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simple stellar populations ( ssps ) , defined as groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition certainly exist in nature . a priori , we can not say that all stellar groups , associations or star clusters are ssps , however . most galaxies certainly are not . conceptually , ssps are appealing because they are easy to model theoretically and their temporal evolution can be followed accurately . all stars of an ssp should have the same initial metal content . at any given time , the stars composing an ssp describe an isochrone in the theoretical hertzsprung russell ( hr ) diagram , which can easily be transformed to an observational colour magnitude diagram ( cmd ) . detailed observations of this kind are available only for resolved stellar populations , either galactic clusters or star clusters in nearby galaxies , or the stars making up the satellites of the milky way . only in these few cases can we reliably establish the simplicity of a stellar population by inspection of its cmd . integrated properties of stellar populations , such as their colours or spectral - energy distributions , are subject to degeneracies ( e.g. , old , metal - poor populations resemble younger , metal - richer ones ) and statistical ( stochastic ) uncertainties ( due to the small number of stars present in low - mass systems ) which , in most cases , prevent us from establishing with certainty if we are observing an ssp . of course , the question as to whether or not star clusters can be described by ssps does not apply to those clusters which have been shown explicitly to host stellar populations of a composite nature , e.g. , resolved clusters where a double or triple main sequence ( ms ) has been detected such as ngc 2808 ( piotto _ et al . _ 2007 ; see also kalirai & richer 2010 ; van loon 2010 ) , or clusters showing evidence of prolonged star formation like @xmath0 centauri ( villanova _ et al . _ 2007 ) , nor to dwarf galaxies like leo a ( cole _ et al . _ 2007 ) or other galaxies in the local group with well - established multiple episodes of star formation ( gallart _ et al . _ 2007 ) .

* stellar evolution ; population synthesis ; spectral evolution ; simple stellar populations ; tp agb stars * in this paper , i review to what extent we can understand the photometric properties of star clusters , and of low - mass , unresolved galaxies , in terms of population synthesis models designed to describe ` simple stellar populations ' ( ssps ) , i.e. , groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition .

0911.0791

i

* stellar evolution ; population synthesis ; spectral evolution ; simple stellar populations ; tp agb stars * in this paper , i review to what extent we can understand the photometric properties of star clusters , and of low - mass , unresolved galaxies , in terms of population synthesis models designed to describe ` simple stellar populations ' ( ssps ) , i.e. , groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition . the photometric properties predicted by these models do not readily match the observations of most star clusters , unless we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the stellar initial mass function . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . the disagreement between the model predictions and observations of cluster colours and magnitudes may indicate problems with or deficiencies in the modelling , and dioes not necessarily tell us that star clusters do not behave like ssps . matching the photometric properties of star clusters using ssp models is a necessary ( but not sufficient ) condition for clusters to be considered simple stellar populations . composite models , characterized by complex star - formation histories , also match the observed cluster colours . [ firstpage ]

the magnitudes and colours predicted by stellar population synthesis models do not readily match observations of unresolved star clusters , which are commonly expected to behave like ideal ssps . this lack of agreement between the model predictions and observations may indicate problems or deficiencies in the modelling , and does not necessarily tell us that star clusters do not behave like ssps . in this review , i have briefly summarized the results of simple simulations which show how the range of colours observed in intermediate - age lmc star clusters can be understood on the basis of current stellar evolution theory , if we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the imf . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . some young clusters are described by supersolar - metallicity models , which may not be realistic for the lmc . there is no need to introduce ad hoc assumptions into population synthesis models ( maraston 1998 ; maraston _ et al . _ 2001 ) , representing a departure from our current understanding of stellar evolution theory , to explain the observed range of cluster colours and magnitudes . the predicted fluctuations in the integrated photometric properties of simulated clusters increase with decreasing cluster mass , as expected on the basis of the results of cervio _ et al . _ ( 2000 , 2001 , 2002 ) . it is worth pointing out that , because of the stochastic nature of the integrated - light properties of star clusters , single clusters may not be taken as reference standards of ssps of a given age and metallicity . it should be emphasized that matching the photometric properties of star clusters using ssp models is a necessary condition for clusters to be considered simple stellar populations , but not sufficient . so far , the single ms and unique ms turnoff required by ssps can be established with certainty only for resolved stellar populations . alongi , m. , bertelli , g. , bressan , a. , chiosi , c. , fagotto , f. , greggio , l. & nasi , e. 1993 evolutionary sequences of stellar models with semiconvection and convective overshoot . i. @xmath16 . _ , * 97 * , 851871 . bertelli , g. , girardi , l. , marigo , p. & nasi , e. 2008 scaled solar tracks and isochrones in a large region of the @xmath78 plane . i. from the zams to the tp agb end for @xmath79 m@xmath3 stars . _ , * 484 * , 815830 . bruzual a. , g. 2002 stellar populations in star clusters : the rle played by stochastic effects . in _ extragalactic star clusters _ , proc . union symp . 207 ( eds d. geisler , e. k. grebel & d. minniti ) , pp . 616624 , san francisco : astron . bruzual , g. 2007 on tp agb stars and the mass of galaxies . in _ stellar populations as building blocks of galaxies _ , proc . union symp . 241 ( eds a. vazdekis & r. f. peletier ) , pp . 125132 , cambridge : cambridge university press . cervio , m. , gmez flechoso , m. a. , castander , f. j. , schaerer , d. , moll , m. , kndlseder , j. & luridiana , v. 2001 confidence limits of evolutionary synthesis models . iii . on time - integrated quantities . _ , * 376 * , 422433 . cervio , m. , valls gabaud , d. , luridiana , v. & mas hesse , j. m. 2002 confidence levels of evolutionary synthesis models . ii . on sampling and poissonian fluctuations . _ _ , * 381 * , 5164 . coelho , p. , bruzual a. , g. , charlot , s. , weiss , a. , barbuy , b. & ferguson , j. w. 2007 spectral models for solar - scaled and @xmath81-enhanced stellar populations . _ mon . not . r. astron . _ , * 382 * , 498514 . cole , a. a. , skillman , e. d. , tolstoy , e. , gallagher iii , j. s. , aparicio , a. , dolphin , a. e. , gallart , c. , hidalgo , s. l. , saha , a. , stetson , p. b. & weisz , d. r. 2007 leo a : a late - blooming survivor of the epoch of reionization in the local group . _ astrophys . j. _ , * 659 * , l17l20 . conroy , c. , gunn , j. e. & white , m. 2009_a _ the propagation of uncertainties in stellar population synthesis modeling . i. the relevance of uncertain aspects of stellar evolution and the initial mass function to the derived physical properties of galaxies . _ astrophys . j. _ , * 699 * , 486506 . conroy , c. , white , m. & gunn , j. e. 2009_b _ the propagation of uncertainties in stellar population synthesis modeling . ii . the challenge of comparing galaxy evolution models to observations . _ astrophys . j. _ , submitted ( arxiv:0904.0002 ) . fagotto , f. , bressan , a. , bertelli , g. & chiosi , c. 1994_a _ evolutionary sequences of stellar models with new radiative opacities . iii . @xmath82 and @xmath83 . _ , * 104 * , 365376 . fagotto , f. , bressan , a. , bertelli , g. & chiosi , c. 1994_b _ evolutionary sequences of stellar models with new radiative opacities . iv . @xmath84 and @xmath24 . _ _ , * 105 * , 2938 . gallart , c. , aparicio , a. , bernard , e. j. , carrera , r. , drozdovsky , i. , hidalgo , s. l. , marn franch , a. , meschin , i. p. , monelli , m. , nol , n. e. d. & rosenberg , a. 2007 studying galaxy formation and evolution from local group galaxies . in _ first light science with the gtc _ ( eds r. guzmn , c. packham , j. m. rodrguez espinosa & s. torres peimbert ) , rev . ( ser . conf . ) , * 29 * , 158158 . girardi , l. , bressan , a. , chiosi , c. , bertelli , g. & nasi , e. 1996 evolutionary sequences of stellar models with new radiative opacities . _ , * 117 * , 113125 . goudfrooij , p. , gilmore , d. , kissler patig , m. & maraston , c. 2006 integrated - light @xmath87 imaging photometry of globular clusters in the magellanic clouds . _ mon . not . r. astron . _ , * 369 * , 697704 . gonzlez lpezlira , r. , bruzual a. , g. , charlot , s. , loinard , l. & ballesteros paredes , j. 2009 tracers of stellar mass loss . i. optical and near - ir colours and surface brightness fluctuations . _ mon . not . r. astron . _ , in press . le borgne , j .- f . , bruzual , g. , pell , r. , lanon , a. , rocca volmerange , b. , sanahuja , b. , schaerer , d. , soubiran , c. & vlchez gmez , r. 2003 stelib : a library of stellar spectra at @xmath88 . _ , * 402 * , 433442 . le borgne , d. , rocca volmerange , b. , prugniel , p. , lanon , a. , fioc , m. & soubiran , c. 2004 evolutionary synthesis of galaxies at high spectral resolution with the code pegase metallicity and age tracers . _ , * 425 * , 881897 . maraston , c. , kissler patig , m. , brodie , j. p. , barmby , p. & huchra , j. p. 2001 the agb phase - transition outside the local group : @xmath21-band observations of young star clusters in ngc 7252 . _ , * 370 * , 176193 . marigo , p. , girardi , l. , bressan , a. , groenewegen , m. a. t. , silva , l. & granato , g. l. 2008 evolution of asymptotic giant branch stars . ii . optical to far - infrared isochrones with improved tp agb models . _ , * 482 * , 883905 . martins , l. p. , gonzlez delgado , r. m. , leitherer , c. , cervio , m. & hauschildt , p. 2005 a high - resolution stellar library for evolutionary population synthesis . _ mon . not . r. astron . _ , * 358 * , 4965 . persson , s. e. , aaronson , m. , cohen , j. g. , frogel , j. a. & matthews , k. 1983 photometric studies of composite stellar systems . v. infrared photometry of star clusters in the magellanic clouds . _ astrophys . * 266 * , 105129 . piotto , g. , bedin , l. r. , anderson , j. , king , i. r. , cassisi , s. , milone , a. p. , villanova , s. , pietrinferni , a. , & renzini , a. 2007 a triple main sequence in the globular cluster ngc 2808 . _ astrophys . , * 661 * , l53l56 . renzini , a. & buzzoni , a. 1986 global properties of stellar populations and the spectral evolution of galaxies . in _ spectral evolution of galaxies _ ( eds c. chiosi & a. renzini ) , pp . 195235 , dordrecht : reidel . snchez blzquez , p. , peletier , r. f. , jimnez vicente , j. , cardiel , n. , cenarro , a. j. , falcn barroso , j. , gorgas , j. , selam , s. & vazdekis , a. 2006 medium - resolution _ isaac newton telescope _ library of empirical spectra . _ mon . not . r. astron . _ , * 371 * , 703718 . villanova , s. , piotto , g. , king , i. r. , anderson , j. , bedin , l. r. , gratton , r. g. , cassisi , s. , momany , y. , bellini , a. , cool , a. m. , recio blanco , a. & renzini , a. 2007 the multiplicity of the subgiant branch of @xmath0 centauri : evidence for prolonged star formation . _ astrophys . j. _ , * 663 * , 296314 .

the photometric properties predicted by these models do not readily match the observations of most star clusters , unless we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the stellar initial mass function . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . is a necessary ( but not sufficient ) condition for clusters to be considered simple stellar populations . [ firstpage ]

0911.0791

c

* stellar evolution ; population synthesis ; spectral evolution ; simple stellar populations ; tp agb stars * in this paper , i review to what extent we can understand the photometric properties of star clusters , and of low - mass , unresolved galaxies , in terms of population synthesis models designed to describe ` simple stellar populations ' ( ssps ) , i.e. , groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition . the photometric properties predicted by these models do not readily match the observations of most star clusters , unless we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the stellar initial mass function . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . the disagreement between the model predictions and observations of cluster colours and magnitudes may indicate problems with or deficiencies in the modelling , and dioes not necessarily tell us that star clusters do not behave like ssps . matching the photometric properties of star clusters using ssp models is a necessary ( but not sufficient ) condition for clusters to be considered simple stellar populations . composite models , characterized by complex star - formation histories , also match the observed cluster colours . [ firstpage ]

like most of its fundamental quantum numbers , the electric charge of the top quark has not been measured so far . alternative interpretations for the particle we believe is the charge @xmath7 isospin partner of the @xmath3-quark are thus not ruled out . for example , since the correlations of the @xmath3-quarks and the @xmath8-bosons in @xmath186 are not determined , it is conceivable that the `` @xmath45-quark '' observed at the tevatron is an exotic quark , @xmath19 , with charge @xmath5 which decays via @xmath187 . this interpretation is consistent with current precision electroweak data @xcite . in order to determine the charge of the top quark , one can either measure the charge of the @xmath3-jet , or investigate photon radiation in @xmath0 events . the latter method actually measures a combination of the em coupling strength and the charge quantum number . combining the results of the two methods will thus make it possible to determine both quantities . in this paper we have explored the possibility of measuring @xmath20 in @xmath188 , assuming that both @xmath3-quarks are tagged . our analysis makes use of both @xmath1 production and radiative top quark decays , and is carried out at the tree level . the em coupling strength is assumed to take its sm value . top quark and @xmath8 boson decays are treated in the narrow width approximation . contributions from radiative @xmath8 decays can be suppressed by simple phase space cuts ( see eq . ( [ eq : radw ] ) ) . the remaining event sample can be separated into a @xmath1 sample , a @xmath25 , @xmath189 sample , and a @xmath25 , @xmath190 sample by imposing invariant mass and cluster transverse mass cuts ( see eqs . ( [ eq : top51 ] ) ( [ eq : top7 ] ) ) . in the phase space region dominated by @xmath1 production , the cross section increases if the magnitude of @xmath20 increases . at the tevatron , @xmath117 annihilation dominates and photon radiation off the incoming quarks constitutes an irreducible background which limits the sensitivity to @xmath20 . in contrast , at the lhc , gluon fusion dominates , and the @xmath1 cross section scales approximately with @xmath118 . in the phase space regions which enhance @xmath0 production with one of the top quarks decaying radiatively ( @xmath78 ) , interference effects between the feynman diagrams where the photon is emitted from the top quark , the @xmath8 boson and the @xmath3-quark line may cause the cross section to either decrease or increase with @xmath191 . for example , for @xmath115 , the @xmath192 cross section via radiative top quark decays is reduced by a factor of @xmath193 to @xmath194 . the changes in the individual cross sections are reflected in the photon transverse momentum distribution in the various phase space regions . we also found that the @xmath143 distribution , where @xmath144 is the @xmath3 or @xmath97-quark with the smaller @xmath105 , is sensitive to the charge of the top quark in the phase space regions dominated by @xmath0 production where one of the top quarks decays radiatively . in order to determine how well one can hope to measure the top quark charge using photon radiation in top quark events in future tevatron and lhc experiments , we have performed @xmath160 tests of the @xmath122 and the @xmath143 distributions in the various phase space regions of interest . at the tevatron , with an integrated luminosity of 20 fb@xmath4 , one will be able to exclude at @xmath6 c.l . the possibility that an exotic quark @xmath19 with charge @xmath5 and not the sm top quark has been found in run i. for smaller integrated luminosities , the number of events expected is very small and it will be difficult to perform a quantitative analysis using differential cross sections . in this case , the ratio of the cross section associated with radiation in top production to the radiative decay cross section may be a useful tool . at the lhc with 10 fb@xmath4 obtained at @xmath175 , it should be possible to measure the electric charge of the top quark with an accuracy of about 10% . for comparison , at a linear collider with @xmath195 gev and @xmath196 fb@xmath4 , one expects that @xmath20 can also be measured with a precision of about 10% @xcite . finally , at a @xmath197 collider it is conceivable that the top quark charge can be determined with an accuracy of better than 1% , if the @xmath24 cross section can be measured with a precision of 2% @xcite . the measurement of the electric charge of the top quark at the tevatron using photon radiation in top quark events is severely limited by statistics . even with an integrated luminosity of 20 fb@xmath4 , @xmath20 can only be determined with a precision of @xmath198 . however , as we pointed out in sec . i , information on the electric charge of the top quark may also be obtained from a measurement of the charge of the @xmath3-jets , and the charge sign of the leptons in semileptonically tagged @xmath3-quarks . this may significantly improve the precision which can be obtained . detailed simulations will be necessary in order to determine how well the top quark charge can be measured using these methods . we would like to thank c. ferreti , h. frisch , b. knuteson , t. lecompte , j. parsons , z. sullivan and j. womersley for stimulating discussions . one of us ( u.b . ) is grateful to the fermilab theory group , where part of this work was carried out , for its generous hospitality . this work has been supported in part by doe grant de - fg02 - 91er40685 , nsf grants phy-9600155 and phy-9970703 , and a nsf graduate student fellowship . f. abe _ et al . _ ( cdf collaboration ) , phys . lett . * 74 * , 2626 ( 1995 ) . s. abachi _ et al . _ ( d collaboration ) , phys . lett . * 74 * , 2632 ( 1995 ) . p. c. bhat , h. prosper and s. s. snyder , int . j. mod . * a13 * , 5113 ( 1998 ) . d. chang , w.f . chang , and e. ma , phys . * d59 * , 091503 ( 1999 ) and phys . * d61 * , 037301 ( 2000 ) . b. grzadkowski and z. hioki , nucl . b585 * , 3 ( 2000 ) and references therein . g. velev , talk given at the top thinkshop@xmath199 , fermilab , november 2000 . t. stelzer and w. f. long , comput . commun . * 81 * , 357 ( 1994 ) . h. murayama , i. watanabe and k. hagiwara , kek-91 - 11 ( 1991 ) . a. denner and t. sack , z. phys . * c46 * , 653 ( 1990 ) . t. affolder _ et al . _ , ( cdf collaboration ) , phys . rev . * d63 * , 032003 ( 2001 ) . b. abbott _ et al . _ ( d collaboration ) , phys . rev . * d58 * , 052001 ( 1998 ) . d. abbaneo _ et al . _ ( the lep electroweak working group ) , cern - ep-2001 - 021 ( february 2001 ) ; hep - ex/0103048 . a. d. martin , r. g. roberts and w. j. stirling , phys . * b387 * , 419 ( 1996 ) . u. baur and e. l. berger , phys . * d47 * , 4889 ( 1993 ) . t. abe _ et al . _ ( american linear collider working group collaboration ) , slac-570 _ resource book for snowmass 2001 , 30 jun - 21 jul 2001 , snowmass , colorado _ , hep - ex/0106055 , hep - ex/0106056 , hep - ex/0106057 and hep - ex/0106058 . e. boos , hep - ph/0009100 , and references therein . ccccc + & @xmath1 & @xmath109 & @xmath121 & + & contribution & contribution & contribution & total + tevatron , @xmath200 & 1.70 fb & 0.12 fb & 0.10 fb & 1.92 fb + tevatron , @xmath201 & 2.37 fb & 0.03 fb & 0.02 fb & 2.42 fb + lhc , @xmath200 & 33.3 fb & 5.78 fb & 4.86 fb & 44.0 fb + lhc , @xmath201 & 111.4 fb & 1.21 fb & 0.97 fb & 113.6 fb + + tevatron , @xmath200 & 0.36 fb & 0.26 fb & 0.13 fb & 0.75 fb + tevatron , @xmath201 & 0.52 fb & 0.07 fb & 0.03 fb & 0.62 fb + lhc , @xmath200 & 0.68 fb & 3.67 fb & 2.26 fb & 6.61 fb + lhc , @xmath201 & 2.25 fb & 0.87 fb & 0.59 fb & 3.71 fb + + tevatron , @xmath200 & 0.11 fb & 0.06 fb & 0.19 fb & 0.36 fb + tevatron , @xmath201 & 0.16 fb & 0.01 fb & 0.05 fb & 0.22 fb + lhc , @xmath200 & 0.15 fb & 1.07 fb & 3.63 fb & 4.85 fb + lhc , @xmath201 & 0.49 fb & 0.26 fb & 0.85 fb & 1.60 fb + .limits achievable at 95% c.l . for @xmath170 in @xmath188 at the tevatron and the lhc . bounds are shown for the photon transverse momentum distribution in the phase space region defined by the @xmath1 selection cuts , and the @xmath122 and @xmath143 distributions of the combined radiative top decay regions . the last row displays the combined limits from the three distributions . the @xmath3-quark charge is given by @xmath162 . the cuts imposed are described in sec . ii . for the @xmath143 distribution , the @xmath122 cut of eq . ( [ eq : top4 ] ) has been replaced by @xmath151 gev . [ cols="^,^,^ " , ]

15.pt we consider photon radiation in @xmath0 events at the upgraded fermilab tevatron and the cern large hadron collider ( lhc ) as a tool to measure the electric charge of the top quark . , it will be possible to determine the charge of the top quark with an accuracy of about 10% .

hep-ph0106341

i

15.pt we consider photon radiation in @xmath0 events at the upgraded fermilab tevatron and the cern large hadron collider ( lhc ) as a tool to measure the electric charge of the top quark . we analyze the contributions of @xmath1 production and radiative top quark decays to @xmath2 , assuming that both @xmath3-quarks are tagged . with 20 fb@xmath4 at the tevatron , the possibility that the `` top quark '' discovered in run i is actually an exotic charge @xmath5 quark can be ruled out at the @xmath6 confidence level . at the lhc , it will be possible to determine the charge of the top quark with an accuracy of about 10% .

the case study of seyfert s sextet presented here is part of a continuing effort to determine whether dwarf galaxies form during tidal interactions among giant galaxies . the sextet appears to be the most logical choice to search for tidal dwarf formation ; it is the most compact of the hickson compact groups , contains two prominent tidal tails , has a low velocity dispersion , and previous ground - based imaging revealed a number of faint , extended objects within the boundaries of the group . however , the results of the _ hst _ imaging of seyfert s sextet show that , contrary to expectations , there is very little evidence for dwarf galaxy formation or any other strong star formation in this group . a large number of both point sources and extended sources were catalogued and photometered from the three wide field images . we find that very few objects are detected in either of the two blue filters , f336w and f439w , and those that are detected in the two red filters , f555w and f814w , have red colors consistent with those of old stellar populations . the majority of the point sources detected appear to be old ( @xmath118 gyr ) and the majority of the extended sources detected appear to be background galaxies . these photometric results contrast sharply with _ hst _ imaging studies of other hcgs , such as hcg92 ( stephan s quintet ) and hcg31 . in hcg92 , @xcite found a number of bright , blue star cluster candidates in the tidal debris regions of this group . the images of this compact group also show bright , blue extended sources in the `` northern starburst region '' and in the tidal tails of ngc7319 and ngc7318a / b . hcg31 contains a significant number of bright , blue point sources @xcite similar to those seen in hcg92 . star - forming regions are also observed in hcg31 that are `` too small to be called galaxies themselves , but are not clearly associated with either galaxy ac or galaxy e '' @xcite . thus , both hcg92 and hcg31 contain what appear to be young star clusters and tidal dwarf galaxy candidates , while seyfert s sextet does not appear to contain a significant population of either type of object . the star cluster candidates identified in this study have photometric properties consistent with those for models of massive ( @xmath119 ) clusters with ages @xmath120 years . the ages of these objects suggest that they are not entirely a primordial population , but may be the product of an interaction within the compact group at some time within the past few gyr . @xcite argue that the optical tail associated with ngc 6027b and the gas that they associate with ngc 6027d may have resulted from an interaction between these two disk galaxies more than @xmath121 years ago . the ages we derive for many of the cluster candidates are consistent with this hypothesis . while there do not appear to be any young star clusters or tidal dwarf galaxies associated with seyfert s sextet , we did identify several candidate dwarf galaxies in the group . this sample includes a few faint , blue extended sources , and two galaxies with peculiar morphologies : an irregularly shaped galaxy located quite near the disk of ngc6027c and an unusual , `` cometary '' galaxy located within the tidal tail associated with ngc6027c . an additional candidate , galaxy 4.2 , has already been ruled out as a member of the sextet ; the hobby - eberly telescope spectrum of this object instead shows that it is associated with ngc6027e , the discordant redshift member of seyfert s sextet . whether or not the other candidate dwarf galaxies are associated with the sextet , they appear morphologically very different from the clumpy , blue tidal dwarf galaxy candidates in hcg92 and hcg31 . the data suggest that there is some fundamental , physical difference between the sextet and the two hcgs that are known to contain young star clusters and tidal dwarf galaxy candidates . one obvious difference between these groups are the types of galaxies contained in each : seyfert s sextet is primarily made up of early - type ( s0/e ) galaxies , stephan s quintet contains spirals , and hcg31 contains mostly irregular galaxies . based on these morphologies , one initial expectation is that the neutral gas content in seyfert s sextet is likely to be lower than that of either hcg31 or hcg92 . radio observations show that the sextet contains only @xmath122 of neutral hydrogen @xcite , about an order of magnitude less than that of hcg31 and hcg92 @xcite . the most recent observations of the gas content of hcg92 @xcite revise the gas mass of this group downward , however it remains at least five times larger than the gas in seyfert s sextet . what appears to be the more significant difference among these three hcgs , however , is nt the gas mass , but the _ distribution _ of the . @xcite present vla neutral hydrogen observations of seyfert s sextet that indicate that the majority of the mass is retained by the disk of ngc6027d , although some gas is found in a tail extending to the east of this galaxy and also in the optical tidal tail associated with ngc6027b . in hcg31 , the vla neutral hydrogen maps @xcite show that the gas is found both in the galaxies themselves and in a large envelope of gas that is plausibly attributed to tidal interactions between the galaxies . the distribution of in hcg92 is found to lie entirely outside of the galaxies @xcite , however . the is concentrated in clouds and tidal tails that are not coincident with the disks of the member galaxies . @xcite proposed an evolutionary sequence based on their vla observations of the content of hcgs . in their model , `` phase 1 '' hcgs are those where the vast majority of the neutral gas remains bound to the member galaxies . `` phase 2 '' hcgs are more evolved in the sense that the galaxies retain some of the gas , while approximately half of the gas mass is found in tidal features . the final , most evolved phase is broken into two subclasses , `` phase 3a '' and `` phase 3b '' . phase 3a groups are those where the gas is almost completely stripped from the galaxies and is found entirely within tidal features , while phase 3b groups are a few rare cases where the entire group seems to be contained in a single cloud . hcg31 is considered a prototype phase 2 group , and hcg92 is considered an extreme example of phase 3a . both @xcite and @xcite find seyfert s sextet to be anomalous ; its gas distribution suggests that the system has not experienced significant dynamical evolution , while optical observations suggest the opposite . we propose one possible scenario for the history of seyfert s sextet that takes into account the following significant factors : ( 1 ) the tidal tails are evidence for interactions among the accordant redshift members some time in the past , ( 2 ) the interactions that have occurred have not triggered star and/or star cluster formation similar to that seen in other merging galaxies and compact groups , ( 3 ) the relatively small amounts of neutral gas in seyfert s sextet remains bound in the one late type galaxy and does not appear to be distributed among the group environment , and ( 4 ) the low velocity dispersion among the member galaxies and the small distances between the member galaxies suggests that future interactions among the galaxies are likely . this accumulated evidence suggests that a number of gas - poor ( and one gas - rich ) galaxies have interacted beginning perhaps as long as 1 gyr or more in the past ( dated by the colors of the red globular cluster candidates ) . the interactions in the group have created the optical tidal tails and perhaps created the elliptical member of the sextet , ngc6027a , as well . the interactions in the past stripped stars from the progenitor galaxies , redistributing them within the group . the evidence for a red , low surface brightness halo encompassing all of the member galaxies , which is seen in our images as well as deeper ground - based images , is further evidence for a redistribution of the galaxies stars within the group . the only ongoing star formation and most of the neutral gas is found within the disk of ngc6027d , the only late type member of the group , suggesting that any interaction that involved this galaxy must have been minor , although the galaxy disk does appear somewhat irregular and perhaps warped . we speculate that further interactions are probably inevitable , and a major interaction between ngc6027d and the other members of the group may trigger the stripping of its neutral gas and star cluster formation throughout the group in the future . moreover , the low velocity dispersion suggests that none of the four large galaxies are likely to escape the group , and thus the group members may merge into a single galaxy , rather than remaining distinct . thus , we believe that we are seeing seyfert s sextet at the `` beginning of the end '' ; we presume that the future interactions will be the end of this group , transforming it into a single galaxy . we wish to acknowledge the help of m. eracleous with data reduction of our het spectra . we also wish to thank j. hibbard for a number of useful discussions . sz acknowledges support from the national science foundation through a research experiences for undergraduates award . this work was supported by nasa stsci and by the nsf under grants nsf ast 00 - 71223 and stsi hst - go-08717.04-a . lllcc alternate names : & & hcg 79 , vv115 , ngc6027 + equatorial coordinates : & & 15@xmath12359@xmath12412@xmath125 @xmath126 @xmath127 ( j2000.0 ) + mean redshift : & & 0.0145 + radial velocity dispersion : & & 138 km s@xmath0 + + galaxies : & & name & type & @xmath128 ( km s@xmath0 ) + & & ngc6027a & e0 & 4294 + & & ngc6027b & s0 & 4446 + & & ngc6027c & s0 & 4146 + & & ngc6027d & sdm & 4503 + & & ngc6027e & scd & 19809 + lrrrr 2.6 & 22.63@xmath1330.25 & 23.28@xmath1330.19 & @xmath134 & @xmath135 + 3.3 & 20.83@xmath1330.11 & 22.42@xmath1330.19 & @xmath136 & @xmath136 + 3.8 & 22.02@xmath1330.20 & 23.20@xmath1330.25 & @xmath136 & @xmath136 + 3.10 & 21.31@xmath1330.18 & 22.54@xmath1330.23 & @xmath136 & @xmath136 + 3.14 & 19.39@xmath1330.06 & 20.42@xmath1330.06 & 21.39@xmath1330.28 & 21.70@xmath1330.59 + 4.1 & 21.86@xmath1330.22 & 22.71@xmath1330.20 & @xmath137 & @xmath138 + 4.2 & 19.58@xmath1330.15 & 20.30@xmath1330.13 & 21.37@xmath1330.22 & 20.98@xmath1330.42 + 4.3 & 20.95@xmath1330.12 & 21.73@xmath1330.13 & 23.01@xmath1330.27 & 22.21@xmath1330.35 + 4.6 & 20.58@xmath1330.12 & 21.74@xmath1330.15 & @xmath136 & @xmath136 +

observations presented here and previous radio observations of the neutral gas content of this group suggest that the interactions that have taken place in the sextet only redistributed the stars from the member galaxies within the group . we speculate that future interactions may be strong enough to strip the gas from ngc6027d and trigger star cluster formation .

astro-ph0208284

c

_ hubble space telescope _ wide field planetary camera 2 images of hickson compact group 79 , seyfert s sextet , are presented . both point sources and extended sources detected on the three wf chips were photometered in four filters : f336w , f439w , f555w , and f814w . unlike other hcgs that have been imaged with _ hst _ , there do not appear to be any candidate young star clusters among the detected point sources . the majority of the point sources that may be star clusters associated with the sextet have red colors consistent with stellar populations older than 1 gyr . a similar conclusion is drawn with regard to the extended sources . the majority of these appear to be background galaxies , but a few candidate dwarf galaxies are identified as potentially associated with seyfert s sextet . however , no blue , star forming objects similar to the tidal dwarf galaxy candidates identified in other hcgs are found among the extended objects identified in this study . a redshift for one dwarf galaxy candidate was measured from a spectrum obtained with the hobby - eberly telescope , and this object was found to have a redshift similar to ngc6027e , the discordant spiral formerly identified as a member of this compact group . the _ hst _ observations presented here and previous radio observations of the neutral gas content of this group suggest that the interactions that have taken place in the sextet only redistributed the stars from the member galaxies within the group . we speculate that future interactions may be strong enough to strip the gas from ngc6027d and trigger star cluster formation .

fast and accurate predictions of binding free energies between proteins and small organic ligands would have significant impact on designing drugs @xcite and other modulators of biological processes . the clear relevance of protein - ligand binding affinity prediction in chemical biology and drug discovery has inspired a vast array of physics - based methods ( for a broad review , see @xcite ) , each with a different trade - off between computational accuracy and speed . on one extreme , molecular docking focuses on speed . docking algorithms are designed to quickly obtain plausible configurations of a protein - ligand complex . scoring functions are then used to rank one configuration versus another . docking programs are commonly assessed by their ability to redock ligands into crystallographic structures from which they have been removed . comparative studies @xcite and blinded exercises @xcite consistently show that docking methods are adept at generating the native pose but are less competent at giving it the highest rank . in this context , it is not surprising that docking scores are poorly correlated with binding free energies @xcite . in contrast , alchemical pathway methods are based on rigorous statistical mechanics . the methods involve sampling from a series of possibly nonphysical thermodynamic states in between end - states where the receptor and ligand are bound and unbound . in the unbound state , the receptor - ligand nonbonded interaction terms may be switched off or the species may be physically separated . in accordance to the established statistical mechanics of noncovalent binding @xcite , the receptor is usually allowed full flexibility . unfortunately , sampling a fully flexible complex from multiple statistical distributions along an alchemical pathway generally requires substantial computing resources ; it has been suggested that most published studies are not fully converged @xcite ! even sampling the ligand binding pose is challenging @xcite . to bypass this difficulty , most pathway calculations pursue relative binding free energies between similar molecules and assume that the binding mode does not change . in absolute binding free energy calculations , ligand sampling issues are usually alleviated by confining the molecule to a specific pose @xcite . within this restricted range of problems , alchemical pathway calculations are amassing a growing track record of accurate prediction ( e.g. @xcite ) . _ the success of these methods suggests that docking may be substantially improved by incorporating rigorous statistical mechanics . _ implicit ligand theory ( ilt ) @xcite , a recently derived statistical mechanics framework for noncovalent association , has the potential to inspire new methods that combine the speed of docking and the rigor of alchemical pathway methods . ilt formally separates receptor and ligand sampling into two distinct stages . because the first stage of receptor sampling does not require a ligand , receptor conformations can be sampled once and used with many different ligands . in contrast , conventional alchemical pathway methods require thorough receptor sampling for every receptor - ligand pair . the second stage is to calculate the binding potential of mean force ( bpmf ) - the binding free energy between a ligand and a _ rigid _ receptor configuration ( eq . [ eq : bpmf ] ) - for each receptor configuration . finally , the standard binding free energy is an exponential average of bpmfs ( eq . [ eq : fe_ilt ] ) . while multiple bpmfs are required to estimate a standard binding free energy , the overall calculation should require less computer time than conventional methods because bpmfs are easier to estimate than binding free energies with a fully flexible receptor . the key reason for this speedup is that a bpmf calculation only requires sampling of the ligand , which usually has many fewer degrees of freedom than the complex . furthermore , nonbonded interactions between a rigid receptor and ligand can be treated by interpolating precomputed three - dimensional grids , a strategy first developed for docking @xcite . once the grid is stored , calculation time no longer depends on the size of the receptor . in contrast , conventional alchemical pathway methods require frequent force evaluation between flexible receptor atoms . as the number of pairwise interactions scales as @xmath1 with n receptor atoms ( neglecting cutoffs ) , the relative efficiency of ilt - based methods will be more pronounced as receptor size increases . in the first paper on ilt , bpmfs were estimated for simple host - guest systems @xcite . here , the focus is on precise bpmf estimation for protein - ligand systems . @xcite previously computed binding free energies between simple ligands and a rigid protein , t4 lysozyme . in contrast , the present work involves more diverse systems . @xcite were equally rigorous , but did not implement specialized methods to significantly speed their calculations compared to flexible - receptor calculations . @xcite developed a fast method based on a number of approximations . as in other bpmf @xcite and standard binding free energy @xcite calculations , hamiltonian replica exchange is applied . the main methodological differences between the current and previous work are the adaptive initialization of thermodynamic states and the use of linearly - scaled interaction grids @xcite with transformation - based smoothing @xcite ; these will be discussed in detail in the section on _ theory and methods_. the method is demonstrated on the astex diverse set @xcite , a curated database of 85 high - quality protein - ligand complexes of pharmaceutical or agrochemical interest . the algorithm is implemented in a new software package , alchemical grid dock ( algdock ) , a python module based on the molecular modeling toolkit ( mmtk ) 2.7.8 @xcite . algdock is available under the open - source mit license at https://github.com / ccbatiit / algdock/.

a binding potential of mean force ( bpmf ) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid . expanding on previous work with host - guest systems , the method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein - ligand interaction strengths . protein - ligand interactions are represented by interpolating precomputed electrostatic and van der waals grids . using a simple estimator for thermodynamic length , thermodynamic states are initialized at approximately equal intervals . the method is demonstrated on the astex diverse set , a database of 85 protein - ligand complexes relevant to pharmacy or agriculture . even with low variance , however , the mean bpmf was sometimes dependent on starting conditions , implying inadequate sampling . within the thermodynamic cycle , free energies estimated based on multiple intermediate states were more precise , and those estimated by single - step perturbation were less precise . the software used to perform these calculations , alchemical grid dock ( algdock ) , is available under the open - source mit license at https://github.com / ccbatiit / algdock/.

1507.03703

i

a binding potential of mean force ( bpmf ) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid . expanding on previous work with host - guest systems , i have developed a method to calculate bpmfs for protein - ligand systems . the method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein - ligand interaction strengths . protein - ligand interactions are represented by interpolating precomputed electrostatic and van der waals grids . using a simple estimator for thermodynamic length , thermodynamic states are initialized at approximately equal intervals . the method is demonstrated on the astex diverse set , a database of 85 protein - ligand complexes relevant to pharmacy or agriculture . fifteen independent simulations of each complex were started using poses from crystallography , docking , or the lowest - energy pose observed in the other simulations . benchmark simulations completed within three days on a single processor . overall , protocols initialized using the thermodynamic length estimator were system - specific , robust , and led to approximately even replica exchange acceptance probabilities between neighboring states . in most systems , the standard deviation of the bpmf converges to within 5 k@xmath0 t . even with low variance , however , the mean bpmf was sometimes dependent on starting conditions , implying inadequate sampling . within the thermodynamic cycle , free energies estimated based on multiple intermediate states were more precise , and those estimated by single - step perturbation were less precise . the results demonstrate that the method is promising , but that ligand pose sampling and phase space overlap can sometimes prevent precise bpmf estimation . the software used to perform these calculations , alchemical grid dock ( algdock ) , is available under the open - source mit license at https://github.com / ccbatiit / algdock/.

this section reviews implicit ligand theory , details the algorithms in algdock , and describes the setup of the bpmf calculations on the astex diverse set . for the noncovalent association between a receptor @xmath2 and ligand @xmath3 to form a complex @xmath4 , @xmath5 , the standard binding free energy is , @xmath6 where @xmath7 is the inverse of boltzmann s constant times the temperature , @xmath8 is the standard concentration ( 1 m = 1/1660 @xmath9 ) , and @xmath10 is the equilibrium concentration of species @xmath11 . activities have been assumed to be unity , a reasonable approximation in the limit of low concentrations . coordinates of the complex , @xmath12 , are partitioned into receptor ( @xmath13 ) and ligand internal ( @xmath14 ) and external ( @xmath15 ) coordinates . based on this partitioning , the interaction energy is defined as @xmath16 , where @xmath17 is an effective potential energy that includes the gas - phase potential energy @xmath18 and solvation free energy @xmath19 @xcite . a bpmf is an exponential average of interaction energies over ligand coordinates in the binding site @xcite , @xmath20 where @xmath21 is an indicator function that takes values between 0 and 1 and specifies whether the receptor and ligand are bound or not . according to ilt , the standard binding free energy @xmath22 is related to an exponential average of bpmfs over boltzmann - distributed receptor configurations @xmath13 , @xmath23 } dr_r } { \int e^{-\beta { \mathcal u}(r_{r } ) } dr_r } \right ) - \beta^{-1 } \ln \left ( \frac{\omega c^\circ}{8 \pi^2 } \right ) , \label{eq : fe_ilt}\end{aligned}\ ] ] where @xmath24 is the volume of the binding site . a bpmf can also be expressed as a ratio of partition functions @xcite , @xmath25 } ~ dr_l d\xi_l } \right ) . \label{eq : bpmf_ratio}\end{aligned}\ ] ] in algdock , bpmfs are estimated by completing the thermodynamic cycle shown in figure [ fig : thermo_cycle ] . , width=322 ] mathematical expressions for individual free energy differences within the cycle are given in table [ tab : b_parts ] . the sum of all the free energy components in table [ tab : b_parts ] is @xmath26 . . * thermodynamic cycle for bpmfs : expressions * [ cols="^,^,^,^",options="header " , ] the least precise free energy estimates between adjacent milestones . counts are based on all simulations or the imprecise subset , when the standard deviation of the total bpmf is greater than 5.0 . [ tab : least_precise ] for systems with poor convergence of bpmf estimates , longer sampling is not necessarily an effective way to improve the precision of free energy estimates . while @xmath27 $ ] usually decreases monotonically with sample size , this trend is not universally true ( figure [ fig : std_fe_cycle ] ) . in some systems there are temporary jumps in @xmath27 $ ] due to instability in determining the equilibrated cycle . more importantly , in other systems , @xmath27 $ ] appears flat , with little or no change with increased sampling . $ ] based on 15 independent simulations of ( a ) the ligand or @xmath28 $ ] based on the ligand simulations and 15 independent simulations of the complex starting from the ( b ) crystallographic , ( c ) docked , and ( d ) lowest - energy observed poses . [ fig : std_fe_cycle],width=641 ] + in some systems , the variance is low but free energy estimates are dependent on the starting poses . when results from all simulations between milestones c&d are grouped together , the standard deviation in many systems no longer converges to within 5 @xmath29 . because converged thermodynamic quantities should not depend on initial conditions , this inconsistency implies that some simulations are not fully converged . when free energy estimates contradict , it is not completely clear which result is most consistent with the force field . false convergence is quantified based on the minimum value , using @xmath30 $ ] . a system is considered to be falsely converged when @xmath31 $ ] is less than 5 @xmath29 but @xmath32 $ ] is greater than 15 @xmath29 . based on this definition , false convergence occurs in a nontrivial fraction of systems ( table [ tab : nconverged ] ) . ultimately , poor convergence and false convergence are caused by incomplete sampling . the most straightforward explanation for incomplete sampling is that a simulation starts and remains trapped in a local minimum distinct from the global minimum energy . indeed , between milestones c&d , most falsely converged calculations starting from the crystal structure ( 4/5 ) and docked poses ( 7/11 ) have no starting pose within 1.0 of the lowest - energy observed pose . however , sampling the lowest - energy structure is not a sufficient condition for complete sampling , as other poses may have a lower _ free energy_. for simulations starting from the lowest - energy observed pose , four systems appear falsely converged between milestones c&d ( formatted by pdb identifier ( @xmath31 , \sigma[f , f_{min}]$ ] ) with @xmath33 in units of @xmath29 ) : 1hww ( 0.353 , 16.1 ) , 1r1h ( 3.95 , 15.3 ) , 1hp0 ( 0.496 , 16.7 ) , 1gm8 ( 0.422 , 15.6 ) . for 1hww ( figure [ fig : dock_last](c ) and ( d ) ) and 1gm8 ( figure [ fig : dock_last](g ) and ( h ) ) , starting from the crystallographic pose leads to a lower estimate of @xmath34 than the lowest - energy pose . for 1hp0 ( figure [ fig : dock_last](e ) and ( f ) ) , a docked pose has the lowest estimated @xmath34 . 1r1h does not appear to sample different poses ; the large @xmath32 $ ] is the result of an outlier with a significantly lower @xmath34 estimate than average .

fifteen independent simulations of each complex were started using poses from crystallography , docking , or the lowest - energy pose observed in the other simulations . benchmark simulations completed within three days on a single processor . overall , protocols initialized using the thermodynamic length estimator were system - specific , robust , and led to approximately even replica exchange acceptance probabilities between neighboring states . in most systems , the standard deviation of the bpmf converges to within 5 k@xmath0 t .

1507.03703

m

a binding potential of mean force ( bpmf ) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid . expanding on previous work with host - guest systems , i have developed a method to calculate bpmfs for protein - ligand systems . the method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein - ligand interaction strengths . protein - ligand interactions are represented by interpolating precomputed electrostatic and van der waals grids . using a simple estimator for thermodynamic length , thermodynamic states are initialized at approximately equal intervals . the method is demonstrated on the astex diverse set , a database of 85 protein - ligand complexes relevant to pharmacy or agriculture . fifteen independent simulations of each complex were started using poses from crystallography , docking , or the lowest - energy pose observed in the other simulations . benchmark simulations completed within three days on a single processor . overall , protocols initialized using the thermodynamic length estimator were system - specific , robust , and led to approximately even replica exchange acceptance probabilities between neighboring states . in most systems , the standard deviation of the bpmf converges to within 5 k@xmath0 t . even with low variance , however , the mean bpmf was sometimes dependent on starting conditions , implying inadequate sampling . within the thermodynamic cycle , free energies estimated based on multiple intermediate states were more precise , and those estimated by single - step perturbation were less precise . the results demonstrate that the method is promising , but that ligand pose sampling and phase space overlap can sometimes prevent precise bpmf estimation . the software used to perform these calculations , alchemical grid dock ( algdock ) , is available under the open - source mit license at https://github.com / ccbatiit / algdock/.

the procedure of determining parton distributions by so - called global fits to data , mainly structure functions , is long established @xcite-@xcite . however , it is a rather more recent development to try to determine the errors on these distributions at the same time . this has come about for a number of reasons . firstly , the sheer amount of data ( full references in @xcite ) sensitive to various parton distributions , and the precision of this data , has become such that an accurate determination of all parton distributions is possible ( with some problems only in difficult to reach regions of phase space , e.g. @xmath0 very near to 1 ) . secondly , the understanding of the experimental errors on this data has reached a new level of sophistication , with the systematic errors being understood far better in terms of their separate sources and correlations . lastly , the theoretical understanding at nlo in @xmath1 has improved so that subtleties due to e.g. heavy quarks are now understood . there are many issues in the determination of errors on parton distributions , and a discussion of these may be found in @xcite . however , one of the main outstanding problems , and the focus of a discussion session at this meeting , is the manner in which one determines precisely the size of the errors .

a discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined . one of the central problems is the criteria used to judge what variation of the parameters describing a set of partons is acceptable within the context of a global fit . various ways of addressing this question are outlined .

hep-ph0205233

i

a discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined . one of the central problems is the criteria used to judge what variation of the parameters describing a set of partons is acceptable within the context of a global fit . various ways of addressing this question are outlined .

in previous works , we have succesfully applied a langevin canonical formalism to the stochastic dynamics of a non - isolated chiral tls when reproducing some quantum thermodynamic functions ( such as , the partition function and heat capacity ) . in this paper , as a continuation and extension of our work , we have tackled the dynamics of the qsr . this resonance is considered as a well known cooperative effect of friction , noise and periodic driving occurring in a bistable system . under the presence of the driving field , the heat capacity has also been analyzed at asymptotic times . we have assumed so far that the tunneling rate is a constant value . obviously , this rate could be considered to also be a function of time . this should have important implications in the detection of qsr in chiral molecular systems . due to the fact that this stochastic dynamics is occurring at ultracold regimes , a sort of bose - einstein condensation could take place . moreover , at this regime , the noise is usually colored with a complex time autocorrelation function . all of these ingredients should be incorporated to such a dynamics in order to improve the description of nonisolated chiral tls . work in this direction is now in progress . leggett , a.j . ; chakravarty , s. ; dorsey , a.t . ; fisher , m. p.a . ; garg , a. ; zwerger w. dynamics of the dissipative two - state system . _ rev . phys . _ * 1987 * , _ 59 _ , 1 - 85 ; _ ibid . _ erratum * 1995 * , _ 67 _ , 725 . guijarro , a. , yus , m. _ the origin of chirality in the molecules of life _ , rsc publishing , cambridge , 2009 . bargueo , p. ; de tudela , r. p. constraining long - range parity violation in gravitation using high resolution spectroscopy of chiral molecules . d _ * 2008 * , _ 78 _ , 1002004 - 1,5 . bargueo , p. ; peate rodrguez , h.c . ; gonzalo , i. ; sols f. ; miret artes , s. friction - induced enhancement in the optical activity of interacting chiral molecules . lett . _ * 2011 * , _ 516 _ , 29 - 34 . dorta urra , a. ; peate rodrguez , h.c . ; bargueo , p. ; rojas lorenzo , g. ; miret artes , s. dissipative geometric phase and decoherence in parity - violating chiral molecules . _ j. chem . phys . _ * 2012 * , _ 136 _ , 174505 . rodrguez , h.c . ; dorta urra , a. ; bargueo , p. ; rojas lorenzo , g. ; miret artes , s. a langevin canonical approach to the dynamics of chiral systems : populations and coherences . _ chirality _ * 2013 * , _ 25 _ , 514 - 520 . rodrguez , h.c . ; dorta urra , a. ; bargueo , p. ; rojas lorenzo , g. ; miret artes , s. a langevin canonical approach to the dynamics of chiral systems : thermal averages and heat capacity . _ chirality _ * 2014 * , _ 26 _ , 319 - 325 . cahn , s.b . ; ammon , j. ; kirilov , e. ; gurevich , y.v . ; murphree , d. ; paolino , r. ; rahmlow , d.a . ; kozlov , m.g . ; demille d. zeeman - tuned rotational level - crossing spectroscopy in a diatomic free radical . * 2014 * , _ 112 _ , 163002 . bargueo , p. ; prez de tudela , r. ; miret arts , s. ; gonzalo , i. an alternative route to detect parity violating energy differences through bose - einstein condensation of chiral molecules . phys . _ * 2011 * , _ 13 _ , 806 - 810 .

stochastic dynamics , within the markovian regime and ohmic friction , some standard quantum thermodynamics functions such as the energy average and heat capacity can be extracted . in particular , special emphasis is put on the so - called quantum stochastic resonance which is a cooperative effect of friction , noise and periodic driving occurring in a bistable system .

1604.03712

c

a langevin canonical framework for a chiral two - level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well - known spin - boson model . from this stochastic dynamics , within the markovian regime and ohmic friction , some standard quantum thermodynamics functions such as the energy average and heat capacity can be extracted . in particular , special emphasis is put on the so - called quantum stochastic resonance which is a cooperative effect of friction , noise and periodic driving occurring in a bistable system .

good quantum numbers , that describe conserved quantities as a quantum system evolves , derive their significance from their connection to the powerful conservation laws of physics . in addition to the familiar examples of spin and crystal momentum , under some circumstances electrons in solids can have an additional quantum number that distinguishes them , which we call the _ flavor _ ; we denote the total number of flavors by @xmath5 . one example of such a system are semiconductors and semimetals that have degenerate conduction - band valleys , the flavor denotes the electron s valley . examples of multi - valley semiconductors include ge , which as shown in fig . [ fig : gebandstructure ] has four degenerate valleys ( n.b . not eight , as valleys at the brillouin zone vertices overlap ) , si has six degenerate valleys , a ge - si alloy has ten degenerate valleys , and @xmath6 has twelve valleys in the @xmath7 band @xcite . the system has been experimentally realized as an electron - hole liquid that forms in drops @xcite . in these systems the number of flavors ( the number of valleys ) is well defined and there are strong coulomb interactions between particles which motivates the analysis . this is in contrast to several other systems in which the number of flavors is poorly defined such as heavy fermions @xcite , charged domain walls @xcite , a super - strong magnetic field @xcite , and spin instabilities @xcite ; or where the number of flavors is well defined but interactions between particles are weak such as ultracold atoms in optical lattices @xcite . the properties of a many - flavor electron gas ( mfeg ) in a semiconductor were first studied analytically for the normal phase by @xcite , and for the superconducting phase by @xcite . recently one of us @xcite extended the mfeg analysis by finding an energy functional and gradient expansion , which allowed the study of inhomogeneous systems . however , the analytical treatment was limited to consider the same contributions to the energy as in the random phase approximation ( these contributions dominate in the many - flavor limit ) . to go further requires numerical calculations , the only example of which for a mfeg to date @xcite used a self - consistent approach for the local field correction formulated by @xcite ( stls ) , see also ref . the method was later applied to charge impurities by @xcite . the calculations of ref . @xcite were performed for @xmath8 , too few flavors to gauge the applicability of the analytic many - flavor approximation , which is estimated to apply at around six or more flavors @xcite . $ ] direction calculated using a plane - wave pseudopotential method @xcite . the fermi energy is at @xmath9 ; below are valence bands with the holes centered around h , above are conduction bands . the first conduction band valley is highlighted in bold , low - lying conduction - band electrons are centered around c. ] in this paper we follow the suggestion of @xcite , and present the results of what are expected to be more accurate diffusion monte carlo ( dmc ) @xcite calculations on the mfeg for @xmath10 , which should allow us to verify the analytical mfeg approach . we then examine aspects of the many - flavor approximation that have not yet been studied computationally : in sec . [ sec : casinoelectrongasdensityresponse ] we compare the analytical density - density response function derived in sec . [ sec : analyticalpolarisability ] with that predicted using dmc . once verified this allows us in sec . [ sec : quantumdotsqmc ] to employ a gradient expansion within density - functional theory ( dft ) to find the ground state of a quantum dot , we compare results with dmc calculations and examine the validity of the gradient expansion . we adopt the atomic system of units : that is @xmath11 . the mass @xmath12 is defined to be the electron mass , @xmath13 , multiplied by a dimensionless effective mass @xmath14 appropriate for the conduction - band valleys , which when @xmath15 will recover standard atomic units . we assume the valleys all have the same dispersion profile and so the same effective mass , @xcite outlined a method of calculating a scalar effective mass for anisotropic valleys . with the above definitions , energy is given in terms of an exciton @xmath16 , where @xmath17 is the hartree energy , and length @xmath18 in terms of the bohr radius @xmath19 . to denote density we use both the number density of conduction - band electrons @xmath20 and the wigner - seitz radius @xmath21 . before presenting the numerical results , to orient the discussion , we describe the basic physics of the mfeg and review the analytical results of ref . @xcite that will be computationally verified in this paper . in a low temperature mfeg , the number of flavors @xmath5 , number density of conduction - band electrons @xmath20 , and fermi momentum @xmath22 are related through @xmath23 at fixed electron density , the fermi momentum reduces with increasing number of flavors as @xmath24 , so each fermi surface encloses fewer states . the semiconductor hole band - structure often has a single valence - band minimum at the @xmath25 point , such as in ge , see fig . [ fig : gebandstructure ] , hence we assume the holes are heavy and are uniformly distributed , providing a jellium background . for a constant number density of particles , the density of states at the fermi surface , @xmath26 , rises with increasing number of flavors as @xmath27 . therefore , the screening length estimated with the thomas - fermi approximation @xcite is @xmath28 , and the ratio of the screening to fermi momentum length - scale varies with number of flavors as @xmath29 . in the many - flavor limit @xmath30 , the screening length is much smaller than the inverse fermi momentum , @xmath31 , and so the dominant electron - electron interactions have characteristic wave vectors which obey @xmath32 . this is in direct contrast to the random phase approximation ( rpa ) where @xmath33 , although in both the many - flavor and the rpa , the same green function contributions with empty electron loops dominate diagrammatically @xcite . these diagrams contain the greatest number of different flavors of electrons , and as @xmath30 therefore have the largest matrix element . since @xmath32 , the typical length - scales of the mfeg are short , this indicates that a local density approximation ( lda ) could be applied . this motivation is in addition to the usual reasons for the success of the lda in dft @xcite , namely that the lda exchange - correlation hole need only provide a good approximation for the spherical average of the exchange - correlation hole and obey the sum rule @xcite . in the many - flavor limit the exact result for the polarizability of a mfeg at wave vector @xmath34 , and matsubara frequency @xmath35 is @xcite @xmath36{\ , , } \end{aligned}\ ] ] which in the many - flavor limit is approximately @xmath37 this quantity governs the density - density response of the mfeg so is important to verify . since eqn . has a simple form it can be used to calculate further properties of the mfeg @xcite , such as homogeneous energy in sec . [ sec : analyticaluniformenergy ] and the gradient expansion in sec . [ sec : analyticalgradient ] , which further motivates its numerical verification . starting from the approximate expression for polarizability , eqn . , it can be shown that the total energy of a mfeg , including all the exchange and correlation contributions is @xcite @xmath38 where @xmath39 and @xmath40 denotes the interacting energy ( which would be zero if electron - electron interactions were ignored ) . in ref . @xcite it was suggested that this relation for the total energy applies over a density range , at @xmath41 accuracy , @xmath42 , which widens with number of flavors as @xmath43 ( see also ref . @xcite ) . considering the number of flavors where the range of validity vanishes indicates that the many - flavor limit will apply if there are ten or more flavors . an alternative estimate for the density range is found in sec . [ sec : groundstateenergyvariation ] by comparing the analytical result with dmc calculations . the applicability of the lda in a mfeg motivates the search for a gradient expansion to the energy eqn . as a way to analyze inhomogeneous systems such as electron - hole drops and quantum dots . the typical momentum transfer in the mfeg is @xmath44 , which defines the shortest length - scale over which a lda can be made , therefore , the maximum permissible gradient in electron density is @xmath45 . a gradient expansion will break down for phenomena with short length - scales , for example mass enhancement @xcite . if electron density is smoothly varying then starting from eqn . , the gradient correction to the energy for a mfeg is @xcite @xmath46 where @xmath47 is the energy of a homogeneous mfeg with density @xmath20 , see eqn . . as discussed in sec . [ sec : analyticalresults ] , this gradient expansion would be useful for dft calculations and so its computational verification is important .

a many - flavor electron gas ( mfeg ) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion monte carlo ( dmc ) calculations . rev . the analytical result for the mfeg is generalized to inhomogeneous systems by means of a gradient correction , the validity range of this approach is obtained . employed within a density - functional theory calculation this approximation compares well with dmc results for a quantum dot .

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a many - flavor electron gas ( mfeg ) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion monte carlo ( dmc ) calculations . the dmc results compare well with an analytic expression derived by one of us [ phys . rev . b * 78 * , 035111 ( 2008 ) ] for the total energy to within @xmath0 over an order of magnitude range of density , which increases with valley degeneracy . for @xmath1 ( six - fold valley degeneracy ) the applicable charge carrier densities are between @xmath2 and @xmath3 . dmc calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate mfeg polarizability for wave numbers @xmath4 . the analytical result for the mfeg is generalized to inhomogeneous systems by means of a gradient correction , the validity range of this approach is obtained . employed within a density - functional theory calculation this approximation compares well with dmc results for a quantum dot .

we have computationally verified the theory of the mfeg presented in @xcite using qmc simulations . in a homogeneous system , dmc estimates for the ground state energy are consistent with theory and the theoretically estimated density range over which the theory applies is consistent with numerical results . the applicable density for @xmath1 @xmath147 corresponds to a charge carrier density between @xmath2 and @xmath3 . the density response function for a mfeg with 24 flavors was found using three methods : density modulation predicted by vmc , and the variation in ground state energy predicted by vmc and also by dmc . the two vmc results underestimated the response @xmath148 , but the dmc results agreed with theory and could distinguish between the exact and a useful approximate expression for polarizability . we used a many - flavor functional including a local gradient approximation in dft calculations of large quantum dots . the dft calculation estimated the ground - state energy and wave function , which were verified by a dmc calculation . we found the high gradient breakdown of the expansion was at @xmath149 , the low gradient breakdown was consistent with the homogeneous mfeg lowest applicable density , and that the gradient expansion was applicable in the intermediate regime . the many - flavor functional , used as part of dft calculations , could be a useful tool for analyzing other multi - valley semiconductor systems . g.j.c . acknowledges the financial support of an epsrc studentship , p.d.h . was supported by a royal society university research fellowship . we thank n.d.m . hine for providing the dotdft code , p. lpez ros and n.d . drummond for help modifying and running casino , r. needs for providing computing time , and a.j . morris for careful reading of the manuscript .

the dmc results compare well with an analytic expression derived by one of us [ phys . the applicable charge carrier densities are between @xmath2 and @xmath3 . dmc calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate mfeg polarizability for wave numbers @xmath4 .

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a many - flavor electron gas ( mfeg ) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion monte carlo ( dmc ) calculations . the dmc results compare well with an analytic expression derived by one of us [ phys . rev . b * 78 * , 035111 ( 2008 ) ] for the total energy to within @xmath0 over an order of magnitude range of density , which increases with valley degeneracy . for @xmath1 ( six - fold valley degeneracy ) the applicable charge carrier densities are between @xmath2 and @xmath3 . dmc calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate mfeg polarizability for wave numbers @xmath4 . the analytical result for the mfeg is generalized to inhomogeneous systems by means of a gradient correction , the validity range of this approach is obtained . employed within a density - functional theory calculation this approximation compares well with dmc results for a quantum dot .

a quantum monte carlo and maximum entropy calculation of the optical conductivity of the infinite - dimensional hubbard model has been presented . the mott - insulating character of the ground state at half filling drives many anomalous behaviors in the normal state near half filling that are similar to those observed in the cuprate superconductors . in particular the system is always a fermi liquid away from half filling , but the fermi temperature vanishes , and the quasiparticle renormalization factor diverges as half filling is approached . as a result , the free carriers in the system initially have a hole - like character ( that changes to an electron - like character at approximately quarter filling ) . the drude width for these carriers grows linearly with temperature for temperatures above @xmath31 , the drude weight grows linearly with doping , and there is a doping and temperature dependent mid - ir peak . these anomalies arise naturally from the presence of a strongly temperature - dependent quasiparticle peak , whose origin is a kondo - like screening of the magnetic moments , and which appears to occur in the hubbard model for all dimensions greater than 1 . the anomalous features in the experimentally measured optical conductivity for the cuprates are usually attributed to either polarons or impurities . however , any purely polaronic theory has difficulty in explaining the magnetic insulating character of the ground state at half filling . the hubbard model naturally describes such an insulating state , and appears to also describe many of the anomalous features present in the experimental data . in light of this fact , it is worthwhile to try to incorporate both the effects of strong electron correlation , and the electron - phonon interaction into a comprehensive theory for the normal state of the cuprate materials . work along these lines is in progress . we would like to acknowledge useful conversations with w. chung , j. keller , y. kim , d. scalapino , r. scalettar , d. tanner , and g. thomas . this work was supported by the national science foundation grant number dmr-9107563 , the nato collaborative research grant number crg 931429 and through the nsf nyi program . in addition , we would like to thank the ohio supercomputing center , and the physics department of the ohio state university for providing computer facilities . j.g . bednorz and k.a . mller , z. phys . * 64 * , 189 ( 1986 ) . for reviews of relevant experiments see c. h. pennington and c. p. slichter , in _ physical properties of high temperature superconductors _ edited by d. m. ginsberg vol.2 ; n. p. ong ibid . ; y. iye ibid . 3 . d.b . romero , c. d. porter , d. b. tanner , l. forro , d. mandrus , l. mihaly , g. l. carr , and g. p. williams , phys . lett . * 68 * , 1590 ( 1992 ) ; see also l. forro , g. l. carr , g. p. williams , d. mandrus , and l. mihaly , phys . 65 * , 1941 ( 1990 ) . for a review , please see t. timusk and d. b. tanner , in _ physical properties of high temperature superconductors _ , vol . 1 , edited by d. m. ginsberg ( world scientific , singapore , 1989 ) , pp . 339407 , g. a. thomas , in _ proceedings from the 39th scottish universities summer school in physics _ , edited by d.p . tunstall , w. barford , and p. osborne ( adam hilger , new york , 1991 ) , pp . 169206 , and references contained therein . anderson , _ frontiers and borderlines in many particle physics _ , proceedings of the international school of physics `` enrico fermi '' ( north holland , amsterdam , 1987 ) , p. 1 ; p.w . anderson , science * 235 * , 1196 ( 1987 ) . f. c. zhang and t. m. rice , phys . b * 37 * , 3759 ( 1988 ) . g. baskaran , p.w . anderson , phys . * b37 * , 850 ( 1988 ) . j. slyom , adv . * 28 * , 201 ( 1979 ) . anderson , physica c * 185 * , 11 ( 1991 ) . varma , p.b . littlewood , s. schmitt - rink , e. abrahams and a.e . ruckenstein , phys . * 63 * , 1996 ( 1989 ) . m. jarrell and th . pruschke , phys . * b49 * , 1458 ( 1993 ) ; th . pruschke and m. jarrell , physica b * 199&200 * , 217(1994 ) . christoph quitmann , ph.d . thesis , aachen 1992 ( unpublished ) . n. bulut , d. j. scalapino , and s. r. white , phys . lett . * 72 * , 705 ( 1994 ) . j. hubbard , proc . r. soc . ( london ) a * 276 * , 238 ( 1963 ) ; m.c . gutzwiller , phys . rev . lett . * 10 * , 159 ( 1963 ) ; j. kanamori , prog . * 30 * , 257 ( 1963 ) . w. metzner and d vollhardt , phys . rev . lett . * 62 * , 324 ( 1989 ) . u. brandt and c. mielsch , z. phys . b * 75 * , 365 ( 1989 ) ; z. phys . b * 79 * , 295 ( 1990 ) ; z. phys . b * 82 * , 37 ( 1991 ) . v. jani , z. phys . b * 83 * , 227 ( 1991 ) . c. kim , y. kuramoto and t. kasuya , j. phys . japan * 59 * , 2414 ( 1990 ) . v. jani and d. vollhardt , int . j. mod . phys . , 713 ( 1992 ) . m. jarrell phys . lett . * 69 * , 168 ( 1992 ) . a. georges and g. kotliar , phys . rev . * b45 * , 6479 ( 1992 ) . j.e . hirsch and r.m . fye , phys . * 56 * , 2521 ( 19 86 ) . m. jarrell , h. akhlaghpour , and thomas pruschke , _ quantum monte carlo methods in condensed matter physics _ , edited by m. suzuki , ( world scientific , 1993 ) . gubernatis , m. jarrell , r.n . silver , and d.s . sivia , phys . b * 44 * , 6011 ( 1991 ) ; and m. jarrell and j.e . gubernatis , to appear . h. keiter and j.c . kimball , intern . j. magnetism * 1 * , 233(1971 ) ; n.e . bickers , d.l . cox and j.w . wilkins , phys . b*36 * , 2036 ( 1987 ) ; th . pruschke and n. grewe , z. phys . b * 74 * , 439 ( 1989 ) . th . pruschke , d.l . cox and m. jarrell , phys . , 3553 ( 1993 ) ; th . pruschke , d.l . cox and m. jarrell , europhys . * 21 * , 593 ( 1993 ) . a. khurana , phys . 64 * , 1990 ( 1990 ) . j. k. freericks and m. jarrell , phys . ( to appear ) ; p. g. j. van dongen , ( submitted to phys . rev . p. f. maldague , phys . b * 16 * , 2437 ( 1977 ) . scalapino , s. white and s. zhang , phys . b , * 47 * , 7995 ( 1993 ) . h. eskes and a. m. ole ' s , phys lett . * 73 * , 1279 ( 1994 ) . s. uchida , t. ido , h. takagi , t. arima , y. tokura , s. tajima , phys . b * 43 * , 7942 ( 1991 ) ; s. uchida , j. phys . chem . solids , * 53 * , 1603 ( 1992 ) . j. orenstein , g. a. thomas , a. j. millis , s. l. cooper , d. h. rapkine , t. timusk , l. f. schneemeyer , and j. v. waszczak , phys . b * 42 * , 6342 ( 1990 ) . romero , et al . ( unpublished ) . g. a. thomas , d. h. rapkine , s. l. cooper , s - w . cheong , and a. s. cooper , phys . lett . * 67 * , 2906 ( 1991 ) ; g. a. thomas , d. h. rapkine , s. l. cooper , s - w . cheong , a. s. cooper , l. f. schneemeyer , and j. v. waszczak , phys . b * 45 * , 2474 ( 1992 ) . s. uchida , h. takagi , y. tokura , s. koshihara , and t. arima , in _ strong correlation and superconductivity _ , edited by h. fukuyama , s. maekawa , and a. p. malozemoff ( springer , tokyo , 1989 ) pp . 194203 . g. yu , c. h. lee , d. mihailovic , a. j. heeger , c. fincher , n. herron , and e. m. mccarron , phys . b * 48 * , 7545 ( 1993 ) . kim , s .- w . cheong , and z. fisk , phys . rev . lett . , 2227 ( 1991 ) . a. s. alexandrov , v. v. kabanov , and d. k. ray , physica c * 224 * , 247 ( 1994 ) .

a monte carlo - maximum entropy calculation of the optical conductivity of the infinite - dimensional hubbard model is presented . we show that the optical conductivity displays the anomalies found in the cuprate superconductors , including a drude width which grows linearly with temperature , a drude weight which grows linearly with doping , and a temperature and doping - dependent mid - ir peak . these anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the fermi energy as @xmath0 , and are a generic property of the strongly correlated hubbard model in all dimensions greater than one .

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a monte carlo - maximum entropy calculation of the optical conductivity of the infinite - dimensional hubbard model is presented . we show that the optical conductivity displays the anomalies found in the cuprate superconductors , including a drude width which grows linearly with temperature , a drude weight which grows linearly with doping , and a temperature and doping - dependent mid - ir peak . these anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the fermi energy as @xmath0 , and are a generic property of the strongly correlated hubbard model in all dimensions greater than one .

it has been well known that the standard lowest order conforming elements can produce numerical locking and checker - board solutions in the approximation of solid and fluid mechanics problems : see for instance @xcite and the references therein . an efficient approach to deal with this case is to employ the nonconforming element method , which has made a great impact on the development of finite element methods @xcite . to approximate pdes using a nonconforming element of order @xmath2 , one needs to impose the continuity of the moments up to order @xmath3 of the functions across all the interfaces of neighboring elements . this condition is known as the patch test @xcite . in two dimensions , the patch test is equivalent to the continuity at the @xmath2 gauss points located on each interface . this implies that a @xmath4-nonconforming element , if exists , must be continuous at the @xmath2 gauss points on each edge . these points ( completed with internal points for @xmath5 ) can be used to define local lagrange degrees of freedom ( dofs ) on the simplex if @xmath2 is odd , but this construction is not possible if @xmath2 is even since there exists a lower - degree polynomial vanishing at all the gauss points @xcite . thus suitable bubble functions are often employed to enrich the finite element space . until now , the triangular nonconforming elements are well studied in the literature ( see , @xcite ) , but the analysis of their quadrilateral counterparts is less complete . even though the triangular or tetrahedral meshes are popular to use , in some cases where the geometry of the problem has a quadrilateral nature , one wishes to use quadrilateral or hexahedral meshes with proper elements . for even @xmath2 , the same trouble exists , that is , there also exists a lower - degree polynomial vanishing at all the gauss points . again , some bubble functions are added to the finite element space @xcite . compared to the triangular case , another trouble for quadrilateral finite element is that the dofs and corresponding polynomial space do not match . usually the number of dofs is bigger than the dimension of @xmath4 . for example , for @xmath6 and @xmath7 , the numbers of dofs are @xmath8 and @xmath9 , respectively , while the corresponding dimensions of @xmath4 are @xmath10 and @xmath11 , respectively . therefore , some additional relations must be imposed or some special functions are added to the finite element space such that unisolvency can be satisfied , see @xcite . the purpose of this paper is to develop a @xmath12-nonconforming element on rectangular meshes . we define the 12 gauss points ( 3 gauss points on every edge ) as the dofs . to obtain an optimal order error estimate , the finite element space must be carefully chosen such that any function in this space is a polynomial of degree no greater than 3 on every edge . meanwhile , we also notice that the values on the 12 gauss points satisfy a linear relation if the degree of a polynomial on every edge is no more 3 , which is a little different from the triangular mesh case . thus we define our finite element space as @xmath13 . therefore , the number of dofs is locally 11 . we prove unisolvency and define three types of local and global bases , one of which is defined associated with vertices and the other two of which are defined associated with edges . then we derive optimal error estimates for second - order elliptic problems in broken energy- and @xmath14-norms . finally , numerical examples are provided , which match our theoretical result very well . this paper is organized as follows . in section 2 the @xmath12 nonconforming element is defined on rectangular meshes . the dimensions and basis functions for dirichlet and neumann problems are given . in section 3 interpolation operators are defined and optimal order error estimates are shown . in section 4 , numerical results for the elliptic problems are presented .

a new nonconforming rectangle element with cubic convergence for the energy norm is introduced . the degrees of freedom ( dofs ) are defined by the twelve values at the three gauss points on each of the four edges . due to the existence of one linear relation among the above dofs , it turns out the dofs are eleven . the nonconforming element consists of @xmath0 . we count the corresponding dimension for dirichlet and neumann boundary value problems of second - order elliptic problems . we also present the optimal error estimates in both broken energy and @xmath1 norms . finally , numerical examples match our theoretical results very well . + * keywords : * nonconforming finite element ; optimal error estimates ; quadrilateral mesh

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a new nonconforming rectangle element with cubic convergence for the energy norm is introduced . the degrees of freedom ( dofs ) are defined by the twelve values at the three gauss points on each of the four edges . due to the existence of one linear relation among the above dofs , it turns out the dofs are eleven . the nonconforming element consists of @xmath0 . we count the corresponding dimension for dirichlet and neumann boundary value problems of second - order elliptic problems . we also present the optimal error estimates in both broken energy and @xmath1 norms . finally , numerical examples match our theoretical results very well . + * keywords : * nonconforming finite element ; optimal error estimates ; quadrilateral mesh

in @xcite kauffman defines an extension of classical knot diagrams to virtual knot diagrams , motivated by gauss codes on the one hand and knots in thickened surfaces on the other hand . several classical knot invariants can be generalized to the virtual theory without much effort , e.g. , the knot group and derived invariants such as the alexander polynomial , the bracket and jones polynomials , and vassiliev invariants ( which can be introduced in different ways , see @xcite and @xcite ) . the present paper deals with a polynomial invariant that is derived from an invariant of links in thickened surfaces introduced by jaeger , kauffman , and saleur in @xcite . the determinant formulation of the polynomial immediately generalizes to virtual link diagrams . it is a laurent polynomial in two variables with integral coefficients that vanishes on the class of classical link diagrams but gives non - trivial information for diagrams that represent non - classical virtual links . especially , examples can be given that the invariant is sensitive with respect to changes of orientation of a virtual knot . furthermore , the polynomial fulfills a conway - type skein relation in one variable and thus it is denoted by the term conway polynomial . in the same way as in the classical case , the one - variable alexander polynomial of a virtual link can be derived from the virtual link group , but the skein - relation for ( a normalized version of ) the classical alexander polynomial can not be extended to the class of virtual links . therefore , this alexander polynomial is different from the conway polynomial mentioned above in a non - trivial way in contrast to the classical case ( and certain generalizations to links 3-manifolds , see for example @xcite , theorem 5.2.11 ) . this paper is organized as follows . after , in section [ virtknots ] , a short introduction into the field has been given , the determinant formulation of the conway polynomial for virtual links is described in section [ invariant ] . some properties of the polynomial are deduced , especially , that the invariant fulfills a conway - type skein relation , and several example calculations are given . then , in section [ alex ] , the alexander invariants derived from the link group , namely , alexander matrix , alexander ideal , and alexander polynomial , are defined and it is shown that the alexander polynomial does not fulfill any linear skein relation . finally , in section [ conrem ] , general problems in extending certain invariants of classical links to the virtual category are described and the direction of further investigations is indicated .

a polynomial invariant of virtual links , arising from an invariant of links in thickened surfaces introduced by jaeger , kauffman , and saleur , is defined and its properties are investigated . examples are given that the invariant can detect chirality and even non - invertibility of virtual knots and links . + _ keywords : _ virtual knot theory , conway skein relation , alexander invariants + _ ams classification : _ 57m25 * on alexander - conway polynomials + for virtual knots and links * + jrg sawollek + december 21 , 1999 ( revised : january 3 , 2001 )

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a polynomial invariant of virtual links , arising from an invariant of links in thickened surfaces introduced by jaeger , kauffman , and saleur , is defined and its properties are investigated . examples are given that the invariant can detect chirality and even non - invertibility of virtual knots and links . furthermore , it is shown that the polynomial satisfies a conway - type skein relation in contrast to the alexander polynomial derived from the virtual link group . + _ keywords : _ virtual knot theory , conway skein relation , alexander invariants + _ ams classification : _ 57m25 * on alexander - conway polynomials + for virtual knots and links * + jrg sawollek + december 21 , 1999 ( revised : january 3 , 2001 )

the characteristic feature of the modern stage in studying mesoscopic systems is a possibility to fix individual properties of investigated objects such as chemical composition , size geometric shape and particle number . the well known example of such investigations is the discovery of electronic shells in alkali metal clusters @xcite . the other branch of researches is connected with recent advances in the development of new techniques for fabricating two- or three - dimensional micro- and nano - structures that enables current experiments to investigate variations of both the exact number of electrons on such mesoscopic structures and their geometrical shapes with a precise control in all dimensions . frequently experiments are produced so that investigated systems may exchange energy with surroundings ( they are embedded in heat reservoir ) , i.e. they are kept at an invariable temperature , however the exchange by particle is absent . thus , such systems constitute a canonical ensemble , and the most appropriate theoretical method for their statistical description is the canonical formalism . the papers of denton , mhlschlegel and scalapino @xcite were the first where the canonical description was developed in applying to electrons in small metallic grains . at that time it was impossible to fix the shape and particle number of each grain . therefore for constructing the canonical partition function denton et al made the simplest assumption that the energy spectrum of free electrons in a metallic grain is equidistant ( the equal level spacing model ) and two - fold degenerated if there is no magnetic field . using reasonable approximations ( @xmath5 , @xmath6 is number of single electron levels ) denton et al established an analytical expression for the canonical partition function . they showed that the main differences between the canonical and grand canonical values of the heat capacity ( @xmath7 ) and magnetic susceptibility ( @xmath8 ) lie at small temperatures @xmath9 ( @xmath10 is the mean level spacing ) . besides they found that at @xmath11 the grand canonical heat capacity exceeds the canonical one by @xmath12 ( @xmath13 is the boltzmann constant ) . the partition function of denton et al takes into account energy variations in an applied uniform magnetic field . they manifest themselves in oscillations of @xmath8 and @xmath7 with growth of the field . such oscillations are typical for charged particle systems @xcite however the strong periodicity in the oscillations is a feature of the equal level spacing . it is worthwhile emphasizing the @xmath0-independence of thermodynamic quantities as functions of @xmath14 in the canonical calculations of denton et al at @xmath15 , @xmath16 . it is caused by a relatively narrow layer of single particle levels near the fermi energy , which mainly contributes to the partition function , and by the identical for any @xmath0 structure of the single - particle energy spectrum in this layer . the canonical formalism was also used by brack , genzken and hansen @xcite for calculations of thermal properties of the valence electrons in alkali metal clusters . in this case free electron energy spectra contain considerable gaps that accounts for enhanced stability of clusters with the magic numbers of atoms . brack et al showed that the shell structure reveals itself in the theoretical heat capacity . however , the difference between the canonical and grand canonical shell effects is quite noticeable only at temperatures which are less than or of the same order as the mean level spacing @xmath17 near the fermi . thus , both investigations , @xcite , point out the region of the temperatures , @xmath18 , where the comparison of the canonical and grand canonical calculations is of the most interest . besides , in the center of attention should be magic electron numbers ( if they appear in the system ) since the existence of such @xmath0 is a consequence of the appearance of an energy gap near the fermi level that enhances the difference between canonical and grand canonical results . it is well known that @xmath18 is the best regime for observing size effects in mesoscopic systems @xcite . therefore the canonical approach at these temperatures can give more precise theoretical information than the grand canonical calculations . in order to calculate the partition function @xmath19 , occupation numbers , internal energy and other thermodynamic quantities brack et al used recurrence relations connecting @xmath19 with those for smaller @xmath0 and @xmath6 . following this procedure they found that @xmath20 calculation steps were needed to obtain the final result , i.e. for @xmath21 ( @xmath22 ) . such method is still manageable for @xmath0 up to a few hundreds , however it could be hardly applied to @xmath0 and @xmath23 . thus the constructing of the effectively working canonical formalism without restrictions on the particle number and applicable to arbitrary spacing distributions is a problem that has to be solved . parallel with the exact canonical calculations in ref . @xcite approximate methods have been suggested for constructing the canonical partition function of the normal ( nonsuperconducting ) systems . one of them ref . @xcite replaces the projection integral over the gauge variable @xmath24 ( @xmath25 ) by the discrete sum that involves @xmath26 terms . these terms depend on @xmath27 ( instead of @xmath24 ) where the integer @xmath28 varies from @xmath29 to @xmath30 . as shown in sec.1 this method can be viewed as the partial projection . it is the more precise the higher is the value of @xmath26 . in ref . @xcite this method was employed by frauendorf and pashkevich to calculate sodium cluster shape and free energies . another method suggested by rossignoli consists in the evaluation of projection integral in the saddle - point approximation . such approach turns out to be quite satisfactory in the case of not very small temperatures and particle numbers as was demonstrated by calculations of nuclear level densities in ref . @xcite . our effective version of the canonical approach is based on the polynomial representation of the partition function . last years such representation is discussed in the literature @xcite , however our practical version of polynomial calculations was elaborated many years ago for a projection method applied to the bardin - cooper - schriffer ( @xmath31 ) function for describing the particle number conserving pairing correlations in nuclei @xcite . there is an obvious analogy between the @xmath31 function and grand canonical partition function for the independent electron model ( @xmath32 ) . both can be represented as products @xmath33 , where @xmath34 for the @xmath31 function is @xmath35 ( @xmath36 , @xmath37 are the bogolubov parameters , @xmath38 is the operator of the fermion pair creation in time conjugated states @xmath39 and @xmath40 ) while for the canonical partition function @xmath34 is @xmath41 , @xmath42 and @xmath43 being the energy of a single -particle state @xmath39 and the chemical potential respectively . after projection onto a fixed particle number @xmath0 both functions gain the form of a @xmath0-th order symmetric polynomial @xmath44 $ ] . this polynomial @xmath44 $ ] consists of @xmath45 terms ( as before @xmath6 is the total amount of employed single - particle states ) and each term in it is the production of @xmath0 different @xmath34 , i.e. @xmath44 $ ] includes all distributions of @xmath0 @xmath31 pairs or @xmath0 electrons over @xmath6 states . for large @xmath6 and @xmath0 the total number of terms in @xmath0 may be enormous , however a hierarchy of terms can be established according to their surviving at @xmath46 ( @xmath47 is the pairing strength ) or @xmath48 . the first term of this hierarchy corresponds to the independent fermion ground state in which all single - particle states are occupied up to @xmath49 . the second group of terms corresponds to simplest excitations : in the @xmath31 theory it is a particle pair @xmath50 above @xmath49 and a hole pair @xmath51 beneath @xmath49 , for free electrons in a cluster it is one particle - hole excitations . the third group of terms corresponds to a shift of two @xmath31 particle pairs or two cluster electrons above @xmath49 . this alignment of many particle - hole excitations continues till all pairs or cluster electrons are lifted above @xmath49 . the common property of the projected @xmath31 and the canonical partition functions is mutual independence of probabilities of particle and hole excitations . this probability depends only on the energy of the single - particle level on which a @xmath31 fermion pair or a cluster electron is located . for the @xmath31 case it is @xmath52 for levels with @xmath53 while for levels with @xmath54 it is @xmath55 , for cluster electrons it is @xmath56 if @xmath57 , or @xmath41 if @xmath54 . thus summing over particle and hole excitations can be performed independently . the contribution of each group of @xmath58-particle excitations to @xmath44 $ ] includes a sum running distributions of @xmath58 electrons ( here we mean cluster electrons ) over particle levels ( with energies above @xmath49 ) . these sums can be also represented as symmetric polynomials , now they are of @xmath58-th order ( @xmath59 ) . analogous polynomials arise for hole excitations , but in this case electrons are distributed over hole levels ( below and including @xmath49 ) . though the convergence of appearing series is absolute its rate is determined by @xmath60 . practically for @xmath61 they include not more than 5 components ( i.e. up to 5 particle-5 hole excitations ) . our calculations for the pairing problem have indicated high effectiveness of the polynomial representation of the @xmath0-projected @xmath31-function @xcite and this paper is devoted to the adaptation of the polynomial representation to the canonical partition function of normal mesoscopic systems . the material is arranged as following . in sec.2 separation of the full configuration space into two parts , inside and outside the fermi sphere , is realized to construct the canonical partition function @xmath62 as a symmetrical polynomial of @xmath0-th order . @xmath62 is expanded in polynomials of lower orders . these series are composed of products of particle `` and ' ' hole polynomials , the order of which points out how many particles and holes take part in excitations allowed for in @xmath62 . in sec.3 these polynomials are employed to one- and two - body density matrices and on this base the canonical expressions for the heat capacity and magnetic susceptibility are compared to the grand canonical ones . sec.4 collects recurrent relations for polynomials we apply in calculations . sec.5 shows that in a wide range of temperatures and particle numbers the elaborated method possesses high convergence and can be used for various types of single - electron energy spectra . the conclusion is given in sec.6 . algebraic details for the equal level spacing model and the exact canonical partition function of the model are considered in appendix .

the number of terms which should be taken into account is weakly dependent on @xmath0 and remains @xmath2 even if @xmath3 . the elaborated method makes canonical calculations to be not more complicated than the grand canonical ones and is free from any limitations on @xmath0 and @xmath4 . , canonical vs grand canonical calculations , mesoscopic systems .

cond-mat0404299

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a practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of @xmath0 independent electrons . drastic simplification of calculations is attained by means of proper ordering excited states of the system . in consequence the exact canonical partition function can be represented as a series in which the first term corresponds to the ground state whereas successive groups of terms belong to many particle - hole excitations ( one particle - hole two particle - hole and so on ) . at small temperatures ( @xmath1 inter - level spacings near the fermi level ) the number of terms which should be taken into account is weakly dependent on @xmath0 and remains @xmath2 even if @xmath3 . the elaborated method makes canonical calculations to be not more complicated than the grand canonical ones and is free from any limitations on @xmath0 and @xmath4 . , canonical vs grand canonical calculations , mesoscopic systems . 05.30.fk , 02.10.ox

quenched disorder is obiquitous in condensed - matter systems , sometimes determining entirely new physical properties and phenomena . for the theoretical explanation of many experimental findings , models of classical and quantum spin systems are employed and - typically - disorder is introduced through a spatial variation of the exchange couplings , of the direction of the axial anisotropies , and of the sign of the couplings . theoretical and experimental studies of model and real physical systems with these kinds of disorder have lead to much new physics . much discussed have been the glassy phases in magnetic @xcite , and superconducting materials @xcite . in superconductors , specially with the advent of high-@xmath0 ceramic superconductors , the role of disorder has become central in the discussion of the physical properties of real materials @xcite . many materials are naturally microstructured and granularity characterises the mesoscopic structures of most systems , leading to a phase diagram often displaying a superconductor - insulator transition at zero temperature due to the charging energy of the grains . as first pointed out by abeles @xcite , when the grain charging energy arising from the charge @xmath1 and capacitance @xmath2 of the grain , @xmath3 ( @xmath4 is the grain diameter and @xmath5 the electronic charge ) is larger than the josephson - coupling energy @xmath6 between nearest neighbors grains , phase coherence is destroyed due to zero - point quantum fluctuations of the local phase of the superconducting order parameter @xcite . granularity can also be realized in a controlled manner in artificially fabricated josephson - junction arrays of coupled superconducting grains @xcite , with a space dimensionality @xmath4 less than @xmath7 . such granular systems can be theoretically modelled by pseudo - spin systems , the spins representing with their states the few relevant quantum charge states of the grains at relatively low temperatures . in such models the pseudo - spin size is the same for all grains corresponding to the assumption that the grain - size distribution is very narrow , or alternatively , of negligible charging - energy disorder . a well known model of this type is the pseudo - spin - one model introduced by de gennes and studied in different works @xcite where only charge states @xmath8 are allowed , corresponding to @xmath9 . however , realistic systems may contain different kinds of disorder , such as a spatial distribution of josephson couplings between grains or / and a distribution of grain sizes , which leads to disorder in the grain electrical capacitances and charging energies . studies of the effects of disorder in the electrical capacitance or charging energy of the grains have appeared recently @xcite . within a mean - field approximation @xcite , charging energy disorder widens the extent of the superconducting phase at the expense of the insulating one . this behavior is consistent with results for the superconductor - insulator transition from quantum monte carlo simulations in two - dimensional models of josephson - junction arrays @xcite with disorder in the diagonal capacitance matrix . earlier calculations for the related boson hubbard model with disorder in the onsite coulomb repulsion @xcite are also consistent with a decrease in the phase coherence threshold and moreover suggest a different universality class from the non - disordered case @xcite . in this work , we consider the effects of charging energy disorder in granular superconducting materials within the pseudo - spin approach . by considering a spatial distribution of the grain sizes , which leads to local charging energy disorder , a quantum pseudo - spin model with random on - site spin sizes can be constructed . a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . spin - size disorder models have seldom been considered in the literature . in the context of classical spin models , spin - size disorder can be readily turned into exchange - coupling disorder ; the physics of quantum systems with spin - size disorder , however , appears to have not been investigated in such depths . it has been considered mostly within the one - dimensional systems : dilution of a quantum spin-@xmath10 2-ladder was studied by sigrist and furusaki @xcite whilst the general problem of a quantum spin chain with random @xmath11 as well as random @xmath12 was considered by westerberg _ et . @xcite within a real - space renormalization - group method showing that these systems belong to a different universality class of disordered spin systems .

charging - energy effects result from the small electrical capacitance of the grains when the coulomb charging energy is comparable to the josephson coupling energy . in the pseudo - spin model , a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . and granular superconductors , josephson - junction arrays , superconductor - insulator transition 74.81.-g , 74.25.dw , 74.40.+k , 64.70.tg

0907.3120

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a quantum pseudo - spin model with random spin sizes is introduced to study the effects of charging - energy disorder on the superconducting transition in granular superconducting materials . charging - energy effects result from the small electrical capacitance of the grains when the coulomb charging energy is comparable to the josephson coupling energy . in the pseudo - spin model , randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors . a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . and granular superconductors , josephson - junction arrays , superconductor - insulator transition 74.81.-g , 74.25.dw , 74.40.+k , 64.70.tg

we have introduced a quantum pseudo - spin model with random spin sizes to model the effects of charging - energy disorder in granular superconducting materials . randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors . a mean - field theory has been developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . the results are qualitatively consistent with previous mean - field calculations in the phase - number representation . the pseudo - spin model should provide a useful framework to study the critical behavior and universality classes in presence of strong charging - energy disorder .

a quantum pseudo - spin model with random spin sizes is introduced to study the effects of charging - energy disorder on the superconducting transition in granular superconducting materials . randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors .

0907.3120

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a quantum pseudo - spin model with random spin sizes is introduced to study the effects of charging - energy disorder on the superconducting transition in granular superconducting materials . charging - energy effects result from the small electrical capacitance of the grains when the coulomb charging energy is comparable to the josephson coupling energy . in the pseudo - spin model , randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors . a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . and granular superconductors , josephson - junction arrays , superconductor - insulator transition 74.81.-g , 74.25.dw , 74.40.+k , 64.70.tg

the inner ( @xmath8 1kpc ) parts of some spiral galaxies show star formation complexes frequently arranged in an annular pattern around their nuclei . these complexes are sometimes called `` hot spots '' and we will refer to these as circumnuclear starforming regions ( cnsfrs ) . their sizes go from a few tens to a few hundreds of pc ( e.g. * ? ? ? * ) and they seem to be made of an ensamble of hii regions ionised by luminous compact stellar clusters whose sizes , as measured from high spatial resolution hst images , are seen to be of only a few pc . the luminosities of cnsfrs are rather large with absolute visual magnitudes ( m@xmath9 ) between -12 and -17 and h@xmath10 luminosities which are comparable to those shown by 30 dor , the largest hii region in the lmc , and overlap with those shown by hii galaxies ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . in the ultraviolet ( uv ) , massive stars dominate the observed circumnuclear emission even in the presence of an active nucleus @xcite . in many cases , cnsfr show emission line spectra similar to those of disc hii regions . however , they show a higher continuum from background stellar populations as expected from their circumnuclear location . the analysis of these spectra gives us the oportunity to measure the gas abundances close to galactic nuclei which , in the case of early type spirals , are expected to be amongst the highest metallicity regions . the importance of an accurate determination of the abundances of high metallicity hii regions can not be overestimated since they constitute most of the hii regions in early spiral galaxies ( sa to sbc ) and the inner regions of most late type ones ( sc to sd ) @xcite without which our description of the metallicity distribution in galaxies can not be complete . in particular , the effects of the choice of different calibrations on the derivation of abundance gradients can be very important since any abundance profile fit will be strongly biased towards data points at the ends of the distribution . it should be kept in mind that abundance gradients are widely used to constrain chemical evolution models , histories of star formation over galactic discs or galaxy formation scenarios . also , the question of how high is the highest oxygen abundance in the gaseous phase of galaxies is still standing and extrapolation of known radial abundance gradients would point to cnsfr as the most probable sites for these high metallicities . accurate measures of elemental abundances of high metallicity regions are also crucial to obtain reliable calibrations of empirical abundance estimators , widely used but poorly constrained , whose choice can severely bias results obtained for quantities of the highest relevance for the study of galactic evolution like the luminosity - metallicity ( l - z ) relation for galaxies .

a study of cicumnuclear star - forming regions ( cnsfrs ) in several early type spirals has been made in order to investigate their main properties : stellar and gas kinematics , dynamical masses , ionising stellar masses , chemical abundances and other properties of the ionised gas . both high resolution ( r@xmath020000 ) and moderate resolution ( r @xmath0 5000 ) have been used . in some cases these regions , about 100 to 150pc in size , the twice ionized oxygen , on the other hand , shows velocity dispersions comparable to those shown by stars . the measured values of the stellar velocity dispersions yield dynamical masses of the order of 10@xmath3 to 10@xmath4 solar masses for the whole cnsfrs .

0801.3078

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a study of cicumnuclear star - forming regions ( cnsfrs ) in several early type spirals has been made in order to investigate their main properties : stellar and gas kinematics , dynamical masses , ionising stellar masses , chemical abundances and other properties of the ionised gas . both high resolution ( r@xmath020000 ) and moderate resolution ( r @xmath0 5000 ) have been used . in some cases these regions , about 100 to 150pc in size , are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9pc estimated from hubble space telescope ( hst ) images . stellar and gas velocity dispersions are found to differ by about 20 to 30km / s with the h@xmath1 emission lines being narrower than both the stellar lines and the [ oiii]@xmath25007lines . the twice ionized oxygen , on the other hand , shows velocity dispersions comparable to those shown by stars . we have applied the virial theorem to estimate dynamical masses of the clusters , assuming that systems are gravitationally bounded and spherically symmetric , and using previously measured sizes . the measured values of the stellar velocity dispersions yield dynamical masses of the order of 10@xmath3 to 10@xmath4 solar masses for the whole cnsfrs . we obtain oxygen abundances which are comparable to those found in high metallicity disc hii regions from direct measurements of electron temperatures and consistent with solar values within the errors . the region with the highest oxygen abundance is r3+r4 in ngc 3504 , 12+log(o / h ) = 8.85 , about 1.5 solar if the solar oxygen abundance is set at the value derived by @xcite , 12+log(o / h)@xmath5 = 8.66@xmath60.05 . the derived n / o ratios are in average larger than those found in high metallicity disc hii regions and they do not seem to follow the trend of n / o vs o / h which marks the secondary behaviour of nitrogen . on the other hand , the s / o ratios span a very narrow range between 0.6 and 0.8 of the solar value . as compared to high metallicity disc hii regions , cnsfr show values of the o@xmath7 and the n2 parameters whose distributions are shifted to lower and higher values respectively , hence , even though their derived oxygen and sulphur abundances are similar , higher values would in principle be obtained for the cnsfr if pure empirical methods were used to estimate abundances . cnsfr also show lower ionisation parameters than their disc counterparts , as derived from the [ sii]/[siii ] . their ionisation structure also seems to be different with cnsfr showing radiation field properties more similar to hii galaxies than to disc high metallicity hii regions .

gas velocity dispersions were measured by performing gaussian fits to the h@xmath1@xmath24861 and [ oiii ] @xmath2 5007 lines on the high dispersion spectra ( figure [ spectra - kin ] ) . stellar velocity dispersions dispersions were measured using the cat lines at @xmath128494 , 8542 , 8662using the cross - correlation technique described in detail by @xcite . late type giant and supergiant stars that have strong cat absorption lines were used as stellar velocity templates . + for the 5 cnsfr observed in ngc 3351 , stellar velocity dispersions are found to be between 39 and 67kms@xmath11 , about 20kms@xmath11 larger than those measured for the gas , if a single gaussian fit is used . however , the best fits obtained involved two different components for the gas : a broad component " with a velocity dispersion similar to that measured for the stars , and a narrow component " with a dispersion lower than the stellar one by about 30kms@xmath11 . these two components were found both in the hydrogen recombination lines ( balmer and paschen ) and in the [ oiii ] @xmath2 5007 line . the narrow component is dominant in the h recombination lines , while the broad component dominates the [ oiii ] one . figure [ velocities ] shows this effect . cnsfr are seen to consist of several individual star clusters , although some of them seem to have an only knot , at the hst resolution . the derived masses for the individual clusters as derived using the sizes measured on the hst images are between 1.8 and 8.7@xmath1310@xmath14m@xmath15 . these values are between 5.5 and 26 times the mass derived for the ssc a in ngc1569 by @xcite and larger than other kinematically derived ssc masses . values for the dynamical masses of the cnsfrs are in the range between 4.9@xmath1310@xmath14 and 4.3@xmath1310@xmath3m@xmath15 . masses derived from the h@xmath1 velocity dispersion under the assumption of a single component for the gas would have been underestimated by factors between approximately 2 to 4 . the masses of the ionising stellar clusters of the cnsfrs have been derived from their h@xmath10 luminosities under the assumption that the regions are ionisation bound and without taking into account any photon absorption by dust . their values are between 8 - 0@xmath1310@xmath16 and 2.5@xmath1310@xmath14m@xmath15 . therefore , the ratio of the ionising stellar population to the total dynamical mass is between 0.02 and 0.16 . the ssc in the observed cnsfrs seem to contain composite stellar populations . although the youngest one dominates the uv light and is responsible for the gas ionisation , it constitutes only about 10% of the total . this can explain the low equivalent widths of emission lines measured in these regions . this may well apply to the case of other ssc and therefore conclusions drawn from fits of ssp ( single stellar population ) models should be taken with caution ( e.g. * ? ? ? also the composite nature of the cnsfrs means that star formation in the rings is a process that has taken place over time periods much longer than those implied by the properties of the ionised gas .

are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9pc estimated from hubble space telescope ( hst ) images . stellar and gas velocity dispersions are found to differ by about 20 to 30km / s with the h@xmath1 emission lines being narrower than both the stellar lines and the [ oiii]@xmath25007lines . we have applied the virial theorem to estimate dynamical masses of the clusters , assuming that systems are gravitationally bounded and spherically symmetric , and using previously measured sizes .

0801.3078

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a study of cicumnuclear star - forming regions ( cnsfrs ) in several early type spirals has been made in order to investigate their main properties : stellar and gas kinematics , dynamical masses , ionising stellar masses , chemical abundances and other properties of the ionised gas . both high resolution ( r@xmath020000 ) and moderate resolution ( r @xmath0 5000 ) have been used . in some cases these regions , about 100 to 150pc in size , are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9pc estimated from hubble space telescope ( hst ) images . stellar and gas velocity dispersions are found to differ by about 20 to 30km / s with the h@xmath1 emission lines being narrower than both the stellar lines and the [ oiii]@xmath25007lines . the twice ionized oxygen , on the other hand , shows velocity dispersions comparable to those shown by stars . we have applied the virial theorem to estimate dynamical masses of the clusters , assuming that systems are gravitationally bounded and spherically symmetric , and using previously measured sizes . the measured values of the stellar velocity dispersions yield dynamical masses of the order of 10@xmath3 to 10@xmath4 solar masses for the whole cnsfrs . we obtain oxygen abundances which are comparable to those found in high metallicity disc hii regions from direct measurements of electron temperatures and consistent with solar values within the errors . the region with the highest oxygen abundance is r3+r4 in ngc 3504 , 12+log(o / h ) = 8.85 , about 1.5 solar if the solar oxygen abundance is set at the value derived by @xcite , 12+log(o / h)@xmath5 = 8.66@xmath60.05 . the derived n / o ratios are in average larger than those found in high metallicity disc hii regions and they do not seem to follow the trend of n / o vs o / h which marks the secondary behaviour of nitrogen . on the other hand , the s / o ratios span a very narrow range between 0.6 and 0.8 of the solar value . as compared to high metallicity disc hii regions , cnsfr show values of the o@xmath7 and the n2 parameters whose distributions are shifted to lower and higher values respectively , hence , even though their derived oxygen and sulphur abundances are similar , higher values would in principle be obtained for the cnsfr if pure empirical methods were used to estimate abundances . cnsfr also show lower ionisation parameters than their disc counterparts , as derived from the [ sii]/[siii ] . their ionisation structure also seems to be different with cnsfr showing radiation field properties more similar to hii galaxies than to disc high metallicity hii regions .

progress in many areas of science and its application is fueled by the ongoing progress to measure and structure small objects . in many cases , light is used as a primary tool for reading or writing . but since light is subject to diffraction , a straightforward implementation is restricted to structures of order of the involved wavelength @xcite . different methods have been invented to surpass this limit , such as near - field imaging @xcite , techniques based on the selective addressing of nearby particles @xcite , resolution enhancement due to non - classical effects @xcite , multiphoton spectroscopy @xcite , quantum lithography with classical fields @xcite , or position - dependent dark states @xcite . among the most fundamental problems in this area is the measurement of the distance between two nearby quantum particles such as atoms . it has been recognized that a precise determination of the interparticle distance is possible down to distances far below the wavelength of the employed light based on their mutual interaction . for small distances , the atoms are coupled by the dipole - dipole interaction , which modifies the optical properties of the system @xcite . this was confirmed in a recent experiment @xcite , and it was found that the resonance fluorescence exhibits characteristic features which enable one to determine the relative distance over a large range of small distances @xcite . the resonance fluorescence has the advantage that it can be observed in the far field , and distance determination via fluorescence is not affected by the usual resolution limitations since the distance information is encoded in the frequency spectrum of the emitted light . similar ideas have also been used for the localization of single particles @xcite . the existing distance measurement techniques based on the dipole - dipole interaction , however , are restricted to two two - level atoms in specific geometries , such as aligned along the propagation direction of the exciting laser field . in most practical cases , however , the relative orientation of the two nearby atoms is unknown , and for similar reasons , it is equally difficult to measure the relative orientation as the distance . thus the question arises , whether the ideas of @xcite can be extended to the case of arbitrary orientation . it turns out that it is not meaningful to study the system of two two - level atoms in the case of arbitrary orientations . the reason for this is the appearance of dipole - dipole couplings between orthogonal transition dipole moments ( ddotdm ) in more general geometries @xcite . the electric field emitted by one of the particles has not only a component corresponding to the emitting transition dipole moment , but also a component along the interparticle distance vector . the projection of the latter field component on a transition dipole moment in the second atom can be non - zero even if it is orthogonal to the emitting dipole @xcite . in a real atom with magnetic level structure , these ddotdm lead to the population of excited states even if they are not driven by the external laser field . thus , the two - level approximation breaks down , and correct predictions can only be expected if the theoretical modelling includes complete zeeman manifolds including all occurring dipole dipole couplings @xcite . motivated by this , here we study the determination of relative distance and orientation of two nearby atoms in arbitrary geometry . the atoms are driven by a single resonant standing - wave laser field , and we make use of the far field resonance fluorescence intensity and spectrum as observables . each atom is modelled as a four - level system with one ground state ( total angular momentum zero ) and three excited states ( total angular momentum one ) , including all relevant dipole - dipole couplings occurring in arbitrary geometries . we start by analyzing the distance determination for the case of a known orientation , and present dressed - state interpretations of the obtained resonance fluorescence spectra in various cases of relevance . next , we describe a method to determine the interparticle distance for arbitrary orientation , which works as long as the particles are sufficiently close to each other . finally , we discuss methods to determine the relative orientation of the two particles , focusing on the two cases of atoms confined in a planar waveguide and atoms on a surface . ( color online ) scheme for the determination of relative distance and orientation of two nearby atoms . the atoms @xmath0 are driven on one transition by a standing wave laser field with rabi frequency @xmath1 and scatter light , which is registered in the far field with a detector . the interatomic distance vector @xmath2 is arbitrary , as shown in the left inset . the right inset shows the level structure of each atom . each atom has a single ground state ( zero angular momentum ) and three excited states ( angular momentum 1 ) . ]

accurate measurement of relative distance and orientation of two nearby quantum particles is discussed . thus , unlike in previous studies , we consider the case of an arbitrary relative orientation of the two atoms . for this , we model the atom with complete zeeman manifolds , and include parallel as well as orthogonal dipole - dipole couplings between all states of the two atoms . we find that it is possible to determine the distance of the two atoms independent of the orientation , as long as the particles are sufficiently close to each other .

0909.5608

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accurate measurement of relative distance and orientation of two nearby quantum particles is discussed . we are in particular interested in a realistic description requiring as little prior knowledge about the system as possible . thus , unlike in previous studies , we consider the case of an arbitrary relative orientation of the two atoms . for this , we model the atom with complete zeeman manifolds , and include parallel as well as orthogonal dipole - dipole couplings between all states of the two atoms . we find that it is possible to determine the distance of the two atoms independent of the orientation , as long as the particles are sufficiently close to each other . next , we discuss how in addition the alignment of the atoms can be measured . for this , we focus on the two cases of atoms in a two - dimensional waveguide and of atoms on a surface .

additive models @xcite provide an important family of models for semiparametric regression or classification . some reasons for the success of additive models are their increased flexibility when compared to linear or generalized linear models and their increased interpretability when compared to fully nonparametric models . it is well - known that good estimators in additive models are in general less prone to the curse of high dimensionality than good estimators in fully nonparametric models . many examples of such estimators belong to the large class of regularized kernel based methods over a reproducing kernel hilbert space @xmath0 , see e.g. @xcite . in the last years many interesting results on learning rates of regularized kernel based models for additive models have been published when the focus is on sparsity and when the classical least squares loss function is used , see e.g. @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and the references therein . of course , the least squares loss function is differentiable and has many nice mathematical properties , but it is only locally lipschitz continuous and therefore regularized kernel based methods based on this loss function typically suffer on bad statistical robustness properties , even if the kernel is bounded . this is in sharp contrast to kernel methods based on a lipschitz continuous loss function and on a bounded loss function , where results on upper bounds for the maxbias bias and on a bounded influence function are known , see e.g. @xcite for the general case and @xcite for additive models . therefore , we will here consider the case of regularized kernel based methods based on a general convex and lipschitz continuous loss function , on a general kernel , and on the classical regularizing term @xmath1 for some @xmath2 which is a smoothness penalty but not a sparsity penalty , see e.g. @xcite . such regularized kernel based methods are now often called support vector machines ( svms ) , although the notation was historically used for such methods based on the special hinge loss function and for special kernels only , we refer to @xcite . in this paper we address the open question , whether an svm with an additive kernel can provide a substantially better learning rate in high dimensions than an svm with a general kernel , say a classical gaussian rbf kernel , if the assumption of an additive model is satisfied . our leading example covers learning rates for quantile regression based on the lipschitz continuous but non - differentiable pinball loss function , which is also called check function in the literature , see e.g. @xcite and @xcite for parametric quantile regression and @xcite , @xcite , and @xcite for kernel based quantile regression . we will not address the question how to check whether the assumption of an additive model is satisfied because this would be a topic of a paper of its own . of course , a practical approach might be to fit both models and compare their risks evaluated for test data . for the same reason we will also not cover sparsity . consistency of support vector machines generated by additive kernels for additive models was considered in @xcite . in this paper we establish learning rates for these algorithms . let us recall the framework with a complete separable metric space @xmath3 as the input space and a closed subset @xmath4 of @xmath5 as the output space . a borel probability measure @xmath6 on @xmath7 is used to model the learning problem and an independent and identically distributed sample @xmath8 is drawn according to @xmath6 for learning . a loss function @xmath9 is used to measure the quality of a prediction function @xmath10 by the local error @xmath11 . _ throughout the paper we assume that @xmath12 is measurable , @xmath13 , convex with respect to the third variable , and uniformly lipschitz continuous satisfying @xmath14 with a finite constant @xmath15 . _ support vector machines ( svms ) considered here are kernel - based regularization schemes in a reproducing kernel hilbert space ( rkhs ) @xmath0 generated by a mercer kernel @xmath16 . with a shifted loss function @xmath17 introduced for dealing even with heavy - tailed distributions as @xmath18 , they take the form @xmath19 where for a general borel measure @xmath20 on @xmath21 , the function @xmath22 is defined by @xmath23 where @xmath24 is a regularization parameter . the idea to shift a loss function has a long history , see e.g. @xcite in the context of m - estimators . it was shown in @xcite that @xmath22 is also a minimizer of the following optimization problem involving the original loss function @xmath12 if a minimizer exists : @xmath25 the additive model we consider consists of the _ input space decomposition _ @xmath26 with each @xmath27 a complete separable metric space and a _ hypothesis space _ @xmath28 where @xmath29 is a set of functions @xmath30 each of which is also identified as a map @xmath31 from @xmath3 to @xmath5 . hence the functions from @xmath32 take the additive form @xmath33 . we mention , that there is strictly speaking a notational problem here , because in the previous formula each quantity @xmath34 is an element of the set @xmath35 which is a subset of the full input space @xmath36 , @xmath37 , whereas in the definition of sample @xmath8 each quantity @xmath38 is an element of the full input space @xmath36 , where @xmath39 . because these notations will only be used in different places and because we do not expect any misunderstandings , we think this notation is easier and more intuitive than specifying these quantities with different symbols . the additive kernel @xmath40 is defined in terms of mercer kernels @xmath41 on @xmath27 as @xmath42 it generates an rkhs @xmath0 which can be written in terms of the rkhs @xmath43 generated by @xmath41 on @xmath27 corresponding to the form ( [ additive ] ) as @xmath44 with norm given by @xmath45 the norm of @xmath46 satisfies @xmath47 to illustrate advantages of additive models , we provide two examples of comparing additive with product kernels . the first example deals with gaussian rbf kernels . all proofs will be given in section [ proofsection ] . [ gaussadd ] let @xmath48 , @xmath49 $ ] and @xmath50 ^ 2.$ ] let @xmath51 and @xmath52.\ ] ] the additive kernel @xmath53 is given by @xmath54 furthermore , the product kernel @xmath55 is the standard gaussian kernel given by @xmath56 define a gaussian function @xmath57 on @xmath58 ^ 2 $ ] depending only on one variable by @xmath59 then @xmath60 but @xmath61 where @xmath62 denotes the rkhs generated by the standard gaussian rbf kernel @xmath63 . the second example is about sobolev kernels . [ sobolvadd ] let @xmath64 , @xmath65 $ ] and @xmath58^s.$ ] let @xmath66 : = \bigl\{u\in l_2([0,1 ] ) ; d^\alpha u \in l_2([0,1 ] ) \mbox{~for~all~}|\alpha|\le 1\bigr\}\ ] ] be the sobolev space consisting of all square integrable univariate functions whose derivative is also square integrable . it is an rkhs with a mercer kernel @xmath67 defined on @xmath68 ^ 2 $ ] . if we take all the mercer kernels @xmath69 to be @xmath67 , then @xmath70 $ ] for each @xmath71 . the additive kernel @xmath72 is also a mercer kernel and defines an rkhs @xmath73\right\}.\ ] ] however , the multivariate sobolev space @xmath74^s)$ ] , consisting of all square integrable functions whose partial derivatives are all square integrable , contains discontinuous functions and is not an rkhs . denote the marginal distribution of @xmath6 on @xmath27 as @xmath75 . under the assumption that @xmath76 for each @xmath71 and that @xmath43 is dense in @xmath29 in the @xmath77-metric , it was proved in @xcite that @xmath78 in probability as long as @xmath79 satisfies @xmath80 and @xmath81 . the rest of the paper has the following structure . section [ ratessection ] contains our main results on learning rates for svms based on additive kernels . learning rates for quantile regression are treated as important special cases . section [ comparisonsection ] contains a comparison of our results with other learning rates published recently . section [ proofsection ] contains all the proofs and some results which can be interesting in their own .

additive models play an important role in semiparametric statistics . additionally , a concrete example is presented to show that a gaussian function depending only on one variable lies in a reproducing kernel hilbert space generated by an additive gaussian kernel , but does not belong to the reproducing kernel hilbert space generated by the multivariate gaussian kernel of the same variance . * key words and phrases . * additive model , kernel , quantile regression , semiparametric , rate of convergence , support vector machine .

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additive models play an important role in semiparametric statistics . this paper gives learning rates for regularized kernel based methods for additive models . these learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel based quantile regression using the gaussian radial basis function kernel , provided the assumption of an additive model is valid . additionally , a concrete example is presented to show that a gaussian function depending only on one variable lies in a reproducing kernel hilbert space generated by an additive gaussian kernel , but does not belong to the reproducing kernel hilbert space generated by the multivariate gaussian kernel of the same variance . * key words and phrases . * additive model , kernel , quantile regression , semiparametric , rate of convergence , support vector machine .

our analysis shows that hod modeling can substantially increase the cosmological power of galaxy clustering measurements , by breaking degeneracies between the clustering of dark matter and the bias of galaxies with respect to mass . changing the shape or amplitude of the matter power spectrum or the value of @xmath1 alters the mass function , spatial clustering , and velocity statistics of the dark halo population in well - understood ways @xcite . our experiments here , which verify the qualitative arguments of @xcite and @xcite , show that changes to the galaxy hod can not mask these changes in the underlying dark halo population . with our highly flexible parameterization of the hod , the set of observables considered here yields @xmath5 uncertainties of @xmath4 in @xmath2 , @xmath1 , and @xmath3 and @xmath7 uncertainty in the combination @xmath387 with @xmath388 . we expect these forecasts to be conservative , as we have not included observables for which we did not have ready analytic approximations , and our assumption of 10% measurement errors is pessimistic in at least some cases . the physical origin of these cosmological constraints is straightforward to understand for simple changes in @xmath1 , @xmath2 , or @xmath270 , as discussed in [ sec : omegam]-[sec : clnorm ] . the general theme of these discussions is that , for a given cosmological model , the spatial clustering of galaxies largely determines the number of galaxies in halos of a given spatial abundance . dynamically sensitive statistics then reveal the halo mass scale , which depends on @xmath2 and @xmath1 . we allow an arbitrary bias @xmath95 between the galaxy and dark matter velocity dispersions within halos , but this freedom does not eliminate the constraining power of dynamical observables because the space velocities of the halos themselves do not change . the main parameter degeneracy is approximately @xmath389 because fixing this combination roughly fixes the halo velocity scale and the abundance of halos at the mass scale of rich galaxy groups . however , the changing shape of the mass function , the differing sensitivities of different velocity measures , and the different @xmath390 dependence of galaxy - galaxy lensing all serve to break this degeneracy . figures [ fig : chgerr ] and [ fig : matrix ] demonstrate that the cosmological constraints emerge from the full web of clustering observables and are not dominated by one or two statistics on their own . constraints on the galaxy hod will themselves provide valuable tests of galaxy formation models . the cutoff regime of @xmath97 is difficult to pin down with the clustering statistics considered here , but for a known cosmological model the relation between average satellite number and halo mass is well determined , and the satellite distribution width @xmath112 , concentration @xmath118 , and velocity bias @xmath95 are measured to @xmath4 , 30% , and 3% , respectively ( fig . [ fig : mcmc_hodpar ] ) . all of these quantities depend in detail on the physics that governs the evolution of satellites in larger halos ( see , e.g. , @xcite ) , while the relative mass of halos that host central and satellite galaxies depends on the efficiency with which halos feed baryonic mass to their central objects ( see , e.g , discussions by @xcite ) . these galaxy formation constraints will be especially powerful when derived as a function of luminosity , stellar mass , or other observables . the two main assumptions built into our modeling are the central - satellite parameterization and environment independence of the hod . the central - satellite distinction appears well rooted in galaxy formation physics , and it allows us to represent the range of plausible galaxy hods more completely with a moderate number of parameters . however , we have confirmed with other tests that if we model galaxy bias with a flexible hod parameterization that does not impose a central - satellite distinction , but instead introduces a characteristic mass for the narrow - to - wide transition of @xmath96 as in @xcite , then we reach almost identical conclusions about the cosmological constraining power of the clustering observables considered in this paper . recent numerical results imply an environmental dependence of halo formation times that opens the door to environmental variation of the hod , especially in the single - galaxy regime . as discussed in [ sec : environment ] , we expect the quantitative impact of such dependence to be small , but potentially significant at the high level of precision we ultimately hope to attain . investigation of environmental dependence effects and methods of allowing for them in hod modeling are a high priority for future work . the cosmological modeling approach advocated here is closely related to the clf method introduced by @xcite and @xcite , who use clustering data and the global galaxy luminosity function to constrain the dependence of the luminosity function on halo mass . in principle , the clf and hod methods are equivalent they are merely differential and integral forms of one another . one can derive the clf from a series of hod fits to galaxy samples with different luminosity thresholds @xcite . conversely , one can integrate the clf to infer @xmath97 for galaxies above a luminosity threshold @xcite . the principal virtue of our hod - based approach is that by focusing on a single , well - defined class of galaxies , we can parameterize the hod in a way that seems likely to capture the predictions of any reasonable galaxy formation model . this kind of comprehensive parameterization is more difficult to achieve for the full clf , and most analyses to date have assumed , for example , that the clf has a schechter form in halos of fixed mass . nonetheless , it is valuable to pursue both hod and clf approaches and test for consistency of conclusions . hod modeling complements rather than replaces the perturbative approach based on large - scale measures that can be modeled with linear or quadratic bias . hod modeling is more complex , but it can take advantage of high - precision clustering measurements on small and intermediate scales . hod modeling can also amplify the power of the perturbative approach , extending its reach further into the non - linear regime and checking its range of validity at a desired level of precision . for example , @xcite show that an hod - based approach to redshift - space distortions can improve recovery of the perturbative parameter @xmath39 that controls large - scale flows . @xcite show that the linear bias model provides an accurate description of galaxy - galaxy lensing for @xmath391 , and they show how to accurately model this phenomenon on smaller scales ( see also @xcite ) . j. yoo et al . ( 2007 , in preparation ) show that the scale - dependent bias factors derived by fitting the projected galaxy correlation function can extend recovery of the shape of the linear matter power spectrum into the mildly non - linear regime . clf and hod analyses of the 2dfgrs and sdss redshift surveys have already produced a number of interesting results , even though they have considered only a fraction of the potential clustering observables . these results confirm , at least qualitatively , many of the basic predictions of current galaxy formation models , including the general form of the mean occupation function , the dependence of this function on luminosity , the existence of a minimum mass - to - light ratio in the halos of @xmath392 galaxies where galaxy formation is most efficient , the large gap between the minimum halo mass for central and satellite galaxies above a luminosity threshold , the sub - poisson fluctuations of @xmath96 that are a consequence of this gap , and the strong preference of galaxies with older stellar populations for higher mass halos @xcite . in combination with cmb data , the cosmological constraints from hod modeling of the sdss projected galaxy correlation function are almost as tight as those from the large - scale galaxy power spectrum , and the two analyses are consistent within their statistical uncertainties @xcite . for the most part , the cosmological inferences from clf / hod modeling of galaxy clustering agree with those from other methods , but matching the mass - to - light ratios of galaxy clusters simultaneously with other clustering data appears to require values of @xmath1 and/or @xmath2 that are substantially lower than the commonly adopted values of 0.3 and 0.9 @xcite . if this conclusion is correct , then the evidence for it should become much stronger as more clustering observables are brought into play and the sdss data set itself moves to completion . we have focused in this paper on the cosmological parameter constraints that can be derived from galaxy clustering alone , using external data only to guide the choice of power spectrum shape and motivate the assumption of gaussian initial conditions . as with perturbative analyses of large - scale structure , the long - term interest lies in combining these constraints with those from the cmb , the ly@xmath11 forest , type ia supernovae , and other cosmological observables . the complementary sensitivities of these observables lead to much tighter parameter constraints . more importantly , conflicts among them could point the way to physics beyond the simplest versions of @xmath43cdm , such as evolving dark energy , a gravitational wave contribution to cmb anisotropy , departures from scale invariance in the primordial power spectrum , non - zero space curvature , cosmologically significant neutrino masses , and so forth . by sharpening the constraints from large - scale structure in the new generation of galaxy redshift surveys , hod modeling can play a critical role in efforts to test the standard cosmological model and , perhaps , discover its breaking points . we thank andreas berlind , jeremy tinker , and jaiyul yoo for valuable discussions on these topics . we thank barth netterfield for suggesting a cubic spline parameterization of the mean occupation function , sandy faber for suggesting the influence matrix investigation , and andy gould for advice on the @xmath0 minimization method . this work was supported by nsf grants ast 00 - 98584 and ast 04 - 07125 . z. z. acknowledges the support of nasa through hubble fellowship grant hf-01181.01-a awarded by the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , for nasa , under contract nas 5 - 26555 . z. z. was also supported by a presidential fellowship from the graduate school of the ohio state university at an early stage of the project .

adopting the framework of the halo occupation distribution ( hod ) , we investigate the ability of galaxy clustering measurements to simultaneously constrain cosmological parameters and galaxy bias . starting with a fiducial cosmological model and galaxy hod , we calculate spatial clustering observables on a range of length and mass scales , dynamical clustering observables that depend on galaxy peculiar velocities , and the galaxy - matter cross - correlation measurable by weak lensing . , the inferred constraints on the galaxy hod provide valuable tests of galaxy formation theory .

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adopting the framework of the halo occupation distribution ( hod ) , we investigate the ability of galaxy clustering measurements to simultaneously constrain cosmological parameters and galaxy bias . starting with a fiducial cosmological model and galaxy hod , we calculate spatial clustering observables on a range of length and mass scales , dynamical clustering observables that depend on galaxy peculiar velocities , and the galaxy - matter cross - correlation measurable by weak lensing . we then change one or more cosmological parameters and use @xmath0-minimization to find the galaxy hod that best reproduces the original clustering . our parameterization of the hod incorporates a flexible relation between galaxy occupation numbers and halo mass and allows spatial and velocity bias of galaxies within dark matter halos . despite this flexibility , we find that changes to the hod can not mask substantial changes to the matter density @xmath1 , the matter clustering amplitude @xmath2 , or the shape parameter @xmath3 of the linear matter power spectrum cosmology and bias are not degenerate . with the conservative assumption of 10% fractional errors , the set of observables considered here can provide @xmath4 ( @xmath5 ) constraints on @xmath2 , @xmath1 , and @xmath3 , using galaxy clustering data _ alone_. the combination @xmath6 is constrained to @xmath7 . in combination with traditional methods that focus on large - scale structure in the `` perturbative '' regime , hod modeling can greatly amplify the cosmological power of galaxy redshift surveys by taking advantage of high - precision clustering measurements at small and intermediate scales ( from sub - mpc to @xmath8 ) . at the same time , the inferred constraints on the galaxy hod provide valuable tests of galaxy formation theory .

almost all astrophysical objects have significant non - thermal processes that result in emission across a broad energy band . even stars exhibit flares which are non - thermal processes . multi - wavelength observations are therefore key to have complete understanding of a variety of astrophysical objects and astrophysical processes . x - ray binaries and active galactic nuclei ( agn ) are prime examples of objects with emission over a wide band . often the most dominant part of the electromagnetic emission is within the optical to hard x - ray band . moreover , these accretion powered sources show intensity variation over a wide range of timescales , from milliseconds which is the time scale for material to go around a low magnetic field neutron star , to years which is the time scale around supermassive black holes in the most powerful of agns . the x - ray variation can be periodic , quasi - periodic , random with flares , bursts and outbursts , and often a mixture of two or more of these patterns . the optical and uv emission also show intensity variations , though not quite as sharp and strong as x - rays . while in some sources one type of emission is known to be reprocessed into another type and therefore , the causal relation between the multiple components are understood to some extent , there are types of sources in which the source of variations , their causes and effects on the other components are not yet understood very well . simultaneous multi - wavelength observations are therefore key to our understanding of the broadband emission mechanism and interrelation between multiple emission processes in x - ray binaries and agns . simultaneous multi - wavelength x - ray and uv - optical observations are however very difficult to carry out . apart from the requirement of coordination between the space - based x - ray observatories and ground - based ( or on a different space telescope like the hst ) optical telescopes , the typical duty cycle for simultaneous multi - wavelength data from such observations is very low , owing to the different nature of good time interval ( gti ) of space and ground based observatories . simultaneous x - ray and uv - optical observations from the same satellite platform can mitigate many of these problems and yield rich dataset . astrosat , with its three co - aligned x - ray instruments and two uv - optical telescopes with a total of three bands is designed to bring in this new capability of quality simultaneous multi - wavelength observation capability . two other space observatories , the xmm - newton@xcite and swift@xcite have limited optical and uv capabilities along with very powerful x - ray telescopes and the new potential of single platform simultaneous multi - wavelength observations have been demonstrated to quite a large extent with these instruments . in addition to the multi - wavelength aspect , the three co - aligned x - ray instruments will also provide very good capability for broadband x - ray measurements , with particular improvement in capabilities in the hard x - ray band of 15 - 80 kev . the large area x - ray proportional counter ( laxpc ) instrument of astrosat has an effective area that is in this range several times larger than any other x - ray instrument , which will enable certain unique measurements like quasi periodic oscillations ( qpo ) in the hard x - ray band , pulse phase - resolved study of the cyclotron resonance scattering fearure ( crsf ) in accretion - powered high magnetic field pulsars etc . the astrosat@xcite is being developed under a large collaboration including several indian organisations and some participation from the united kingdom and canada . though the mission has been delayed , it is expected to be launched in 2013 . in the following sections we give a brief description of the instruments onboard astrosat and discuss some of the main science topics that will be addressed with the laxpc , and with simultaneous observations with the uvit telescopes , with particular emphasis on x - ray binaries and compact objects .

, astrosat will provide unprecendented opportunity for simultaneous multi - wavelength observations , which is of immense value in study of highly variable sources , especially x - ray binaries and active galactic nuclei . the large area x - ray proportional counters ( laxpc ) of astrosat , which has the largest effective area in the hard x - ray band compared to all previous x - ray missions , will enable high time resolution x - ray measurements in the 2 - 80 kev band with moderate energy resolution . here we give a brief summary of the payload characteristics of astrosat and discuss some of the main science topics that will be addressed with the laxpc , and with simultaneous observations with the uvit telescopes , with particular emphasis on x - ray binaries and compact objects .

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astrosat is an astronomy satellite designed for simultaneous multi - wavelength studies in the optical / uv and a broad x - ray energy range . with four x - ray instruments and a pair of uv - optical telescopes , astrosat will provide unprecendented opportunity for simultaneous multi - wavelength observations , which is of immense value in study of highly variable sources , especially x - ray binaries and active galactic nuclei . the large area x - ray proportional counters ( laxpc ) of astrosat , which has the largest effective area in the hard x - ray band compared to all previous x - ray missions , will enable high time resolution x - ray measurements in the 2 - 80 kev band with moderate energy resolution . here we give a brief summary of the payload characteristics of astrosat and discuss some of the main science topics that will be addressed with the laxpc , and with simultaneous observations with the uvit telescopes , with particular emphasis on x - ray binaries and compact objects . the possibility of aiding gravitational wave experiments is also briefly mentioned .

the perturbative particle - vibration - coupling ( pvc ) model for odd - particle - number nuclei emerges naturally from the self - consistent green s function theory @xcite . it describes the polarization of the nucleus when one particle is added or removed @xcite , and its results can , in principle , be directly compared against experimental data . as used in nuclear physics , the perturbative pvc method employs one - particle or one - hole states ( or one - quasiparticle states ) coupled with the rpa or qrpa excitations of an even - even reference nucleus , and the residual nucleon - nucleon interaction that mixes these states at second - order perturbation theory . numerous pvc calculations of increasing level of sophistication have already been performed , see , e.g. , refs . @xcite and excellent recent reviews thereof available in refs . @xcite . an alternative to describing odd nuclei within the perturbative pvc calculations are the energy - density - functional ( edf ) methods , see , e.g. , refs . @xcite , which use blocking of single - particle ( s.p . ) or quasiparticle orbitals . to distinguish these methods from the full pvc approach , in the present study we call them mean - field polarizations or polarization corrections . the advantage of blocked mean - field calculations is that they are non - perturbative and variational . as it turns out , the effects obtained within the blocked mean - field methods are substantially different and , in general , weaker than those obtained from the perturbative pvc @xcite . this discrepancy between models , even when using exactly the same interactions and model spaces , needs to be solved , and this is the main purpose of the present work . the link between the mean - field and perturbative methods has been proposed long time ago @xcite . here , we identify several approximations that are required to firmly establish such a link , and we also extend the derivations to edfs based on density - dependent interactions and to those that include pairing correlations . since the determination of mean - field polarizations requires breaking symmetries , no numerical comparison of the two approaches , such as given here , is available up to now . as required by a thorough comparison , both in the mean - field and ( q)rpa calculations we use full self - consistency and exactly the same particle - hole edfs , pairing interactions , and model spaces . the paper is built around two main chapters presenting theoretical derivations in sec . [ sec2 ] and appendix [ sec5 ] , and numerical results in sec . [ sec3 ] . for theory , we present results pertaining to the hartree - fock ( hf ) approximation ( sec . [ sec2.2 ] ) , density functionals ( sec . [ sec2.4 ] ) , and pairing correlations treated within the hartree - fock - bogoliubov ( hfb ) framework ( sec . [ sec2.3 ] ) . then , results of calculations are discussed for the density - independent ( sec . [ sec3.1 ] ) and density - dependent ( sec . [ sec3.2 ] ) particle - hole interactions , and for paired systems ( sec . [ sec3.3 ] ) . conclusions are given in sec .

background : : : models based on using perturbative polarization corrections and mean - field blocking approximation give conflicting results for masses of odd nuclei . purpose : : : systematically investigate the polarization and mean - field models , implemented within self - consistent approaches that use identical interactions and model spaces , so as to find reasons for the conflicts between them . methods : : : for density - dependent interactions and with pairing correlations included , we derive and study links between the mean - field and polarization results obtained for energies of odd nuclei . we also identify and discuss differences between the polarization - correction and full particle - vibration - coupling ( pvc ) models . results : : : we have identified and numerically evaluated self - interaction ( si ) energies that are at the origin of different results obtained within the mean - field and polarization - correction approaches . the simplest deformed mean - field approach that does not break parity symmetry is unable to reproduce full pvc effects .

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background : : : models based on using perturbative polarization corrections and mean - field blocking approximation give conflicting results for masses of odd nuclei . purpose : : : systematically investigate the polarization and mean - field models , implemented within self - consistent approaches that use identical interactions and model spaces , so as to find reasons for the conflicts between them . methods : : : for density - dependent interactions and with pairing correlations included , we derive and study links between the mean - field and polarization results obtained for energies of odd nuclei . we also identify and discuss differences between the polarization - correction and full particle - vibration - coupling ( pvc ) models . numerical calculations are performed for the mean - field ground - state properties of deformed odd nuclei and then compared to the polarization corrections determined by using the approach that conserves spherical symmetry . results : : : we have identified and numerically evaluated self - interaction ( si ) energies that are at the origin of different results obtained within the mean - field and polarization - correction approaches . conclusions : : : mean - field energies of odd nuclei are polluted by the si energies , and this makes them different from those obtained by using polarization - correction methods . a comparison of both approaches allows for the identification and determination of the si terms , which then can be calculated and removed from the mean - field results , giving the self - interaction - free energies . the simplest deformed mean - field approach that does not break parity symmetry is unable to reproduce full pvc effects .

we have in this paper constructed a theory based on non - equilibrium thermodynamics that reduces the immiscible _ two - phase flow _ in porous media to a _ one - phase _ flow problem . let us now consider a three - dimensional isotropic porous medium . let @xmath215 be a point somewhere in this porous medium . the theory that we have developed can then be summarized by the following set of equations , @xmath216 @xmath217 and @xmath218 here ( [ conc-1 ] ) is the conservation law for the wetting saturation . this expression becomes the buckley - leverett equation @xcite if we set @xmath219 , see equation ( [ eqn21 ] ) and take the incompressibility of the fluids into account . the non - wetting saturation @xmath220 has been eliminated by using the incompressibility of the two fluids . this implies that @xmath221 is build into the equation set . equation ( [ conc-6 ] ) is the three - dimensional version of equation ( [ eqn20 ] ) . the three - dimensional version of equation ( [ eqn18 ] ) is @xmath222 . this equation follows by taking the derivative of ( [ conc-5 ] ) with respect to @xmath32 and using ( [ conc-6 ] ) . hence , this equation is also contained in ( [ conc-1 ] ) to ( [ conc-6 ] ) . it may replace either of the equations ( [ conc-5 ] ) or ( [ conc-6 ] ) . these equations are all conservation laws , the last two express power input equals dissipation . thus , they transcend the details of the porous medium . equations ( [ conc-1 ] ) to ( [ conc-6 ] ) are 7 equations . there are ten variables @xmath32 , @xmath223 , @xmath224 and @xmath225 . the three equations that close the system of equations are the _ constitutive equations _ @xmath226\;,\ ] ] containing the detailed physics of the system . we see that the constitutive equation does not contain the seepage velocities of the immiscible fluids , @xmath224 and @xmath225 , explicitly . only the saturation @xmath32 enters . hence , the constitutive equation ( [ conc-7 ] ) can be interpreted as that of a single fluid depending on one extra variable , @xmath227 . hence , the equation set ( [ conc-1 ] ) ( [ conc-7 ] ) reduces the immiscible two - phase flow problem in porous media to a one - phase flow problem involving a complex fluid . this viewpoint permeates recent work on the effective permeability of immicible two - phase systems where it is suggested that two fluids behave as if they were a single bingham plastic @xcite . we may clarify this point even further by eliminating the two fluid velocities @xmath224 and @xmath225 in equations ( [ conc-1 ] ) to ( [ conc-6 ] ) . the equation set then reduces to a single equation @xmath228 together with the constitutive equation ( [ conc-7 ] ) , we now have a closed set describing effectively a single fluid with a velocity field @xmath223 which transports an active scalar @xmath32 . in this manuscript we have considered a single driving force that induces the flow : the pressure gradient . other forces such as buoyancy , temperature gradients and chemical driving forces can be incorporated in the non - equil - ibrium thermodynamics formalism used in section [ diss ] . the same is true for the introduction of more immiscible fluids than two . hence , equations ( [ conc-1 ] ) to ( [ conc-6 ] ) may be generalized to include these additional complications . the authors thank eirik grude flekky , knut jrgen mly , thomas ramstad , per arne slotte and marios valavanides for interesting discussions on this topic . ah , sk and is thank vista , a collaboration between statoil and the norwegian academy of sciences , for financial support . ss thanks the norwegian research council , nfr and the beijing computational science research center csrc for financial support . k. t. tallakstad , h. a. knudsen , t. ramstad , g. lvoll , k. j. mly , r. toussaint and e. g. flekky , steady - state two - phase flow in porous media : statistics and transport properties , phys . rev . lett . * 102 * , 074502 ( 2009 ) . k. t. tallakstad , g. lvoll , h. a. knudsen , t. ramstad , e. g. flekky and k. j. mly , steady - state simultaneous two - phase flow in porous media : an experimental study , phys . e * 80 * , 036308 ( 2009 ) . e. m. rassi , s. l. codd and j. d. seymour , nuclear magnetic resonance characterization of the stationary dynamics of partially saturated media during steady - state infiltration flow , n. j. phys . * 13 * , 015007 ( 2011 ) . s. sinha , a. t. bender , m. danczyk , k. keepseagle , c. a. prather , j. m. bray , l. w. thrane , j. d. seymor , s. l. codd and a. hansen , effective rheology of two - phase flow in three - dimensional porous media : experiment and simulation , submitted to trans . ( 2016 ) . r. g. bentsen and j. trivedi , on the construction of an experimentally based set of equations to describe cocurrent or countercurrent , two - phase flow of immiscible fluids through porous media , transp . in por . media , * 99 * , 251 ( 2013 ) . m. moura , e. -a . florentino , k. j. mly , g. schfer and r. toussaint , impact of sample geometry on the measurement of pressure - saturation curves : experiments and simulations , water res . 51 * , 8900 ( 2015 ) .

based on non - equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two - phase flow in porous media . these equations together with the conservation of saturation reduces the immiscible two - phase flow problem to a single - phase flow problem of a complex fluid .

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based on non - equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two - phase flow in porous media . these equations together with the conservation of saturation reduces the immiscible two - phase flow problem to a single - phase flow problem of a complex fluid . we discuss the new equation in terms of the relative permeability equations . we test the equations on model systems , both analytically and numerically .

to discuss the problem of missing strength of gamow - teller ( gt ) transitions , one needs to study the distribution of transition strength over the excitation energy . a convenient tool for that purpose is the strength function of gt transitions @xmath3 where @xmath4 is the energy of the @xmath5 state reckoned from the ground state of a target nucleus , @xmath6 . usually , it is assumed that the effect of missing strength can be explained ( reproduced ) by including 2p2h admixtures into the wave functions of nuclear states involved . in order to check this assumption , we consider the energy - weighted moments of the gt strength function @xmath7 for positive integer @xmath8 . in the first section , we calculate the moments in the random phase approximation , the second random phase approximation and within the fragmentation problem . in the second section , we argue that the explanation of missing strength requires that the particle - hole residual interaction has a specific feature , it should intensively mix the @xmath9 and @xmath10 particle - hole configurations . the example of such an interaction is presented and the strength function of @xmath11 transitions in @xmath12 is demonstrated . in the third section , the calculations of total muon capture rates by complex nuclei are discussed . the fourth section contains the analysis of spin - isospin transitions in @xmath13 nuclei observed in muon capture , and in @xmath14 and @xmath15 reactions . the main results are collected in conclusion .

the manifestations of spin - isospin nuclear response in nuclear muon capture are discussed . tetereva@xmath2 + _ @xmath1 joint institute for nuclear research , dubna , moscow region , 141980 , russia + @xmath2 skobeltsyn institute of nuclear physics , lomonosov moscow state university , moscow , 119992 , russia _

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by analyzing the energy - weighted moments of the strength function calculated in rpa and beyond it is shown that the explanation of the effect of missing strength of gamow - teller transitions requires that residual interaction produce high - excited @xmath0 particle - hole collective states . the example of this interaction is presented . the manifestations of spin - isospin nuclear response in nuclear muon capture are discussed . v.a . kuzmin@xmath1 and t.v . tetereva@xmath2 + _ @xmath1 joint institute for nuclear research , dubna , moscow region , 141980 , russia + @xmath2 skobeltsyn institute of nuclear physics , lomonosov moscow state university , moscow , 119992 , russia _

the energy weighted moments of strength function of gt transition , @xmath170 , are calculated in the rpa , srpa and within the fragmentation problem . considering @xmath171 and @xmath172 we have shown that the effect of missing gt strength should be reproduced as the result of interaction among the particle - hole excitations , without including the 2p2h configurations . hence , the residual interaction in the spin - isospin channel must intensively mix the @xmath173 and @xmath10 particle - hole states . the example of this interaction is presented . it is shown that the experimental strength function of @xmath11 transition in @xmath12 can be reproduced rather well in the whole region of excitation energy . total muon capture rates were calculated for several nuclei using two variants of residual interaction . theoretical total rates of muon capture by medium nuclei practically do not depend on the residual interaction used in calculation . in heavy nuclei theoretical rates are higher than experimental ones . the excess depends on the residual interaction , and the difference between theory and experiment is the largest when the residual interaction , which forms the high - excited collective states , is used in the calculation . the existence of these states is assumed by the effect of missing gt strength . it is shown that the distributions of transition strength over the excitation energy in @xmath13 nuclei extracted from weak and electromagnetic processes are in conflict with the ones obtained from charge - exchange nuclear reactions . in particular , no quenching of spin - isospin transitions is found in the rates of partial allowed muon capture @xmath174 . rowe , rev . phys . , * 40 , * 153 , ( 1968 ) a.m. lane and j. martorell , ann . phys . , * 129 , * 273 , ( 1980 ) f. gantmacher , theory of matrices , vol . 2 , ams publishing , 2000 s. drod , s. nishizaki , j. speth and j. wambach , phys . rep . , * 197 , * 1 , ( 1990 ) a. bohr and b.r . mottelson , nuclear structure , vol . 1 , new york , amsterdam , 1969 v.v . voronov and v.g . soloviev , fiz . chast . at . yadra , * 14 , * 1380 , ( 1983 ) [ sov . j. part . nucl . , * 14 , * 583 ( 1983 ) ] v.a . kuzmin , theoret . i matemat . fiz . , * 70 , * 315 ( 1987 ) [ theor . and math . phys . , * 70 , * 223 ( 1987 ) ] g.f . bertsch , p. f. bortignon and r.a . broglia , rev . phys . , * 55 , * 287 ( 1983 ) g.j . mathews , s.d . bloom and r.f . hausman , jr . c , * 28 , * 1367 ( 1983 ) s. drod , v. klempt , j. speth , and j. wambach , phys . b , * 166 , * 18 ( 1986 ) s. drod , f. osterfeld , j. speth , j. wambach , phys . b , * 189 , * 271 ( 1987 ) a.i . vdovin and v.g . soloviev , fiz . chast . at . yadra , * 14 , * 237 , ( 1983 ) [ sov . j. part . nucl . , * 14 , * 99 ( 1983 ) ] t. wakasa _ et al . _ , phys . c , * 56 , * 2909 , ( 1997 ) v.a . kuzmin , yad . * 58 , * 418 , ( 1995 ) [ phys . atom . nucl .. * 58 , * 368 , ( 1995 ) ] ; k. junker , v.a . kuzmin , t.v . tetereva , eur . phys . j. a , * 5 , * 37 ( 1999 ) v.v . balashov , g.ya . korenman , r.a . eramzhyan , poglozhenie mezonov atomnymi yadrami , m. , atomizdat , 1978 , 294 pp ( in russian ) r.a . eramzhyan , v.a . kuzmin , and t.v . tetereva , nucl . a , * 642 , * 428 ( 1998 ) ; v.a . kuzmin , t.v . tetereva , k. junker , and a.a . ovchinnikova , j. phys . g : nucl . part . phys . , * 28 * , 665 ( 2002 ) c. gaarde _ et al . , phys . a , * 369 , * 258 ( 1981 ) t. suzuki , d.f . measday , and j.p . roalsvig , phys . c , * 35 , * 2212 ( 1987 ) b. goulard and h. primakoff , phys . rev . c , * 10 , * 2034 ( 1974 ) e. kolbe , k. langanke , and p. vogel , phys . c , * 62 * , 055502 ( 2000 ) t.p . gorringe , _ et al . , _ phys . c , * 60 , * 055501 ( 1999 ) p.m. endt , nucl . phys . a , * 521 * , 1 ( 1990 ) c. lttge , _ et al . , _ phys . c , * 53 , * 127 ( 1996 ) ; y. fujita , _ et al . , _ phys . rev . c , * 55 , * 1137 ( 1996 ) p. von neumann - cosel , a. richter , y. fujita and b.d . anderson , phys . c , * 55 , * 532 ( 1997 ) b.h . wildenthal , prog . , * 11 , * 5 ( 1984 ) a. etchegoyen . , b.a . brown , w.d.m . rae , msucl report no . 524 , michigan , 1986 v.a . kuzmin and t.v . tetereva , yad . fiz . , * 63 , * 1966 ( 2000 ) [ phys . at . nucl . , * 63 , * 1874 ( 2000 ) ] p.m. endt , nucl . phys . a , * 633 * , 1 ( 1998 ) ch . brianon , _ et al . , _ nucl . a , * 671 * , 647 ( 2000 )

by analyzing the energy - weighted moments of the strength function calculated in rpa and beyond it is shown that the explanation of the effect of missing strength of gamow - teller transitions requires that residual interaction produce high - excited @xmath0 particle - hole collective states . the example of this interaction is presented . kuzmin@xmath1 and t.v .

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by analyzing the energy - weighted moments of the strength function calculated in rpa and beyond it is shown that the explanation of the effect of missing strength of gamow - teller transitions requires that residual interaction produce high - excited @xmath0 particle - hole collective states . the example of this interaction is presented . the manifestations of spin - isospin nuclear response in nuclear muon capture are discussed . v.a . kuzmin@xmath1 and t.v . tetereva@xmath2 + _ @xmath1 joint institute for nuclear research , dubna , moscow region , 141980 , russia + @xmath2 skobeltsyn institute of nuclear physics , lomonosov moscow state university , moscow , 119992 , russia _

nowadays the family of iron pnictides is a well - established and important prototype system for unconventional high - temperature superconductivity . starting with the first famous compound @xcite in 2008 , today several different sub - families with a wide structural variety are known . all different groups of iron pnictides share some common physical properties , such as their interesting and sometimes puzzling magnetic behavior . most compounds show a phase transition at low temperatures from a tetragonal to an orthorhombic crystal symmetry which is typically accompanied by the formation of long - range antiferromagnetic order.@xcite it is common believe that the suppression of these phase transitions for example by chemical substitution is crucial for the emergence of unconventional superconductivity.@xcite although it is obvious that an understanding of the magnetic fluctuations in the iron pnictides is mandatory to unveil the physics underlying the superconductivity , this task has proven to be more complex than anticipated.@xcite for example , there was discussion in the literature whether the magnetic moments are better described by an itinerant@xcite or a localized@xcite model and there is up to now no consensus concerning the role of correlation effects@xcite . furthermore , the magnitude of the magnetic moments is difficult to reproduce within density functional theory ( dft ) and it is known to be quite sensitive to computational parameters.@xcite one of the most important experimental tools to get insight into the electronic structure of the iron pnictides is angle - resolved photoemission spectroscopy ( arpes ) . there are numerous publications on this topic , although it was shown that dft calculations have typically problems to reproduce all features of the arpes spectra correctly.@xcite this is often ascribed to strong correlation effects , although this question is still under discussion.@xcite another important difficulty which so far is often ignored is the connection between the magnetic phase of the iron pnictides and the resulting consequences for arpes . this is due to the formation of twinned crystals during the phase transition from tetragonal to orthorhombic and it results in mixed magnetic domains which are orthogonal to each other . macroscopic tools like arpes or transport measurements can so only see the averaged information , while information on the anisotropy is lost.@xcite this is a huge drawback considering a comprehensive study of the electronic structure in the iron pnictides , as it is known that the in - plane anisotropy plays a significant role.@xcite in experiment it is possible to effectively detwin the crystals by applying uniaxial stress during the measurement . this was already done successfully for the 122-prototype in the undoped and in the co - doped case . however , such measurements are connected with several technical difficulties and consequently they are rarely done.@xcite yet , to fully understand the electronic properties of the iron pnictide superconductors in a comprehensive way and to get a deeper insight concerning the influence of the in - plane anisotropy in the magnetic phase such studies are absolutely mandatory . although there is nowadays experimental data on detwinned crystals showing clearly the anisotropy in the fermi surface there is hardly any theoretical work focusing on this problem of magnetic anisotropy in arpes data . in this work this issue is addressed by a comprehensive dft study on the magnetic phase of and on the corresponding arpes spectra . the computational results can be directly compared to the available experimental arpes data on detwinned crystals.@xcite in order to deal with this complex situation the korringa - kohn - rostoker - green function ( kkr - gf ) approach is used , which was already shown to be indeed a very useful and accurate tool to deal with the iron pnictides.@xcite the impact of disorder due to substitution is dealt with by means of the coherent potential approximation ( cpa ) , giving results fully compatible to supercell calculations and more reliable than those based on the virtual crystal approximation ( vca).@xcite

by means of one - step model calculations the strong in - plane anisotropy seen in angle - resolved photoemission of the well - known iron pnictide prototype compounds and in their low - temperature antiferromagnetic phases is investigated . the fully - relativistic calculations are based on the korringa - kohn - rostoker - green function approach combined with the coherent potential approximation alloy theory to account for the disorder induced by co substitution on fe sites in a reliable way . the results of the calculations can be compared directly to experimental spectra of detwinned single crystals . in particular the local density approximation can capture most of the correlation effects for the investigated system without the need for more advanced techniques . the results are also used to discuss surface effects and it is possible to identify clear signatures to conclude about different types of surface termination .

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by means of one - step model calculations the strong in - plane anisotropy seen in angle - resolved photoemission of the well - known iron pnictide prototype compounds and in their low - temperature antiferromagnetic phases is investigated . the fully - relativistic calculations are based on the korringa - kohn - rostoker - green function approach combined with the coherent potential approximation alloy theory to account for the disorder induced by co substitution on fe sites in a reliable way . the results of the calculations can be compared directly to experimental spectra of detwinned single crystals . one finds very good agreement with experiment and can reveal all features of the electronic structure contributing to the in - plane anisotropy . in particular the local density approximation can capture most of the correlation effects for the investigated system without the need for more advanced techniques . in addition , the evolution of the anisotropy for increasing co concentration @xmath0 in can be tracked almost continuously . the results are also used to discuss surface effects and it is possible to identify clear signatures to conclude about different types of surface termination .