @xmath301 ) , we obtain @xmath455 for @xmath456 sufficiently large . similarly , we also have that @xmath457 because @xmath458 is comparable to @xmath133 up to the multiplicative factor @xmath459 ( cf .
remark [ r.stable-unstable-sizes ] ) , we deduce from the computations of the previous paragraph that @xmath460 for @xmath456 sufficiently large . at this point
, it remains only to prove that @xmath444 for some @xmath225 .
for this sake , we denote by @xmath461 so that , by definition , the elements @xmath462 have the form @xmath463 with @xmath464 , @xmath465 , and @xmath466 @xmath467 for some words @xmath468 verifying @xmath469 @xmath470 in particular , an element of @xmath441 has the form @xmath471 where @xmath472 and @xmath473 are infinite concatenations of elements of @xmath310 and the symbol @xmath474 serves to mark the location of the entry of index @xmath475 of the bi - infinite sequence @xmath476 . in case i.a ) , we choose @xmath490 such that @xmath491 for any @xmath492 ( because of the local monotonicity of @xmath7 along stable and unstable manifolds ) . by , it follows that @xmath493 for some @xmath275 . on the other hand , by , we also know that , for some @xmath281 , the function @xmath7 obeys the lipschitz estimate @xmath494 for any @xmath495 . from these estimates , we obtain that @xmath496 @xmath497 for any @xmath495 and @xmath492 .
now , we observe that the usual bounded distortion property ( cf . remark [ r.bounded-distortion ] ) implies that @xmath498 for some @xmath499 . by plugging this information into the previous estimate
, we have @xmath496 @xmath500 since we are dealing with case i.a ) , i.e. , @xmath488 , we deduce that @xmath501 @xmath502 next , we note that @xmath503 if @xmath504 is sufficiently large : indeed , since @xmath505 , we know that @xmath506 ; on the other hand , the usual bounded distortion property ensures that @xmath507 for some constant @xmath508 , so that @xmath503 for @xmath509 . in particular , for @xmath302 sufficiently large , we have that @xmath510 for any @xmath495 and @xmath492 .
now , we recall that @xmath511 , so that @xmath512 by definition , this means that there are @xmath513 and @xmath514 with @xmath515 and , _ a fortiori _ , @xmath516 here , we used for the first equality . combining this with , we see that @xmath517 therefore , in case i.a ) , we conclude that @xmath518 where @xmath519 since @xmath525 and @xmath526 , we see from the usual bounded distortion property ( cf .
remark [ r.bounded-distortion ] ) that , if @xmath361 is sufficiently large , then @xmath527 for @xmath523 , and @xmath528 for @xmath485 . by plugging this into the argument for case i.a ) ,
one deduces that @xmath529 for @xmath523 , and @xmath530 for @xmath485 , where @xmath531 and @xmath532 [ p.horseshoe-extraction ] let @xmath536 , @xmath537 be a complete subshift associated to a finite alphabet @xmath310 of finite words on @xmath139 , and @xmath538 the subhorseshoe of @xmath8 associated to @xmath310 .
then , for each @xmath59 , there exists a subhorseshoe @xmath539 , a rectangle @xmath540 of some markov partition of @xmath541 , a @xmath211-diffeomorphism @xmath542 defined in a neighborhood of @xmath540 respecting the local stable and unstable foliations , and an integer @xmath543 such that @xmath544 and @xmath545 given @xmath59 , we consider the symbolic sequences @xmath550 associated to @xmath551 , @xmath552 and we take @xmath553 large enough such that @xmath554 and the subhorseshoe @xmath555 of @xmath546 associated to the complete subshift generated by the alphabet @xmath556 has hausdorff dimension @xmath557 denote by @xmath64 the rectangles of the markov partition of @xmath558 induced by @xmath559 . by construction , we can find an open set @xmath560 such that @xmath561 is disjoint from the markov rectangles @xmath562 associated to @xmath563 , @xmath564 , @xmath565 , and @xmath566 . in particular , there exists @xmath194 such that @xmath567 . hence ,
if we take an appropriate periodic point in @xmath568 with a symbolic sequence @xmath569 , then the sequences of the form @xmath570 with @xmath571 , @xmath572 , have the property that @xmath573 is attained for values of @xmath574 corresponding to the piece @xmath575 and , moreover , @xmath576 whenever @xmath577 does not correspond to @xmath575 . furthermore , @xmath578 for all @xmath579 and @xmath580 as above .
next , we denote by @xmath581 the markov rectangle associated to the periodic orbit @xmath582 and we define two maps @xmath583 and @xmath580 from @xmath584 to @xmath8 in the following way . given @xmath585 , let us denote by the corresponding sequence in @xmath441 by @xmath586 where @xmath587 for all @xmath588 .
we set @xmath589 for each @xmath588 , and we introduce the point @xmath590 , resp .
@xmath591 , of @xmath546 associated to the sequence @xmath592 resp .
@xmath593 indeed , we note that @xmath591 was constructed in such a way that @xmath597 for some @xmath574 . thus , we have a sequence @xmath598 with @xmath599 corresponding to a position in the piece @xmath600 of @xmath590 so that @xmath601 converges to @xmath602 and , _ a fortiori _
, @xmath603 also , if @xmath604 and @xmath605 are sequences where @xmath606 are positions in pieces @xmath607 of @xmath590 with the property that @xmath608 then one of the following two possibilities occur : the sequence @xmath609 has a bounded subsequence or the sequence @xmath609 is unbounded . in the former case , we can find @xmath610 such that @xmath611 has a subsequence converging to @xmath612 and , hence , @xmath613 in the latter case , there exists a subsequence of @xmath611 converging to an element @xmath614 , but this is a contradiction with because @xmath615 this proves our claim .
it follows from our claim that @xmath616 where @xmath617 .
therefore , one of the closed subsets @xmath618 has non - empty interior in @xmath619 ( for some @xmath620 ) and , _ a fortiori _ , we can choose a subhorseshoe @xmath621 and a rectangle of @xmath622 of some markov partition of @xmath621 such that @xmath623 this completes the proof of the proposition .
let @xmath628 with @xmath629 and @xmath194 . by proposition [ p.ta ] , we can find @xmath225 and a complete subshift @xmath444 on a finite alphabet @xmath310 on finite words of @xmath139 such that
@xmath630 by proposition [ p.horseshoe-extraction ] and theorem [ t.dimension-formula ] , we see that @xmath631 | arxiv |
Champs is a former commune in the Orne department in north-western France. On 1 January 2016, it was merged into the new commune of Tourouvre au Perche.
See also
Communes of the Orne department
References
Category:Former communes of Orne
Category:Orne communes articles needing translation from French Wikipedia | wikipedia |
Oh My Goddess! Oh a Wish
Frigga sat and looked at the wish list for the next fifty candidates. It had arrived; the wish that she knew was coming was finally here and now so was the problem of who was to get it. She sat back in her chair and talked to Kami sama.
Belldandy answered the call, it was her first this week "Hello you've reached the Goddess Technical Helpline, we will be there in a moment to grant your access request" She put the phone down and watched the mirror accept the destination then stepped through.
She stepped out into the bathroom of a western house and looked around, a single man lived here she looked at the litter tray, with a cat. She smiled as she walked out of the door "Hello"
"Interesting, I'm in the lounge" the voice was weary but interested. There was no hint of fear, rather amusement. Belldandy looked and saw the light coming from the open door, then a man appeared and looked at her his eyebrows rose as he saw her "Tea or coffee?"
"Coffee please"
"Sorry for the mess, make yourself comfortable" he indicated the room he'd come from and walked unsteadily into the kitchen.
Belldandy looked at the room, it was middle sized by the standards of the day, there were two chairs and a glass table a desk and some racks with books CD's and DVD's on the shelves, the radio was quietly playing some classical music. It was a comfortable room with a few papers scattered about but lonely at the same time, there were little indications of others in the room, visitors were infrequent. She sat in the chair, this was well loved by both residents, the man and the cat, almost as if summonsed the cat appeared hopped onto the table and walked towards her, it stopped and looked closely into her eyes then sat on her lap and curled up purring loudly.
"I'll take him off if you want" the man said as he placed a small tray next to her "I'm sorry but I don't use milk"
"He's fine here" Belldandy sipped her coffee "It's very nice, I don't need the sugar"
She watched as he took his own "I do" he grinned then drank his own "Now who and what are you?"
"My name is Belldandy I'm a goddess and I've come to grant you a wish; one wish only" she held up a single finger. This was the part Belldandy enjoyed as she could read what he really wanted but as she read her smile faded and her mouth formed an O of shock.
"Looks like you know what I want; drink your coffee first and then I'll tidy up a little" he made another cigarette and lit it drawing the smoke deep.
"Ah may I use your phone please" Belldandy asked when he'd finished his smoke
He handed over his phone "I'll go and get ready"
Belldandy turned as she left the bedroom and looked back at the man lying on the bed, tears were starting in her eyes as she made her way back to the mirror. Frigga was waiting when she arrived.
"I'm sorry it had to be you for that one, but Kami said that it had to be left to chance, go home and rest until you feel better"
She sat in her chair and turned her screen on, the cat butted her head "It's alright, he's at peace now" the cat curled into her lap and purred happily, he knew his old master had been in excruciating pain and now he had a new mistress.
End file.
| fanfiction |
Dragon Ball Z Cell Learns Something New
_**Cell learns something new.**_
Cell hovered above the Pacific Ocean. He knew Goku was on this planet somewhere, and it was simply a case of locating him.
What a stupid, pathetic planet. Honestly, only one person on this ridiculous rock had the power to stand up to him and that person wasn't even a native.
Once Goku was dead and gone, this useless place was next.
Where to look? Then, why look? Surely with as much power as Goku had, then it should be a cinch to sense him.
Right thought Cell. He looked around. Best do this on solid ground, flying without concentrating meant he might get hit by some flying machine or something, and that would do his reputation as a galaxy-class fighter no good at all.
He saw a small atoll not too far away. That'll do he thought and flew straight over and landed on the shore.
"Okaaayy" He said to himself, and then started to concentrate.
He reached out with his mind, feeling for power levels. He felt the minute power of sports stars, he let his mind wander all over America, then Europe, then Asia. Nothing.
Then he remembered, Goku raised his power level when he fought, so sensing like this was futile – under everyday circumstances, and especially from a distance, he'd vanish in the crowd.
Cell ambled over to a nearby patch of grass and sat on it. "Bugger!" he said with feeling.
Another plan needed then. How else could he find that awkward bloody Saiyan?
"Why search for him? Why not make him come to me?" Exclaimed the annoyed Cell.
All I have to do, thought Cell, is to go to some group of humans and cause enough mayhem that Goku comes running .
Right, where's that best place? What do I know about these people? America. That'd do.
With that, Cell flew over to the United States.
He stopped a few miles from the California coast. "Okay" he said to himself. "I'm here, now what? I feel like an unprepared tourist. I know nothing of these people."
He went higher and gazed over the country before him.
"Let's find somewhere to wreck" he muttered.
He chose a direction and flew for a while and found himself over what he would later find out to be Virginia. He looked down and focussed on a random building. He flew lower, and realised he could hear something coming from his target. It was something he'd never heard before, or at least never paid attention to. He was intrigued and had to find out what he was listening to. He considered his target from above: A w-shaped building with a vaguely loudhailer-shaped building very close to it. It was early in the evening, so he figured he could land on the roof without being noticed, so he gently touched down, and crept to the edge.
Something about this...this...noise was...good.
Goku could wait; Cell found he was enjoying what he was hearing. He stood for a while just listening and trying to comprehend. Someone, some human, was...singing.
He looked down over the edge at all the earthlings. They were all reacting to this...sound. He had to know more.
Question 1: Where am I?
Question 2: What am I hearing, and why do I like it?
Question 3: How do I find out without disturbing the sound?
He retreated back to the centre of the roof, and gently flew up so that he could gauge his surroundings better. He saw a road sign and flew over to it: It declared the building to be 'The Wolf Trap'. "Interesting name" he muttered.
He flew closer to the W-shaped building and noticed an advert on the wall, proclaiming tonight to be "Women of Country". He went to the building's roof and watched the stage, transfixed as the singer launched into another song.
He sat down. Fighting Goku, or anyone else for that matter could go to hell. This was so much better. He vowed to learn more about this 'Country Music", and watching the rest of this - he sought for a word – performance would be a start.
As he sat on the roof, he started idly thinking as the music washed over him: Why was I created? To defeat pretty much everyone around and then destroy the Earth. If I destroy the earth, all this will be gone, and I don't like that idea one bit. Maybe all this fighting isn't a good idea. That thought seemed to strike at the very core of his being, as that was why he was made in the first place. This music seemed to be tearing down everything he was. Before hearing this, it was destroy and kill all the way, now that just didn't matter anymore.
An hour and a half later, the concert came to a close. Cell was still on the roof of the W-shaped building, in a mild state of shock.
Why did Dr. Gero or his computer not tell him of all these things? Useless old fart. No matter, he knew now and that seemed to be important.
He flew off into the darkness to see where this new train of thought would take him.
A year later Goku was in Japan. Chi-chi had talked him into taking her to a concert in Osaka. As they entered the arena, Goku saw a familiar figure. Chi-chi looked at him "What's wrong Goku?" she asked.
"It's Cell. What the hell is he doing here?" Goku could feel his energy levels automatically start to rise.
Cell turned around and grinned the biggest grin "Goku! I would just love to stop and fight, but this is neither the time nor the place. Actually that being said, no I wouldn't like to stop and fight. I'd much rather listed to the music if it's ok with you."
"Wha..what?" You always fight! It's what you do!" stammered the stunned Saiyan warrior.
"Nah, I'm over that now. I may have been created to destroy the planet, but to be honest, I'd rather learn guitar."
Goku blinked and then realised that Cell was wearing..jeans and a Hawaiian shirt.
"Oh." Said Goku. He couldn't work out if he was relieved, disappointed, or just plain confused.
"It's like this, warrior-boy. Last year I made a discovery: country music. Since then I've heard classical, rock, pop, rap, reggae and pub bands. As it turns out, fighting is rubbish compared to that. I've even tried Karaoke. How strange is that? I have to say no-one is more surprised than me. So if you'll excuse me, I've got a front row seat to find."
With that, Cell turned and made his way to his place.
After the concert, he did indeed start to learn guitar. And thoroughly loves it.
End file.
| fanfiction |
How is voltage generated due to difference in temperature in a thermocouple? [duplicate]
**This question already has answers here**:
[Thermo-Emf variation with temperature](/questions/112270/thermo-emf-variation-with-temperature)
(2 answers)
Closed 9 years ago.
How is voltage generated due to difference in temperature between the two junctions of a thermocouple? What happens to the electrons at the junctions of the two materials and how do they behave when they are immersed in hot and cold medium?
If you take a length of copper wire at the same temperature, then the average kinetic energy of an electron, and therefore electron density, is the same through out the wire, balancing the metal ion density. The copper wire is electrically neutral at every point on average.
Now heat one end. This raises the average kinetic energy of electrons while reducing the electron density here, giving rise to an electron charge density gradient along the wire. The metal ion density meanwhile doesn't change much in comparison because of their much higher mass, and you no longer have cancellation of the electron and metal ion charge densities at each point along the wire. Hence you get a net charge density gradient along the wire, an electric field that opposes any further average diffusion of electrons at every point at equilibrium, and therefore a voltage across the ends.
It turns out that the voltage you get across the ends depends upon the type of metal you use because of its physical properties. Obviously, this is going to influence how mobile the electrons are, and their eventual density in equilibrium when you heat one end.
So upon connecting two different wires in series but heated at the junction, you'll get a net voltage at the other ends maintained at the same temperature, because the voltage across the ends of each wire are different.
| stackexchange/physics |
prostate cancer ( cap ) is the second leading cause of cancer death among american men , killing 29,000 men each year .
the us preventive services task force ( uspstf ) cited the substantial rate of prostate cancer overdiagnosis ( 1750 % ) and overtreatment as justification for discouraging the use of prostate specific antigen ( psa ) for early detection of prostate cancer @xcite.the problem of overdiagnosis is caused by the inability to distinguish aggressive cancer from non - aggressive cancer .
preferential detection of aggressive cancers would improve outcomes in men who need treatment while sparing men with non - aggressive cancers the harms of treatment .
this is critically important because non - aggressive cancers are slow growing and rarely harmful , while aggressive cancers pose a substantial risk of morbidity and mortally @xcite . yet , current methods of prostate cancer detection , including the use of conventional ` blind ' biopsy , detect more non - aggressive cancers than aggressive cancers .
multiparametric mr is a powerful imaging technique that is useful for detection of aggressive cap .
however , evaluation of the images is plagued by inter - radiologist variability .
state - of - the - art computerized learning models for multiparametric imaging are often affected either by the inaccuracy introduced by improper registration of multiparametric mr images , or by overfitting caused by the incorporation of a large set of potentially relevant imaging features @xcite . moreover ,
current computerized diagnosis systems are hindered by the computational complexity of processing a large set of features ; in fact , it is believed that only a fraction of them are important for the characterization of prostate cancer aggressiveness . to tackle these issues ,
a common trend in the literature is to compute only a few representative features from the multi parametric mr images for cap diagnosis ( e.g. statistical features @xcite , histogram based features @xcite , edge - based @xcite , texture features @xcite ) .
however , the manual selection of features is biased since the selected small feature subset captures only a restricted characteristic of the prostate cancer lesion . to the best of our knowledge ,
no systematic study exists that evaluates the performance of a wide range of distinct quantitative imaging features for efficient characterization of aggressive cancer tissue in the prostate gland .
the purpose of this study is to develop an automated multiparametric image analysis model that can recognize aggressive cap ( gleason score @xmath0 7 ) based on a set of discriminative imaging features computed from three multiparameteric mr image sequences : t2 weighted imaging , diffusion weighted imaging ( dwi ) , and apparent diffusion coefficient mapping ( adc ) .
the aims are : ( i ) perform precise selection of the most discriminative group of quantitative imaging features from a large feature space that captures a comprehensive description of the lesion and its surrounding tissue extracted from multiparametric mr images ; ( ii ) incorporate the discriminating features into a prediction model that can provide fast , efficient and reproducible diagnosis of cap .
we acquired multiparametric mri exams in 79 patients : 40 patients with aggressive cancer ( gleason score @xmath0 7 ) and 39 patients with non - aggressive cancer ( gleason score < 7 ) .
for each patient , the multiparametric mr image set includes t2-weighted ( 3.0 t , 3@xmath1 slice thickness ) images , diffusion - weighted images ( b values @xmath2 ) and apparent diffusion coefficient maps .
all the images were acquired in the axial plane , and an expert radiologist identified and circumscribed the suspicious lesion in a single slice through the largest section of the lesion on each sequence .
the histopathology result of the image - targeted biopsy using mri - ultrasound fusion was recorded for each patient , including the gleason score .
the gleason score varies from 0 - 10 , with 10 representing the most aggressive cancer and 0 representing benign lesion .
our proposed approach is shown in fig . [ fig : workflow1 ] where the key components are the following : * creation of feature matrix * - we compute a comprehensive set of quantitative imaging features from the multiparametric mr images that are potentially relevant in delineating an exhaustive characterization of a lesion in the prostate gland and the normal tissue surrounding the lesion .
table [ table : features ] shows the quantitative features that we extract , which is a broad and overlapping range of features that captures a comprehensive set of characteristics of the lesion and the surrounding tissue . in total , we extract 488 dimensional feature vector from each mr image sequence and concatenate them into a large feature matrix with 1464 features : @xmath3=\{f_{adc}[488],f_{dwi}[488],f_{t2}[488]\}$ ] , where @xmath4 $ ] , @xmath5 $ ] , @xmath6 $ ] are the features extracted from adc , dwi and t2 images . after the computation , we normalized the feature matrix @xmath3 $ ] so that each feature vector ( a column in @xmath3 $ ] ) are centered at 0 with a standard deviation of 1 .
* selection of discriminative features and train the computerized model * - we have created a prediction model based on elasticnet regularized regression @xcite that combines @xmath7 penalties of lasso and @xmath8 penalties of ridge to overcome the limitations of incorporating high dimensional features for relatively small number of samples .
based on the gleason score derived from the biopsy results , the patient cohort is divided into two groups : ( i ) aggressive - gleason score @xmath0 7 , and ( 2 ) non - aggressive - gleason score @xmath9 7 .
the biopsy based classification ground truth and the normalized feature matrix ( @xmath3 $ ] ) are the only inputs to our predictive model .
we performed shrinkage of the large quantitative feature matrix ( @xmath3 $ ] ) while maintaining the pairwise correlation between features , and selected a set of discriminative features for distinguishing aggressive from non - aggressive tumor type .
finally , training and testing of the model was conducted using 10-fold cross - validation , and we evaluated the accuracy of cap aggressiveness diagnosis by constructing a receiver operating characteristic ( roc ) curve .
the ranking of the imaging features is derived by analyzing the coefficient of the features computed by the 10 fold cross validated elastic net .
we achieved 58% sensitivity and 87% specificity at an roc operating point where the model gave the best trade off between sensitivity and specificity . without registering the multiparametric mr images
, the roc curve for the cap aggressiveness diagnosis yielded an area under the curve ( auc ) of 0.73 ( see figure [ fig:2].a . ) which is comparable with the auc value achieved by a published method @xcite that performs elastic registration between multiparametric mr images .
moreover , our model not only derives a diagnosis , but it allows the clinicians to reason on the computerized diagnosis outcome by presenting the multiparametric image feature ranking .
figure [ fig:2].b shows a trace plot of a grid of lambda values ( 100 values of lambda ) used in the model and the corresponding feature coefficient values generated by the model . by exploiting the trace plot , in figure
[ fig:2].c we present digest version of the feature selection results of the model which produced maximum auc value .
the feature acronyms are the same as in table [ table : features ] , concatenated with image sequence identifier at the front . on total
, only 44 discriminative predictors were selected from the feature matrix @xmath3 $ ] . the lesion boundary roughness feature computed from the diffusion weighted image
is ranked as the most dominant feature ( figure [ fig:2].c .
row highlighted in blue ) . lesion shape and texture extracted from
t2 mr images appeared to be the second and third most discriminative features for detection .
texture and contrast profile of the lesion computed from adc maps are ranked within top ten features , whereas the lesion contrast profile is not discriminative for t2 . in our model with multiparametric mr imaging , diffusion weighted imaging is ranked as the most informative sequence for cap aggressiveness detection , while when the diffusion weighted imaging anlyzed alone , the auc value was 0.60 .
in the paper , we propose a method for classifying the cap aggressiveness from quantitative analysis of features extracted from multiparametric mri images .
our method uses three different multiparametric mr image sequences , extracts quantitative image features , and incorporates learning from the aggressiveness classification based on the gleason score by utilizing the most discriminative features .
interestingly , the top five discriminative features are extracted from either dwi or t2 mri , and the feature with largest coefficient value , dwi lesion boundary , represents a novel feature for predicting prostate cancer aggressiveness that is not currently examined by radiologists to assess prostate lesions .
the model allows real time feature extraction as well as automatic classification for unknown cases .
our method is also advantageous in that we need not register the multiparametric mr images .
our results appear promising on our limited sized dataset .
studies in larger independent datasets would be helpful to confirm our results .
our study also was limited to analysis of 2d images , and volumetric analysis of features could improve the results . in the future
, we will extend our model by including a more comprehensive volumetric characterization of the lesion .
k. chamie , g. a. sonn , d. s. finley , n. tan , d. j. margolis , s. s. raman , s. natarajan , j. huang , and r. e. reiter , `` the role of magnetic resonance imaging in delineating clinically significant prostate cancer , '' _ urology _ , vol .
83 , no . 2 ,
pp . 369375 , 2014 .
s. wang , k. burtt , b. turkbey , p. choyke , and r. m. summers , `` computer aided - diagnosis of prostate cancer on multiparametric mri : a technical review of current research , '' _ biomed research international _ , vol .
2014 , 2014 .
p. c. vos , t. hambrock , c. a. hulsbergen - van de kaa , j. j. ftterer , j. o. barentsz , and h. j. huisman , `` computerized analysis of prostate lesions in the peripheral zone using dynamic contrast enhanced mri , '' _ medical physics _
35 , no . 3 , pp .
888899 , 2008 .
p. liu , s. wang , b. turkbey , k. grant , p. pinto , p. choyke , b. j. wood , and r. m. summers , `` a prostate cancer computer - aided diagnosis system using multimodal magnetic resonance imaging and targeted biopsy labels , '' in _ spie medical imaging_.1em plus 0.5em minus 0.4em international society for optics and photonics , 2013 , pp .
86701g86701 g .
p. tiwari , j. kurhanewicz , m. rosen , and a. madabhushi , `` semi supervised multi kernel ( sesmik ) graph embedding : identifying aggressive prostate cancer via magnetic resonance imaging and spectroscopy , '' in _ international conference on medical image computing and computer - assisted intervention_.1em plus 0.5em minus 0.4emspringer , 2010 , pp .
666673 .
e. niaf , o. rouvire , f. mge - lechevallier , f. bratan , and c. lartizien , `` computer - aided diagnosis of prostate cancer in the peripheral zone using multiparametric mri , '' _ physics in medicine and biology _ , vol .
57 , no . 12 , p. 3833
, 2012 .
s. viswanath , b. n. bloch , j. chappelow , p. patel , n. rofsky , r. lenkinski , e. genega , and a. madabhushi , `` enhanced multi - protocol analysis via intelligent supervised embedding ( empravise ) : detecting prostate cancer on multi - parametric mri , '' in _ spie medical imaging_.1em plus 0.5em minus 0.4eminternational society for optics and photonics , 2011 , pp . | arxiv |
Defining Kraus operators with normal distribution
I am interested in defining Kraus operators which allow you to define quantum measurements peaked at some basis state. To this end I am considering the Normal Distribution. Consider **a finite set of basis states** $\{ |x \rangle\}\_x$ and a set of quantum measurement operators of the form
$$A\_C = \sum\_x \sqrt{\mathrm{Pr}(x|C)} |x \rangle \langle x|.$$
I want to prove that $A\_C$ defines valid **Kraus operators**. If I consider the Normal distribution
$$\mathrm{Pr}(x|C) = \frac{1}{\sqrt{2 \pi \sigma^2}}e^{-\frac{(x-C)^2}{2 \sigma^2}}~~~~\text{where } x \in \{-M,-M+1,...,M \}$$
where $C$ is the mean, $x$ the random variable and $\sigma^2$ the variance, then
$$\int\_{-\infty}^\infty \mathrm{Pr}(X=x|C)\,dC = \frac{1}{\sqrt{2 \pi \sigma^2}}\int\_{-\infty}^{\infty}e^{-\frac{(x-C)^2}{2 \sigma^2}}dC = 1.$$
Thus it follows that
$$\int\_{C}A\_C^{\dagger}A\_CdC = \int\_{-\infty}^{\infty} \sum\_{x}\mathrm{Pr}(x|C) |x \rangle \langle x | dC = \sum\_x \bigg[\int\_{-\infty}^{\infty}\mathrm{Pr}(x|C)dC\bigg]|x \rangle \langle x | = \sum\_x |x \rangle \langle x | = 1 $$
hence we have shown $$\int\_{C}A\_{C}^{\dagger}A\_C dC = 1$$ hence $A\_C$ satisfies the conditions necessary for $\{A\_C \}\_C$ to be Kraus operators.
**Question:**
Please advise if my working and conclusion that $\{A\_c \}\_C$ are valid Kraus operators is correct? Also, there are only a finite number of states $\{ |x \rangle \}\_{x}$ yet the index $C$ is continuous and unbounded, so for some $C$ (the mean), the peak of $Pr(x|C)$ will be well outside the range of any $|x \rangle$. I don't think that this is a problem, but I'm not sure about this...
Thanks.
>
> Please advise if my working and conclusion that $\{A\_c \}\_C$ are valid Kraus operators is correct?
>
>
>
Your workings and your conclusion that $\{A\_c \}\_C$ are valid Kraus operators are correct.
>
> Also, there are only a finite number of states $\{ |x \rangle \}\_{x}$ yet the index $C$ is continuous and unbounded, so for some $C$ (the mean), the peak of $Pr(x|C)$ will be well outside the range of any $|x \rangle$. I don't think that this is a problem, but I'm not sure about this...
>
>
>
This is not a problem.
If all the $x$ in your finite set are bounded by some constant $|x|<M$, and you take some $C>M$, then you know that the norm of the corresponding Kraus operator is
\begin{align}
||A\_C||^2
& = \mathrm{Tr}(A\_C^\dagger A\_C)
= \mathrm{Tr}\mathopen{}\left(\sum\_x \mathrm{Pr}(x|C)|x \rangle \langle x|\right)
= \sum\_x \mathrm{Pr}(x|C)
\\ & \leq \sum\_x \mathrm{Pr}(M|C)
= N \, \mathrm{Pr}(M|C)
\end{align}
if you have $N$ measurements, and this is exponentially small in $(C-M)^2/\sigma^2$. In other words, those Kraus operators are exponentially close to zero and they do not meaningfully contribute to anything.
>
> I would like some reassurance about some minor technical aspect of my workings, and some validation of my status as a competent student of physics.
>
>
>
For the sorts of questions you've been asking, we can indeed provide that, but I would suggest that this is not necessarily the best use of your rep or of everyone's time. This kind of interaction is much more fruitful in person, and I would strongly encourage you to find a faculty member (or other such professional) to whom you can ask this kind of thing in person. It is quicker but, more importantly, the personal and interpersonal aspects of that kind of relationship are even more important to developing a healthy relationship with physics.
(Or, more specifically: this is obviously my interpretation, and I apologise if I'm overstepping here. However, please do take a good look at why exactly you're asking this style of question, where you've already solved the problem in full, and whether there are other ways to handle them that give you more in the end.)
| stackexchange/physics |
Electro-pop outfit MMEADOWS is Kristin Slipp and Cole Kamen-Green. Kristin and Cole are perhaps best known for their work as part of Cuddle Magic -- a Brooklyn and Philadelphia-based chamber-pop band that Bob Boilen (of NPR's All Songs Considered) says is one of his new favorites -- but the duo, together and separately, have also written and recorded with Beyonce, performed with Cyndi Lauper and Kimbra, and made beats with Yuka C. Honda.
Until 2016, with the surprise release of a refreshing, modernized rework of Sade's "No Ordinary Love," Kristin and Cole managed to keep MMEADOWS [mostly] a secret, meeting late at night to chip away at a body of work. The quasi- clandestine nature and dark setting of these midnight meetings found a way into the duo's new music through undulating low frequencies, ecstatic vocal melodies, and sizzling analog synths.
"Kristin Slipp's vocal is a mesmerizing tool, reminiscent of Sylvan Esso in the way it punctuates the surrounding instrumentation; thought the track itself offers something far more restrained."
"Their deep-seeded love for heart wrenching melodies and passionate lines are evident in singer Kristin's soul as it pours from the speaker..." | slim_pajama |
Harry Potter The Unspeakable Mysteries of the Lemon Drop
**Title:** The Unspeakable Mysteries of the Lemon Drop
**Summery: **Where were the Unspeakables on that fateful night that Harry Potter and friends journeyed to the Ministry of Magic? What does the locked room in the Department of Mysteries contain? WHAT DO DUMBLEDOR'S LEMON DROPS MEAN!?
**Rating:** K+
**Warning:** This OneShot will make you stupider with each sentence. Proceed with caution…
**Disclaimer:** I hereby disavow all connection to the Harry Potter Series. This message will self destruct in five seconds…
* * *
_Once more the wall spun and became still again. Harry approached a door at random and pushed. It did not move. _
_"What's wrong?" said Hermione. _
_"It's…locked…" said Harry, throwing his weight at the door, but it did not budge. _
_"This is it, then, isn't it?" said Ron excitedly, joining Harry in the attempt to force the door open. "Bound to be!" _
_"Get out of the way!" said Hermione sharply. She pointed her wand at the place where a lock would have been on an ordinary door and said, "_Alohomora_!" _
_Nothing happened. _
_"Sirius's knife!" said Harry, and he pulled it out from inside his robes and slid it into the crack between the door and the wall. The others all watched eagerly as he ran it from top to bottom, withdrew it, and then flung his shoulder again at the door. It remained as firmly shut as ever. What was more, when Harry looked down at the knife, he saw that the blade had melted. _
_"Right, we're leaving that room," said Hermione decisively. _
_"But what if that's the one?" said Ron, staring at it with a mixture of apprehension and longing. _
_"It can't be, Harry could get through all the doors in his dream," said Hermione, marking the door with another fiery cross as Harry replaced the now-useless handle of Sirius's knife into his pocket. _
_"You know what could be in there?" said Luna eagerly, as the wall started to spin yet again. _
_"Something blibbering, no doubt," said Hermione under her breath, and Neville gave a nervous little laugh. _
—Harry Potter and the Order of the Phoenix, pages 775-776, American Version.
* * *
Ah, if only they knew. For at this moment, not feet away from the other side of the door threw which Harry and Co. had just tried to force entry, a topic of the utmost serious of sorts was commencing…
"Clearly the sugary substances express how sweet living life can be!" Unspeakable number 56 was saying, gesticulating wildly. "Or perhaps how joyful the Light is when it had triumphed over the Dark!" Scribes scratched franticly as the crowds ponder this development.
"Surely the term 'CANDIES' must be an acronym of something much greater!" excitable number 42, who was posing as a homeless person, called out. "Perhaps **C**lassified **A**gency of** N**otoriously **D**angerous** I**mportant **E**dible **S**ubstances?"
The crowd fell silent, contemplating just how psychologically deep Albus Dumbledore's web of unhealthy food stuffs was. After meditating on this matter for many days and many nights (though it was only a few moments really), a woman stood to put her two cents in.
"We must recall that Albus Dumbledore offers these alleged confections to all that enter his domain." the lady mused. "Perhaps he is, indeed, referring to how sweet a second chance is."
"And he offers these sugar coated items to represent the offering of a second chance to all!" another women cried out, following the line of thinking. The crowd murmured their agreement, and again commented on the old coot's cleverness.
"He often offers an object called a 'lemon drop'." a man with gray hair observed, motioning for his presentation to be brought in. The experiment was floated in by a team of highly trained Unspeakable. "Notice how this 'hard candy' seemed to dissolve when saliva is added!" the man pointed out as he added exactly 20 mL of human saliva to a lemon drop strait from the Headmaster's office. The crowd gasped as the sugary treat slowly began to melt.
"Surely Dumbledore is implying that existence melts away within the human race!" someone shrieked. The crowd gasped again and looked at the gooey lemon drop with a new respect.
"I think that Dumbles is just a weirdo with an obsession for candy!" a little boy offered his opinion. The crowd gaped at the child's immaturity.
"Number 89, GET THAT KID OUT OF HERE!" the Head of Department yelled, eyes popping. "That child is _obviously_ oblivious to the subtleties that comprise Albus Dumbledore's mind!"
"Come on, Simon." 89 mumbled to his still-grinning son. "You just don't understand the implications of the world."
"What are those crazies doing, stealing Mr. Dumbles' lemon drops?" 'Simon' asked his father curiously as they made their way to the doors.
"It'll all become clear when you're older…"
As the pair's voices' and footsteps faded, the Council of Unspeakable regained order.
The Head of Department massaged his temples, muttering, "I hate bring-your-child-to-work-day," before focusing once more on the center of the room.
A man in the front row poked the icky-drop cautiously, as if expecting the yellow stuff to eat him.
"This is beyond mortal comprehension!" the Head Unspeakable continued louder now, eyeing the icky sweet with fear. "We must act on this!"
"What shall we do?" a brunette beside him gasped.
"There is no hiding from the evidence!" a blonde man reasoned fearfully, pointing at the puddle of yuck which was now attracting flies.
"We shall do what all governments do when discovering something that will change the world!" the second-in-command declared. The room waited with bated breath for the verdict to be announced. "We must..." the guy paused for dramatic affect.
"Deny it vehemently, and lock it away for all of time!"
There was a collective sigh of relief from his co-workers as they agreed with this suggestion. As one, they all rose to their feet and exited the Room of Mysteries into the circular room that connected the entire Department to one another. The Head Unspeakable locked the door behind him with a flourish and added the password to close it.
"Under the rug!" he cried. After the door closed with that funny squishing sound that he absolutely loved, the Head Unspeakable turned around with the rest of the team, ready to exit gloriously into the main part of the Ministry in all their mysterious glory, when he suddenly caught sight of a very much demolished chamber.
Silence. Then-
"89! I'll heave your head for this!" Number 1 howled, stamping his feet immaturely. "77 and 45! CLEAN IT UP!"
"I'm not cleaning _that_ up!" said numbers whined.
"Do it _NOW_, DAMMNIT!" the Head shrieked, eyes popping.
"Why don't _you_ do it then!?" number 77 bleated plaintively.
"BECAUSE _I'M_ THE BOSS!" was the screeched reply. "It says so on my underwear!"
"How do we know what you say is true?" one guy asked suspiciously.
"You must present evidence," random guy number 34 agreed.
"I'm not showing you my _underwear_!"
"Then _I'm_ not cleaning this up!" number 77 squealed indignantly. The other Unspeakables nodded solemnly in agreement.
That seemed fair.
"FINE!" the Head Unspeakable shouted, eager to not have to clean, and turning around to speak the password. "Then we shall have a meeting to decide exactly who shall clean the Circle Room!"
There was general assent as the Unspeakables filed once more into the Room of Mysteries.
Just as the last Unspeakable shut the door, another across the hall sprung open with force, and a mad-looking woman rushed threw the room, shortly thereafter followed by a murderous-looking boy.
But that was of no importance to the oblivious Unspeakables of the British Ministry of Magic. There we far more important things to be discussed on this night…
* * *
What can I say… the plot bunny ate my homework… Review?
**—Skyfly64**
End file.
| fanfiction |
Xbox Addict Asylum > Original Xbox > General Discussions > Post your thoughts for new game ideas
View Full Version : Post your thoughts for new game ideas
I would like to see a High Lander game. Going around chopping off heads through time. It could be a really neat game with an endless story.
Anyone remember the old games Life Force, Contra, Gost & Gobblins, by Nintendo. Geat games.
I wish the Play Station tiles, Tencu 2, and Contra come to the x-box.
siayajin
Not exactly a new game idea, but with the sudden influx of "retro games" like metroid, ninja gaiden, contra, and even robocop, why haven't developers thought about redoing a Teenage Mutant Ninja Turtles game?
It's something I couldn't figure out. I mean, it was a great arcade game back in the day, yet when it was released for the consoles, Konami never made it into a 4player game, even though there are 4 turtles to choose from, along with at least 30 good and bad guys, and don't forget the 4player adapters so it's not like having 4 people playing wasn't possible.
If they were to make it into a game like Hunter, which is a great example of a 4 player action game, it would definitely be fun to play, like a lighter side to Hunter. Maybe even some melee mini games on the side. But please, don't do another TMNT fighting game, or at least make it a good fighting game this time.
Crazy Joe
what i don't get is why Midway hasn't made a new NBA Jam, they have made games for every other sport, but abandoned the original midway sports franchise. | slim_pajama |
Roswell 1. Introduction
****
When I am King
by Jeevus LaJiggles
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****
Introductory Information
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Disclaimer: I'll say this once and have it stand for all chapters. I don't own Roswell or any of its characters. I do own the original characters listed below, as well as any that may appear later. The story is mine as well. If you want to borrow any of the characters just let me know and make sure they're returned safely.
This story takes place approximately 18 years after Graduation. All of the events in the original series occurred.
Shortly after graduation the gang settled in a small town about a half hour outside of Boston. Michael and Maria, realizing they were meant to be together, married shortly thereafter. Within a year, both Maria and Liz were pregnant. Liz gave birth to a daughter, Elena Isabel Evans, on November 8, 2003. Maria had twins, a boy and a girl, on December 29, 2003. The boy was Nathan Michael Guerin and the girl was Abigail Rose Guerin. Not long after the births, Ava came to Roswell to search out her duplicate. Finding the entire pod squad gone, along with their human friends, she turned to Sean, another drifter like herself. Lonnie and Rath had long since killed one another and she was all alone, as was he, so they went in search of the others, finding them based on information given by Amy DeLuca-Valenti. Ava and Sean settled down with the others, who were glad to accept her not only because she had proven herself loyal in the past, but also because of the warning given to Liz by Future Max about needing Tess/Ava for survival.
Years passed and the children grew up happy and healthy with alien powers and tendencies as strong as their parents'. Eventually Kyle and Isabel drifted together, married, and, in 2014, had a son, Alexander James Valenti. Ava and Sean stayed together but never married and were always drifting from place to place, sometimes gone for months at a time but always returning.
This fic is based primarily on the teenage children of the Pod Squad. Though the original gang is mentioned, they only play a small role in the story. The original characters are as follows:
Abby Guerin: Daughter of Michael and Maria, twin sister to Nathan. She is very beautiful with her mother's looks and singing ability. She has long, golden brown hair and hazel eyes. She is sensible, unlike either of her parents, and is often lost inside her thoughts. She often feels like an outsider for several reasons, but is still a genuinely happy person.
Nathan (Nate) Guerin: Son of Michael and Maria, twin brother of Abby, boyfriend of Lane. He is tall, strong, and well-built, much like his father. He has short, well-managed :) sandy brown hair and sparkling green eyes. He is more carefree and fun-loving than his sister, making him the perfect match for Lane, but he also has a deep and caring side, which he shows primarily to his sister. He is very defensive of those he cares about.
Elena (Lane) Evans: Daughter of Max and Liz, girlfriend to Nate and best-friend to Abby. She is pretty and well-built, with dark curly hair to her shoulders and deep, dark eyes. She is a free-spirit (unlike Max and Liz) and will generally do anything (within reason) for a good time. She is also smart, though, and very self-assured.
Connor Anderson: the mystery man. Tall, dark, and handsome.
2. Prologue
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****
Prologue: The Beginning of a Great Tale
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__
Antar 2030
It was growing late and the young boy still would not settle himself. A bath would not soothe him and his eyes showed no signs of sleep. Frustrated, the father of the boy called the mother in.
"I can't get him to bed. He listens to you. Please?" she sighed but smiled.
"Very well." The man left the woman and the boy alone and she walked over to her young son, who was playing happily on the ground. She tilted his face up towards hers.
"Hello little one," she said. "Are you giving your father a hard time again?" The boy happily nodded.
"Daddy wants me to go to bed, but I don't want to," he replied, looking back at his toys and continuing his activity.
"Well, Daddy is right. It is time for bed. Past time, actually." She picked the squirming boy up and lay him in his bed, pulling the blankets snugly around him.
"But I'm not sleepy," he protested. She sat next to him on the bed and wrapped her arms around his small figure.
"How about I read you a story? Will that help you sleep?" He thought for a moment and then nodded.
"Read the High King story, Mommy," he begged, grabbing the well-worn book from the bedside table. The woman took the book and sighed.
"This one again?" she asked. He nodded. She opened the book and began, transporting the boy into a world of legend, where a magical couple would come to save the world. The story was a short one, and soon the woman had finished.
"And so the High King and Queen will come to rescue us from ourselves and, through their grace, knowledge, and power, we will be saved." The woman closed the book and set it on the bedside table. The boy looked up at her.
"Mommy, is that really the end of their story? Is that all?" She smiled at him.
"No," she said. "It is only the beginning. The beginning of a great tale." She closed her eyes and thought. Thought on the past, thought on the tale of the High King and his Queen, the couple that had saved the five worlds from themselves...
3. Strangers and Revelations
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****
Chapter 1: Strangers and Revelations
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__
July 2020
Abby jerked awake and gasped for breath. That was the fourth time in a week she had had that same dream, the dream she had been having for years. She was on a rocky mountain in the middle of the desert. All she could see was the stars, the V-shaped constellation burning brightest. Suddenly she realized there was another person with her. A man, whose face she couldn't see. All she knew was that he was familiar, yet a stranger. He reached out to take her hand and then, out of nowhere, a bright light surrounded them. The man began to lead her into the light and, right as they entered the object the light emanated from, she turned to look at his face. And then she woke up, sweating. "Damn," she said, looking at the clock. It was only 3:30 and she was sure she'd never get back to sleep. "You're going crazy, Abby. Seeing strange boys in your dreams; you're starting to ACT like an alien." She climbed out of her bed and sat at her desk and began writing. She really didn't know who the letters were to, but she wrote them nearly every night. Lately she had suspected they were meant for the guy in the dream, but she didn't know. After she had finished the letter she closed the journal she kept them in and went to the kitchen to get a cup of tea.
As she walked back upstairs to try to get some sleep, Abby noticed the light on in her brother's room. Knocking on the door, she was greeted with a grunt. A second later the door was unlocked and Abby wandered in, sitting on the bed.
"Up late, aren't you, little sis," Nathan said, sitting back down in his chair.
"I could say the same for you," she replied, using the same mocking tone. "Just climb back in the window?"
"Nah, I actually got in about midnight. I just couldn't sleep." Nate had been dating Elena, daughter of their parents' best friends, for a year and a half now, and they tended to stay out very late most nights.
"Oh, Lane wouldn't put out, huh?" Abby joked, tossing her brother's stuffed soccer ball in the air.
"Please, Abbs, don't ask about my sex life. You know how much that creeps me out," he begged, knocking the ball from her hand.
"Believe me, not as much as the idea of my best friend and twin brother sleeping together does," she whispered under her breath.
"Why are you up so late, anyway?" Nate asked.
"I just couldn't sleep," Abby sighed.
"Another dream?" he asked with concern. Abby nodded and he moved over to the bed, wrapping his arms around her. "See anything else this time." She shook her head.
"No, it's the same thing every time. Rocks, stars, guy, light. And then I wake up right before I see his face. I just wish I could see who it was in the dream. He feels so familiar, and yet so strange. It's driving me insane."
"Well, maybe if you try taking control of the dream, you can see where it's going."
"I tried, it's like the dream is in control of me. I don't like it. Maybe we could ask Aunt Isabel to dreamwalk me and find out what happens."
"Are you sure you want to do that? I mean, it may work, but first you'd have to deal with one of Uncle Max's crazy interrogations. Is it worth it?" Abby laughed.
"You're always so down on Uncle Max. He's just trying to take care of us."
"Just think about it before you do anything. You never know what else she might see, huh?" He nudged her in the shoulder and smiled, and she responded by punching him lightly in the gut.
"Well, I'm going to try to get some sleep. You should do the same. Remember, Di and Phil are coming into town tomorrow so we get the joy of helping Lane watch Alex while Uncle Max and Aunt Isabel go to pick them up." She walked towards the door.
"Oh believe me," he replied deviously, "I haven't forgotten how you're going to watch Alex while Lane and I have fun."
"You just keep thinking that, Space Boy," she laughed, adopting their mother's nickname for their father. "Just keep thinking that."
"Night, sis," he laughed, launching the stuffed soccer ball at the door as she closed it. Abby smiled and then went back to bed, hoping the rest of her night would remain dream-free.
~*~
"C'mon Abby, get up. We're gonna be late!" The disdainful sound of her brother's voice kept playing in her head, but Abby chose to ignore it. She pulled the blanket over her head to block the noise and sunlight, and burrowed back into her pillow. All would have been fine, if not for her brother's stupid powers. Within a few seconds she heard the "click" of the lock being opened and soon she was on the floor in a pile of covers. She looked up angrily to see her twin brother, Nathan, standing above her.
"Why I outta..." she grumbled, kicking him.
"You outta what?" he replied, mocking her as he dragged her to her feet. "Say 'thank you, darling big brother for waking me when I was running late'? That's what I thought."
"You're not my big brother and I'm going back to bed."
"10 minutes, baby. I won the 'let's get born race'. Now get dressed or no food for you. It's already 10:30." He walked out of the room. Realizing the time Abby rushed to get dressed and ready and then headed for the kitchen. Nate was already there, enjoying a bowl of some overly sugary cereal mixed with Tabasco sauce. Abby plopped down next to him.
"Why did you let me sleep so late?" she asked grumpily, pouring a bowl of cereal for herself. "We're supposed to be at the Evans's at one and you know I have a million things to do before then."
"You looked tired last night, like you haven't slept a lot lately. Since you were actually getting some sleep, I thought I'd let you enjoy it." Abby smiled at him.
"Wow," she exclaimed. "My brother showing he DOES know the meaning of the word 'kindness.' Call the police, he's been abducted and replaced with an alien.... oh wait, he IS an alien." Nate smirked at her crack and then responded by slyly shoving her out of her chair.
"Ow," she said, standing back up and rubbing the sore spot where she had fallen. "Was that really necessary?" He nodded and then went back to eating.
Shortly after finishing breakfast and running their errands, Abby and Nate jumped in the red Jetta their parents had bought them for their sixteenth birthday eight months ago and headed to the Evans's house, home of Max, Liz, and their best friend, Elena. Max and his sister Isabel were going to pick their adoptive parents, Phillip and Diane Evans, up at the airport and the whole clan was rallying at the Evans house to greet them. Of course, Max's wife Liz and Isabel's husband Kyle were at work, so that left the teenagers stuck with babysitting the youngest alien in the bunch, Kyle and Isabel's six year old son, Alex. Later in the evening there would be a dinner at the Evans house that everyone, Max, Liz, Elena, Kyle, Isabel, Alex, Michael, Maria, Abby, and Nathan, would attend to welcome Phillip and Diane. If Ava and Sean were in the area they might stop by, but it was unlikely since they often disappeared for weeks at a time inexplicably, traveling the world and avoiding the settled life that neither Ava nor Sean desired.
No one knew why Phillip and Diane had suddenly decided to visit, but word had it that there was a big surprise they planned on unveiling shortly after arrival.
Once at the Evans's, Abby took to playing with Alex while Nathan and Elena went to her room for some "quality time." Abby sighed but consented as usual. Back when they were children, the three had been like the Three Musketeers. They were the same age, had the same family, and shared the same secret. As they grew older, however, things changed. Lane and Abby became good girlfriends, sharing all their secrets, but Lane and Nate became a lot more than that. Eventually their attraction for one another became unbearable and they started dating when they were fourteen. Nearly two years later they were still together, but, as their relationship had grown stronger and more serious, Abby had begun to feel more and more left out. That's when her strange dreams had started.
About a half an hour had passed since Max and Isabel had left to wait for their parents at the airport and Abby and Alex were coloring happily in the living room when there was a knock on the door. Abby got up to answer it and found Phillip and Diane, as well as a stranger, on the other side.
"Phil, Diane, what are you guys doing here?" she exclaimed, going to hug Diane. "Your flight wasn't supposed to land for another 15 minutes."
"I know," Diane said, "but the airport bumped us off our flight and told us we could take an earlier one or a later one, so of course we came early."
"Well, I'm glad to see you," Abby said. At this point she noticed the stranger with them. He was a tall young man, about 19 or 20, with dark hair and dark eyes. He was very intense and the moment Abby locked eyes with him she lost all sense of time and reality.
"Grandma, Grandpa," Alex shouted, running to his grandparents and bringing Abby out of her daze. She blushed and stepped backwards.
"Why... Why don't you guys come in and I'll go get Lane," she stuttered, unable to remove her eyes from the dark haired man's gaze. Phil, Diane, and the boy walked in, Diane clutching Alex in a tight embrace. Abby ran up the stairs, flushing as she went to Lane's room and banged on the door.
"We're kinda in the middle of something," came an angry reply from the other side of the door.
"Well pull your pants up, Nate, 'cause Phil and Diane are here," Abby managed to order, still thinking about the man downstairs. She heard a few curse words muttered on the other side of the door and some banging around as her brother and Lane struggled to dress quickly. In a few seconds Lane burst through the door.
"Are my Dad and Aunt Iz with them?" she asked, gasping for breath and straightening her shirt.
"No, they took an earlier flight," Abby replied. Lane looked relieved. "But, there is some guy with them that I don't know, so no Czechoslovakian stuff, ok?" Nathan came out the door at that instant and, nodding in acquiescence, they all headed downstairs. Abby heard Lane gasp as they approached her grandparents and the boy, but she was too busy being lost in his eyes to take much notice. There was a short reunion between Lane and her grandparents before she greeted the young man.
"Oh, Lane, honey, we're sorry," Diane apologized. "It was rude of us not to introduce you. This is Connor, ..... your.... our.... a ... friend of ours. Connor, honey, this is Nathan, Abby, and our granddaughter Lane. We told you about them, remember?" Connor nodded, not taking his eyes from Abby.
"Yeah, it's nice to meet you all." Abby smiled at him and then examined her shoes. There was an awkward pause and then Lane spoke up.
"Well, I better go call Dad and Aunt Iz and tell them you're here." She paused. "Abby, why don't you come with me?" Abby looked confused and then got the idea.
"Oh, yeah, sure," she said. "We'll be right back." She and Lane rushed into the kitchen and Lane pulled her aside.
"I think I know that guy," she whispered.
"Do you think he's... you know... him?" Abby asked. Lane nodded.
"You saw him, how could he not be?"
"Well, we won't find out in here, so call your Dad and let's get back in there." Lane stared at her.
"Wait, why are you blushing so much? You wouldn't have a crush on 'mystery man,' would you?" Abby hit her in the shoulder and handed her the phone.
"Dial," she commanded. Lane took the phone and called her father. She informed him that the grandparents had arrived early and they had a guest with them. But, it was the tail end of the conversation that Connor and Nate caught as they walked into the kitchen in search of the girls.
"And Daddy," they heard Lane say. "I think he's your son. No, I don't know for sure, but I feel it, you know. I'm almost certain he's Zan.... why else would he be here?" She hung up the phone and looked up to see Connor and Nate standing in the doorway, Nate staring at Connor and looking like he had been hit by the truck of realization. There was a long silence and then Connor spoke.
"So, you know," was all he said.
4. Getting to Know You
*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*
****
Chapter 2: Getting to Know You
*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~
There was complete silence in the room for what seemed like an eternity. Finally Connor spoke.
"How'd you know.... or did you? I didn't just give myself away, did I?" Lane shook her head and spoke with great care.
"No, no, I... I had an idea. I don't really know how... it's just that you look so much like my dad... and, I don't know, I just feel it.... like I'm supposed to know you or something." Connor shook his head.
"Well, I guess it's better that it's out now, rather than me having to lie about it." Lane walked over and timidly went to hug him. He responded likewise.
"So, you're like, my brother than," she said, starting to cry happily. Connor smiled and nodded.
"Yeah, I always wanted a little sister and now I have one. I couldn't wait to meet you once Phil and Di told me about you." Lane wiped her eyes and smiled.
"I'm glad you're here.... and Dad will be too." Connor sighed.
"Let's just wait and see about that," he said. Lane shook her head.
"No, you don't know him like I do. He will be thrilled... he loves you. He talked about you all the time when I was little... I never really understood, but you made him happy." At this Abby, who had remained silent until now, took the opportunity and spoke up.
"She's right, you know," she said, locking eyes with Connor. "When we were little he always talked about you. We always thought it was kind of creepy, the way he was almost obsessed with you, but my dad explained that, just like if one of us was gone, he just wanted to remember you. I know Uncle Max will be thrilled.... you'll see." She paused, not knowing if she should say what else she was thinking. "And I'm glad you're here too.... now there's four. We always felt like there should be four." Nathan nodded in agreement, as did Lane. Connor silently thanked Abby in his mind, all while continuing to stare into her eyes. He did know why, but she seemed to be the most amazing person he had ever met. Eventually, under his constant gaze, she blushed and looked away.
"Well," Nathan spoke up, clearing the air, "Phil and Di are probably wondering what happened to the four of us, and we really need to rescue them from Alex, so...." Connor nodded, noting Nate's emphasis on the word "four." He could tell he was going to like him. Connor escorted Lane out of the room and was followed by Nate and Abby. He was glad this part was over, now he had to deal with meeting his father.
Within an hour Max and Isabel were home and Max was easily able to see that Connor was truly Zan, the son had given up for adoption shortly after birth. The reunion between father and son was an emotional one, with Max being both amazed and upset to discover that his son was, in fact, not human. He was quite the contrary actually, having even more alien characteristics than his daughter, Elena. Tess, Connor's mother, had committed one more evil before dying, separating father and son with a lie, knowing the goodness in Max would persuade him to attempt to give Connor a normal life since he thought his son was just that, normal.
Unfortunately, Connor had been anything but normal, and had suffered for it. Although his adoptive parents, Denise and Sam Anderson, had given him a wonderful life, he always felt he had something to hide, which was made worse by the fact that he didn't know what it was that he was hiding. His powers developed at a young age and, unlike his father, aunt, and Michael, he could harness them easily and developed them more fully. Not only could he heal, like his father, but he could sometimes read minds, had an ESP connection to people he was close too, and could often see the future thorough pre-destination dreams, which he could do nothing to control. One such dream had been the one that had told him his parents would die in a car accident, which they did shortly after his eighteenth birthday. This event caused him to seek out his past, leading him to Phillip and Diane Evans and, eventually, to Max.
After Connor had been thoroughly interrogated and accepted by the clan, not just Max and Isabel but also Liz, Michael, Maria, and Kyle, it was decided he would stay with Max and Liz. He had applied to and been accepted at Boston College in high school, before his parents' deaths, but had taken a year off in his search for Max. He planned on attending this fall and Max was more than willing and eager to allow his long-lost son to live with him while doing so. Liz was happy to see Max so happy and Lane was thrilled at the prospect of finally having her big brother home. After the jubilant shared dinner that evening, everyone went home with a new sense of amazement.
Later that night, Connor lay on his new bed and thought about his mother. From what his father and grandparents had said, she was a horrible person. His new goal, now that he had a home and a family, was to learn about his mother and, in doing so, maybe learn more about himself. He was particularly interested in meeting Ava, his mother's duplicate. She lived in the area but was often away, as she was right now. Connor believed that he might be able to discover something by meeting her, seeing as how, biologically, she was also his mother.
Other than his mother, the only thing he could think about was Abby. She was, he ascertained, the most beautiful creature alive. And the sweetest, and the kindest, etc. He had never been quite so crazy over a girl, especially since he felt like he knew her from somewhere before. He felt a strong pull toward her and didn't know why. At least he was content in knowing that, since she was his sister's best-friend and a fellow Czechoslovakian (he had laughed when he first heard the use of the word), he would be seeing a lot of her. Sighing, he slept peacefully for the first time in a year and a half, knowing he was safe in his new home and being happy for the first time in a long time.
**
**~*~
Early the next morning Connor and Lane left the house to spend a day getting to know one another. They planned on shopping for clothes to last Connor until his belongings arrived from New Mexico and Maine, where he had lived with his adoptive parents. Lane also planned on showing Connor around the town and finding out as much as she could about her new older brother. Connor planned for the same and was amazed with what he discovered about his little sister. By the end of the day, he felt he knew her entire life story, and, though he was a little more guarded, she his. He knew her favorite color was light yellow, which she liked because of her dark hair and eyes, that she and Nathan had been dating for two years, that she was a very smart girl with aspirations to be an author, and that she loved her parents dearly, even if her father was somewhat uptight and her mother was a little too conservative.
In fact, it seemed, Lane was the free spirit of the family. She was only 16 but was very self-assured and knew exactly who she was and what she wanted. But she also knew how to have fun. Connor was delighted with her; she was exactly what he had always wanted in a little sister. He was only three years her senior so they had many things in common, as well as their inherent alien tendencies. By the end of the day they were great friends. Connor, a little more reserved but equally as intelligent and fun-loving, found his little sister charming, while Lane enjoyed the quiet, shy exterior to the great guy inside, who was just like her father, only much more fun.
A few days passed and Lane and Connor grew closer, as did Max and Connor. Max tried to do everything possible to make-up for lost years with his son. Lane was happy because this kept Max off her back about her late outings with Nate and Liz was happy because the inner turmoil Max had been having for nineteen years was finally healed, allowing them to be closer than ever.
As Lane and Connor became more like siblings, Connor was included more in the time she spent with her best friend and boyfriend. This allowed Connor to get closer to both Nate and Abby. He and Nate were good friends within a week, as he had predicted, but he was still shy around Abby and couldn't figure out how to break that wall down. Abby herself was doing everything possible to fight the attraction she was feeling. It was uncharacteristic for her to fall for a guy so deeply, and with the alien complications she never did. But this was different, not only because he was also an alien, but also because of what she was feeling. She felt pulled to Connor magnetically and didn't know how to handle the new situation. This was complicated by the fact that the two were often left alone while Lane and Nate spent time alone. Most of this time was, however, spent with the two working for opposite goals. Abby was fighting her attraction to Connor and, while they were becoming good friends, Connor was starting to want more. He felt driven to have more, as if it were a necessity.
~~**~~
About a month after Connor's arrival, it happened, and their relationship finally changed. Max and Liz were out on a romantic evening, while Michael and Maria were spending time together at home, requiring their two children to be gone. The four teenagers were relaxing at the Evans house, watching a movie. Abby and Connor sat on the couch, a pillow and popcorn bowl between them, while Nate lay on the floor with Lane's head in his lap. Eventually those two began making out. Abby chucked popcorn at them.
"You two are disgusting... can't you keep your hands off each other for an hour?" Lane started cracking up as Nate tickled.
"No," he laughed, looking up at his sister. "We go back to school in three weeks and we've got to enjoy each and every moment we've got left." Abby sighed and Connor looked at her and laughed. She responded by chucking popcorn at him. He grabbed a handful and prepared to retaliate when Lane stood up and dragged Nate up with her.
"We're going to go somewhere more private," she explained. "You kids have fun." Connor and Abby smiled as nicely as they could muster, waiting patiently for the pair to leave. When they were gone, Connor chucked the handful of popcorn at Abby. Pretending to look shocked she turned away innocently and then, after a few moments, dumped the whole bowl on his head. Connor laughed and, after wiping the popcorn off, they went back to watching the movie.
Within a few minutes, however, Abby caught Connor watching her out of the corner of his eyes. She shut off the movie, turned on the light, and smiled at him.
"What?" she asked innocently. He laughed.
"You've got popcorn in your hair," he responded, actually thinking about how beautiful she was. She blushed, wiped it away, and then looked angry.
"Well if I do, it's your fault, jerk," she shouted, allowing the tension to brew for a few minutes before bursting into peals of laughter. Connor laughed with her.
"I hate when you do that," he said. "I can't read you when you play with my mind like that." Abby moved an inch closer and leaned toward him a bit.
"Well, maybe I don't want to be read," she whispered. Connor, overwhelmed by the beautiful, seductive creature in front of him, moved another inch closer.
"But I always read people.... it's my gift. Why won't you let me read you?" Abby blushed and looked down.
"I... I just don't want people to know what I'm thinking," she stuttered, and then laughed.
"I've got to remain a woman of mystery, you know?" Connor laughed with her.
"Well, you are a mystery, at least to me... that might be why I like you so much." He stopped at this and looked in her eyes, waiting for a response. Abby suddenly got uncomfortable and inched away.
"You're trying it again," she said. Connor scooted closer, trapping her with the arm of the sofa.
"I'm sorry," he said, placing a hand over hers. "It's just natural for me to want to know what the people around me are thinking. I think I try so much with you because you can resist it. You can put up that wall... I want to take it down and see you..." Abby blushed and smiled.
"Maybe you will someday," she said. Connor smiled. Then it happened. Abby felt like something was controlling her, but she didn't fight it. She leaned in and kissed him. It was soft at first, but, as they moved closer, it became harder and more passionate... neither wanted it to end. Their bodies together felt like the most natural thing, and Connor could see Abby. Not what she was thinking, but her past. He saw her childhood with her brother and felt how much she loved him. He also saw how much she was hurt when Nate and Lane left her to do things together. This made him love her more, and all he wanted was to protect her. His arms already around her, he tightened his embrace as they kissed more deeply.
Then, all of a sudden, Abby pulled away. She stared at Connor for a second and he looked confused. Flustered, she tried to compose herself and stood up.
"I'm... I'm sorry," she said, grabbing her things. Connor stood up after her.
"No, no, don't be... it was incredible. I..."
"No!" she interrupted. "It shouldn't have happened and I'm sorry. Tell Nate I went home." Without looking back she marched out the door, ignoring Connor's calls so he wouldn't see the tears forming in her eyes. He just stood in the doorway and looked confused.
5. Her Father's Daughter
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****
Chapter 3: Her Father's Daughter
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Abby sat at her vanity, staring into the mirror at her tear-streaked face. "What is happening to me?" she asked herself out loud. She had spent the last hour crying over what had happened with Connor and still didn't completely understand it. She had wanted to kiss him. She had even been the one to initiate the kiss. But, she hadn't expected it to be like that, and she had gotten scared. The emotions she felt coming from him and the sensations she had in her body were too much.
The kiss had begun well and she had been fine at first. His lips felt incredible against hers and her whole body was responding to him. She had been kissed before, but never like that. The coolest thing had been that, as they were kissing, she could feel his emotions, how happy he was and how much he cared for and wanted her. As their kiss deepened she had seen flashes of what she guessed was his past, and these came with emotions as well.
She saw him when he was a child and felt how scared he was when he first discovered his powers. She saw him as a teenager and felt how much like an outsider he felt, having no one to share his secret with. And she saw him on the day his parents died, and felt his pain. All of this only amazed Abby, and made her care about him even more. For a second she thought she could even love Connor, and that's when she pulled away. She was frightened, not by the thought of love, but by what she had seen when she thought she might love him. At the moment this thought crossed her mind, she received the most powerful of all the flashes, the dream that had been plaguing her for years. But this time she saw the man in the dream, and he was Connor. Shocked and frightened she had pulled away and then been both embarrassed and confused. The only way she knew how to handle the situation was to leave, and leave fast.
When she had arrived home she had run to her room, thrown herself on the bed, and cried. Her mother, Maria, had come up to comfort her, but was little help because she didn't know what was hurting her daughter. Now Abby sat, staring at her own reflection, trying to understand everything. Trying to understand why she had been drawn to Connor since the day they met and trying to understand why she saw him as the man in her dream. Soon there was a knock on the door followed by Nate asking to come in. She dried her tears and tried to look happy as she invited him in, but he didn't fall for it. He crossed the room and hugged her.
"What did he do to you?" he demanded, looking into her eyes. Abby fought the tears off.
"Nothing," she answered honestly. "It was just a stupid misunderstanding, nothing more.
All my fault." Nate looked into her eyes and saw that this was the truth.
"Are you gonna be ok?" he asked. She nodded and he continued, "If you're not I'll crush him like a little bug." She laughed for the first time in a few hours.
"I'd like to see that," she giggled, knowing full well that, while Connor, being the son of the king, would come out victorious in any battle, Nate would certainly put up one hell of a fight.
"I bet you would," he joked, laying an arm on her shoulder. "You still want to go through with tomorrow then?" he asked. The next evening the four had planned on going to see one of their favorite bands in concert in Boston, and, then, they had reservations to stay the night in a hotel, with separate rooms for boys and girls, of course. Abby nodded.
"Yeah, I just freaked out momentarily. I'll be fine as long as he doesn't hate me or something." Nate smiled.
"I doubt that," he said. Then he thought for a second. "So what exactly did happen?" Abby blushed and looked down.
"I kissed him... and then I freaked out and took off." Nate laughed.
"So, my baby sister can't deal with the whole intimacy issue," he teased. "Mom's gonna love this one.... that's always what she's complaining about with Dad." Abby didn't laugh but punched him in the shoulder, hard. "Hey," he said, rubbing where she had hit him.
"You will not tell Mom," she hissed. He nodded.
"Jeez, you're a real basket-case sometimes, you know that?" She nodded happily.
"Yes, I do. Now go. I need to be a basket-case by myself for a while." He stood up to leave, chuckling. "Oh, and Nathan," she said as he approached the door, "I'm NOT your baby sister." He laughed, knowing how much the ten-minute age difference annoyed her and she laughed with him.
"Night, sis," he said, closing the door behind him.
"Goodnight," she whispered in reply, secretly glad she had him. Nathan had always been the best thing in her life (not that she'd let him know that). Even though they were the same age, he had always been her protector and defender, from the moment they were born. She really loved him, and he her.
Abby sighed and walked to her desk, thinking about what she would say to Connor the next day. She was certain he would hate her, but was hoping otherwise. She took out her journal and, without realizing it, began to write one of her frequent letters, this time with an addressee.... Connor.
~*~
The next evening Abby and Nate showed up at the Evans's house at 5 pm as planned. They had planned on taking the Jetta to Boston, enjoying the concert, grabbing a bite to eat, and then collapsing in their hotel room. All four were packed and ready to go, but Connor was having some doubts. After what had happened the previous evening with Abby, he wasn't sure if he should come along or not. He was confused about her reaction to their kiss, especially since he could sense her emotions and knew she had been enjoying it. When Abby and Nate showed up, Lane greeted them rather disappointedly and informed them that Connor had decided not to go. Upset, Abby immediately went up to his room to see him.
When she entered, he was laying on his bed, listening to music.
"Hey," she said. He remained silent but nodded slightly in her direction. Upset, she hurriedly continued. "Are you upset with me? Because I understand if you are, but I'd like to talk about it. I mean... well, I don't really know what I mean, I just know that I'm sorry." Connor sighed, sat up, and motioned for her to sit in the chair at his desk.
"I just don't understand," he began, "and I guess I don't know what to think. I mean, I thought we were on the same page here.... you know, you kissed me, not the other way around... and then you just freak out and take off without another word. Did I do something wrong? Did you suddenly realize that it was all some big mistake? What? Just explain to me why and I'll try to understand." Abby examined her shoes carefully and they sat for a while in silence. Finally, gathering courage, she looked up at him and spoke.
"I don't know. I just got scared. I'm not sure if it was a mistake or not, I just know that I was kind of overwhelmed and reacted badly. I'm sorry, but that's all I can say. I just hope you can understand that this is all very new for me." Connor nodded.
"Yeah, that's fine," he sighed. "I was just hoping that maybe we could be closer, you know, and then all this happened." Abby nodded.
"I'm sorry about all of this. Maybe we can figure it out later, but you are coming to that concert. It wouldn't be the same without you." She looked at Connor pathetically, begging him to come with her eyes. There was no way he could say no.
"Ok," he consented, "but we need to sort this all out when we get back." Abby jumped up and hugged him, taking his breath away.
"Thank you so much," she whispered in his ear. "You won't regret this." They left the room and went downstairs.
"So, you coming, man?" Nate asked when they came down. Connor nodded and looked at Abby.
"Yeah," he replied, "I'm coming."
"Good, then lets get out of here," Nate said, grabbing the keys to the Jetta. They all piled into the car for the drive to Boston, Nate driving with Lane in the passenger seat and Abby and Connor in the back, sitting silently. The entire trip was relatively uneventful, with Abby and Connor not really speaking and the mood obviously more somber than it should be. Every once in a while Abby swore she caught Connor staring at her out of the corner of his eye, but he always looked away in time to look innocent. When they arrived at the concert they went in, grabbed some souvenirs, and headed into the crowd.
The opening act was ok, but Abby and Lane used it to talk, mostly about Connor, while Nate took it as an opportunity to introduce Connor to some of his friends who were there. When the band came on they met up again and were carried from their troubles by the music. Within an hour Abby and Connor seemed to be their old selves again and were dancing and singing and having a good time. Nate and Lane were, of course, making-out. At one point Connor leaned in to ask Abby if the other two ever quit, to which she replied in the negative, and both felt their temperatures rise. The fun had erased the memories of the awkwardness the previous evening and they were acting like good friends. Connor was, in typical male fashion, taking the chance to blatantly check Abby out, head to toe, without being conspicuous. He had looked her over before, several times, but he had never seen her like this. Her shirt drove him nuts, being a tight, red tank top with a plunging V-neck and a bare midriff. With her golden-brown hair and hazel eyes, red was definitely her best color. Her pants were tan and equally as tight as the shirt, causing more than one passer-by to stare, making Connor want to make more than one passer-by suffer. He was having the time of his life with Abby, and she with him.
The night wore on and, as their fun increased, their feelings for one another increased with it. During the last song Abby turned to Connor and said something.
"What?" he shouted, unable to hear her over the roar of the music and the fans. She moved closer, pressed her body against his, wrapped an arm around his neck, and spoke into his ear.
"I said I'm glad you came." He looked down, took her free hand in his, looked into her eyes and replied.
"Me too." Then he kissed her. It wasn't like the night before, but softer, more gentle, more caring. And Abby, though she had the same vision, didn't pull away. Eventually, as the house lights came up, it ended and she looked into his eyes.
"I'm REALLY glad you came," she repeated, pulling away to go find her brother and Lane.
~*~
The four left the concert hall and went to their hotel, too exhausted to eat. By their parents' designation, the girls had a room and the boys had a room. Unfortunately for their parents, Lane and Nate had different ideas and, within a half an hour of arrival, Abby had been kicked out of her own room. In her pajamas and with nothing else to do, she wandered to the door of Connor and Nate's room, where Connor was alone, and knocked.
"Yeah," came the reply. She hesitated.
"Connor," was all she said. Within a few seconds the door was open and she walked in.
"Nice place you have here," she joked, sitting on the sofa. Connor resumed his position on the bed and placed the book he had been reading aside.
"What do you need?" he asked, feeling slightly uncomfortable that Abby was in his room, wearing nothing but a tight tank top and boxers. She smiled uncomfortably.
"I can leave if you like," she said, standing up.
"No," Connor immediately said. She sat back down.
"What are you reading?" she asked, motioning toward the book on the bedside table.
"A Brave New World," he replied, picking the book up nonchalantly and showing it to her.
"Ah," she said nodding, "happy pills, meaningless sex with multiple partners, and government controlled genetic conditioning... a classic." He laughed.
"I take it you've read it?"
"Just once," she replied. "It disturbed me beyond all reason and I haven't been able to pick it up since." He lay it back down.
"So why are you in here, anyway?" he asked, restating his earlier question.
"Nate and Lane are.... you know," she replied, motioning to the room next door. He nodded in understanding. "I got kicked out and needed somewhere to stay. I guess they actually took it seriously when I told them to get a room." Connor laughed.
"Well, you can stay here then," he offered. "I'd hate to find you sleeping in the hall in the morning or something."
"Thanks," she said, snuggling down on the couch with the blanket she had brought with her. Connor reached up and turned out the light, feeling exhausted yet exhilarated. After a few minutes of listening to her turn on the couch, however, he was feeling something entirely different. He turned the light on, unable to withstand the temptation any longer.
"Sorry," she said, sitting up. "I'm keeping you up, aren't I?" He thought the answer to himself, but restrained from telling her.
"No," he lied, "I was just worried you wouldn't be able to sleep over there. That couch isn't all that comfortable." She smiled at his concern. He took a deep breath and then said what he really wanted to, "You know, this bed's really big and, if you wanted, you could sleep up here too. There's plenty of room." Abby stared at him.
6. New Developments
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Chapter 4: New Developments
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Abby continued to stare at Connor. He was beginning to feel very awkward. He gulped, prepared to defend himself if she answered in the negative.
"Are you sure?" she asked after an uncomfortable pause. Connor nodded. He couldn't believe he had just asked her to share his bed. She stood up, walked over to the bed, and slid in next to him, ensuring there was at least a foot of space between them.
"There," he said, "I'm sure you'll be much more comfortable now." _More comfortable but less able to sleep_, he thought to himself. Abby, who had been settling in to her new position looked at him in shock. She had heard what he just thought.
"What?" he asked, seeing her stare at him. Abby paused a moment.
"Nothing," she answered, deciding to keep this little bit of information to herself. The two lay there, facing each other, neither wanting to close their eyes first. After an uncomfortable few minutes, Connor spoke up.
"I had a really great time tonight," he said. "I'm really glad you decided to invite me along. And I'm glad you talked me into coming." Abby smiled.
"I'm glad you came. I would've been lonely without you. And... and I'm sorry that I ever made you feel unwelcome or uncomfortable."
"You are the last person to make me feel unwelcome," he replied, reaching out to hold her hand. "And, most of the time, I'm most comfortable around you. I feel like my soul is at rest when we are together. It feels natural." Abby blushed and smiled shyly, running her thumb along the palm of his hand. Connor stared at her, feeling her skin against his hand and using every fiber of his being to control the urge to pull her to him right there. He felt like two things were battling inside him and he was afraid that, at this rate, he would lose the battle.
"So...." Abby said.
"Yeah?" Connor asked in reply, glad for the distraction from his ever-growing desire.
"Well," she began awkwardly, "I know we said we'd discuss 'us' when we got back, but, since we're here now, I was just wondering where exactly we stood." Connor sighed a breath of relief mingled with happiness. There was no doubt in his mind that he wanted her and she had just reveled, in her own special way, that she felt the same. He moved closer to her, until there were just a few inches separating their bodies.
"We are... wherever you want us to be," he said with conviction. "I don't want to scare you or drive you away, but I'm completely certain of my feelings for you. There is no doubt in my mind that I want to be with you. You are the most beautiful, amazing, wonderful person I have ever known. I want you so much, Abby." Abby, touched moved even closer to him, until her breasts were touching his chest and their faces were only inches apart.
"I wasn't going to say this," she said. "And I wasn't going to do this. I just didn't want to get involved, not with you or with anyone." Connor's smile disappeared as he heard this, thinking he had read her emotions wrong.
"But," she continued, "I don't have control over it. I tried to control it, but it's like a whole other part of me, as if something in me is drawn to you and I couldn't prevent it even if I tried. The funny thing is, as much as I thought I would, I don't want to try. I want you too... you mean so much to me." With that she leaned in to kiss him, and she most definitely did not pull away.
As they kissed Connor pulled Abby against his body, rolling on his back to allow her to lie on top of him. She complied and stretched out over his body, pressing hard against him as their kisses deepened. She could feel every muscle in his body straining, pulsing, and begging for her touch. His hands explored her body, wanting to know every inch of her.
"I can't stop myself, Abby," he groaned, pressing her harder against him. She slowly pulled away, until she was sitting astride him, feeling his desire against her. She looked into his eyes and both saw and felt how much he loved her. And she knew then that she loved him too. She had known it from the day she met him, maybe even before then, but this was the first time she had felt it.
"I don't want you to," she said honestly, pulling the shirt she wore off. Connor swore his heart stop when she did this.
"Are you sure?" he asked, his hands traveling up and down her sides wanting to go farther but not wanting to push her.
"Absolutely," she answered, laying back on him and resuming their kiss, allowing him to roll on top of her. He felt parts of her body he hadn't before and his desire to keep going increased. Trying to fight the urge to continue, he slowed his pace, forcing himself to withdraw his hands.
"Connor," she moaned throatily, causing his former resistance to collapse. "Don't stop," she begged. "Don't stop at all." And he didn't. Kisses became more passionate, hands went further, more clothing was discarded, and the new couple made love.
Unbeknownst to the two, as their bodies joined a glow, coming from them, filled the room. It became only stronger as they continued, and, eventually, escaped the confines of the room and found its way into the sky. Around the world, there were only a few who could see it.
~*~
A few miles away from the hotel where Abby and Connor lie, Max Evans was suddenly awoken by a strange feeling. Something pulled him out of the bed he shared with his wife and towards the window. There, he saw a beam of strong light in the distance. The light did not look like the artificial light of the city, but was stronger and seemed to have a purpose. Staring at the column of light, he noted that it extended straight up into the sky, straight towards the constellation where his home lie.
Turning away from the window he shook his wife awake and lead her to see it.
"Max, I don't see anything," Liz said, sleepy and confused. "Where is it, because I must be missing it."
"I don't see how you could miss it, Liz," he answered in awe. "It's filling the whole sky and glowing so brightly. And look, it leads right up to the V-constellation, almost as if that is its destination." Liz stared hard, but still saw nothing. Suddenly the couple was removed from their respective searches by the phone. Liz ran over and picked it up.
"Hey, Michael... no, we were both awake.... Yeah, Max sees it too.... No, I don't." She walked over to her husband and handed him the phone. "He wants to talk to you."
"Maxwell," Michael said when Max answered the phone, "what the heck is going on?"
"I don't know, Michael," Max answered truthfully. "Do you see it too?"
"See it?" Michael shouted. "Of course I see it. How could I not?! It's filling the whole sky." Another voice on the line interrupted, as Max heard Maria tell Michael that she did not see it. "What the heck is going on, Maxwell?" Michael repeated.
"I'm not sure, but I think this is a sign meant only for us," Max answered. "I wonder if Isabel...." In answer to his question he heard a beep, indicating there was another call. "Hold on, Michael, I think Isabel is calling me." Max clicked over and Isabel was frantic.
"Oh God, Max, please tell me you see it," she said before he could even greet her.
"Yeah, I do," he replied, "and Michael too." She breathed a sigh of relief on the other end.
"Thank God, I thought I had gone insane. Here I was staring at this beam of light and Kyle couldn't see it and I didn't know what to think."
"Michael and I think it might be a sign or a signal meant only for us. We need to find Ava and see if she saw anything."
"Good," Isabel agreed. "Why don't the three of us meet at your place tomorrow and see if we can figure out what this is and see if we can contact Ava, ok?"
"That sounds good to me," Max replied. "I'll let Michael know. Goodnight, Iz."
"Goodnight, Max," she said before hanging up. Max clicked back over to Michael.
"Michael, Isabel saw it too, but Kyle didn't."
"I think your theory is pretty well grounded then," Michael replied.
"Yeah," Max said. "Isabel thinks we should meet tomorrow afternoon at my house and see if we can figure this out. She also thinks we need to find a way to contact Ava."
"If she saw what we saw, I'm betting she'll be contacting us very soon," Michael replied.
"That's a thought," Max said. "I'll see you tomorrow, ok?" Michael answered in the affirmative before ending their conversation. Each of the three aliens went back to bed, staring in the sky until the light disappeared.
~*~
After their experience, Abby and Connor lay in bed together, curled in one another's arms. Connor stroked Abby's hair and Abby, avoiding eye contact, played with the hem of the shirt she had recently thrown on.
"That was great, you know," he said after a long, awkward pause. Abby nodded.
"Yeah," she replied, in a daze. Connor looked at her with concern.
"Does it hurt at all?" he asked.
"Some," she replied, "but it's not so bad anymore." Connor placed his hand on her lower abdomen and used his energy to heal her pain.
"You should have said something sooner," he said, burying his face in her hair and increasing his hold on her body. After a few moments he continued, "Do you regret it?" Abby turned to face him.
"No," she answered honestly. "Not in the least." He smiled at her and folded her back into his arms, where they both quickly fell asleep.
~*~
Across universe, on another planet in another galaxy, a young man rushed into an office.
"Your eminence," he gasped, but was stopped by the wave of a hand before he could continue.
"I saw it," was all the man with his back to him said.
"King Larek, is it true then?" the young man asked. "Have the High King and Queen been found?" Larek turned and faced the young man.
"You saw the beacon," he replied. "You do not need an answer to that question. If the legend is true, the High King and Queen have indeed found one another, and we will now be able to find them."
7. Many Meetings
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Chapter 5: Many Meetings
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The next morning Abby awoke to light streaming in her face. She turned away from the window and snuggled against Connor's chest. She felt his fingers running through her hair and knew he was awake.
"Morning," she said, reaching across his stomach to take his free hand in hers. "How long have you been up?"
"A while," he answered, kissing the top of her head gently. "I thought about waking you, but you looked so peaceful and I liked watching you sleep."
"I'm glad," Abby sighed contentedly, tracing tiny circles on his abdomen.
"Glad for what?" he asked, slightly confused. She lifted her head up and turned to look at him.
"Glad you didn't wake me," she answered. "I can be pretty evil when someone wakes me up... I'd hate to hurt you in an early morning rage." He laughed.
"I don't think you could hurt me," he joked, hoping to provoke her.
"Oh yeah," she replied, catching on quickly. "Just watch." With that she straddled him and began tickling him ferociously, happy to prove her point. The tide quickly turned, however, when Connor, the stronger of the two, rolled her off him and pinned her on the bed, returning the evil tickles.
"Ok, ok, I give up," Abby gasped. "You are way stronger than I am." Connor paused and then continued his tickling.
"I'd like to stop," he lied, "but I'm being controlled by aliens. They just keep telling me 'tickle her, tickle her.'" Abby tried without luck to end the relentless tickling.
"Please," she finally gasped. "I don't think I like this game anymore." Connor stopped and looked into her eyes.
"You only don't like it because you're losing." Abby nodded.
"That's right," she agreed. "And I hate to lose." Connor lay down on top of her.
"Well, maybe we should play a game that you know you can win," he suggested. She nodded happily and he leaned his head in and kissed her. His hands traveled across her body and they continued to kiss more passionately.
"What the hell is going on here!?" Nate shouted when he entered the room. Connor looked up and started to get up, but not quickly enough. Before he had pushed himself off Abby Nate had already thrown him off her, onto the floor. He stalked over, grabbed Connor up again, and punched him, hard. His hand reeled back to deliver a second blow when both Abby and Lane grabbed Nate and tried to pull him off Connor. Abby was furious.
"What the hell do you think you're doing?" she shouted at her brother as she shoved him on the couch. Nate was not about to sit there without a fight.
"Me!" he shouted, standing back up and looking her square in the eye. "What were you just doing? I leave you alone for one night and I find you half-naked with a stranger."
"He's not a stranger," Abby growled, "and you have no right being in our business."
"You're my sister," he retorted. "You bet your life it's my damn business." Abby backed away from him.
"Just don't even talk to me," she said, turning away. Nate looked at Lane for help, but she was busy tending to her brother's wounds. "Abby, don't be like this," he begged.
"Be like what, Nate?" she asked. "Huh? Cause I don't know what you want me to be like. Do you just want me to spend the rest of my life alone, watching you have all the fun, always being the odd man out? That's not what I want and that's not what I'm going to do." She stalked out of the room and down the hallway. Nate chased after her.
"Abby, don't walk away from me," he shouted as she stormed down the hall. She turned around, tears covering her face, and walked back to him.
"I'm sorry," she said, "but I can't live my life by your rules. Can't you just be happy for me?" She started to walk back away, but Nate stopped her, grabbing her shoulder and wheeling her back around.
"I can't be happy for you because I'm too busy being scared for you," he said. "I know you and Connor are close, and I know you've been lonely, but I don't want to see you get hurt, and I think you will."
"The only way I will is if you hurt me, Nate." He ran his hands through his hair and sighed.
"If this is what you want, fine," he finally conceded. "But please be careful. The last thing I want is for something bad to happen to you. I love you too much." Abby hugged him.
"I love you, too," she whispered, "and I WILL be fine. You'll see." He nodded.
"I hope so." She took his hand and they went back into the room together.
"Man, I'm sorry," Nate said sincerely to Connor when they arrived. Connor nodded.
"It's ok," he said, reaching up and healing the black eye that had begun to develop. "I guess I would have done the same thing if I had been in your situation."
"Well, either way, I'm sorry," Nate repeated. The four quickly dressed and headed out of the hotel and back home.
~*~
Later that day there was a meeting at Max and Liz's house. Max, Michael, Liz, Isabel, Maria, and Kyle were there to discuss the light the aliens had seen the night before.
"So basically, we know it was some kind of a sign, a signal or something," Isabel said, pacing across the room. "And that's it? I mean, what does it mean, why did it happen?"
"Unless someone contacts us we have no way of finding out what it means," Max stated.
"But why did we only see it, Max?" Michael asked. "Abby and Nate both said they didn't see anything, and if your kids had seen it, I'm sure they would have said something."
"Alex saw it," Isabel said, looking up. "He asked me this morning about the pretty light in the sky."
"Okay then," Michael said. "Maybe it could only be seen from our houses. The kids were in Boston last night, they wouldn't have seen it if that's the case."
"That's a possibility," Max said.
"Well, who do you think would be trying to contact you, and why?" Kyle asked.
"Maybe someone from our home planet," Max said. "I mean, according to what Tess said, things were in shambles when she was left. Maybe Kivar was overthrown and they want us to come back."
"Wait," Maria said, getting very angry very quickly. "They just let you sit here for 20 years and then, once you've established lives and are happy, they come to take you away. They can't do this!" Michael wrapped an arm around her, trying to calm her down. Isabel and Liz also looked hysterical, turning to their respective husbands for comfort.
"We don't know that, it's just a theory," Max quickly interjected. "Right now we don't know anything. We'll just have to wait and see."
"What about Ava?" Liz asked. "Has anyone managed to contact her yet?"
"Sean called our house this morning," Maria offered as an answer. "He said Ava got really disturbed in the middle of the night and took off, muttering something about a king or something. When she came in this morning she went straight to sleep and didn't say anything. He said he's bringing her home and they should be here in a few days."
"Good, good," Max said. "It sounds like she might know something. Until we can talk to her, we're pretty much clueless."
"Unless someone 'else' contacts us first," Michael mentioned.
"Well, that remains to be seen. For all we know this light wasn't anything. It could have just been a fluke or something. It might not mean anything." Everyone nodded and their meeting ended.
~*~
On another planet, in another galaxy, there was a great commotion in the Council Hall.
"What do you mean?" a voice shouted from the gallery, asking the question all wanted the answer to. Larek turned in the direction of the voice.
"I mean precisely what I say," he said with conviction. "The beacon has been sent, the signal received, and the High King and Queen have been found." At this an angry man stood and walked across the floor to Larek.
"Impossible," Kivar said angrily. "The story of the Royal Couple is a myth, a bedtime story for children and nothing more. Do not tell me you believe this."
"Yes," Larek said with assurance, "I do." Kivar muttered something under his breath. "What was that?" Larek asked, staring into Kivar's eyes.
"I said," Kivar answered, straightening up, "that there is no need for a High King. It would only bring disruption when we are balancing so precariously on an uncertain peace."
"Exactly," Larek shouted, turning to the members of the Council, "an uncertain peace. The legend foretold that the High King and Queen would come to us in the hour of our greatest need and bring peace to this troubled star system. That time is now!" Murmurs were sounded among the members of the gallery, as they quietly debated this new information among themselves.
"Quiet!" Kivar ordered. "This is ridiculous. Larek would have you put your faith in a fairy tale. Put your faith in me and in your leaders. That is where the peace will lie." Larek, who was listening to Kivar with a smirk, stepped forward.
"I believe, Kivar, that the only reason you object is because you fear for your crown," he said. Kivar began to protest but Larek stopped him. "No, don't try to deny this, for we all know it to be true. The signal was sent from Earth, meaning the High King and Queen are likely descended from one of the "Royal Four" of your planet. If this be the case, you have a reason to worry. You are sitting on an uncertain throne, Kivar, ruling in its rightful owner's absence. It is quite likely that, when the Royal Couple arrive, the owner of that throne will return with them. Then where will you be? At the mercy of your enemy, of course."
"The coming of the King and Queen would mean a loss of power for you as well, Larek," Kivar growled. "They would rule over us all, not just my planet."
"You mean Zan's planet," Larek corrected. "And I am well aware of this. The High King and Queen would take control over all five of our planets, be the supreme authority, an emperor of sorts. But we will still remain the rulers of our own planets, answering only to the Royal Couple. I will lose some power to their will, all of you will, but I am willing to accept this if it means a return to peace and prosperity." Kivar's anger was apparent on his face.
"I refuse to allow MY planet, as well as the others, to be ruled by a group of humans," Kivar shouted.
"That is enough!" Kathana, the Queen of the planet Jacobni stood and walked to Larek and Kivar. Her regal and commanding presence made the two men step down. "You two are acting like children. You speak of peace, yet argue over the way to it. Cease this persistent arguing now." Larek nodded.
"Kathana is right, we don't need arguing, we need a plan."
"Well what is your plan," Kivar sneered.
"I have a team prepared to leave for Earth immediately to bring us the High King and Queen... and the Royal Four, if they are involved. Also, I am prepared to make contact and confirm their location and that the Royal Couple is indeed with them." The members of the council nodded approvingly.
"Fine then," Kathana said. "Let us put it to a vote."
"No," Kivar said. "This is not a democracy, there will be no vote. I say they will not return. You need my planet's cooperation, and Antar will not cooperate."
"Silence!" Kathana roared, causing Kivar to quiver. "Our planets may not be democratic, but this council most certainly is. There will be a vote," she said, "and if you do not cooperate, we will make you cooperate."
"Thank you, Kathana," Larek said, nodding in her direction. He turned to the other members of the Council. "Now let's hear the votes of the other rulers, you know my mind." A page stood up and began reading the roll and marking the votes.
"King Larek of Fallor, yea for recovery of the Royal Couple. King Sero of Zallini, how vote you?" Sero paused and thought for a moment, a look of concern on his face. After a moment he spoke.
"I am uncertain if this is the best move for all, but action needs to be taken. Zallini votes for the mission."
"A vote of yea for King Sero. Lord Kivar, how votes Antar?"
"You know my vote," Kivar hissed. "A resounding no for Antar."
"Very well," the page continued, "a vote of nay for Antar. King Hanar of Daglomar, how vote you?"
"Yea," Hanar said with certainty.
"A vote of yea for Daglomar. And finally, Queen Katana, how vote you?" Katana looked at Larek and smiled.
"Jacobni will support Fallor in their endeavor." Larek smiled thankfully at Katana. She ruled the most powerful of the five planets in the star system. Without her support his plan would never survive. Katana turned towards Kivar.
"Well, Lord Kivar, it seems you are very lonely in your decision. Care to change it?"
"Never," Kivar growled menacingly, approaching Katana with a look of hatred. "Antar will have nothing to do with this."
"Very well," Katana said. "But remember, Kivar, you may not want anything to do with the High King and Queen, but the people of Antar do. The Council of Leaders has made its decision and, in opposing it, you have lost our support. Go back to your planet and see how long you last." Kivar turned and left the council hall. Larek stepped forward again.
"I will send a message to Fallor to send the emissaries to Earth at once and, at a time you deem appropriate, I will contact the Royal Four of Antar."
"Very well," Katana answered. "If there is no other business, then the council is dismissed. I ask all of you to return to your planets and prepare your people for the arrival of the High King and Queen."
8. A Good Night
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Chapter 6: A Good Night
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Three days had passed since Abby and Connor's night together, three days since the signal had gone off. In the three days since, they had tried to spend every possible moment together, attempting to learn everything they could about each other. The two had officially started dating, and, after some momentary concern from various family members, everyone had accepted it. Now they lie side by side on Connor's bed talking.
"These past couple of days have been incredible," Abby said, looking up at Connor. He brushed the hair out of her face.
"I know exactly what you are saying," he said, leaning in and kissing her softly. She responded and kissed him back, slightly harder. Connor reached across the few inches separating them, wrapped his arm around her waist, and pulled her across the bed to him. He started to kiss her harder while running his hands over her body.
"Wait," she said, pushing herself away from him. "Remember, we agreed we were going to slow down a little?"
"Yeah, we did," Connor agreed, if not a little unhappily. "I just want you so bad sometimes I forget." Abby smiled at him.
"I get that same feeling too, but it's not as crazed as it was that first night. I loved it, don't get me wrong, but I felt like I couldn't control myself, you know. I mean, I wanted to keep going, but I knew I should stop, but I couldn't. It almost seemed as if there was something else in control of me, and I don't like feeling like I'm not in control. I've never felt that way with anybody before."
"Well I hope not," Connor laughed, rubbing her hand softly. "But I know what you're saying. I wasn't in control either. I still want you, but now I feel like I'm more in control than I was that night. It was just like you said, like something else was controlling me. It was great, and, believe me, I'm up for a reprise whenever you are.... but I'm willing to wait until you're ready." Abby smiled and kissed him softly.
"When you go and talk like that it makes me feel REALLY ready, but I want to wait a little, to make it more special the next time."
"Every time I'm with you is special." Abby laughed and rolled over on her back.
"Ok, now you're just trying to get into my pants," she giggled. He climbed on top of her.
"Yeah, I am," he answered, smiling before he kissed her, "but I can deal with just getting in your shirt." They began kissing, attempting to restart their physical relationship at the beginning.
~*~
Downstairs there was a knock on the door and Max answered. A slightly hysterical Ava and a very confused Sean walked in. Max brought them to the living room and had them sit down.
"Good, I'm glad you guys are finally back," Max said. He looked at Ava. "Did you see it too?"
"Uh huh?" she said, visibly shaken.
"Well, what was it?" Max asked. "You seem to know more than the rest of us."
"I'm not sure," she answered. "I just know it's important. Very important. And it's not meant for us specifically, but for all of our race."
"But, my kids didn't see it, nor did Michael's."
"I don't know," Ava said honestly. "Maybe they were sleeping or something. I woke up for it, but maybe they're different because they're younger. Or maybe because they haven't lived on Antar before."
"Sean said you mentioned something about a king or something the night you saw it. What was that about?"
"I don't know, Max. I've been really confused since it happened. I really don't remember what I said that night. I know I knew what it meant when I saw it, but now I don't remember. I'm... I'm sorry." Sean rubbed her back, attempting to calm her.
"Hey, it's ok," Max said, "none of us know anymore than that either. We just wanted to know if you knew anything extra."
"I'm just sorry I can't help you anymore." Max nodded, understanding Ava's constant need to prove herself to them.
"Maybe we should go home and let her get some sleep," Sean said to Max, standing up.
"Wait," Max said. Ava looked up at him. "There's one more thing I want you to know before you go."
"What is it?" Ava asked. Sean was visibly frustrated, wanting to get Ava home and not stand around debating intergalactic light beams.
"It's just, Zan, my son with Tess.... I guess our son, found me about a month ago. His name is Connor now and he's been living with me. He really wants to meet you, I think he thinks of you as his mother, and I just wanted to give you a little advanced notice." Ava's eyes brightened and she stood up, evidently very excited.
"Is he here right now?" she asked. Max nodded. "Well," she continued, "can I see him then? Maybe just to say hi or something?" Max nodded again and smiled, glad she was so happy about this. Connor was, after all, biologically her son.
"He's upstairs in his room, with Abby," Max said. "I'll run up and see if he wants to come down." Ava nodded and Sean, frustrated and knowing he was going to be there for a while, sat back down.
Max went upstairs to Connor's room and knocked on the door.
"Hey, Connor," he said, "I need to talk to you for a minute." Max smiled to himself as he heard some shuffling and hurried movements on the other side of the door, knowing he had interrupted something.
"Yeah, come in," Connor choked out after a few moments. Max opened the door to see his son sitting up against the headboard of his bed with the TV remote in hand, pretending to turn it off, and Abby sitting at the end of the bed reading a magazine. Max laughed; they were definitely amateurs at this. He walked in the room.
"Big fan of 'Maxim,' Abby," he asked, gesturing at the magazine she was pretending to be engrossed in. Abby looked at the cover and silently cursed herself.
"Oh uhm, yeah," she answered, smiling up at Max, obviously flustered "It's got great articles... very interesting, you know."
"Yeah, I know," Max replied, doing his best to hold back the laughter.
"So, Dad, what'd you need?" Connor interjected, trying to get Max out of there as quickly as possible. Max smiled. He loved hearing Connor call him 'Dad.'
"Connor, you said you wanted to meet Ava, your mother's duplicate, and she's downstairs," he began. "She just wants to say hi and hopes that maybe...." Max stopped talking because Connor was already out the bedroom door and headed down the stairs. He and Abby amusedly followed the boy. Connor slowed when he reached the bottom of the stairs and saw Ava.
"Hi," she said, slowly approaching him. "I'm Ava." He walked closer to her.
"I'm Connor," he spoke in a barely audible voice before tentatively hugging her. "It's really great to finally meet you." Ava was moved. She put her hand on his cheek.
"You look so much like your father," she whispered to him, thinking about her now-deceased lover Zan, Max's duplicate, and how much she loved him. Connor smiled at her, able to feel the love she had for Zan radiating off of her. He took her hands in his own.
"I know you're not actually my mother," he began, "but I'd still like to get to know you... find out more about you. You're my only connection to her and, in a sense, you are my mother." Ava smiled through a tear of happiness. All her life she had wanted to have children. After she had left Lonnie and Rath and settled down with Sean and the others she had thought that was what would happen. Unfortunately, neither she nor Sean were stable enough for a child, since they were restless, slightly irresponsible, and always on the move. Hearing this boy tell her that she was his mother was the most incredible experience of her life. She wrapped him in a tight hug.
"I want to know everything about you, and I want you to know me," she said to him. "As much as you think of me as your mother, that's how much I think of you as my son." They stood there, in front of everyone, hugging for the longest time. Finally Sean, who was becoming both very bored and very jealous by this time, cleared his throat. Ava turned to him.
"Don't you think it's time to go, baby?" he asked. She nodded.
"Connor, this is my boyfriend, Sean," she said. Connor nodded in Sean's direction. "I need to get going, but we'll get together sometime soon, ok?" Connor nodded and hugged her one last time, not really willing to let his new mother go.
After their hug ended, Max walked Ava and Sean to the door while Connor and Abby returned to his room. Max made a mental note to interrupt them more often, if only for humor purposes. He did the same with Lane and Nate, though it was slightly different because Lane was still, in his mind, his baby girl. Plus, those two were becoming old pros at hiding what they were doing. It was nice to have some fresh meat.
Once back in his room, Connor shut the door, pressed Abby against it, and kissed her passionately. He took her breath away.
"What was that for?" she asked when he had finished. Connor had a huge smile on his face.
"Oh, I'm just incredibly happy right now," he replied, "and wanted to make things better by kissing the prettiest girl in the world." Abby blushed but then responded by kissing him back, harder, until she had, with the force of her body, pushed him onto his bed.
"I love you," she said once they were on his bed, lying side by side. Connor paused before speaking.
"Where did that come from?" he asked.
"I just felt it," she responded. "Watching you with your mom, I knew. I love you." He pulled her back to him.
"I didn't say this before, because I was afraid of scaring you," he began, " but I love you, too. I would have said it sooner, but you rarely ever let me feel your emotions or see what you're thinking, and I'm just really insecure about...." She kissed him to stop his talking.
"Say it again," she commanded. Connor happily obliged.
"I love you." She began kissing him again, molding their bodies together.
"I think this whole waiting thing is highly overrated," she panted into his ear. "Especially when you've already been together before." Connor nodded in mock seriousness.
"I agree completely," he said, his hands quickly sliding her shirt off. "In fact," he continued, placing kisses over her body, "I think we should take extreme measures to prevent conforming to this silly idea. We are, after all, not of this world." Abby mumbled an agreement and he continued.
~*~
Later in the evening Abby left to go home. She was flushed and exhilarated when she walked down the stairs to the front door, having had one of the better evenings of her life. Max was in the next room reading.
"Abby," he said, stopping her before she could make a quick escape. She turned around to face him, afraid he knew what they had been doing and was angry.
"Yeah, Max?" she asked, trying to look innocent.
"I just wanted to warn you that your shirt was on inside out." He laughed as Abby looked down, realized he was telling the truth, and rushed out of the room in embarrassment. "Good night, Abby," he shouted, laughing as he shut the front door. Liz was behind him.
"You need to go talk to Connor about this," she said sternly. He turned to face her.
"I know," he said. "I just don't want to be some overbearing parental figure." Liz laughed.
"Just think about if you were Michael," she replied. "Think about the way you acted when Nate and Lane started dating." Max nodded.
"I think I'll go talk to him," he said quickly, jogging up the stairs in a flash.
Max knocked on Connor's door and Connor told him to come in. He walked over to his desk and sat down in the chair.
"I need to speak with you about something," he began. Connor put down the book he was reading and turned to face Max.
"Sure, about what?" he asked.
"Abby," Max said. Connor paled and tensed. He cleared his throat and scratched his head, visibly nervous.
"Um, ok," he said.
"Well," Max began, "I just want you to keep in mind a few things. Remember she's three years younger than you, she's my best friend's daughter, and you two haven't really been together very long. In fact you've only known each other for a month." Connor knew exactly where this was going but tried to play dumb.
"Yeah," he said slowly, "I know all that. Was there anything else?"
"I know what's going on between you two." All the blood left Connor's face and he laid a death grip on the pillow next to him.
"You do?" he managed to choke out, hoping maybe Max was thinking of something else.
"Yeah, you guys don't hide it very well," he said. "And I don't mind, hell, I understand, but I just want you to keep those things in mind, and, also, just be careful. Make sure you're using protection, and be good to her." Connor nodded.
"Of course I will," he said. Max started to stand up.
"Good," he said, "Because you do realize if you hurt her you're a dead man." Connor laughed nervously.
"It's not something you have to worry about, and we are careful," Connor reassured. Max said goodnight and left. Connor, still slightly shaken, lay awake for a while thinking about the events of that evening, which now ranked as one of the best nights of his life.
9. Making Contact
Before we start I thought I'd answer a few questions you guys had.
First, Abby has the same general powers all the original aliens had and her special ability is something similar to mind warp. She doesn't mind warp because she knows the trouble it can cause (Tess), but she can, using this ability, bend people to her will. Basically she can get into their minds and leave a suggestion, which the person will think is their own idea. This is discussed further in later chapters.
As for Jesse and the Evanses, this was all taken care of years ago. Basically, about 8 years after they left, Jesse met a woman and wanted to get married. To do this he needed a divorce from Isabel. Using the postmarks on letters Isabel had been sending them for years, the Evanses were able to track the aliens down. Isabel, who was with Kyle by this time, was more than happy to give Jesse a divorce, and she and Max stayed in contact with their parents after that. They've never actually been back to Roswell, however, because they all wanted to leave that part of their past behind.
Ok, here you go. Remember to review!
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Chapter 7: Contact
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__
Three Weeks Later
Abby walked Connor to the door and kissed him softly.
"Goodnight," she whispered and quietly shut the door behind him. She turned to go upstairs but was stopped by a voice in the dark.
"What were you two doing up there?" Maria hissed from the other room. Abby slowly walked into the room and turned the light on, realizing she had been caught.
"We were just, talking, you know," she lied pathetically. Maria rolled her eyes.
"Please," she said, "I'm not stupid. You don't just talk to a guy alone in your room till 2 am. Now what were you really doing."
"We were talking," Abby said defensively. She then lowered her eyes and whispered softly, "most of the time."
"Ah hah!" Maria exclaimed, standing up. "So something was going on, you admit it." Abby remained silent, refusing to give herself away. "Give it up, kid," Maria continued. "I already know what was going on, I just think we need to have a talk." Abby sighed.
"Sorry, Mom, that's just not something I really want to talk to you about."
"Well tough luck, sweetie, you don't get a say in this. Now sit!" Abby quickly obeyed, sitting on the sofa as commanded. "Ok, since you've decided to start sleeping with people without first consulting me, there's a few things we need to discuss." Abby nodded.
"Ok," she said.
"First of all," Maria began, "are you crazy!!!!? You are sixteen years old. You don't have sex. That's just a fact, not an opinion. You're not ready!"
"Mom, don't," Abby begged. "Please just don't give me a lecture about this. I was obviously ready because I made the decision."
"You made the decision, he didn't push you?" Maria asked suspiciously.
"No, he didn't push me. He was wonderful. After the first time I was scared and wanted to slow down for a while and he was even willing to do that. He's great." Abby smiled to herself, thinking about how wonderful Connor really was.
"Well, that's great," Maria said sarcastically, "but it doesn't change the fact that you're having sex. Are you two being careful? You know, taking precautions?" Abby nodded.
"Yeah, yeah, every time," she said. "We're not stupid, Mom." Maria laughed.
"Well that remains to be seen," she said. "How long has this been going on?" Abby paused before answering. She knew her mom would flip out if she told her the truth, told her that they had slept together before they even started dating. As much as Maria tried, Abby didn't think she'd understand the physical and mental connection she shared with Connor.
"A while," she answered cautiously.
"How long is a while," Maria pressed. Abby gulped.
"A couple of weeks." Maria flipped out.
"A couple of weeks?" she asked. "A couple of weeks! You've only known him two months. Dear God, how easy are you?" Abby started to cry. "Oh baby, I'm sorry, I didn't mean it like that."
"You just don't understand," Abby sobbed. "I love him, I really do. It's like he's my soul mate or something. I feel complete when he's with me."
"I understand, I do," Maria said. "I just worry about you. You're my baby, and you're so young. I just want to take care of you." Abby wiped her eyes.
"I appreciate it," she said. "Really I do, but I'm not as young as you think, and I can take care of myself."
"I know," Maria said. "I just still think of you as a little girl, when you're really all grown up. I don't know if I can handle it." Abby hugged her.
"Thanks, Mom," she said. Maria smoothed her daughter's hair down.
"Just promise me you'll be careful," she begged. Abby nodded and got up to leave. "And don't let your father find out. He'll kill Connor." Abby nodded in agreement.
"Believe me, I live in constant fear of that." Maria smiled and Abby went upstairs to bed.
~*~
On the planet Fallor in a galaxy far away, King Larek was sitting in his office attending to some business at hand. A royal page entered.
"Your highness, Queen Katana of Jacobni is here to speak with you," he said. Larek looked up.
"Send her in," he replied. The page left and Katana entered.
"Larek," she said, crossing the room and greeting him.
"It's good to see you again, Katana," he said. "What can I do for you?"
"I was considering your offer to contact the Royal Four and learn if the High King and Queen are with them."
"Yes," Larek said, "what is your decision?"
"I would like you to contact them. It will help our emissary find them more easily, and, if they are with the Royal Four, it will give them time to prepare for their departure."
"Very well, Katana," Larek said nodding. "I will prepare for communication immediately."
~*~
The next evening Abby and Connor lie on a blanket on the dock of the small lake in their town, alternating conversation and kissing.
"I wish tomorrow wasn't Monday," Abby said, pulling away from Connor and laying her head back on the pillow and looking up at the stars. Connor had started college the week before and Abby was going back to high school the next morning.
"I know, but school does have some advantages," he said, kissing her again.
"Like what?" she asked, smiling.
"You learn cool stuff," he said.
"Care to elaborate?" she asked, snuggling closer to him to block off the wind.
"If ever any beauty I did see, Which I desir'd, and got, twas but a dream of thee*," he whispered in her ear. She sighed contentedly but then, after a second, popped up.
"What do you mean 'which I desir'd and got'?" she demanded. He sat up after her.
"I didn't mean anything," Connor insisted. "I was just quoting the first thing that came to mind. I swear I didn't mean anything by it." Abby smiled to herself, realizing Connor wasn't going to catch on to her joke.
"So now you're saying that you don't mean the things you say to me?" Abby asked angrily, turning towards him.
"No.... that's not it. Come on, Abby, you know what I mean." She moved away from him.
"I'm not listening," she said, turning her back towards him. He inched closer to her and pushed her hair to one side, moving in to wrap his arms around her.
"No," she said, pushing him away. He sat back and thought a second.
"They flee from me that sometime did me seek, with naked foot stalking in my chamber*," he whispered, with a questioning look in his eyes. Abby turned around and laughed.
"You are adorable," she said, pushing him back down and kissing him before lying back next to him.
"You were joking all that time, weren't you?" he asked incredulously. She laughed.
"Yeah, I was wondering if you would figure it out or not." He pulled her tighter.
"I hate that you won't let me feel what you're feeling," he whispered. "Why won't you? I love you, you know." She turned her face towards him.
"I know," she said. "I love you too, but I'm just not comfortable with that yet. So, anyway, what did you mean by 'which I desired, and got'?" This threw Connor off for a second.
"Well.... I mean.... um.... I just wanted to tell you that you were beautiful. I didn't mean to make you think there was anybody else, ever. There's only you." He kissed the palm of her hand and looked pleadingly into her eyes. She smiled.
"Well, maybe you should find a better way to say it then," she commanded, snuggling against his chest. After a few moments he spoke.
"She walks in beauty, like the night of cloudless climes and starry skies; and all that's best of dark and bright meet in her aspect and her eyes.*" Abby reached up and kissed him softly.
"I liked that," she whispered.
"I thought you might," he replied, kissing her again.
~*~
There was a knock at the door and Max went to answer it, finding Brody Davis on the other side.
"Brody?" Max asked, slightly confused. He hadn't seen Brody since they left Roswell, and he was certain Brody didn't know where he lived.
"It's Larek," he replied, walking into the house. Max shut the door behind him.
"You're here about the light, aren't you?" Max asked.
"You know about the beacon?" Larek asked, surprised.
"No," Max replied. "We don't know what it was, we just saw it."
"Well, I'm here to tell you about it, so I need you to get the others here. There's alot to cover and you know I don't have much time." Max nodded and quickly got his friends and family on the phone. Within a half hour they were all there.
"So what's going on, Larek?" Max asked once they were all assembled. "What was that light about?"
"Well, back in our star system we have a legend," Larek began. "A myth really, or so we thought. It said that, when our worlds were torn apart and were in the greatest need, a High King and Queen would be born to us and they would unite and rule over our five kingdoms. The legend says that, when they are ready for their burden, they will find one another and a sign will be given. The light was the sign the legend spoke of." He looked at everyone assembled.
"So how does this affect us?" Isabel asked. "And, why would we see it on Earth when it was meant for your home planet."
"Don't forget that it's your home planet as well," Larek said.
"Still," Kyle interjected. "Why would they see it here, and why could only they see it?"
"The signal is only visible to people from our home star system, it's programmed into our biology." He paused for a second.
"You still haven't explained why you're here," Michael said, "and why we could see it on Earth."
"The answer to both of those questions is simple," Larek said. "The signal came from Earth."
"That means the King and Queen, or whatever, are here, on Earth, right?" Isabel asked. Larek nodded.
"Yes, hence my visit. We need to find out who the Royal Couple are, and, since you four are the only people from our star system on this planet, we imagine you know."
"But we don't know," Isabel said. "And, even if it did, why do you need to find them?"
"An emissary is on its way," Larek answered. "It has been since the day after the signal was given. It is being sent to your planet to retrieve the High King and Queen and bring them back. Obviously, since they're likely to be connected to you, you will be welcome to come back as well."
"What about...." Max began, but Larek stopped him.
"Kivar was against the retrieval in the first place, his citizens were not. His government is being overthrown as we speak. The people of Antar are clamoring for your return."
"Wait, wait...." Isabel said. "You want us to just give up our lives, leave our families, and come to a home we don't remember because some mythical couple may have been found. That's crazy."
"No, you're not being forced to come," Larek stated. "And, if you do decide to return, your families will be welcome. Remember, you are royalty and your public will eagerly accept any member of your family."
"Ok, so what we have so far is that this light means, according to legend, that some magical, mystical royalty has been found that will rule over all of our planets," Michael began, "and because of this you are traveling across the universe, overthrowing governments, and offering to bring us and our families home?"
"Yes," Larek answered matter-of-factly.
"How long do we have to think about this?" Ava asked.
"The emissary will arrive on Thursday morning at 1 a.m. It will stay only long enough to retrieve the High King and Queen and, if you are with them, you," Larek answered.
"How do you plan on finding the High King and Queen?" Max asked.
"That's where you come in," Larek answered. "We were hoping that, given the proper information, you could identify them."
"What do we need to know?" Kyle asked.
"They would be young and alien, obviously," Larek said. "Probably between 15 and 20. They would also likely be a relatively new couple. According to the legend, when they reached maturity and were able to handle their responsibility, an uncontrollable biological urge would draw them together and, once it had, the signal would be given. Basically, on the night they were first together physically, the signal would go off, alerting the people of our five worlds that their High King and Queen had found one another and reached both physical and mental maturity, making them ready to rule."
"I still don't quite understand this," Sean said. "What you're saying is that two alien kids grow up, find one another, get all hot and, when they sleep together, some signal is sent letting you know where they are?"
"Yes, basically," Larek answered. "And this happened on the night the signal was sent; they would have been together for the first time on this night. Do you have any idea who they are?" The nine people in the room looked around in silence. Suddenly a look of understanding and fear came on Maria's face.
"Oh my God," she whispered, just loud enough for everyone in the room to hear. They all looked at her, but she and Max locked eyes and she knew he was thinking the same thing.
"You know who they are?" Larek asked. Maria looked at Max and then at Larek and nodded.
"Well," Michael pressed, "who are they?" Max looked at Maria, then at Michael.
"Abby and Connor," he answered. Everyone in the room looked at him in shock.
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*The poems Connor quotes from are, in order, "The Good Morrow" by John Donne, "The Lover Showeth How He is Forsaken of Such as He Sometime Enjoyed" by Sir Thomas Wyatt, and "She Walks in Beauty" by George Gordon, Lord Byron.
10. Decisions
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Chapter 8: Decisions
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Abby laughed at what Connor had just said as he opened the door to his house. They took their jackets off and turned to go upstairs when Michael grabbed Connor by the neck and pressed him against the wall, holding him with a death grip.
"I should kill you right now," he whispered menacingly. "Who the hell told you that you could lay a hand on my daughter?" Connor struggled to get away and Abby also pleaded with her father, but neither had much success. Another person walked into the hallway a second later.
"Let him go, Michael," Max ordered. "We have more important things to worry about." Michael paused for a moment and then nodded, releasing his grip on Connor, who fell to the floor gasping for breath. Abby checked to be sure he was fine and then looked into the next room and saw her mother, Liz, and Ava standing there.
"Mom, you said you wouldn't tell him," Abby said, visibly upset. She helped Connor off the floor and rubbed his back gently, glaring at her father.
"That's not exactly a primary concern right now," Max said, ushering her, Connor, and Michael into the room.
"We're not finished yet," Michael whispered to Connor as they walked into the room together. Connor gulped and moved away from him.
"What's going on here?" Connor asked as they entered the room, rubbing his neck where Michael had held him.
"You two might want to sit down," Liz said. Both looked concerned and did just what she said.
"Mom, what's happening here?" Abby asked, looking pathetically for help. Maria sat next to her and wrapped an arm around her, looking to Max for comfort.
"I think you should tell them, Max," she suggested. Max nodded.
"We need to know something first," Max began, "and it's kind of personal, but we need a truthful answer." Abby and Connor nodded. "On the night you went to the concert last month, did you, well, um, sleep together?" There was a long silence. Abby looked at Connor and he at her. Finally she looked at Maria and nodded.
"Yeah, yeah we did," she admitted. Michael, who had been pacing on the other side of the room, lunged towards Connor, a hostile look in his eyes.
"I'm gonna tear you apart, you little..." he growled before being stopped by Max.
"Calm down, Michael," Max said. "Now, when this happened, was it the first time?" Connor nodded and reached for Abby's hand. Max sighed and looked at Liz, who looked at Maria, who looked at Michael, who looked at Ava, who looked at Max. "There's our answer," Max said, "It's them."
"What do you mean?" Abby asked. "Mom, I still don't understand what's going on."
"Sweetie," Maria said in a choked voice, "there's something we need to tell you, and you may not understand at first. Really, we still don't." Abby gripped Connor's hand tighter.
"Ok," she said, "then tell us." Maria looked at Max and he began again.
"Our home planet, Antar, is one of five in a star system. Years ago these five planets worked together, peacefully. Eventually there was some sort of falling out and war began, and has continued ever since. No matter how hard they try they can't seem to work their differences out."
"What does this have to do with us?" Connor asked.
"I'm getting to that," Max replied. "Not long after the wars broke out, a wise man of some sort prophesized something. He said that the war would go on for many years, and, when the five planets had reached their time of greatest need, a messiah of sorts would be sent to them. The savior would be in the form of a couple, a High King and Queen, that would rule over the five planets and bring peace to the star system. The couple would function as a unit and neither would work without the other. Apparently, based on other information we've received from Larek and what we already know, that couple, the High King and Queen, is you." The two just sat there in utter silence for a few minutes, no one knowing just what to say.
"What... what does that mean?" Abby choked out.
"Basically," Max said, "you two are the supreme rulers of the five planets of our star system. Each planet has its own ruling family, but you rule over all of them."
"I know this is alot to think about," Liz said.
"Wait..." Connor said, standing up. He started walking to the other side of the room but, after coming a bit too close to Michael, he changed his mind. "Why are you even telling us this? We don't live on Antar; we're not there to rule. Why does it even matter?"
"You will be," Ava answered. Connor and Abby both looked at her. "Your signal kinda told them where to find you, so they're coming to get you. Larek said you'll have a choice, but you have until Thursday morning, around one, to make that decision. That's when the ship will arrive."
"Ship?" Abby asked. Maria stroked her hair.
"To take you... 'home'," she said.
"But this is home," Abby protested. "I don't want to go anywhere. I don't want to leave you."
"We would come with you," Max mentioned. "All of us." Connor had been silent for a time, watching Abby with worried eyes. He finally spoke up.
"We have until Wednesday night to decide?" he asked. Max nodded. "You guys would come with us?" Another nod. "We would be rulers... over everybody?" Yet another nod. He motioned for Abby to follow him into the next room.
"I know you don't want to leave, but think about it. It would be a fresh start for all of us. Our destiny." Abby looked at him with uncertain eyes.
"You want to go," she said, asking and stating in the same sentence.
"I do and I don't. If you decide you don't want to, I wouldn't consider it. But, think about it for a few days before you decide. We're like their only hope or something. Abby, you're my Queen. Don't even think about all of the power we'd have, think about what we'd accomplish. We would unite five kingdoms that have been warring for centuries. It's a prophecy.... It's our destiny."
"That's crap," Michael said, walking to Abby and pushing Connor away. "There's no such thing as a destiny. We make our own destiny. Don't tell my daughter anything different, and don't try to make her do anything she doesn't want to."
"Daddy, it's ok," Abby said as he wrapped an arm around her protectively. "He won't make me do anything. This will be my decision, Connor already said so." She looked at Connor. "I just need time to think about this, alone." He nodded.
"Take your time, just remember what I said."
"We're leaving now," Michael said, leading Abby away. She pulled back.
"Just a second, Daddy," she protested. "I'll be right there, I just want to say goodbye." Michael nodded but glared at Connor. He left them to collect Maria. Abby turned to Connor. "Sorry about that," she said. He shook his head.
"Don't worry about it," he said. "I'm glad he's so protective of you. It means you'll be taken care of whenever I'm not around." She smiled for the first time since they had arrived at his house.
"I can take care of myself," she said, lightly punching him on the shoulder. He took her arm and used it to pull her body into his.
"Still," he said, clinging to her protectively as she nuzzled into his neck, "I like to think you're being taken care of." She looked up and kissed him lightly.
"I'll call you after school tomorrow," she promised. "And I'll think about all of this tonight very carefully." He nodded.
"Don't worry," he said. "I'll support whatever decision you make, and I'll stand by you no matter what. I want you to choose based on what you want the most." She nodded and he kissed her. "Bye."
"Bye," she whispered in return, turning and going out to her parent's car.
~*~
The car ride back to their house was silent and, when they arrived, Abby immediately went up to her room, laid down, and cried. She had never felt so overwhelmed, scared, and pressured before. Then again, her decisions had never affected the lives of thousands of people before. There were plenty of things to consider before announcing a decision, but Abby already knew what that decision would be.
She had known since she had seen that look in his eyes. That look of complete and utter longing he had gotten when Ava said they were going home. Although she didn't quite understand it, Abby realized Connor must have some kind of attachment to their planet because he was born there. "He told me to make the decision on my own, though," she thought to herself.
Part of her wanted to go very badly. The idea of meeting people like herself thrilled her. But then again, she was more human than alien, and they wouldn't really be like her at all. The idea of the power thrilled her, but it also scared her. What little girl hadn't dreamt of being a princess? She was being told that she could be, no, already was, the High Queen of five planets. Not cities, countries, or kingdoms. Five separate planets. That also meant, however, that was even more people who could be affected by her mistakes. Five times as many lives she could ruin if she screwed up.
Then, on top of her fears and desires, she had to consider her family, as well as the rest of the aliens. If she and Connor left, they would all go with them. Even the humans, meaning her mom, Aunt Liz, and Uncle Kyle would be the outcasts on the strange planet, not the aliens. They never said what they wanted; they all placed the decision on her, letting Abby decide which course of action all of their lives would take.
Suddenly Abby was very angry, at Connor for letting her make the decision for him when he really wanted to go and at her parents for letting her make the decision when she didn't think she was ready to make that kind of life-altering choice. "But you are," she thought to herself. "That's why all of this is happening. Uncle Max said it occurred because we were both capable of handing our destiny, of ruling these planets and making this decision."
Then, she thought of all the people in the galaxy far, far away where her father had come from. They were all depending on her. They all wanted her to come, to come and save them. As if things weren't complicated enough as they were, she had to consider the thoughts and feelings of millions of her alien subjects. "I can't handle this," she thought. Then that nagging little voice that was already annoying her came back, "But you can. You are a High Queen. You were born and pre-destined to do this. It's part of who you are. You can do this because you will." She knew her answer, but also knew she would need the input of others. She needed her brother, and went to go find him.
"Nate," she said, coming into his room. "I need your help." He looked at her and could see immediately something was wrong.
"What did he do to you?" he asked, sitting up, ready to go kick some alien butt.
"Nothing, nothing, this has nothing to do with Connor. Well, almost nothing. Anyway, he's wonderful, he always is. This is completely different." Nate motioned for her to sit next to him.
"Shoot," he said.
"If you were given the opportunity to be the omnipotent ruler of a large group of planets, would you?" she asked. He looked slightly confused and taken aback. This was obviously not the question he had expected. After a moment he spoke.
"Yeah," he said, "I probably would. I mean, think of all the power that comes with that. Even if you didn't do anything with it, it would be great. And, if you did do something with it, you could accomplish great things. Then again, I've always thought I was destined for great things."
"Yeah," she joked, "Maybe someday you'll get promoted to assistant janitor." He pushed her.
"Why do you ask, anyway?" he asked.
"Oh, no reason...." she lied. "I was just wondering. My real question is a little more important. If you had the chance to go to our home planet and live there, with all of us going, would you want to?" This required a bit more thought.
"Everyone alien-related would come?" he asked. She nodded. "Then I don't think it would make much difference. I'd have everyone I cared about with me. I mean, we never got close to any humans other than the obvious, and they'd all come along. Maybe it'd be cool to go see where we came from and meet people of our own race." Abby nodded.
"Thanks for the input," she said, rising. Nate reached out an arm to stop her.
"Wait," he said. "Sit." She obeyed. "Now tell me why you're suddenly so interested in all of this." She sighed, looking at the clock, which already read 1:03 a. m. This was going to be a long night.
"Are you comfortable?" she asked. "Because this is going to take a while."
~*~
The knock on his window woke Connor from his sleep. He groaned and then looked at the clock. It read 3:56 am. He turned over to go back to sleep, but the knock was persistent. Finally he sat up and saw Abby on the other side, perched on the tree outside his window. He quickly got up and let her in.
"What they heck are you doing here?" he asked, pulling her in. It had been raining and she was soaking wet. She shivered as he peeled off her wet clothing, wrapped her in a blanket, and hugged her close.
"I was thinking and I couldn't sleep, so I decided to go for a walk and then it started raining, so I came here." Connor knew this made no sense but decided to ignore it, laying her onto his bed, climbing in next to her, and wrapping a blanket around both of them.
"This is really freaking you out, isn't it?" he asked. She nodded. "Please don't let it bother you. I don't want you to do anything you don't want to." She turned her head to look at him.
"How can you say that," she asked, "when I know you want this so badly?"
"Because it's the truth," he replied. "I'd hate myself if I forced you into doing something you didn't want. I don't want any regrets. I want this to be your decision."
"It's not though," Abby whispered. "It affects everybody, and everybody wants me to decide. I'm not ready for that, and, if I can't handle it, how can I handle making decisions for five planets worth of people?"
"Because we're a team, remember? Dad said that neither of us could rule without the other because we both have talents and personalities that are suited to different areas of leadership. You can do it because I'll be there to help you." Abby snuggled against him.
"Maybe we shouldn't talk about it anymore," she suggested. He held her tighter.
"Yeah," he replied. "We both have to get up in 3 hours. I know I'll sleep better with you here, so let's just sleep, and don't let anything bother you." With that they closed their eyes and went to sleep.
A few hours later the sun was up and Connor gently nudged Abby awake.
"C'mon," he whispered softly, "I'll give you a ride home." She rolled over and looked at him.
"I have something to tell you first," she said. Connor stroked her hair and looked into her eyes. "I want to go. I know this now. I want to fulfill my destiny, and I want to be your queen." He hugged her.
"You already are my queen," he whispered, rubbing her back gently.
"There's one thing," she added. He pulled away and looked concerned. "I don't want to go if anyone else doesn't want to. I don't want to make anyone I care about come just because I said so."
"Ok," Connor said nodding. "Tonight we'll have a meeting. We'll tell everyone our decision and then have each of them make the decision for themselves. Anyone who wants to come with us can come to meet the ship when it lands. If everyone doesn't come, we won't go."
"I like that plan," Abby said, folding herself back into Connor's arms. "I love you."
"I love you, too," he whispered. They laid there a while. "Are you going to school today?" he asked, realizing the time.
"No," Abby said, shaking her head. "It seems kind of pointless if we're going to be leaving the planet in two and a half days. I'd rather just spend this time taking in all of the things I'm going to miss." He nodded.
"I'm with you on that." They both closed their eyes and were going to go back to sleep when, suddenly realizing something, Connor spoke up. "You know, it's not fair for you to be laying in my bed like this with no clothes on." Abby had forgotten he had taken her wet clothes off the night before and laughed, thankful for the comedic relief.
"Well," she said seductively, her hands traveling down his chest, "I guess we'll have to take yours off too."
~*~
That evening everyone was gathered in the sitting room of Max and Liz's house.
"We've made a decision," Connor told them. Abby nodded her head and he continued. "We're going." Everyone looked slightly shocked.
"But," Abby said, "not everyone has to come with us. We've made this decision because we want to do what's right and we want to do what we were both born to do. No one else has to do this." Everyone in the room looked very confused.
"What she's trying to say is that we realize you all have lives established here and there are many reasons each of you have for not wanting to come with us. It's your choice. The ship to take us home is arriving around 1 a.m. on Thursday morning at Lafayette Point. Abby and I will be there to meet it. Anybody who wants to come can either drive with us or meet us there. If you don't want to leave, just don't show up, no questions asked."
"Is this the plan then?" Michael asked, standing up with a furious look in his eyes. "You're just going to take my daughter, my underage daughter, off the planet and tell me I don't have to come with her? Abby, did you make this decision on your own, or did he tell you what to decide?"
"This was my decision, and these are my terms. I don' want any of you to come against your will, so each of you get to make your decision. I hope you'll all decide to come with me, I love you all, but, if you don't, I'll understand."
"Well, I'm coming for sure," Michael said. "You're not going anywhere without me, and especially not with him." He stepped menacingly towards Connor but was stopped by Maria's arm.
"I'm coming then, too," she said, looking into Michael's eyes. Nate agreed.
"You're my twin, Abbs. You can't go anywhere without me, you wouldn't know what to do." Lane looked at Nate and then at Abby and her brother.
"I wouldn't have anything to do without you three. I want to come too. Besides, think of all the fun alien mischief we could cause on another planet... especially with you two in charge." Hearing this, Max and Liz looked at each other.
"We're coming too," they said in unison. Ava stepped forward and hugged Connor.
"You're like my son," she whispered. "And I only just found you. I really have nothing keeping me here; I'm coming too."
"If she's going, I might as well go too," Sean said. "I'd get bored otherwise." Connor looked at Abby, who was smiling because their plan was working. Being given the choice, they were all coming on their own. Then she looked at her Aunt Isabel and Uncle Kyle, who were sitting off to the side, whispering. Alex was playing on the floor next to them, happily unobservant of the goings-on around him.
"Aunt Iz," Abby whispered, afraid Isabel would decide not to come. Isabel and Kyle looked up. Kyle whispered something to Isabel and she smiled.
"We're coming too," she finally said. Abby ran over and hugged her.
"Great," Connor said, already beginning to assume a position of leadership. "Then we're all going. I suppose that's it. We have two days left on Earth; I guess we should all see about tying up loose ends."
11. The Departure
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****
Chapter 9: The Departure
*~*~*~*~*~*~*~*~*~*~*~
The two days until the ship was to come passed all too quickly for everyone involved. Each person spent time saying good-bye to friends and colleagues and tying up loose ends. The packing was the hardest part, for everything important in their lives had to fit into a few small bags. They were all leaving the planet they had called home for years to go to one they had no memory of.
On day of departure, Abby, worried and stressed, was finishing some last minute packing in her room when she realized something. She ran out of her room and to her parents', searching for her mother.
"Mom," she gasped when she found Maria. "I need to talk to you." Maria nodded, for she had been expecting this for some time. Abby sat down on the edge of her parents' bed. "I can't do this. I don't know how to be a leader; I don't know how to make life or death decisions. This isn't going to work because I'm going to fail... and then all those people will suffer because of me." Maria sat next to her and stroked her back.
"This will work, because you'll make it work," she said reassuringly. "You've never failed at anything you've ever done. You don't let yourself fail. Remember when you wanted to play the piano, but your fingers couldn't stretch enough to reach all of the keys? You sat at that bench for hours on end each day, refusing to give up, until you could do it. This is the same thing . . . only on a slightly bigger scale. The difference is you have a partner in this. I know Connor. He'll do anything he can to make this easy on you, and I can see the makings of a great leader in him, as long as you're with him to give him strength and determination." Abby nodded.
"I know you're right, I know I can do this. I'm just so scared." Maria hugged her.
"Honey, it's alright to be scared. Hell, I'm scared. Your father won't admit it, but he's scared. We're all scared. And you have alot more to be scared over. But, you'll be fine; I know this. You'll find strength in that fear and turn it into good."
"Thanks, Mom, I needed that," Abby said, standing. She felt much better.
"I know," was all Maria said. "I love you, hon." Abby smiled.
"I love you, too, Mom," she repeated. "And you're right. I can't do this without Connor. But I also couldn't do it without you." With that she left to finish her packing and wait patiently for Connor, who was coming early that evening, to arrive. There was something she wanted very much to tell him.
~*~
Connor arrived at Abby's house at 8 p.m. as planned. They were leaving at 11 in order to reach the landing sight around 12:30. Both wanted to spend their last few hours on Earth together.
"I have something to tell you," Abby said excitedly, when he entered her room.
"Ok," he said, sitting on her bed.
"I've figured it out," she proudly announced, sitting next to him. He looked confused, so she continued. "I know why this is going to work. Why they say neither of us is any good without the other. How the two of us are going to manage to rule five planets."
"Please tell me then," Connor begged, "because I don't have the slightest clue. I'm scared to death." Abby smiled and ran a hand through his hair.
"I'm scared too," she said. "But strength comes from fear, and we'll need plenty of that." Connor nodded.
"We're two different personalities," she began. "Do you agree?" He nodded. "I'm more friendly and personable, not just with people I know, but also with strangers. I put people at ease when they're with me, and people like me. You're more quiet and reserved. You know how to judge people for who they are, and you know how to make wise, informed decisions. The only time you make snap decisions is when you're really passionate about something, like going home." Connor again nodded, and she continued. "I'm more of the people person, you're more of the behind the scenes guy. It's perfect. And, furthermore, our talents are matched together perfectly."
"Explain," Connor urged, not quite understanding this last part.
"You can read people," she stated. "You try it all the time with me and I know you do it with everyone around you. I can do it to a smaller extent, you know, reading people's emotions when they are really strong, but that's more of a human quality. My main talent is my ability to influence people in smaller decisions. I can get into their mind and leave ideas there, you know, to help them make the decision that I want them to make. These two abilities, yours and mine, work together. You can see what people are thinking, and I can 'help' them to think another way, if necessary. It works."
"I can see that," Connor said. "Why the sudden epiphany?"
"I was scared to go," she answered, "and my mom helped me see that I could handle this. She told me that you would help me handle it, and that's when I realized that's what this is all about. We help one another, emotionally, psychologically, and rationally. Well, and physically too. That's why this will work, and also why it'll only work if we're together. We're meant to be together.... designed to be together."
"This will work," Connor echoed, kissing her. "You and I will make it work." She kissed him again and he started to pull her onto the bed.
"Wait," Abby said, pulling back up. "There's one more thing." He sat up again.
"What?" he asked. She took his hands in hers and moved as close to him as she could get.
"You say I'm closed off to you," she began. "You are always trying to read me, and I won't let you, because I'm afraid. I'm afraid of what you might think. To do this, to leave this planet to go be the High King and Queen in another galaxy, we need to trust one another completely, and have nothing between us. My father and mother went through the same thing when they were younger. He wouldn't let her see him because he was afraid to let people in. When he did, however, it only made them closer. I want us to be closer, like they are." She looked into his eyes. "I want you to see me." With that, she let the defenses built up in her mind down, and Connor could see everything she thought.
He could see the present, as well as the past he had already seen. He could see how incredibly frightened she was of leaving, but how certain she was it was the right decision. He felt how much love she had for him, and how much trust she was giving him. He could see her every thought. He pulled her closer to him and kissed her, and, in doing so, transmitted his thoughts and feelings to her. They sat together for an eternity exploring one another's minds, learning all there was to know. Connor had never seen this far into any person's mind, and he had never been able to show anyone his. Their connection was magical.
~*~
The hours passed and it was time. Near 1 a.m. they all stood in the decreed spot, waiting for this transport to arrive. Abby sat with Connor, the two of them having a reassuring conversation with their minds. Everyone looked scared and unsure. No one knew what would happen. Then, right on time, a ship landed. It wasn't what they had expected. It was smaller, about the size of a small bus, but very tall. A man who looked completely human stepped out of the large doors.
"Greetings all," he said, walking forward. "I've taken this shape because it is the most familiar to you. My real shape is something different, as you will find soon enough. In a few moments you will board this transport. A larger ship is waiting above the Earth's atmosphere. We will travel in it to Jacobni, the capital planet of our star system. The journey is a long one and, as you have probably realized, will take close to a month." He paused for a moment, looking around at all the people, human and alien alike, in front of him. "I assume you are all coming?"
"Yes," Max said, stepping forward. "That's not a problem, is it?" The man shook his head.
"Not at all," he replied. "I've just realized several of you are human, and I wasn't sure."
"The humans are coming too," Michael said defensively, wrapping an arm around Maria. "We were told this would be acceptable."
"It is," the man said. "And now for introductions. I am Orophan, from the planet Antar. I am a shape shifter, as I believe they are called down here, a member of the King's special service, the Gizmod. Two of our rank were sent with you when you first traveled here. We protect the King and his family from danger, hence my being on this journey. I need to make a list of all who will be traveling with me, both for your safety and for arrangements upon your arrival." Max stepped forward.
"I'm Max," he said, "or Zan as I was once called." Orophan looked up from the paper he was recording this on.
"My liege," he said, bowing. "We have long awaited your return. Except for a few heretics who serve Kivar, my order has been in exile under his rule. With news of your return he has been overthrown and your throne restored. The men of my order wait patiently to serve you once again." Max nodded and continued.
"This is my wife, Liz, and my daughter, Elena," he said, gesturing at the appropriate people. Orophan nodded. "Over there is my sister, Isabel, and her husband, Kyle. The boy is their son, Alex." Orophan looked at Isabel for a second.
"Vilandra," he said, with more than a hint of disdain in his voice. Isabel looked upset.
"No," Max said, a stern and kingly tone in his voice, "Isabel. Vilandra is dead, and Isabel is most certainly not her." Orophan bowed again.
"Your pardon, my liege," he said. Max nodded, as did Isabel.
"Over there is Ava and Sean," Max said. Orophan wrote this down. "He," Max continued, pointing at Michael, "is my friend Michael, or Rath as he was once called." Orophan bowed to Michael. "The woman is his wife, Maria, and over there is his son, Nathan." Orophan wrote this down and then surveyed the group, noting the two teenagers who had yet to be named.
"And those?" he asked, pointing.
"My son, Connor," Max answered proudly, "and Michael's daughter, Abigail. Apparently, they are the reason for this trip." At this, Orophan dropped the board he had been writing on and walked to Abby and Connor, kneeling before them.
"My King and Queen," he began. "It is my greatest honor to protect you on the journey to our home and to serve you afterwards." Connor nodded and Abby looked bewildered. Orophan stood. "I will go and prepare for take-off," he said, "and you will all follow." He walked inside the dark ship and everyone gathered their belongings, preparing to follow. As they walked forward, Abby realized something. She surveyed her surroundings and then looked at Connor.
"Oh my God," she whispered to him. "My dream, this is my dream." He took her hand, just as in the dream, and lead her to the ship, which suddenly came on and blanketed them in light. She looked into his eyes, as in her dream, and knew everything would be fine. They were going home.
12. A Journey in the Dark
~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*
****
Chapter 10: A Journey in the Dark
~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*
Inside the ship was cool and dark. At the front they could vaguely see another man in the pilot's seat. There was a group of seats in the back of the craft and then another closer to the front. Orophan directed the group to the back seats, but brought Abby and Connor to the more forward seats.
"You'll be able to see our take-off better from this position, majesties," he explained. Abby glanced back to see that her family was safe and comfortable before sitting. Orophan sat in the co-pilot's seat and gave orders for the ship to depart.
Shortly after everyone was seated the small vessel rose into the air, very quietly and smoothly. It quickly traveled into the sky, its altitude increasing with dizzying rapidity. Abby watched with fear and sadness as her planet, Earth, disappeared below her. She knew it was likely she would never return here, and that made her very sad. Connor, able to read her thoughts, took her hand and sent a calming vibe to her. He knew, somehow, that everything would be ok, and this made Abby feel much better. They continued to watch the ground below become smaller and smaller, until they could see it no longer. Within a matter of minutes they had broken through the Earth's atmosphere and entered the dark void of space.
During the process of leaving, Connor had become very interested. If he was soon to be the ruler of the planet that created this transport ship, he wanted to know about it.
"How does this ship rise so quickly and quietly?" he asked Orophan. The man smiled at what was, on his home planet, a naive question.
"The mechanics on Daglomar, the planet that built this ship, are far ahead of Earth's. In fact, the technology that can be found on each of the five planets is so far advanced it makes the Earth look prehistoric. This ship has a different engine than you would be used to. It runs on stored light energy, photons, and therefore makes no noise and can generate a massive amount of power in a short time." Connor nodded, fascinated by the idea. Abby glanced out the window and caught sight of the Narnath, the ship that would take them home, and had a question of her own.
"How do you keep such a large ship hidden from satellites and radar?" she asked.
"As I said," Orophan began, "the Earth's technology is almost non-existent compared to ours. Our ship is simply cloaked from their radar. Even if they knew we were here, they still couldn't see us." Abby nodded. The ship decelerated and moved toward the Narnath. Orophan stood.
"It was a pleasure conversing with you, your highnesses," he said to Abby and Connor. "I hope we will have more similar opportunities once you are safely aboard the ship." He walked further back where everyone else was seated. "In a few moments we will be aboard the Narnath, one of the most powerful ships known to our star system. Our journey will take, as I mentioned before, approximately a month. If there is anything you desire while on board that is in our power to provide, you will have it. There is a full staff on board whose sole purpose is to make your journey comfortable. While they have been trained to expect strange behavior from you, it would be prudent of you to remember one thing. No matter who you were on Earth, you are royalty here. Each of you is a member of the Royal House of Antar. In addition, you travel with the Royal Couple's envoy. People will want to serve you; let them." Each person nodded, showing they understood this order. In fact, certain members of the traveling party were more than willing to let people serve them.
The ship descended onto a receiving platform and was pulled into the loading bay of the Narnath. Orophan stepped off the ship, spoke with a man outside, and then returned.
"Come," he said, "and do not trouble with your luggage. It will be delivered to your rooms within a few minutes." Everyone stood and walked, with great trepidation, off the ship. None of them expected what was awaiting them on the platform. A large group of servants and military officers were there, all bowing in respect before the High King and Queen. Orophan lead the group forward to a man who looked to be rather important. He walked forward, surveying the group.
"My Lord High King," he said, bowing to Connor. He turned to Abby, kissed her hand, and bowed again, "My Queen." He stood and examined the rest of the group, bowing in turn to Isabel, Michael, Ava, and Max. After he had finished his examination of the travelers, he spoke.
"I am Aranth, the personal secretary of King Larek of Fallor. He arranged this mission personally and asked that I see it through. Orophan, with whom you traveled thus far, is the second in command on the Narnath. Our staff is fully devoted to fulfilling your every desire; just let us know if there is something you need. Rooms have been prepared for you according to the list Orophan has sent me. If you have any other questions or requests, please feel free to come to me." He handed each of them a map. "This is a basic outline of the ship. It is rather large and formidable to newcomers. Each of your rooms, as well as mine and Orophan's, are marked. My personal dining room and office is where we will meet to discuss any concerns you may have. I will also have private meetings with each of you here, once you are all settled. I believe that is all for now. You must be tired, so I will see you to your rooms." Abby gripped Connor's hand tightly and looked behind her at her brother. He looked as scared as she did. Michael's eyes found his daughter's and he gave her a reassuring nod. Abby turned around and they all followed Aranth.
Following Aranth they quickly reached the wing of the ship devoted to their personal quarters. Each family had a small apartment with enough rooms to fit their family, depending on its size. After a quick examination of the size and layout of their apartment, everyone was pleased. Everyone but Michael, that is.
"Where is my daughter staying?" Michael asked, realizing there wasn't a room for Abby in him and Maria's apartment and becoming angry.
"Their rooms are marked on the map," Orophan answered, motioning for his King and Queen to follow.
"No," Michael stated simply, blocking Abby's path forward. "Abby is staying here with us. She's not going to share a room with him. She's still a child." Abby shot Michael a death look.
"She is not a child anymore, My Lord," Aranth stated simply. "She is a queen, and the queen does not sleep with her parents. And besides, you do not expect to sleep away from your wife, why should your daughter sleep away from her husband?" Michael was about to say something in protest and then stopped, confused.
"But, we're not married," Abby said, equally confused. Connor realized what Aranth was talking about.
"Yes we are," he said. She turned to face him. "We were married before we were born. We've been married all of our lives." Abby nodded, vaguely understanding, and Aranth looked pleased that his High King was so clever. Abby turned to her parents.
"I'm just down the hall," she said, motioning towards her room on the map. "You can see me anytime. I'll miss you, but they're right, I'm not a child anymore. I'm a Queen." Maria could see the regal quality emerging in her daughter and hugged her tight, trying not to cry.
"Come to me anytime you need anything, baby," she whispered and Abby nodded. She turned to her father, who looked away.
"Daddy, please don't do this," she begged. Michael looked at her and through the grown woman, the queen, he saw a scared little girl. It was the same little girl whose hurts he had mending, whose bad dreams he had chased away. He had played with this little girl, spent long nights comforting this little girl, and loved this little girl. He loved his daughter. He hated to lose her to Connor, but she would always be his in his heart.
"I don't agree with this," he began, "but I understand. Go, be with him, but remember I'm always here." Abby hugged her father tight, remembering all the times they had had together.
"I love you, Daddy," she whispered. He nodded, unable to say anything for fear of crying. Abby turned to Nate.
"You know you can come bother me all the time?" she said, more than asked. He nodded and hugged her.
"I'll miss you anyway," he said, kissing her cheek. Abby pulled away and looked at her family one last time, then walked down the hall to her new room and new life.
~*~
After settling in their rooms and arranging a meeting with Aranth for the next day, the High King and Queen sat next to one another on the bed they were to share. There they had a conversation but spoke no words.
"You're sad," Connor said with his mind, reaching out to Abby and gently stroking her hand.
"Yeah," she replied in the same way, "but I'll be ok. I'm happy too." He nodded.
"I know. I'm just more worried about the sad part of you."
"That part will be ok," she responded. "It just needs time to get used to this new arrangement.
"You're not upset that we're living together.... or that we're married, are you?" he asked, concerned.
"I thought you would have read my mind to find that out by now," she stated. He shook his head.
"I could, but those are your private thoughts. Just knowing they're there for me to look at, that your walls are down, is enough. I won't invade your personal thoughts." She smiled at him.
"Thank you," she replied. He repeated his question about her feelings. "No, I'm just kind of overwhelmed. I mean three days ago I was just Abby, a slightly abnormal high school student who lived with her parents and had a gorgeous boyfriend. Now I'm Abby, High Queen of several planets light years from her home, and I'm living with my husband, who is still gorgeous, by the way." Connor laughed.
"If all of your thoughts are this good, I'm going to have to invade them more often."
"I like talking to you with my mind," Abby said. "Think of all the fun we can have with this."
"I have been," Connor replied. "There's a world, galaxy, of trouble we could cause with this. But, in all seriousness, just remember you are still the same person. The only difference is a few small details about your personal life. You're still my Abby, and I still love you." She leaned over and kissed him, and, then, finally spoke.
"I think I'm actually glad you're my husband," she said. "I need someone like you around. You make all my troubles seem not important." She stood up and walked to her few suitcases, beginning to unpack her pajamas.
"Tired?" Connor asked. She nodded. He went over to his belongings and did the same. He then surveyed the pile of suitcases and bags in front of them. "I think we should wait until tomorrow to unpack," he said. Abby agreed, so they changed and went to bed.
~*~
The next morning Abby awoke to Connor staring at her face.
"What are you doing?" she asked.
"Looking at my wife," he answered. She smiled happily.
"I like the sound of that," she said. "You're my husband." He nodded and then looked around.
"Do you think it's morning?"
"I guess," Abby replied. "I can't tell without the sun or clocks, but I feel like I've been sleeping for some time."
"Me too," Connor agreed. There was a knock on the door.
"Your highnesses," came the voice of a strange woman on the other side of the door. Abby and Connor rose quickly and wrapped themselves in their robes before unlocking the door for her to enter.
"The man called Max has sent me to tell you that your party is meeting in his private dining room this morning for breakfast. You have an hour." Connor nodded and Abby thanked her. After she left they set to work quickly dressing and getting ready before going to eat with their family.
The day passed quickly enough for the two. After breakfast they had returned to their rooms to explore and unpack before meeting Aranth for a lunch meeting. He informed them they would be meeting with him every afternoon at the same time so he could instruct them in their duties as High King and Queen, as well as give them a history of the five planets. After lunch they met Nate and Lane and went to exploring the ship, meeting many interesting crewmembers. Later that evening the two shared a quiet evening meal alone in their new 'house.' They stayed up late talking and planning, both starting to become excited about their new life.
~*~
The next few weeks continued in much the same way, with the new couple attempting to balance family time, personal time, study time, and alone together time. The mornings were usually with their parents, early afternoons with Aranth, late afternoons with Nate and Lane, and evenings alone. As the days passed, Abby and Connor grew closer and began to act more as if they were married. The ability to speak to one another with their minds increased to the point where they did not have to be together, or even near one another, to do so.
The afternoons the two spent with Aranth proved to be very interesting and informative. He taught them first of the history of the five planets. The ruling families, the wars, the political strife, and the advancements. Then he taught them of the customs and culture of each planet. Antar, where the High King's palace was being built, was a lush, tropical planet with many large cities and centers of technological advancement interspersed with wetlands. Of the five, it was the one most similar to Earth. Years ago it had been the most powerful of the five planets. When Kivar took over, however, it lost most of its beauty and power. It was hoped the return of King Zan would change this.
After learning of the planets, Abby and Connor were taught their roles as High King and Queen. Apparently they were very powerful. In fact, they were the most powerful people in all the galaxy. Their job was similar to that of both a figurehead and a dictator. They were in charge of all five planets, but the individual rulers of each planet would take care of the daily business. The High King and Queen would serve to override their decisions if it was necessary and to make the highly important decisions.
When the Narnath landed, Abby and Connor would first be taken to their palace, which was near the palace of the King of Antar, allowing them to be close to their family. After they had settled they would travel to each of the five planets individually and meet the ruler of the planet and greet its people. Once this was done, they would return to their palace and begin their duties as High King and Queen. Orophan would stay with them as their chief councilor.
~*~
On the day before the ship was scheduled to arrive on Antar, their last day with Aranth, he had a gift for them. When they arrived for lunch and their lesson he informed them there would be no lesson that day. They ate together for the last time and then, before they left he stopped them.
"I have something for you before you go, your Highness," he said, looking at Abby. "It's in my office." Abby nodded and looked at Connor.
"I'll go wait back in our room," he said. He left and she followed Orophan into his office.
"I know you did not completely understand your destiny when you first heard it," he began. He pulled a small book out of a drawer. "This is the legend King Larek spoke of when he visited your parents on Earth. This book was written by a prophet shortly after the warring began. He foresaw it in a dream and knew it would come to pass. This book has been used as a bedtime tale for small children on all of our planets for centuries. I had it translated into your language so you could read it and see." Abby took it and looked it over carefully.
"Thank you," she said in awe.
"It was my pleasure, milady, as it has been my pleasure to serve you." He bowed and she left, quickly going to find Connor.
Once in her bedroom, where she had found him, Abby sat in a chair and began to read the book carefully. Connor sat and watched her, amazed by how excited and interested she was.
"What's got you so interested in that book, babe?" he asked. She looked up at him.
"It's us, Connor. This book is about us, and it was written centuries before we were born. It just interests me, I suppose, finding out why we are what we are, seeing what people thought we would be like." He nodded, coming closer to understanding her interest. She simply wanted answers, wanted to find out who she was. She continued reading and he watched her, finding in her mind the legend she was reading on the page.
13. Coming Home
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Chapter 11: Home
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Early the next morning Abby woke to an empty bed. She searched the apartment for Connor but couldn't find him anywhere. All of their belongings were packed and piled by the door; the ship was landing that morning. Quickly throwing on the elegant robes Aranth had given her to wear for the landing, Abby left in search of her husband. After checking both Nate and Lane's rooms and Max's home, she turned to her parents. Her mother hadn't seen him, but her father was apparently missing as well. Worried, Abby left in a huff, checking up and down the corridor.
"So you're saying you don't want us together? Isn't it a little late for that?" Abby stopped when she heard Connor's angry voice coming from within a room. She put her ear against the door.
"I didn't say that," Michael said. "I said I didn't want my daughter with you. I can't stop her and I won't try."
"That's good, because she's my wife," Connor retorted, his voice rising. "You can't keep us apart so please don't try. And you know what, Michael? I don't appreciate this in the least. I've done nothing but love and care for her since the moment I met her. I've never hurt her and I've never done anything to earn this hatred."
"You took my daughter away from me. She's too young, she needs her family."
"She's a grown woman. She was going to leave you some day. I just gave her somewhere safe to go. At least you know she'll always be protected with me."
"But she'd be safer with me. I'm her father." Abby couldn't listen to them argue anymore.
"Would you two please stop this?" she demanded, bursting into the room. "Quit arguing about me all the time and quit fighting over me. This is ridiculous. Dad, Connor's right. I'm grown up and don't need you to watch over me. All always love you, but I'm all grown up now. And Connor, my Dad's right too. Maybe this all happened too soon and maybe I'm too young. Please respect my father's opinion on the subject." Connor nodded.
"Fine," he said. "I can do that."
"Daddy," Abby said, turning to Michael. "I'm grown up. I have a husband. Whether you like it or not, things have changed. Please let them change. I'm not asking that you like Connor or this new situation, I'm asking that you accept it and allow me to live my life." Michael sighed.
"Yeah," he replied. "I can do that."
"Good." Abby hugged him and then took Connor by the hand. "I'll see you when we land, Daddy." Michael nodded and Abby and Connor left.
~*~
A few hours later the ship was landing. Everyone was assembled and waiting. Everyone was scared. Abby spoke to Connor in her mind.
"What if they don't accept us?" she asked, trying not to show her fear to the others around her. Connor turned his head towards her and touched her hand gently.
"They will accept us," he said with certainty. "And, besides, even if they don't, we still have each other, and our families. We can always go home."
"I hope you're right," she replied.
"I am, I think. Are you afraid?"
"No," Abby answered with certainty.
"I am," Connor said honestly. "Why aren't you scared?"
"The first time I met Aranth privately, he told me something. He said we would be tested many times on our journey and we would be afraid."
"Yeah," Connor said, "He said the same thing to me. What does that have to do with not being afraid?"
"He also told me to be a better leader I needed to be strong and not afraid. The people would look to us for strength. Remember what the book about us said? The motto the people follow in our honor? 'Fear is the mind-killer. Fear destroys strength, so strength must destroy fear before it can develop.' I'm just practicing what we will apparently preach."
"Well haven't you gotten clever," he stated with a smirk.
"Yes," she replied, trying not to laugh. To a casual onlooker they were standing in silence. If Abby were to laugh, their secret would be discovered, and they guarded their secret very carefully. The door before them opened and they followed Aranth onto their new world.
"Welcome to your new home, your Royal Highnesses," Aranth said, gesturing to the wide spread of subjects before them.
"Home," Connor whispered. "Abby, we're finally home." Abby smiled at him.
"Yeah, honey," she agreed, looking at all of her new subjects, bowing before them. "We're home."
~*~
Abby laid down on the expansive bed of her new bedroom. Connor collapsed next to her.
"That was the most exhausting day of my life," she sighed, curling against him.
"It's only the beginning," he replied.
"Don't remind me," she begged, closing her eyes to find the world of dreams.
Their day had been more than exhausting. The action had been non-stop from the moment they stepped off the ship. First they had to greet the people of Antar, the planet where their palace was located. Then they toured the capitol city of the planet and meeting all the people important to their reign. Among the people there to greet them were the rulers of the other four planets. After the tour of the city, the two were quickly rushed into meetings with the four rulers to discuss diplomacy and policy. This made Abby's head ache, but Connor definitely enjoyed it. Once their initial meetings with the four rulers were over, there was an official ceremony to welcome the High King and Queen and officially grant them power over the five planets. Immediately following this there was another ceremony, where Abby and Connor, as High King and Queen, reinstated Max as the King of Antar and to make the humans citizens of the planet under the protection of both the King of Antar and the High King and Queen.
By the time the ceremonies had ended Abby and Connor were exhausted. Before being allowed to go home and relax, however, they had to attend a diplomatic dinner in the King of Antar's home. To the public it was a dinner of the rulers to discuss diplomacy and other political matters. Privately, it was the last chance Max, Michael, and Maria had to have their children to themselves before they moved into their own home and officially became independent. The rulers of the other four planets were there as well to become acquainted with the Royal Couple and, more specifically, their large and interesting Earth-family.
After the meal Abby and Connor finally came to their new home, the High King's Palace, in the center of the city. Quickly changing and preparing for bed, they were passed out within an hour of arrival.
~*~
The next few days continued much the same. There were official meetings to attend, subjects to greet, and a home to get settled into. By the end of the week the two were slightly more comfortable with their hectic schedule and with their new home. After they were settled, the first real act of the High King and Queen was to travel on a diplomatic mission to each of the other four planets, greeting the planets' people and meeting with their rulers. Since they had already met each of the leaders, this task was not at all daunting.
First they visited Fallor, the planet ruled by their parents' old friend, Larek. Larek was particularly fond of Connor because he was Max's son. Abby loved Larek's home, as well as the planet itself. The diversity of life on the planet was incredible. Beyond that, the habitat of the citizens boggled the mind. The primary living arrangement of the Fallorians was in trees. The planet was populated with forests and huts in trees seemed the most agreeable way for the race to live. Larek's palace was, however, located on the ground. The people of Fallor had a physique more suited to climbing than the other races of the five planets, so their diplomatic center was located on the ground, where others could more easily reach it. Abby and Connor stayed in Larek's palace for a week, touring all of Fallor and meeting as many of its people as possible.
After Fallor they moved on to Zallini, which was ruled by Sero. He was a nice enough man who, overall, seemed very happy with Abby and Connor. Zallini itself was the largest of the four planets, but most of it was covered with water. Unlike on Antar, however, the water wasn't like water on Earth. It was red and thick and very dense. The parts of the planet that were not covered in this water, called "carboth" by the Zallinians, were filled with hills and mountains. Most of the Zallinians actually lived in huts inside the hills, or caves inside the mountains. They had tried building homes on land originally, but the fierce carboth-storms Zallini suffered would always destroy them. Soon it just became an evolutionary adaptation to use nature as their home. Abby and Connor stayed here for a week as well, meeting the people, touring the planet, and discovering the joys of swimming in carboth.
After Zallini, Daglomar was the next planet to visit. Abby didn't care for it in the least, and she found the leader of the planet, Hanar, less than charming. Connor liked him, for he was definitely a man's man, but the planet lacked character. The whole planet, from top to bottom, was plains. Not plains and hills, or plains and rivers, or plains and woodlands, but just plains. One could see miles by looking into the distance, for often nothing blocked the scenery. The planet was plain boring. The one thing it did boast was an assortment of wildlife, which the hunting of was the primary entertainment. Abby and Connor only stayed four days here, and it was four days too many in Abby's opinion.
Finally the two came to Jacobni, the most powerful planet of the five, ruled by Queen Katana. Jacobni was, interestingly enough, the smallest of the five planets. Instead of boasting of interesting natural wonders or fascinating wildlife, Jacobni had technology. While all five planets had incredible technology, Jacobni oozed it. The whole planet was one large, impressive city. Both Abby and Connor were in awe of its enormousness and wanted to spend forever exploring it. After a week and a half, however, they had to return home. Their one-month tour of the five planets was over and they had to deal with official business.
And the first piece of official business was the judgment of Kivar.
~~~**~~~
A/N: Yes, I stole from Frank Herbert, as I believe everyone should do at least once. I just love that line and think it's very true. If you have no idea what I'm talking about, here you go:
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The Bene Gesserit Litany against Fear
from the series of Dune Novels
I must not fear.
Fear is the mind-killer.
Fear is the little-death that brings total obliteration.
I will face my fear.
I will permit it to pass over me and through me.
And when it has gone past I will turn the inner eye to see its path.
Where the fear has gone there will be nothing.
Only I will remain.
14. The Judgement of Kivar
We're almost done. Keep those reviews coming, people!
Special thanks to Roswell428 for finding the huge mistake in the last chapter. It's been fixed, so check it out if you want to.
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Chapter 12: The Judgement of Kivar
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Immediately upon arriving on Antar the High King and Queen had new business to attend to. They met with their advisor, Orophan, to be briefed.
"When Kivar's government was overthrown he was captured by the Gizmod to await judgment. Now that you have comfortably taken over your role in the government, it is time for his judgement," Orophan explained.
"Why do we have to do this?" Abby asked.
"You have supreme control over all of this star system. Kivar was once a ruler of Antar. Even though he is no longer in power, no one can judge him but you. Only you have power over the rulers of the five planets."
"So what exactly do we have to do?" Connor asked.
"Basically, you will hear the wrongs committed by Kivar, against the throne of Antar as well as against your own leadership, and make judgment based on these facts. I believe it is similar to a trial on your old planet."
"Except there's no jury, no defense, no chance," Abby said, feeling a bit sorry for Kivar.
"That is the way things are done here, your Highness," Orophan explained. "I know it may be different to you, but it is for the best. If you allow others to question your authority, you will lose it." Abby nodded.
"I understand but I still feel kind of bad about it," she said. Connor placed a hand on her shoulder.
"We choose what will happen to him, right?" he asked. Orophan nodded.
"The people will want justice for the wrongs he has committed," he explained. "But his fate is entirely in your hands."
"There you go, Abby," Connor said. "We can be merciful, if it's warranted. It's not unfair."
"I suppose you're right," she conceded. "And besides, I don't know everything he's done in the past but, from what I can tell, he's not exactly the greatest person. He probably doesn't deserve an impartial trial."
"That's the spirit," Orophan cheered. "Remember you were born specifically to do this job. You know how to do it better than anyone else. You will know how to handle Kivar better than anyone else." Abby nodded.
"When is this all happening?" she asked.
"Tomorrow morning you will meet with Kivar and the leader of the Gizmod. He will lay out all of Kivar's wrongdoings and, if he likes, Kivar will give explanations and ask for mercy. It will then be up to you to make your decision."
"Ok," Abby said. "Tomorrow then. Thank you, Orophan."
"It was my pleasure, my lady," he replied bowing.
~*~
That night Abby sat on her bed, brushing her hair, with Connor laying next to her. She had spent the entire day pondering the issue of Kivar.
"What do you think we should do about Kivar?" she finally asked, laying her brush on the bedside table and turning to Connor.
"I'm not sure," he replied. "Part of me thinks maybe we should pardon him, or banish him or something, but the other part hates him and wants him dead. He killed our parents once, you know."
"Yeah," Abby agreed, nodding. "Actually he tried to do it twice. Aunt Isabel told me once about how he came for her and tried to kill our fathers. She said he's a really frightening man."
"Do you think we should have him, I don't know, executed or whatever?" Connor asked.
"I don't know. I was always against the death penalty, but I don't know that I see any more options. We can't really let him live. You know he'd just try to take power again."
"That's probably very true," Connor agreed. "People like that don't give up very easily. For all we know he's scheming how to get us to let him off and then how to stage a coup or something." Abby laughed.
"That's probably true," she agreed.
~*~
Outside a man was peering in the window, watching and listening to Abby and Connor's conversation.
"Keep on laughing, Your Highness," he said with a sneer. "You won't be laughing much longer.
He turned away from the window, keeping his ear tuned to the room. As the conversation between Abby and Connor continued, he went over his plan again. There was only one variable that remained unaccounted for.
"How am I going to get them apart?" he asked himself as he turned back to the window. He searched both of their minds for an idea and found exactly what he was looking for.
"Very well," he said to himself. "Now let's get this underway."
~*~
Abby turned from Connor and glanced towards the window.
"I suppose we won't know what to do until we hear what he has to say tomorrow," she said.
"Yeah," Connor replied, turning off the light on his side of the bed. "Just a few more hours and then we'll know." He settled down in the bed and pulled the covers up. "I'm going to sleep. You should try to get some rest too." Abby, barely listening, walked towards the window.
"Yeah," she said. "Goodnight." Something outside caught her attention. Looking closer, she saw the flash of some animal running by. It was an animal from Earth, but what it was she could not say. Intrigued, she decided to investigate. "I'm gonna go for a walk in the garden. I need to think." Connor, half asleep, barely heard her.
"Have fun," he mumbled, before allowing sleep to claim him. Abby wrapped her robe around her body and slipped on some shoes. Quickly and quietly she exited the room and ran out of the palace, hoping to find the creature before it vanished. She entered the gardens outside her bedroom and traveled through them quietly, looking for the horse.
After a few minutes of walking up and down the rows of the labyrinth-like garden, Abby began to get chilled. She decided the horse must have been a figment of her imagination and began to walk the long trek back to her room. As she walked back down the path she had taken, she felt a familiar presence. She knew someone else was there, but wasn't sure who. They felt very familiar, yet something was remarkably different.
"Hello," she said, looking around her. "Is someone there?" After a moment of silence she heard a rustle. Fear began to grip her, but she pushed it away.
"This is the High Queen speaking," she said in her most regal voice. "Whoever is there, I demand that you show yourself." The rustling continued and, after a moment, Connor stepped out from behind a nearby tree.
"Starting to get all Queenly, are you babe?" he asked, stepping towards her.
"Oh, Connor," she gasped. "You scared me so much. I didn't know who was there. You should have said something." He wrapped his arms around her and smiled.
"Well," he explained. "I couldn't sleep without you next to me, so I decided to come looking for you. I didn't mean to scare you, Abby." She smiled.
"It's okay," she said. "It's a welcome surprise." She leaned into him and kissed him. After a few seconds she broke away and stared at him.
"Connor?" she asked, confused. The images she had seen when she kissed him were not anything like she was used to seeing. They were darker, more malicious. She saw places and things she had never seen before. She tried to back away, but she was too late. Before she had taken a step back a wicked grin had spread onto his face and a needle was inserted into her back. Abby's body fell to the ground.
~*~
"Abby!" Connor shouted, bolting upright in bed, sweat pouring down his face. He reached for Abby but found a void in her place. He shouted to her in his mind and received no answer. Quickly he climbed out of bed and ran from the room, searching for his wife.
Connor ran up and down the halls, calling Abby's name and checking in every room. Within a few minutes the entire staff had been awoken by his hysteria. The entire palace was searched top to bottom to no avail.
"Did she not say where she was going, my King?" one of the servants asked.
"No, no she didn't," Connor said. "Wait, I remember her saying something right before I fell asleep, but I can't remember what. I was so tired. She said she was going out.... but where?" The servant immediately called for a group to search the palace grounds and, if necessary, the city. Connor paced back and forth, worried. He kept calling to Abby in his mind but received no reply.
"Your Highness, please, think," the servant begged. "If she told you where she was going our search would be easier."
"I am, I am," Connor said angrily. He stepped towards the servant with a hostile look in his eyes. "Do you not think I want to find my wife?" The servant backed away.
"I'm sorry, my Lord. I meant nothing of the sort." Connor walked away and continued pacing, trying to remember what Abby had said. Finally he looked up in realization.
"The gardens," he exclaimed. "She said she was going for a walk in the gardens." He ran out of the palace and towards the gardens.
"Abby!!!" he shouted, traveling as fast as he could through the expansive area. Finally he came upon some members of the search party.
"My Liege," one man said. "We found these." He handed a small bundle to Connor. It was one of Abby's slippers and a tiny needle.
"What is this?" he asked, holding up the needle.
"It is black-market," the man explained. "It is used to inject poison, usually." Connor fell to his knees.
"No," he whispered. He continued calling out to Abby through their connection but received no reply.
~*~
Abby awoke with a start in a strange location. She groggily looked around, recognizing nothing. Feeling the ropes that bound her hands, she slowly began to remember what that happened.
"Where am I?" she asked, frightened. A candle was lit and she could make out that she was in a cave of some sort. A voice spoke to her. A familiar voice.
"You are in hiding with us," Connor's voice said.
"Connor?" she asked. "What's going on here?" More candles were lit and she could see there were several people in the room. Except, she noted, they were not people. They had a strange appearance, one that was like nothing Abby had ever seen before. The only person in the room who looked human was Connor. But was he Connor?
The man that looked like Connor spoke again.
"You are being held hostage by the Flad-adan," he explained. "There is no escape, so do not even consider it. I know what you are thinking." Abby looked at him, frightened, and tried desperately to restore the mental block she had kept up when she first met Connor.
"I demand to be released," she said, attempting her most regal tone. The Connor-man only laughed, as did the strange creatures in the room.
"You are in no position to demand anything, Highness," he sneered, leaning over her and pushing her down. "I am in charge here. You are at my mercy." Tears formed in Abby's eyes. In her mind she repeated tried to build up courage, but to no avail.
"Please," she gasped. "Let me go." The man backed away a bit and looked her over carefully in a way that made Abby feel less than comfortable.
"Now why should we let such a pretty thing go?" he asked.
"I'm very powerful," Abby said, attempting to sway his mind with her powers as she spoke. She couldn't seem to get into his mind, however. Where her powers had been there was some sort of foggy void. She tried persuasion. "I can get you anything you desire if you free me." The man seemed to consider this for a second.
"We will set you free when we get what we want from your dear husband."
"What do you want?" Abby asked, expecting the worst.
"Kivar's freedom," the man replied. He ran a hand down Abby's face and placed it on her shoulder. "And you will not be safe until he has it."
15. Imprisonment
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Warning: This chapter is not nice. It's dark and meant to be that way. It will not make you feel happy and good. I promise it will get better later, but this is necessary for now. Don't read it if you don't feel comfortable. That is all.
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Chapter 13: Imprisonment
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Abby sat in the dark, alone and cold for what seemed like an eternity. She tried to call out to Connor in her mind but couldn't find her way through the muck. Finally the door to the room she was in opened and the man walked in carrying a candle and a plate.
"You've been here for a while now," he said. "You must be hungry." He sat down next to her. Abby had to remind herself that he was not, in fact, her husband. He looked just like Connor and, when he was nice, he even sounded like him.
He offered her a bite of what was on the plate. Abby was starving but she refused to open her mouth, not wanting to be a complacent prisoner.
"Come on," he ordered, his voice losing the soft tone. "I know you're hungry, just eat." Abby kept her mouth shut. He sighed and then grabbed her chin. "I don't want to hurt you, so just open your pretty mouth and eat." Abby relented and took a bite. He continued to feed her. After they had finished he stood up to leave.
"Could you loosen these ropes, or take them off, or something?" Abby asked, trying her best to look cute and innocent. She had been struggling with the bonds for several hours and her wrists had been rubbed raw from the action. He laughed.
"Not just yet," he said. "Maybe after a while, but those will be of use to us soon." He laughed again, sending chills down her spine, and then left her alone again in the dark.
~*~
After a while the man returned. He sat down again and looked at Abby, who had fallen asleep.
"Wake up, little Queen," he whispered, softly nudging her. She opened her eyes, looked at him, and then scooted away. "Don't worry," he said. "I won't hurt you. Yet." Abby stared at him, frightened but not wanting to show it.
"What do you want, then?" she asked. He looked up and down her body with a sick grin.
"Well, I know what I want, but I'm here to talk to you. I'm assuming you're getting bored all alone in the dark." Abby shuddered at the gleam in his eye, but decided to talk if it would at least keep him off of her.
"Where are we?" she asked.
"I told you once before," he answered with a sigh. "You're in my secret hide-out. That's all you need to know."
"Fine," she replied. "Who are you?" He smiled.
"I was wondering how long it would take you to ask that." He thought for a moment. "Well, since I've blocked your connection with your husband, I suppose I can just tell you. I am Kivar's son."
"I didn't think Kivar had a son," Abby said. "No one every told us about you. And, if you're Kivar's son, why are you a shape-shifter?" He chuckled.
"At least you know your Antarian history," he said, moving closer to her. Their bodies were now touching and Abby was becoming queasy because of it. "Kivar's not my actual father. He adopted me as an infant and raised me in secret. He said I was his secret weapon and my time would come. He was right." He paused for a moment. "As for your other question, I'm not a shape-shifter. I couldn't do it if I wanted to, and I really don't want to."
"Why, why do you look like Connor, then?" Abby asked, confused and scared.
"Because," he said, moving his face towards hers. "I am Connor." He kissed her softly and she received the same visions she had gotten in the garden.
"No you're not," she insisted. "I know Connor. You're not him."
"Well," he said, backing away again. "I'm not actually Connor. My name is Cirdan. He and I do share the same genes, though. Genetically we are the same person. But, mentally, I'm far superior." Abby tried not to laugh at the idea of this creep being superior to her Connor. "Why do you think Kivar wanted Tess to bring Max's child to him? Why do you think he sent Connor back? Kivar has been preparing for King Zan's return for years. He was fairly certain he would never return but, in case he did, I was his safety." Abby nodded, understanding. Kivar was far more conniving than she had originally thought.
"Why kidnap me, then?" Abby asked. "Why not just storm the palace with your little army of whatever those things are..."
"Flad-adan," he interrupted.
"Yeah, Flad-adan," she repeated before continuing. "And take power? Wouldn't that have been easier and quicker?" He nodded.
"Yes, it would have been, but this all was quite a shock. We hadn't planned on Kivar being captured when he was, so we have no plan to work from. We're basically lost without his leadership." He sat back in thought for a moment.
"You know," he said, "You're asking an awful lot of questions. I think it's my turn to ask the questions." Abby's eyes widened as he moved closer to her again and ran a hand down her body, caressing her skin.
"Do you like that?" Biting her lip and trying to move away, Abby answered.
"No, please stop." He smiled his most disgusting smile and continued downwards. He stopped the movement to play with her breasts a bit and then continued downwards, reaching her thighs. She cursed herself for wearing such a flimsy nightgown to go walking in. Every muscle in her body tightened as he explored her, finding her most sensitive regions and enjoying them.
"What about that? I know you like that."
"No, I don't. Please stop," she begged. "Why are you doing this?" He pulled her away from the wall and laid her on the ground.
"Because I can," he hissed, climbing on top of her. "And because, when my genetic duplicate finds you so desirable, how can you expect me not too?" Abby struggled desperately, but the bonds around her wrist were too tight and he was too heavy. Her struggling only heightened his arousal and, before long, he had claimed her as his own.
After finishing with her Cirdan left the room and Abby lie curled on the ground, crying.
~*~
Back at the palace, Connor was desperate. Something kept telling him Abby wasn't dead, despite what his closest advisors were saying. Shortly after she had gone missing the King of Antar and his court were summoned. Now they were arriving. Connor was pacing in the foyer as they entered the palace.
Maria looked panicked and Michael lunged at Connor, stopped only by the High King's substantial number of bodyguards, who had been watching him closely since the Queen had disappeared.
"You promised you would take care of her!!!" Michael shouted at him. "You said nothing would hurt her as long as she was with you. I'm going to kill you if she's not alive. I should have never trusted my daughter with you." Connor knew he should be frightened, but he was in far too much distress to notice.
"Michael," Max said, placing a hand on his shoulder in an attempt to calm him. "Shouting at one another won't help anything. We need to concentrate on finding her." Maria, who had been standing quietly, broke into sobs and sank to the ground. Liz sat next to her and wrapped her arms around her. Michael, feeling helpless, fled the room. Max looked at his son, who had resumed his frantic pacing.
"Connor," he began, "Calm down. The only thing you can accomplish by acting like this is making yourself sick." Connor looked at his father.
"How can I be calm when she's not here? She's missing, Dad, and she might be dead. I can't feel her anymore." Max placed a supportive arm around his son.
"Don't worry," he said. "We'll figure it out. I promise." Connor nodded and, for the first time since Abby's disappearance, broke into tears, sobbing on his father's shoulder. Max stayed with him for a while and then, once the tears had subsided, left to go find Michael. Maria left Liz's embrace and went to Connor, finding comfort in being close to the last person to see her daughter.
Max searched the palace for Michael, worrying about what he might do in his state of hysteria. Finally he found him in Abby and Connor's bedroom, sitting on their bed, staring into space.
"Michael," Max said cautiously, entered the room. Michael looked up at him and Max could see the tears running down his face.
"I don't know what to do, Max," he said. "I can't help her. My baby needs me and I can't help her." Max sat next to Michael.
"I'm not going to lie to you, Michael," he said. "Things look bad, but there's still hope. We need to concentrate on finding a way to help her right now, instead of berating ourselves and others for not being able to." Michael nodded.
"I know, I'm just so scared for her. I love her so much, Maxwell." Max nodded.
"I know," he said. "Believe me, I know." One of the first things he had done when he had heard the news was to go in search of Lane, just to make sure she was fine. "C'mon, let's go back downstairs. Maria needs you right now, Michael." He nodded and stood, wiping his face.
"We have to find her," he said. "We have to."
~*~
Abby lay cold and shivering on the ground, not really caring what happened to her. She wanted so much to die. The door had opened and closed on several occasions, but she had taken little notice. First some kind-looking woman had brought her a blanket. Then Cirdan had come to check on her. Finally the woman had returned to clean her up. Abby knew not much time had passed, but it seemed like an eternity. She knew she had to find a way to contact Connor. She knew she needed to find a way out of there.
After a while the door opened again and Cirdan entered along with one of the strange creatures she had seen when she first awoke. He walked over to her and she sat up and inched away.
"Relax, my precious, I don't want you for myself right now," he assured her, gently, almost lovingly, stroking her cheek. Abby relaxed a bit, but not much.
"Bind her feet," Cirdan ordered to the creature. Abby tried to fight it, but the creature had her feet tied together within a matter of moments.
"Good to see some of that feisty nature's left in you," Cirdan said, enjoying the show. "That could be useful later." Abby's temper flared. She hated this man so much.
"What do you want?" she hissed, not really caring if he killed her at the moment.
"It's time to put our plan into motion," he explained. "It's time to let your husband know you're not actually dead." Abby stared at him, shocked. "Oh yes," Cirdan said, answering her silent question. "He believes you to be dead and, believe me, he is suffering for it." Abby fought to free herself, simply so she could kill the detestable man in front of her. He laughed.
"Are you ready, my lord?" the creature next to him croaked. Cirdan nodded and the creature moved to Abby, laying her flat on the ground and holding her there. Cirdan walked over and withdrew two needles from behind his back.
"You see," he explained as he went to work, "We need to send a message Connor will receive loud and clear. He'll fear for you and then, when he gets our demands, he'll cooperate. I'm sure you've noticed I've blocked your telepathic abilities. This will free them up, but just a little. It'll be enough for him to sense your presence, but not enough for you to talk to him or work any of your powers on me." With that he plunged one of the needles into the back of her neck.
Abby lay there for a few minutes, feeling woozy. Then, suddenly, her senses cleared up. She could work the part of her brain that had been so foggy and distant a few moments ago. Cirdan watched her and, when he was sure the medicine had worked, he spoke.
"I bet you're wondering what this other needle is now, aren't you." Abby looked at him with apprehension. She had long since forgotten that she shouldn't show fear, and she was most definitely afraid. He sat down next to her and ran a hand through her hair.
"Oh, Abby," he sighed. "I feel like we've become so close since you arrived. We've eaten together, we've talked, we've made love...." Abby hissed and he looked down at her. "You know, in a way, I love you." He looked off in the distance for a moment and then looked back down at her. "Well, I hate to have to hurt you, but I don't really have a choice." With that he stuck the needle into her abdomen, pushing its contents inside of her.
Abby lay there for a moment, wondering what was going to happen. Then it came. The pain. Abby had never felt anything like it before. It was a burning, blinding pain that started in her abdomen but quickly spread throughout her body. Her muscles tensed, her back arched, and sweat poured down her body. She wanted so badly to scream, but she wouldn't allow him the pleasure of hearing it. In her mind, however, she screamed, and screamed loudly.
~*~
Connor awoke screaming. He had been sleeping for the first time since Abby disappeared. Lane, who was watching over him, rushed to his side.
"What, Connor, what is it?" she asked, panicked.
"Abby, Abby," he said hysterically. "She's alive, I can feel her. She's in so much pain. I can hear her screaming. Oh God, I can hear her screaming." Lane held her brother in her arms and yelled for Nate, who was in the next room, to get their parents. Within a few minutes Max, Michael, Maria, and Liz were in the room.
"What's going on?" Max asked, voice elevated.
"Connor says Abby's alive," Lane said, looking at her father. "He says she's in pain. He can hear her screaming." Maria found refuge in Michael's arms and Michael stared off into space, not knowing what to do.
"The pain," Connor gasped, sweating and crying. "It hurts so much; it burns." He could feel everything that Abby felt and was so frightened for her. Max looked helplessly at Lane and then wrapped an arm around Liz. Connor continued shaking and, after a few moments, fell into a deep sleep.
Lane stood up and walked over to Nate, who took her in his arms. For the first time since this began, he spoke up.
"You guys have been in meetings with all these people all day. You have to have some idea what's going on." Max looked at Michael and Michael looked at his son.
"We think Kivar's behind this," Michael said. "In fact, we're pretty certain. He denies it, but we're having him brought here in hopes that we can get it out of him."
"I'll kill the bastard if he hurts my sister," Nate growled. Michael nodded in understanding.
"Not if I kill him first," he said. Everyone stood in the room, helpless, no one knowing better than the next what to do.
~*~
After a few minutes the pain had stopped and Abby had gone limp. Her eyes were tightly closed and she lay there whimpering, tears running down her face. If she had wanted death before, she begged for it now.
Cirdan had the creature cut the bonds on her legs and arms and then dismissed him. He took Abby's limp body into his arms and held her against him. She didn't protest and she didn't try to escape. Abby was exhausted and her body ached. She knew she despised this man, but she just wanted to be held. He looked like Connor, smelled like Connor, and felt like Connor. Now that his anger had passed and the soft voice returned, he even sounded like Connor. Abby was so afraid, so upset, so tired, she let herself believe it was Connor, and she let herself be held. Pleased, Cirdan pulled her tight against him and rocked back and forth, rubbing her back as he whispered soothing words to her.
"I'm sorry my love, but I had to do that," he explained. "I had to get through to him, and that was the only way I could make the impression I needed to. I promise I'll never hurt you like that again. I love you." He continued to hold her until her breathing slowed some and her grip on his shirt released. He looked down at her and felt something new. This emotion was strange to him; it was very different. He stood with her in his arms, walked to the door, and spoke as he walked out carrying her.
"I was thinking that maybe, when this is all over, Father would let me keep you around. I can kill him, Abby, and I can make you forget him."
16. A Plan Develops
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Chapter 14: A Plan Develops
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Abby woke up in a strange room. She was laying on a soft bed and the room was actually as warm and inviting as one could expect in a cave. The woman who had cared for her earlier was in the room, sitting quietly in a chair. She looked up when she saw Abby move.
"Oh, you're finally awake," she said happily. She was an old woman and looked, considering the circumstances, very pleasant. Her presence comforted Abby some.
"Where am I?" she asked, sitting up. Remnants from the pain before still lingered and she grimaced.
"Oh, here, honey," the woman said, walking over and handing Abby a cup. She looked at the lady for reassurment and then drank. The cool liquid quickly spread throughout her body and dulled the pain.
"Thank you," she said, handing the woman the cup.
"It's not a problem, dear," she said, sitting on the bed next to Abby. "Cirdan ordered that every possible measure be taken to assure your comfort." Abby gagged hearing that name but the woman took no notice. "That's why you're here of course. He thought that damp, dark cell wasn't good enough for you and wanted you to be comfortable and happy. This is the nicest room he could provide that could still be properly guarded. He really is a wonderful man, you know. I'm sure you don't think so, but soon you'll see it." Abby looked at this woman in shock and amazement. How could someone who seemed so nice defend such an evil man?
"I don't think I'll ever see anything like that," Abby said, shaking her head. The woman patted her hand.
"Oh, sure you will deary," she assured her. "Cirdan may come off as a little harsh at first, but that's just his father's influence. I raised him to be a sweet boy, and he still is at heart."
"You raised him?" Abby asked. The woman looked at her as if she had just come out of a daze.
"Yes, didn't I mention that?" she asked. "Well, anyway, I was his nanny. Lanna is my name, if you'd like to know. He was such a sweet boy. It was just he and I here, and those creatures, for most of his life. Kivar didn't want anyone to know the boy existed. I think that hurt Cirdan quite a bit, you know, thinking his father was ashamed of him. Of course, when he was older, Kivar started coming around more to train Cirdan. They grew close... or at least Cirdan developed some sort of a bond to Kivar. I'm not really sure. Anyway he changed Cirdan quite a bit. He warped the sweet boy I had raised, made him colder, more serious, and distant. I don't like it in the least, but I still see my little boy every once in a while." Abby just stared at the woman, attempting to digest everything Lanna said. She kept on babeling and Abby just nodded not really knowing what to think. For the first time since the evening she had been kidnapped, she laughed. Then the door opened.
Cirdan walked in and Lanna looked up at him and smiled, finally relenting the incessant jabbering.
"Dear boy," she smiled, walking to him. "I was just telling the darling here about when you were still a wee one." Connor smiled and nodded, looking at Abby over Lanna's shoulder.
"I'm sure she enjoyed that, Nan," he said, patting her on the shoulder. "Why don't you go see about getting her something to eat? I'll keep her company." Abby gulped apprehensively as Lanna nodded and left, leaving her alone with Cirdan.
He walked over to the bed and sat down. Her body tensed and she inched closer to the wall, trying to get away from him. He reached over and took her hand, looking into her eyes.
"Do you like it better here?" Abby relaxed a bit but remained defensive. She wanted to tell him just what she thought, but the look in his eyes, a pathetic lonely one, made her stop.
"Yeah," she replied, nodding. "It's much nicer. Thank you." After she had said it she cursed herself for encouraging him, but the look on his face was worth it. She imagined it must have been horrible to have a father like Kivar and it kind of began to explain his personality. Still, nothing could forgive his behavior.
"I'm sorry about Nan," he said, attempting to break the silence. "She's just a lonely old woman. She doesn't like the Flad-adan, so I'm all she has to talk to." Abby nodded.
"It's ok," she said. "I like having her here." He scooted closer to her, bringing his legs up onto the bed.
"You know," he said, "I'm lonely too." His hand traveled down the side of her face, gently stroking the outline. She tensed and visibly grimaced.
"Don't worry," he said in a soothing voice. "I won't force you anymore. I don't want to hurt you ever again." Abby relaxed but she wasn't sure if she could trust him. His face, eyes, and voice showed her Connor, but her memories of the previous day kept coming back.
"I... I... I don't feel comfortable with this in the least," she finally said, getting bold and pushing his hand away. Anger flashed across his eyes and then, after a moment, passed. He took her hand and kissed it.
"I understand," he said. "I need to win you, and I promise I will."
"No, I'm married," she insisted. "You won't win me." The anger came again and this time Abby could see him struggling to repress it.
"Remember, you're here with me now," he whispered, attempting to keep the anger out of his voice. "You may as well stop thinking of your husband. I'm him now." Abby shuddered and wanted to scream out that Cirdan could never be Connor, but she was stopped by Lanna reentering with food. Her stomach growled and Abby smiled happily.
"Here you go, dear," Lanna said. "I'm glad to see you two are getting along." She sat the tray down on her bedside table and smiled. Connor smiled back.
"Come on, Nan," he said. "Let's leave Abby alone for a while and let her eat." Lanna left and Connor rose to follow her. He looked back at Abby.
"Press the buzzer if you need anything," he said, gesturing to the intercom at the door. "Everything that's in this room is yours, so feel free to use anything. There are clothes, books, paper, and other stuff. Please, let me know if you need anything else." Abby smiled and nodded. He opened the door wide and faced her again. "And, as you see, this door is always guarded so don't even think about trying to escape." Abby's smile disappeared as she saw the two guards waiting outside. Connor shut the door and left her to herself.
~*~
Kivar was led into a room filled with people. Though he recognized only Orophan, Max, Michael, Isabel, and Ava, Liz, Maria, Connor, Kyle, Nate, Lane, and Sean were also there. He smirked when he saw Isabel and was led to a chair. Max walked to him.
"Well, isn't this an interesting turn of events," he said, smiling down at Kivar. He sneered upwards but didn't dignify Max with a reply.
"Well," Max continued, "If the pleasantries are done, let's get down to business." Kivar smiled at Max, hatred in his eyes.
"What can I do to help you?" he asked, a mocking tone in his voice. Michael, who had contained himself until this point, rushed forward.
"You can tell us what the hell you've done with my daughter!" he exclaimed menacingly, bearing down over Kivar.
"Michael," Max said softly. He relented and stepped back. Kivar laughed.
"It's good to see some things haven't changed..." Kivar said. Michael glared at him but his expression didn't change. Seeing this was getting nowhere, Connor stepped forward.
"Maybe you should let me take care of this," he said, walking towards Kivar. "You can all wait in the next room; I'll call you when you're needed." Michael started to say something but was stopped by Maria, who led him with the others out of the room. Connor sat on the table in front of Kivar.
"Good," he said. "Now that we are alone, we can talk a bit."
"What do I have to say to you?" Kivar asked, not impressed in the least. Connor looked very regal in the High King's robes and, to most, was a formidable figure. Kivar was undeterred, having raised a son to be exactly like Connor in every way.
"Well, we can just talk," Connor said. "How are you liking your accommodations?" Kivar laughed.
"What, going to be the kind king? Why don't I believe that?" Connor smiled and shrugged.
"Just trying to make sure you're comfortable," he said.
"Well," Kivar replied, "I'd be alot more comfortable if, say, you and your family were dead and I was in charge. But, considering the situation, I'm doing fine, thank you." Connor smiled and laughed.
"I'm glad to see you're retaining your humor, Kivar," he said, pretending not to notice the blatant threat.
"Well," Kivar said, "Just trying to lighten the mood a bit." There was a pause before he continued. "But I'm sure you didn't ask me here to discuss my sense of humor. Why don't you just ask it?"
"Ask what?" Connor said innocently.
"As the brute put it ever so poetically," Kivar began, "Where the hell your wife is." Connor shrugged.
"I'm sure you'll tell me in your own good time," he said. "I wouldn't want to pressure you." Kivar was a little put off by this. He had expected a demand for answers, not a casual disregard for them.
"Well," he said, "If you must know, she's still alive." Connor nodded.
"I suspected as much."
"Do you want to know how to get her back?"
"If you'd like to tell me." Kivar stammered for a minute.
"Wait, I know what you're trying to do," he said. "You're trying to get me to reveal where she is. It's not going to happen like that."
"I'm not sure what you're talking about," Connor said, shrugging. "But if you don't feel comfortable continuing, then don't." Kivar sat back a moment.
"Fine, I won't. But I feel I should tell you that you can get her back."
"Very well."
"She's being held for ransom, you know."
"I imagined as much."
"Her captors want my release. And they want you to give your power over to me." Connor thought for a moment.
"And if we just kill you?"
"She dies as well." He nodded thoughtfully.
"Of course I'll have to discuss your proposal. I'll get back to you on it." He remained calm and carefree, calling for the guards to remove Kivar, who was beyond bewildered at this point. After he had left the room, Connor called everyone else back in.
"Well," Michael said, walking over, "Did he buy it?" Connor smiled as largely as he had in a long while.
"Perfectly. He didn't have a clue what was going on. After seeing your display, very well done, I might add, he thought we had no clue what we were doing. Then he expected me to demand her return and was very thrown off by the fact that I didn't seem to care. It was so easy." Maria stepped forward, pushing Michael aside.
"So you got the info, right?" she asked. Connor nodded. "It's a system of caves in the mountains outside the city. She's being held by his son, Cirdan. Kivar doesn't seem to know much else. He doesn't have contact with them, I think. He did tell me their demands for her release, though."
"What are they?" Max asked. Connor smiled.
"Well first he mentioned he wanted all of us dead," he said, laughing. "As if he had the chance. But their actual demands are Kivar's release and me giving up my power." Max snickered.
"He really had no idea what you were doing, did he?" Connor laughed.
"Not a clue." Nate, who looked pleased but was definitely not laughing, walked over.
"We've still got problems, guys," he said. Connor and Max stopped laughing and looked at him. "Those are big mountains; we don't know where the caves are. And, even if we find them, how do we find Abby in them? And I imagine she's being very well guarded." The humor disappeared from the group.
"Abby's still alive," Connor said. "That's what's important. I'll try and contact her and see what she knows. Maybe, with her help, we can find the caves." The group nodded, all having recently become aware of Abby and Connor's telepathic connection, and Connor left them. He went to his room and lay down, trying with all his mental ability to contact his wife.
~*~
Abby lay in bed, eyes closed. She was still somewhat tired from her ordeal the day before, and sleep seemed the best diversion. The door opened and she felt him enter the room. His presence was becoming easier and easier for her to sense, especially when his emotions were strong. She lay there quietly, hoping he would think she was sleeping and leave. Instead he crept across the room and slid into the bed next to her, wrapping his arms around her.
Abby had to keep herself from wretching but remained still with slow breathing. Cirdan nuzzled into her neck and closed his eyes, quickly finding sleep. Abby lay there for a while, contemplating her situation, and then fell asleep, both comfortable and uncomfortable in his arms.
As she was walking through the world of dreams Abby felt a presence similar to Cirdan's yet different, and a voice whispering for her to wake up. Opening her eyes and realizing there was no one in the room besides Cirdan, she listened again. After a second the voice came again in her mind.
"Are you there?" It was a familiar voice, but one she wasn't quite sure she could remember.
"Yes, who is this?"
"You've only been gone two days and you've already forgotten me." Finally she realized who she was talking to, memories of her husband coming back to her.
"Connor. Connor," she said to him in her mind. "I was starting to think I might never see you again. The idea of hearing you seemed far too unreal."
"I haven't been able to contact you since you disappeared, but you contacted me last night. Since then I've been trying to reestablish the connection, but this was the first time it worked." Abby thought for a moment to herself, trying to remember when she had contacted Connor. Then she remembered the pain, and realized he must have felt it as well. Reminded of the horror the man who held her could bring, she was very scared again.
"Get me out of here, Connor, please," she begged him.
"We're working on it," he promised. "Are they hurting you there?" Abby was about to answer in the affirmative but stopped. Connor was worried enough. He didn't need the guilt of her suffering on him.
"Not so much," she lied. "They're actually taking good care of me, but I'm scared." Connor wondered about the pain he had felt the day before, but pushed it out of his mind.
"Do you have any idea where you are?"
"No," Abby replied. "They don't tell me much."
"Tell me what you know. We might be able to work with it."
"I'm in a cave," she replied. "This guy named Cirdan is the leader. He claims to be Kivar's son, but he's adopted. There are alot of strange creatures around here. Cirdan calls them Flad-adan. I don't know anything else."
"We might be able to work with that," Connor said. "I'll speak with Orophan and see if he can figure it out. We've interrogated Kivar, so we know some things. Don't worry, Abby, we'll get you out of there. I promise." Abby breathed a sigh of relief and felt Cirdan stir next to her.
"I've got to go," she said to Connor in a bit of a panic. "They're coming and they'll know if I'm talking to you."
"Ok," he replied. "I'll contact you again when we know the plan. And Abby, stay safe. Do whatever you have to to stay safe."
"I will," Abby replied. "I love you. Tell my family I'm ok."
"I will, and I love you too." With that he was gone and her senses became attuned to the room once again. She could sense Cirdan's emotions, and he was very angry.
"You're trying to leave me, aren't you?" he whispered, grasping her shoulder tightly and turning her towards him.
~*~
After contacting Abby, Connor had immediately gone to his family.
"I spoke with her," he announced, walking into the room with a grin. Maria looked up, joy on her face.
"Is she ok?" Michael asked.
"Yeah," Connor replied, feeling very happy. "She says they're taking good care of her."
"Good," Michael said. "Did anything she have to say help us at all?"
"Kind of," Connor replied. "She said she was in a cave, which we already knew, and was being held by a man called Cirdan, who claimed to be Kivar's son."
"Did she say which cave she was in?" Orophan asked impatiently. He had been advising them through the whole process and had been the one who suggested Kivar's involvement all along.
"No, but she said there were a bunch of strange creatures there... called Flad-adan or something." Orophan looked very excited.
"I know where she is!" he exclaimed. Everyone looked at him confused. "The Flad-adan is a radical group of Antarians who, unhappy with the government, broke away from society long. They live in caves outside of the city. Over time they adapted to fit their habitat and became different... they're not like us anymore. They're strongly against the monarchial government and allied themselves with Kivar when he was in power. They even traveled to Earth in an attempt to kill you. I believe you called them 'The Skins.'"
"So you know where their caves are?" Michael asked. Orophan nodded. "Then lets go get my daughter.
17. The Rescue
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Chapter 15: The Rescue
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"You're trying to leave me," Cirdan repeated, growing angrier. Abby was panicked. His eyes displayed a fierce anger she had yet to see. She had seen him angry before, but he had never been like this. He gripped her arm tightly and pulled her up from her resting position.
"I take care of you, treat you well, and you repay me by trying to escape?" He squeezed her arm tighter and pulled her closer to him. Abby shook with fear, trying to figure out just what to do. His grip was getting tighter and he kept on shouting. She thought quickly, realizing it may be the difference between life and death.
"No, no I'm not," she said in a whisper. This stopped his ranting and he loosened his grip slightly. "I'm not trying to leave you." Cirdan thought for a moment before the malicious look returned.
"I don't believe you," he hissed, tightening his grip again. "I heard your thoughts. You want to find a way out of here." Abby thought quickly.
"No, no, that's not it," Abby insisted, shaking her head. "I was just thinking about how I'd like to go outside. I haven't seen the sun or breathed fresh air in a few days. I would never try to escape." Cirdan's expression softened.
"Do you mean that?" he asked hopefully. Abby gulped silently.
"Yeah, yes," she said, nodding. Cirdan smiled.
"You want to stay with me? Do you love me?" Abby's stomach retched, but she maintained her composure. She remembered Connor's words, "Do whatever you have to to stay safe." She knew what she had to do.
"Yes," she answered, her expression changing to a wide smile. "How could I not? You've taken such good care of me?" Cirdan became ecstatic. He wrapped his arms around her and then kissed her.
"I knew this would happen eventually, if I just had faith. I love you too, you know." He kissed her again and pressed himself hard against her. She kissed back but her stomach turned and it took all her willpower not to push him away. Eventually he picked her up and lay her back on the bed, climbing on top of her. Within a matter of moments he had discarded both of their clothing and proceeded to consummate their newfound love, with Abby outwardly appearing to comply but inwardly screaming.
~*~
Back at the palace the rescue mission was well underway. Immediately after contacting Abby and deducing her location, a reconnaissance team had been sent to find the correct location of the cave. This was done easily enough, as Cirdan did not cover his tracks well.
Now the forces were assembling. First there was the group that would break the outer defenses. Michael led this group, and it was comprised of a few palace soldiers. The outer defenses were few, a couple of guards at the most. Cirdan had tried to make his cave as inconspicuous as possible by posting few guards, but, apparently, he had little luck. After the entrance to the cave was secure, the search and recovery team, led by Nate and Connor, would enter and search for Abby. Connor would use their connection to attempt to find her and, as he did this, Nate's team would find and capture Cirdan. After everyone was safely out the cave would be destroyed, killing all of the rebellious Flad-adan within.
They had to be swift in their actions, because Abby's like was at stake. One small mistake, one delay, and she could easily die. It had been a day since the contact, and they were already ready to attack. With a word from the High King, the troops were on the move.
~*~
Abby lie in bed, staring at the ceiling. She couldn't sleep, and hadn't since she betrayed her husband in what she thought was the worst way possible. Cirdan hadn't left her side since, taking his meals with her and sleeping in her bed, among other things.
The constant attention, the constant supervision, the constant need to put up a facade, and the constant lying was quickly taking a toll on her health. She kept reminding herself she was only keeping her promise to do whatever necessary to stay safe, but it didn't help.
It was now almost a day since she had spoken to Connor and she was beginning to worry. What if it didn't work? What if he couldn't save her? What if he was killed? What if she was stuck here with Cirdan forever? She shuddered at the thought. Could she learn to love him? She looked at the man sleeping next to her and pondered this. No, she realized. She'd die before she would spend forever with him.
Sensing he was about to wake she closed her eyes and feigned sleep.
"Wake up, my love," Cirdan whispered, stroking her hair and lightly kissing her lips. Her eyes fluttered open and she faked a smile.
"Good morning," he whispered.
"Is it morning?" she asked. It was impossible for her to tell without seeing the light of the sun.
"Yes," he replied. "Come, dress. I'll ring for breakfast."
He walked over to the intercom and Abby went to dress. She looked in the mirror and shuddered. The lack of sleep, as well as the hunger from not eating as much as she should and the constant fear, was taking its toll. Dark circles had formed beneath her eyes and she looked thin and pale. She was revolted at her appearance, but smiled because maybe, just maybe, Cirdan would be too. Maybe he would stop wanting her and, eventually, she would be free. Or he would just kill her. The smile disappeared and she went to work dressing.
From the bathroom she suddenly heard Cirdan's voice rise and become panicked. She couldn't hear what he was saying, but something told her that her cavalry had arrived. Why else would he panic? She smiled again and began working faster. Cirdan entered the bathroom and smiled upon seeing her.
"I have to run out for a few minutes," he said, keeping his voice calm. Abby looked at him innocently.
"Why?" she asked. "Is something wrong?" He changed his expression for a moment as a shadow of doubt passed over his eyes, but he quickly brightened.
"No, no," he replied, kissing her lightly on the forehead. "A few of the Flad-adan are having some difficulties. Nothing I can't handle." She could sense the fear emanating off of him and she inwardly smiled, realizing she was correct. He quickly left and she hurried getting ready, confident in the knowledge she would soon be gone from this place.
~*~
A few minutes later Abby sat on the bed quietly waiting. Humming softly, she thought fondly on how wonderful it would be to finally see the sun again, to sleep in her own bed, next to her real husband, and to see her family. Joy emanated from her. She felt a voice touch her mind and her joy increased.
"I missed you," Connor said to her in her mind. She smiled.
"Not nearly as much as I missed you," she replied. "Are you coming to get me?" He replied in the affirmative.
"Yes, we're already in the cave. Your dad got us in and now we're trying to find you."
"Are you well armed?" Abby asked worriedly. "There's alot of Cirdan's soldiers here."
"Yeah," Connor replied. "We're very well prepared. Now, I need you to help me find you."
"How are you going to do that?" Abby asked. "I don't know where I am."
"Just keep talking to me. Your presence in my mind becomes stronger the closer I get."
"Ok," Abby said. "But hurry. I miss you so much." She continued talking to Connor for a few minutes, asking him about what had happened while she was gone and about her family.
Within a few minutes, however, Cirdan rushed into the room, obviously panicked. He ran over to Abby and hugged her close.
"We have to get out of here," he gasped, grabbing her hand. "They've come for you and they've got a larger force than I thought. They're trying to take you away from me." Abby didn't know quite what to say. If she kept up her show he might take her somewhere where Connor couldn't find her. If she revealed her lie, she might die.
"What do you want to do?" she finally asked. He looked relieved.
"There's a secret passageway out of here. No one knows about it but me, so no one will be able to tell where we've gone. Quickly, we need to go." He pulled Abby towards the door but she faltered a bit. Feeling her resistance, Cirdan knew immediately what was going on.
"You do want to go with me, don't you?" he asked, looking hurt. "You said you loved me." Abby stared at him. She was so scared, but couldn't stomach lying any longer. She didn't answer, though, and, within a second, his hand was at her throat. He repeated his question. She shouted in her mind for Connor to hurry before steeling her resolve and looking Cirdan in the eyes.
"No," she answered. "I have no desire to go with you anywhere. And I don't love you. I never have." Cirdan's face changed to that of incredible anger. His grip tightened on her throat, cutting off her air supply.
"So you have made your choice," he growled, crushing her throat in his hands. Within a matter of minutes Abby's vision went black.
~*~
Connor was running panicked with a few of his soldiers behind him. All had been going well. He was coming closer to finding Abby and, all of a sudden, she had shouted to him in panic and then been silenced. The shout had been loud enough to tell him her exact location, but the problem was getting there unhindered and quickly. He ran and left soldiers behind him as he went, fighting off any groups of Flad-adan that resisted.
Finally, after what seemed to be an eternity, he reached the door. He could feel Abby's presence within, but it was muted quite a bit. He quickly dispatched the guards and opened the door, preparing himself for almost anything. He was not, however, prepared for what he saw.
In the room he saw himself. He was strangling Abby. He stood there for a moment, not knowing how to react. His image turned towards him and smiled deviously.
"You're too late," he hissed. "Your precious bride is dead." He released his hand and Abby fell to the floor. Connor needed little more than this to provoke him and he attacked. Within a moment Cirdan fell to the floor dead. Connor stood in the doorway in shock for a few minutes, looking at Abby's lifeless form on the floor. Eventually Nate joined him, having been called by the soldiers after Connor entered the room.
"She's dead," Connor said when he saw Nate standing next to him. Nate pushed Connor out of the way and ran to his sister's side. He couldn't bear the idea of his twin sister being dead and wasn't willing to believe it. He laid his head on her chest in sorrow, trying to keep the tears from forming. Suddenly he felt his head shift and looked up in amazement.
"No she's not," he stated simply. "She's not." Connor looked down at Abby in time to see her lips part slightly and a short gasp of air enter her lungs.
~*~*~*~*~*~*
Alright guys, there's only one more chapter and an epilogue after this to go and they're already written. To get them posted, you have to review. I know you're lurking out there; I can see you. I promise it won't hurt to submit a short lil review. Help me out a bit here, guys. If Nemis can have 1000 reviews by chapter 40, I can have at least 40 by chapter 18... pwease?
18. Finally Going Home
Thanks for _finally_ reviewing, everyone... It really does help to know there are actually people reading this. Don't forget to review just because this is the last chapter, it might encourage me to write something else someday soon.
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Chapter 16: Finally Going Home
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Abby lie in a haze, opening her eyes only to be blinded by light. After a moment the realization hit her. Light meant she was no longer in the cave, which meant that she was free. Not caring about the pain she sat up and opened her eyes, examining her surroundings.
Within a few seconds someone was next to her, hugging her tightly.
"We were so worried you wouldn't wake up," Nate whispered, holding onto his sister as tightly as he could without hurting her. Abby began to cry, so happy to see her brother again and so happy to finally be safe.
"I missed you so much, Nate," she whispered, hugging him back. He pulled away and looked at her.
"I'm just so glad you're alive," he said, staring into her eyes for reassurance. She smiled a real smile, something that felt really good to do.
"Where are Mom and Dad?" she asked. "And Connor? I want to see them." Nate smiled. We've been taking shifts watching over you. Connor just left but I can get him back here in a bit. I'll get Mom and Dad too." Nate disappeared for a few minutes and Abby happily settled back onto her pillow.
She thought about how wonderful it would be to get back to her normal life. She closed her eyes and thought about each person she loved in turn, her excitement growing by the second. Mostly she thought about Connor and how happy she would be to finally see him after all this time.
Nate returned and sat next to her.
"Mom and Dad are on their way now," he told her. "Connor will take longer because the palace is further from here and he was asleep when I called. I'm sure he'll be here soon, though." Abby smiled.
"Thank you," she said.
"No problem. I'm just glad to have you back. You've got your own personal servant for at least a few weeks." Abby laughed.
"So that's all I had to do to get you to listen to me? Get kidnapped by a psychopath?"
"Apparently so," he joked, happy that his sister was feeling well enough to joke. They continued their playful twin banter until their parents showed up, Maria immediately rushing to her daughter's side and Michael standing back looking at her, trying to fight the tears that were already beginning to form.
"I was so worried about you, baby," Maria sobbed, clutching her daughter desperately. "I was so afraid I'd never see you again." Abby smiled.
"I'm fine, Mom, I'm fine now," she replied and Maria kissed her cheek.
"I know honey," she replied. "I'm just so happy this is all finally over and you can come home as soon as you're better."
"Believe me, you're not nearly as happy as I am, Mom," she replied. She glanced past her mother and saw Michael standing in the doorway watching her.
"Daddy," she said in a whisper that was barely audible. It was all Michael needed. Maria stood out of the way and he rushed over to his daughter, taking his chance to embrace her as if he would never let go. Neither spoke, as neither had to. Abby had always understood Michael in a way no one else could, and now he was doing the same for her. They sat that way for a while, no one in the room speaking. Then Connor arrived.
He walked into the room and beamed, deliriously happy to see her awake and happy. Her reaction was not, however, nearly as pleasant.
One look at Connor and the smile disappeared from her face. She did not see her husband, the man she loved. Rather she saw him, her captor and her tormentor. They were the same in physical appearance, and her tormented mind could not distinguish.
Within a matter of seconds she was screaming uncontrollably. This quickly changed, however, and she was soon curled into a ball, crying and rocking back and forth. It all surfaced when she saw him. The pain, the torture, the things she had had done to her, and, worst of all, the things she had done. She wasn't able to control her reaction and no one was able to console her.
Connor tried at first, running over and hugging her, but this only made her delirium worse. She yelled for him to stop touching her, shouting over and over again with limbs flailing. Michael pulled him away and wrapped his daughter in his arms. Abby continued to shake and sob and he looked at Connor.
"Don't you see what's happening?" he asked angrily. "You're upsetting her. You need to get out."
"I'm not upsetting her," Connor rebutted, but he knew it wasn't true. They had all seen Cirdan's body. They all knew exactly what was happening now. She thought he was Cirdan. Maria quickly ushered him out of the room before turning back to comfort her daughter. Safe in Michael's arms her sobs soon dissipated and she fell into a deep sleep.
Connor could only stand on the other side of the door and watch, feeling helpless and alone.
~*~
Two weeks had passed since Abby had been rescued, but her condition had not improved. She would speak to her parents and her brother, but could not stand to be around Connor. Every time he attempted to see Abby, her condition would worsen and it would take several hours before she could even speak. Seeing him made something inside her snap.
After a few attempted visits, Michael asked Connor not to return. Everyone agreed that Abby would recover better if she didn't have continual setbacks every time he visited. Abby was moved to a facility where she could live comfortably and freely but always have someone to talk to.
Several months passed in this place and Abby, under the careful guidance of trained counselors, began to improve. The weight of her experience was being lifted off of her and she was beginning to be happy again.
She had several visitors and never had the chance to be lonely. Nate stayed with her most of the time and her parents visited regularly. The others came to see her at intervals, but Connor never did. As she improved she began to notice his absence and was both relieved and upset by it.
Abby carried extreme guilt with her, on top of the other emotions left from her experience. Ever since she had accepted that Cirdan was dead and she was indeed safe, she had felt regret. She was happy that Cirdan was dead. Ecstatic, even. What bothered her now were the memories of what she had done to stay safe while in his care. The things she had submitted to; the things she had allowed to be done to her; the things she had pretended to enjoy.
Once Abby had been healed, she worried only about her actions. She stayed in the facility only because she couldn't deal with lying to Connor and she couldn't bear to think what his reaction would be if he discovered the truth. She had betrayed him and she couldn't forgive herself. Despite his instructions to do whatever necessary to stay safe, she doubted he would forgive her either.
~*~
It had now been nearly a year since the kidnapping. Abby was safe and healthy, but she still would not come home. Nate, who had remained Abby's closest confidante during her seclusion, finally asked her the question nobody had dared to before.
"What happened to you in that cave? What did he do to you to make you close yourself off so much?" Abby sighed but answered. She had realized long ago that her family must wonder about her captivity but was grateful they did not ask. Now was the time, though.
"This is really hard for me to talk about," she replied, tears already forming in her eyes. Nate looked upset but nodded.
"I understand," he said.
"No, you don't. It's hard for me to talk about, but it's time you guys understood. But don't expect it to be a nice story." He nodded and sat back, wondering what his sister was about to tell him.
Abby began and told him the whole story, beginning in the garden when she was captured, continuing to when she was in the dark cave. She told him about the evil things Cirdan did to her, how she was tortured. Then she stopped. Nate looked at her, waiting for more.
"Abby, that can't be the end," he insisted. "You were gone for several days; you've only covered about a day and a half." She looked up at him, tears very visibly running down her face. She wanted to tell him so badly. She had told no one, not even the counselors who had heard everything else and helped her through it.
"If I tell you the rest," she began, "It can never leave this room. Never. It's between you and I only." Nate nodded.
"Of course."
"And, please don't hate me after I tell you... I already hate myself enough." Nate looked frightened for her and wrapped an arm around her.
"I could never hate you," he said, kissing the top of her head and holding her close. Abby sat in silence for a minute and then began.
Now she told him about how Cirdan was a sick and twisted individual, who craved love and sought for it in Abby. And she told him about the danger she had been in, and how she had protected herself from it, giving herself to Cirdan willingly, claiming to love him.
When it was over Nate could say nothing. He held Abby for the longest time and she cried out all of the emotions she had kept pent up inside of her, finally allowing herself to be forgiven. Finally he spoke.
"If I'd had known I would have killed him myself, before Connor even had the chance. Don't blame yourself for that. It's not your fault and no one else would ever blame you." She nodded but was still upset.
"You're right," she said. "I need to go home now and move on with my life, but I'm still worried that Connor will blame me. I'm worried that he won't be able to forgive me." Nate understood exactly and knew he needed to help her.
He left not long after and went immediately to the High King's Palace. She needed Connor's forgiveness before she could come home, and Connor needed to know there was something for him to forgive. Nate would not break his promise to his sister, but, when he met with Connor, he did tell him something.
"You need to go to her," he said. "And you need to go to her now." Connor needed little more prompting.
~*~
Later that day Abby sat in the garden at the facility, reflecting on all that had transpired that day. The tears from her encounter with Nate still flowed, but not as heavily and only when she thought of certain things. She knew more than ever that she wanted to go home, and she knew there was something she needed before she could.
Admiring a flower, she was lost in these thoughts for sometime. Connor saw her like this and fought back his own tears. She felt his presence before he spoke.
"I was wondering when you'd come," she said, not turning around. He stopped. Was she angry?
"They told me you would recover better without me. I didn't want to interfere. I still don't but I missed you too much to wait any longer." He started walking closer. She hadn't turned around yet but the sun shined in her long hair, drawing him to her.
"You're not interfering," she said, still not facing him. "I missed you too." He stopped walking a few inches away from her and stood.
"Abby..." he began, but she interrupted, standing and facing him. He could see the stains where tears had lingered.
"I'm ready to come home," she said. He stood there for a moment, not sure what to say. He wanted her to come back to him so much, but he didn't want to pressure her. She had been through too much already. She didn't take his silence well.
"Don't you want me to come home?" she asked, hurt. He quickly replied, tentatively wrapping his arms around her. He was still afraid to touch her.
"Of course I want you home. I want that more than anything, I just don't want to pressure you into coming home too soon. Are you sure you're ready?" She nodded and sat back down, bringing him with her.
"I am, but I don't know that you are." He looked confused and she continued, "Things happened to me Connor, you know that. Bad things. But you don't know what. I'm afraid you won't want me anymore when you know what happened... what I did." He touched her face softly, for a moment reminding her of Cirdan. She shuddered.
"I'm sorry," he said, withdrawing his hand. She grabbed it and placed it back where it was. It was time for the healing to begin.
"No," she insisted. "Don't be sorry. I have some bad memories, but stuff like this replaces them and makes me better." He nodded. He remembered that Nate had said she had a long story to tell and that he needed to hear it all to understand.
"Show me?" he asked. "I want to understand so I can help you. Nothing can change the way I feel about you." Abby sighed but nodded. She needed his forgiveness to feel whole again, and he needed to know in order to give it.
"You're right. It's time you knew." She took his hands in hers and leaned her forehead against his, staring into his eyes. She sent him the images of her imprisonment, from the first horrible day, to later when she was actually happy, to the time she spent with Cirdan on her own accord, attempting to deceive him. Connor pulled away at the end and looked at her. She waited apprehensively, afraid he wouldn't accept what had happened to her and what she had done. He stared at her for a minute before gathering her into his arms and kissing her cheek.
"I'm sorry," he said. "I wish it would have been me instead." He rubbed her back and she cried on his shoulder. After regaining her composure she pulled back a little and searched his eyes.
"You're not mad then?" she asked. "You don't hate me for what I did?" He shook his head.
"You did what you had to to keep yourself alive. That's all that matters. You did nothing wrong." He leaned in and kissed her, hoping she wouldn't pull away. She didn't. Finally he pulled away and stood, reaching a hand to her.
"Come on," he said, prompting her to take his hand. "Let's go home." She smiled and accepted his hand and they went back to the palace together.
The end
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Alright, so it's over. *sob* There's an epilogue to match the prologue (go read it if you haven't; it was just added recently) and it'll be up soon. And don't forget to review! ;)
19. Epilogue
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Epilogue
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The boy stared at his mother, who had not spoken for several minutes, eyes glassy and staring into the distance.
"Mommy," he finally said, drawing her attention. Abby looked down at her son.
"Yeah, honey?" she asked, forgetting what they had been speaking about only a few minutes before.
"You told me there was more to the story. What else happened?" Abby looked into her baby boy's eyes. He was so young and still so innocent.
"That's a story for another night," she answered, kissing him softly on the top of his head. "Just be content in knowing that they do live happily ever after."
"They do?" he asked innocently.
"Yes," Abby replied, hugging him close to her. "They do. There are good times and there are bad times, but they most definitely live happily ever after." He smiled.
"I'm glad."
"I am too, sweety. I am too." She rose from the bed and he slid down comfortably into his pillows. She pulled the blankets snugly around him and then shut off the light next to his bed. She kissed his cheek and then stood to leave.
"I love you, Mommy," the boy said. Abby smiled.
"I love you too," she replied before shutting the door behind her. Connor stood in the hallway outside.
"Is he asleep?" he asked. Abby smiled and took his hand.
"He's getting there," she answered.
"How'd you do it?"
"Oh, I told him his favorite bedtime story," she replied, leaning into his warm embrace.
"Are you ever going to tell me what that story is?" he asked, looking playfully into her eyes.
"Maybe someday," she replied, kissing him and then leading him towards their bedroom. "For now I'll just say that it's a very familiar story." They laughed together as they entered their room and he held her snugly in his arms as they both fell asleep.
"Yes," Abby thought to herself. "It is most defiantly happily ever after."
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Thanks to everybody for reading and reviewing! I hope you enjoyed it.
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| fanfiction |
during the latest phases of their evolution , high mass stars experience significant mass loss , both through strong stellar winds and eruptive events , that drives these objects out of the main sequence through short and poorly constrained instability phases .
the class of luminous blue variables ( lbvs ) consists of luminous ( @xmath1(l / l@xmath2 ) and massive stars that are believed to go through a short but violent transition from the main sequence towards the wolf - rayet stage @xcite , although their link to other advanced evolutionary phases of massive stars such as supernovae is still open @xcite . during their evolution ,
lbvs lose a huge quantity of mass from their original envelope , leading to the formation of extended circumstellar nebulae ( lbvn ) , whose masses are thought to be on the order of a few solar masses . in the galactic context , despite the relative small number of confirmed and candidate members , lbvs represent a significant stage of the cosmic cycle of matter , as they contribute to the chemical enrichment of interstellar medium in dust and heavy elements @xcite .
the census of galactic lbvs performed by @xcite reported 12 effective members and 23 candidates , but new candidates have recently been identified via the mid - infrared images of the galactic plane obtained with the multiband imaging photometer for spitzer ( mips ; * ? ? ? * ) and the infrared array camera ( irac ; * ? ? ? * ) onboard the spitzer space telescope @xcite .
the overall scenario of lbv evolution is currently under debate and the nebula formation mechanism , i. e. intensity , duration and geometry of the mass - loss events , is not well established .
the study of the gas and dust content of the nebula which surrounds the star may provide significant clues that will enable us to understand the mass - loss processes that govern its evolution , as well as the drastic changes that take place in the immediate circumstellar environment @xcite . by exploring the characteristic of the mid infrared continuum emission , which traces the warm dust , and of the recombination lines and radio continuum emission , which trace the ionized gas
, we can study the relationship between these different components which coexist in the stellar ejecta with the aim of gaining valuable insights about the formation and shaping mechanisms at work in the circumstellar envelope .
in particular , radio observations offer the additional possibility to reveal the ionized gas well inside the dusty envelope and , therefore , allow to determine in great detail its spatial distribution without suffering from intrinsic extinction @xcite .
the infrared source was originally classified as a planetary nebula on the basis of its infrared colors @xcite and of the observed 1.4 ghz flux @xcite .
subsequently , the detection of mid - infrared extended emission around this object @xcite , together with observations of strong photometric and spectroscopic infrared variability @xcite and its position in the hr diagram led to a definitive classification of as a lbv . on the basis of radiative transfer calculations
, @xcite derived a @xmath3 = 6.4 and a temperature @xmath4 kk for the central star , which appears surrounded by a nebula of gas and dust characterized by a possible c / o mixed chemistry .
recently , @xcite , in a detailed analysis of long term monitoring of the near infrared photometric and spectroscopic properties of , showed that it has been highly variable over the last 20 years .
near - infrared photometric variability greater than one magnitude has been observed with moderate variation in temperature ( @xmath5kk ) , which is consistent with variations of stellar radius .
multi - frequency vla observations have revealed an extended , asymmetric , and quite structured nebula and revealed the central core of the lbv , whose radio properties are typical of a stellar wind , with a current mass - loss of @xmath6 @xcite .
this value is consistent with those determined by @xcite from the nlte atmospheric code , which indicates a variation of the mass loss rate from @xmath7 to @xmath8 between 2002 and 2006 , associated with a decrement of @xmath9 from 15.5 to 11.0 kk .
the present work is a part of an effort to better understand the physical conditions in a sample of galactic lbv nebulae , conducted by using state of the art instruments available at mid infrared and radio wavelengths .
we present the results obtained for the lbv iras 18576 + 0341 by combining mid infrared and radio maps having comparable spatial resolution , obtained using visir at very large telescope ( vlt ) and very large array ( vla ) .
the images allow us to study the detailed morphology of the circumstellar envelope , in order to understand the origin of the apparently contradictory spatial structures seen in the resulting maps @xcite .
to map the dust distribution in the lbvn associated with iras 18576 + 0341 , we have obtained high angular resolution and high sensitivity n and q - band images with visir @xcite , the vlt imager for the mid - ir mounted at the cassegrain focus of the vlt unit 3 telescope ( melipan ) .
the observations were carried out on 2007 july 19 and 26 through the pah2 filters , centered on known pah features ( @xmath10 ) and adjacent continuum ( pah2@xmath11 , @xmath12 , @xmath13 ) , and in q1 ( @xmath14 , @xmath15 ) .
we also used the neii filter ( @xmath16 , @xmath17 ) and its adjacent continuum ( neii@xmath11 @xmath18 , @xmath19 ) as a tracer of ionized gas to compare with the radio images .
all the observations were performed under very good and stable weather , with an optical seeing of about @xmath20 .
the target was observed at airmasses ranging between 1.2 and 1.4 .
we used a fixed pixel scale of @xmath21 , resulting in a fov of @xmath22 .
the standard chopping / nodding technique was adopted for subtraction of the sky background as well as the telescope s thermal emission : secondary mirror chopping was performed in the north - south direction , with a chop throw of @xmath23 and telescope nodding was applied in the opposite direction with equal amplitude . to further improve the image quality ,
a random jitter pattern with a maximum throw of @xmath24 was superimposed on the nodding sequence .
a complete log of observations is summarized in table 1 .
data were reduced following the standard visir pipeline ( version 1.7.0 ) , consisting of co - adding of frames after flat fielding and removal of bad pixels .
the chopped and nodded images were then combined to make one image in each filter .
three mid - ir standards were observed just before and after the target acquisition to flux calibrate the data .
such observations were also used to determine the fwhm of standard star images and thus to derive the actual angular resolution of our final maps .
values of the fwhm for each filter are reported in table 1 .
we observed iras 18576 + 0341 on the 2004 october 12 at 4.8 ghz ( 6 cm ) and 1.4 ghz ( 20 cm ) , with a bandwidth of 100 mhz using the vla in a configuration , providing a typical beam size of @xmath250.36@xmath26 and @xmath251.3@xmath26 respectively .
for all the observed bands , 1824 + 107 was used as phase calibrator and the flux density scale was determined by observing 3c 48 .
the data processing was performed using the standard programs of the nrao * a*stronomical * i*mage * p*rocessing * s*ystem ( aips ) .
we compared the images made from the a - configuration data with our earlier images obtained using the c configuration @xcite to confirm that long term variability was not present in our data .
after the calibration process , the a - configuration _ uv_-datasets were combined with the earlier observations performed at the same frequencies using the vla in c configuration and presented in @xcite and images have been produced at both wavelengths .
this allowed us to obtain high resolution maps of the entire nebula and , in the same time , fully recover all the extended emission .
the mapping process was performed by using aips task imagr with a variety of weighting schemes and the dirty maps were * clean*ed down as close as possible to the theoretical noise .
the final uniform - weighted ( robust -5 ) maps have a synthesized beam of 038@xmath27036 and 139@xmath27127 , and rms noise of 0.04 mjy beam@xmath28 and 0.1 mjy beam@xmath28 at 6 cm and 20 cm , respectively . the noise level ( rms ) in the maps
was estimated by analyzing an area on the map ( using task imean ) , whose dimension is of the order of more than 100 @xmath29 away from the phase center and free from evident radio sources .
all five visir images , shown in figure [ ir_im ] , have a similar morphology , with an extended circumstellar envelope surrounding a central source that is clearly visible until almost 13 @xmath0 m . in figure [ ir_im ]
we show the images obtained in the filters pah2@xmath11 , neii@xmath11 and q1 . from all the filters we derived a shell diameter of approximately 7@xmath26 , corresponding to a size of 0.35 pc at a distance of 10 kpc @xcite .
we performed aperture photometry of the central object in each image by using the idl procedure atv , while the nebula contribution at each wavelength has been determined by integrating the flux emitted in a selected area of @xmath30 .
the photometric results are summarized in table [ visir - phot ] . on the basis of their iso sws spectrum
, @xcite pointed out a strong difference between the iras and the simulated iso photometry , concluding that the dusty envelope around iras 18576 + 0341 should have been very extended with some of the flux observed by iras falling outside of the largest iso aperture ( @xmath31 ) .
however , we fully recover the iras 12 @xmath0 m flux density ( f@xmath32=58.48 mjy ) , implying that , at least at 12 @xmath0 m , all of the emission is from the compact 7@xmath26 source . with respect to the previous mid - infrared images @xcite that discovered the presence of a roughly circularly symmetric nebula around iras 18576 + 0341 ,
our higher resolution and sensitivity allow us to probe finer details of the dust distribution .
the brightness of the shell varies around its circumference , with the major contribution to the flux coming from the north - west part of the nebula .
the condensations , detected by @xcite as an arc located in the north side of the shell , now shows up as a clumpy structure with two major peaks located at 50 degrees in the east - north direction and about 2@xmath26 from the central star .
it appears that the northern and the southern emission peaks reported by @xcite were an effect of the limited sensitivity and spatial resolution of their maps . from our visir maps ,
no hints for the claimed optically thin edge - on dust torus surrounding the central object are evident , but only a suggestion of a possible spherical inner shell whose edges are strongly structured .
it is possible to isolate the pah feature at @xmath33 by subtracting the image obtained at the adjacent continuum ( pah2@xmath11 ) from the the pah2 image .
we have performed this subtraction after registering the images on the central object and normalizing them to the continuum as derived from a fit to the iso spectrum @xcite .
the difference image is shown in figure [ pah ] .
the @xmath33 pah emission appears to be located in the inner shell with an higher concentration in the north - west part of the ring where the most of the thermal dust continuum emission originates .
the [ ] emission , which should trace the ionized gas , can be isolated following the same procedure , i. e. , by subtracting the adjacent continuum image at @xmath34 ( neii@xmath11 ) from the @xmath35 image .
the striking result , shown in figure [ neii ] , demonstrates that the [ ] emission has a very different distribution compared to the dust and pah tracers . as [ ]
emission is a ionized gas tracer this result suggests that significant difference exist between the dusty and ionized stellar ejecta ( sec .
[ ion_gas ] ) . assuming that the extinction is constant across the images and that the flux that we have mapped is due to optically thin thermal emission from dust grains , we may use the neii@xmath362 and q1 images to produce a ratio map . in this case
the observed intensity is given by @xmath37 and using the wien approximation ( @xmath38 ) for the blackbody expression @xmath39 , the ratio of the intensities at two different frequencies @xmath40 and @xmath41 is given by : @xmath42 the optical depth @xmath43 depends on the chemical composition and on the size @xmath44 of the grains .
there is an open controversy on the nature of dust grains present in the nebula surrounding iras 18576 + 0341 @xcite , indicating that it is possibly a mixed - chemistry object where features due to silicates and those related to carbon ( pah ) coexist . in this paper
, we follow @xcite and adopt for @xmath45 and @xmath46 , @xmath47 in the case of graphite and 1.27 in the case of astronomical silicates . for each pixel of the map ,
we derive the dust temperature inverting equation [ rapporto ] @xmath48 } \ ] ] the dust temperature has been computed only at those pixels whose brightness is greater than @xmath49 , corresponding to @xmath50 in the maps . in this derivation , we assume a constant temperature along the line of sight for each pixel .
the resulting dust temperature map is shown in the left panel of figure [ tempmap ] .
the temperature map can be used to examine dust temperature gradients across the nebula .
we see that the color temperature values are confined to a relatively narrow range , from @xmath51 130 to 160 k in case of graphite grains .
slightly lower values ( @xmath52 ) are obtained if instead a mixture of silicate grains is assumed .
the higher temperatures are reached at a distance of about 2 from the center .
to more clearly see the temperature distribution as a function of radius , in the right panel of figure [ tempmap ] we show radial cuts of the temperature map along diameters obtained at steps of @xmath53 . to evaluate the mass of the dust in the envelope , an optical depth map at @xmath54 is required .
this can be obtained by inverting eq.[trasporto ] , using the value of the temperature found in each point of the map and the observed intensity .
if the medium is homogeneous , the optical depth is given by @xmath55 , where @xmath56 and @xmath57 are the the density of the medium and the thickness of the envelope , and @xmath58 is the absorption coefficient per mass unit .
the mass behind each optical depth map pixel , whose area is 0075 @xmath27 0075 , is given by @xmath59 , and @xmath60 the area source corresponding to one map pixel , which is @xmath61 assuming a distance of 10 kpc @xcite .
a value of @xmath62 and @xmath63 at @xmath64 has been adopted in case of graphite and silicates , respectively @xcite . integrating over all the pixels with brightness higher than 3 @xmath65
, a total dust mass of @xmath66 ( @xmath67 ) is derived in case of graphite , and @xmath68 ( @xmath69 ) in case of silicates . @xcite
provide an estimate of total dust mass of @xmath70 assuming a toroidal morphology for the entire dust emitting region and a radius of @xmath51 14@xmath71 .
this value is compatible with our results if scaled down to the extent of the mid - infrared emitting dust shell that is resolved in our images . because the mid - ir observations we present only trace the cooler dust component in the nebula , our dust mass estimates
should be considered as lower limits to the total dust mass in the lbvn .
the dust column density along the line of sight @xmath72 ( figure [ taumap ] , left panel ) can be used to infer the density @xmath73 inside the nebula .
although its distribution is clumpy , as already noted , with a higher concentration of dust in the north - east part , a roughly spherical symmetry around the central star can be assumed .
cuts of the column density map along diameters , obtained at steps of @xmath53 averaged together , are shown as a thin line in the right panel of figure [ taumap ] .
we modeled the density distribution assuming a radial dependence . for this purpose
, we built a 3d matrix , sampled with a step corresponding to the pixel size of the visir maps ( @xmath74 cm ) in all the three spatial dimensions .
we found that the density must increase as a function of radius from the center , although it is not possible to discriminate among several radial dependencies .
as an example , the radial column density profile obtained assuming @xmath75 , with a smooth at the edge , is shown as a thick line in figure [ taumap ] , right panel .
this analysis shows that in the inner part of the nebula the density is low and it increases strongly with the distance from the star .
this could indicate : + a ) an episode of strong mass loss at a previous time ; + b ) the dust is processed by the uv radiation field of the star in the inner part of the nebula .
+ c ) a combination of the two .
+ the maximum of @xmath73 is at @xmath76 from the center , corresponding to a linear distance of 0.15 pc ; assuming the same expansion velocity @xmath77 measured from the br@xmath78 line @xcite , the mass loss episode should have occurred about 2000 years ago . the continuum emission associated with at 5 ghz and 1.4 ghz
is shown in figure [ radio_maps ] .
the spatial resolution achieved in the final image is about 13 in the l band and 04 in the c band .
the images confirm the structure of the source as detected at higher frequencies @xcite : a compact , slightly resolved core , most likely associated with the stellar wind from the central object , surrounded by an extended ionized nebula with a remarkably similar shape and extension at all wavelengths . as expected ,
the combined effect of reduced spatial resolution and of intrinsic contribution at low frequency prevent us from detecting the core component and discerning it from the extended nebula in the 20 cm map ; on the contrary , the higher spatial resolution in the 6 cm map allows us to clearly resolve the compact source .
the total radio flux densities associated with the entire source have been derived by summing the contribution of all the pixels contained in the radio source ( aips task imstat ) , while the flux density of the central object object has been obtained by fitting a two dimensional gaussian brightness distribution to the map ( aips task jmfit ) .
the results are reported in table [ tab_radio ] .
to better separate the core component from the remaining diffuse emission , the flux density from the compact core at 6 cm has been determined by fitting a two dimensional gaussian brightness distribution to the map obtained with the a configuration data alone .
the resulting flux density of [email protected] is in accordance with the flux density extrapolated from measurements at higher frequencies assuming a stellar wind spectrum , as reported in @xcite .
the final images in figure [ radio_maps ] show that the radio emission from the circumstellar ionized nebula is asymmetric with respect the central core , extending out in the northwest direction , with the brightest radio region located about 36 to the north of the central core in the 6 cm map .
the diffuse emission is remarkably similar to that detected at all the other observing frequencies , with similar extent of about 7@xmath26 .
the southern component , which contributes about 25% of the total mid - infrared emission , is not present in any of the radio maps .
a certain degree of asymmetry is also present in the radio emission of other lbvns , such as @xcite and @xcite .
this may indicate that extremely asymmetric mass loss can be quite common in lbvs .
the overall morphology of the radio nebula agrees very closely with the spatial distribution of the [ ] line emission .
the contours of the [ ] map , superimposed on a gray - scale image of the 6 cm data , is shown in figure [ neii ] .
it is evident how the emission in the [ ] line follows quite faithfully that of the radio continuum . such resemblance between the two maps is unsurprising , as both are tracers of the thermal ionized gas . to search for the existence of denser regions with different opacity through the nebula , we computed the spectral index map by comparing the 6 cm with the 0.7 cm image obtained in the first epoch .
the images have comparable spatial resolution .
we computed the spectral index , defined by the relation s(@xmath80 ) @xmath81 @xmath82 , using the maps produced with the same beam and cellsize for each pixel with a flux density of at least three times the rms noise at both the wavelengths .
the resulting map , shown in figure [ sp_map ] , shows evidence of the stellar wind component , characterized by spectral index of @xmath83 @xmath25 0.8 , and the extended halo having a much flatter radio spectrum ( @xmath83 @xmath25 -0.1 ) , which is typical of free - free thermal emission .
however , the image shows some patchiness probably associated with local density clumps .
we note the presence of a second component with spectral index of @xmath83 @xmath25 0.9 located about 15 to the south of the central core , in the direction of the southern infrared emission peak in the dust nebula .
such a component , which is clearly visible in the radio map reported in figure 1b in @xcite , is probably due to the presence of a dust condensation whose thermal emission contributes to the flux observed at 7 mm .
the most striking result of our observations is the clearly dissimilar morphology of dusty and gaseous components of the nebula , which seem to have quite different spatial distribution .
this is immediately apparent in figure [ figcol ] , which shows the composite image obtained by superposition of the 6 cm and the 17 @xmath0 m images .
the ionized nebula , in fact , extends beyond the dust shell in the n - e direction , and the radio and [ ] maps do not contain any indication of the symmetric shape seen in the mid - infrared continuum maps .
different scenarios can be envisioned that could account for all the discussed findings and provide a complete picture of the source .
as the continuum infrared maps seem to exclude an asymmetry in the mass loss , the asymmetry in the distribution of the ionized gas could be ascribed to one of the following possibilities : ( a ) direct photo - ionization from an external source , ( b ) variation in the density of the interstellar medium into which the ejected material is expanding , or ( c ) uv radiation from the central star leaking through a hole in the opacity of the circumstellar nebula .
the hypothesis of direct photo - ionization can not be ruled out because of the high visual extinction of roughly a@xmath84 28 mag @xcite towards .
the surveys available at this moment , in fact , do not have the sensitivity needed to detect a main sequence star of spectral types o to b as it would appear at a distance of 10 kpc in this direction
. for the same reason , not even the inspection of our radio maps allow us to exclude the presence of such kind of source , although no radio emission has been detected in our map around the location of the nebula .
on the basis of the analysis from panagia @xmath85 felli ( 1975 ) , in fact , the flux density expected at 6 cm from a spherically symmetric , isothermal and fully ionized stellar wind at a distance of 10 kpc is about 1.6@xmath2710@xmath86 mjy , assuming a stellar temperature of 10@xmath87 k , a terminal wind velocity of 10@xmath88 km s@xmath28 and a mass loss rate of 10@xmath89 .
the resulting flux is thus very close to the noise of the radio map .
on the other hand , based on at the near - infrared images from the two micron all sky survey ( 2mass ) toward the position of , we found that north - east rim of the ionized cloud is facing a source designed as in the 2mass all - sky catalog of point sources @xcite and located at position @xmath90 .
this is a distance of 47 from the central star of iras 18576 + 0341 , just in the direction where the nebula ionization appears to be strongest .
however , based on the above considerations and the near - ir colours derived from the de - reddened 2mass magnitudes , we exclude the possibility that such a source could be an early type main sequence or supergiant star able to provide the energy needed for the nebula ionization
. we can also consider the hypothesis that the ionized gas surrounding the lbv originates from the interaction of the mass outflow from the central star with a high density medium surrounding the star , such as clumps or perhaps circumstellar material .
we can make an order - of - magnitude check of the plausibility of this scenario on the basis of the theory outlined by @xcite , who modeled the shock - ionization scenario and derived the radio continuum emission under optically thin conditions . in their formulation ,
the effective optical depth of the emitting region is directly connected to the outflow characteristics , and a simple relation exists between the radio flux density in the optically thin regime and the wind momentum rate : @xmath91^{0.1 } \left [ \frac{t}{10 ^ 4\,k}\right]^{0.45 } \left [ \frac{\dot { m}}{10^{-7}m_{\odot}yr^{-1}}\right ] \left [ \frac{v_\infty}{100\ , km\,s^{-1}}\right]^{0.68 } \left [ \frac{d}{kpc}\right]^{-2}\ ] ] in this formula , @xmath92 is the radio flux observed at frequency @xmath80 , @xmath93 represents the fraction of the stellar wind that is shocked and produces the observed radio continuum emission , @xmath94 is the mass loss rate , @xmath95 is the terminal velocity of the wind , @xmath96 is the wind temperature and @xmath97 the distance to the source .
adopting @xmath980.3 and a temperature of 10@xmath87k , the density flux of about 100 mjy observed at 6 cm can be provided by isotropic mass loss rate ranging from 7@xmath2710@xmath86 to 3 @xmath2710@xmath99 m@xmath100yr@xmath28 for an assumed wind velocity varying from 500 to 200 km@xmath101s@xmath28 , which are parameters values comparable with those derived for and other lbvs observed giant eruptions @xcite . due to the many unknown parameters this estimate is only suggestive , but it shows that with typical parameters the shock emission model can produce the observed flux .
on the other hand , in absence of an external factor ( source ) , the ionization of the circumstellar nebula could be explained exclusively by the direct photo - ionization from the central object . in this case , as derived in paper i , the lyman continuum flux of a b0-b0.5 supergiant can account for the measured radio flux .
this scenario , however , involves the presence of some kind of inhomogeneity ( asymmetry , anisotropies ) in the circumstellar material that has not been observed in our mid - ir images .
it is , in fact , difficult to understand the departures from symmetry of the radio and [ ] images except in terms of density or optical depth variations in the cloud .
the very different spatial distribution of circumstellar dust and ionized gas might reflect an anisotropy in the same mass loss event that could have excavated the mid - ir emitting dust , or may indicate that distinct ejection events have been collimated differently by the interaction with the circumstellar material ejected in previous phases .
such interactions could have affected the grain size distribution throughout the nebula , causing an anisotropy in the opacity of the dust grains which are competing with the gas in the absorption the uv radiation @xcite .
we have presented new high - resolution mid - infrared and radio imaging observations of iras 18576 + 0341 .
these observations provide an unprecedented view of the detailed spatial structure of the circumstellar envelope surrounding the central massive star , and highlight the different distribution of dust and gas component in the nebula .
these data allow us to perform a spatially resolved analysis of dust temperature and optical depth , and to derive the high resolution spectral index map of the observed radio emission .
we found that the dust properties seem to be essentially the same everywhere in the nebula and the spectral index map is consistent with optically thin free - free radiation , except for the wind component from the central star .
we thus conclude that the clumpiness observed at all wavelengths has to be ascribed to local density enhancements .
we also described the possible scenarios that could account for the asymmetry in the spatial distribution of the ionized material .
we suggest that the gas ionization could be caused by uv - radiation from an external source or by the impinging of the mass outflow upon an obstacle like a denser circumstellar medium .
alternatively , the asymmetry could be ascribed to uv photons leaking out from the central object thought a hole in the circumstellar envelope .
although we are unable to rule out any of the discussed frameworks , it is worthwhile to note that the last scenario conflicts with the relative minor spatial variations of dust temperature and optical depth resulting from the analysis of our mid - ir images .
this work is based on observations made with the visir instrument on the eso vlt telescope ( program i d .
079.d-0748a ) .
the very large array is a facility of the national radio astronomy observatory which is operated by associated universities inc . under cooperative agreement with the national science foundation . ,
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lett . and comm , 27 , 299 cutri r. m. et al .
2003 , _ the irsa 2mass all - sky catalog of point sources _ , nasa / ipac infrared science archive , http://irsa.ipac.caltech.edu/applications/gator fazio g.g .
2004 , apjs , 154 , 10 garca - lario , p. , manchado , a. , pych , w. , pottasch , s .r . 1997 , a&as , 126 , 479 gvaramadze , v. v. , kniazev , a. y. , fabrika , s. , sholukhova , o. , berdnikov , l. n. , cherepashchuk , a. m. , zharova , a. v. 2010a , mnras , 405 , 520 gvaramadze , v. v. , kniazev , a. y. , fabrika , s. 2010b , mnras , 405 , 1047 humphreys , r. m. , davidson , k. 1994 , pasp , 106 , 1025 hrivnak , b. j. , volk , k. , kwok , s. 2000 , , 535 , 275 .
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, , 694 , 697 umana , g. , buemi , c. s. , trigilio , c. , & leto , p. 2010
, , 718 , 1036 van hoff , p. , a. , m. , weingartner , j. , c. , martin , p. , j. , volk , k. , and ferland , g. , j. , 2004 , , 350 , 1330 wachter , s. , mauerhan , jon c. , van dyk , schuyler d. , hoard , d. w. , kafka , s. , morris , p. w. 2010 , aj , 139 , 2330 white , s. m. 2000 , , 539 , 851 ccccccc + filter & date & ut & integration time & airmass & fwhm + & & & ( s ) & & @xmath102 + pah2 & 2007 - 07 - 26 & 04:56 & 700 & 1.2 & 0.27 + pah2@xmath11 & 2007 - 07 - 26 & 05:15 & 700 & 1.3 & 0.28 + neii & 2007 - 07 - 19 & 06:21 & 700 & 1.4 & 0.30 + neii@xmath11 & 2007 - 07 - 19 & 06:01 & 700 & 1.4 & 0.32 + q1 & 2007 - 07 - 26 & 05:48 & 180 & 1.4 & 0.38 + | arxiv |
Harry Potter 1. Chapter 1
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**This is my second fanfic, and I must say, I'm rather excited about it.**
**I've had the story line in my head for a good year now, but it always ends a different way each time I go back to think about it. So, I'll just have to see where this particular one goes. I've also always wanted to write a Harry Potter fanfic, but I've just been very scared to.
**
**Hopefully, though, that will go away.**
**Enjoy!**
* * *
**I Dreamed a Dream**
Though the weather outside Hogwarts was at it's best in months, the atmosphere behind it's sold oak doors was becoming increasingly ominous. The Headmaster had not been seen by any of the students or staff at meals during the week, and what students found even more surprising was that, along with the Headmaster, two other faculty members had also remained absent.
At first, the recognition of Professor Snape's absence was met by relieved sighs and joyful outbursts; however, as soon as Madame Pomfrey, the school's mediwitch, and Headmaster Dumbledore had joined his disappearance, the school was left in a state of confusion. The chaos ensued when news came forth that there was no one available at Saint Mungo's to temporarily hold Madame Pomfrey's place, and quidditch was forced to an abrupt end.
It wasn't long before rumors traveled throughout the school - each with their own twisted explanation. Loyalties were questioned, alliances were formed, and the inevitable theory that He-Who-Must-Not-Be-Named was involved in the large scheme of things. A smaller war in the midst of a much larger one was threatening to erupt, for this had not been the first time Professor Snape had mysteriously gone missing; and, of course, one happening such as this occurred one time too many in the eyes of the corrupt Ministry of Magic, who believed that no man with a past was completely innocent until he had long since died for the cause.
What no one saw, however, was the struggle that had been occurring in the very chambers that belonged to Professor Snape…
* * * * * * * * * *
"Poppy, how is he?" Headmaster Dumbledore asked.
"I've tried everything, Albus, but he has yet to respond to any of it." The Mediwitch replied effortlessly, but her eyes betrayed her, reflecting the long hours she had worked in the previous days.
"There's nothing more you can do?"
Poppy turned back to stare at the still form of Professor Snape sleeping peacefully on the bed, before replying, "We can only pray." Dumbledore's only response was a curt nod, before he made his way towards the fire place.
"Where are you going?"
"I have an idea. It may not work, but it may as well be our last chance to save him."
"When can I expect you to return?"
"I cannot say," he began, "for there are some things that need a bit more than a slight push to get them going; but as the muggles say, 'If at first you don't succeed, try and try again.'" With this statement, Dumbledore threw a handful of floo powder into the fireplace and vanished in a burst of blue flames.
* * * * * * * * * *
Though many adolescents - particularly the males - had heard of Fleur Delacour, they were never aware of the existence of her step-sister. In fact, with her lack of blonde hair, blue eyes, and French accent, Leia was rarely assumed to be a Delacour at all. Her father was Reynaud-Toussaint, who traveled to The State's in hope of furthering his research on communicable muggle diseases. It was there that he met his first wife, a muggle by the name of Bronwyn; however, after a year of trying to make their marriage work, it seemed as if the only good thing that resulted from their partnership was the birth of their daughter.
Leia remained living with her mother in The States until her eleventh birthday, when she received her letter from Beauxbatons Academy. Upon realizing that Beauxbatons was located in France, she immediately wrote her father. Reynaud was undoubtedly ecstatic with the news and insisted she move to France with him in order to begin her wizarding education. Leia agreed, and days later, she was introduced to her step-mother, Appolline, and her step-sisters, Fleur and Gabrielle. Although her appearance and American accent made her the black sheep, the part-veela women welcomed her into their family with exceptional ease.
As years passed and Leia's education furthered, it was clear to her family - and the rest of the adult population in the wizarding world - that she was an incredibly gifted child. From the minute she stepped into the flourished halls of Beauxbatons, Leia began absorbing every piece of knowledge that was available to her. By her third year, her skills had matched well-known and very powerful witches and wizards across the country, including Albus Dumbledore, who was drawn to the girl after witnessing her success in the Triwizard Tournament a year before. Her advanced powers were rejoiced by many, but the Ministry, however, had quite a different perspective.
In the summer leading into her fourth year, Leia had received owls from various newspapers, all of which asked for exclusive interviews. When Leia politely declined, her face along with the headline 'Leia Delacour: Future Dumbledore or Voldemort?' was published on the first page - the article was rarely ever in her favor. The Ministry's general dislike towards her heightened, when they learned that she had secretly taken both her OWL and NEWT exams early, enabling her to not only graduate from Beauxbatons in only her fifth year of school, but also cease any of the actions that the Ministry took to monitor her.
The next three years of her life were spent in what people believed to be isolation. Very few people saw Leia, and even fewer had heard from her, including her family, whose only communication with her was through a letter she sent once a month assuring them of her good health and safety. It appeared that she had completely disappeared; however, the Headmaster of Hogwarts knew very well that this was untrue. Since the year Leia walked away with the Triwizard Cup, Albus Dumbledore had made sure that he had kept in touch with her. Eventually their relationship through letters turned into one more intimate, consisting of sitting down for tea and conversation every Tuesday of every week. He had grown to think of her as a daughter, and she, in turn, loved and trusted him just as equally. Unfortunately, even he was unable to prepare her for the events that would change her life indefinitely and irrevocably…
* * * * * * * * * *
Leia laid sleeping on her living room couch with her body facing the TV. She had come home earlier than she expected and immediately set out to make up for lost sleep. Though she had no position or steady income, she lived happily off of a large trust fund and always managed to keep herself busy.
Her dining room table was rarely used for eating or entertaining company. Instead, she found a more practical use for it, layering it's surface with dozens of thick textbooks and papers summarizing her months of research. Her kitchen was also rarely used. More of her books filled the oven, and cabinets were left bare, except for a small box of Poptarts located on the top shelf. She had no time for herself, her health, or her needs. Her work consumed her, and no matter how many times Dumbledore had pleaded with her to tread carefully, she could not pull herself away from it. It was the equivalent to her as a child is to a mother, and she would make sure it grew to be great, even if it meant making personal sacrifices along the way.
It was the sound of someone flooing inside of her house that awoke her. She moved carefully in order to appear as if she was still asleep, grasping her wand tightly with her right hand. In one quick movement, she was on her feet with her wand pointing straight at the throat of the intruder.
"Dumbledore!" She stated with wide eyes, returning her wand to her pocket. "I wasn't expecting you. I'm very sorry."
"No worries, my dear. No harm done."
"Are you alright?" She asked, looking him over in search of injuries or a copy of the Daily Prophet. It was very unlike him to come unannounced.
"I'm afraid not." He sighed before continuing, "I must ask something of you, Leia, that I would never ask, unless I was absolutely sure that it would be a significant blow to our cause otherwise. Last night, an Order member, Severus Snape, was severely injured. I have done everything in my power to stop his condition from worsening, but I have been unsuccessful."
"Severus Snape? The death eater?"
"Ex-death eater, Leia." He corrected.
She sighed, moving to look out the window in a moment of deep contemplation. She had not planned on returning to the wizarding public until after her research was completed. It would have assured her a higher opinion in the people's eyes than the Ministry could ever dream of having, and this time, they could not take it away from her; but Dumbledore truly needed her. She knew deep within herself that she could not deny his request, especially when the man he had spoken about obviously meant so much to him.
Dumbledore watched as she stood there thinking, and his eyes continued to follow her as she disappeared into her bedroom. When she had not returned after a period of time, he began to doubt that she would ever come out. These doubts, along with a majority of his sadness, immediately vanished as she emerged from her room, holding her jacket with one arm and carrying a number of books with the other.
She looked at him and the fireplace expectantly. "Well, what are you waiting for? Let's go."
* * *
**A/N ::** **I'm very happy with the way it turned out. I'm still very scared that I won't do justice to JKR's characters, but I am trying. I'm sure I'll get better as the story goes on.**
**Hope you enjoyed it.
Next chapter will be posted asap.**
2. Chapter 2
**I Dreamed a Dream: Chapter Two. **
* * *
Snape's condition was just as severe as Dumbledore had made it out to be. He was dying. The fact alone was made evident by his slow heart beat and plunging weight loss. She had reread her books a dozen times, searching for something that would lead her to a cure. Unfortunately, her luck was draining just as fast as his health.
Though she was hesitant at first about having someone other than Albus in the room, Leia quickly warmed up to the Poppy woman. She had been an immense help - pulling out some of her own textbooks and explaining to Leia what she had attempted thus far. Her methods were exact; everything she had tried was something Leia would have done as well, but it left very few options on what to try next.
"Any luck?" Dumbledore called from the doorway. A tray of tea and small sandwiches levitated behind him, settling on top of the table that was located in front of the two women. Leia allowed Poppy to answer, continuing to focus on the text in her lap.
"None, Albus. We've tried some additional techniques that Leia found in her books, but none of them had lasting effects. Soon, though. Soon." Her last words were spoken with a kind of soft urgency, as if she was trying to convince herself that they would find a cure in the next few days. Leia reached out and patted her hand, smiling in reassurance before turning back to her book.
"What do you suggest, Leia?"
"I've been troubled by an idea for quite some time now. I think it could work - well, we've got nothing to lose in any case, have we? It's just your permission that I'd need. I assume your library contains a restricted section?"
"It does," he began as he walked towards the door, motioning for Leia to follow. "Poppy, if you would, look after Severus, while I escort Leia to our library. You know how to contact me, if needed."
Poppy nodded in acknowledgement as the two left. Their voices, deep in conversation, bounced off of the thick walls, echoing throughout the empty hallways.
* * * * * * * * * *
Four hours later, Leia was still working diligently in one of the more lavishly furnished corners of Hogwart's Library. It turned out that Hogwarts was filled with more information than Leia had originally expected to find. She had more than eleven books on ancient medicine, which was uncommon in modern society. It was a forgotten art. The wizarding population had become so unknowledgeable about it, that only witches and wizards of exceptional skill could reproduce it's magic. Leia was confident. She could do this - for Severus, for Poppy, for Dumbledore, for herself. It was just a matter of practice…
* * * * * * * * * *
After three days of minor experimenting, Leia found herself nearly drained of all her energy. Seeing this, Dumbledore insisted that she allow him to prepare a set of chambers for her. "It cannot be comfortable sleeping on an armchair, Leia," he reasoned; however, after she continued to persist in telling him that it was unreasonable for such a feeble and temporary situation, the twinkling in his eyes was replaced with a stern look of disapproval, and his suggestion was replaced with a command.
The rooms he had prepared for her were simple, and Leia reluctantly admitted how nice it was to be in a bed again. He was right -- as Dumbledore always was -- when he had told her that a chair was not a comparable substitute, but Leia refused to back down on her belief that it was unnecessary, especially when she refused to sleep away precious hours that could be used for work.
Instead, she prompted each pillow to her liking and spread her books in surrounding areas on the bed. She worked swiftly throughout the night with the aid of Invigorating Draughts and large quantities of coffee. Reading over the part involving incantations, Leia closed her eyes. _Peaceful mind_, it read. She pushed her thoughts to the back of her mind and tried to ignore each of the individual sounds in the room. She held her arms out in front of her, making sure her palms were face down and parallel with the bed. _Counter clockwise hand notions over the wound, speaking the incantation clearly.
_
She remained in that position for a considerable amount of time before slowly opening her eyes. She had hoped to see the magic illuminating her outstretched hands; however, what she saw instead made her blush in embarrassment. Across the room, sitting comfortably on an armchair, was Dumbledore, and even the half-crescent glasses he wore could not hide the look of amusement on his face.
Leia groaned, hiding her face in her hands. "You couldn't have at least coughed to get my attention!?" She asked, throwing a quill in his direction.
"I didn't want to disturb you," he chucked in reply, "After all, you looked rather concentrated."
"I was practicing ancient magic."
"Ah, difficult stuff from what I remember."
"Very."
"If you would," he began, sitting up from his spot on the chair and coming to sit on the foot of the bed, "allow me to take a look at what you have gathered. You may find me to be of some assistance."
She handed him the book she had been reading from, and the work continued on until the early hours of the morning. Dumbledore had called on a house elf to bring a tray of tea, while Leia finally allowed her head to rest against her pillow, slowly succumbing to sleep. Moments before she dozed off completely, however, she was woken by someone shaking her rather fiercely.
"What?!" She yelled, rubbing her eyes in order to see her attacker clearly. It was Poppy, and she looked as white as the sheets Leia was tangled in.
"It's Severus, Leia. He's woken up, but he's in serious pain. We don't know what to do or how to stop it! Nothing we've tried has worked. You must come! Dumbledore is there with him now. Hurry!" She exclaimed, helping her out of the bed.
As they neared the dungeons, Leia could hear the frightening screams of pain coming from Severus. The agony he was clearly in caused them to run the remaining distance to his chambers. Poppy nearly knocked the door off of it's hinges as she entered with Leia following closely behind. In front of her was Severus Snape, but not in the peaceful state she had last seen him in. His eyes remained shut, but his face was distorted in pain as if he was suffering from some terrible nightmare. He thrashed his body about, trying to fight off invisible offenders, and was positively soaked with sweat. His screams echoed throughout the room in deafening bouts. She looked at Dumbledore, who was trying his best to steady Severus, for directions.
"Leia, you must attempt it," Dumbledore stated softly but with great urgency. His meaning was not lost on Leia.
"But I haven't mastered it! I haven't even successfully tried it! You have no idea what you're asking of me. The consequences are _dire_, Albus!"
"The entire situation is dire. You must do this," he said in finality. He gestured for Poppy to hold Severus down from the other side, so that Leia was able to work efficiently. She stared at the poor man thrashing about on the bed and thought of the possibilities that could result from this one act of magic. If she did not do it correctly, he would die, and if she chose not to try, he would also die. She pulled up her sleeves and crawled on top of the bed and over to where he laid. Straddling him, she gently removed his shirt and placed her hands over his bare chest. _Please, please, please let this work_, she begged in her mind repeatedly. With all the commotion in the room, she found it difficult to clear her head.
"Can one of you please put a silencing spell on him? I will not be able to do this properly with all of his yelling!" She stated in frustration. They did as she asked, and with a quick flick of a wand, Severus' screams became inaudible.
Leia tried once again to clear her mind, finding this attempt much more successful than the last. She closed her eyes and repeated the incantations to herself, moving her hands slowly over his chest and face.
"Albus, it's not working! It's not going to work!" Poppy cried, tears flowing freely from her eyes in evident horror.
"Shush, Poppy. You must give her time. She can do this."
To Leia, these words came across as whispers. She tried harder to block them out, turning them into a soft buzzing noise in her ears. She continued her repetitions in satisfaction as she began to feel the slight warming sensation the book had said would occur. Dumbledore and Poppy watched as her hands became illuminated, glowing in the purest shade of white. The thrashing beneath her decreased in violence, until it stopped completely. It had work. She heard Dumbledore warn her to not lose her focus. She would need to keep going in order to fully drain the dark magic from his body. Once again falling into her state of peace, she moved her hands steadily across each of his arms, his chest, his head, and down to the bottom of his legs. She only stopped, when she felt the familiar pressure of Dumbledore's hand on her shoulder. She opened her eyes and looked up at him with a triumphant smile across her face.
"I did it!"
He smiled back with pride glittering in his eyes. "Yes, you did."
She moved off of Severus, planting her feet firmly on the ground; but as she tried to get into a standing position, her legs gave out from beneath her. If it had not been for Dumbledore's quick reflexes and the assistance of Poppy, her face would have collided with the cold, stone floor. "It seems that the magic has not only drained Severus of whatever it was that was affecting him, but it has drained you of your energy as well," he explained softly, before moving on to scold her, "Not that your excessive neglect to your health has helped the matter!" They carried her over to a nearby chair, placing her in it's comfort with a blanket and pillow ready for her. Choosing to ignore his last comment, she fell peacefully asleep.
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**A/N :: Sorry that it took so long. I had quite a few things going on the last week or so, but I am back and motivated. Hope you enjoy it!**
3. Chapter 3
**I Dreamed a Dream: Chapter Three**
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Leia's eyes fluttered open. The light in the room was faint, but enough to produce a sudden headache. She let her hands wander in front of her as she sought a way to get up without causing herself further pain. As her feet hit the floor, she peered out in front of her through squinting eyes. They were still sensitive to the modest light, and she was happy to allow them all the time they needed to adjust as long as it meant that her headache would subside. It did, and in time, she was able to make out a dark figure in the bed across from her.
Severus Snape appeared remarkably better than he had throughout the past week. His complexion had gone from sickly to it's normal pale color; and his body was no longer breaking out into a cold sweat, as if he had run for miles before collapsing on top of the bed. His breath was even, and the conniptions he suffered from were no longer a reoccurring threat. He was at peace, and so was the team that brought him there.
What was different, however, was that his eyes, which for as long as Leia had been there were always closed, were now open. His black eyes were emotionless, but the fierceness of them bore deep into her soul. She felt vulnerable, but couldn't find it in herself to look away. Something about him intrigued her.
They sat staring at one another in silence for several moments, before Leia took the initiative, realizing that he would probably never talk to her willingly. She didn't understand why he made her feel strange. She had never had a problem speaking to Dumbledore, and he had made an intimidating name for himself by the time she had met him. No; this man was no Dumbledore.
"I'm Leia," she stated, leaning over and holding out her hand for him to shake.
He looked at her hand in disgust, evidently not interested in returning the friendly gesture. "Professor Snape. Severus Snape."
"Yes, I know. You don't think Dumbledore would ask me to help his dear Potions master and forbid me access to his name, do you?" She quipped, hoping it would melt some of the ice between them. It didn't, for he merely sneered at her.
"And what else has the old man informed you of? My favorite past-times or flavors of tea, perhaps?" His voice dripped with sarcasm, but Leia, use to such behavior from her own father, was amused.
"No, no. Nothing like that, but if I were to guess, I'd take you for the type of man to like his tea black, no sugar."
"And how right you would be," added a new voice to the conversation. Dumbledore stood at the entryway, his eyes twinkling with happiness at seeing Severus in good health. "How are you, my boy?"
"Fine enough to not need a babysitter, Albus," he replied, quickly glancing at Leia.
"Come now, Severus. That's no way to treat our guest, especially one who has helped you as much as she has."
"Quite right. Thank you, Miss--"
"Delacour."
"Ah, yes. Thank you, Miss _Delacour_, but as you can see, I no longer need your assistance," he stated, looking straight into her eyes. He gave her no time to reply, and instead, looked back towards Dumbledore, before continuing, "Does that suffice?"
Leia could not help the frustrating sense of confusion swell deep inside her. She had saved him, so why was he acting so poorly towards her? Of course, from the stories Dumbledore had told her about him, she never expected him to fall on his knees and kiss the hem of her robes; but she expected _something_, and it definitely was not this.
"That's enough, Severus," said Dumbledore, who was clearly unhappy with his friend's rude behavior. "Leia has agreed to stay for the duration of the week to make sure you stay in good condition. We wouldn't want a relapse now, would we, Severus?" Dumbledore's twinkle-less eyes appeared to stare right through Snape, causing him to mutter a reluctant "no."
He was unhappy, and Leia could not help but feel a bit of pity for him. The last few nights must have been more of a trial for him than they were for her, and now, just as he probably wished to get back to his job and his life, he was being forced into bed rest. As her old companion lead her out of Snape's chambers in hope of putting food into her concaving stomach, she looked back. He still stared at her, but his eyes did not hold the same cold fierceness that they had before. This time, Leia was unsure of what she saw in his eyes, but it was the something she had been hoping for.
* * * * * * * * * *
Severus watched as the woman sitting across from him attempted to get up. Her dark hair shielded her face, disabling him from making out her identity; but as she readjusted herself to stop whatever pain plaguing her, her hair shifted and allowed him a perfect view of her face. She was beautiful. Her dark hair suited her pale complexion, which was even more complimented by her thick, pink lips and high cheek bones. She was young, but her entire disposition seemed stressed, as if she was never allowed the time to relax.
When she recovered and began to fully wake, he found her staring at him. Her eyes traveled over him, no doubt assessing the damage that was caused previously, and he watched as her eyes seemed to glaze over with relief, when she found he was perfectly fine.
"I'm Leia," she told him, after noticing he was also awake. Leia…her name sounded familiar, but he was unable to tell where he had heard it before.
Frustrated with his own state of confusion, he looked down at her hand distastefully and gave her his own name. When she nearly laughed, explaining that she already knew, he had wanted to hex her, deciding that he had had enough of her company, whoever this girl was. His frustration grew, when he realized his sarcasm amused her, instead of frightening her or shattering her spirit. She was clearly much different from his first-year students.
Dumbledore entered the room, his eyes twinkling in their usual blasted way. He was surely the reason for the girl being in his chambers, sticking her nose in business that did not concern her. He bit his tongue, though, knowing he would lose such a fight with the old man.
As he tried to quickly thank the girl in an effort to make her leave, he realized she had not told him her last name. He waited expectantly for her to fill in his trailing silence, but it was Dumbledore that answered.
"Delacour."
Delacour. Leia Delacour. He searched the darkest parts of his brain in hope of finding some recollection of her or perhaps a family member before her. Finally, he had some luck. Dumbledore had informed the staff of a young woman, whose powers matched his own and would work with them to fight for the cause. So, _this _was the girl. The girl that spited the Ministry time and time again; the girl that befriended Albus Dumbledore at the tender age of fifteen; the girl whose beauty was said to make even the goddess Aphrodite blush in jealousy.
An acidic taste formed on his mouth, causing him to rethink his new discoveries. She was beautiful, yes, but hardly _that _beautiful -- not to mention arrogant and unbearably irritating. He would have to make it a personal goal of his to make sure she spent as little time near him as possible.
Unfortunately, there seemed no way to get rid of her. Dumbledore had set his mind on making her stay, and it appeared that she was just as forced in the manner as he was. _Ah, well,_ he thought dismissively, but a small, unexplainable emotion welled up inside of his chest as he caught her eye one last time. There was something about her; and though he couldn't put his finger on what it was, he knew that it would continue to bother him to no end.
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**A/N :: It's a bit shorter than the other two chapters, but I had a craving to write and knew I was a bit late getting this one out there for my few dedicated readers. Hope you like it!**
**Another week or so for chapter four, I think. That's a safe bet.**
**& thank you for your supportive comments.**
4. Chapter 4
**So, here you go. Sorry it took so long. I had end of the year finals and such, but I'm finally through with school. I think this is one of my favorite chapters so far. Hope you enjoy it!**
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**I Dreamed a Dream: Chapter Four**
Leia remembered much of Hogwarts from her fifth year. She had read about it's vast history from numerous books, including her personal favorite, _Hogwarts: A History_. The diverse staff was one of her interests. Beauxbatons, along with many other wizarding schools, was known for their human staff, but Hogwarts had been the only school in the course of centuries to branch out from that. Ghosts, giants, dwarfs…the list went on, ending with Dumbledore, of course, who was her main focus.
Even then, she never would have guessed that they would be as close as they were. After all, he was the great Albus Dumbledore, the one who had killed the dark wizard Grindelwald, and she was just a fifth year, trying to make something out of herself. It had started out with letters, but moved on to weekly visits a few months after the tournament took place; eventually, he had become somewhat of a second father to her, always watching out for her and teaching her a number of new tricks.
Now, they sat side-by-side under the Whomping Willow tree, sipping tea and enjoying the fresh air. Silence had become customary between them with neither one needing to continue speaking in order to feel comfortable. They were at peace, and they were happy.
Severus' attitude towards her had not changed. His usual cold disposition remained so, until she explained to Dumbledore that he appeared to be fine and could do without her. That was perhaps the only time he managed to be civil with her. Leia looked back on the moment, when Severus bowed slightly to her from the back of Dumbledore's office, before grinding out a painful 'thank you' and taking his leave. He had spent the entire week treating her as if she was the one to torture him, and she had begin to think that there may not be a basis for friendship between them after all. A thought which strangely stung her heart.
Sadly, his civil manner was short lived. Apparently, Dumbledore had failed to mention their weekly gatherings, causing him to be cruelly ambushed by her presence that afternoon, when she attempted (and failed) at apparating into Dumbledore's office.
"I hope you realize that you have just ruined a very expensive rug," he sneered, looking down at her petite form, which was covered in dirt and sprawled across his living room floor.
"I was trying to apparate outside of the castle. I thought it might be easier that way," she explained, wincing in pain as she realized her knees were bleeding.
"Well, well," he began, the smirk on his face becoming even more prominent. "Leia Delacour, the child said to be of remarkable talent, cannot even manage to apparate from one place to another? I dare say, even Potter can do something as simple as that. What a pity."
Realizing he had no intention of helping her up, she gritted her teeth and pushed herself up and off of the floor. "You're awfully hard on the boy. From what I hear, he's quite the young gentleman. Jealousy, perhaps?" She knew that she was entering dangerous territory the minute the words left her lips. They were not old friends, who could tease or joke around with each other; no, their relationship -- if you could even call it by such a term -- was young and less than ideal.
She watched as his eyes, which were once the color of pure black coal, turned crimson, as if someone had lit them ablaze; but before he could insult her or pull out his wand, she immediately blurted out a quick apology. "I was out of line." He seemed to accept this and hurried from the room, leaving her alone and without a guide to the main floor. She couldn't understand why she wasted any of her time speaking to him. She found him intriguing and infuriating all at the same time, and he…well, he never gave her the impression that he cared about anything at all.
He was miserable almost every second of every day, and on the rare occasions that he wasn't, he was still disturbingly serious and unfriendly. Still, since the very moment their eyes met, she could not shake the feeling that there was something else -- something deep within him that she couldn't see. Perhaps, it was the same thing Dumbledore saw the night Snape asked for his help some many years ago. Either way, she found her previous doubts about him had vanished, leaving in it's place a thin, but stable, ribbon of trust.
* * * * * * * * * *
"So, you never explained to me what importance my presence served today," Leia called to Dumbledore, who was walking a few meters away from her in the Forbidden Forest.
"Very true, my dear; however, I do recall mentioning that patience was required for this particular evening." His eyes, she noticed as he glanced back at her, twinkled far more than usual in the moonlight. They complimented the stars above them, even if their light was significantly less astrological.
"Touché."
They had been walking for a little over a half hour, pushing past the underbrush of the forest and stumbling over broken tree branches. Each had their wand out, but so far, they were unneeded. As they delved deeper and deeper into the forest, she heard loud, malicious roars, causing her heart to quicken along with the slow pace she kept. Finally, just as she was ready to begin complaining again, she noticed Dumbledore had stopped and was staring past a group of entwining trees.
She moved closer behind him, peering over his shoulder. Her eyes widened in astonishment. Of all the things Dumbledore had shown or told her in the past few years, this was one of the most surprising. In front of them, kept in large, thick cages, were an assortment of dragons. Red eyes were seen glowing in the darkness within them, and fire sprouted out from the holes like roots at the bottom of a flower pot. They were beautiful creatures, even with their bad temper and fatal behavior.
"I thought you'd appreciate this," she heard Dumbledore say, stepping aside and allowing her a closer view of them.
She moved around the cages carefully, avoiding the chaos that would arise if she made the creatures feel threatened. "What breeds?"
"We have a Chinese Fireball, a Common Welsh Green, and a Swedish Short-Snout. All breeds that can be raised in captivity or tamed after extensive training. Quite safe, I assure you."
"You seem to think I doubt your judgment, Dumbly," Leia remarked with a playful glint in her soft, emerald eyes.
"Never, my dear. Never," he assured her as he moved to stand next to her and patted her hand. "We are ahead of ourselves this year, though most of the credit should rightfully go to Hagrid. Terribly eager, he was, to get near another dragon after the last incident."
"Have any bets on who will represent you?"
"I wouldn't dare guess. The last time Minerva and I tried anything of the sort, I was left alone and wandless to clean her classroom for months. She's competitive to no end."
Leia laughed heartedly at the images that were forming in the back of her mind, Dumbledore scrubbing the floor and numerous desks that were scattered across Professor McGonagall's classroom. She knew he had done such things in his days as a student, but she could never quite grasp it. He was human, but she always thought of him as something more, something _better_, like his own breed of self. They maneuvered themselves around the cages for another hour, talking and observing the creatures in endless wonder, before heading back to the castle. It was getting far too late, and Leia still had books at home that she wished to conduct further research on.
"Thank you for that," Leia said as she entered Dumbledore's office and walked towards the fireplace. "You know how much I love dragons."
"Of course, my dear. I'll inform you as soon as the Goblet gives the chosen names. I was hoping you'd be able to discuss your own experiences with those selected as words of caution. You and I both know how the competition has changed many a witch and wizard who has entered it unprepared."
She only nodded at this, trying to offer a small smile but failing to do so. She had won her own competition, yes, but every triumph had it's sacrifices -- it's own particular price. She shook the memories from her mind, not allowing them to resurface, and grabbed a handful of floo powder.
"I'll see you as soon as you call, then."
And with that, she was gone.
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**A/N :: Next chapter will hopefully be up soon. I'm trying to make it so I update every week, but it's a lot harder than I imagined. I also want to add a quick thank you to the few avid readers I have. I'm glad a lot of people are favorite-ing my story. It means a lot to me.**
5. Chapter 5
**I Dreamed a Dream: Chapter Five
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Leia had been experimenting with a number of spells she had been creating, when Dumbledore's letter arrived. Although he was always one to admire and welcome change, he never followed the procedure that usually occurred in making it happen. So, she was not at all surprised with the sudden appearance of O. Henry at her living room window. O. Henry was an owl Dumbledore had chosen for his own personal use, and seeing as the owl had been enrolled in Dumbledore's service since before Leia had even crossed his path, she imagined it was well past the age it should be venturing out of Hogwarts.
She gave the window a slight push to invite Henry in, watching as it settled itself on her mahogany coffee table and ruffled it's feathers for comforts sake. The letter, which was tied none-to-comfortably to it's leg, caused it to hobble as it scooted closer to her. It's eyes were tired from the flight, but also determined to see it's task through. She cut the letter free, using a knife she had been working with earlier, and unfolded it, careful not to ruin it within her grasp. She always hated ruining things that were so prettily prepared, especially the fine stationary Dumbledore used, even if he had refused to reveal his source of supplies to her.
_Leia,_
_The champions have been chosen. Come quickly. I fear there is much going on that we are unaware of. _
_Yours truly,_
_Dumbledore_
She threw the letter on her couch immediately after reading it. This year, she thought to herself as she threw her coat over her shoulders, was becoming _very_ interesting _very_ fast. The owl cooed, looking at her expectantly, but she was in too much of a hurry to write up a reply stating she would be there momentarily. It was implied, of course, in the urgency of his letter. "Stay here and rest," she said firmly to the frustrated owl. "I'll be back for you later." She reached into the flower pot beside her fireplace, grabbing a large fistful of floo powder, and threw it at her feet, causing green flames to envelope her.
In the process of flooing, Leia had closed her eyes. When she reopened them, she found herself safely within Dumbledore's office. The portraits greeted her in friendly manners, and Fawkes sang to her arrival, nudging her hand with it's beak. His prized gadgets were in the same spots they had always been in, and the tea left on his desk made it evident that his room was in use; however, it was not Dumbledore she found.
"Severus," she stated, staring at him in shock as he leaned against a nearby wall with his arms crossed over his chest.
"Miss Delacour."
"What are you doing here?"
"The headmaster has asked me to personally escort you to where the four selected champions are located. The ministry wrote to him not but a moment ago, requesting his immediate attention. I assure you that I did not relish the job currently at hand when it was first presented to me; but alas, I'm here."
She swallowed the retorts that were sharpening her tongue, readying themselves for attack, and mustered a short, "How sweet." It was, in his own sociopathic way, sweet. After all, she wouldn't have put it past him to leave her alone and waiting in Dumbledore's office. But Dumbledore trusted him, and although he often put people's best attributes before their worst, she knew this much was true: Severus Snape was nothing if not reliable.
"Come," he stated simply, turning around and guiding her down the winding staircase. They walked through the hallways without speaking to one another. Half way through the journey, however, Leia deemed the silence unbearable, enough so that she was willing to attempt a conversation with the dark and mysterious man in front of her.
"So, how long have you taught Potions here?" She tried, but was answered with a mere snort of a laugh. It was something. "Alright, well…do you enjoy teaching Potions?"
"I would not teach it, if I found it an unpleasant subject."
"Yet, you don't seem particularly pleased," she remarked, happy to hear him reply this time.
"Nor would you be, if you had to waste a majority of your life on something that is seemingly impossible."
Her interest was caught. "And what would that be?"
"That, Miss Delacour, would be the teaching aspect."
Leia laughed, unable to help herself. "Ah, I can see what you mean. I wonder, though, how you managed to obtain the Head of Slytherin House position, if you look upon your students with such disdain."
"It was the position of the professor before my time teaching here, so naturally, as I took on his position, the title was passed on to me."
"However reluctant you were?" She inquired with genuine interest.
"No. I could have given it to anyone who wished to obtain it."
"But you didn't. Why?"
"That is none of your business," he answered quickly, turning around to face her, his face emotionless and his eyes cold. "I'm afraid this petite tête-à-tête must come to an end. The chosen students are right down the hall -- third door to the left. I trust you can find your way there without further assistance."
She had no time to reply, for he was halfway down to hall by the time she had opened her mouth in an attempt to say goodbye. She watched him go, noticing how his cloak billowed behind him. _Like a bat_, she thought, smiling as she realized what many of the students had said was true. She looked back in the opposite direction once he disappeared and began walking towards where the champions were located. Her destination was made obvious by the light inside, illuminating the cracks in the door. Voices were heard, soft but urgent, and shadows peeking through the bottom of the door showed her the movement of those inside.
She knocked twice in politeness before permitting herself entry. The room, itself, was crowded with trophies, all of which, at a glance, appeared to be for quidditch. Three couches were placed further in the room and atop of them sat the champions and their advisors, all except Dumbledore, of course.
"Hello, I'm Leia. Professor Dumbledore sent me." She watched with delight as Madame Maxime strolled over to her, arms wide with welcome, bending down to hug her.
"Leia, my dear. Comment t-appelle tu?? I hope your father iz well."
"Bein, merci. And you? Prepared to take another victory for Beauxbatons, I see."
Madame Maxime laughed, delighted to bring up old triumphs. She had always been quite a competitive witch. "Oh, I hope so. Eet would be wonderful to win again, but they have that _boy_."
She spoke the last word so disdainfully, Leia immediately peeked with interest. "What boy?"
"The chozen boy. The won that defeated He-Who-Muzt-Not-Be-Named all thoze yearz ago. The one with the zcar."
Leia's eyes widened. Harry must be the reason Dumbledore had needed her there so urgently. She was delighted, of course, never having met Harry before, but confused as well. Dumbledore had mentioned that they had raised the age to seventeen in order to compete. How did he possible get mixed up in it?
She excused herself from her former headmistress' presence, shaking hands with Karkaroff, before making her way towards the champions of Hogwarts. Cedric Diggory was the first boy she walked up to, wanting to save Harry for last. He was courteous and the utmost definition of a gentleman, as he sat up and offered her his seat. She politely declined. Then came Harry, who sat a bit further into the room than the others, obviously embarrassed that he had been the source of the sudden burst of panic.
"Hello, Harry." She said as she neared him, her hand held out for him to shake.
He took it, giving it a quick shake, before introducing himself. "Harry Potter. Nice to meet you."
"I believe the pleasure is all mine. Dumbledore talks quite a lot about you."
"You're friends with him? Have you spoke to him? Does he know why my name was chosen?"
"Whoa, Harry. One question at a time, please. As for your first question, yes. I met him when I was close to your age actually, and I was competing in this exact tournament." She watched his eyes grow with curiosity, but before he could ask any further questions, she went on explaining, "But that's tale for another day. As for your second question, he sent me an owl just a few moments ago, asking me to report here immediately. I must say, I'm very surprised to see you here. How'd you sneak your name into the Goblet?"
"I didn't," stated Harry defensively, sick of having to explain himself.
"Then I'm afraid we're at a loss, Harry. Perhaps one of the older boys put it in the Goblet themselves as a joke?"
"No, the charm around the Goblet made sure that the people who entered into the competition only entered once."
Leia regarded him curiously. She didn't believe him to be lying, but nor did she believe him to be safe in the eyes of the others. They would call him a cheat and look upon him with suspicious eyes, waiting for him to use Dumbledore's favor to get ahead of their precious champions. As much as she loved Madame Maxime, she knew her beastly competitive nature very well; and Karkaroff was far from angelic as well. Troubled times were ahead, and there was no turning back for either of them now.
"Harry," she stated, looking the boy in front of her firmly in the eyes. "Is it alright if I share this conversation with the Headmaster?"
"Of course."
Leia nodded at him with a slight smile of reassurance. A familiar feeling of obligation swelled up within her breast. He appeared to be everything Dumbledore had said he was: determined, kind, and honest. He had the heart of a hero, and one day, he would make them very proud; but he was still just a boy, and like any other, he needed help.
She said goodbye, hugging her former Headmistress, and exited. While taking in her surroundings, Leia realized how lost she truly was. She thought of asking Harry or Cedric to escort her to Dumbledore's office, but quickly dismissed it. They had enough on their minds as of now. She would be fine. After all, the more time she spent in Hogwarts, the more she felt she would remain there. She had a purpose now, and it was not just the simple demand of fighting alongside aurors at the final battle. No, she had much more to do than _that_.
So, humming quietly to herself, Leia decided to continue on by herself. She knew she would have to become familiar with the castle eventually, and could think of no better way than exploring her surroundings with no general direction or knowledge. She scoffed at the slight anxiety she was beginning to feel. It was only Dumbledore's office. She had been there plenty of times. How hard could it possibly be?
* * *
**A/N: It took me a while. I've had slight writers block, and then had to fight off the feelings of deleting this story altogether. I'm not exactly sure what I think of it yet. I'm just having fun with it and seeing where it goes.**
**I'm glad to see that you all are still enjoying it. I've gotten quite a few emails from the site informing me of people who had favorited it and such. That makes me smile. Anyway, I hope you enjoy this chapter. I'm trying to include more dialogue, because I know that's what I mainly look for in a fanfic, especially since too much detail can drag it down a bit.**
**Let me know whatcha think. :)**
**Oh, and yes. Hahaha, writing a french accent out is not my particular area of expertise, hahah!**
6. Chapter 6
**I Dreamed a Dream - Chapter Six**
By the time Leia had found her way back to Dumbledore's office, the moon had settled itself high above the castle and the stars were sparkling with a fierce brightness; and the cloud of frustration that had gradually settled itself over her head darkened considerably when she caught sight of swishing black robes beside Albus' periwinkle blue through the slight opening of the door.
As she neared it, their voices became clearer. It seemed that they were arguing, but Severus' voice was more rushed and furious. The child deep within her urged her to wait and listen. If she walked in, their conversation would be put to an immediate end and neither would tell her what it was they were speaking of. Pressing herself against the wall beside the door, she focused all her attention on the two that were standing in the room a few feet away.
"Severus," Dumbledore addressed him. "Has it ever come to your attention that perhaps it is you with the problem?"
Severus' silence answered his question in the negative.
"She saved your life, when I could not. She came out of her own self-imposed exile to save you. She did not have to, but she did. And all the while, you are treating her as if she was just another one of your students that was unfortunate enough to stumble upon one of your more foul moods."
"So, what is it you expect me to do, Albus? Invite her for tea and pumpkin pasties? Or, perhaps you mean for me to ask her what she thinks of the latest controversial newsstands across Diagon Ally? Both of which giving the girl some false sense that I am actually fond of her--"
Dumbledore's hand shot up to stop him, and his eyes held an unspoken threat. Composing himself, he walked over to the door and opened it completely, peering off to the side where Leia had tried to conceal herself. "Welcome, my dear. Do come in."
Leia's face flushed with embarrassment. She shouldn't have been surprised that Dumbledore had known she was eavesdropping. He had caught her in much worse scenarios before, always knowing exactly what she was up to before she knew it herself.
"Severus." She greeted him while sending a glare in his direction to indicate she had heard him voice his dislike towards her.
His emotionless expression did not falter, nor did his unwillingness to answer her back.
"You talked to Harry?" Dumbledore asked, though his eyes were back on Severus with the same unpleasant gleam.
"Yes, I did. He said he didn't put his name in--"
"Of course he said he didn't put his name in the goblet, Miss Delacour. Are you daft enough to think he would not lie through his teeth to save himself from the threat of punishment?"
"What is it with you? Must you always think that everyone has an ulterior motive or something to hide? I happen to believe Harry!"
Snape sneered. "You and the rest of the world, it seems."
"And what has Harry done to earn such strong, negative feelings towards him?" Leia countered, her eyes fierce.
With two quick strides, he was a mere inch away from her. His eyes holding the same dark intensity. "That is none of your business!"
Dumbledore chose that moment to intervene, bringing himself between them. "Leia! Severus! Enough of this! Sit down at once. You're acting like third years."
They reluctantly complied and stepped away from one another, but their livid composures and frosty glares never faltered. Deciding that it was safe enough to carry on, Dumbledore broke the lingering feel of tension by continuing the conversation.
"You are sure," he began, "that Harry did not put his name in the Goblet?"
"Without a doubt," Leia confirmed whole-heartedly.
"A classmate, perhaps?"
"I asked that as well, but Harry seemed quite convinced that none of the other students -- or even his friends, for that matter -- would do such a thing. They were all too preoccupied with plans to get their own names in it."
The room entered yet another period of silence with Dumbledore deep in thought, Severus grinding his teeth in irritation, and Leia too tired to do much about either. She walked around Dumbledore's office, her fingers grazing the surfaces of the various tables and walls. She found comfort within it's walls, even with the air as thick as it had become. The portraits of previous Headmasters and mistresses were as still as muggle portraits. Their chests rising and falling in deep, sleeping breaths were all that gave their life away.
An urgent knock at the door broke all three away from their private thoughts, and a moment later, Professor McGonagall walked in. Tendrils of hair had strayed from her usually perfect bun, and her facial expression betrayed every thought that flowed through her keen mind. She was worried.
"Every year, Albus!" The Professor exclaimed. "Every year the boy is subjected to some disastrous plan of murder. This can't go on Albus. You First the dark mark, now this?"
"What do you suggest, Minerva?" Dumbledore asked quietly.
"Put an end to it! Don't let Potter compete!"
"You heard Barty. The rules are clear."
"Well, the devil with Barty and his rules!" The Professor proclaimed, her voice raising in agitation. "And since when did you accommodate the Ministry?"
Dumbledore opened his mouth to reply, but Snape interrupted their exchange, pulling himself back out from the shadows and into the main heat of things.
"Headmaster," He began slowly, watching both carefully in order to measure each of their responses. "I, too, find it difficult to believe this a mere coincidence; however, if we are to truly discover the meaning of these events, perhaps we should, for the time being, let them unfold."
Both Leia and Professor McGonagall's mouths dropped in shock. What was he proposing? Did he truly intend to place Harry in front of harm's way, offering him up as if he were a sacrifice? McGonagall beat her to the point, and once again, her voice rose, but this time, she was livid.
"Do nothing? Offer him up as bait? Potter is a boy not a piece of meat!"
The room entered a still, tense silence once more as Dumbledore considered what each had said. Seconds seemed like minutes, and minutes seemed like hours, before Dumbledore finally turned away from each of them, seeking some sort of comfort in the sight of his Pensieve.
"I agree… with Severus," was Dumbledore's final words on the matter, unable to stand further talk on the matter.
Severus' famous smirk was inching it's way across his lips, while McGonagall and Leia stood shaking with confusion - both feeling as equally betrayed as the other. It was unreal. How could Dumbledore so easily throw away the safety that protected his most beloved student? And how could Severus, someone Dumbledore trusted with every fiber of his being, so willingly offer the idea? It seemed as if their worlds had been spun around and upside down. None of it made any sense.
"Come on," Leia heard faintly, as a hand pressed against her back, ushering her towards the exit. She glanced behind her to see Minerva, her eyes holding a sympathetic gleam. She nodded and they left, but not before either of them could send their last few glares in Snape's direction.
His emotionless expression never faltered as he watched the two leave; however, something in him shifted when he saw how pained the younger woman was - something Severus had not felt in quite a long time. And so, after feeling such an emotion, Severus decided to waste no further time, uttering a short goodbye to the Headmaster, and left to return to his chambers, hoping to drown it out with a few shots of Firewhiskey and Dreamless Sleep potion.
* * *
Took pieces of the conversation from the fourth movie to make up Dumbledore, Minerva, and Severus' conversation. I wanted to really place myself into the events, instead of just completely making up everything as I went along. I wouldn't have to spend nearly as much time finding loopholes that way, hahah. Sorry it's so short, though. That kind of sucks, I agree.
It took me awhile to get it up again, I know. School's starting up, and I have to focus on a bunch of college-prep stuff. So stressful. I'm sure a number of you have already gone through it and know exactly how it feels.
Anyway, thank you, my loyal readers.
Reviews are welcome as always.
I'll get chapter seven posted asap!
xoxox
End file.
| fanfiction |
We've seen them and you probably have to...the images of ravaged polar bears, hunting for food, with the outlines of their ribs showing. In case you need a reminder of why every degree matters in the fight against climate change, here is National Geographic's video.
Since 1979, Arctic ice has lost approximately 80% of its volume. Although the ice builds up during the winter, it has not been enough to compensate for the losses since 1979.
A decline in sea ice is a major threat to the polar bears, currently listed as vulnerable on the Endangered Species List.
Yes, polar bears can swim but their main food source - seals - are losing their ice too. As the Arctic sea ice continues to retreat every year, seals become harder to hunt and bears have to travel much further to find them.
The drifting ice can also act as a sort of conveyor belt. What was once a stable, hard surface for the polar bears to hunt and live on, looks almost like a patchwork quilt, with large patterns of open water.
Polar bears are now facing the ultimate conundrum: expel more energy and burn calories to travel further than ever before for food and solid ice or stay put and hope their ice stays intact, with a food source.
They are also appearing in places they have never been spotted before and the most recent standoff lasted more than 36 hours.
With Arctic ice declining even more every decade, we need to act soon or we could see an ice-free Arctic summer by 2030.
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the current global crisis of untreatable multidrug - resistant pathogens has long been associated with the imprudent use of antimicrobials in multiple ecosystems : hospitals , communities , agriculture , horticulture , and aquaculture .
the finding of resistance in domestic honeybees reveals yet one more environment that demonstrates the profound ramifications of long - term antibiotic use .
( 1 ) on the microenvironment of the honeybee gut provides a particularly exquisite and detailed example of the evolutionary diversity incurred by the long - term use of a single antibiotic , tetracycline , within this industry .
the origins of the resistance genes themselves are obscure but are presumed to derive in part from tetracycline use in other ecosystems .
for instance , tetracyclines are commonly used as growth promotants in animal husbandry ( 2 ) .
so it is no surprise that tetracycline resistance has emerged among food animals , and meaningfully , the determinants for tetracycline resistance are frequent .
study reveals the profound effects of tetracycline use in beekeeping on the normal gut flora of the honeybee , effects that can potentially have far - reaching impacts on the proliferation and dissemination of resistance genes in the greater environment .
it is not often that one finds defined ecosystems which allow , by their very nature , comparisons among different , relatively confined populations . in their examination of the enteric flora of honeybees ,
the data show a correlation between antibiotic usage , namely , oxytetracycline , to prevent bacterial infections in beehives , and the high frequency of determinants for resistance to tetracycline among the honeybee intestinal flora .
what is striking is the variety of tetracycline resistance genes ( eight different ones ) that are identified in this small ecosystem .
while the bee flora is largely gram negative , the determinants found are associated with both gram - positive and gram - negative bacteria , suggesting a nonindigenous origin . while heterogeneous , these tetracycline resistance genes are highly similar , genetically , to those found in bacteria associated with people and farm animals . in contrast , in europe , little tetracycline is used on honeybee hives , and the bees do not harbor high frequencies of tetracycline - resistant organisms , nor do bumblebees sampled in the wild .
it is interesting to note that although the enteric bee flora contains many different tetracycline - resistant strains , the beehives that tian et al .
( 1 ) studied were not obviously diseased and apparently did not harbor foulbrood pathogens .
thus , in this study group , tetracycline resistance did not thwart treatment , since tetracyclines were not being used against disease . instead , drug use supported and encouraged the propagation of non - disease - causing bacteria bearing resistance genes .
the bacterial strains themselves are normal constituents of the bee gut flora , but the diversity of tetracycline - resistant strains suggests that the resistance genes that they carry were recruited from other environmental sites , including other bees and beehives .
the detection of resistance genes among noninfectious strains fits with the conclusion drawn by the reservoirs of antibiotic resistance ( roar ) project of the alliance for the prudent use of antibiotics ( http://www.apua.org ) , namely , that the vast majority of antibiotic resistance determinants reside not in clinical isolates but in non - disease - causing strains ( commensals ) ( 3 ) .
in fact , a high frequency of tetracycline resistance is already reported among the native fecal floras of animals and people ( 2 , 4 ) .
one might wonder if the propagation of tetracycline - resistant commensals by tetracycline exposure protects bees from colonization by resistant , disease - causing bacteria .
there may not be an easily available niche for entry of disease agents , since the entire ecosystem is colonized with tetracycline - resistant competitors .
the density of the beehive population and the bee intestinal flora potentiates the exchange of resistance genes by two modes of transfer : the resistance genes , which can move between bacterial hosts via mobile genetic elements , and the bees , which can pick up and physically transport tetracycline - resistant bacteria among themselves . our own studies , performed on a farm , showed that escherichia coli organisms bearing antimicrobial - resistance genes were carried on flies from farm animals to other animals ( 5 ) .
as both a collector and potential disseminator of resistance genes , the honeybee ( and the fly ) is a kind of barometer for the spread of resistance determinants among different environments . while no disease was described in the tian et al .
study ( 1 ) , potential movement of resistance genes to bacterial pathogens in honeybees is always a threat and in fact was documented in foulbrood pathogens beginning in 1996 ( 6 ) .
neither we nor tian et al . assayed for the antibiotic itself , but such studies could have identified the drug s presence , location , and concentration in the honeybee environs and could also have helped to determine whether a correlation exists between the presence of the antibiotic and the resistant flora .
study presents a compelling picture of a gut flora that is rich in tetracycline resistance genes selected by tetracycline and carried by bees as they visit flowers and interact with the hive .
do the tetracycline - resistant bacteria exist as a permanent part of this gut ecosystem , or are they only transiently present ? in the case of honeybees , it appears that the resistant bee flora is constantly replenished and has consequently established a stable tetracycline - resistant ecosystem .
studies of human volunteers reveal a similar pattern . in his 1988 study of human subjects ,
denis corpet compared the gut bacteria of antibiotic - free volunteers who consumed either normal or only cooked food ( 7 ) .
corpet recorded a dramatic decrease in tetracycline resistance frequency in volunteers placed on diets of only cooked food , a finding that suggests that uncooked foods provide a steady source of tetracycline - resistant bacteria .
likewise , contact with tetracycline and tetracycline - resistant bacteria helps honeybees maintain their tetracycline - resistant flora .
it would also have been quite illustrative to conduct a prospective study that examined the timely acquisition of the different resistance determinants .
such a study could help to define their environmental origins , the participating microbial hosts , and the timing and means by which they eventually become stable members of the gut flora .
certainly , the resistance genes associated with the bees are part of a larger ecosystem of resistance genes .
the fact that they are highly homologous with the tetracycline resistance genes identified in clinical isolates and among animals suggests that this exchange of resistant determinants is recent and reflects an ongoing process . despite the fact that penicillin was never used on these hives , tian et al .
this seeming paradox is reminiscent of prior studies that show that prolonged use of a single antibiotic can lead to multidrug resistance .
the genetic basis of this phenomenon resides on plasmids and transposons . in studies of chickens on a farm , 3 months of oxytetracycline use in animal feed led to the appearance of bacteria resistant not only to tetracyclines but also to penicillins and other antibiotics ( 8) .
similarly , single - drug resistance leads to multidrug - resistant selection in farm dwellers ( 8) . the same phenomenon was reported in people taking antibiotics for prolonged periods of time , as for acne , where susceptible skin flora will emerge with resistance , initially to the antibiotic used and later to other antibiotics as well ( 9 ) .
the emergence of resistance to multiple drugs after the application of a single drug is an important concept in understanding gene spread .
all this prompts us to view the many antibiotic - exposed environments as ecosystems that are undergoing processes of gene acquisition and dissemination .
clearly , the comparison here of europe and the united states is telling . in europe ,
honeybee - producing farms avoid antibiotic use for their bees because it tends to be ineffective , can lead to resistance , and favors weak , disease - prone hives .
thus , some bee keepers prefer to destroy infected hives because of the unintended consequences of antibiotic treatment for the ecosystem and environment ( 6 , 10 ) . in fruit orchard husbandry , prophylactic spraying of antibiotics
may be helpful in thwarting disease but also carries the consequence of spreading antibiotic resistance , either through selection by drug residues or through gene transfer ( 10 ) , as described in this study of bees .
we have learned that antibiotic use in any environment will lead to changes in the floras harbored by animals , insects , and people sharing that environment .
it may be small , as with honeybees , or large - scale , as seen in food animal production .
tetracyclines are commonly used in animals and in people and are easily shed in the environment as residues .
thus , it may not be so surprising that use of oxytetracycline in honeybees would select for all these different determinants , which themselves could have been preselected by tetracycline use in other nearby environments .
the findings raise several questions : why are some tetracycline resistance determinants more commonly found than others ? do the resistance determinants provide an advantage to the growth and survival of the bee existing in a
why did it take 45 years of oxytetracycline application before disease - causing bacteria emerged with tetracycline resistance ?
despite many years of investigation , these and other pressing questions have still eluded definitive answers , and studies directed at these issues will go far in providing a deeper understanding of the complex nature of antibiotic resistance spread and how it can be more successfully contained . | pubmed |
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the galactic thin and thick disks are two distinct stellar populations in terms of age distributions and kinematics .
the chemical trends in the two systems are also most likely different although recent works give conflicting results , see e.g. chen et al .
( 2000 ) and fuhrmann ( 1998 ) .
we show that the abundance trends for oxygen are different for the thin and thick disks .
the selection of thin and thick disk stars was based on kinematics and is fully described in bensby et al .
( 2003a , in prep ) .
we calculated gaussian probabilities for each star that it belongs to the thin and thick disk respectively ,
using the galactic velocity components @xmath6 , @xmath7 , and @xmath8 of the stars . stars with high probabilities of belonging to either the thin or the thick disk were then selected .
the sample consists of 21 thick disk stars and 42 thin disk stars .
spectra were obtained with the ces spectrograph on the eso 3.6 m telescope with a a resolution of @xmath9 and a signal - to - noise @xmath10 .
telluric lines were divided out using spectra from fast rotating b stars .
further details are given in bensby et al .
( 2003b , in prep ) .
oxygen abundances were determined through fitting of synthetic spectra to the observed spectra . the forbidden oxygen line at 6300 that has a blend of nickel in its right wing . at low metallicities
this blend is often negligible , but becomes severe at higher metallicities .
this is illustrated in fig . 1 where we plot synthetic and observed spectra for three stars at different metallicities .
fe and ni abundances have been determined from our feros spectra ( r@xmath11 ) by measuring equivalent widths of approximately 140 fei , 30 feii , and 50 nii lines for each star ( bensby et al .
2003a in prep . )
the two plots in fig .
2 presents our results .
these are our findings : + * 1 . *
the thin and thick disk stars clearly show different abundance trends .
this is a strong indication of their disparate origin and different epochs of formation . +
* 2 . * a turn - down for @xmath2 $ ] at @xmath5\sim -0.35 $ ] for the thick disk stars , from being roughly flat , continuing down to solar values .
this feature is most likely a signature of the onset of snia . +
the thin disk stars show a shallow decrease when going from the lowest metallicities to solar values , _ not _ showing a knee .
this implies that the star formation rate in the thin disk was quite low compared to that in the thick disk . +
* 4 . * at super - solar metallicities the trend found at sub - solar metallicities continues linearly for the thin disk stars .
in contrast nissen and edvardsson ( 1992 ) found @xmath2 $ ] to level out at these metallicities .
however , they did not take the nii blend in the [ oi ] line into account , which becomes important at these metallicities , see fig . 1 .
this result has implications for different models of supernova yields , and will be investigated further .
all stars have also been observed with the feros spectrograph and abundances for other elements have been determined ( na , mg , al , si , ca , sc , ti , v , cr , mn , fe , co , ni , zn , y , ba , eu ) . for the @xmath12-elements
we find the same signature from the onset of snia in the thick disk which appears to be absent in the thin disk , see feltzing et al .
( 2002 ) and bensby et al .
( 2003a , in prep ) , in good agreement with the trends we find for oxygen .
a few stars merits , due to their positions in fig . 2 , further comments : two thick disk stars at @xmath5\sim-0.3 $ ] and one thin disk star at @xmath5\sim-0.6 $ ] .
the latter may be due to the fact that the thick disk also contain stars with `` cold '' kinematics .
the first two are a bit harder to understand but their kinematics might have been heated through close encounters or they might have been kicked - out from a double or multiple stellar system . | arxiv |
bronchiectasis is defined as irreversible , abnormal dilatation of one or more bronchi with chronic airway inflammation and results in a chronic cough , sputum production , recurrent chest infection , and airflow obstruction.1,2 according to us data , the estimated prevalence of bronchiectasis is 53 cases per 100,000 adults.3 seitz et al reported that prevalence of bronchiectasis was 1,106 cases per 100,000 people.4 the prevalence increases with age and is higher in females . as it is a chronic disease , bronchiectasis may lead to a decrease in exercise capacity and cause difficulty in performing daily living activities .
ryu et al reported that depression and anxiety are more prevalent in subjects with chronic airway diseases , and this is associated with low quality of life and impaired adherence to therapy.5 similarly , although psychiatric disorders such as anxiety and depression are related to worsened respiratory symptoms , increased health expenditure , and noncompliance with therapy in the patients with chronic pulmonary diseases , it may frequently be overlooked in daily practice.6,7 there are a limited number of studies on the prevalence of depression and anxiety in either pediatric or adult cases with bronchiectasis , which is a significant chronic pulmonary problem.810 in the present prospective study , we aimed to investigate the presence of depression and anxiety in outpatients with non - cystic fibrosis bronchiectasis using the hospital anxiety depression scale .
in addition , we evaluated the relationship between sociodemographic , clinical factors and depression and anxiety in adult patients with bronchiectasis .
a total of 133 patients with stable bronchiectasis who were diagnosed using high - resolution computed tomography ( hrct ) enrolled to the study .
cases with cystic fibrosis , malignancy , interstitial pulmonary disease on hrct and acute exacerbation of bronchiectasis were excluded .
an acute exacerbation was defined as having at least three of the following criteria : worsened dyspnea and coughing , an increase in the amount and purulence of sputum , hemoptysis , fever ( 38c ) , worsening in clinical examination , and the presence of new signs on a chest x - ray .
demographic data , body mass index , marital status , education , occupation , smoking status , and comorbidity status were recorded for all patients .
in addition , clinical characteristics of the patients , medications , the use of nebulizers ( nebulizer is used for inhaled betamimetic and/or inhaled steroid drugs ) and long - term oxygen therapy ( ltot ; long - term oxygen therapy is extended use of oxygen ; oxygen therapy is delivered as a gas from an oxygen source like concentrator ) , number of emergency and hospital admissions and intensive care stays within the last year , and pulmonary function tests were recorded . after clinical and radiological examination ,
hads was developed in 1983 by zigmond and snaith , and validity and reliability were performed.11 hads questionnaire is a test consisting of 14 questions , of which seven are used to assess depression and the remaining seven are used to assess anxiety .
the answers were evaluated in the form of four - point likert - type scale .
while the cutoff value is 7 for depression , it is 10 for anxiety in the turkish version .
validation of the turkish version of the test was done in 1997.12 the study protocol was approved by the local ethics and clinical research committee of the yedikule chest diseases and thoracic surgery training and research hospital .
statistical analyses were carried out using spss statistics for windows , version 20.0 ( ibm corporation , armonk , ny , usa ) .
descriptive data were presented as mean standard deviation , and median ( range ) , when there is not a normal distribution . the univariate analyses to identify variables associated with patient outcome according to the hads scores ( anxiety and depression )
was investigated using chi - square and fisher exact tests . for the multivariate analysis ,
the possible factors identified with univariate analyses were further entered into the logistic regression analysis to determine independent predictor of patient outcome .
lemeshow goodness of fit statistics were used to assess model fit . a 5% type - i error level ( p<0.05 )
a total of 133 patients with bronchiectasis were enrolled in this study . the mean age of patients was 49.514.5 years ( range , 1877 years ) , and 81 ( 60.9% ) of the patients were females .
the mean diagnosed time of the study group was 6.84 years ( range , 1 month30 years ) .
the clinical symptoms of the patients included in this study are summarized in table 1 .
no statistically significant difference was found between the groups with high and low depression and anxiety scores regarding symptoms ( cough , sputum , dyspnea , and hemoptysis ) ( p>0.05 ) .
concerning medical therapies , 111 ( 83.5% ) were receiving bronchodilators , 17 ( 12.8% ) were using nebulizers , and 14 ( 10.5% ) were on ltot .
when comparing medical therapy for bronchiectasis and had scale scores , no statistically significant difference was found between the groups ( p>0.05 ) .
furthermore , no relationship was found between the use of a nebulizer , ltot and depression and anxiety ( p>0.05 ) .
the mean hads score was 10.98.3 ; the mean depression score was 4.84.3 , and the mean anxiety score was 6.14.7 .
the cutoff point for depression and anxiety was taken as 7 and 10 , respectively , and therefore , 28 ( 21.1% ) patients had depression , and 53 ( 39.8% ) had anxiety .
depression score was related to the family situation ( living without a partner ) , previous depression history and admission to the emergency department within the last year .
anxiety score was related to female gender , employment , family situation ( living without a partner ) , previous depression history , and admission to the emergency department within the last year ( table 2 ) .
the first stepwise multivariate model for depression was performed which included the variables : age , gender , family situation , comorbidity , hospitalization , admission to an emergency department within the last year , and history of depression and anxiety .
this model showed that living with a partner ( odds ratio [ or ] 0.17695% , 95% confidence interval [ ci ] : 0.4590.675 , p=0.011 ) and admission to the emergency department in last year ( or 4.236 , 95% ci : 1.27714.0522 , p=0.018 ) were independently related to depression . when the symptoms were added to the model , only hemoptysis ( or 0.255 , 95% ci : 0.6870.948 , p=0.041 ) was a significant predictor of high scores of depression ( table 3 ) .
however , pulmonary function tests did not affect the risk of depression in adults with bronchiectasis .
the multivariate model was performed including age , gender , employment , family situation , comorbidity , admission to the emergency department within the last year , hospitalization within the last year , and history of anxiety and depression for anxiety .
this analysis identified four variables related to increased risk for clinically relevant anxiety : living with a partner ( or 0.075 , 95% ci : 0.0150.358 , p=0.001 ) , education level ( < 8 years ) ( or 7.613 , 95% ci : 1.5143.2570 , p=0.014 ) , admission to emergency department within the last year ( or 3.177 , 95% ci : 1.0419.695 , p=0.04 ) , and history of depression ( or 7.170 , 95% ci : 2.31722.1847 , p=0.001 ) ( table 4 ) . when symptoms and/or pulmonary function tests were added to the analysis , none of the symptoms were independent risk factors for anxiety , with living with a partner , education level ( < 8 years ) , admission to an emergency department within the last year and history of depression remaining significant .
in the present study , we found that depression and anxiety ratios were high in adults with bronchiectasis , similar to that found in previous studies.8,9 clinically significant depression was associated with living with a partner , admission to the emergency department within the last year and hemoptysis .
also , anxiety was significantly associated with living with a partner , education level ( < 8 years ) , previous depression history and admission to the emergency department within the last year . today , depression and anxiety are an important health problem in both developed and developing countries . according to data from the world health organization , the prevalence of depression ranges from 3% to 16.9%.13 despite the availability of studies on the prevalence of depression and anxiety and the related risk factors in chronic respiratory diseases , particularly in copd
, there is a limited number of studies published on the prevalence of depression and anxiety in adult patients with bronchiectasis.5,14,15 a limited number of previous studies in the literature reported a higher prevalence of depression and anxiety in bronchiectasis cases in comparison to general population.8,9 olveria et al reported depression symptoms in 12.68% and anxiety symptoms in 18% of bronchiectasis cases evaluated by the hads.9 girn moreno et al in their article published in 2013 , reported depression in 34% and trait and state anxiety in 55% of non - cystic fibrosis bronchiectasis cases .
they indicated that depressive symptoms were more prevalent in females and that anxiety was associated with the daily amount of sputum and presence of bacterial colonization in the sputum.8 in the present patient population , female gender was associated with anxiety ; however , no relationship was found between the amount of sputum and depression and anxiety . a study on patients with copd , which is also a chronic airway disease , assessed depression , anxiety , pain , and quality of life and reported more severe anxiety and depression and poorer quality of life in the female patient group.16 most of the earlier studies indicate female gender as an independent risk factor for depression and anxiety . in the present study ,
investigating the relationship between respiratory symptoms and depression and anxiety in bronchiectasis cases , we found that only hemoptysis was an independent risk factor for depression , while anxiety was not associated with any of the symptoms .
goldbeck et al found that hemoptysis and recurrent pneumothorax were associated with anxiety , whereas impaired pulmonary function tests and being a lung transplant candidate were associated with depression in 670 patients with cystic fibrosis aged between 12 and 64 years.17 hemoptysis is a common and distressing symptom in bronchiectasis cases , particularly during exacerbations .
for this reason , recurrent hemoptysis , in particular , may promote depressive mood despite the fact that we failed to determine any relationship with anxiety .
olveira et al investigated depression and anxiety symptoms and health - related quality of life in 93 bronchiectasis cases.6 in this study , age was found to be associated with both depression and anxiety .
likewise , another study reported that the prevalence of anxiety and depression increases but the quality of life decreases with age.9 this may result from the fact that the disease becomes chronic and loss of respiratory functions and comorbidities accompany the disease with aging . in the present study , however , we determined no relationship between age and depression and anxiety .
this may have resulted from a limited number of cases . in the recent study ,
olveira et al evaluated the relationship between depression / anxiety symptoms and quality of life in bronchiectasis patients.6 olveria et al determined depression symptoms in 20% and anxiety symptoms in 38% of bronchiectasis cases and found that the amount of sputum was associated with depression , whereas exacerbation was an association with anxiety . in another study by olveria et al , the number of exacerbations in the previous year was found to be higher in bronchiectasis cases with anxiety.6 in our study , the prevalence of anxiety and depression was as high as in the study by olveria et al.6 however , we questioned the number of emergency room admissions and hospital stays within the last year , but we did not ask history of exacerbations . while hospital stay was not associated with depression or anxiety , emergency room admissions within the year was determined to be an independent risk factor for anxiety and depression .
a study investigating the depression - related factors in copd , chronic airway diseases like bronchiectasis reported that emergency room admissions and hospital stay were more frequent in cases with depression but exacerbations were not significantly high.15 in the present study , patients were inquired for emergency room admissions for respiratory problems within the last year , but whether these were exact exacerbations of bronchiectasis was not investigated .
there is strong evidence that a presence of anxiety and depression in cases with chronic respiratory diseases such as bronchiectasis impairs adherence to therapy and reduces patients quality of life.9,16,18 in the present study , however , adherence to therapy or quality of life was not assessed , although we inquired the patients about their medication use .
considering particularly the fact that adherence to therapy was associated with the frequency of exacerbations and survival , identification and treatment of anxiety and depression gain more importance .
some studies have investigated the relationship between pulmonary function tests ( fev1 , fvc , and fev1/fvc ratio ) and depression and anxiety . particularly in copd ,
fev1 and fvc are considered to be the risk factors for depression.5,15 girn moreno et al conducted a study in cases with non - cystic fibrosis bronchiectasis and found no significant relationship between fev1 and depression or anxiety.8 like girn moreno et al,8 in olveira et al s study there was no relationship between fev1 and depression or anxiety in patients with bronchiectasis.9 in the study by oleary et al , no relationship was found between fev1 and hads scores.19 likewise , the present study found no relationship between fev1 , fvc , fev1/fvc and depression and anxiety .
this may be related to the limited number of cases and/or differences in the extent of disease on hrct .
living with a partner has been found as an independent risk factor for both depression and anxiety . moreover
olveira et al reported a similar result about education level.6 it is difficult to explain why living with a partner is associated with depression and anxiety .
furthermore , patients with high depression and anxiety scores were not referred to psychiatric evaluation .
in conclusion , patients with non - cystic fibrosis bronchiectasis are at increased risk for anxiety and depression . admission to an emergency department within the last year and living with a partner
also , hemoptysis was correlated with depression , and education level , previous depression history was associated to anxiety .
untreated and undetected depressive and anxiety symptoms may increase physical disability , morbidity , and health care utilization .
future research is needed to address the impact , early detection , and management of anxiety and depression from bronchiectasis . | pubmed |
The United States Census of 1960, conducted by the Census Bureau, determined the resident population of the United States to be 179,323,175, an increase of 18.5 percent over the 151,325,798 persons enumerated during the 1950 Census. This was the first census in which all states recorded a population of over 200,000.
Data availability
Microdata from the 1960 census are freely available through the Integrated Public Use Microdata Series. Aggregate data for small areas, together with electronic boundary files, can be downloaded from the National Historical Geographic Information System. Personally identifiable information will be available in 2032.
State rankings
City rankings
Notes
External links
Historical US Census data
1961 U.S Census Report Contains 1960 Census results
United States Census, 1960
Category:United States Census
United States | wikipedia |
we investigated the in vitro susceptibility of various cell cultures and embryonated eggs to usutu virus infection .
human ( hela ) , green monkey ( vero ) , equine ( ed ) , bovine ( mdbk ) , porcine ( pk-15 ) , rabbit ( rk-13 ) , canine ( mdck , dk ) , feline ( cr ) , hamster ( bhk-21 , bf ) , rat ( c6 ) , and turtle ( th1 ) permanent cell lines , as well as primary horse kidney ( eqk ) , chicken embryo fibroblast ( cef ) , and goose embryo fibroblast ( gef ) cell cultures were tested .
cells were propagated in earle 's minimal essential medium ( mem ) ( gibco invitrogen , paisley , uk ) containing l - glutamine , antimicrobial drugs , and 10% fetal calf serum ( fcs ) .
the cells were regularly subcultured by employing standard techniques . to 1-day - old confluent monolayers of the permanent cell lines and primary cell cultures , grown on the surface of chamber slides , the austrian usutu virus strain vienna 2001-blackbird ( genbank accession no .
the virus was originally isolated in vero cells in 2001 from the brain homogenate of a blackbird found dead in the area surrounding vienna .
the second virus passage was used for the experiments ; 50% tissue culture infective dose ( tcid50 ) was determined , and aliquots of the virus were stored frozen at 80c until used .
the virus was added to the cells , which were then incubated at 37c for 1 h. thereafter , the inoculum was removed , the cell cultures were washed once with phosphate - buffered saline ( pbs ) , and mem containing 2% fcs , l - glutamine , and antimicrobial drugs were added .
for all cell types , controls were cultivated simultaneously and treated in the same way as the infected cultures with the exception that mem was used for inoculation .
all cell cultures were incubated at 37c for 3 to 5 days ; then the medium was removed and the monolayers were fixed with chilled ( 20c ) acetone .
the cells were stained with hematoxylin - eosin ( he ) and examined microscopically . in parallel ,
immunohistochemical ( ihc ) testing was carried out on the cell cultures by using the avidin - biotin complex technique , with a polyclonal antiserum raised in mice against wnv antigens , for which cross - reactivity with usutu virus had been demonstrated previously ( 1 ) .
the number of antigen - positive cells was evaluated microscopically and scored ( see table ) . * ihc , immunohistochemical ; scoring criteria : ( + ) , 1%5% positive cells ; + , 6%25% positive cells ; + + , 26%50% positive cells .
embryonated chicken eggs ( strain lsl white , which was derived from the strain white leghorn ) , originating from a specified pathogen free ( spf ) herd ( valo eggs , lohmann , cuxhaven , germany ) , were injected into the allantoic sac with 6 x 10 tcid50 of usutu virus at the age of 10 days .
the eggs were incubated together with mock - infected controls at 37.5c for further 4 days and were checked daily by transillumination . on day
4 postinfection the eggs were opened , and the embryos were fixed in 4% buffered formaldehyde solution .
histologic sections were made from paraffin - embedded organs of the embryos , and the slides were analyzed by light microscopy after he and ihc staining , respectively , as described above .
three to 4 days after inoculation , pronounced cpes were observed in usutu virus infected vero and pk-15 cell cultures as well as in gef cells .
the first foci of cell rounding and subsequent shrinkage of the cells were observed on day 2 or day 3 postinfection , when groups of 4 to 8 cells , but also single cells , showed rounding and degeneration ; within 1 day the affected cells lost their adherence to the bottom of the flask and floated in the medium . within
typical usutu virus cpe is shown in he - stained vero cells in figure 1 .
the mock - infected vero , pk-15 , and gef control cell cultures did not show any cpe .
the other investigated cell types inoculated with usutu virus did not develop visible cpe within a period of 5 days , and they were also negative by microscopy after he staining .
however , by ihc with cross - reactive wnv - antiserum , focal virus multiplication was detected in all cell cultures , independent of animal species and tissue type , except chicken embryo fibroblast cells ( figure 2 ) .
the percentage of usutu virus antigen positive cells varied from 1% ( dk ) to 50% ( gef ) ( table ) . in the case of hela cells , different clones adapted to the propagation of human rhinoviruses ( hela rhino ) and herpes simplex viruses ( hela hsv ) , respectively , were also tested , but they gave the same results as the commonly used ( atcc ) hela cells by he and ihc staining .
cytopathic effect ( cpe ) of vero cells caused by usutu virus infection , 4 days postinfection ( hematoxylin - eosin staining ) .
immunohistochemical ( ihc ) tests were performed by using a polyclonal antibody to west nile virus , which cross - reacts with usutu virus .
a ) vero control ; b ) vero infected ; c ) cr [ define ] ( feline ) control ; d ) cr infected ; e ) goose embryo fibroblast ( gef ) [ define ] control ; f ) gef infected ; a , b ) bar = 50 m ; c f ) bar = 100 m .
the usutu virus infected chicken embryos did not show any lesions when investigated by gross and histopathologic examination after 4 days of incubation and were negative by ihc as well . to rule out
the slight possibility that the usutu virus strain used for inoculation underwent a change in cell tropism during the 2 passages in vero cells , cef , vero , pk-15 , mdck , and dk cells , as well as embryonated chicken eggs , were reinfected with the original usutu virus isolate ( before passaging ) ; the results were identical to the results obtained with usutu virus passaged twice before use .
the appearance of cpe in flavivirus - infected cell cultures depends on the virus and host cell type , as well as on moi levels and incubation time employed ( 8) . in many cases , the presence and multiplication of flaviviruses do not inhibit significantly the host cell macromolecular synthesis , resulting in noncytopathic persistent infections ( 9,10 ) .
pathogenesis and virulence of flaviviruses are influenced in vivo by several virus- and host - dependent factors , including the role of defective interfering particles , viral receptors , neurovirulence , immune - response ( e.g. , antibody - dependent enhancement ) , and host resistance genes ( 8) .
although some of these processes are not yet fully understood , the basic requisite of any pathogenic effect is the host susceptibility to the virus infection .
this study demonstrates that usutu virus can infect cell cultures of various tissue types derived from a wide variety of animal species , including cell lines of human origin . since only vero ,
pk-15 , and gef cells develop cpe after usutu virus infection , these cell lines and cell culture are the most appropriate ones for diagnostic purposes ( e.g. , virus isolation , plaque reduction neutralization test ) . as demonstrated by ihc , considerable differences have been found in the susceptibility of the various cell lines and cultures to usutu virus infection and in the extent of spread of the infection ; even cell lines derived from the same animal species and organ varied significantly in their susceptibility to usutu virus infection , e.g. , mdck cells strongly support usutu virus multiplication , while dk cells are far less susceptible . both of these cell lines , however , have been derived from dog kidneys . on the other hand , the differences between the 2 canine kidney cell lines might also be the consequence of different random mutations ( e.g. , in genes of the interferon or other innate defense systems ) that allowed the cells to immortalize .
since in austria , usutu virus infects wild birds and causes high death rates , especially in blackbirds , one would think that birds are most susceptible hosts for the virus .
therefore , the finding that both the chicken embryo fibroblast monolayers and the chicken embryos are apparently resistant to usutu virus infection was unexpected .
usutu virus , however , is not the only flavivirus with such contradiction in host spectrum .
ilheus virus , a south american mosquitoborne flavivirus belonging to the ntaya virus group ( 7 ) , also naturally affects wild birds and produces plaques in primary rhesus kidney cells and various established cell lines ( vero , ps , bhk-21 , and llc - mk2 ) , but not in avian cells ( 8) .
preliminary results of our chicken experiments with usutu virus also support that idea that the domestic chicken is resistant to the infection , even when young .
further investigations involving different bird and mammal species will be necessary to show the most important host species , natural reservoirs , and vectors of usutu virus and to estimate its epidemiologic impact and possible threat to domesticated animals and to the human population . | pubmed |
Diffeomorphism invariance and energy momentum conservation
I was reading Sean Carroll book "Space-Time and geometry", in the appendix B he derives the energy momentum conservation from the diffeomorphism invariance of the action, however I don't understand a step in the derivation.
I will put some context before asking the question.
He starts with the action for matter fields $S\_{m}$ (in the context of general relativity), and takes de variation of the action
$$ \delta S\_{m}=\int d^{4}x \frac{\delta S\_{m}}{ \delta g\_{ab}}\delta g\_{ab}+\int d^{4}x \frac{\delta S\_{m}}{ \delta \psi} \psi$$
The matter field equations tell us that $\delta S\_{m}/\delta \psi=0$, then
$$\delta S\_{m}=\int d^{4}x \frac{\delta S\_{m}}{ \delta g\_{ab}}\delta g\_{ab}= \int d^{4}x \sqrt{-g} T^{\mu\nu}\nabla\_{\mu}\xi\_{\nu}$$
Where I have used the definition of Lie derivative (I use the letter $\zeta$ to denote the lie derivative) of the metric
$$ \delta\_{\xi}g\_{\mu\nu}=\zeta\_{\xi}g\_{\mu\nu}=2\nabla\_{(\mu}\xi\_{\nu)}$$
And the definition of energy momentum tensor
$$T\_{ab}=\frac{-2}{\sqrt{-g}}\frac{\delta S\_{m}}{\delta g\_{ab}}$$
Next, in the equation (B.25) Sean Carroll makes
$$\delta S\_{m}=\int d^{4}x \sqrt{-g} T^{\mu\nu}\nabla\_{\mu}\xi\_{\nu}\\
=-\int d^{4}x \sqrt{-g} \xi\_{\nu}\nabla\_{\mu} T^{\mu\nu}$$
I don't understand how he can change the covariant derivative, it looks like some kind of integration by parts, but I don't see what happened to the boundary term.
Boundary terms are always assumed zero in these considerations. After all, non-zero would mean that some energy-momentum is incoming/outgoing. Inside can't be conserved if that's the case.
You can of course write a more comprehensive conservation law by including how much comes in/out (integration over the boundary), but this is not the point here.
| stackexchange/physics |
Mass Effect 1. Chapter 1
_I thought it might be fun to get some stories of Kaidan out that don't involve Shepard or romance. So, if this teaser interests you, send a review and I will write some longer, more interesting stories about Kaidan before he was assigned to the Normandy. I currently accept anonymous reviews._
* * *
Sixteen-year-old Samantha Keller stood at the door to Kaidan Alenko's room. Or, at least, what had become his room after the Alliance had ruled Vyrnnus' death a "training accident." Kaidan was two years older than her, and they didn't run in the same circles, but Sam had heard that Kaidan was barely eating and not really talking. She knew his friends were avoiding him. Now that they had seen the death biotics could cause with their own eyes, they were not dealing with it well. He needed to talk to someone, though. Sam decided she just wouldn't take no for an answer.
Sam hit the door chime. Nothing happened.
"You can let me in or I can hack the door, it's up to you," Sam said. "But I'm not going away."
There was a long sigh over the intercom. "Sam, do you even know how to hack a door?"
"It will probably take me a while," Sam admitted, "and I'll probably make a mess of it. They might have to cut it open if I mess it up too bad, right? Easier if you just open the damn door."
"I have a migraine."
"The hell you do," Sam retorted. "I'm getting my omni-tool out. Last chance."
There was no response. Sam actually wasn't the best at bypassing door locks, but one of her trainers had insisted they all learn the basics in case they were ever captured or something. It took her a bit, but she eventually got the door open. The room was dimly lit, and Kaidan was sitting on his bunk, knees to his chest, staring blankly at the wall. Sam pulled over a desk chair and sat next to his bed.
"Congratulations on getting the door open," Kaidan said. "Now please, just leave me alone."
"You've had enough alone time, Kaidan," Sam said. "I'm not going anywhere. I know we aren't exactly the best of friends, but I care about what happens to you, and you are having a major freakout. You need to talk."
"No, I don't. He's dead, and I killed him, and I don't want to talk about it. Or anything else."
Sam didn't say anything, but she didn't make any move to get up, either. After about five minutes of silence, Kaidan spoke up.
"The psychologist already tried this trick," he said wearily. "It didn't work."
Sam didn't say anything. Another ten minutes went by.
"All of my friends are avoiding me," he said finally. "Why are you here?"
"You want an honest answer? Because I'm grateful."
"That's pretty bloodthirsty," Kaidan said bitterly.
"I don't mean I'm grateful that Vyrnnus died," Sam explained. "I'm grateful you stood up to them. I'm grateful the program will be shut down."
"Well, my friends aren't grateful. They're just freaked out. And Rahna… Rahna is afraid of me now," Kaidan whispered. "She's as afraid of me as she was of _him_."
Sam bit back on her initial response. Rahna was afraid of everything, except letting other people take punches for her. Kaidan had it bad for her, though, and he was hurting.
"I'm sorry to hear that, Kaidan," Sam sighed. "I hope she gets past it. But even if she doesn't, the fact that you stood up to him will make all of our lives better. Including hers, whether she can see that or not."
"There must have been another way for me to stand up to them."
"Yeah, Kaidan. I tried that." Sam looked over at Kaidan. "I asked a couple of the doctors to file a report with child services. It got me a lot of alone time with Marshall Nash."
For the first time, Kaidan looked her in the eye.
"I didn't know that," he said softly. Marshall Nash was the primary hardware researcher for the BAaT program. He handled the kids branded as troublemakers personally, and all of them came out of his room quieter. Rumors of what happened when kids went off alone with him were whispered, and even the mildest ones were pretty bad.
"It wasn't pleasant. I didn't want anyone to know. A couple of my friends suspected, but…I didn't want to talk about it," Sam said. "I was afraid they wouldn't understand, or would think I was lying, or that they would crack if they knew about it."
"You don't have anything to be ashamed of," Kaidan said. "If he hurt you, it wasn't your fault."
"Just like it wasn't your fault that Vyrnnus lost his mind and tried to kill you."
Kaidan looked away.
"I'm not asking you to tell me your big dark secret just because I told you one of mine," Sam sighed. "I'll settle for some normal conversation, and maybe you eating a little bit of food before they put an IV in you. Please."
There was a long silence before Kaidan looked back at her.
"Yeah, okay. I guess I could tell you how to bypass a door properly."
Sam stopped by every day before he left, making sure Kaidan had company. Eventually, she didn't have to talk him into eating or leaving his room anymore. When he was packing his bags to leave the station, he asked her why she'd done it. She just shrugged and said it seemed like he needed a friend.
Kaidan told her then that if she ever needed a friend, he would be there. They stayed in touch. They didn't message often, but every time they did the friendship picked right up where it left off. In a way, they were like brother and sister, bound together by shared experience. Some things, you couldn't understand unless you'd been there.
2. Chapter 2
Kaidan stared out the window of the transport. Yet another broken-down shuttle to yet another lousy mining job. Yet another stop on his never-ending quest to find a job that sucked so much they couldn't afford to discriminate against him.
He sighed and leaned his head back against the headrest, trying to ignore the strange smells assaulting him from all corners of the cabin.
_I knew you had it in you, boy. What took you so long?_
Kaidan suppressed a groan as Vyrnnus' voice sounded in his head, as it had done most nights in the year since Kaidan had killed his instructor. Only then, with the turian's dying breath stuttering out in blue bubbles of turian blood, had Kaidan understood. All the beatings, all the harassment, every injustice was meant to provoke them, make them stronger, and make them strike out with the skills they had learned. What Vyrrnus had done was still wrong, but it wasn't until those words had come out that Kaidan understood Vyrnnus had meant well in his own twisted, sadistic way.
It would have been easier if he had never realized that.
Kaidan ran his hand over his tired eyes, realizing that sleep would elude him once again. Even if he _could_ sleep, he didn't want the other passengers to see him in the middle of a nightmare. At least he'd been able to avoid a migraine so far. This transport was headed for a small mining facility on some asteroid in the Traverse, and it was crowded with a variety of people, human and non-human alike. Kaidan had nothing against the hanar, but bioluminescent speech was like a special kind of torture in the middle of a migraine, even without the strangely loud translation into spoken language.
Giving up on sleep, Kaidan pulled his datapad out of his duffel and linked it to his omni-tool. He may as well check on the mail he'd been putting off reading.
The letter from his mother was expected, and unwelcome. It was yet another reproachful reminder that he hadn't spoken to his father in a while. Kaidan was well aware that he hadn't spoken to his father, and he didn't plan on changing that in the foreseeable future. There were several messages from people trying to sell him things. One promised an "all natural herbal strength enhancer, discovered from the ancient secrets of the protheans" that was supposed to be as effective as gene therapy for a fraction of the price. A fraction of a lot was still a lot, especially for something that almost certainly wouldn't work and would probably land a person in the hospital. He deleted that, along with its companion messages offering larger genitalia, proven ways to get rich quickly, and LIVE chat with an asari dancer.
No, he would _not_ keep that one. He had few credits as it was.
The last message was from Sam. She had sent him several messages in the last year, and offered more than once to send him money. As welcome as it would have been, Kaidan refused to take her up on it. Sam was barely sixteen when she left Jump Zero, and had become an emancipated minor shortly after that. Kaidan had no doubt money was at least as hard for Sam to come by as it was for him. He'd manage, as he had frequently told her. His brow furrowed in irritation. If this was another offer…
But it wasn't. Sam had just turned seventeen, which made her old enough to attend the Arcturus Military Academy. The message was to tell him that she had been accepted to the academy and was planning to be a marine. Despite the ambivalence Kaidan felt toward the Alliance in general and the military in particular, he couldn't help but smile at the thought of one-point-five-meter-tall Samantha Keller as an Alliance Marine. She'd probably be really good at it, though; she was sure as hell pushy enough.
As his eyes scanned to the bottom of the message, he saw that Sam had included some information on the most recent settlement between Conatix and the former students of the BAaT training program. The money they were required to cough up was minimal, especially considering the after-effects of what they had done to the kids. One thing that caught his eye, however, was their obligation to pay for higher education for the students who qualified. It specifically included correspondence classes via extranet.
"I know you don't want anything from Conatix, Kaidan," Sam said at the bottom of her message, "but they owe this and more to all of us. Take their damn money, because if you don't the bastards will just keep it."
That was interesting. Maybe… no, he didn't care. They could keep their damn money. Kaidan didn't need or want help from anyone. He'd make it on his own.
And yet, here he was, on another filthy transport headed to another filthy, hard-labor job. He hadn't wanted to attend school, he had been too afraid of the reception he'd get. On Earth, biotics had to register, and most universities kept a roster of their biotic students. Even in schools where those lists were kept quiet, they were routinely hacked. Biotics had been harassed and even killed for being on those lists. Correspondence classes would eliminate the need to register as a biotic with the school. Kaidan had looked into it once, but most student assistance wouldn't cover long-distance learning.
Maybe it wouldn't hurt to fill out the form, at least. Sam was right; if he didn't claim it, Conatix or its shareholders would just keep it. Besides, if he could get some sort of education, maybe he wouldn't have to spend the rest of his life in places like this.
3. Chapter 3
"I think she likes you, Alenko."
Kaidan looked up from his datapad at the table across from his in the company cafeteria. Jen Corazon was there, talking with several other women. Kaidan sighed. Jen was one of the office workers on the Twerg mining colony. She had bleach blonde hair, painted fingernails, and was very… friendly. Her makeup sparkled almost as much as her personality. She _was_ pretty, though, so Kaidan didn't manage to look away quite fast enough. Jen caught his eye and waved her fingers at him, blowing him a kiss.
"Not interested." Kaidan looked back down at his datapad, blushing furiously, while the girls at the table laughed.
"Oh, come on, Alenko," Ted pushed. "Nobody's saying you need to marry the girl. _She's_ certainly not going to say it. This is a lonely place, is all. No reason why consenting adults can't have a little fun. And word has it Jen is a _lot_ of fun."
"I don't know that I want that much experience," Kaidan shrugged. "Especially since most of her experience comes from the other guys here. In the six months I've been here I think she's had 'a little fun' with twelve guys."
"But she _likes_ you."
"She'll change her mind," Kaidan replied.
"Man, you are such a downer," Ted muttered. "All you do is… whatever it is you're doing now."
"Classes," Kaidan replied. "I'm working on a degree in applied technology."
"See, now that's why she likes you," Ted smiled. "You have _plans._ Unlike the rest of us. Why are you even here, man? You're smart and polite and way too good for a place like this."
"I'm here for the same reason everyone else is," Kaidan said, not looking up from his datapad.
"Everyone else is here because Coorta Mining Company is too cheap for a damn background check."
"I know."
"So what the hell did you do that makes you want to avoid a background check?" Ted pushed. "Was it drugs?"
"No."
"Well, if it was, I wouldn't care," Ted shrugged. "That's why I'm here. Matter of fact, I bet I could get you—"
"No drugs, Ted," Kaidan interrupted. "There are enough accidents here as it is, and I have to stay with it enough to watch my back, because we all know the company isn't doing it."
"So you don't do drugs, I've never seen you drink, you don't chase tail, and you don't seem like the fighting type, so what could you have done?"
"Ted, I really don't want to talk about it," Kaidan snapped, pinching the bridge of his nose. Ted meant well, he really did. In fact, if he wasn't on whatever drug he was on right now he'd probably have dropped it already.
"I know! Loitering." Ted said it with triumph. "You got caught organizing the socks into alphabetical order by color in one of those snooty clothing places, and they sent you to court."
"You caught me." Kaidan's voice was flat, and he didn't look up from his datapad.
"Okay, look, kid, seriously now," Ted said, "most of the guys are pretty sure you think you're too good for the rest of us. That could start to cause you some problems, you know?"
"What do you mean?" Kaidan asked, finally looking up.
"I mean there's a bunch of mean people out here who are starting to get a little stir-crazy after several months in this tiny little base," Ted replied. "There are a few who are going to start looking to make trouble, and when they do you're going to be one of the first they look at."
"And what makes you think that will change if I try to fit in?" Kaidan asked. "I don't know if you noticed, Ted, but I don't really fit in well."
"You should at least try," Ted told him, "even if it doesn't work out so well. Let them know you're not stuck up. Or at least that you aren't afraid of them."
"Because then the bullies will leave me alone. Right."
"Because then you won't have to deal with them by yourself," Ted shot back. "This place is a shithole, Kaidan, and you need friends. More friends than one old druggie, anyway."
"I don't think of you as an old druggie, Ted," Kaidan said.
"Thanks, kid, but it isn't about what you think," Ted sighed. "Look, whatever you're trying to run from, you're not going to get very far away from it if it isn't actually behind you. Take it from me. I've been there."
_No, you haven't,_ Kaidan thought. _Nobody has, that's the problem._ But Ted was trying to help, so Kaidan didn't voice his thought. Instead he shrugged.
"At least remember what I said, kid." Ted stood up. "It will make sense eventually, if you let it." With that, Ted walked away.
Kaidan went back to his classwork. The harder he worked on it, the faster it would be done, and the sooner he could try to get out of places like this one.
A few minutes later, he was deep in concentration on a particularly difficult equation when a shadow fell over the table. Kaidan smelled her perfume before even looking up. Jen Corazon wore a very noticeable fragrance, and he felt his eyes pounding a bit in response to it. Not her fault, really, but it was frustrating just the same. Knowing he couldn't really get out of it now, Kaidan looked up.
"Hi, handsome," Jen said, smiling down at him. "Mind if I have a seat?"
"Um, no?" Kaidan stammered. She smiled sweetly and settled into the chair.
"Thanks," she said, flipping her hair over her shoulder. The movement drew attention to her low collar and the assets underneath. Kaidan tried not to look, but only succeeded in yanking his eyes away quickly after they had moved of their own volition to her revealing neckline. He swallowed hard as he blushed. Jen simply smiled, showing she had noticed, which made Kaidan blush even harder.
"What are you doing?" she asked, pointing at the datapad in such a way that her hand was very close to his.
"Classes," Kaidan replied. "Trying to do better than, well, I didn't mean that the way it came out."
"There's no shame in trying to do better than here, Kaidan," Jen said. "Don't worry about it."
"Okay."
"Do I make you nervous, Kaidan?" she laughed.
"Pretty girls always make men nervous," Kaidan said without thinking.
"You think I'm pretty?"
"Yes, and you _know_ you're pretty," Kaidan replied. He felt his brain finally take over from… well, from whatever had been doing the thinking, or lack thereof, until now.
"Well, I do put a lot of work into it."
"It pays off. Look, Jen," Kaidan coughed. "I think you're very attractive, but I'm not, I mean, you're just… more than a guy like me can handle. Maybe."
"Really?" she said, her voice taking on a hard edge.
"I didn't mean that to be insulting," Kaidan clarified. "Really, I didn't, it's just that I'm not used to… a woman like you being interested in a guy like me." He looked up at her with what he hoped was sincerity. He didn't realize that he also looked a bit terrified. Jen looked into his eyes a moment, then leaned back slightly.
"Oh my God," she said softly. "You _haven't _yet, have you?"
"I don't see how that's anybody's business but mine," Kaidan replied, still blushing.
"It isn't," she agreed, "but it explains a few things. I just thought a guy that looked like you would have a bit more experience by now. You must have had chances."
"Not that many, really," Kaidan muttered.
"Seriously?" she laughed.
"I was kind of sheltered growing up," he said.
"What, were you in some kind of juvenile detention?"
"It felt like it, but no." Kaidan sighed. "Look, um, Jen. I don't really want to talk about my screwed up childhood, if that's okay with you."
"Attractive, polite, and doesn't want to go on about how the galaxy has screwed him over," she said to herself. "Why, oh why, couldn't I have met you after someone had broken you in?"
Kaidan just raised an eyebrow to that. It was a little offensive, really, but the sparkle in her eyes and the plunging neckline took a lot of the sting out of it.
"Sorry," she said. "That wasn't very sensitive of me. I'm not used to having to worry about it with this bunch. Look, I'll make you a deal. I'll stop coming on so strong, and I won't push anything, but I want you to come to a party with me. A bunch of us are getting together after shift end tomorrow, and you seriously need to get out more."
"I don't know…"
"Kaidan." Her voice was serious for the first time since she'd sat down. He looked at her. "This place will eat you alive if you stay holed up like this. And it seems like you're actually a nice guy, so it might be a little hard for you to handle. You might get hurt."
Actually, it was far more likely that someone else would get hurt if Kaidan was backed into a corner. As far as he was concerned, that was much worse.
"Okay," he said. "I'll go to the party."
Jen smiled, and this time it was much more natural. As pretty as she was, when the predatory look fell off her face she was downright beautiful.
"You should smile like that more often," Kaidan said before he could stop himself.
"Like what?"
"Like you mean it."
"You don't have any idea that you're saying all the right things, do you?"
Kaidan blushed.
"Tomorrow, Kaidan. Meet me at my apartment, it's in the directory. Seven in the evening. Don't be late." With that, she sauntered back over to her table. It took tremendous effort, but Kaidan somehow managed not to watch her as she swished away from him.
He tried to go back to his work, but he found it was impossible to concentrate with the scent of Jen's perfume hanging in the air. What had he gotten himself into?
4. Chapter 4
Jen hadn't needed to warn Kaidan not to be late. He hadn't been less than fifteen minutes early for anything since Brain Camp. He did make sure he didn't show up at her door quite that early, though. He knew very little about women, but he knew enough not to pressure a woman into being ready before she wanted to be. Still, he found that he just couldn't stand outside until it was exactly seven, so he knocked on her door at five 'til.
If she'd been pretty in the cafeteria, Jen was a vision now. She was still a little too polished for Kaidan to really feel comfortable, but beautiful nonetheless. Kaidan felt horribly under-dressed next to her, wearing casual pants and the only sweater that he owned that didn't have holes in it, but the way Jen looked him over suggested she wasn't disappointed.
For his part, Kaidan was starting to get irritated with all the blushing she was causing. He'd had years of biofeedback training. He could control the eezo nodules in his nervous system with a precision most humans could never attain. Why couldn't he stop the blood from rushing to his face when he was around Jen? It was something he was going to have to work on. It wouldn't do to have his emotions so easily read, especially around a group of hard frontier miners, most of whom had a criminal record of some sort.
"Are you ready?" he asked. "I can wait outside."
"No, I'm ready, let's go," Jen smiled.
The party had been set up in one of the empty docking areas in an abandoned area of the station. Kaidan grimaced when he felt the music through the floor outside the doors.
"Don't like the music?" Jen asked.
"Sometimes I get migraines," Kaidan replied. "It's okay, though. It doesn't always happen."
"You let me know if this gets to be too much for you," Jen told him. Kaidan nodded. When they got inside, Kaidan realized that a large portion of the station was already there. He was also relieved to see that the lights were steady instead of flashing. Flashing lights would have been a much bigger problem than loud music.
There was alcohol, of course, and a low haze of some sort of drug being smoked. Kaidan was surprised when Ted Harris came up to him.
"Well, look who made it," Ted smiled, slapping Kaidan on the back. "We'll get you a beer."
Kaidan almost refused, but he thought about what Ted had told him about fitting in. One beer probably wouldn't hurt anything, especially if he was careful not to drink it too fast.
"Okay," Kaidan agreed. "Jen, you want something?"
"I'll come with you," she said. "I like to get my own drinks." Kaidan wasn't sure if some guys would be offended by that, but he figured it was probably smart of her. He smiled encouragingly and offered his arm to her, and they followed Ted to the bar.
Ted was making it his mission in life to introduce Kaidan to as many people as possible. Kaidan was polite, friendly even, but he didn't let his guard down. Some of the people were nice enough, but others had that set to their shoulders and that look on their face that reminded him of the worst people at Brain Camp. As he smiled and shook hands with people, he kept a mental list of those he thought he needed to keep an eye on. Finally, Jen pulled him out to the dance floor.
"I don't really dance," Kaidan objected.
"Everyone dances, Kaidan," she said, pulling on his arm, "it's just that not everyone dances well. We're just here to have fun, so who cares if you're any good?"
"I don't even know what to do!"
"Just follow my lead."
Jen proved a remarkable teacher. Kaidan may not have been a good dancer by the time she was done showing him the moves, but he was at least a little more confident that he wasn't making a _complete_ fool out of himself. To his surprise, he was also enjoying himself. Eventually he forgot to be tense and to watch all the people and all of the exits and just danced with Jen.
Which, of course, is when the trouble started.
In the middle of the dance floor, one of the other miners walked up to them. He was a very tall, well-muscled man, and obviously drunk. From the look on Jen's face, she wasn't happy to see him.
"Hey, Jennie-girl," the man said. Johannes, Kaidan remembered. He was on the night crew, and was trouble even on the job. "We never finished our _dance_ the other night," Johannes said.
"I never agreed to that particular dance, Johannes," Jen said. Her voice was cool and her expression hard, but Kaidan saw the slight clenching of her hands as the man drew closer.
"Don't tell me you didn't want to," Johannes said, and he reached out to grab her by the arm. Kaidan was faster, grabbing the man's arm in a strong grip and squeezing on the muscle.
"She just told you that she didn't want to," Kaidan said firmly. "You need to respect that and back off. Now." Kaidan put himself between Jen and Johannes and let go of the man's arm. There was no trace of the shy technical geek now. He could see Jen looking at him in surprise out of the corner of his eye, but he didn't want to draw his attention away from Johannes to give her a reassuring glance. This had to be handled carefully or it would get out of hand, and he couldn't afford to miss anything. Reminding himself to stay calm, and forcing himself not to fall back on his biotic abilities to defend himself, Kaidan waited.
He saw the punch coming, probably before Johannes even knew he was going to throw it. Rather than duck, or re-direct the blow, Kaidan simply turned into it, allowing Johannes' fist to connect just enough to know that the blow landed. He tasted blood from where his lip had been shoved into his teeth, but he knew from long experience that the damage wasn't very bad. He turned to look at Johannes, who seemed shocked that his prey wasn't already on the ground.
"You sure you wanna do this?" Kaidan asked. "You leave now, you just walk away. You keep going, this gets a lot more serious." Johannes seemed to consider that for a moment. Kaidan was pretty sure the man would refuse to back down. It was an issue of saving face now. His reason for taking that first hit had more to do with the crowd. One-on-one, Johannes had no idea who he was dealing with. If the crowd turned against Kaidan, though, he wouldn't have a chance.
Johannes glanced around at the circle that had formed around them, which Kaidan was happy to see was inching away from the two men. He saw Ted Harris come up and pull Jen out of the way. Johannes looked down at him.
"You sure you want to mess with me?" the man asked Kaidan. "I've killed men before, you know."
"What makes you think I haven't?"
That caused Johannes to pause for a moment, but then he laughed and threw his next punch.
Johannes was powerful, but he was drunk and probably not used to fighting people who had any real combat training. Kaidan may not have been a marine, but Brain Camp taught him how to defend himself, and Vyrnnus had tested it. Johannes went for the big, heavy punches, which Kaidan could see coming almost immediately. He dodged one hit, then another, then turned into a third, soaking the damage so he could reach vital pressure points. With every hit Kaidan landed, Johannes grew more enraged, and the more enraged Johannes got the more obvious his next punch was. It was only a couple of minutes before Johannes was on the ground. Kaidan was hurt, but not badly. Certainly not as badly as everyone was sure he would be when the fight started.
With a grimace, Kaidan wiped the blood off his face and turned to Jen. He was pretty sure this wasn't the way to show a girl a good time. Much as he expected, Jen was staring at him, wide-eyed. Kaidan refused to think of Rahna, refused to let his emotions show on his face. Whether coming to the party had been a bad idea was something he could agonize over later. Right now, it was time to go.
"Jen," Kaidan said, as calmly as he could. "I think I'm ready to leave. Would you like for me to walk you back?" He tried to ignore the wide-eyed stare Ted Harris was giving him. Apparently a lot of people had underestimated Kaidan.
Jen seemed to shake off her shock and stepped forward.
"Yes, I'd like that," she said, her voice as even as Kaidan's. "Thank you." They walked out of the cargo area. The other party-goers just stared as they walked away.
Kaidan waited until they were halfway down the hall before stopping.
"Jen, I'm sorry," he said. "I didn't want to fight him. I know I probably scared you—"
"_Yes_ you scared me, you idiot!" Jen said angrily, looking up at Kaidan with unshed tears in her eyes. "I thought he was going to _kill_ you when that fight started! Do you have any idea what that man is capable of? He's a monster, and you're this nice guy and suddenly you're going toe-to-toe with him and I thought you were going to die because of _me._"
This wasn't what Kaidan had expected. He thought she would be afraid _of_ him, not _for_ him.
"I—I'm sorry, Jen. Really."
"And now you're apologizing for stepping in?" Jen demanded.
"That's… not a good thing?"
"No! Yes. I don't know," Jen flung herself at Kaidan, who awkwardly wrapped his arms around her. "I'm sorry. I'm grateful, Kaidan, I am. I just… it was a shock. Thank you for defending me." She pulled back and looked at him. "Why were you apologizing?"
"I thought you'd be afraid of me," he said softly.
"You thought I'd be afraid of _you_? I—_look out!_"
Kaidan turned to where Jen was looking and time slowed down. There, impossibly, was Johannes, and he was reaching in his jacket. Looked like he was done with fistfights. Without thinking, Kaidan brought up his left arm and a biotic barrier shimmered into place. As Johannes pulled the weapon out, Kaidan shoved Jen through an open doorway on the side of the hall. A couple of accelerated rounds slammed into his barrier, propelling him forward and causing the blue shimmer to dissipate.
"You _dusted_, kid?" Johannes asked, laughing as his footsteps echoed closer to the room they were hiding in. "I knew you weren't the nice guy you made yourself out to be. Come on out. You put up a good fight. Leave the girl and maybe I'll let you live."
Briefly, Kaidan considered the situation. Leaving Jen was not an option for a number of reasons. He was unarmed, and while he was good at defending himself there was no way he was going to dodge a bullet. The only thing he had to fall back on was his biotics. The image of Vyrnnus dying on the sterile floor of the training room flashed in his head, and he thought that if he were alone, he might just take his chances without biotics. But he wasn't alone. Jen was still there, and if he got himself killed she would be helpless. There was only one real option. He started gathering dark energy, preparing for Johannes.
_Just don't hit him as hard as you can,_ Kaidan thought. _If I hold back a little, it probably won't kill him._
Johannes rounded the corner, and Kaidan flung his arm out. The mnemonic triggered his biotic throw, and Johannes went flying, hitting the wall and sliding to the ground. The pistol fell from his limp hand. Anxiously, Kaidan ran over to him. He picked up the pistol, engaged the safety, and handed it to Jen.
"Hold this," he said. Wide-eyed, she took the weapon from him without a word. Kaidan turned to check on Johannes. Relief flooded through him as he felt a pulse in Johannes' wrist, and a quick glance showed that nothing seemed to be broken too badly.
"We need to call the paramedics," Kaidan said, looking at Jen. She was still holding the gun exactly as she had when he'd given it to her, staring at him in wide-eyed shock.
"Jen," he prompted gently.
"Yeah. Paramedics. Okay."
"You're afraid of me _now,_ aren't you?" Kaidan said, his voice sad.
"I—not _precisely._" Jen closed her eyes. "You're not sand-blasted or anything, are you?"
"No," Kaidan replied. "I never touch red sand or anything like it."
"So that—with the blue and the—that was just _you_?"
"Me, a bunch of implants, and a lot of training," Kaidan said. "But, yes. Jen, I have to call…"
"Yeah, okay," she said.
Kaidan called for the paramedics and base security as Jen tried to collect herself. It didn't take them long to arrive.
The security officers asked them what happened. Jen told them that Kaidan had surprised Johannes and tackled him after the man had missed with his first shots. She didn't mention the biotic display. Kaidan wasn't sure why she didn't, but he followed her lead. The investigation wasn't very intense. Coorta's security was less interested in justice than it was in quiet, and Johannes had been a troublemaker. In a surprisingly short amount of time, he and Jen were alone in the hallway.
"You didn't say anything."
"Not here," she said. "Let's go back to my apartment. We can talk there."
It was a long, tense walk for Kaidan. He had no idea what Jen was thinking, but all he could think about was Vyrnnus, and Rahna, and what would happen if word got around the base that he was some kind of freak.
When they got to her apartment and closed the door, Jen seemed to have collected herself.
"Are you running because you killed someone with… your abilities?" she asked.
"No, I'm not running."
"But you did kill someone."
"A man pulled a knife on me," Kaidan said. It was an oversimplification, but this night was complicated enough. "I'm not in trouble for it. I'm not proud of it, but I'm not in trouble. But if you're wondering why I'm _here,_ it's because I'm a registered biotic, and that shows up on a criminal background check, even if you're not a criminal. It makes it very hard to keep a job. That's it, Jen, I swear. I would never—I don't want to hurt anyone. I'm so sorry…"
She took a deep breath and looked up at him.
"So, that sheltered upbringing of yours, that was training," she said. "Training for that stuff you did."
"Yeah. Jen, I'm sorry if I scared you…" he trailed off as she held up a hand. She looked at him, her eyes suddenly far older than he'd seen them before.
"You spend a lot of time apologizing," she said. "You spend a lot of time worrying about scaring people. That's what makes people think you're easy pickings, Kaidan. They see you worried and a little scared, and they don't realize you're scared of yourself."
"Shouldn't I be?"
"I don't know, Kaidan," she sighed. "Only you can answer that question. But I've known a lot of monsters, and you don't seem like one of them. What you did, it was unsettling. But it wasn't nearly as bad as what Johannes wanted to do. I was surprised, but I'll get over it. When a real monster gets a hold of you, it leaves scars that don't really heal. But I'm guessing you know that."
"Yeah," Kaidan sighed. "I'm starting to figure it out."
Jen walked toward him, running her hands along his shoulders.
"I should thank you," she said, her voice husky, "for saving me." She pulled him down into a kiss. Kaidan was so shocked that he let her do it, but as she started to tug at the hem of his sweater he pulled back. This didn't feel right.
"Jen," he murmured. "Stop."
"Why?" she asked. "I'm grateful, and you're attracted to me, and you need someone to show you that you're not a monster. This will take care of all of that."
"I can accept a thank you," he said.
"This would say it better."
"Would it?" Kaidan put his hands on her shoulders and looked her in the eye. "I don't know where you've run into monsters before, Jen, but I have a feeling it has a lot to do with how you're trying to thank me right now."
"You don't know anything," she said angrily, turning away.
"Maybe not," Kaidan admitted, "but I feel like I'd be taking advantage of you if I let this go any farther. And that's not the way to prove to myself that I'm not a monster. I didn't help you with any strings attached, Jen. I just didn't want anything bad to happen to you. I didn't expect anything in return, and I don't want… I don't want something this intimate to be a business transaction. You—we _both_ deserve better."
Jen stood silently with her back to him for what seemed like a very long time.
"You are going to make someone very happy someday," Jen sighed, turning back to him. "Where the hell were you when I was growing up?"
"Trapped in a government facility being taught how to kill people with my mind," Kaidan replied.
Jen let out a surprised laugh. "Somehow, that fits in perfectly with my view of the universe."
"Jen," he said, "you know I can't stay. If word gets out about what I did, if people believe whatever Johannes is probably going to tell them, I'd be in danger. And you probably would be, too. Biotics have been killed for far less than what I did here tonight."
"Yeah," she said, "I know."
"Jen, is there anywhere you can go?" he asked. "I don't know why you're working here, but there must be some way you can get away from it."
"I spent a lot of time messed up, Kaidan," she said. "I think I might have run through all my chances. There aren't many people who want to hire someone with a record, even if it's just for drugs and… well, other non-violent crime."
"You might be surprised," Kaidan said. "I don't have much, but I could pay for your ticket off of here, as long as you don't go too far. And maybe… did you ever get caught stealing?"
"They never made it stick. It won't show up in a background check. And I have money for a ticket, I just don't have anywhere to go."
"I have a cousin who has a shipping business," Kaidan said. "Maybe he could get you started. Even if you didn't work with him long, it would at least help you get some work references."
"You would do that for me?"
"Yes, if it gets you away from here. You're too good for this place."
Jen shook her head at that, but apparently decided not to argue.
"If your cousin could do this, why don't _you_ go work for him?" she asked.
"Well," Kaidan said, "_he_ likes me well enough, but his wife is kind of afraid of me."
"Bitch."
Kaidan laughed. "Be nice. If I can arrange this, you'll have to deal with her."
"No one's ever tried to help me like this before," she said.
"You've been hanging around the wrong people."
The next day, Kaidan arranged for passage and sent a message to his cousin, explaining as much of the situation as he felt he could. It turned out not to be much. Still, his cousin said he was willing to give her a shot, if he vouched for her. They parted ways on some transit hub in the middle of nowhere; Jen off to start her new life, and Kaidan throwing himself into the difficult task of finding himself a job. Life had gotten difficult again.
Still, Kaidan found that he felt better than he had in a long time. It was strange, after everything that had happened. His experience with Jen had left him reconsidering his definition of what a monster was. Maybe he didn't fall into that category as much as he had believed. He still wasn't sure how he felt about the abilities that set him apart so much, but Johannes hadn't needed anything like that to hurt people. In fact, if he hadn't had those abilities, Johannes _would _have hurt people. And while Jen wasn't exactly comfortable with the biotics, she hadn't rejected him as Rahna had. As much as it scared her, she appreciated that he'd been able to help her.
It was something to think about.
Kaidan found himself applying for jobs where his background would most definitely be checked. Let them look. A dozen places might reject him, but maybe there would be one that didn't. He wasn't hiding from himself anymore.
**(A/N: Whew. Sorry it took me so long to move on with this story. It went in a direction even I didn't expect when I finally got back to it. Sorry if it was a bit too grim for you, but as they say, it's a long hard road out of hell. Still, I'm pretty sure we're past the worst of the angst.**
**Please review, if you'd be so kind. I appreciate feedback. It's like chocolate, except less fattening and it travels better over the internet. Thanks!)**
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| fanfiction |
Doctor Botrell is a village and distrito in the Guairá Department of Paraguay.
Sources
World Gazeteer: Paraguay World-Gazetteer.com
Category:Populated places in the Guairá Department | wikipedia |
because they are the simple consequence of the well established auscultatory method , blood pressure ( bp ) measurements are usually obtained from the definition of only two specific points of the bp curve , ie , peak systolic bp and end diastolic bp .
after the advent of antihypertensive therapy and following the results of therapeutic trials in populations of subjects with hypertension , it was proposed that cardiovascular effectiveness could be better evaluated from systolic bp than from diastolic bp . however , these standard definitions are oversimplified and now require substantial revision .
blood pressure is the force applied per unit area on a given vessel , which determines the flow of blood .
pressure and flow result from the properties of the heart as a pump and the characteristics of the arterial system .
however , pressure and flow vary during the cardiac cycle and are therefore called pulsatile pressure and flow . when the bp curve is submitted to fourier analysis and written as a series of sine waves , these waves are called oscillatory pressure and flow .
the zero term equals the mean value ( mean arterial pressure ) of bp , and the harmonics are the oscillatory terms , summarized by pulse pressure ( pulse pressure = systolic bp diastolic bp , see figure 1 ) .
after world war ii , a group of cardiovascular physiologists suggested that the pulsatile bp curve could be better described when divided into two components , ie , a steady component ( mean arterial pressure ) and a pulsatile component ( pulse pressure ) , as shown in figure 1 .
this review focuses on , firstly , the description of the hemodynamics of untreated hypertension according to the basic principles defined from mean arterial pressure and pulse pressure , and , secondly , application of these principles to the study of angiotensin blockade .
perindopril was the first angiotensin - converting enzyme ( ace ) inhibitor to be studied in subjects with hypertension using mean arterial pressure and pulse pressure .
the role of the other ace inhibitors in the mechanisms of angiotensin blockade is indicated in the appendix .
large arteries have two distinct functions.14 the first consists of transporting blood from the heart toward peripheral tissues in order to satisfy their metabolic needs .
this function requires the presence of a steady pressure gradient , represented principally by mean arterial pressure . in order to define this gradient , mean arterial pressure , calculated from the cross - sectional area under the bp curve divided by cardiac cycle time ,
the second function of large arteries consists of instantaneously accommodating the volume of blood ejected from the left ventricle of the heart , storing part of the stroke volume during systolic ejection , and carrying this volume during diastole , thereby ensuring continuous perfusion of organs and tissues at the peripheral level .
this specific function of arteries is usually described in terms of elasticity or stiffness of the aorta or an individual artery and is usually associated with the generation of wave reflections .
large artery elasticity or stiffness is usually determined from systolic and diastolic changes in artery diameter , coupled with measurement of local pulse pressure , which is the difference between systolic bp and diastolic bp.14 however , the most common method for evaluating arterial stiffness is based on the study of pulse wave velocity , ie , the velocity of the bp propagation wave along a given conduit artery , eg , the aorta .
pulse wave velocity can be determined from measurements of pulse transit time and the distance travelled by the pulse between the common carotid and femoral arteries .
aortic pulse wave velocity ( carotid to femoral ) can be measured by applanation tonometry , mechanotransducer , or doppler probes and is regarded as the gold standard for determining arterial stiffness , independent of wave activity .
the technique of applanation tonometry is widely used to evaluate central bp and also wave reflections through the determination of the augmentation index , a noninvasive parameter ( figure 2 ) .
the augmentation index is a measure of the contribution that wave reflection makes to the central pressure wave .
it is defined as the difference between the second and first peaks ( p2-p1 ) corresponding to systolic bp and is expressed as a percentage of the pulse pressure .
therefore , the augmentation index is a quite indirect measure of systemic stiffness and is mostly a direct measure of wave reflection , a parameter defined later in this review .
it is widely accepted nowadays1 that the aortic bp curve represents the mathematical summation of an incident pressure wave , coming from the heart through ventricular ejection , and a reflected wave depending on a given arterial or arteriolar site characterized by three independent parameters , ie , the value of reflection coefficients , the degree of arterial stiffening , and the distance between the heart and the site of reflecting points ( figure 3 ) . under normal conditions , the complex interaction between these parameters is responsible for the physiologic amplification of the pressure pulse observed between central and peripheral arteries , whereas mean arterial pressure remains almost constant along the arterial tree . under pathologic conditions ,
as frequently observed in elderly people , particularly those with hypertension , both increased arterial stiffening and reflection sites closer to the heart ( ie , reflection sites at the level of arteriolar or arterial bifurcations ) cause the backward pressure wave to return sooner ( ie , during the systolic component of the aortic bp curve ) , resulting in a greater summation between the forward and backward waves and consequently a higher aortic pulse pressure and systolic peak.2,3 in older subjects with hypertension , such changes are responsible for a peculiar hemodynamic pattern involving a disproportionate increase of systolic bp over diastolic bp , with potentially a loss in pulse pressure amplification . finally , in the past , hypertension was simply defined from high mean arterial pressure , associated with elevated systolic bp and diastolic bp .
mean arterial pressure divided by cardiac output enables calculation of vascular resistance , considered to be an index of the caliber of small arteries .
increased vascular resistance some decades ago was considered to be the unique and universal hallmark of hypertension .
this changing definition is due to the high frequency of systolic hypertension in the elderly , which generates mainly increased arterial stiffness and disturbed wave reflections but not necessarily increased vascular resistance .
the point to consider here is that the ace inhibitor perindopril is able not only to decrease mean arterial pressure but also , through its effect on conduit arteries , to decrease brachial pulse pressure57 and , even more selectively , central ( carotid and aortic ) pulse pressure ( see table 1 ) .
we and others have shown in many previous clinical studies that ace inhibitors may increase arterial diameter and decrease arterial stiffness independently of changes in mean arterial pressure.8,9 in addition , ace inhibitors have been shown to act selectively on the backward aortic pressure wave , causing the reflected wave to return during the diastolic ( but not the systolic ) component of the bp curve , thus reducing aortic pulse pressure and systolic peak much more than brachial pulse and systolic bp .
thus , the decrease in arterial stiffness and change in the pattern of pulse wave reflections observed with perindopril contribute significantly to a decrease in bp through arterial ( and not exclusively arteriolar ) effects .
both in animals and in humans , there is strong evidence to support this assumption , particularly following long - term treatment with ace inhibition .
firstly , in spontaneously hypertensive rats and in patients with systolic hypertension and end - stage renal disease , ace inhibition restores the aortic pulse pressure amplification normally observed from central to peripheral arteries , causing a more substantial decrease in carotid than in brachial systolic and pulse pressure.6,7 secondly , in subjects with essential hypertension , ace inhibitors decrease brachial systolic bp more than -blocking agents for the same decrease in brachial diastolic bp and mean arterial pressure.10 reason ( preterax in regression of arterial stiffness in a controlled double - blind study)11 was the first clinical trial to investigate the long - term effects of antihypertensive drug treatment on central systolic bp and pulse pressure , aortic stiffness , and wave reflections .
administration of perindopril , combined with a low dose of the diuretic indapamide , was compared with the effect of the -blocking agent atenolol for one year . for the same diastolic bp and mean arterial pressure reduction , perindopril plus indapamide lowered systolic bp and pulse pressure more than atenolol ( figure 4 ) . moreover ,
the reduction was significantly more pronounced centrally ( carotid artery ) than peripherally ( brachial artery , figure 5 ) .
although the two drug regimens lowered pulse wave velocity equally , only perindopril plus indapamide reduced central ( carotid ) pulse pressure and augmentation index.13,11,12 central pulse pressure and augmentation index remained unchanged with atenolol . furthermore , perindopril plus indapamide decreased cardiac hypertrophy more than atenolol .
this effect was attributed to the augmentation index decline , indicating that the reduction of cardiac mass was related to central wave reflections.1315 furthermore , on drug treatment , the selective lowering of systolic bp ( but not diastolic bp ) with perindopril plus indapamide was significantly predicted by the baseline pulse wave velocity value .
thus , reason emphasized the predictive values of pulse wave velocity , central systolic bp , and pulse pressure in the mechanisms of bp reduction in hypertensive subjects.16 a confirmation of all these findings was obtained later from ascot ( the anglo - scandinavian cardiac outcomes trial ) in which the role of central bp as predictive of cardiovascular events was further confirmed.17
mechanical forces involve pulsatile and steady pressure components but also have to integrate some biologic components , including those relating to structural and biochemical factors acting on arterial vessels .
focal adhesion formations of extra - cellular matrix and integrin - specific signaling in vascular smooth muscle cells are essential for mechanotransduction of angiotensin blockade within the arterial wall .
dense plaques , which are composed of cytoskeletal proteins linked to the extracellular matrix by integrin receptors , are major sites of anchorage between vascular smooth muscle and the extracellular matrix .
they interact with extracellular matrix components , including fibronectin ( ligand for 51 and v3 ) , vitronectin ( ligand for v3 ) , and laminin ( ligand for 61).18 interactions of specific extracellular matrix proteins with their integrin receptors play a central role in transmitting mechanical forces to vascular smooth muscle.19,20 many of these integrins are capable of forming complexes with fibronectin , a glycoprotein that plays an important role in the organization and assembly of the extracellular matrix .
when cyclic mechanical strain is applied to matrixes containing different adhesion proteins , fibronectin produces one of the largest mitogenic responses in rat vascular smooth muscle.20 in addition , expression of fibronectin and its 51 receptor are increased in the spontaneously hypertensive rat aorta .
the increase of fibronectin may reflect an increased number of mechanical attachments between the extracellular matrix and collagen fibers within the media . from a mechanical point of view ,
these changes have been studied in situations involving normal or increased sodium intake in the presence of angiotensin ii and/or aldosterone stimulation and blockade.2126 with a normal sodium diet , angiotensin or aldosterone blockade reduces mean arterial pressure and pulse pressure , and decreases collagen accumulation , fibronectin , and its integrin receptor . on a high sodium diet , mean arterial pressure , but not central pulse pressure , is reduced in association with collagen accumulation , increased fibronectin , and increased arterial stiffness .
it is worth noting that the mechanical contribution of mean arterial pressure and pulse pressure may vary markedly according to age or the vascular territory involved.27 thus , pulse pressure mechanotransduction may predominate in the heart rather than in the brain or kidney because only the former territory involves active periodic autocontractions .
furthermore , with increasing age , reflection coefficients are located much closer to target organs ( ie , the heart , brain , or kidney ) .
this finding suggests that pulsatility and wave reflections may be transmitted to these organs in the presence of a defect in myogenic tone .
this defect is commonly observed in subjects with type 2 diabetes mellitus , those with uninephrectomy or obesity , and often in older patients with systolic hypertension.2831 finally , many factors linked to mechanical stress , particularly pulsatility and wave reflections , may affect each particular organ locally , thereby modulating or interacting with a local hormonal system .
a typical example would be subjects with hypertension and type 2 diabetes mellitus in whom perindopril reduces both systolic bp and renal events . in conclusion , the renin
aldosterone system has been considered for many years only as a hormonal factor of the basis of hypertension and its treatment . with the development of antihypertensive therapy ,
the same system has come to be understood as a modulating antioxidative and anti - inflammatory factor contributing to the reduction of cardiovascular morbidity and mortality through its antifibrotic effects , mainly observed in the elderly and particularly in the large arterial system . | pubmed |
Proof of the set of compatible observable have a bound
Sakurai states that
>
> We can obviously generalize our considerations to a situation where there are several mutually compatible observables, namely,
> $$[A,B]=[B,C]=[A,C]=\cdots=0$$
> Assume that we have found a maximal set of commuting observables, that is; we can't add any more observables to our list without violating the above.
>
>
>
I don't understand, How are you sure that you always found such a bound? Is there any proof or reasoning that can be given?
The statement is correct but physically a bit misplaced as it stands (I like Sakurai's book however).
The existence of a maximal set of commuting observables, strictly referring to the statement in the question, arises immediately from *Zorn's lemma*. However it is easy to prove that a maximal such set contains infinite many operators even if the Hilbert space is finite dimensional.
To be precise, in the general case of unbounded observables, "commuting observables" should understood in the sense that *the spectral measures of the observables commute*, even if the observables themselves do not, in view of problems with different domains.
Nevertheless, that is not the physically correct definition of maximal set of commuting observables, because it is not restrictive enough, since it does not consider the fact that functions of a set of compatible observables commute with these observables! This is the reason why I wrote that the set always contains infinite elements. (Maybe it is later stated in the book, now I cannot check and I am referring to the portion of text presented above).
The physically correct definition, producing in some cases finite sets of observables is the following one.
A **maximal set of mutually compatible observables** is a set of mutually compatible observables such that every observable that commutes with the elements of the set is a function of them.
In this case there are important concrete examples of maximal sets of mutually compatible observables and and an explicit "existence proof" is the best a physicist should wish. Consider a particle with spin $1/2$, hence described in $L^2(\mathbb{R},dx)\otimes \mathbb{C}^2$. A maximal set of mutually compatible observables is made of the position operator $X$ and the spin operator $S\_z$ along $z$. (The proof of this fact is not trivial.)
It is not difficult to prove that if $A\_1,\ldots, A\_n$ is a maximal set of mutually compatible observables each with *point spectrum*, then a simultaneous non-destructive measurement of them produces a *pure state* as post measurement state. Measurements of maximal set of mutually compatible observables are therefore used to *prepare* pure states.
| stackexchange/physics |
the essence of any organism is the spatial and temporal expression pattern of its gene repertoire . while the genome provides the template
transcription factors ( tfs ) are often termed the master regulators of gene expression . by binding to the dna
, they tightly control where and when the nearby target gene is expressed . despite their importance as a fundamental component of biological systems for all organisms across the tree of life ,
hitherto transcription factor identification has been largely based on genome annotation pipelines that use pairwise sequence comparisons ( 1 ) , which detect only those factors similar to known genes , or on functional classification schemes that amalgamate many types of proteins into the category of transcription factor ( 2 ) . using a novel transcription factor identification method , our online resources , the dbd transcription factor database provides transcription factor predictions for all completely sequenced genomes .
databases of transcription factors to date have focused on single or small groups of genomes .
they are largely based on manual literature curation , pairwise sequence comparison and functional classification schemes .
genome specific resources include : regulondb for escherichia coli k-12 ( 1 ) , dbtbs for bacillus subtilis ( 3 ) , flybase ( providing tf as well as other annotation ) for drosophila ( 4 ) , tfdb for mouse ( 5 ) and transfac for eukaryotes ( 6 ) .
regulondb and dbtbs are databases of transcription factors and their target genes for their respective genomes ( e.coli k-12 and b.subtilis ) .
dbtbs also provides information about the pfam domains , but this is purely extra information and is not used for prediction .
flybase is a more general resource for drosophila that compiles information from the fly genome projects and literature curated annotation , including listings of known transcription factors .
it is built by : selecting proteins annotated by gene ontology ( go ) as transcription factors , manual curation and addition of close homologs using pairwise sequence comparison .
the manual curation involves addition of known tfs that are missed by go and removal of those that seem to be erroneously classified by go .
similarly , transfac ( 6 ) is list of eukaryotic transcription factors based on manual literature curation .
others have made use of these resources to compile their own lists , for example , messina et al .
( 7 ) used transfac together with go annotation of uniprot and flybase to seed sequence and hidden markov models ( hmms ) searches , followed by manual curation , to identify human factors .
their aim was to produce a rough list of factors as a starting point for array experiments across species . because the experiments were large - scale surveys , the study favoured over- rather than under - prediction .
this liberal approach to false positives meant that the final set included a range of proteins that are not sequence - specific dna - binding transcription factors .
( 8) used curated lists of factors in combination with blast sequence searches to identify the transcription factors in four eukaryotes : arabidopsis , drosophila , caenorhabditis elegans and saccharomyces cerevisiae .
they used the multiple sequence comparison tool psi - blast , seeded with known viral regulatory proteins , to identify viral transcription factors .
( 10 ) also used multiple sequence comparisons , focusing on zinc finger transcription factors in mouse .
computational studies of transcriptional regulation have used domain assignments in an ad hoc ( uncalibrated ) way to identify transcription factor proteins for particular groups of genomes ( 11,12 ) .
finally , trsdb ( 13 ) use position specific scoring matrices describing dna - binding motifs to identify and classify transcription factors for nine eukaryotic genomes .
all of these resources list transcription factors for an individual or small group of organisms .
their underlying approach is identification by literature review , which means the proteins identified must be known ( and published ) factors . for most of the datasets
the only scope for inclusion of uncharacterized transcription factors is via pairwise sequence searches , capable of identifying close homologs .
some resources also use functional classification schemes ; however , these are firstly prone to error ( due to inclusion of regulatory but non - dna - binding factors ) and secondly , they too are produced by literature review and pairwise sequence search .
these methods are not comprehensive with respect to either the genomes they cover , transcription factor families included or both . a second group of resources include compilations and predictions of transcription factor binding sites : e.g. match ( 14 ) , jaspar ( 15 ) and mapper ( 16 ) . while these tools are not directly comparable to our database , they are complementary , providing information about the dna sequences that transcription factors recognize .
the prediction method described here is applicable to all genomes across the tree of life .
it has been quantitatively evaluated and is capable of accurately identifying both known and previously uncharacterized transcription factors that bind specifically to dna .
the prediction method behind dbd identifies sequence - specific dna - binding transcription factors through homology using profile hmms of domains .
the collection of hmms is taken from two existing databases ( pfam and superfamily ) , and is limited to models that exclusively detect transcription factors that specifically recognize dna sequences .
it does not include basal transcription factors or chromatin - associated proteins , for instance .
based on comparison with experimentally verified annotation , the prediction procedure is between 95 and 99% accurate . between one - quarter and
one - half of the genome - wide predictions represent previously uncharacterized proteins . at present , dbd consists of predicted transcription factor repertoires for more than 150 completely sequenced genomes ( to be periodically updated ) , their domain assignments and the hand - curated list of dna - binding domain hmms .
users can browse predictions by genome or domain family , search using sequence identifiers and view tf domain architectures .
protein sequences can be submitted for automatic prediction and all transcription factors lists are available for download grouped by genome .
the potential applications of predictions are broad ranging , from single protein to multi - genome studies .
we expect that the main use of our database will be for prediction of transcription factor repertoires for particular genomes .
the predictions also provide the starting point for use in high - throughput experiments that characterize the nature of regulation .
for example , measuring characteristics of genes such as expression levels across different tissues or identifying dna - binding sites .
examples of large - scale experiments that have used tf repertoires as a starting point are studies by messina et al .
two recent analyses carried out large - scale chip - chip experiments of s.cerevisiae transcription factors with the aim of identifying transcription factor target genes ( 17,18 ) .
our predictions may also be of interest to theoretical biologists and are already being used for comparative genomics studies in fungi and insects .
we begin with a detailed explanation of the transcription factor prediction procedure and rationale for its design .
the second section discusses a series of tests that were used to evaluate the performance of the method .
finally , we describe the web interface and explore the biological significance of this information .
transcription factors regulate gene expression by binding to dna near their target genes . some are sequence - specific , recognizing only particular dna sequences , while others are basal , binding to a more general promoter ( e.g. tata box or initiator sequence ) . here
we are concerned only with the sequence - specific dna - binding transcription factors , because these proteins are important for differential regulation of gene expression . to function as a sequence - specific dna - binding transcription factor
, a protein must contain a domain that binds to dna in a sequence - specific manner .
our approach uses protein structure ( through domains ) and remote homology recognition , to accurately , and sensitively identify transcription factors .
it can be automatically applied to any genome to identify both known and previously uncharacterized factors .
we use profile hmms from the superfamily ( 19 ) and pfam ( 20 ) databases to identify proteins that contain sequence - specific dna - binding domains .
the advantage of transcription factor prediction based on hmms of dna - binding domains is two - fold .
first , it is more sensitive than conventional genome annotation procedures , because it uses the powerful multiple sequence comparison method of hmms .
secondly , it recognizes only transcription factors that use the mechanism of sequence - specific dna binding , as opposed to functional classification schemes that amalgamate many types of proteins into the category of transcription factor ( e.g. co - activators or co - repressors and chromatin modification enzymes ) .
the two hmm libraries that we use , superfamily and pfam , both represent domains , but they differ in their method of construction and definition of domains . briefly , superfamily contains hmms of domains of known three - dimensional structure based on the domain definitions of the structural classification of proteins ( scop ) database ( 21 ) .
each scop domain is used as a seed to build a model representing its family . in most cases ,
one scop superfamily is represented by a set of models that each recognize a subset of superfamily members .
in contrast , the pfam hmms are built from hand - curated multiple sequence alignments .
groups of sequences are identified by manual literature review as belonging to the same family , they are aligned and used as the seed for an hmm .
this model is used to search a large sequence database in order to detect more distant or poorly characterized family members .
the newly detected sequences are included in a second alignment which is used to build a final , broader hmm representing the family .
the variation in domain definition and method of construction means that pfam and superfamily differ in their coverage . by including both databases in our prediction method
the dbd website indicates the number of transcription factors identified using each database and the tf domain architectures .
we manually inspected all 2537 scop ( version 1.61 ) and 7677 pfam ( version 16.0 ) families , and identified 110 and 141 , respectively , that represent sequence - specific dna - binding domains . from this annotation , we selected the hmms that represent these families from the superfamily and pfam databases .
for pfam , selection of relevant models was straight - forward because each family corresponds to an hmm , and these models are specifically designed to recognize only members of the family . for superfamily , model selection is less straightforward because superfamily models are designed to identify members within a scop superfamily rather than a scop family .
for example , the putative dna - binding domain superfamily is made up of five families that are involved in : rna - binding , general ( non - sequence - specific ) dna - binding as well as sequence - specific dna - binding transcription factors . for this reason , our manual
, we selected models that were seeded by proteins classified in the scop database as sequence - specific dna - binding and assessed their potential to match non - dna - binding domains using a scop all - against - all test .
for example , in the case of the putative dna - binding domain superfamily all scop sequences were searched against the hmms . in two cases ,
one of the dna - binding family models gave a significant match ( or cross - hit ) to a non - dna - binding sequence . to ensure accurate identification of sequence - specific dna - binding transcription factors
in total 13 models representing 12 families and 5 superfamilies were excluded ( supplementary table 1 ) .
separate from these cross - hits , there are a small number of families where the overwhelming majority of members are sequence - specific dna - binding domains , but some representatives have other functions ( possibly in addition to their dna - binding role ) .
for example , c2h2 zinc fingers may bind rna rather than dna and proteins containing a zinc finger domain carry out multiple functions ( including but not exclusively sequence - specific transcription regulation ) ( 10 ) . in these rare cases ,
we include the domain ( and its hmm ) and accept that this may generate a small number of false positives .
this process allowed selection of 141 pfam and 210 superfamily models ( 110 families ) representing sequence - specific dna - binding domains .
to make a prediction as to whether a protein is a transcription factor , we search the amino acid sequence against the hmm libraries and designate the protein to be a transcription factor if it has a significant match to a model we annotated as representing a sequence - specific dna - binding domain .
to evaluate the accuracy of the prediction process , we carried out a series of tests on groups of sequences that had been experimentally annotated as transcription factors .
the first test considers only proteins of known structure in order to check our annotation of scop domains .
the second test considers the largest available set of 1.5 million proteins including sequences from across the tree of life , providing a large - scale assessment of the hmm - based prediction in order to determine our accuracy and coverage statistics .
the final set of tests focuses on individual genomes , evaluating performance in comparison to manually curated lists of factors . as discussed above ,
the primary use of our database is expected to be for prediction of transcription factor repertoires for individual organisms .
this final test is designed to directly assess our performance on whole genomes , allowing users to ascertain the level of confidence they should expect for repertoire predictions .
the aim of the first test was to assess the accuracy of the underlying approach ( that is , transcription factor identification via manual inspection of scop ) , without adding the complexity of domain prediction . the sequence set was from the pdb ( 22 ) , including only proteins of known structure with curated domain composition from scop . by including only proteins with known domain composition , we eliminated any potential error introduced by incorrect assignments by the hmms .
we used the go annotation ( 2 ) of the pdb proteins as a standard list of known tfs .
the go functional classes that represent the transcription factors are shown in table 1 ( supplementary table 2 provides a comprehensive list , including categories we classified as expression related ) .
it should be noted here that when we manually inspected proteins classified by go as transcription factors , we found that the set also includes some basal ( i.e. non - sequence - specific ) factors and chromatin remodelling proteins .
when we examined pdb proteins identified by us as containing a sequence - specific dna - binding domain , we found that more than 99% ( 393 ) are classified by go as tfs .
the remaining 1% ( 4 ) are classified by go as nucleic acid binding and have not been allocated to a go sub - category ( details are shown in table 2 ) .
this test illustrates the validity of both the underlying approach , prediction based on structural domains , and our hand curation of the scop domains .
next , we aimed to evaluate the prediction method as a whole , including the domain assignment step using superfamily and pfam .
the sequence set used was from the uniprot database ( 23 ) , the most comprehensive catalogue of proteins available including more than 1.5 million sequences .
as a standard for comparison , we used the experimentally verified go annotation for uniprot ( that is we excluded homology based annotation ) .
we searched the pfam and superfamily hmms against the uniprot sequence set to derive a set of predicted transcription factors . in order to evaluate the accuracy of our method , we calculated the number of predicted tfs for which go supported our prediction .
that is , go annotated the protein as being a member of one of the categories shown in supplementary table 2 .
this benchmark established our accuracy to be between 95 and 99% ( table 3 ) .
this means that we expect 5 out of 100 of our predictions to be incorrect .
manual inspection and literature search of the false positives suggests that at least one - half are in fact experimentally verified sequence - specific dna - binding proteins .
many of the remaining putative false positives have little annotation , but any provided is supportive of the suggestion that these proteins are transcription factors .
conversely , we calculated the coverage of our method to be between 60 and 67% by counting the number of proteins that go annotates as a transcription factor but we fail to predict .
closer inspection of these proteins showed that many are not actually sequence - specific dna - binding tfs , but are involved in some other expression related process ( e.g. basal transcription factors and chromatin proteins ) .
this means that the false negative rate of one - third should be considered an upper bound .
we expect to miss some tfs because we rely on hmm domain assignments which are known to give incomplete coverage [ depending on the genome , between 30 and 60% of amino acids lack a domain assignment ( 19,20 ) ] .
closer inspection of the 358 known tfs that we categorized as carrying out some other ( non - expression related ) function indicates that limitations in the homology detection are likely to be to blame ; more than 60% of this set have no domain assignments at all . at the same time
, it must be noted that our predictions encompass as many transcription factors again that are unclassified in go ( 37840 novel compared to 20246 known tfs ) and these additional predictions are expected to be at least 95% accurate ( table 3 ) .
therefore , despite the incomplete coverage , our method predicts many transcription factors that are unannotated .
the final group of tests involved comparison with curated lists of transcription factors for individual genomes .
first , we considered s.cerevisiae , using a list of 160 factors curated from literature by luscombe et al .
we predicted 169 transcription factors : 125 ( 74% ) of these were known , 5 ( 3% ) seemed to be false positives and 39 ( 23% ) were novel , previously unannotated proteins .
of these , one - half had no domain assignments and the remaining one - half had some domains assigned but no dna - binding domain .
these results confirm that our annotation provides good coverage ( 78% ) . a second manual analysis of predicted transcription factors for the mouse genome identified an even higher proportion of proteins of unknown function . shown in table 4 ,
assuming the same false - positive rate as for the known factors , this means we have identified 590 new mouse transcription factors , increasing the size of the repertoire by more than 90% . in summary , we have developed an automatic , broadly applicable method for predicting sequence - specific dna - binding transcription factors .
based on an evaluation using a large set of annotated protein sequences , we find that it is accurate ( 95 to 99% correct ) and has good coverage ( between 60 and 78% identification rate ) .
the transcription factor prediction method described above is broadly applicable to any genome or sequence set
. as we have shown , the results are both reliable and have good coverage .
this means that by applying the method to complete genomes , it is possible to predict transcription factor repertoires for organisms .
this type of information is invaluable to both bioinformaticians and biologists interested in gene regulation or expression . in order to make our method accessible to the scientific community
, we have developed an online database ( ) with pre - computed predictions for more than 150 completely sequenced genomes .
users can : browse predictions by genome or dna - binding domain , search for particular sequence identifiers or domains and submit their own amino acid sequence for prediction .
the web interface also allows users to download the domain assignments and list of dna - binding domain hmms as text files .
the superfamily and pfam annotation as well as predictions for all genomes are available as text files .
superfamily and pfam domain architectures are illustrated for each transcription factor , with colour indicating the domain family .
examples of the number of transcription factors we identify across eukaryotic genomes is shown in table 5 . the proportion of proteins that are transcription factors increases from fungi to insects to mammals .
that is , between 2.6 and 3.9% of the unicellular eukaryotes ' proteins are transcription factors compared to 5% for fly and almost 10% for mouse and human .
figure 3 shows the number of transcription factors in each genome compared to their total number of genes .
this exponential increase in transcriptional regulatory proteins compared to genome size has been observed previously , based on go functional categories , for bacteria ( 25 ) and genomes across all three kingdoms of life ( 26 ) .
we have developed a broadly applicable method for automatically predicting sequence - specific dna - binding transcription factors .
the procedure uses hmms from the superfamily and pfam databases to identify proteins that contain sequence - specific dna - binding domains .
a thorough evaluation showed that the method is both accurate ( 95 to 99% correct ) and has good coverage ( between 60 and 78% of known factors were identified ) .
however , the most exciting feature of our method is that we also predict many novel , unannotated transcription factors .
for example for mouse we find over 600 new factors amounting to more than a 90% increase in the tf repertoire .
we have applied our prediction method to more than 150 completely sequenced genomes from across the three kingdoms of life and implemented a web interface to make the data publicly accessible . while the method described here represents a significant advance in the field of transcription factor prediction , adapting our system to use profile - profile methods ( rather than profile - sequence ) for remote homology detection is almost certain to increase sensitivity and coverage . aside from generally improving domain assignments ,
profile - profile comparison could be used to make direct family level assignments for scop . until now
, any researcher hoping to study transcriptional regulation would need to devise a list of putative factors for consideration .
this database provides the first quantitatively evaluated transcription factor prediction set for all completely sequenced genomes .
a domain is assigned to a particular protein when one of the hmms matches a region of sequence with an e - value less than or equal to 0.001 for superfamily or greater than or equal to the trusted cutoff for pfam .
for example , the small dark - blue boxes represent the zinc finger c2h2 type dna - binding domains .
proteins with at least one dna - binding domain assigned are selected as putative transcription factors .
the designation of dna - binding is based on our manual curation of pfam and superfamily models .
each predicted transcription factor is listed with two rows for the superfamily and pfam domain architectures .
domains are represented as rectangles , coloured according to their family and horizontally located based on their position in the amino acid sequence .
clicking on a domain takes the user directly to that family in the relevant domain database .
proteins are ordered based on their domain architecture . for ease of navigation ( in particular for large genomes ) , the list of transcription factors is split into pages with 50 entries per page by default .
users can navigate between pages using previous / next or clicking on a page number .
number of genes in each of 151 genomes versus transcription factor predictions . the number of genes ( x - axis , log - scale ) is plotted against the number of predicted transcription factors ( y - axis , log - scale ) .
sequence - specific dna - binding transcription factor go categories these five categories are from the molecular function ontology and have been selected because they include sequence - specific dna - binding transcription factors .
go annotation of our predictions for pdb proteins to evaluate the prediction method for proteins with known three - dimensional structures , we compared our results with the experimentally derived go annotation of the pdb database .
the first column of numbers indicates the go annotation of proteins in our predicted tf set .
( annotated as tf based on experimentation rather than homology in go . ) the remaining 1% are classified as nucleic acid binding .
this means they may be transcription factors , but there is insufficient functional annotation to make a sub - categorisation . to evaluate the prediction method , we compared our predictions with the experimentally derived go annotation of the uniprot database .
the first column of numbers indicates the go annotation of proteins in our predicted tf set .
99.8% of predictions are corroborated go ( annotated as tf ) , giving a false positive rate of 0.2% ( expression related and other function ) .
the final column is our annotation of all the proteins go annotates as transcription factors .
unclassified row. this shows that we identify 67% of known transcription factors , or conversely , we miss about one third .
manual inspection suggests that some of the missed proteins may in fact be basal factors and therefore have been correctly excluded from our set .
it should also be pointed out that we predict 37840 transcription factors that are not classified or of unknown function according to go .
functional annotation of predicted mouse transcription factors annotation was taken from the mgd ( 27 ) .
transcription factor predictions in eukaryotes genome size and number of predicted transcription factors are indicated for thirteen eukaryotes including 10 unicellular fungi and three multicellular animals .
organisms have been arranged according to the percentage of their proteins that are transcription factors . | pubmed |
EFFECTS OF SEXUAL DIMORPHISM ON TWO STRAINS OF BROILER BIRDS (ANAK AND SHAVER)
Authors: Kareem, O. L., Zubair, J.I., Useni, S. S. and Zanna, A.
The study was conducted to determine the effects of sexual dimorphism on two strains of broiler birds (Anak and Shaver). A total of one hundred and eighty two (182) chicks comprising thirty six (36) and fifty three (53) female of Anak and forty four (44) male and forty nine (49) female of Shaver was used, respectively. Body parameters that included body weight, body length, body girth, shank length, drumstick length, thigh length, keel length and wing length were taken fortnightly from day old up to eight weeks of age which hitherto were used to determine the effects of sexual dimorphism at each stage of two broiler strains (Anak and Shaver). The mean body weight at 0, 2, 4, 6 and 8 weeks of age were 47.78g, 227.15g, 596.73g, 965.38g and 1366.67g for Anak male and 49.78g, 227.15g, 545.10g, 923.8g and 1233.0g for Anak female respectively. The respective values in Shaver were 46.74g, 183.92g, 513.10g, 957.70g and 1313.64g for Shaver male and 47.53g, 154.36g, 422.20g, 776.67g and 1102.04g for Shaver females. It was concluded that body weight of Anak and Shaver broilers were similar (P>0.05) at 0 and 6 weeks of age while that of Anak were significantly heavier at 2, 4 and 8 weeks.
Keywords: Strain, Sex, Dimorphisms and Broilers
*Correspondence: E-mail: EMAILADDRESS, Phone: PHONENUMBER | slim_pajama |
economic and financial systems are strongly interconnected , with several units being linked to each other via different types of interactions .
important examples are provided by trade networks ( where economic agents exchange goods or services in return of money ) and credit networks ( where financial institutions lend and borrow money from each other ) .
analysing the intricate structure of economic networks is crucial in order to understand economic dynamics , especially under stress conditions : for instance , the recent global financial crisis has witnessed the role of the increased interconnectedness of the interbank network in the collapse of the system @xcite . in particular , while individual banks felt safe minimizing their individual risk by diversifying their portfolios , the simultaneous diversification of all portfolios resulted in an unexpected and uncontrolled level of mutual dependency among all banks , amplifying the effects of individual defaults @xcite .
as another example , understanding the structural organization of international trade networks is crucial in order to measure and characterize economic integration and globalization @xcite .
a particularly interesting question is whether the temporal evolution of a real economic network is _ quasi - stationary _ , i.e. whether the system undergoes smooth structural changes controlled by a few driving parameters .
when this is the case , the behaviour of the network is largely controllable and predictable in terms of the dynamics of those parameters . on the other hand , the lack of stationarity may result in abrupt transitions and uncontrollable dynamics . in this extended version of the paper presented at the workshop complex networks 2013 ( organized within the international conference sitis 2013 ) and published in the related proceedings @xcite
, we address the problem of the ( non-)stationarity of real economic networks by studying whether they are found to be typical members of an _ evolving quasi - equilibrium ensemble of graphs _ with given properties @xcite .
roughly speaking , we identify a set of purely topological properties , expected to evolve in time as the natural result of the internal evolution of the network s economic units and we check whether the evolution of the entire network can be simply traced back to the changes in the selected properties .
such properties are treated as _ constraints _
@xcite , since , in some sense , they are assumed to be the ` independent variables ' undergoing an autonomous evolution , while the other properties of the network , treated as ` dependent variables ' , are assumed to vary only as a consequence of the former @xcite .
if the observed network properties are systematically found to be in agreement with what expected from the evolving enforced constraints , we can conclude that the real network is quasi - stationary and driven by the dynamics of the constraints .
if the network slightly deviates from the equilibrium expectations , but the deviating patterns are coherent at all times , the network can still be considered consistent with a quasi - stationary one , even if not completely driven by the chosen constraints . finally ,
if the network significantly deviates from the quasi - equilibrium expectation , showing different deviating patterns at different times , then it should be considered a non - stationary one .
we will consider two case studies : the _ international trade network _
( itn ) , defined as the network of world countries connected by directed import / export relationships ( of which we analyse six decades , i.e. 1950 , 1960 , 1970 , 1980 , 1990 and 2000 ) @xcite and the _ dutch interbank network _ ( din ) , defined as the network of dutch banks connected by directed lending / borrowing relationships ( of which we consider 44 quarterly snapshots spanning 11 years , i.e. 1998 - 2008 ) @xcite . for simplicity , we will consider both networks in their purely binary and directed representation , i.e. as graphs where directed links are either present or absent , regardless of their magnitude .
we find that , during the considered intervals , the itn is almost perfectly quasi - stationary , with trade patterns being in systematic agreement with an equilibrium ensemble of graphs specified only by local properties @xcite .
by contrast , the din turns out to be strongly non - stationary , displaying different dynamical regimes @xcite . as signatures of the major structural changes undergone by the din , we find striking early - warning signals of the interbank crisis of 2008 .
these early - warning signals are defined in terms of the deviation of certain dyadic and triadic topological properties from their quasi - stationary expectations .
an important role appears to be played by dangerous ` debt loops ' with different levels of interbank reciprocity .
in this section we introduce the formalism that we use to study the stationarity of real economic networks ( but applicable , generally speaking , to any real - world evolving network ) .
let us first consider a single ( static ) snapshot of a real network .
such snapshot can be uniquely specified by the _ adjacency matrix _ @xmath0 , with entries @xmath1 if a link from node @xmath2 to node @xmath3 is there , and @xmath4 otherwise .
let us denote the real network by the particular matrix @xmath5 .
given a set of topological properties that we may choose as constraints ( symbolically denoted as @xmath6 ) , it is possible to construct a _ statistical ensemble _ of graphs , @xmath7 , such that the expected value @xmath8 of the constraints over @xmath7 is equal to the value @xmath9 observed on the real network @xmath5 @xcite .
the least - biased way to construct this ensemble is that of assigning each graph @xmath10 a probability @xmath11 such that shannon s entropy @xmath12 is maximized , under the constraint @xmath13 where @xmath14 denotes the value of the properties @xmath6 measured on the particular graph @xmath0 .
the solution of the maximization problem is the exponential distribution @xcite
@xmath15 where the so - called _ hamiltonian _
@xmath16 is the linear combination of the chosen constraints and the _ partition function _ , given by @xmath17 , is the normalization constant @xcite .
the parameters @xmath18 are the _ lagrange multipliers _ that can be set equal to the particular value @xmath19 such that the expected value of each constraint is equal to the observed one . the value @xmath19 that realizes eq.([exp ] ) can be shown to be also the value that maximizes the log - likelihood @xmath20 @xcite .
once the unknown parameters have been found , it is possibile to evaluate the expected value of any other topological quantity of interest , @xmath21 , as follows @xmath22 if the real network is a typical member of the ensemble , the knowledge of the constraints will be enough to reproduce the original network ; otherwise the knowledge of additional properties will be required .
we have recently proposed a completely analytical method allowing one to compare any topological property of the real network with the corresponding expected value over the constructed ensemble , in the fastest possible time @xcite .
we now show how it is possible to extend the above ideas to study whether a _ dynamically evolving _ network is consistent with a quasi - equilibrium ensemble . given a temporal sequence @xmath23 of snapshots of a real network and a set of constraints @xmath6
, we have a different observed vector @xmath24 for each timestep @xmath25 .
thus , a different maximum - entropy graph ensemble , such that the ensemble average @xmath26 equals @xmath24 , can be generated for each timestep @xmath25 .
now , in order to check whether the evolution of the real network is consistent with a quasi - equilibrium process driven by smooth changes in only a small set of its topological properties , @xmath27 can be taken to be precisely the temporal sequence of desired properties .
then , by iterating the aforementioned procedure on all snapshots , it can be checked whether the real network s evolution is consistent with that of the quasi - equilibrium ensemble generated by the dynamics of @xmath24 .
one of the most important examples is when the driving property is the _ degree sequence _
, i.e. the number of links of each node .
if @xmath28 denotes the degree of node @xmath2 , then the vector @xmath29 denotes the degree sequence of the entire network . specifying the degree sequence as the driving quantity amounts to choose @xmath30 .
being a completely local property , the degree of a node is the quantity most prone to be interpreted in terms of intrinsic economic features ( such as wealth , income , capitalization , etc . ) characterizing that node .
for instance , the degree of countries in the itn is strongly and non - linearly correlated with the gross domestic product ( gdp ) @xcite . in this interpretation , assessing that an economic network undergoes a quasi - equilibrium evolution driven by the dynamics of its local topological properties ( e.g. the degree sequence ) allows one to conclude that the network s evolution is driven by the changes of intrinsic node - specific economic variables . in the appendix
we briefly discuss what are the possible local properties that can be defined in a directed network .
this leads us to the introduction of three different ensembles : the _ directed random graph model _ ( drg ) , defined by the _
total number of links of the network , @xmath31 , _
@xcite , the _ directed configuration model _ ( dcm ) , defined by the _ in - degree _ and _ out - degree sequences _ , @xmath32 and @xmath33 , @xmath34 ( i.e. the directed generalization of the concept of degree ) @xcite and the _ reciprocal configuration model _ ( rcm ) , defined by the _ reciprocated degree _ , _ non - reciprocated in - degree _ and _ non - reciprocated out - degree sequences _ , @xmath35 , @xmath36 , @xmath37 , @xmath34 @xcite .
since they assume that the network arises as a simple combination of purely topological properties , the drg , the dcm and the rcm are typically treated as _ null models _ , i.e. simple models expected to fail in reproducing the data , but useful precisely because they can highlight interesting patterns in the real system in terms of deviations from the null hypothesis . here , the systematic accordance with a null model throughout the considered time period would indicate a quasi - equilibrium network evolution driven by the constraints defining the null model itself . in some sense
, a good but incomplete accordance could still indicate a quasi - stationary evolution , as long as the deviating patterns were always the same and with the same amplitude . in this case , the dynamics of the network would not be entirely driven by that of the constraints themselves . by contrast , a network out of the quasi - equilibrium dynamics generated by the chosen constraints would display wild and irregular deviations from the null model s expectations . since the constraints specified in the drg , the dcm and the rcm are global , node - specific and dyad - specific respectively , the simplest non - trivial ( i.e. higher - order ) properties to monitor are _ dyad - specific _ ( in the case of the drg and dcm ) and _ triad - specific _ ( in the case of the rcm ) , i.e. involving , respectively , pairs and triples of nodes .
for this reason , in this paper we analyse in detail the so - called _ dyadic _ and _ triadic motifs _ @xcite .
dyadic motifs are defined as the 3 non - isomorphic topological configurations involving two connected nodes in directed networks ( see fig .
[ fig_dy ] ) .
similarly , triadic motifs are defined as the 13 non - isomorphic topological configurations involving three connected nodes in directed networks ( see fig .
[ fig_mot ] ) .
the number of occurrences @xmath38 of a particular motif @xmath39 , either dyadic ( @xmath40 ) or triadic ( @xmath41 ) , can be written in two equivalent ways .
the first one employs products of adjacency matrix elements , @xmath42 , and is suitable when using the drg and the dcm .
the second one employs the mutually excluding quantities @xmath43 , @xmath44 and @xmath45 and is particularly useful when using the the rcm . for instance
, the abundance of the dyadic motif @xmath46 can be calculated as @xmath47 its expected value under the drg and the dcm reads @xmath48 while its expected value under the rcm reads @xmath49 equivalently , the abundance of the triadic motif @xmath50 can be calculated as @xmath51 its expected value under the drg and the dcm is @xmath52 while its expected value under the rcm is @xmath53 given a real network @xmath5 , the usual way to compare the observed and expected abundance of motifs is by means of the so - called _ z - scores _ , i.e. the standardized quantities @xmath54 } \label{eq : z}\ ] ] where @xmath55\equiv\sqrt{\langle n_{m}^2\rangle^*-(\langle n_{m}\rangle^*)^2}$ ] is the standard deviation of @xmath56 under the null model
. if the observations were exactly reproduced by the null model , then the @xmath57-scores would be exactly zero .
on the other hand , significantly large positive or negative @xmath57-scores indicate an over- or under - estimation of the motifs empirical abundance respectively .
the meaning of the @xmath57-scores is well defined for normally distributed variables ( e.g. for dyadic motifs ) : in this case , the deviations can be nicely quantified in terms of probabilities , as the intervals @xmath58 select regions enclosing a probability of @xmath59 , @xmath60 and @xmath61 , respectively .
choosing one of the above values as a threshold allows the identification of significantly deviating patterns .
while for non - normally distributed variables ( e.g. for triadic motifs ) it is impossible to attach probabilities to @xmath57-scores , large values still highlight the most deviating patterns and their temporal evotion still enables to assess the ( non-)stationarity of the network . since the values of @xmath62 are sensitive to the number of nodes , when it is necessary to compare the @xmath57-scores of networks with different size , or of differently sized snapshots of the same network , a size - independent measure is needed . for this reason ,
it is customary to normalize the @xmath57-scores by introducing the _ significance profile _
@xcite defined as @xmath63 and measuring the _ relative _ importance of each motif with respect to the other ones .
while the @xmath57-scores are unbounded quantities , @xmath64 lies between @xmath65 and @xmath66 .
equipped with the techniques and formalism described so far , we now start showing the results of the empirical analysis of the first of the two economic networks mentioned in the introduction , i.e. the itn . in the binary , directed representation of the itn , nodes represent world countries and a directed link from node @xmath2 to node @xmath3 represents the existence of an export relation from country @xmath2 to country @xmath3 . the initial number ( 85 ) of countries roughly doubles during the time period considered ( 1950 - 2000 ) , mainly because of many colonies becoming independent and the soviet uniot disgregating into many states .
this expansion of the network and the simultaneous globalization process have caused a significant increase in the number of links @xcite , as well as considerable variations in the nodes degrees as well .
this circumstance makes the itn an ideal example for testing whether an economic network undergoes a quasi - equilibrium evolution driven by the dynamics of the local properties .
-scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the itn in the years 1950 , 1960 , 1970 , 1980 , 1990 and 2000 , under the dcm ( @xmath67 , first and third panel ) and the rcm ( @xmath68 , second and fourth panel ) . the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 .
2014 ieee . reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=39.3% ] + -scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the itn in the years 1950 , 1960 , 1970 , 1980 , 1990 and 2000 , under the dcm ( @xmath67 , first and third panel ) and the rcm ( @xmath68 , second and fourth panel ) .
the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 . 2014 ieee
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=37.7% ] + -scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the itn in the years 1950 , 1960 , 1970 , 1980 , 1990 and 2000 , under the dcm ( @xmath67 , first and third panel ) and the rcm ( @xmath68 , second and fourth panel ) .
the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 . 2014 ieee
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=39.5% ] + -scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the itn in the years 1950 , 1960 , 1970 , 1980 , 1990 and 2000 , under the dcm ( @xmath67 , first and third panel ) and the rcm ( @xmath68 , second and fourth panel ) .
the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 . 2014 ieee .
reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=39.5% ] we avoid the use of the drg as a meaningful null model , on the basis of the following simple considerations .
the single parameter of the model , i.e. the probability coefficient @xmath72 , coincides with the link density , which throughout the evolution of the itn is approximately @xmath73 @xcite .
this means that the drg would predict a network structure where the presence of each link is determined by simply tossing an almost fair coin .
this oversimplified model is completely uninformative , i.e. is almost equivalent to a model where no piece of information is available about the network , and is of course unable to reproduce any property of the real itn . moreover , since the drg is defined only in terms of the total number of links , or equivalently in terms of the average degree of vertices , interpreting this quantity as a local driving property of nodes amounts to completely neglect the inter - node variability of the economic factors determining the degree of a country .
we therefore focus on the dcm and the rcm .
the results of the anaysis of the @xmath57-scores , as defined in eq.([eq : z ] ) , are shown in fig .
[ fig_wtw ] . under the dcm ,
the @xmath57-scores indicate large deviations between observations and expectations , and the agreement worsens as the network evolves .
these results confirm that , while some higher - order properties of the itn were previously found to be well - reproduced by constraining the nodes degrees @xcite , the triadic patterns are irreducible to the in- and out - degrees themselves @xcite .
by contrast , the agreement improves substantially under the rcm : now , all the @xmath57-scores ( with the only exception of motif 8) lie within the error bars @xmath74 .
this indicates that , once the number of reciprocated and non - reciprocated links of each node are separately controlled for , the triadic structure of the network is almost completely explained .
moreover , the shape of the profiles is more stable than under the dcm .
all these findings indicate that the rcm should be preferred to the dcm , the reciprocity structure playing a strong role in shaping the topology of the itn @xcite .
it should in any case be noted that the @xmath57-scores profiles display a high degree of stability .
the panels of fig .
[ fig_wtw ] also show the significance profiles for all 13 motifs , as defined in eq.([eq : sp ] ) .
we find that discounting the effect of the increasing size of the network makes the curves of the 6 different snapshots collapse to a single profile .
this effect is obviously more evident under the dcm , since under the rcm the @xmath57-scores of the different snapshots were already largely overlapping .
-scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the 44 quarterly snapshots of the din between 1998 and 2008 , under the dcm ( @xmath67 and @xmath75 , first and third panel ) and the rcm ( @xmath68 and @xmath76 , second and fourth panel ) . the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 .
2014 ieee . reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.4% ] + -scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the 44 quarterly snapshots of the din between 1998 and 2008 , under the dcm ( @xmath67 and @xmath75 , first and third panel ) and the rcm ( @xmath68 and @xmath76 , second and fourth panel ) . the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 . 2014 ieee .
reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=37.7% ] + -scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the 44 quarterly snapshots of the din between 1998 and 2008 , under the dcm ( @xmath67 and @xmath75 , first and third panel ) and the rcm ( @xmath68 and @xmath76 , second and fourth panel ) .
the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 . 2014 ieee .
reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.9% ] + -scores ( first and second panel ) and significance profiles ( third and fourth panel ) of the 13 triadic , binary , directed motifs for the 44 quarterly snapshots of the din between 1998 and 2008 , under the dcm ( @xmath67 and @xmath75 , first and third panel ) and the rcm ( @xmath68 and @xmath76 , second and fourth panel ) .
the dashed , red lines represent the values @xmath69 , the dotted , purple lines the values @xmath70 and the dot - dashed , pink lines the values @xmath71 . 2014 ieee
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.9% ] so , even if in absolute terms many structural quantities change ( the number of nodes , the number of links , the degrees , etc . )
, under both null models the significance profiles are extremely stable , clearly pointing out that the deviating patterns are systematic and the relative importance of each motif remains constant .
the above results indicate that the itn is almost completely consistent with a quasi - equilibrium network driven by the local ( non-)reciprocated degrees @xmath77 , @xmath78 and @xmath79 .
even if the latter vary considerably over time , presumably under the effect of complicated economic and political processes ( such as the creation of new independent states , globalization and the establishment of reciprocated relationships ) , once these processes are reabsorbed into the evolution of the local constraints , the quasi - equilibrium character of the network becomes manifest .
we now turn to the analysis of the din .
we consider a data set where nodes are dutch banks and a link from node @xmath2 to node @xmath3 indicates that bank @xmath2 has an exposure larger than 1.5 million euros and with maturity shorter than one year , towards a creditor bank @xmath3 @xcite .
we consider 44 quarterly snapshots of the network , from the beginning of 1998 to the end of 2008 .
the last year in the sample represents the first year of crisis , i.e. when the recent financial and banking crisis became manifest . during the evolution of the din , the number of banks and the number of connections ( both total and per vertex ) changed only moderately @xcite .
since the entity of the variation of these quantities is much smaller throughout the evolution of the din than in the case of the itn , we might expect the din to display even more stable patterns than the itn .
however , as we now show , the opposite is true .
if we repeat the calculation of the @xmath57-scores and significance profiles that we used to produce fig .
[ fig_wtw ] , for the din we obtain the corresponding fig .
[ fig_din1 ] .
what we find is that , unlike the itn , the din displays highly non - stationary profiles , with no collapse of all the different snapshots onto a unique curve .
notice that the moderate change of quantities like the network s size makes the rescaling defining the significance profile practically unnecessary : in fact , the din @xmath57-scores do not differ so much from the din significance profiles , as shown in fig .
[ fig_din1 ] @xcite .
this confirms that the evolution of the triadic profiles is not due to changes in the size of the network , and is a genuine effect .
many motifs have , in different periods , both positive and negative @xmath57-scores , indicating a complete inversion of their significance ( from under - representation to over - representation and vice versa ) .
the large ( in absolute value ) @xmath57-scores and their wild temporal fluctuations indicate that , unlike the itn , the din behaves like an out - of - equilibrium network , whose driving dynamics can not be captured by the selected constraints alone .
however , under both null models we can identify relatively stable triadic profiles if we partition the entire 11-year period into four subperiods .
these periods are 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 , and 2008q1 - 2008q4 ( where @xmath80q@xmath2 denotes the @xmath2th quarter of year @xmath80 ) .
this is shown in fig .
[ fig_din2 ] under the dcm and in fig .
[ fig_din3 ] under the rcm .
both figures show the four subperiods separately and the almost complete collapse of all snapshots within each subperiod .
thus , we can conclude that the overall non - stationary dynamics of the din can be approximately decomposed into four relatively stationary phases connected by major structural transitions . within each stationary subperiod ,
considerations analogous to those we made in the example of the itn may apply . by contrast , across subperiods major structural changes occur , and the description of the network is irreducible to the change of the bank - specific variables directly affecting the degrees of the corresponding nodes .
if we label the fourth subperiod as the ` crisis ' phase , the triadic profiles of this period can be considered as the ` topological fingerprints ' of the crisis .
it is interesting to notice that these fingerprints were to a large extent anticipated by the significance profiles of the third subperiod ( 2005 - 2007 ) . we might therefore interpret the latter as a sort of latent ` pre - crisis ' phase .
remarkably , the most dramatic change of the significance profiles turns out to occur between the second and third subperiods , not between the third ( pre - crisis ) and fourth ( crisis ) ones as one might naively expect .
this indicates that the main structural transition occurred at the beginning of the pre - crisis phase and not at the onset of the crisis itself , suggesting that monitoring the evolution of the triadic profiles could potentially represent a way to detect early - warning signal of interbank crises . )
for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] + ) for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] + ) for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] + ) for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] ) for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] + ) for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] + ) for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
2014 ieee .
reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] + ) for the four subperiods ( from top to bottom ) 1998q1 - 2000q2 , 2000q3 - 2004q4 , 2005q1 - 2007q4 and 2008q1 - 2008q4 .
. reprinted , with permission , from proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) , pp .
530 - 537 ( edited by ieee ) ( 2014).,title="fig:",scaledwidth=38.8% ] the above consideration suggests that an important analysis to perform is plotting the temporal evolution of the @xmath57-scores over time , for each motif separately . in this case using the drg as an additional null model turns out to provide interesting insights .
we recently found that the dyadic @xmath57-scores of the din , if calculated under the drg , appear to suddenly collapse to their final values only when the crisis is already manifest @xcite .
in particular , the top panel of fig . [ fig_din4 ] shows the temporal evolution of the 3 dyadic motifs , highlighting the limited role of the homogeneous benchmark in signaling the upcoming event . while the drg correctly identifies the global structural change provoked by the economic crisis ( emphasizing that the critical configuration is ` anomalous ' with respect to the previous decade ) , it does not provide any useful early - warning signal .
note that the fact that the drg correctly identifies the ` crisis ' only in terms of dyadic properties is in any case a fundamental result showing that there are clear signatures of the crisis in the din s topology . without this preliminary observation ,
looking for early - warning signals in the evolution of the dyadic properties themselves would have no empirical justification . performing the same analysis under the dcm yields a completely different result @xcite .
the bottom panel of fig .
[ fig_din4 ] shows that in this case the dyadic @xmath57-scores undergo a gradual evolution towards the collapsed configuration , thus providing an early - warning signal of the crisis .
remarkably , after a period of minor fluctuations , all the trends of the dyadic @xmath57-scores show a sudden inversion of sign at the beginning of 2005 , thus backdating the beginning of the din s major structural change three years before its dramatic manifestation in 2008 @xcite .
it is very important to check whether the above findings extend to triadic ( and in principle higher - order ) motifs as well .
indeed , in over - the - counter ( otc ) markets ( where transactions between two banks are not disclosed to third parties ) , triadic motifs are the smallest structural patterns where systemic risk starts to build .
while within a dyad both banks are clearly aware of all the connections existing between them , within a triad each bank is only aware of its connections to and from the other two banks , and not of the possible connections existing among the latter .
for instance , as was pointed out e.g. in ref .
@xcite , in motif number @xmath81 ( see fig . [ fig_din5 ] ) the bank a is prepared to the direct default of banks b and c , but it is not prepared to the indirect effects of b s default through bank c , precisely because it ignores that b and c are linked .
this can lead to an underestimation of ` counterparty risk ' . by looking at fig .
[ fig_din5 ] , we see that the @xmath57-score of this particular motif shows very different behaviours under the dcm and the rcm . in the first case , it seems to display the same kind of trend as the dyadic @xmath57-scores , i.e. to reveal a pre - crisis phase interpretable as an early - warning signal .
however , since any triad is necessarily a combination of three dyads , the reason for the behaviour of a triad as a whole might simply be the combined result of the trends of the three underlying dyads . while the dcm is not able to control for this effect , the rcm is , precisely because in this stricter null model the dyadic properties are separately controlled for at each node .
indeed , fig .
[ fig_din5 ] shows that the ` early - warning ' character of motif 5 completely disappears under the rcm , and that the values of the @xmath57-score are now not very significant .
this proves that this motif is not particularly relevant in itself .
-scores of the 3 dyadic , binary , directed motifs ( @xmath82 - @xmath83 , @xmath84 - @xmath85 , @xmath86 - @xmath87 ) for the 44 quarterly snapshots of the din under the drg ( top panel ) and the dcm ( bottom panel).,scaledwidth=49.0% ] the triadic patterns that turn out to be much more relevant to systemic risk are the _ directed loops_. note that in a circular loop of three banks , each of the three banks involved is not aware of counter - party risk looping back to itself , thus creating additional dependencies among potential defaults not incorporated in their bilateral risk pricing . also note that circularity is not necessarily associated with strong risk externalities by itself , but _
unreciprocated circularity _ is .
for example , within a full dyad risk loops back between the two banks as well ; however , both parties are _ aware _ of it and can properly include the increased correlation in their risk pricing . by constrast , at the triadic level , loops of length three involving an increasing number of reciprocated dyads ( i.e. motifs number 9 , 10 , 12 and 13 , see fig . [ fig_din6 ] ) are increasingly less prone to the risk externality .
unreciprocated loops can therefore be considered to be a sort of ` autocatalytic risk loops ' . since longer loops have smaller probabilities of cascading defaults , the most dangerous autocatalytic risk loops are presumably those involving three banks . in fig .
[ fig_din6 ] we show all the four directed loops , in decreasing order of dyadic reciprocity .
we note that , while for the less dangerous loops ( @xmath88 and @xmath89 ) the behaviour is similar to that of motif 5 , i.e. the @xmath57-scores are no longer significant under the rcm , the more dangerous loops ( @xmath50 and @xmath90 ) are strongly significant .
these motifs are not just the result of the combination of the participating dyads .
remarkably , the trend of motif @xmath90 leads to the identification of an even ` earlier ' phase of structural change ranging , approximately , from 2000 to 2005 ( i.e. the beginning of the ` pre - crisis ' phase ) .
this behavior is so peculiar to justify the denomination of this period as ` cyclic anomaly phase ' @xcite . our previous discussion seems to suggest that , during the ` cyclic anomaly ' phase , banks might have systematically underestimated risk externalities @xcite .
-scores of motif @xmath81 under the drg ( @xmath82 , top panel ) , the dcm ( @xmath67 , middle panel ) and the rcm ( @xmath91 , bottom panel).,title="fig : " ] -scores of motif @xmath81 under the drg ( @xmath82 , top panel ) , the dcm ( @xmath67 , middle panel ) and the rcm ( @xmath91 , bottom panel).,title="fig:",scaledwidth=54.0% ]
in the present paper we have proposed a way to investigate whether real economic network are in or out of equilibrium , by introducing the concept of quasi - equilibrium graph ensembles driven by the dynamics of local constraints and relating the stationarity of a network to its _ statistical typicality _ with respect to a chosen ensemble .
so , ` stationarity ' here does not mean constancy of the numerical values of certain topological quantities across time : it means that the newtork s evolution is systematically driven by the dynamics of the chosen constraints , and so by the process determining the evolution of the constraints themselves .
so , even if the quantities usually investigated in network theory as the number of nodes and the nodes degree vary over time , the explanatory power of the chosen constraints may remain constant .
our empirical results show that the itn and the din display two completely different behaviours : while the itn is an equilibrium network , the din is an out - of - equilibrium one .
the in- and out - degree sequences of the itn always fail in explaining the triadic structure , although they have been shown to enclose the necessary information to reproduce properties like the degree - degree correlations and the clustering coefficient @xcite . on the other hand
, we found that the rcm , which also constrains the numbers of reciprocated links , can replicate the triadic structure almost perfectly .
this confirms the important role of reciprocity in economic networks .
it turns out that the 44 temporal snapshots of the din do not collapse to a single profile ( under both null models ) and that four sub - periods with different profiles can be distinguished .
the present analysis seems to suggest the following scenario : after the ` cyclic anomaly phase ' , where many risky patterns were established ( all the partly reciprocated loops - motifs @xmath92 - were much less abundant than the completely unreciprocated loop ) , banks started to not trust each other anymore .
in fact , even if during the ` pre - crisis ' phase , the loops with small or no reciprocation - motifs @xmath93 - became increasingly under - represented , also the reciprocated dyads became increasingly under - represented . as explained in @xcite ,
they might have redirected their links , increasing the systemic risk while avoiding mutual interactions and , in so doing , pushing the system towards the critical configuration .
these results seems to indicate that the otc transactions indeed have the potential to create unintentional , but destabilizing , patterns , feeding into the debate on how otc markets can be monitored and regulated .
this work calls for future studies aimed at understanding the potential of monitoring the non - stationary properties of interbank networks within the framework of bank regulation .
so , even if on one hand the non - stationary character of the din makes the description of the system more complicated than that of equilibrium networks such as the itn , on the other hand it provides a key piece of information that in this case might open the potential to detect early - warning signals .
the _ directed random graph model _ ( drg ) is the directed version of the erdos - renyi random graph @xcite .
the only quantity defining the latter is the _ total number of links _ , @xmath94 , of a given network .
in an economic context , they represent the total number of trading relations observed in the particular system . given the extreme diversity of the agents playing a role in economic and financial systems , the only ( global ) constraint defining the drg
can not be expected to reproduce all the properties of interest .
nevertheless , it can still clearly signal a readjustment of the system s structure of interest taking place at a global level .
the drg hamiltonian is @xmath95 and the resulting probability for the generic network , @xmath0 , is @xmath96 where @xmath97 with @xmath98 @xcite . given a real network @xmath5 , the parameter @xmath99 can be set to the value @xmath100 that maximize the likelihood of @xmath5 , or equivalently that enforce eq.([exp ] ) .
the latter reads in this case @xmath101 once the unknown variables are numerically determined , the expected value of any adjacency matrix entry simply becomes @xmath102 .
the latter can be used to immediately calculate the expected value @xmath103 of any topological quantity @xmath21 of interest @xcite . by directly solving eq.([drgsys ] ) , one finds that the parameter @xmath72 is nothing else than the network _ connectance _ , also known as _ link density _
, i.e. @xmath104 .
in a directed network @xmath0 , for each node @xmath2 one can separately define the number @xmath105 of out - going links , or _ out - degree _ , and the number @xmath106 of in - going links , or _ in - degree_. the in- and out - degree are the simplest node - specific local properties .
they often reflect some nontrivial node - specific dynamics and are typically extremely heterogeneous in real economic networks @xcite . if the in- and out - degree of all nodes are both included as constraints in the vector @xmath6 , one obtains the so - called _ directed configuration model _ ( dcm ) @xcite .
the dcm hamiltonian is @xmath107 and the resulting probability coefficient for the generic network , @xmath0 , simply factorizes as a product over pairs of nodes : @xmath108 where @xmath109 with @xmath110 , @xmath111 @xcite .
given a real network @xmath5 , the parameters @xmath112 and @xmath113 can be set to the values @xmath114 and @xmath115 that maximize the likelihood of @xmath5 , or equivalently that enforce eq.([exp ] ) .
the latter reads in this case @xmath116 once the unknown variables are numerically determined , the expected value of any adjacency matrix entry simply becomes @xmath117 .
the latter can be used to immediately calculate the expected value @xmath103 of any topological quantity @xmath21 of interest @xcite .
a more stringent choice of local properties in directed networks allows one to distinguish between _ reciprocated _ and _ non - reciprocated _ links . for a given node @xmath2
, we might separately count the number @xmath79 of non - reciprocated out - going links , the number @xmath78 of non - reciprocated in - coming links and the number @xmath77 of reciprocated ( out - going and in - coming at the same time ) links .
mathematically , these three different ` degrees ' are defined as @xmath118 , @xmath119 and @xmath120 respectively , where @xmath43 , @xmath44 and @xmath45 . the graph ensemble where each of the above three quantities is specified for every node is known as the _ reciprocal configuration model _ ( rcm ) @xcite .
note that , once the three generalized degrees @xmath79 , @xmath78 and @xmath77 are specified , the ` simpler ' out- and in - degrees @xmath121 and @xmath122 are automatically specified as well , but the opposite is not true . in an economic setting ,
the reciprocity of economic interactions reflects important properties , such as trust or preference . separately controlling for reciprocated and non - reciprocated interations means additionally controlling for the heterogeneity of these properties of nodes .
even if the constraints are now non - linear combinations of the adjacency matrix entries , the probability still factorizes as a product of dyadic probabilities , making the model analitically solvable @xcite .
the maximization of the likelihood function leads to the following system of equations : the addenda in the three equations above correspond to three different probability coefficients , that we denote as @xmath126 , @xmath127 and @xmath128 respectively .
these coefficients separately specify the probability of having , from node @xmath2 to node @xmath3 , a non - reciprocated out - going link , i.e. @xmath129 , a non - reciprocated in - coming link , i.e. @xmath130 , and two reciprocated links , respectively , i.e. @xmath131 . d. g. acknowledges support from the dutch econophysics foundation ( stichting econophysics , leiden , the netherlands ) with funds from beneficiaries of duyfken trading knowledge bv , amsterdam , the netherlands . wells , s. ( 2004 ) financial interlinkages in the united kingdom s interbank market and the risk of contagion .
_ bank of england working paper .
available at : http://www.bankofengland.co.uk/research/documents/ + workingpapers/2004/wp230.pdf_. van lelyveld , i. & int veld , d. ( 2012 ) finding the core : network structure in interbank markets .
_ dutch national bank working paper .
available at : http://www.dnb.nl / en / publications / dnb - publications / dnb - working - papers - series / dnb - working- + papers / working - papers-2012/dnb276178.jsp_. squartini , t. & garlaschelli , d. ( 2014 ) economic networks in and out of equilibrium . _ proceedings of the ninth international conference on signal - image technology & internet - based systems ( sitis 2013 ) _
, 530537 ( edited by ieee ) , doi : 10.1109/sitis.2013.89 .
bargigli , l. , lionetto , a. & viaggiu , s. ( 2013 ) a statistical equilibrium representation of markets as complex networks .
_ university of florence working paper n. 23/2013 .
available at : http://www.disei.unifi.it/upload/sub/pubblicazioni/repec/ + pdf / wp23_2013.pdf_. bargigli , l. , di iasio , g. , infante , l. , lillo , f. & pierobon , f. ( 2013 ) the multiplex structure of interbank networks . _ university of florence working paper n. 26/2013 .
available at : http://www.disei.unifi.it/upload/sub/pubblicazioni/repec/ + pdf / wp26_2013.pdf_. musmeci , n. , battiston , s. , caldarelli , g. , puliga , m. & gabrielli , a. ( 2013 ) bootstrapping topological propertoes and systemic risk of complex networks using the fitness model .
_ journal of statistical physics _ , * 151 * , 720734 .
stouffer , d. b. , camacho , j. , jiang , w. & nunes amaral , l. a. ( 2007 ) evidence for the existence of a robust pattern of prey selection in food webs .
_ proceedings of the royal society b : biological sciences _ , * 274 * , 19311940 . | arxiv |
Traditionally a degree in the medicine is closely associated with acquiring as much hands-on experience as you can. You can't go through medical school without visiting the chemistry lab or visit/see patients at the local hospital.
But this dogma is slowly changing. Now you can enroll with some medical online college degree programs. It might seem counterintuitive at first, but the large volume of medical knowledge in conjunction with the evolution of pedagogical methods leaves the door open for online learning.
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While a medical degree cannot and should not be taken 100% online, taking some medical internet courses can come really handy for students training to become professionals in these fields. Consider this, with an online college degreeprogramyou could study the theoretical aspects from home, thus leaving only the practical aspect to be taken of.
Since medicine is a very complicated field, it's only natural that some aspects would elude you. Fortunately, thanks to online education you can easily supplement your knowledge by taking a few additional internet courses to get you on the right track.
Full online degrees in medical fields are also available. For example, you can enroll with a Health Management B.Sc at the Northeastern University or a Gerontology undergraduate degree at the Washington State University.
While these degrees won't allow you to become a doctor, they offer the opportunity to work in the medical field. But as we mentioned above, even full medical degree students can find benefits with online education.
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This is just an example of scholarship program available for medical students, but a quick search online will reveal many, many other options, as well.
All you need to do is keep searching on a regular basis, as new opportunities are probably added on a weekly basis. Good luck!
I am interested but I am poor I can\'t afford, please how can I be assisted!
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I need assistance for higher education. | slim_pajama |
Gundam Seed 1. The False Peace
Hey, ShadowsofVanity here, I decided to take this story over from my previous account, InvictusUnum. The first couple of chapters are as they were then, and so really short, but later chapters will be appropriately long.
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Gundam SEED: Journey
Phase One
The False Peace
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_It is the year 70 of the Cosmic Era, and tensions are rising between Earth and the ZAFT organization. Due to the Bloody Valentine Tragedy, these tensions exploded into an all-out war. It seemed a foregone conclusion that the Earth Alliance, with it's superior numbers, would be victorious. However, these initial assessments proved false. Almost eleven months have passed since the conflict began, with no end in sight..._
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The Space Colony of Heliopolis
It was, as usual, warm and sunny in the park near the high school, and students walked the paths, played games, or simply lay sprawled in the grass, talking gossiping cheerfully back and forth. Some, pleasantly tired from their antics, crawled under shady trees and napped comfortably, alone or with their significant others for company. Laughter and cheering permeated the warm air, adding a sense of carefree joy to the air, the kind that will sneak up on you and bring a smile to your face with ease and without warning. Over them all soared a small, green robotic bird, the head of which was slowly turning back and forth as it scanned the people on the ground, clearly looking for someone. Apparently seeing who it was looking for, it dived, zeroing in on one of the many gazebos that were scattered about on the park. Back-winging, it settled onto the top of a laptop computer. The aforementioned laptop belonged to one Kira Yamato, a tall 15 year old, who was dressed in a black shirt and pale green pants. Relatively long brunette hair didn't hide his amethyst eyes, but was just long enough to get in the way as he tried to type. Beside him sat another teen, a beautiful young woman with gold-honey colored skin and blond hair which partially hid her pale purple eyes. Both of them were focused on their work, one hand holding a sheaf of papers while the other danced across their keyboards in a rapid and steady tempo. She was dressed in blue jeans and a vibrant tie-dye T-shirt. Both teens chatted easily and relaxed, not getting distracted from their work in the least by any discussion.
"Heyyy! Kirrraaaaa!" a youthful male voice yelled. "Aiiilyynnn!"
Both teens looked up and spotted two other teens coming towards them across the grass.
"Hey Tolle, Mir. What are you guys up too?" Kira asked as he smiled up at his friends. Tolle Koenig and Miriallia Haw had been together since the sixth grade, and it didn't seem likely for anything to change. Moreover, it had been Tolle and Mir who had gotten Kira and Ailyn Custos (Kira's companion in the Gazebo) to realize their mutual attraction to one another and actually helped prod them into a relationship. Long story short, Kira had been poked and prodded incessantly by his friends, Tolle and Mir the most, into asking her out, but he had hemmed and hawed for so long that they had decided to...manipulate circumstances to give him a little help. All or Kira's friends loved him dearly. He was kind, smart, and always willing to do anything for a friend, no matter how risky, but he was shy and pessimistic when it came to people he didn't know. Finally, Tolle and Mir had faked a pair of love letters, forging Kira's and Ailyn's handwriting, and placed them in the pair's lockers. When they had met, each thinking it was the other's idea, and figured out what had happened, they had been highly embarrassed. Kira had attempted to flee immediately, but Ailyn had grabbed him and kissed him. Needless to say, Kira slowed way down long enough for Ailyn to tell him that she really did like him. They had started dating, and the first thing they did was plot revenge on Tolle and Mir, a cause in which they succeeded in brilliantly. While they had been embarrassed and exacted their revenge, they had secretly thanked their friends for helping them to break the ice. That had been almost sixth months ago, and now Ailyn, or "Lyn", was a welcome and integrated member of what had now become known as The Gang.
"Oh, Professor Kato is looking for you again. He told us to bring you two too him right away." Tolle replied easily, looking at a newsreel on Kira's screen. "Something on the war?"
"Yeah, Taiwan, apparently." Kira said maximizing the screen. A man in a suit with a microphone stood in a city. Two GINNs were in the background, with gunshots and screams that were easily audible in the distance.
"I am within 7 kilometers of Kaohsiung, where the sounds of fierce combat continue to echo!" the reporter said over the din.
"If this is footage from last week, they may have already taken over Kaohsiung!" Tolle said, and Kira nodded.
"Yeah…" he said, closing his laptop and starting to pack up.
"Kaohsiung isn't very far from us, is it? Will the Homeland be alright?" Mir asked, sounding worried.
"Birdy!" said the green robotic bird, taking off from Kira's shoulder.
"Sure!" Tolle said, smiling reassuringly at his girlfriend. "There is nothing to worry about! Oh, they're close by, but our nation is neutral. Can't see Orb turning into a warzone!"
"Really? Then…I guess we're okay." Mir said slowly, sounding somewhat reassured.
Kira watched Birdy fly in circle's, waiting for him, and remembered when he had gotten it…
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Start of Flashback
_Kira and Athrun stood on a path through a park, cherry blossoms blowing past in the brisk wind._
_"The PLANTS and Earth will see eye to eye." Athrun had said confidently. "There will be no war." Athrun held out his hands to Kira, who returned the gesture. A small, green robotic bird jumped from Athrun's palms to Kira's. "The evacuation doesn't mean a thing. You'll join me later at the PLANTs, right Kira?"
_
End of Flashback
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_Athrun, how wrong you were. Where are you know, how are you, and what are you doing?_Kira thought, still watching Birdy.
"Kira?" said Tolle, sticking his face in front of Kira's with a look that said he had been trying to get Kira's attention for a while and was trying to decide if Kira had fallen asleep or something.
"Waugh!" Kira cried, flailing backwards from his friend's suddenly close face.
"Seriously, what's up with you anyway?" Tolle asked, rolling his eyes as he straightened up while Ailyn and Mir giggled at Kira's antics. "Let's go."
"Uh, yeah, sure." Kira said, finishing packing Ailyn's things as well as his.
"Kira, I'm perfectly capable of getting my own stuff, you know!" she said, the mock severity of her tone ruined by the smile on her face.
Kira just smiled a little shyly at her and held out his hand to here in a mixed offering for her to take it and for her to join them. Smiling easily back at him, Ailyn reached out to take his hand, but stopped when a beeping sound was heard. All four teens automatically checked their phones. Tolle, Mir, and Kira put theirs away, all declaring it wasn't them, but Ailyn was staring at her phone in appalled shock.
"Lyn? What's wrong?" Kira said instantly, seeing the look on his girlfriend's face. He started towards her, but she stepped away rapidly, shaking her head hard.
"N...nothing." she said, although it was obvious that something was wrong. "Listen, umm…I need to go make a call." She continued, turning and running the other way, yelling over her shoulder that she would catch up later. The three teens that she had left behind looked after her, confused and deeply concerned.
"Is it just me, or did she look scared?" Kira murmured, eyes following her until she was out of sight.
"Yeah, but you know her, Kira. She is best left alone at first when she is like this." Mir said gently, and Kira nodded in reluctant agreement. He had plenty of experience with his girlfriends sporadic and sometimes worrying bouts of isolationism.
"Okay, let's head over to the Proff's. I'm late as it is." he said finally, leading his friends to the taxi stop.
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Meanwhile, Ailyn had found a secluded spot in the forested section of the park. Reaching into her bag, she took out a small case, containing a small screen and camera, which she opened and placed on the ground, after flipping a small power switch inside of it. Pulling out her phone, she flipped it open and entered a few numbers before putting it to her ear. The screen in the box flashed to life, showing a young man.
"Code in, please." His voice said from her phone, and Ailyn, now no longer sounding like a carefree and happy student with a boyfriend, spoke in cold, hard tones.
"Coding in. I.D. number ZF-1183XV41Z. ZAFT Special Agent…Ailyn Elsman, reporting in." she said, saluting.
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That's the first original chapter done.
2. Secrets of Heliopolis
A/N: Second Chapter that was previously published.
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Gundam SEED: Journey
Phase 2
The Secret's of Heliopolis
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_Previously: Kira, Miriallia, Tolle, and Ailyn are introduced to us. Ailyn is shown to be a ZAFT spy and we receive our first glimpse of Rau Le Creuset._
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"Code in acknowledged. Ailyn Elsman of the Le Creuset team. Commander Le Creuset will be with you shortly. Stand by." Ailyn nodded and the screen blanked. She nibbled on her lip, waging a mental war. She had already betrayed her home enough as it is, and she was averse to doing it more, but to not betray her home and friends would mean that she would have to betray her brother and ZAFT. Unless….perhaps she could tell the Commander only about the units she had already reported, but not the others? After that, she could simply…disappear. Go to Orb, get a new name, then come back in a while and rejoin the others. Her brother would be in no extra danger, and her friends would never discover her secret. She nodded to herself, her decision made, and waited for the Commander.
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On the bridge of the _Vesalius_, the communications technician turned away from his console to face a tall man with blond hair who wore the white and black uniform of a ZAFT commander. Over the upper half of his face, he wore a white mask.
"Sir, Agent Elsman is on the line, as per you communications order. Shall I patch her through to your terminal?" he asked, and the blond masked man shook his head.
"No, just put her onto the main screen for the bridge." He replied, and the comm. tech nodded. Tapping a few keys, he patch Ailyn's signal through to the large screen above the viewport on the bridge.
Down in Heliopolis, Ailyn blinked. From what she could tell, the entire bridge could see-and hear-her. She saluted to the camera, and Le Creuset returned the salute.
"Report, Ailyn." He ordered, and she lowered her hand, but remained at parade rest.
"Yes sir. I have only to report that the Mobile Suits being built here were still in their hangers five hours ago, although I have reason to believe that they will be getting moved very soon. The Earth Forces may have already begun transferring them over to the Assault Ship that is being constructed here as well. At this time, I know where the ship is, so eliminating it should be simple. I am sending you the relevant data now."
"Excellent. Well done. The team is suiting up now, and should be ready to take all six machines after they eliminate the spaceship. The operation will commence in 45 minutes. Make sure you are someplace safe. Our people will find you after things cool down and smuggle you out."
"Yes sir, thank you sir. Operation commences in 45 minutes. I understand!" Ailyn replied, appearing to be every inch the willing and loyal soldier.
Le Creuset nodded a dismissal and shut down the link. He sat in his chair and smiled to himself. He had been waiting for so long, manipulating the world, and now it was time. Time for the curtain to rise on his little play.
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Ailyn, on the other hand, was leaning against a tree and crying. She hated this. She had already decided to betray her nation, but it was too late. She had less than an hour to try and protect her friends, evade detection, and somehow not get picked up by ZAFT. She felt so lost. At first, she had hated everything about this place, everything it represented. The stars were for the Coordinators, not lowly Naturals, and especially not a bunch of Naturals to cowardly to pick a side, instead insisting on remaining _"Neutral"_. Then Miriallia had approached her. Surprised, Ailyn had rebuffed her offers of friendship, rather aggressively and rudely. Far from being put off, however, Mir had simply seen it as a challenge, and had wormed her way past the barriers in Lyn's heart. Before Lyn knew what had happened, they had become friends, and Mir was bringing her along when what she called "The Gang" hung out. There she had met Kira, and Tolle, and Kuzzey, and Sai, and even Flay. They had all accepted her with ease, and she had found it so strange that a bunch of Naturals would be so friendly. With amusing ease, they had destroyed all of her ridiculous misconceptions about Naturals and about Orb itself. Peace, she realized, was an amazing thing. The peace that came from Neutrality, and the lack of conflict, was something to be admired and envied.
Then, the last thing she would have expected happened. She had started to fall for Kira. She hadn't tried to, didn't want to, and didn't even realize that it was happening, but by the time she did, she couldn't have stopped it even if she had wanted to. She expressed her feelings to Mir, who had not reacted as expected. Instead of being annoyed or overprotective of her friend, or using it as gossip, she had rolled her eyes, said that it was about time, and helped her to figure out how to, as she put it, "land him." Lyn didn't know how she felt about treating Kira like some sort of fish, but she had appreciated the support. One thing had followed another, and they had started dating. Then it struck her how bad it could be if anyone back in the PLANTs found out that she was dating a Natural. Her brother and his friend Yzak would raise nine kinds of hell if they found out, and she knew that her superiors would assume that she was compromised. Then, quite by accident, she had found out that Kira was actually a First Generation Coordinator. She had been the happiest girl alive; because that meant that she and Kira could be together without any…repercussions. She had hoped to get him to join ZAFT eventually, especially since she could see that he had extraordinary abilities, even among Coordinators, but he had been violently opposed to both sides when she asked him which side he supported. He had declared his distaste for killing and war in general and rightfully pointed out that he and his friends were obvious evidence for the point that Naturals and Coordinators could get along, and even be close friends. Ailyn had to admit, his reasoning was very strong, and she agreed with him. But now…he would hate her when he found out, she was sure of it… She dashed away her tears angrily. This wasn't the time to feel sorry for herself. Even if he ended up hating her, she was going to follow this path all the way to the end. She pushed herself off of the tree and, pausing only long enough to push a button in the small comm. case, walked away. Behind her, unwanted and abandoned, the comm. case sat on the ground. A few seconds later, with a small explosion, it shattered into a thousand pieces, leaving no trace except a small scorch mark on the grass.
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Morgenroete Factory District-Professor Kato's Office.
Ailyn walked through the double doors leading into Professor Kato's office, and stopped, surprised. Everyone in The Gang, except for Flay, was there. A girl with blond hair that no one seemed to know, since no one was talking to her, stood in the corner. Kira was busy talking to two people that Ailyn didn't recognize, a girl with long midnight-black hair and a boy with spiky blond hair. It was obvious that he knew them, and knew them well. Seeing Kuzzey, who was standing against the wall, alone and the closest of the group who wasn't busy, she sidled up next to him and whispered:
"Hey Kuzzey."
"Hey Lyn, you alright? Kira, Mir, and Tolle told us you looked scared earlier. Kira wanted to go looking for you, but Mir stopped him." Kuzzey murmured back.
"It…it was nothing. It's fine now." Lyn whispered, relieved that her friend had stopped Kira. "Who's the blond chick, and more importantly, who are those two, and how do they know Kira?"
"A pair of old friends apparently. They know Kira from when they all lived back on the Moon. They were here when he arrived. He was pretty surprised, to say the least. The blond is apparently the Proff's guest, and was told to wait here."
"Guess Kira is a pretty popular guy, huh?" Ailyn murmured to herself, eyeing the girl as she smiled at Kira, but unfortunately for her Kuzzey noticed both the words and the look, and chuckled softly.
"I wouldn't worry about her, Lyn. She and the blond guy are together. Besides, we all know that Kira would never look at another girl. _You_ should know that."
Ailyn blushed, not only at having got caught in the act of jealousy, but at the fact that she had been worried about it in the first place. She knew Kira wasn't like that, and now that she looked closely, Kuzzey was right. The way that the girl and the male blond interacted and the way they stood around each other was clearly in a romantic way, while the way they interacted with Kira was more of a sibling-esque attitude. Just then Kira noticed her standing over by the door, half hidden behind Kuzzey.
"Lyn, come over here, I need to introduce you!" he called, and she blushed as she walked over and Kira planted a kiss on her cheek before wrapping an arm around her and facing the other couple.
"Guys, this is Ailyn. Ailyn, this black haired devil is Faith London. Be careful around her, she's a tomboy and a beast." Kira said, before yelping as Faith smacked him upside the head.
"Quiet fool! You may give her the wrong impression!" she said with a smirk. "I ought to beat ya!"
"You already did, and she doesn't need me to give her a bad impression, you can do that by yourself." Kira muttered, rubbing the side of his head. "That hurt!"
"Aye, Kira. Ye should have known better than to say such things with the Wildcat around." The blond grinned, his thick Scottish brogue making his words almost indecipherable. "Pleased to meet you, Ailyn. The name is Cu Hawke."
"I'll show you "Wildcat" later, you big lout." growled Faith, and Cu just wiggled his eyebrows at her.
"Do you promise, love?" he relied cheekily.
Faith blushed a fascinating shade of scarlet before laughing. Looping her arms around Cu's neck she gave him a prolonged kiss. Ailyn, thoroughly bewildered, looked at Kira, her eyes questioning, and he nodded with a wide grin.
"Yeah, that's just the way they are. They've been like that forever, so you might as well get used to it."
"How long is forever? They seem extremely close." Asked Ailyn, as the other couple had yet to come up for air.
"7 years or so. They may not act like it, but these two idiots are in their early 20's. Anyway, they were just telling me that they moved up here just a week ago. They've been living in Orb for some time now. Evidently, they found out that I lived up here, and decided to join me."
"Aye, just like old times." Cu said, as he and Faith finally broke apart. "And it doesn't look like you had any trouble building up another entourage, have you now?"
"It's not like that, Cu, and you know it." Kira said, frowning at his old friend, but Cu just smirked.
"You have always been the one who has people following him. You're just one of those easygoing, leader-types. Might as well get used to it."
"I don't want to." Kira muttered a little petulantly, and all three of his companions laughed.
Ailyn smiled, but her smile faded quickly. Elsewhere, at this moment, she knew that ZAFT soldiers were preparing to attack. She had to get started.
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Elsewhere in Heliopolis, six ZAFT redcoats and 12 regular greens flew down a ventilation shaft on their backpack thrusters. Coming to a four way intersection, the lead redcoat held up a closed fist. As his fellow reds gathered around him, he looked down through a grating at the large white warship in the secret hanger beneath them. Looking up, the leader made several hand signals to his fellows, and the entire group split up, spreading out and planting explosive charges at key points around the hanger.
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Outside Heliopolis
"It's time." Rau said simply, gesturing towards Heliopolis.
"Aye, aye!" Captain Ades replied, rotating his command chair forward. "Weigh anchor! _Vesalius, _moving out!"
The two ZAFT warships activated their powerful main engines, coming around the asteroid at high speed. GINNs shot out of their hanger, activating their thrusters and rocketing towards the colony.
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Heliopolis Control Room
"Chief Controller!" yelled a tech over the whooping alarm.
"Calm down! Cut of that alarm!" the Chief Controller ordered, grabbing a headset from a nearby worker. "Approaching ZAFT vessels, cease your advance at once! Your actions are in a direct violation of you treaty with our nation! I repeat, ZAFT vessels, cease your advance at once!"
"Sir, electrical interference emanating from the "ZAFT vessels"!" reported the man the Controller had taken the headset from. "This is clearly a hostile act!"
"Damn it all! Launch the defense drones, before they take the harbor over!" the Chief Controller said, trying to keep himself together.
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The Bridge of a _Marseille-III_ class transport ship of the Earth Forces
"What's the situation?" asked Lieutenant Mu La Flaga as he flew onto the bridge.
"Two ships, _Nazca_- and _Laurasia_-class. We confirmed the launching of mobile suits prior to the commencing of jamming interference."
"Have Luke and Gale board their Moebius units, but don't have them launch yet!" Mu ordered, heading for the door. "I'm launching too!"
Within moments, Mu was climbing into his Moebius Zero's cockpit. Strapping in, he started to bring it online.
"Lieutenant La Flaga?" the captain asked, clearing asking for further instructions.
"Launch the ship, the harbor is about to be taken over." He said, before switching to his flight's channel. "Gale, Luke, you two _stay together and cover each other_! If it gets too bad, retreat! Is that understood?"
"Yes, sir! We understand sir!" they replied in unison, and Mu grunted in approval.
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Secret Hanger Complex: Control Room
"Captain! What do we do?" shouted an Earth Forces officer.
"Calm down! If we launch, we will be playing right into their hands!" The Captain said sternly. "Let Heliopolis handle this!"
As the timers clicked down to 4:26 left before detonation, the ZAFT team flew at increasing speeds down the ventilation shaft, knowing that they were running out of time.
Back in the control room, the Captain was busy conversing with someone on the phone.
"Yes, I know!" he said firmly. "We're prepared to launch if we have to!" he slammed the phone back down, then turned to a black haired women in the uniform of an Ensign, and a blue haired man in the uniform of a Chief Petty Officer. "Ensign Badgiruel, you and Chief Neumann get Lieutenant Ramius for me, and commence transfer of the G-weapons!"
"Sir!" they saluted and flew away, headed for the central shaft.
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_Vesalius's _Bridge
"We will move in as soon as we eliminate the mining operations." Rau ordered softly.
"Yessir!" confirmed the pilot as defense drones started launching from the colony.
As the counters hit 19 seconds, the ZAFT pilots were almost at their target. The Earth Forces convoy moved ever onward, carrying their precious cargo to the ship. All throughout the colony, the people of Heliopolis went about their lives. Innocent, carefree and happy, they had no idea how much their realities were about to get shattered. People shopped, children played in the park, Kira attempted to fix a malfunctioning robot suit with Tolle inside as everyone else laughed.
Then, in an instant, it was over. The charges detonated, washing over the ship in waves of fire. Two charges detonated on either side of the control booth for the hidden hanger, and the Captain barely had time to scream before he and everyone else inside the booth was consumed.
Natarle Badgiruel looked behind her at the sound, and didn't even have time to yell out before the shockwave swept down the shaft, picking her up like a doll and throwing her into the wall, knocking her unconscious instantly.
All the students stumbled as the building suddenly rocked sideways.
"What was that?" Sai cried. "A meteoroid?"
_Damn it all, it's started. I have to get everyone out of here!_ Ailyn thought desperately. _But how? I had wanted to have them near the shelters beforehand! It might be too dangerous to head there now!_
All of a sudden, the blond girl ran out the door and down a side hallway that lead straight to the factories.
"Hey, hold it!" Kira shouted, charging after her.
"Kira! Come back!" Ailyn shouted, but the loving, protective fool simply yelled over his shoulder that they had to get to the shelters, and he would deal with the blond. Moments later, the floor collapsed behind him, cutting off any chance of them following him.
"Sai, Tolle, Kuzzey, you three take Mir to the shelters. We three are going after Kira. That fool needs someone to watch his back!" Cu ordered, and the others nodded.
"Wait, what about you guys?" Mir shouted as she was pulled away.
"Don't you worry about us; we know a thing or two about this place!" Faith called out, before shutting the door. "Now, anyone know a parallel route to the area?" She looked straight at Lyn, and raised her eyebrows.
"I…yes, I do." She said, leading them over to a door marked "KATO" on the far wall, near where the blond had been standing. She tried the handle, only for it to be locked. "Can you guys open this?"
"Leave it to me!" said Cu, pushing her aside gently. He took a deep breath, and then lashed one foot out in a powerful blow. His foot connected with the door, which smashed off of the hinges and fell down the stairs the door had concealed. "Good thing I didn't ram it with my shoulder. I would need the hospital." He said, staring down the steep staircase.
"C'mon, there are some things down here that can help us protect Heliopolis, and Kira." Ailyn said, pushing past him and starting down the stairs.
"Oh? You mean the GAT-X030 Werewolf, the GAT-X911 Assault, and the GAT-X231 Renegade?" Faith said, and Ailyn stumbled slightly in shock. "Are those what you're talking about, Miss Ailyn Elsman, ZAFT pilot and spy?"
Ailyn froze in horror. _They knew!_
"How did you know?" she asked in a strangely flat voice, and they laughed.
"Kira doesn't know this, but Cu and I work for the Orb Special Forces. We were sent up here to pilot the Werewolf and the Assault, which were being built secretly for the Orb military. As for you, Orb's intelligence division is exceptional."
"Are you going to tell…Kira?" she whispered.
"No, but answer me this:" Faith said, her voice suddenly growing cold, and Ailyn heard the distinctive sound of a handgun being cocked. "Did you just use your relationship with Kira as a cover, or was it genuine?"
"It was genuine, but he will never forgive me for lying about who I was." Ailyn said sadly.
"Don't count on it. We know Kira, and he will forgive almost anything." Faith said, and Ailyn hear a pistol being holstered. "Let's get going. We need to get to those units and protect this colony. Besides, you have proven your loyalty to him by betraying ZAFT, just like us. He makes people want to forget about the war…and what has been lost." Faith sounded so sad that Ailyn turned around.
"What…what happened to you?" she asked tentatively.
"Cu and I…we're Coordinators too, just like you. Our parents were killed in the Bloody Valentine. We hated Naturals so much, we accepted a mission posting to the Moon for an assassination ordered by Chairman Zala, but….we met Kira. And his friends from the Moon. Over half of them were Naturals. What happened to you happened to us. We couldn't find it in ourselves to hate them any longer, and sp we went to Orb. There, we heard some things that made us…leery of ZAFT. Growing genocidal factions, things like that, so we joined Orb. And here we are."
Ailyn turned around and kept walking, feeling ashamed. She had brought something painful up to them, and she regretted it deeply. "C'mon guys, 300 yards to the hangers." She murmured, setting off at a trot.
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Factory District: Above Ground
Kira caught up with the blond and grabbed his arm. A blast of wind whipped down the tunnel, blowing the strangers hat off, and Kira looked on in shock.
"You...you're a, a…girl!" he exclaimed, the tactless words escaping him as his mouth betrayed his shocked brain.
"Yeah, what did you think I was?" she snapped back, but wrenched her arm out of his grip and started walking away before he could reply. "You should go back. There's something I have to check up on, ALONE."
"Easy for you to say! The way back is blocked!" Kira said, coming up beside her and looking around. Grabbing her arm, he started to pull her down on of the passageways. "C'mon, this way!"
"Let GO of me, you JERK!" she yelled, and Kira looked back at her, amused. She certainly was a loud one!
"Jerk, huh?" he asked, before noticing the tears in her eyes.
"I…I just never thought that we'd get…involved!" the girl said, half sobbing.
_None of us did. Why would they do this?_ Kira thought to himself, but aloud he affected a calm and reassuring tone, saying: "C'mon, there ought to be shelters left over in the next block. C'mon now, RUN!"
Murrue Ramius gunned down yet another ZAFT pilot, and felt a small flash of triumph, but it faded quickly. Most of her men were down, and she herself was almost out of ammunition.
Behind her, she heard a voice yell something. Whipping around, she emptied the last few rounds in her current clip at the source. Shockingly, the people who made the sound were able to get out of the way, and she felt a surge of guilt as she saw what they were.
"Those were…children?" she muttered. She shook of her guilt as they dashed towards the shelters, and she reloaded her rifle, facing forward again. Not two minutes later, she heard another youthful voice yelling for her too look out behind her. She slid down off of her perch, spinning around as she did, and heard several bullets spang off of her old perch, exactly where her head would have been. She emptied an entire clip into the ZAFT pilot that had snuck up behind her, and turned to look at the voice that had saved her life. It was one of the kids she had almost shot, a young man with brown hair. Nearby, one of her last troopers went down, and an opportunistic ZAFT attempted to charge forward. Drawing her pistol, Murrue dispatched him with a pair of shots, and then gestured to the kid.
"Get down here!"
"No thanks, I'm headed for the shelters in the next block!"
"There isn't anything left behind that door!" A large explosion from the door to the next block added punctuation to Murrue's comment. The kid dashed several feet down the catwalk, and Murrue froze in horror as the kid vaulted over the edge. That was a 30 foot drop! He couldn't possibly….her mental horror screeched to a halt as blank shock overcame her. Landing lithely on the shoulder of the 105, the kid rolled onto the arm, slid down it, and jumped onto the torso. Murrue's final soldier managed to take down a ZAFT redsuit, but was promptly gunned down in return as another dashed sideways, strafing the soldier's position, killing him instantly. Murrue spun around, firing her pistol at him while he fired his rifle at her. She missed him by inches, while his short burst bit into her shoulder. The ZAFT soldier worked his weapons bolt and then dropped it, pulling out a combat knife and charging. Kira ran down to the woman, wanting to protect her. He stood in front of her, and met the ZAFT soldier's eyes. The he stared in surprise. This couldn't be! He wouldn't be here, not as a soldier!
"Ath…run?" he whispered, and the soldier's eyes widened and his jaw dropped.
"Kira?" he gasped, and the two old friends stared at each other. Neither could comprehend that the other was there, then, doing what they were.
Murrue took advantage of the pause to raise her pistol, pointing it at Athrun, who quickly hit his thrusters, flying away and over to the next unit, the X-303. He paused outside the hatch and watched as the Earth Forces officer pushed Kira into the mobile suit they were on, before jumping in and closing the hatch. As explosions shattered the hanger around them, Athrun climber into his unit, and two mobile suits broke their bonds and rose to their feet amid the flaming wreckage.
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_Second Chapter reposted._
3. Heliopolis Besieged, Part One
Note that my Kira is still kind and gentle, but he is also more mature, thanks to Ailyn's influence. Since she has been trying to push him into joining ZAFT ever-so-subtly, she has been get his naiveté under control, resulting in a more realistic world view.
If anyone one was wondering why Patrick Zala was referred to as Chairman in the last chapter, that's because he is Chairman of the National Defense Committee, NOT yet Supreme Council Chairman.
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Gundam SEED: Journey
Chapter 3
Heliopolis Besieged, part one
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Miguel Aiman, of the Le Creuset team, was bored. He had hoped that there would be at least some excitement to this mission, but the only foes he had had to engage had been a few drones and a pair of missile trucks. It was almost insulting. He stepped carefully over the streams of fleeing people as he headed for the Athrun and the others had attacked, hoping to get some more action. When he was about ten yards away, the roof of the hanger exploded, and a pair of strange looking mobile suits appeared. One was emitting Athrun's signal, but the other wasn't emitting a ZAFT transponder, or any IFF signal whatsoever. Quickly adjusting his radio, he hailed Athrun's unit.
"Athrun!" he called, turning his mobile suit to face the 303. "What…?"
"The rest of the team failed." Athrun's voice came back, sounding both bitter and distracted. "The other unit has been boarded by an Earth Forces officer."
Miguel cursed angrily and eyed the other unit with loathing. Whoever was in there was a dead person, and if there wasn't enough of the suit left to analyze, then that was too damn bad. A lot of his friends had been in that ground team. He drew his sword, turning towards the other unit. Swinging his sword at it, he expected a swift kill, but the enemy unit's armor emitted a buzz that could be heard over his audio pickups, and the unit's armor turned white and blue as it raised its arms into a defensive X over its head, blocking his sword. Miguel's eyes widened as he leapt backwards. He hadn't even scratched it!
"It's a system known as "Phase Shift Armor"." He heard Athrun explaining. "In addition to changing the unit's color, it renders the GINN's sword effectively useless, while reducing the effectiveness of projectile weapons significantly as well. At least, as long as the power holds out." Miguel's rear cameras showed Athrun's unit turn red, before Athrun used head mounted Igelstelung CIWS guns to destroy a pair of EA missile trucks that had just roared around the corner.
"I'll handle this one, Athrun! You get that unit out of here and back to the Commander before it gets damaged." Miguel said, firing his rifle at the feet of the other unit, hoping to cause it to fall, but it just staggered sideways.
Athrun stared at the screen that showed the unit Kira was in, his expression agonized. _Kira? No, of course not. How could he be here? It was someone else, that's all. Someone similar._Athrun thought to himself, displaying the ever-impressive human ability to lie to oneself in the face of overwhelming evidence to the contrary. He activated his thrusters and soared towards the harbor and from there a rendezvous with the _Vesalius_.
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Miguel, meanwhile, was busy slashing at the Strike with his sword.
"It doesn't matter how good your armor is…." He yelled triumphantly as he sent it reeling." if you can barely move!" With another blow, he sent it stumbling straight into a building. It picked itself up and dodged his next blow, backing away. Miguel grinned. He had it cornered now. There was another building complex behind it, so it couldn't back up anymore. He leveled his sword like a spear and thrust its point straight towards the cockpit.
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Inside the Strike's cockpit, Kira gasped. The rear camera's showed Mir, Tolle, Kuzzey, and Sai right behind them. If they fell or got hit, his friends would die. Time seemed to slow down as he watched the GINN's sword come towards the cockpit. Shoving the women's hands out of the way, he sent the Strike to one knee. The GINN's sword screeched off of his right shoulder, and he hit the thrusters, accelerating the Strike into a full force body slam that sent the unprepared GINN flying onto its back. Murrue was shocked. This kid had saved their lives and sent that GINN flying, and he was a civilian child!
"How did you…?" she started, but was cut off almost immediately as the kid spoke in an almost harsh voice.
"There are still people around here! If you're going to drive something like this, you need to make better use of it!"
Meanwhile, the GINN was struggling to get to its feet.
"This is ridiculous! How can they expect to run a complex machine with this kind of OS?" The kid gripped as he scanned the aforementioned OS.
"It hasn't yet reached the completion stage, it can't be helped!" Murrue protested, feeling a little insulted. Who was this kid?
"Please, move aside!" Kira urged, and she stared at him. The GINN was now almost standing again."Hurry!"
Kira brought out the built in keyboard, and his hands started flying across the keys. Murrue stared in awed shock at this teen who was effortlessly reprogramming top secret military hardware. _This kid…._ She thought to herself, a suspicion forming in her mind. The now standing GINN activated it's thrusters and charged. Kira glanced up from his keyboard and squeezed one of many triggers. His two Igelstelung, freshly calibrated, spat fire, sending a salvo of Vulcan rounds slamming straight into the GINN.
"What….?" Miguel cried in shock. All of a sudden the enemy could aim! He had to finish this quickly, before he ran out of power. He swung his blade in a brutal sideswiping slash, then gasped in shock as the enemy sidestepped easily, then lunged forward, one fist lashing out in a powerful blow that sent his GINN flying into yet another building. Kira didn't spare his opponent another glance but instead continued programming. Murrue continued to stare incredulously as he muttered to himself as he typed.
"Take the calibrations and reset the zero-moment point and CPG. Connect Control Module to Quasi-Cortex Molecular Ion Pump. Rebuild neural linkage network. Update meti-motor cortex parameters. Restart feed. Forward control, transfer functions. Correct for corealis deviation. Online!"
"What is with this guy? Now he's moving better!" Miguel grumbled, angry. He sheathed his sword, given its lack of success, and decided to opt for a longer ranged engagement. His first three rounds slammed home, rocking the enemy back on his heels but otherwise doing no damage.
Kira hit his thrusters and leaped into the air, flying with easy as he dodged the follow up shots from the GINN.
"Weapons…." He muttered absently as he brought the menu up. "Igelstelung Vulcans and Armr Schneider Combat Knives….THATS ALL THERE IS?" He shouted, before selecting the knives angrily. They popped out of their hip-mounted, internal bays and slid into waiting hands. The GINN fired on him as he landed, but he dodged every shot. The stray bullets slammed into the ground around him as he charged.
"Argh! Damn piece of Earth TRASH!" Miguel howled in rage. He was getting humiliated by a damn _Natural_, of all things!
"No! Don't do that here!" Kira shouted, as several bullets came terrifyingly close to his friends. "Stop it!" Lifting off, he flew straight at the GINN, dashing around its flank and slamming his blades into the shoulders of the GINN, instinctively knowing that this would be where the arm hydraulics connections would be. The GINN's arms hung limp as sparks flew.
"Damn it! Hydro's not responding!" Miguel growled, fiddling with his controls. "Argh!" He yanked on the handle that blew out the GINN's back panel while simultaneously activating the self-destruct. He flew away quickly on his pilot suit's jetpack, eager to get out of the blast radius. Murrue noticed his hasty departure and got an ominous feeling.
"Step away from the GINN!" she cried to the kid, but it was too late. The GINN exploded as its power core went critical, sending pieces of the mobile suit flying everywhere. Kira and Murrue yelled out as the shockwave sent the Strike flying. Kira, secure in the pilot's seat, was only shaken up, but Murrue, who was loose in the alcove behind the seat, tumbled across the cockpit. Her head slammed into its wall and she was instantly rendered unconscious.
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Inside the ruins of the main shaft, Natarle slowly regained consciousness as something bumped into her from the front and sent her drifting into the wall. She moaned in discomfort, her eyes opening as she tried to grasp her surroundings. Looking to see what had hit her, she saw the bloody corpse of one of the men who had entered the shaft with her. Gasping, and fighting down the bile in her stomach, she pushed him away and looked around.
"The ship…! Where's the Archangel?" she said aloud, before heading down the shaft.
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Meanwhile, outside the colony, a GINN raced away from the now-heavily damaged _Marseille-III_.
"We've lost control!" shouted the helmsman, and the Captain barely had time to scream before the out of control ship smashed into the side of the colony and vanished in a fireball as it crumpled like a tin can. Before the fireball had time to fade, the Moebius Zero raced past, pursuing the GINN that had downed it.
"Argh, can't we do something about this difference in battle strength?" Mu shouted as he locked on and launched his gun barrels, snapping of a shot from his main cannon as he maneuvered into position. The single shot destroyed the GINN's gun, and Mu opened fire with all four gunbarrels, blasting off the GINN's right arm even as it tried to draw its sword. It swiftly withdrew and he swooped off for other prey.
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On the bridge of the _Vesalius_, the pilot controller shouted a report.
"Olar has been damaged! Emergency landing! Fire crew to B deck!"
"In a single battle such as this, Olar has taken damage?" Ades said incredulously.
"From the looks of it, we have an unforeseen problem." Rau said calmly, still reclined comfortably in his chair. "A rather annoying fly buzzing about."
"Laser beacon detected from Miguel Aiman! It's an emergency!" called out the same controller.
"Hmm. If that weapon is effective enough to take out Miguel's mobile suit…" Rau said, pushing himself out of his chair and towards the lift at the rear of the bridge. "It's all the more reason that we can't neglect the last one."
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Murrue came to with a groan as she reached to cradle her head to try and banish the horrible headache that she had. She grimaced, however, when she moved the arm that had a bullet hole in it.
"Hey, don't move around too much. We gave you some first aid, but…" scolded a pretty young woman with clear blue eyes and brown hair from where she sat at Murrue's right side. Raising her voice, she called out over Murrue. "Hey, Kira! She's awake!"
"Great, I'll be right there!" she heard a familiar young voice yell in the immediate area of to her left. By the time she had turned her head-wincing the whole time-the young man from before was kneeling down beside her. He looked at her with concern, and her eyes widened a little. She hadn't noticed it before, but his eyes were a pale amethyst, and that in and of itself confirmed her suspicions. No Natural could have eyes of that color. She attempted to sit up, but the young man gentle laid a hand on her right shoulder to stop her. "You really shouldn't be moving, ma'am. Ath-erm, that Zaft pilot's bullet missed your shoulder blade and exited from your back, but without the ability to give you stitches we are relying on clotting to keep the wound closed. Move around too much and you will start bleeding freely again."
"Hey, have some water." The young women said gently, holding a water bottle out, which Murrue took gratefully with her good arm while the young man, Kira, propped her up enough so she could drink without choking.
"Thank you for that, I appreciate it, as well as the first aid." She said quietly after draining the bottle, leaning back heavily against the Kira for a moment before shaking herself and moving to stand.
"Easy, now. Earth Forces soldier or not, you need to be careful with that wound." Kira warned her, hands held ready to catch her if she stumbled or lost her balance. Murrue, reacting quickly at his words, pulled out her pistol and pointed it at him. His eyes widened briefly, then narrowed dangerously as he shifted in front of his female friend and tensed subtly, eyes never wavering from the gun. Murrue knew that the instant the barrel wavered in a direction that was not towards one of his friends or himself, he would be on her in a flash of Coordinator speed. "That's not too friendly; after I saved your life and Mirialia patched your shoulder up and gave you water. But then, what else can you expect from an Earth Forces soldier who is conducting illegal military affairs in Heliopolis and getting our colony attacked by ZAFT?"
"What I want to know is how you knew I was Earth Forces, and how you reprogrammed that machine." Murrue asked firmly, ignoring the guilt that bit at her when he mentioned saving her life, and his friend performing first aid. Now was not the time to be nice and gentle, it was time for answers.
"It's fairly obvious." Kira said dryly, almost sarcastically. "Let's see, the Mobile Operating System of that Mobile Suit had the O.M.N.I logo and name, ZAFT is attacking the colony…oh! And I recognizing some of the coding _because I helped create it!_Of course, I was under the impression it was for a project of Professor Kato's, but since he is Morgenroete, and Morgenroete help build this, I am going to assume that he gave you the rudimentary O.S. and was going to give you the refined versions as I finished them? Did I miss anything?"
Murrue blinked at him in shock, before nodding slowly. It all made a lot of sense, and she was rather embarrassed by some of the obviousness in the kid's logic progression. The fact that he was the whiz kid, one of them anyway, that Kato was always gushing about was surprising, but only mildly so.
"What are you planning to do now, Earth Forces officer?" the voice of the young women who had been next to her when she woke cut into her thoughts, and she looked around to see the hard glares she was receiving from all the students.
"You kids have been witness to military secrets of the Earth Forces. Until I find some superior officer to tell me otherwise, you have to stay with me. For securities sake." She replied calmly, although she had no idea where she was supposed to find a superior officer in all of this mess.
"In case you missed it," one of the other young men, a tall blond with glasses said a trifle coldly. "We're citizens of Heliopolis, and that means that we're neutral. So we don't have to do what you say."
"This is a military matter, so the military has jurisdiction. As it is, I can let you kids go if you help me with the unit and getting in touch with any Earth Forces personal remaining in the colony." Murrue snapped back, starting to lose her patience.
The students were silent for a long moment, all looking at Kira to see what he would say, as if he was the leader of the group. Which, it seemed to Murrue, he was. Hard amethyst eyes stared into her own brown for a long moment before Kira nodded sharply.
"Fine, Earth Forces officer. We play by your game, but we had better be allowed to go to the shelters soon. One more hazard level, and they will lock down, and we will be stuck out here." He said firmly, before gesturing to his friends. "I'm Kira Yamato. The girl who patched you up is Miriallia Haw, the blond kid is Sai Argyle, the bluenette with the hoodie is Kuzzey Buzzkirk, the curly haired fellow is Tolle Koenig. What do we call you, Miss Earth Forces officer?"
"Murrue Ramius, Lieutenant Murrue Ramius." She replied, finally lowering her pistol, although she did so slowly and without taking her eyes off of Kira. The young man mererly returned her look before turning and heading towards the Strike. "Where are you going?"
"To get on the radio and finish editing the O.S. while I can." He called over his shoulder as he placed on foot onto the harness and activated the winch, pulling himself to the cockpit and getting inside.
"What do you need us to do?" Sai asked quietly, and she looked at him for a long moment.
"The number 5 equipment trailer from that hanger over there." She replied, pointing to one of the few intact hangers left. "It will have weapons and a fresh power supply and charger for the Strike. After that, it depends on what else needs doing."
The kids scattered as she continued assigning tasks, and she turned to survey the wreckage that had been a peaceful colony before she and her fellows brought ZAFT down upon them. Shaking off her guilt, she sat down to wait\t for results to her orders. _It's unfortunate that their homes are in danger, their peaceful existence shattered, but for Earth to survive, it had to be done. These units were all we had, and now everything rests on the 105._
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"Geez, how many doors am I going to have to smash my way through?" Cu griped as the two girls stepped through the now-door less frame. "Honestly, talk about paranoia!"
"Just the way it is, babe, and being the big, strong man of the group, it is your unenviable job to open the doors for us pretty ladies." Faith replied, not sounding the least bit sympathetic of her lover's plight as she continued down the incredibly long passageway. "How much longer until we reach the hidden hanger, Ailyn?"
"Ten, maybe 15 minutes. Several more doors along the way, too." The ex-ZAFT spy replied, the corners of her mouth curling upwards slightly at Cu's renewed complaints.
The trio moved deeper into the hidden facility, hurrying as best they could, aware that hundreds of thousands of lives could hang in the balance.
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"Ensign Badgiruel!" Chief Petty Officer Newman said, floating up to join her outside the lounge containing the corpses of the deceased crew and command staff of the _Archangel_. "Glad to see you're alright!"
"Chief! Glad to see you as well. Come on, let's get to the _Archangel_. I have an idea." Natarle replied, glad to see someone alive, and Neumann nodded readily as the pair headed off down the access tunnel to the _Archangel_'s hidden hanger.
Fifteen minutes later, the same Chief Neumann was looking at her like she was insane. Something he had not actually ruled out as a possibility, to be honest.
"Ma'am, we don't know what condition the ship is in, and even if it is safe to start it up and launch her, we have barely a 5th of the crew we need, maybe a little bit more!"
"Just follow the computers instructions!" she snapped in reply, before tacking on a dig to get him moving. "You _can_ handle that, can't you Chief?"
Neumann merely gave her a cold glance before getting into the pilot's seat and beginning the long startup sequence, silently cursing the Captain and other senior officers for leaving him with nothing more than a wet-behind-the-ears rookie Ensign with delusions of grandeur. Hell, he could smell the Academy on her still, and he had been serving in the military before this war had even thought about getting started, as the numerous gold rings on the sleeve of his dress uniform coat attested to. Still, she had given him and order, and Chief Petty Officer Newman was going to follow them, even if only to show Badgiruel that he was the best at what he did, and didn't need instructions from a newbie like her!
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That's a wrap for now! Obviously, some things are changing from the actual anime, but all with good reasons. After all, if I make it to similar to canon, what's the point in writing it? Anyway, REVIEW!
End file.
| fanfiction |
How to find the compounds that form the solid (chemical formulas)
If we have a solution that contains water and potassium sulfate (K2SO4).
And we add to this solution :
Du magnesium chloride (MgCl2) and lead nitrate (II) (Pb(NO3)2)
What would the compounds that form the solid (chemical formulas)?
Where is my mistake?
2 H2O + K2SO4 --> 2 KOH + H2SO4
MgCl2 +Pb(NO3)2 --> PbCl2+Mg(NO3)2
I feel something that doesn't make sense
Your first reaction is wrong. You can't just form sulphuric acid from its salt, or more simply sulfate. It will just form bisulfate in some extent, with an equilibrium reaction, not a one way arrow.
PbCl2 formation is expected since it is poorly soluble it will be precipitated.
Look for the most insoluble union in similar cases, it will be precipitated.
In the first reaction with water and potassium sulfate, Postassium Sulfate (K2S04) does not react with water(H2O) but rather dissolves in it. And since it readily dissolves in water, it is considered readily soluble and there is no hydrolysis. It neither releases or absorbs and energy and is considered a dissociation reaction. In the second reaction with the magnesium chloride and lead nitrate, the products will be PbCl2(s) and Mg(NO3)2(aq). Lead chloride is a solid because lead and chloride and form a nonsoluble compound whereas NO3 is very soluble so it makes Mg(NO3) soluble in an aqueous solution.
| stackexchange/chemistry |
the @xmath0cdm model a universe dominated by cold dark matter and a cosmological constant is a successful model of the universe at large scales @xcite . however , as more observations are made and computational power becomes available , discrepancies in the model have been found below galactic scales .
cosmological simulations show that the dark matter halo of a milky - way - sized galaxy , in addition to having a smooth component with well - known density profiles @xcite , should be populated by substructures , or subhalos @xcite .
this theoretical prediction has not been supported by observational evidence , as many efforts over the past two decades have failed to find enough satellite systems in the milky way to account for the predicted abundance @xcite .
this discrepancy is called the _ missing satellite problem_. competing solutions to the missing satellite problem can be roughly classified into two types astrophysical and physical .
astrophysical solutions , on one hand , postulate that the predicted subhalo abundance is correct , but the subhalos have too little stellar content to be observable directly . for example , reionizing radiation or stellar feedback @xcite can suppress star formation in a subhalo . this class of solutions is founded on the absence of baryonic processes in those cosmological simulations which predicted the subhalo abundances . physical solutions , on the other hand , postulate that the predicted subhalo abundance is incorrect , as our understanding of cdm may be incomplete .
alternative dark matter solutions , such as warm dark matter @xcite , self - interacting dark matter @xcite , or inflationary models with non - scale invariance @xcite offer mechanisms to suppress structure formation at small scales .
clearly , the predicted difference between these two types of solutions is the number of subhalos . in order to test the @xmath0cdm model at sub - galactic scales , measuring
the true abundance of subhalos is an important step .
tidal streams or simply `` streams '' are remnants of stellar systems such as globular clusters ( gcs ) or dwarf galaxies ( dgs ) as they are tidally disrupted by a massive host . when the stars become unbound from the progenitor , the stars trace an elongated tail which wraps around the massive host .
tidal remnants have long been useful probes for studying the gravitational potential of the milky way ( e.g. , * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
in particular , @xcite first used simulations to show that the encounters between the stream stars and subhalos can dynamically heat up the stream , which can be used to probe the presence of subhalos .
moreover , a key influence that subhalos have on streams is that the stream stars near the point of the encounter get scattered into different orbits by the perturbation , causing an abrupt decrease in stellar density in that region of an otherwise smooth stream . using the abundance of subhalos obtained from high - resolution simulations @xcite
, it has been predicted that streams in the milky way described by the @xmath0cdm model should contain many `` gaps '' @xcite . in the past decade , many streams in the milky way have been found ( see @xcite for a list ) .
two streams of particular interest to us are pal-5 @xcite and gd-1 @xcite .
both streams are detected as long , narrow tidal tails with length - to - width ratio of @xmath3 .
these two streams are interesting as they show varying densities longitudinally along the streams .
it is not clear whether those density variations correspond to subhalo perturbations .
other possible origins of those density variations include clumping due to the coherence in the epicyclic orbits of stream stars @xcite and jeans instabilities @xcite .
the ultimate goal of this study is to test whether the gaps observed in streams are consistent with the prediction by the @xmath0cdm model . @xcite and
@xcite independently made the first predictions by simulating ideal streams with massless particles in the presence of orbiting subhalos .
in particular , @xcite derived analytical expressions of the gap formation rate as a function of a stream s intrinsic properties , which are readily comparable to observations .
however , neither of the aforementioned studies self - consistently modeled the realistic disruption of the progenitor system . in this study
, we measure the gap formation rate by modeling a stream s formation and its interaction with subhalos using n - body simulations .
this paper is organized as follows .
section 2 describes the details of our simulations , including the subhalo abundances and density profiles that we adapt , and the details of the star cluster and the resulting model stream .
section 3 focuses on the method of detecting gaps in a simulated stream .
the method of using match filters is inspired by analyses for observations , but modified here to analyze simulations .
section 4 contains detailed discussion of our key results , including the phenomenology of gaps and comparisons with previous analytical predictions and observations .
section 5 is a summary of our results .
the host galaxy is modeled as a dark matter halo , as well as a set of subhalos which orbit around the halo s potential .
a milky - way - sized halo is modeled with a static spherical navarro - frenk - white ( nfw ) profile @xcite with @xmath4 kms@xmath5 located at @xmath6 .
each individual subhalo is modeled by a spherical hernquist profile @xcite @xmath7 for simplicity , compared to einasto profiles which produce better fits in simulations but are more complicated to compute @xcite .
we use the formula found in @xcite , which approximates the results from both @xcite and @xcite , where @xmath8 is independent of galactocentric position , and is related to @xmath9 by @xmath10 we use the mass and spatial distributions of the subhalos from the results of the aquarius simulations @xcite , where the mass function is independent of the spatial distribution .
the mass function is a power law @xmath11 and the spatial distribution follows an einasto profile @xmath12 \right\}.\ ] ] the subhalos velocities are initialized with a gaussian distribution where the velocity dispersion is the solution to the isotropic jean s equation @xcite using the halo s potential . the subhalos orbit around this potential as test masses .
the progenitor of the stream , which is an approximation to a globular star cluster , is initialized using @xmath13 particles of equal mass as a king model with parameters @xmath14 , total mass @xmath15 , and a core radius of @xmath16 kpc .
this results in a zero - density radius of @xmath17 kpc .
each n - body particle in the system interacts with the dark matter halo s and subhalos potentials . with the galactic center at the origin , the satellite is initially put at @xmath18 kpc and velocity @xmath19 kms@xmath5 .
the resulting orbit is confined on the @xmath20-plane with eccentricity @xmath21 , peri- and apogalacticon at @xmath22 and @xmath23 , respectively .
the azimuthal and radial periods are about 0.70 gyr and 0.47 gyr , respectively .
we use gadget-2 @xcite for our n - body simulations .
since the public distribution does not have functionality for external potentials , we modify the code such that in every time step , an external acceleration term which accounts for the potentials of the halo and all the subhalos is added to the accelerations of all the particles after their n - body interactions are computed .
each of our simulations lasts 10 gyr , and we impose a maximum time step of 1 myr .
the particle softening is 5 pc .
each simulation produces 500 snapshots , one every 20 myr , and each consists of the positions and velocities of the n - body particles and subhalos .
the star cluster is modeled as an n - body system which forms a stream as the cluster is disrupted by the tidal field of the massive host . when the cluster is isolated , the energies of the individual particles are conserved to a few percent over 10 gyr . using the softening as minimal impact distance
, the relaxation timescale in the core is @xmath24 , which is much greater than the orbital period at @xmath25 .
figure [ fig : massloss ] shows the mass enclosed inside 0.103 kpc of the star cluster s center it is orbiting in the absence of subhalos . because the stream is repeatedly stretched and compressed longitudinally along the eccentric orbit , the mass enclosed in a fixed radius is not always decreasing in time .
the bottom panel of figure [ fig : massloss ] shows that the mass loss is driven purely by bulge shocking @xcite , as the periodic bursts have exactly the same period as the radial period of the orbit .
.,width=336 ] figure [ fig : stream_sigma_width ] shows the velocity dispersion and traverse fwhm of our simulated stream without any subhalos .
the stream is chosen so that its properties are on the same orders of magnitude as pal-5 @xcite and gd-1 @xcite . in the derivation in @xcite ,
the gap formation rate is expressed as a function of galactocentric distance of the orbit and width of the stream . for our simulated stream ,
we adapt average values of 22 kpc and 0.3 kpc , respectively , over the entire stream . in a time
independent and spherical potential @xmath26 , three interesting conserved quantities are the radial , azimuthal , and latitudinal actions where @xmath27 respectively @xcite , where @xmath28 and @xmath29 are the apo- and pericentric distances of the orbit , respectively .
since our stream s orbital plane is the @xmath20-plane , @xmath30 ( though not exactly 0 because the stream has a finite thickness ) , so we only consider @xmath31 and @xmath32 . for simplicity
, we ignore the progenitor and only consider the particles which have already escaped from the cluster , so when computing @xmath31 we assume that the potential due to the progenitor s potential is negligible .
@xmath31 and @xmath32 are useful since their dispersions are the origins of the stream s average width .
for example , in the epicyclic approximation @xcite where @xmath33 and @xmath34 are the epicyclic frequency and amplitude , respectively , the radial motion can be written as @xmath35 where @xmath36 is an arbitrary phase angle .
then it can be shown that @xmath37 where @xmath38 and @xmath39 are the orbital frequency and radius of the guiding center , respectively .
clearly , dispersions in both @xmath34 and @xmath39 can affect the width of the stream .
therefore , conserved quantities @xmath31 and @xmath32 are especially valuable in understanding the width of the stream .
figure [ fig : jr_lz_distribution ] shows the distributions in @xmath40 when the stream is 8 gyr old .
the two lobes at higher and lower @xmath32 are the trailing and leading branches of the stream , respectively .
the absolute dispersions in @xmath31 and @xmath32 are on the same order of magnitude , in rough agreement with the formula @xmath41 @xcite . in section [ sec : gap_morphology ] , we will show how the spread in actions affects the morphology of stream gaps .
plots similar to figure [ fig : jr_lz_distribution ] can be found in @xcite where they used angle - action variables extensively to study the relation between the stream and the orbit .
a similar plot can also be found in @xcite , but in scaled energy and angular momentum which were first used by @xcite to describe the dynamics of tidal streams . for our stream at 8 gyr without any subhalos .
along the entire stream with the progenitor masked out , 50,000 unbound particles were randomly selected to be placed on this map .
each pixel in this map represents the density of particles in that bin .
the two symmetric lobes are the two branches of the stream .
similar plots can be found in @xcite , and a plot in scaled energy and angular momentum in @xcite.,width=336 ]
@xcite divided their subhalo mass spectrum into separate mass ranges in order to resolve the contributions from each mass range . using the same approach
, we divide the subhalos from @xmath42 to @xmath43 into 13 mass ranges ( table [ table : subhalo_massrange ] ) .
each mass range contains incrementally more subhalos , starting from the higher mass end toward the lower mass end . in the higher mass end
, the mass ranges are chosen such that the increase in subhalo masses are roughly the same . in the lower mass end ,
the mass ranges are chosen such that the increase in subhalo numbers are roughly the same . in each set of subhalos
, we reduce their numbers by eliminating those whose orbits are always inside the perigalacticon and outside the apogalacticon of the progenitor s orbit .
the largest subhalo in our simulations has a length scale of @xmath44 ( equation ( [ eqn : subhalo_size ] ) ) , so all the subhalos with perigalacticon ( apogalacticon ) larger ( smaller ) than that of the progenitor s orbit by @xmath45 will interact minimally with the stream .
this allows us to safely eliminate the subhalos with perigalacticon larger than @xmath46 , and apogalacticon smaller than @xmath47 .
we run 14 simulations 1 `` smooth stream '' without any subhalos , and 13 `` @xmath0cdm streams '' containing the subhalos in the mass ranges in table [ table : subhalo_massrange ] with identical initial conditions and dark matter halo potential .
this allows us to resolve the effects of the lower mass subhalos whose existence are in question .
cccccc @xmath48 & 203 & @xmath49 & 30 & @xmath50 + @xmath51 & 593 & @xmath52 & 98 & @xmath53 + @xmath54 & 1,392 & @xmath55 & 220 & @xmath56 + @xmath57 & 3,160 & @xmath58 & 476 & @xmath59 + @xmath60 & 7,038 & @xmath61 & 1,101 & @xmath62 + @xmath63 & 16,394 & @xmath64 & 2,576 & @xmath65 + @xmath66 & 41,515 & @xmath67 & 6,539 & @xmath68 + @xmath69 & 67,599 & @xmath70 & 10,563 & @xmath71 + @xmath72 & 91,601 & @xmath70 & 14,337 & @xmath73 + @xmath74 & 121,181 & @xmath75 & 18,872 & @xmath73 + @xmath76 & 145,220 & @xmath75 & 22,578 & @xmath77 + @xmath78 & 171,163 & @xmath75 & 26,586 & @xmath77 + @xmath42 & 194,726 & @xmath75 & 30,253 & @xmath77 gaps are manifested as local minima in the linear density along the stream . to obtain the linear density along a stream in an eccentric orbit , we first fit the stream with two degree-6 polynomials
one each for the leading and trailing streams in polar coordinates centered at the galactic center .
the points along each line are spaced at 0.002 radians apart . between each pair of
adjacent points a cylinder of radius 1 kpc is drawn which lies lengthwise along the pair of points .
the linear density is then the number of particles inside this cylinder divided by the length of the cylinder .
this spacing is chosen so that the gaps as wide as the stream are well resolved .
the method used to find gaps in stream densities is inspired by the technique first used by @xcite to find gaps in observations .
they used matched filters of the estimated shape of a density gap at various length scales to look for positions in the stream which potentially contain gap signals .
the filter consists of a local minimum which is the underdensity of stars , and two local maxima on both sides of the minimum due to conservation of mass ( figure [ fig : filter_scales ] ) .
this method is similar to the wavelets approach , where the integral of the filter function is constructed to vanish inside a certain domain .
the potential gap signals are then easily identified as local maxima in the convolution between the filter and the signal . to obtain the significance of each potential gap signal against noise , @xcite produced bootstrap samples from the sky background . with the simulations in this study , we can estimate noise levels using the smooth stream . note that the `` smooth stream '' itself is not totally smooth . as we will show in section [ sec : gap_counting ] , there are large density fluctuations near the progenitor due to the coherent in epicyclic motion of the particles , as first explained by @xcite .
when the particles become unbound from the progenitor , they pile up near the base of their cycloid trajectories , creating epicyclic overdensities ( hereafter eo ) along the stream . although this intrinsic process to mimic gaps can be confused with gaps caused by subhalos , eos are only apparent within @xmath79 away from the progenitor in our streams ( figures [ fig : density_gaps_whole_massrange0 ] and [ fig : density_gaps_central_massrange0 ] ) .
the details of the dynamics of eos is beyond the scope of this study , but this effect can be understood in terms of orbital actions .
eos occur due to coherent epicyclic motions of the particles , which nevertheless have finite dispersions in orbital actions ( figure [ fig : jr_lz_distribution ] ) and are not perfectly coherent .
therefore , although the escaping particles orbits stay roughly coherent in the first few clumps , their orbits eventually drift out of phase as they travel along the stream .
this explains why the density peaks of eos further downstream are not as apparent as the peaks closer to the progenitor @xcite . after masking @xmath80 of the smooth stream centered at the progenitor ,
the rest of the smooth stream is simply noise .
our method to find gaps in a given stream can be summarized as follows . 1 .
compute @xmath81\ , f\left ( \frac{2(x - x^\prime)}{s } \right ) dx^\prime \label{eqn : cs } \ ] ] where @xmath82 is a matched filter function @xcite , and @xmath83 is the filter scale .
@xmath84 is the mean of @xmath85 inside @xmath86 $ ] , the domain in which the integral of @xmath87 itself vanishes .
each potential gap signal would appear as a local maximum in @xmath88 .
this convolution is computed at 12 logarithmically spaced filter scales from 0.1 to @xmath2 ( figure [ fig : filter_scales ] ) , and then all the local maxima of each stream are sorted by @xmath89 .
2 . repeat the above step using the smooth stream , but with @xmath90 kpc from the progenitor masked along the stream .
the set of local maxima in @xmath91 from this convolution is the noise , which are also sorted by @xmath92 .
each local maximum in the signal set are compared against the noise set .
a signal element at any position along either branch of the stream that ranks higher than 99% in the noise set is identified as a gap .
inevitably , this method may detect the same gap at 99% confidence at different scales but in very close proximity . to avoid over - counting
, we employ the following scheme to eliminate overlapping gaps .
first , we define an overlap as two gaps whose @xmath89 local maxima are identified at @xmath93 and @xmath94 that are within @xmath95 away from each other along the stream , where @xmath96 .
when this occurs , the gap with higher @xmath89 eliminates the lower .
our gap detection method requires no prior knowledge whether a given gap is an eo or a subhalo perturbation , both of which can be identified as a series of over- and under - densities .
when we count the number of gaps in the end , eos will be included .
one key result of our study is that gaps due to eos are distributed very differently in lengths compared to gaps due to subhalo perturbation . .
with a physical scale @xmath83 , the integral of @xmath87 vanishes inside @xmath97 .
the roots of each filter are located at @xmath98 so that the gap length is simply the distance between the roots .
we search for gaps at 12 logarithmically filter scales from 0.1 to @xmath2 in order to minimize the chance of detecting the same gap at multiple scales.,width=336 ]
according to @xcite , gaps in general are diagonal and not perpendicular to the stream due to a gradient in angular momentum ( hence a gradient in orbital velocities ) across the width of the stream , which can shear a gap longitudinally .
figure [ fig : jr_lz_distribution ] allows us to estimate the shearing effect in our streams using the distributions in angular momenta . for each branch of the stream ,
the fwhm spread in angular momentum is about @xmath99 . for a narrow stream at @xmath100 ,
the spread in velocity is @xmath101 .
therefore , a gap that spans the width of the stream will be sheared by less than @xmath102 per gyr .
figures [ fig : stream_maps_smooth ] and [ fig : stream_maps_lcdm ] show the time evolution of the smooth and a @xmath0cdm stream , respectively , from 7 to @xmath103 .
the eos near the progenitor appear to shear by different amounts at different times , but this is due to the radial oscillation in the orbit where the radial period is @xmath104 . upon closer inspection of figure
[ fig : stream_maps_lcdm ] , we also note that not only do subhalo gaps have complicated morphologies , but their orientations flip back and forth in a radial period due to the spread in @xmath31 . nevertheless ,
comparing panels of the same radial phase at one radial period apart , the end points of each gap across the width of the stream do not shift by any appreciable amount .
rather , the morphologies of the subhalo gaps are already apparent as each gap first appears .
if the linear density of a stream is calculated by integrating the entire thickness of the stream in traversing slices along the stream , then the contrast of the gap will be reduced .
this is because the edges of the gaps are not perfectly straight across the width of the stream , so dividing the stream into slices will smear out the density contrast . to investigate how much the smearing will affect gap detection , we calculate the linear densities in two ways .
( 1 ) integrating cylindrical slices of radius 1 kpc along the stream , hereafter the `` whole width , '' where 1 kpc was chosen to cover the entire thickness of the whole stream . ( 2 ) integrating only the cylindrical slices of radius 0.04 kpc centered along the best fit line of each branch of the stream , hereafter the `` central width , '' where 0.04 kpc is chosen to mimic the gd-1 s observed width of 0.08 kpc @xcite .
this central width then encloses about 30%40% of the mass of the whole width , depending on its orbital phase where , for example , the stream is radially compressed during pericentric passage .
the stream is then aligned to cartesian coordinates where the horizontal axis is the offset position along the stream from the progenitor , and the vertical axis is the radial offset from the galactocentric distance of the progenitor .
this is done by tracing a best fit line along the stream . for each segment in the line ,
the particles in between the end points of the segment are rotated such that the galactic center points toward the @xmath105 direction in this plot .
note that the vertical axis has been scaled 30 times the larger than the horizontal axis.,width=336 ] subhalos from 7 to @xmath103 , aligned to cartesian coordinates similar to the smooth stream in figure [ fig : stream_maps_smooth ] .
compared to the smooth stream , this @xmath0cdm stream shows much more structures at various scales . in general , whether by eos ( mostly inside @xmath106 ) or by subhalo perturbations , gaps have complicated morphologies and do not even have straight edges across the width of the stream.,width=336 ] figures [ fig : density_gaps_whole_massrange0][fig : density_gaps_central_massrange13 ] show the densities along the whole and central widths of the smooth stream and a @xmath0cdm stream from 3 to @xmath107 .
the streams younger than @xmath108 are not shown as the stream is @xmath109 long at those ages , so the gaps are dominated by very prominent eos . moreover
, the stream itself does not yet have a large enough cross section to produce enough gaps for meaningful statistics . in each panel ,
the shaded columns represent the gaps that are found on the scale of the columns widths .
although these gaps are identified as being 99% significant , the density contrasts of the gaps have not been quantified . for the rest of this paper , we assume that all gaps identified at 99% significance can be observed . note that because the gap finding process is applied independently to each snapshot , the shaded columns do not necessarily represent the time evolutions of individual gaps .
instead , the shaded columns show the general distributions of gaps both in space and in gap lengths .
our gap finding method is has a number of problems . in the smooth stream ( figures [ fig : density_gaps_whole_massrange0 ] and [ fig : density_gaps_central_massrange0 ] ) , our method by construction identifies 1% of the noise as gaps
this is why there can be spurious gaps detected well beyond 5 kpc away from the progenitor , even though eos tend to form very close to the progenitor .
also , the overall profile of the stream density can sometimes be confused as a gap as well .
one example is a gap at @xmath110 at @xmath111 in figure [ fig : density_gaps_whole_massrange13 ] , where a smooth density gradient from 3 to @xmath112 is mistaken as the right half of a long gap . at the 95% confidence limit , both kinds of false positives are quite common and can often be identified by eye .
for the results below , we show gaps that are 99% significant , which minimizes the occurrence false positives . .
the progenitor is centered at @xmath113 and is masked out .
shaded columns are gaps identified at 99% confidence at the scale depicted by the columns widths.,width=336 ] along the central line of the stream.,width=336 ] cdm stream with subhalo masses @xmath114 , integrated for the whole thickness of the stream.,width=336 ] cdm stream with subhalo masses @xmath114 , integrate for only a cylinder of diameter @xmath115 along the central line of the stream.,width=336 ] following the idealized experiments in @xcite , @xcite derived an analytical relation between gap formation rate @xmath116 which is the cumulative number of gaps longer than length @xmath117 per unit stream length per unit time as a function of gap length ( hereafter the `` gap spectrum '' ) such that @xmath118 where @xmath119 , and we adapt @xmath100 for the average galactocentric radius of the stream . in this section
we aim to study the validity of equation ( [ eqn : gaprate_gapsize_formula ] ) in our self - consistent stream .
we set the `` length '' of each gap as the scale @xmath83 of the matched filter which identified the gap ( section [ sec : gapfinding ] ) figures [ fig : density_gaps_whole_massrange0 ] and [ fig : density_gaps_central_massrange0 ] show the gaps identified in the smooth stream integrated using the whole thickness and central thickness , respectively .
clearly , the gaps due to eos are clustered at @xmath79 on both sides of the progenitor , and all the gaps have very similar sizes .
the measured @xmath116 would peak at short gaps and quickly drops off beyond @xmath120 .
equation ( [ eqn : gaprate_gapsize_formula ] ) is meant to describe an idealized gap spectrum produced by subhalos , and not by eos .
a key result of this study , as discussed below , is that the gap spectrum for subhalo gaps looks very different than the gap spectrum for eos .
the existence of gaps longer than @xmath44 would be an indication that processes other than eos are responsible for the gaps .
furthermore , subhalo gaps can be found everywhere along the whole stream .
eos can only be observed in the immediate vicinity of the progenitor .
as an ideal case , equation ( [ eqn : gaprate_gapsize_formula ] ) ignores the visibility of gaps when the same position of a stream suffers impacts by multiple subhalos at different times .
for instance , after one major impact by a massive subhalo which results in a long and high contrast density gap at an early time , subsequent impacts by less massive subhalos in that same region at a later time may not be visible .
gap overlapping can be minimized by the following experiment .
we run 13 separate simulations with the same initial conditions as the star cluster , but the subhalo masses are selected differentially from table [ table : subhalo_massrange ] .
this allows each stream to interact with an independent set of subhalos of a very small range of masses .
overlapping can still occur within the same simulation for each set of subhalos ( hence a small number of gaps can still be eliminated ) , but to a much lesser extent than using integrated mass ranges .
figure [ fig : ru_summed ] shows the measured gap spectrum from the gaps collected from all 13 simulations using independent sets of subhalos . in the top panel which includes all gaps , the measured gap spectrum matches equation ( [ eqn : gaprate_gapsize_formula ] ) reasonably well
however , this is a coincidence as the gaps contain eos which are not described by equation ( [ eqn : gaprate_gapsize_formula ] ) . in an attempt to eliminate eos , in the bottom panel of figure [ fig : ru_summed ] ,
the gaps that are located within @xmath2 away from the progenitor are eliminated .
when computing the gap formation rates in these cases , the number of gaps are divided by a stream length which is reduced by @xmath80 and a stream age which reduced by @xmath121 ( i.e. , the age of the stream when it is @xmath80 long ) .
this allows us to facilitate a fair comparison of gap spectra against the cases which include all gaps in the entire stream . comparing the two panels in figure [ fig : ru_summed ]
, we can see the masking of the @xmath80 around the progenitor reduces the abundance of shorter gaps .
this is expected since that region of the stream contains mostly eos which occur at scales @xmath122 . in general
it is difficult to tell whether a given gap within @xmath2 is due to eos or subhalos , so in the process some subhalo gaps near the progenitor may have been eliminated as well .
whether equation ( [ eqn : gaprate_gapsize_formula ] ) is a good description of the gap spectrum in a general stream likely requires more simulations with varying orbital parameters .
nevertheless , it is apparent that the gap spectrum does not depend strongly on the age or the integrating width for the linear density of the stream .
however , it is still an ideal case since a stream realistically interacts with all the subhalos at the same time . as we show in the following section
, gap overlapping can significantly alter the gap spectrum . .
in the top panel , all gaps identified ( including eos ) are included in the measured gap spectra . in the bottom panel ,
the gaps located within @xmath2 away from the progenitor are eliminated , and the stream lengths and ages are adjusted .
since the gaps are mostly independent , the gap spectra follow the analytical prediction reasonably well .
, title="fig:",width=336 ] . in the top panel ,
all gaps identified ( including eos ) are included in the measured gap spectra . in the bottom panel ,
the gaps located within @xmath2 away from the progenitor are eliminated , and the stream lengths and ages are adjusted .
since the gaps are mostly independent , the gap spectra follow the analytical prediction reasonably well .
, title="fig:",width=336 ] we now consider the validity of equation ( [ eqn : gaprate_gapsize_formula ] ) for stream gaps in the presence of all subhalos in each cumulative mass range in table [ table : subhalo_massrange ] .
figure [ fig : ru_all ] compares the measured gap spectra of both the whole and central streams for three mass ranges , with and without the gaps within @xmath2 away from the progenitor .
clearly in all cases , the ideal gap spectrum over estimates the measured spectrum by nearly an order of magnitude due to gap overlapping .
similar to the simulations with independent sets of subhalos ( figure [ fig : ru_summed ] ) , the gap spectra produced by full sets of subhalos do not have strong dependence on stream age and integrating width .
the only exception is the youngest stream shown at 5 gyr which consistently has higher @xmath116 than the older streams .
however , when the gaps near the progenitor are eliminated , the numbers of gaps at @xmath111 in all cases decrease significantly , where the gap spectra are dominated by a single gap at @xmath123 , and a number of extremely short gaps .
this is likely because the stream is still young , and the effective length of the stream ( after masking @xmath80 centered at the progenitor ) is only @xmath124 .
this eliminates a significant part of the stream , making its stream statistics unreliable .
the weak dependence of the gap spectrum on the integrating width for linear density is also worth noting .
figure [ fig : stream_maps_lcdm ] shows that gaps in general have much more complicated morphologies than straight edges across the width of the stream .
the explanation for these morphologies requires detailed understanding of how subhalo perturbations manifest in a self - consistent stream , which is beyond the scope of this study .
while @xcite studied the dynamics of subhalo perturbations for an idealized stream , we defer the self - consistent case to a future study .
perhaps the most surprising result is that the gap spectra do not show obvious dependence on subhalo masses .
the spectra are difficult to distinguish between the mass range of subhalos which causes the gaps .
this is in disagreement with @xcite which derived a relation between the length of a gap and the mass of the subhalo that caused it such that @xmath125 from this formula , it is reasonable to expect the inclusion of lower - mass subhalos to show more gaps at the shorter end . in their ideal simulations , however , @xcite did not account for the time evolution of each gap .
an example can be seen in figures [ fig : density_gaps_whole_massrange13 ] and [ fig : density_gaps_central_massrange13 ] .
the gap located at about @xmath126 at @xmath127 evolves into a much longer gap centered at about @xmath128 at @xmath107 .
evidently equation ( [ eqn : length_mass ] ) requires revision for self - consistent streams before it can be used to understand the relation between gap spectra and subhalo masses . in all cases . in the top three panels ,
all gaps identified ( including eos ) are included in gap spectrum . in the bottom
three panels , the gaps located within @xmath2 away from the progenitor are eliminated , and the stream lengths and ages are adjusted .
compared to figure [ fig : ru_summed ] , the simulated gap spectra here no longer follow the analytical prediction because of overlapping between the gaps.,title="fig:",width=336 ] in all cases . in the top three panels ,
all gaps identified ( including eos ) are included in gap spectrum . in the bottom
three panels , the gaps located within @xmath2 away from the progenitor are eliminated , and the stream lengths and ages are adjusted .
compared to figure [ fig : ru_summed ] , the simulated gap spectra here no longer follow the analytical prediction because of overlapping between the gaps.,title="fig:",width=336 ] we now consider the issues when interpreting gap spectra from observations .
a gap spectrum for gd-1 has been observed by @xcite , but we emphasize that the gap spectra from our simulated streams in this study should not be directly compared to the one in @xcite because our models for both the star cluster and the galaxy halo are chosen in favor of a simple interpretation , and may be missing some complications discussed in section [ sec : other_effects ] .
we first project each stream onto sky coordinates . for simplicity
, we put the hypothetical observer at the center of the galaxy , and then project each particle onto the azimuthal and altitudinal plane in galactocentric coordinates .
since the our stream progenitor is orbiting along the @xmath20-plane in a spherical potential , the smooth stream appears as a straight line along the azimuthal direction , and each @xmath0cdm stream appears only a few degrees off the azimuthal plane due to subhalo perturbations .
the density along the stream is simply the number of particles in bins of @xmath129 in the azimuthal direction .
the match filter approach to detect gaps remain the same as the analysis above , but the 12 filter scales ( figure [ fig : filter_scales ] ) are now logarithmically spaced in angular units from @xmath130 to @xmath131 , and the noise levels are obtained from the regions at @xmath132 , rather than @xmath133 , away from the progenitor .
the choice of bin size and filter scales are on the same orders of magnitude as @xcite , but putting the hypothetical observer at the galactic center may affect angular sizes by factors of @xmath134 . to ensure that the behaviors of the simulated streams are typical , we simulate each @xmath0cdm stream 10 times with the same initial conditions for the star cluster , but different realizations of the same subhalo distributions . at the end
we take the median numbers of gaps of the 10 streams to avoid outliers .
one surprising result from section [ sec : lcdm_stream_with_all_subhalos ] is that the gap spectrum has little to no dependence on age and subhalo masses .
to investigate what this means when interpreting observations , the top panel of figure [ fig : numgaps_time ] shows the cumulative numbers of gaps longer than @xmath130 ( i.e. , all gaps detected in the entire stream ) as functions of time . at @xmath135
, the numbers of gaps due to subhalos vary according to the orbital phase of the stream progenitor .
the `` bursts '' in numbers of gaps in the @xmath0cdm streams occur when the streams are stretched as they passes through the pericenters of their orbits . at @xmath136 ,
on the other hand , this correlation does not exist for two reasons .
first , our detection method ( section [ sec : gapfinding ] ) uses the parts of the stream that are @xmath133 ( before sky projection ) or @xmath132 ( after sky projection ) away from the progenitor in order to estimate noise . at @xmath136 ,
the length of the stream varies between a few to @xmath137 , which may not be long enough to estimate noise .
second , in only @xmath111 the stream does not yet have enough time and to interact with subhalos .
both the total number of gaps and the dynamical age of the stream are difficult to measure , as the some parts of a stream may not be observable .
we define a more useful quantity @xmath138 which is the cumulative number of gaps longer than a given gap length per unit stream length . in other words , leaving the age of the stream as an unknown , @xmath138 differs from @xmath116 in section [ sec : gap_size_distribution ] by a normalization by age , and that @xmath138 is after sky projection . in the next section
we show that gaps due to eos and subhalos have very different @xmath139 distributions which are directly observable . .
each colored line represents the median of 10 realizations of an identical subhalo distribution ( with @xmath43 as upper mass limit ) , and the black thick line represents the smooth stream .
bottom : the vertical dashed lines are visual guides which show that the variation of the number of gaps are correlated with the orbital phase of the stream progenitor .
these plots show that the cumulative number of gaps in a stream on average is increasing in time , but instantaneously the number of gaps observable can have an even stronger dependence on the orbital phase of the stream than on the stream s dynamical age or subhalo masses.,width=336 ] another important distinction between simulations and observations is the signal - to - noise ratio ( s / n ) . at 5 and @xmath103 our smooth stream
is represented by about 60,000 and 80,000 particles in total , respectively ( figure [ fig : massloss ] ) .
@xcite estimated that the @xmath140 visible segment of gd-1 consists of 3000 stars . at an average distance of @xmath141 ,
the visible segment is @xmath141 long . in our simulations , after 5 and @xmath103 , the average stream lengths are about 20 and @xmath142 , respectively ( figure [ fig : massloss ] ) .
this means that our simulated stream should be represented about eight times fewer particles in order to be comparable to observations . with the progenitor masked , we reduce the number of particles in the stream by randomly sampling the stream using two , four , and eight times fewer particles than the original stream .
the particle reduction applies to both the stream of interest and the smooth stream which is the source for estimating noise .
this allows us to investigate the importance of high s / n .
note that in our simulation each particle is equivalent to about @xmath143 , which is less massive than the typical stars that are detected in observations .
our simulations are not meant to be physical models of the real stream . in this section ,
we are only concerned about matching the numbers of particles in the simulations to the numbers of stars in the observation .
as the stars escape from the progenitor , the stream s self - gravity becomes negligible @xcite , and the particles masses are no longer important .
figure [ fig : reduction_gaps ] shows the density profiles of the @xmath0cdm stream with subhalo masses @xmath144 at @xmath103 projected onto the sky .
the panels show the gaps detected in the same stream after three levels of particle reduction . even after reduction by a factor of eight
, the stream appears to have retained most of its gaps despite a lower s / n . in figure [ fig : gd1_reduction ] , each line shows the median of ten gap spectra from the same stream but with 10 realizations of the same subhalo distribution . in each panel , the solid ( dashed ) lines represent the times when the progenitor is at the pericenter ( apocenter ) of its orbit .
when the stream is compressed and stretched as it oscillates radially ( see figure [ fig : massloss ] ) , its length can differ by up to a factor of two .
careful inspection of figures [ fig : numgaps_time ] and [ fig : gd1_reduction ] shows that during pericentric passages , the numbers of gaps are at maximum , but @xmath138 is at minimum because the stream length is also at maximum . for a @xmath0cdm stream at high s / n ( upper left panel in figure [ fig : gd1_reduction ] ) , the gap spectra are not sensitive to this oscillation , except with an excess of shorter gaps and fewer longer gaps , which are expected as the stream , including its longitudinal structure , is compressed during apocentric passage . at low s / n ( lower left panel in figure [ fig : gd1_reduction ] ) , however , the gap spectrum during apocentric passage is consistently higher than that during pericentric passage .
this is because the length of the stream is insensitive to the s / n , but the number of gaps is not .
therefore , high s / n data for the stream is important when studying stream gaps .
otherwise , the spectrum may be over- or underestimated depending on the orbital phase .
the right panels in figure [ fig : gd1_reduction ] show the gap spectra of the smooth stream .
they are also somewhat sensitive to s / n , but the most obvious difference from the spectra of @xmath0cdm stream is the shape of the spectra .
this is especially obvious during pericentric passage where the gap spectra rapidly drop off to zero for gaps longer than @xmath145 . even during apocentric passage ,
the gap spectra remain flat at gap lengths @xmath146 .
if the gaps originated from subhalo perturbations , then the gap spectrum should be steep and extend well beyond @xmath147 .
cdm stream with subhalos of masses @xmath144 at 8 gyr , projected onto the sky .
each panel represents a stream whose number of particles have been reduced by the factor indicated and binned at @xmath129 throughout . without reduction ( top panel ) , the stream contains about 80,000 particles .
the stream retains most of its gaps even after particle reduction by a factor of eight.,width=336 ] an interesting confusion for gd-1 in particular is that gd-1 s progenitor has not been identified .
if gd-1 s progenitor has evaded observation , and the observation corresponds to a segment of the stream which is close enough to the progenitor such that eos can be observed , then gd-1 may be a poor choice as a probe for missing satellites .
however , this is unlikely because eos are observable only in a small segment of the stream , and subhalo gaps are observable everywhere along the stream .
another possibility is that gd-1 s progenitor may have been completely disrupted . in this case
, the tidal radius of the progenitor approaches zero .
since the spacing between eos are proportional to the tidal radius of the progenitor , this means that the eos should also fade away as the progenitor is disrupted @xcite . therefore , despite its lack of progenitor gd-1 should be a viable probe for missing satellites .
the gap spectrum of gd-1 has been measured by @xcite .
the spectrum show presence of gaps at all lengths between @xmath148 and @xmath149 , which is sufficient to rule out a smooth and spherical potential . to facilitate a conclusive analysis on the origin of the gaps in gd-1 , we need to consider a much more realistic model which include the effects discussed in section [ sec : other_effects ] .
we consider the effects of subhalos as massive as @xmath43 , since the effects by more massive subhalos are not relevant to us .
gaps caused by subhalos at these masses produce long gaps with high - density contrasts .
for example , an obvious gap located at @xmath126 at 4 gyr shown in figures [ fig : density_gaps_whole_massrange13 ] and [ fig : density_gaps_central_massrange13 ] are caused by a @xmath150 subhalo .
in fact , the perturbation by @xmath151 ( @xmath152 ) subhalos can be so catastrophic that the stream is warped and divided into segments . as a result ,
a stream which originated from one progenitor can be observed as a few separate streams .
observations of pal-5 s and gd-1 s gaps , on the other hand , show small - scale density fluctuations in a long , narrow stream , so these two streams are not sensitive to subhalos above @xmath43 . by coincidence , this upper limit approximately coincides with the upper limit beyond which the models of warm dark matter can be no longer be distinguished from cdm .
therefore , @xmath43 is a reasonable upper limit where our simulations can be useful . in the low - mass end
, we only consider the effects of subhalos down to @xmath153 . from a separate simulation of the same stream but with only the subhalos with masses @xmath154 , the density profile is indistinguishable from the smooth stream , and the gap statistics are identical .
furthermore , section [ sec : lcdm_stream_with_all_subhalos ] shows that the gap spectra have very little dependence on mass . changing the mass lower limit from @xmath155 to @xmath156 produced indistinguishable gap spectra .
this means that subhalos less massive than @xmath157 , even though they are much more abundant than those of higher masses ( equation ( [ eqn : subhalo_massfunction ] ) ) , have minimal effects on our stream .
the milky way has about 160 known gcs @xcite , and a few hundred dgs brighter than @xmath158 after bias corrections ( see @xcite for a review ) .
it is interesting to ask whether these known satellite systems , rather than the truly `` missing '' satellites , can contribute to the observed stream gaps .
typical gcs have masses @xmath157 , which correspond to the low end of our mass spectrum of subhalos . in the same mass range , though , there are orders of magnitudes more subhalos ( e.g. , @xmath159 subhalos at @xmath160 ) than gcs , so gcs are unlikely to contribute significantly to observed stream gaps . on the other hand , dgs
are commonly found at @xmath161 @xcite which is the high end of our mass spectrum of subhalos . at that mass range ( @xmath162 subhalos at @xmath163 ) , the number of known dgs are only 1 order of magnitude below the number of subhalos , so dgs may contribute to some observed gaps
. however , a common limitation in understanding the contributions from both gcs and dgs is their orbits , especially when the kinematics of these satellites are not well constrained .
as done in our simulations ( section [ sec : subhalo_mass_ranges ] ) , subhalos that do not approach the stream s orbit will interact minimally with the stream .
table [ table : subhalo_massrange ] shows that in our realizations of subhalos , only @xmath164 of them would approach to within @xmath165 of gd-1 s orbit .
this means that most known satellites may never interact with a gd-1-like stream , and that stream gaps , if they were indeed due to satellites and were not eos , are more likely due to satellites that have never been observed . in order to keep our results simple , the galaxy
is modeled as stationary , spherical nfw potential , the subhalos as static , test masses , and the satellite as a collisionless king model .
these models ignore a number of known dynamical complications . _ two - body relaxation . _
the star cluster is modeled as a collisionless system with relaxation timescale of @xmath166 .
globular clusters typically have relaxation timescales of @xmath167 ( * ? ? ?
* edition ) , so mass loss should originate from dynamical evaporation , in addition to tidal disruption . as a result , the star cluster should be disrupted even faster than we measured in figure [ fig : massloss ] .
this may have an important effect on the formation of gaps , which depends on the details of the dynamics of a stream @xcite .
the relation between gaps and mass loss mechanism will be investigated in a future study .
_ dynamical friction ( df ) .
_ both the star cluster and subhalos should suffer from df as they orbit around the dark matter halo .
comparing the magnitudes of the accelerations due to df and due to the orbit , @xmath168 for both the star cluster at 22 kpc and a @xmath169 subhalo at 100 kpc , where @xmath170 is the log of the ratio of the maximum and minimum impact distances @xcite .
therefore , df is negligible throughout our model .
_ disk shocking : _
@xcite found that the evolution of pal-5 is driven by the tidal shocks when crossing the galactic disk , which is not modeled in our simulations .
the orbit of pal-5 in @xcite has peri- and apogalacticon at 5.5 kpc and 19 kpc , respectively , whereas our smooth stream has peri- and apogalacticon at 15 kpc and 30 kpc , respectively .
being farther away from the the galactic center , if our simulations contained a disk , its effect should be less severe for our simulated stream than pal-5 .
moreover , @xcite concluded that disk shocking is not responsible for the observed structure in pal-5 , while @xcite concluded that eos persist even under the influence of disk shocks , so the absence of a disk should not significantly change our conclusion .
the gap formation rate with and without subhalos in the presence of a disk is beyond the scope of this study . _
halo shape and collapse history : _ @xcite found that the shape of the halo potential can have a larger effect than subhalos have on the over all structure of a stream . however , their simulations focused on streams which originated from dgs at @xmath171 , as well as subhalos at @xmath161 which is the high end of our mass spectrum of subhalos .
the small gaps from a stream originating from a gc in a non - spherical halo has yet to be studied .
in fact , since the initial collapse of the entire halo , the potential can not be stationary throughout a hubble time , which is the timescale of our simulations . in the future
, we aim to repeat a similar study using potentials which resulted directly from high resolution simulations such as @xcite and @xcite .
the self - consistent halo and subhalo potentials from those simulations can eliminate the idealized models in section [ sec : models ] .
for the first time , we used n - body simulations to model the disruption of a collisionless star cluster which formed a narrow stream similar to pal-5 and gd-1 , and we investigated the phenomenology of gaps that originated from the perturbations by subhalos predicted in the @xmath0cdm cosmological model .
analytical predictions of stream gap statistics in previous studies were all based on massless particles distributed to mock realistic streams , but the dynamics of gaps have never been studied in self - consistent models . with a stream from a self - consistent model
, we characterized the gap length distribution which can be used as a tool to understand the origin of stream gaps seen in observations .
the properties of the subhalos in our simulations were approximations to those in the aquarius simulation @xcite .
we ran 14 simulations of the same stream 1 without any subhalos ( the smooth stream ) , and 1 for each cumulative mass range in table [ table : subhalo_massrange ] ( the @xmath0cdm streams ) . in each stream
we looked for gaps using a matched filter approach previously used by @xcite and @xcite .
we found that , in addition to subhalo perturbations , the overdensities of particles due to their epicyclic motions as the progenitor loses mass @xcite can also produce gaps .
therefore , even without subhalos , `` gaps '' can appear within @xmath172 away from the progenitor .
for the first time , our match filter approach accounted for these eos together with the gaps due to subhalo perturbations .
@xcite first noted that subhalos gaps were typically diagonal and not perpendicular to the stream due to the range in angular momenta across the width of the stream .
we investigated whether this could be a hindrance to gap detection . by measuring the distribution of angular momenta in our simulated stream
, we estimated that the two ends of a gap across the width of a stream were sheared by no more than a @xmath102 per gyr .
rather , subhalo gaps show complicated morphologies which were already imprinted into the stream as soon as the gaps first occurred .
in addition to integrating the entire thickness of the stream , we also considered the case where the linear density are integrated using only the central 0.08 kpc of the stream in order to minimize the impact of gaps morphologies .
we found that the resulting gap rate spectra the two cases were similar .
therefore , gap morphology does not affect our conclusion .
we tested the validity of the idealized gap spectrum @xmath116 , or the cumulative number of gaps per unit stream length per unit stream age as a function of gap length @xmath117 , derived by @xcite .
we found that overlapping gaps in the stream can significantly reduce @xmath116 , and that the dependences of @xmath116 on subhalo masses and stream age are smaller than its dependence on the stream s orbital phase .
therefore , the stream s orbital phase must be known when interpreting gap formation rates in observations .
we considered how to interpret gap spectra from observations by projecting the stream onto the sky , and for each @xmath0cdm stream we also simulated them using ten realizations of the same subhalo distributions .
one observational concern is the s / n of the stream s detection .
we down - sampled our simulated streams with less particles in order to match the s / n which is similar to the gd-1 detection @xcite .
our result indicated that at gd-1 s s / n , the gap spectrum can be biased by the orbital phase of the stream .
in addition , we compared gap spectra produced purely by eos and by eos and subhalos together in a @xmath0cdm halo .
we showed that the gap spectra of the former are limited in gap lengths , and that the latter have a much larger variety of gap lengths .
this can be a powerful method to identify the origin of gaps in streams .
therefore , high s / n data such as those from _
gaia _ will be very useful for using stream gaps to constraint the abundance of subhalos .
the dynamics of stream gaps depend on the details of the dynamics of the stream itself .
we adapted a few tools such as match filter and scaling relations which were derived from idealized simulations . in a future study
, we aim to use self - consistent streams to repeat experiments akin to @xcite , @xcite , and @xcite , where the details of individual gaps can be studied in controlled experiments , in order to revise the aforementioned tools that is applicable quantitatively to realistic streams .
we thank the anonymous referee for valuable comments , which inspired us to expand the content of this paper .
computations were performed on the gpc supercomputer at the scinet hpc consortium .
scinet is funded by : the canada foundation for innovation under the auspices of compute canada , the government of ontario ; ontario research fund - research excellence , and the university of toronto . | arxiv |
WightFibre is the cable network operator on the Isle of Wight. WightFibre provides telephone and broadband internet services. It is the last remaining cable company in the UK which is not part of Virgin Media, which since March 2006, has operated more than 95 of cable services in the UK.
Historically WightFibre has operated a hybrid fibre-coaxial network HFC service around 25 of the Island. In November 2017 WightFibre secured £35M of funding from Infracapital Partners ICP, part of M&G Investments matched funded by private investors and the UK Governments Digital Infrastructure Fund. This funding is allowing WightFibre to upgrade its HFC network to a full-fibre Fibre to the PremiseFTTP network and to extend coverage to around 60,000 homes on the island.
WightFibre's Gigabit Island project commenced in Autumn 2018. By January 2019 the rollout of the new full fibre network was in full flow. The first 50,000 homes are expected to be complete by December 2020. Broadband speeds of up to 900Mb are on offer.
Company History
The Isle of Wight Cable and Telephone Company IOWCTC was formed in 2000 and commenced offering service on the island in January 2001. IOWCTC was taken over by CLS Holdings in 2002 and rebranded to Wightcable. CLS Holdings sold the assets of Wightcable to private investors in 2005 who formed WightCable 2005 Ltd. New branding was introduced, services upgraded and internet speeds increased. When Virgin Media acquired Smallworld in 2014 this left WightFibre as the sole independent UK cable company.
In 2012, WightCable changed its name to WightFibre, promising increased internet speeds up to 100Mbit/s, and introducing IPTV with high-definition channels and on-demand services. A £500,000 investment saw the launch of 50Mb broadband in July 2012, 100Mb broadband in September 2012 and 152Mb broadband in 2013. The company advertised heavily and returned to growth in October 2012. A small scale trial of the company's new IP based TV service was held in Nov & Dec 2012 but technical difficulties and difficulties in striking content agreements led to the cancellation of the project in 2013.
In February 2013 WightFibre was acquired by Keith Young, a serial entrepreneur who was also an original investor in Easynet since purchased by Sky. The management team remained in place and the company's strategy remained unchanged. Keith Young invested in the company to accelerate the turnaround. WightFibre has partnered with two Isle of Wight-based wireless operators Click4Internet and Wight Wireless to extend island coverage with plans to improve that coverage to provide speeds of 50Mb to 80Mb throughout the island. In 2015 WightFibre acquired Click4Internet.
In November 2017 WightFibre was acquired by Infracapital Partners as part of its £35M investment in the company.
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WightFibre
Category:Cable television companies of the United Kingdom
Category:Companies based on the Isle of Wight
Category:Internet service providers of the United Kingdom
Category:Telecommunications companies established in 2001 | wikipedia |
A contradiction, probably from confusion
All things in nature tells us that high entropy is easier to happen.
But then why does it takes energy to break bonds, in order to achieve high entropy.
Any thing in gaseous state has higher potential energy than it is in solid state. But that creates less stability.
Processes in nature that lead to an increase in the entropy of the system are in general favourable, but entropy alone is not the deciding factor!
If we were to follow a full proof we would have to consider Carnot engines and such but for now the result that we are interested in is called the Clausius statement. It is the Clausius statement that really defines the second law and the direction of spontaneity. The Clausius statement leads us to define two parameters depending on the experimental conditions: either the [Helmholtz free energy](https://en.wikipedia.org/wiki/Helmholtz_free_energy) $A$ (when working at constant volume) or the [Gibbs free energy](https://en.wikipedia.org/wiki/Gibbs_free_energy) $G$ (under conditions of constant pressure). In practice it is much easier to work with $G$ since we can expose our reaction mixture to the atmosphere and call it constant pressure.
It is these [thermodynamic potentials](https://en.wikipedia.org/wiki/Thermodynamic_potential) $G$ and $A$ that determine the overall thermodynamic picture of spontaneity of a given process.
If we work with the Gibbs potential, after some mathematics we can easily express by the following equation:
\begin{equation}
G=H-TS
\end{equation}
Where $H$ is the enthalpy of the system, $T$ is the temperature and $S$ is the entropy. For a given process it is the Gibbs energy that determines the spontaneity of the reaction. Crudely put, the starting material will have a certain $G$ value and the products will have a certain $G$ value, if the change in $G$ over the course of the reaction is negative then we say it is spontaneous. If it is positive it is not spontaneous.
We can clearly see that the condition for spontaneity is not solely dependant on the entropy alone rather it is also a function of the enthalpy too. Further the entropic contribution to the $G$ is dependent on the temperature indicating that there will be a certain threshold temperature for an endergonic process.
An endergonic process is characterised by having a positive enthalpy change, requiring energy to occur. If the "amount" of energy the process requires is very large then the change in enthalpy will also be large and as we can see this makes the change in $G$ for the process become less favourable.
Moving on, we can now see that a given process will have a certain energy barrier... an activation energy if you like. Whether a process is thermodynamically spontaneous or not one has to consider the Kinetics too! A simple yet ubiquitous model for Kinetics is the [Arrhenius equation](https://en.wikipedia.org/wiki/Arrhenius_equation) which in general says the rate of reaction decreases for processes with a higher energy of activation.
Turning the later part of your question. The most stable phase (state of matter) is dependent on the conditions of the reaction. The most stable phase for the given combination of temperature and pressure will prevail in the reaction mixture. In practice this leads to the state with the lowest value of $G$.
Solids actually liberate energy when they come together, especially ionic solids! This energy is called the Lattice energy and it is relative to all the reactants in their gaseous state (as ions). (look at [Born-Lande equation](https://en.wikipedia.org/wiki/Born%E2%80%93Land%C3%A9_equation) for more info)! So although gaseous species will have a higher entropy due to all the rotational vibrational freedom they have ... the state of matter is dictated by $G$.
Without the full mathematical argument behind what I have said I feel my answer will be incomplete, but I hope it helps you :)
| stackexchange/chemistry |
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