Datasets:

Hendrik-a

/

dancer-data

like 0

astro-ph0408508

i

recently , strong evidence has been presented that a sub - class of type iin supernovae ( sn ) ( ` n ' stands for narrow h@xmath2 ) includes rare sn ia events exploding in a dense circumstellar medium ( csm ) ( hamuy et al . 2003 ) . to date , the new variety comprises three events : sn 2002ic , sn 1997cy and sn 1999e ( cf . deng et al . statistical arguments indicate that the new family constitutes less than one percent of all sn ia ( chugai & yungelson 2004 ) . all these supernovae remain very luminous after the light curve maximum , which is related to the cs interaction . a light curve model of sn 1997cy suggests that the cs envelope within @xmath3 cm contains several solar masses ( chugai & yungelson 2004 ) . two options for the origin of the csm have been proposed ( hamuy et al . 2003 ) : mass - loss by a supergiant in a binary scenario of sn ia ( whelan & iben 1973 ) or the mass - loss by a single supergiant in the sn1.5 scenario ( iben & renzini 1983 ) . the similarity of sn 2002ic events seems to favour the sn1.5 scenario , with the progenitor mass around @xmath4 ( chugai & yungelson 2004 ) . the possible scenario of a c / o white dwarf ( wd ) merging with the co - core of a supergiant companion ( livio & riess 2003 ) faces a serious problem in explaining the short time lag between the ejection of the common envelope and the explosion ( chugai & yungelson 2004 ) . the study of the cs interaction and modeling of the spectra should elucidate the late evolution and the origin of these interesting events . an important recent conclusion is that sn 2002ic interacts with an equatorially concentrated csm ( deng et al . this statement is based upon the interpretation that line profiles in sn 2002ic are too broad compared with the predictions of a spherical model . also , spectropolarimetric observations of sn 2002ic reveal the presence of polarization which is likely to be related to the csm ( wang et al . the claimed asymmetry of the csm may have an important implication for the problem of the evolutionary scenario , because the single and binary scenarios are likely to possess different degrees of symmetry . the aspherical model predicts variations of the emission line profiles of sn 2002ic - like supernovae viewed from different angles . however , all three known objects ( see deng et al . 2004 , their fig . 1 ) show similar shapes and widths of spectral features . this fact implies that , despite the detected polarization of the emission from sn 2002ic , the interaction possesses a high degree of sphericity . in view of this , we investigate a spherical model here . we attempt to explain the light curve , the ca ii line profiles and the quasi - continuum of sn 2002ic - like events on the basis of a circumstellar interaction model . we rely on the spherical approximation , although we allow for local deviations from sphericity ( e.g. clumpy structure ) . we start with the simulation of the cs interaction dynamics and the bolometric light curve of sn 2002ic using the thin shell approximation ( section 2 ) . although the model is the same as before ( chugai & yungelson 2004 ) , we include more realistic ejecta abundances , which affects the light curve . we then analyse the line formation in the inhomogeneous intershock layer and propose a simple treatment of this problem ( section 3 ) . using this approximation we simulate the ca ii line profiles and the quasi - continuum of sn 2002ic with the kinematic parameters of the interaction model . we demonstrate that the spherical model successfully accounts for the basic observational properties of sn 2002ic and discuss implications .

we propose a model to account for the bolometric light curve , quasi - continuum and the ca ii emission features of the peculiar type ia supernova ( sn ) 2002ic , which exploded in a dense circumstellar envelope . ( 2004 ) . stars : mass - loss supernovae : general supernovae : individual ( sn 2002ic )

we propose a model to account for the bolometric light curve , quasi - continuum and the ca ii emission features of the peculiar type ia supernova ( sn ) 2002ic , which exploded in a dense circumstellar envelope . the model suggests that the sn ia had the maximum possible kinetic energy and that the ejecta expand in an approximately spherically symmetric ( possibly clumpy ) circumstellar environment . the ca ii and quasi - continuum are emitted by shocked sn ejecta that underwent deformation and fragmentation in the intershock layer . modeling of the ca ii triplet implies that the contribution of the o i 8446 line is about 25% of the 8500 feature on day 234 , which permits us to recover the flux in the ca ii 8579 triplet from the flux of 8500 blend reported by deng et al . ( 2004 ) . we use the ca ii doublet and triplet fluxes on day 234 to derive the electron temperature ( k ) in the ca ii line - emitting zone and the ratio of the total area of dense fragments to the area of the shell , . we argue that ca ii bands and quasi - continuum originate from different zones of the shocked ejecta that reflect the abundance stratification of the supernova . stars : mass - loss supernovae : general supernovae : individual ( sn 2002ic )

astro-ph0408508

c

the aim of this paper was to develop a unified model for the light curve and spectrum of sn 2002ic assuming approximate spherical symmetry . our principal result is that the ca ii line profiles and the quasi - continuum are consistent with the interaction model provided that the sn ia has the maximum possible kinetic energy . the high explosion energy is in line with the high peak absolute magnitude of sn 2002ic . according to hamuy et al . ( 2003 ) , at light maximum sn 2002ic was as bright as @xmath238 ( @xmath239 km s@xmath22 mpc@xmath22 ) . given the contribution of the veiling continuum of about @xmath240 mag on dec . 3 in @xmath125 band ( @xmath241 ) ( hamuy et al . 2003 ) , we conclude that the peak absolute magnitude of the sn ia was @xmath242 , close to that of extremely bright sn ia , sn 1991 t ( @xmath243 , cf . fisher et al . 1999 ) . the magnitude at the maximum coincides also with that predicted by the detonation model det1 ( hflich & khokhlov 1996 ) . this coincidence is another justification for our choice of the high kinetic energy for the sn 2002ic event . yet , as we noted above , the strong ca ii emission lines indicate that the explosion should be different from the det1 model in the sense that the degree of incineration in the outer layers should be lower to produce enough ( @xmath244 ) ca - rich fe - poor material . modeling of the spectra of the fragmented cool dense shell formed in the intershock layer provides strong evidence that the quasi - continuum and ca ii lines are emitted by different zones . this presumably reflects the stratification of the composition of the sn ejecta in the sense that the outer layers responsible for the ca ii lines are fe - poor , while the inner layers responsible for the quasi - continuum are fe - rich . the fe - poor ejecta are shocked earlier and , therefore , spread throughout the intershock layer , while fe - rich ejecta are shocked later and thus have not yet mixed with the fe - poor material at @xmath245 d. this picture predicts that at a later epoch ( @xmath246 d ) both fe - poor and fe - rich shocked components should be mixed with each other . as a result , the ca ii doublet must disappear at a later epoch due to the mixing of the ca ii line - emitting gas with optically thick quasi - continuum emitters . sn 1999e showed a gradual disappearance of the ca ii 3945 doublet in spectra between days 139 and 361 ( rigon et al . 2003 ) , in accord with these expectations . the high luminosity of the ca ii doublet and triplet in sn 2002ic on day 234 indicates that the dense shocked ejecta form a structure with a large area ratio , @xmath247 . a high area ratio ( @xmath248 ) is also preferred by the quasi - continuum model . the area ratio , which is common in the treatment of the physics of mixing fluids ( e.g. , catrakis et al . 2002 ) , has not been used before in the interpretation of optically thick emission lines from an intershock layer . it was recognized earlier that the interpretation of the x - ray and radio emission of an interacting sn depends on the presence of a mixing layer , while the h@xmath2 emitted by the mixed dense material may reveal the fine structure related to the rt spikes ( chevalier & blondin 1995 ) . here we add to the list of effects of the mixing layer the crucial role of the large area ratio for the interpretation of the ca ii lines and quasi - continuum in sn 2002ic . the fact that the area ratio in sn 2002ic on day 234 is large , @xmath1 , suggests that we observe an advanced stage of the mixing of dense shocked ejecta in the intershock zone . experiments on the mixing of fluids show that the interface between fluids reveals fractal behavior . specifically , the cumulative area of the interface above the scale @xmath249 is @xmath250 , where @xmath251 ( sreenivasan et al . 1989 ) . if this law also holds in the case of the mixing of the dense shocked ejecta in the intershock layer of sn 2002ic , then the dense gas should produce structures with scales as small as @xmath252 . the minimum linear scale that corresponds to the thickness of the dense fragments should be even smaller , @xmath253 , where @xmath254 is the original thickness of the cds ( section [ sec - mech ] ) . it would be interesting to check the possibility of creating the mixing layer in sn 2002ic with @xmath1 in numerical experiments using high resolution 3d hydrodynamical simulations , although it seems to be beyond the capabilities of present - day computers . to estimate the area ratio from a numerical experiment , one needs to find the average number of intersections of dense peaks with the radius in the intershock layer @xmath255 . the area ratio is then @xmath256 . we do not yet fully understand all the mechanisms responsible for the major spectral features seen in the late emission from sn 2002ic . in addition to the h@xmath2 line , an important issue ignored in our study is the problem of the o i 8446 emission , although it is not a dominant constituent of the 8500 bump anymore . the oxygen excitation mechanism should predict the absence of strong o i 7774 in sn 2002ic . the fluorescence pumping of o i 8446 in the h@xmath2-emitting gas ( deng et al . 2004 ) meets this requirement . this mechanism predicts a comparable intensity of o i 11287 . the absence of this line in the spectrum of sn 1999e around @xmath257 d ( rigon et al . 2003 , their fig . 6 ) casts doubt on the fluorescence mechanism . an alternative possibility is that the o i 8446 line is emitted by the oxygen - rich matter in the outermost layers of the sn ejecta due to non - thermal collisional excitation by secondary electrons that are created by high energy photoelectrons . excitation by secondary electrons also yields a high o i 8446 / o i 7774 intensity ratio ( stolarski & green 1967 ) . an interesting possibility that ly@xmath2 pumping line of fe ii 8451 might contribute to 8500 band instead of o i 8446 , as was the case , possibly , for sn 1995n ( fransson et al . 2000 ) , seems unlikely here because of the absence of another strong ly@xmath2 fluorescent band of fe ii at @xmath258 . despite of a possible presence of a large amount of oxygen in the cool shocked sn gas ( up to @xmath259 ) , the strong [ o i ] line is not expected . adopting boltzmann population for @xmath260 k and oxygen mass of @xmath261 one gets the luminosity of this line of about @xmath262 erg s@xmath22 , i.e. , a factor of @xmath263 lower compared to the luminosity of the observed `` 6300 '' emission band on day 244 . in view of the possibility that our hydrodynamic model may underestimate the expansion velocity of the sn / csm interface by about @xmath264% , we discuss the implications for our model . the emergent x - ray luminosity from the forward shock in the standard model is comparable or even exceeds the optical bolometric luminosity after maximum light ( see fig . [ f - blc ] and fig . [ f - xlc ] ) . hence , there is an extra energy reservoir which might , in principal , be transformed into the optical band under the proper conditions . this possibility could be realized in a model of interaction with a clumpy csm . as a result of ( i ) softer x - rays from cloud shocks than for a smooth csm , and ( ii ) the larger geometrical probability of absorption of x - rays from clouds penetrating the sn ejecta , the optical output from the interaction should be larger . therefore , the same bolometric luminosity can be produced for a lower average cs density and higher expansion velocity of the sn / csm interface compared with a smooth csm . the spherical geometry of the cs interaction of sn 2002ic , advocated here , finds additional support from statistical arguments already mentioned in the introduction . we know three events of sne ia in a dense csm ( sn 1997cy , sn 1999e , sn 2002ic ) and they show similar widths and shapes of spectral features at a similar phase ( see deng et al . 2004 , their fig . this fact suggests that a bi - polar structure of the sn / csm interface with high aspect ratio is unlikely . at first glance the picture of spherical interaction is incompatible with the detection of intrinsic polarization of sn 2002ic radiation at a level of @xmath265 % ( wang et al . simple estimates show that the thomson scattering in a moderately aspherical cs envelope with @xmath51 is not able to produce such a high polarization . the issue may be resolved in a model in which the polarization is acquired in the scattering of the sn radiation on the dust in a distant ( @xmath266 cm ) aspherical csm . the resemblance of the light curves for all three sn 2002ic - like events ( see deng et al . 2004 ) suggests a similar regime of mass - loss from their presupernovae and a common origin of the progenitors . as mentioned before ( chugai & yungelson 2004 ) , the uniformity lends support for the sn1.5 evolutionary scenario suggested by iben & renzini ( 1983 ) . yet we do not rule out the binary scenario . in this case , the wd companion should be a supergiant with the mass @xmath267 ( the cs envelope , @xmath268 , plus the supergiant core , @xmath269 ) . in the binary scenario , there is no clear reason for the supergiant to have experienced strong mass loss just before the sn explosion . the synchronization of the vigorous mass loss and the sn event might be a more natural outcome in the single agb star scenario with the c / o core approaching the chandrasekhar limit . a general belief is that chandrasekhar mass white dwarfs can not be produced from intermediate - mass single stars because the growth of the c / o core during the thermal pulsation stage is prevented by the removal of the hydrogen envelope ( blcker 1995 , and references therein ) . in this regard , it is highly remarkable that at least two supernovae ( sn 2002ic and sn 1997cy ) exploded in dwarf galaxies , as already noted by chugai & yungelson ( 2004 ) . dwarf galaxies are characterized by low metallicity , which thus might explain why the co core of an asymptotic giant branch star is successful in attaining the chandrasekhar limit before the hydrogen envelope is lost ( chugai & yungelson 2004 ) . an evidence for the low metallicity of the presupernova of sn 2002ic comes from our modelling of the ca ii lines and quasi - continuum ( sec . [ sec - cont ] ) . the possibility of sn1.5 explosions in metal - poor galaxies was suggested also by zijlstra ( 2004 ) . it would be interesting to check whether all the host galaxies of sn 2002ic - like supernovae are actually metal deficient . if the suggested link between sn 2002ic - like events and low metallicity is correct , then their occurrence rate relative to normal sn ia must increase with the redshift for @xmath270 , when the average cosmic metallicity was lower than solar . if sn 2002ic - like events stem from sn 1.5 explosions , their low fraction of sn ia , @xmath271% , can be used to estimate the the fraction of white dwarfs created with a mass similar to the chandrasekhar mass . if only @xmath272% of all wds can become sn ia , this suggests that only @xmath273 of white dwarfs in our galaxy were formed with a mass close to the chandrasekhar mass . since these white dwarfs are likely to have formed in a metal poor environment , they are probably very old ( age @xmath274 yr ) and thus of low luminosity , @xmath275 ( prada moroni & straniero 2003 ) . the number of known cool white dwarfs is low , @xmath276 ( salim et al . 2004 ) , and will probably remain too low for the nearest future to test the idea whether high mass white dwarfs were produced during early epochs when the metallicity was low . the possible link between sn 2002ic - like supernovae and hypothetical sn1.5 events , combined with arguments in favour of a high energy sn ia event in this case , raises the question of whether conditions in a hot chandrasekhar mass c / o wd that just got rid of the remnants of the hydrogen envelope favour a wd explosion with a high kinetic energy of ejecta . the sn1.5 origin of sn 2002ic suggests that the initial mass at the main sequence is @xmath277 . with the chandrasekhar core and @xmath28 in the dense cs envelope we expect that about @xmath278 had to be lost at the previous agb stage . this means that outside the dense cs envelope ( @xmath279 cm ) there should be a dense red supergiant wind with a velocity of the order @xmath280 km s@xmath22 and a mass loss rate of @xmath281 yr@xmath22 . keeping in mind the analogy with sn 1979c , this wind may be revealed in the infrared ( ir ) as an ir echo ( dwek 1983 ) , and in the radio as a result of cs interaction ( chevalier 1982a , weiler et al . however , the radio emission from the distant sn 2002ic ( @xmath282 mpc ) may pose a difficult challenge to detect . if the radio luminosity is comparable to that of sn 1979c ( weiler et al . 1986 ) then the expected radio flux from sn 2002ic around 1000 day should be of the order of @xmath283 mjy in the @xmath284 cm band , which is close to the detection limit of vla . a more promising target for the detection of the late time interaction of sn 2002ic - like supernovae with the presumed agb wind is sn 1999e at a distance of @xmath285 mpc , or any closer sn 2002ic - like event that will be discovered in the future . note , that at the epoch of the interaction with the dense cs shell ( @xmath286 d ) , the radio emission is severely attenuated by free - free absorption at wavelengths @xmath287 cm . with the parameters used in our models , and adopting temperatures for the shell and wind in accordance with the models of lundqvist & fransson ( 1988 ) , we find that free - free absorption is a likely reason why the observations of berger & soderberg ( 2003 ) and stockdale et al . ( 2003 ) did not detect radio emission from sn 2002ic . a better understanding of the phenomenon of sn 2002ic - like events requires an accurate energy audit , for which the direct detection of the x - ray emission as well as ir measurements are important . sn 2002ic - like events at an age of @xmath43 days are excellent targets for chandra , xmm and integral .

the model suggests that the sn ia had the maximum possible kinetic energy and that the ejecta expand in an approximately spherically symmetric ( possibly clumpy ) circumstellar environment . the ca ii and quasi - continuum are emitted by shocked sn ejecta that underwent deformation and fragmentation in the intershock layer .

we propose a model to account for the bolometric light curve , quasi - continuum and the ca ii emission features of the peculiar type ia supernova ( sn ) 2002ic , which exploded in a dense circumstellar envelope . the model suggests that the sn ia had the maximum possible kinetic energy and that the ejecta expand in an approximately spherically symmetric ( possibly clumpy ) circumstellar environment . the ca ii and quasi - continuum are emitted by shocked sn ejecta that underwent deformation and fragmentation in the intershock layer . modeling of the ca ii triplet implies that the contribution of the o i 8446 line is about 25% of the 8500 feature on day 234 , which permits us to recover the flux in the ca ii 8579 triplet from the flux of 8500 blend reported by deng et al . ( 2004 ) . we use the ca ii doublet and triplet fluxes on day 234 to derive the electron temperature ( k ) in the ca ii line - emitting zone and the ratio of the total area of dense fragments to the area of the shell , . we argue that ca ii bands and quasi - continuum originate from different zones of the shocked ejecta that reflect the abundance stratification of the supernova . stars : mass - loss supernovae : general supernovae : individual ( sn 2002ic )

1202.2797

i

the seyfert 1 galaxy mcg-6 - 30 - 15 is the primary `` disk - line '' target , in which a relativistically broadened iron k - emission line is suggested to originate in the innermost region of the accretion disk around the black hole ( e.g. , tanaka et al . mcg-6 - 30 - 15 is also known to exhibit characteristic x - ray spectral variations ; inoue & matsumoto ( 2001 , 2003 ) , fabian et al . ( 2002 ) and matsumoto et al . ( 2003 ) reported significantly small variability in the iron line energy band of mcg 6 - 30 - 15 . it is found that the energy - dependent root mean square ( rms ) variability is suppressed around the iron line energy , particularly in longer timescales . inoue and matsumoto ( 2001 , 2003 ) proposed that the absorbed spectrum due to photo - ionized warm absorbers mimic shape of the strongly red - shifted iron line , and variation of the warm absorbers may explain the apparently small variability in the iron line energy band . on the other hand , miniutti and fabian ( 2004 ) proposed that the suppressed variability in the iron line band may be explained by the general relativistic light - bending effects , which take place in the very vicinity of the black hole . miniutti et al . ( 2007 ) claim that the suzaku spectrum of mcg-6 - 30 - 15 is in fact consistent with the light - bending model . niedwiecki & ycki ( 2008 ) and niedwiecki & miyakawa ( 2010 ) independently re - examined the light - bending model , and concluded that it is possible to explain the suppressed variability in the iron energy band assuming a particular configuration and movement of the illuminating source . ycki et al . ( 2010 ) , on the other hand , claim that the light - bending model is not able to explain the suzaku spectrum , if a broader energy range is adopted than used by miniutti et al . ( 2007 ) . the primary question in mcg-6 - 30 - 15 is whether the iron line is truely broad and its little variability is a consequence of the general relativistic light bending effects or not . the critical point to address the problem is to model the underlying continuum spectrum correctly , since the broad iron line parameters are dependent on the choice of the continuum spectral model . in fact , on one hand , miller , turner , and reeves ( 2008 ) claim that the `` disk - line '' is not required , when the continuum spectrum is modeled with multiple warm absorbers . on the other hand , reynolds et al . ( 2009 ) argue that the absorption - dominated model over - predicts the 6.4 kev fluorescent line emission , and the disk - line model is more physically reasonable . miller et al . ( 2009 ) counterargue that the calculation in reynolds et al . ( 2009 ) neglects opacity at the 6.4 kev line energy , and conclude that variation in the partial - covering fraction may dominate the observed x - ray spectral variability . however , the partial covering scenario by miller et al . ( 2009 ) requires a number of free parameters to model the observed spectrum . therefore , in order to examine the partial covering scenario , reducing the number of parameters , if possible , and constructing a concrete physical picture to explain the spectral variation is certainly intriguing . recently , using the suzaku data taken in january 2006 , miyakawa et al . ( 2009 ) ( hereafter paper i ) found a clear correlation between the intensity in the 6 10 kev band and the spectral ratio of 0.5 3.0 kev / 6 10 kev in a time - scale of @xmath9 sec . essentially the same spectral correlation was confirmed for longer timescales up to @xmath814 years in the rxte data ( miyakawa 2010 ) . paper i adopted a spectral model composed of a direct power - law component , its reflection component by a neutral matter ( with the solid - angle @xmath10 ) , two warm absorbers with different ionization states . the observed spectral variation requires change of the apparent slope of the direct component , whereas the shape and intensity of the reflection component being invariable . a mildly broad iron emission line was required at @xmath11 kev with an intrinsic width of 0.29 kev ( 1 @xmath12 ) and the equivalent - width 100 ev ; such an extremely broadened `` disk line '' as is claimed by miniutti et al . ( 2007 ) was not required . in this paper , following paper i , we attempt to comprehensively understand spectral variability of mcg-6 - 30 - 15 using suzaku and chandra archival data . our goal is to find a spectral model which can naturally explain the observed spectral variation of mcg-6 - 30 - 15 with a minimum set of free - parameters . if we are successful to construct such a reasonable spectral model , we will see if the relativistically distorted iron emission line is truely present or not in the energy spectrum . we believe this is an important step forward to fully understand x - ray spectral properties of mcg-6 - 30 - 15 , seyfert galaxies , and black holes .

we propose a simple spectral model for the seyfert 1 galaxy mcg-6 - 30 - 15 that can explain most of the 1 40 kev spectral variation by change of the partial covering fraction , similar to the one proposed by miller et al . ( 2008 ) .

we propose a simple spectral model for the seyfert 1 galaxy mcg-6 - 30 - 15 that can explain most of the 1 40 kev spectral variation by change of the partial covering fraction , similar to the one proposed by miller et al . ( 2008 ) . our spectral model is composed of three continuum components ; ( 1 ) a direct power - law component , ( 2 ) a heavily absorbed power - law component by mildly ionized intervening matter , and ( 3 ) a cold disk reflection component far from the black hole with moderate solid - angle ( ) accompanying a narrow fluorescent iron line . the first two components are affected by the surrounding highly ionized thin absorber with and . the heavy absorber in the second component is fragmented into many clouds , each of which is composed of radial zones with different ionization states and column densities , the main body ( , ) , the envelope ( , ) and presumably a completely opaque core . these parameters of the ionized absorbers , as well as the intrinsic spectral shape of the x - ray source , are unchanged at all . the central x - ray source is moderately extended , and its luminosity is not significantly variable . the observed flux and spectral variations are mostly explained by variation of the geometrical partial covering fraction of the central source from 0 ( uncovered ) to.63 by the intervening ionized clouds in the line of sight . the ionized iron k - edge of the heavily absorbed component explains most of the seemingly broad line - like feature , a well - known spectral characteristic of mcg-6 - 30 - 15 . the direct component and the absorbed component anti - correlate , cancelling their variations each other , so that the fractional spectral variation becomes the minimum at the iron energy band ; another observational characteristic of mcg-6 - 30 - 15 is thus explained .

1202.2797

c

[ phenomenological_inte_section ] we have seen that suzaku and chandra energy spectra of mcg6 - 30 - 15 are successfully described by the three - component model introduced with equation ( [ eq2 ] ) . we found @xmath42 , normalization of the heavily absorbed component , is anti - correlated with normalization of the direct component , @xmath41 ( bottom panels of figures [ relation_for_the_slice_spectra ] and [ relation_for_the_slice_spectra_nh ] , and figure [ direct_absorbed_20ksec ] ) . the spectral variation indicates that the `` total normalization '' , @xmath149 , ( equation [ eq3 ] ) is not so variable , while the covering fraction , @xmath151 , ( equation [ eq4 ] ) and column - density of the low - ionized warm absorber are in sync and more significantly variable ( figure [ correlation_20ksec ] and [ 20ksec_par_var ] ) . how should we interpret this characteristic spectral variation ? since @xmath177 and @xmath178 represent amounts of the non - absorbed and absorbed fluxes emitted from the central x - ray source , respectively , the anti - correlation is naturally understood that a rather constant x - ray source is partially obscured by absorbing matters with variable covering fraction , @xmath151 . the `` difference variation function analysis '' introduced by inoue , miyakawa and ebisawa ( 2011 ) also confirms that the ( @xmath149 , @xmath151 ) parameter - set is more orthogonal and fundamental than the ( @xmath41 , @xmath42 ) parameter - set . correlation between the low - ionized absorber @xmath101 and @xmath151 ( bottom panel of figure [ correlation_20ksec ] ) is understood as follows : the low - ionized absorber represented by @xmath179 is optically thin ( table [ miyakawa_model_ave_suzaku ] ) , so that @xmath180 on the other hand , the same absorption effect can be expressed by a partial covering model with a fixed column - density as , @xmath181 @xmath182 namely , @xmath183 that is seen in the bottom panel of figure [ correlation_20ksec ] . as we have seen , the observed spectral variation of mcg-6 - 30 - 15 is primarily explained by variation of the partial covering fraction , @xmath151 . below , we designate our model as the `` variable partial covering model '' . in the framework of the variable partial covering model , the suzaku intensity - sliced spectra in 1 40 kev is explained mostly by change of the covering fraction . using the total normalization @xmath149 and the covering fraction @xmath151 , our three - component model ( [ eq2 ] ) is rewritten as follows : @xmath184 in equations ( [ eq9 ] ) and ( [ eq6 ] ) , only variable parameters are @xmath151 and @xmath149 . in figure [ covering_fraction_change ] and table [ table1_slice ] , we show an example of the simultaneous fit of the suzaku intensity - sliced spectra with variable @xmath151 ( the same dataset as used in section [ sec : sliced ] ) . the eight intensity - sliced spectra are successfully fitted with the constant normalization , @xmath185 photons s@xmath33 @xmath2 at 1 kev ( except the brightest one where @xmath149 is 1.5 times higher ) , while @xmath151 is variable from 0.63 ( dimmest ) to null ( brightest ) . the well - known small variability in the iron energy band ( section 1 ) is also nicely explained in the framework of the variable partial covering model . in order to see energy dependence of the variation at a specific timescale , we took the following method to calculate the `` difference variation function '' , @xmath186 ( inoue , miyakawa and ebisawa 2011 ) : ( 1 ) we choose a time - interval of interest , @xmath187 , to investigate for spectral variations ; here , we take @xmath18840 ksec . ( 2 ) energy spectra are calculated for every @xmath189 , namely , 20 ksec . ( 3 ) for every two contiguous energy spectra , we recognize the `` brighter spectrum '' and the `` fainter spectrum '' , @xmath190 and @xmath191 , respectively . ( 4 ) we average all the brighter spectra and all the fainter spectra . ( 5 ) thus , for a given time - period @xmath187 , we create a single `` averaged bright spectrum '' @xmath192 and a single `` averaged faint spectrum '' @xmath193 . ( 6 ) we calculate difference of the averaged bright spectrum and the averaged faint spectrum relative to the average , as @xmath194 in figure [ cov_fac_simulation ] , we show the difference variation function thus calculated at a timescale of 40 ksec . together , we show a model prediction of the difference variation function calculated in the framework of the variable partial covering model ( eq . 29 in inoue , miyakawa and ebisawa 2011 ) , where the covering fraction @xmath151 is assumed to be the major variable parameter , while the total normalization @xmath149 adds minor fluctuation . agreement of the observation and model calculation is obvious . next , we estimate physical parameters of the warm absorbers in equation ( [ eq6 ] ) , @xmath22 , @xmath23 and @xmath43 , which are high - ionized warm absorber , thin low - ionized warm absorber and thick partial absorber , respectively . we provide suffixes , @xmath195 and @xmath196 to distinguish column densities and ionization parameters of these warm absorbers . in the following , @xmath197 is distance from the central x - ray source to the absorber , @xmath198 is a representative thickness of the absorbing region along the line of sight , and @xmath199 is density . ( 90mm,90mm)figure10.eps ( 90mm,90mm)figure11.eps ccccccccc state & slice 1 & slice 2 & slice 3 & slice 4 & slice 5 & slice 6 & slice 7 & slice 8 + + @xmath32 ( @xmath54 @xmath29 ) & + + @xmath32 ( @xmath56 @xmath29 ) & + log @xmath31 & + + @xmath151 & 0.632 & 0.356 & 0.269 & 0.195 & 0.181 & 0.166 & 0.122 & @xmath200 + + @xmath201 ( @xmath202 ) & + @xmath32 & + log @xmath31 & + + 10@xmath60ph / s/@xmath61 at 1 kev & & 2.71 + + & + + & + + @xmath32 ( @xmath35 @xmath29 ) & + log @xmath31 & + + photon index & + @xmath65 ( kev ) & + + pexrav k ( 10@xmath120 ) & + + cosincl & + + line e ( kev ) & + sigma ( kev ) & + norm ( @xmath67ph / s/@xmath61 ) & + edge e ( kev ) & + maxtau & + line e ( kev ) & + sigma ( kev ) & + norm ( @xmath68ph / s/@xmath61 ) & + line e ( kev ) & + sigma ( kev ) & + norm ( @xmath67ph / s/@xmath61 ) & + reduced chisq ( d.o.f ) & + + [ table1_slice ] first , in general , we note the following relations hold : @xmath203 @xmath204 for the luminosity , we take the representative value @xmath205 erg / s , which is valid for order estimation , since the flux variation is much less than an order of magnitude . from model fitting ( table [ table1_slice ] ) , @xmath206 @xmath207 10@xmath208 erg cm / s , @xmath209 @xmath207 10@xmath210 @xmath2 . hence , @xmath211 our analysis has indicated that the high - ionized warm absorber is constant , while partial covering fraction is variable . this suggests the variable partial absorbers be embedded in the largely extended , static high - ionized warm absorber . hence , we assume @xmath212 @xmath8 @xmath213 , and take @xmath214 10@xmath215 cm and @xmath216 10@xmath217 cm@xmath120 for typical parameters of the high - ionized warm absorbers . from model fitting ( table [ table1_slice ] ) , @xmath219 10@xmath220 erg cm / s , @xmath221 10@xmath222 @xmath2 . hence , @xmath223 here , we may further constrain the parameters of the partial absorber from variation timescale of the partially absorbed component . in our variable partial covering model , typical variation timescale ( @xmath224 sec ; figure [ 20ksec_par_var ] ) corresponds to the crossing time of the x - ray absorbing clouds in front of the x - ray source . we will call these clouds as the `` low - ionized clouds '' , hereafter . assuming that size of the x - ray source and that of a low - ionized cloud have similar dimensions , the crossing timescale is expressed as @xmath225 , where @xmath226 is the velocity of a low - ionized cloud . hence , @xmath227 where @xmath226 is normalized to a typical velocity of the broad line region ( blr ) clouds . combining @xmath228 and @xmath229 , we estimate parameters of the partial absorbers as follows : @xmath230 @xmath231 note that a low - ionized cloud may have internal ionization structures , which we will see below . in our variable partial covering model , the low - ionized warm absorber ( @xmath23 ) and the partial absorber ( @xmath43 ) are closely associated . presumably , they are different parts of the low - ionized clouds . we point out that presence of such internal structures in the blr clouds is also suggested in mrk 766 ( risaliti et al . 2011 ) . in our model , the low - ionized warm absorber has a fixed column - density @xmath201 with a variable partial covering factor ( equation [ eq9 ] ) ; we simply write this column density as @xmath101 below . from model fitting ( table [ table1_slice ] ) , @xmath232 @xmath2 and @xmath233 10@xmath234 erg cm / s . if we take the distance of the low - ionized clouds @xmath235 , @xmath236 @xmath237 note that values of @xmath238 and @xmath239 are between those of the high - ionized absorber ( @xmath240 cm@xmath120 and @xmath241 ) and the partial absorber ( @xmath242 @xmath2 and @xmath243 ) , respectively . the thickness @xmath244 is much smaller than that of the partial absorber @xmath245 cm . therefore , the low - ionized absorber is considered to be in the boundary layer between the low - ionized cloud and the high - ionized warm absorber . we may call this putative layer as the `` cloud envelope '' . meanwhile , it is known that there takes place thermal instability in the range of @xmath246 erg cm / s ( reynolds @xmath21 fabian 1995 ) . therefore , it is reasonable that the cloud envelope continuously connects the partial absorber in the low - ionized cloud and the surrounding constant high - ionized warm absorber . we notice the thomson optical depth ( @xmath247 ) of the partial absorber is about unity . presumably , this is not just a coincidence , but suggests that the low - ionized cloud has internal density gradients extending up to more than unit thomson optical depth , such that attenuation with continuously different optical depths is approximated by unit thomson optical depth . thus , the low - ionized cloud may well have central , cold thomson thick cores ( @xmath248 @xmath2 ) , which are completely opaque to incoming x - rays . we may not see these `` x - ray blockers '' directly , but if we take into account the effect of the x - ray blockers , the weak anti - correlation between the total normalization @xmath149 and the covering fraction @xmath151 ( top - panels of figure [ correlation_20ksec ] ) might be explained . [ cols="<,^,^,^,^,^,^,^",options="header " , ] finally , we present a physical picture surrounding the x - ray source to explain the observations . in table [ tab : absorbers ] , we summarize parameters of the absorbers in our model . basic points of our variable partial covering model are the following : 1 . observed x - ray flux and spectral variability is primarily caused by random passages of the low - ionized clouds in front of the central x - ray source . a typical size of each low - ionized cloud is @xmath245 cm and a typical velocity is @xmath249 cm / s ( equation [ sizeofcloud ] ) . central x - ray source is not always fully blocked , nor fully exposed . the covering fraction is variable between null to @xmath250 ( table [ table1_slice ] ) , and it fluctuates by an amplitude of @xmath251 % ( figure [ 20ksec_par_var ] ) . we may estimate the average covering fraction @xmath252 from intensity - sliced spectra as @xmath252 = @xmath253 , where @xmath254 and @xmath255 are exposure time for each spectrum and the total observation , respectively . we thereby obtain @xmath256 0.3 . the integrated covering fraction is considered to be about 0.1 for blr ( e.g. , blandford et al . thus , our results suggest that the partial absorption takes place in the blr , and the low - ionized clouds corresponds to the blr blobs . we may estimate number of the absorbing clouds in the field of view , @xmath257 , and size of the central x - ray source , @xmath258 , as follows . assuming that fluctuation of the covering fraction , @xmath259 , is determined by statistical fluctuation of the number of clouds , @xmath260 , @xmath257 is estimated as @xmath261 . the average covering fraction , @xmath262 , may be written as @xmath263 , thus , @xmath264 cm . typically , blr blobs have a velocity of @xmath226 @xmath8 10@xmath265 cm / sec . assuming the kepler velocity has a similar value , @xmath266 500 @xmath267 , where @xmath267 is the schwarzschild radius . identifying this with @xmath268 10@xmath269 cm ( equation [ eq : r2 ] ) , the central black hole mass of mcg-6 - 30 - 15 is @xmath270 . thus , the central x - ray source ( @xmath271 cm ) is extended to @xmath272 around the black hole . besides variation of the blr coluds , the x - ray source is variable on a timescale down to @xmath8 1 ksec ( inoue , miyakawa and ebisawa 2011 ) , which may be compared with the free fall time , @xmath273 . then , the intrinsic source variation arises at a few times the schwarzshild radius , around the innermost stable circular orbit . we point out that solid angle of the low - ionized clouds seen from the x - ray source should be much smaller than 4@xmath27 , otherwise we will have to see strong fluorescent lines from the clouds . if a thick absorber with @xmath274 @xmath2 covers the power - law component completely ( @xmath275 ) , equivalent width of the iron line to the reflection component is @xmath8 1 kev . considering @xmath276 0.3 and the ratio of the reflection component to the direct component , 10 to 1 , the expected iron line equivalent width is @xmath8 30 ev . as mentioned in subsection 5.5.2 , we found the fit improves if a mildly broad disk - line is added , where the best - fit inner radius and the equivalent width are @xmath277 200 @xmath90 and @xmath278 ev , respectively ( table [ miyakawa_diskline_model_ave_suzaku ] ) . these mildly broadened , weak iron emission lines may well be expected from fluorescence in the blr clouds . figure @xmath279 gives a schematic view of internal structure of the low - ionized cloud and the variable partial covering model surrounding the black hole . the low - ionized cloud ( blr cloud ) has internal ionization structure . a putative blocker in the core would block the incoming x - rays completely . the main body of the low - ionized cloud is the thick partial absorber surrounding the core . still the outer cloud envelope corresponds to the thin low - ionized warm absorber . central x - ray emission region around the black hole is mildly extended , and partially covered by these low - ionized clouds . variation of the covering fraction explains most of the observed flux and spectral variations . finally we comment that the idea of partial covering is not new for mcg-6 - 30 - 15 to explain its spectral shape and varaition ( e.g. , matsuoka et al . 1990 ; mckernan and yaqoob 1998 ; miller , turner and reeves 2008 , 2009 ) . recently , similar partial covering models are proposed to explain spectral variations of ngc 3516 ( turner et al . 2008 ) , mrk 766 ( risaliti et al . 2011 ) and other seyfert galaxies ( turner & miller 2009 ) . presumably , partial covering of rather constant x - ray source is a common mechanism in seyfert galaxies . it is of interest to study spectral variations of seyfert galaxies systematically to see if the observed x - ray variablity is truely due to intrinsic luminosity variation or explained by partial covering of the constant source .

the heavy absorber in the second component is fragmented into many clouds , each of which is composed of radial zones with different ionization states and column densities , the main body ( , ) , the envelope ( , ) and presumably a completely opaque core . these parameters of the ionized absorbers , as well as the intrinsic spectral shape of the x - ray source , are unchanged at all . the central x - ray source is moderately extended , and its luminosity is not significantly variable .

we propose a simple spectral model for the seyfert 1 galaxy mcg-6 - 30 - 15 that can explain most of the 1 40 kev spectral variation by change of the partial covering fraction , similar to the one proposed by miller et al . ( 2008 ) . our spectral model is composed of three continuum components ; ( 1 ) a direct power - law component , ( 2 ) a heavily absorbed power - law component by mildly ionized intervening matter , and ( 3 ) a cold disk reflection component far from the black hole with moderate solid - angle ( ) accompanying a narrow fluorescent iron line . the first two components are affected by the surrounding highly ionized thin absorber with and . the heavy absorber in the second component is fragmented into many clouds , each of which is composed of radial zones with different ionization states and column densities , the main body ( , ) , the envelope ( , ) and presumably a completely opaque core . these parameters of the ionized absorbers , as well as the intrinsic spectral shape of the x - ray source , are unchanged at all . the central x - ray source is moderately extended , and its luminosity is not significantly variable . the observed flux and spectral variations are mostly explained by variation of the geometrical partial covering fraction of the central source from 0 ( uncovered ) to.63 by the intervening ionized clouds in the line of sight . the ionized iron k - edge of the heavily absorbed component explains most of the seemingly broad line - like feature , a well - known spectral characteristic of mcg-6 - 30 - 15 . the direct component and the absorbed component anti - correlate , cancelling their variations each other , so that the fractional spectral variation becomes the minimum at the iron energy band ; another observational characteristic of mcg-6 - 30 - 15 is thus explained .

1202.2797

c

we have analyzed suzaku and chandra archival data of mcg-6 - 30 - 15 and constructed a new model to explain the observed spectral variation . our main conclusions are summarized below : 1 . we have shown that the observed energy spectra and spectral variation can be explained by the `` three - component model '' ( equation [ eq2 ] ) that includes ( 1 ) a direct power - law component , ( 2 ) a heavily absorbed power - law component by thich photoionized material , and ( 3 ) a cold disk reflection component far from the black hole . the first two components are affected by two warm abosrbers having different ionization states . the ionized iron k - edge of the heavily absorbed component and spectral curvature due to the warm absorbers explain most of the seemingly broad `` disk line '' spectral feature . consequently , general relativistic interpretation of the broad iron emission line feature in mcg-6 - 30 - 15 is not confirmed . the claim that mcg-6 - 30 - 15 is a kerr black hole with nearly extreme rotation assuming the relativistic line - broadening ( e.g. , miniutti et al . 2007 ) is questionable . 3 . we propose the `` variable partial covering model '' , in which a central , moderately extended x - ray source is partially covered by variable low - ionized clouds in the line of sight . in this model , observed x - ray spectral variation is primarily caused by change of the partial covering fraction of the central source . these absorbing clouds presumably correspond to the fast - moving broad line region ( blr ) clouds . the authors would like to thank profs . p. ycki , y. terashima , y. ueda and k. makishima for fruitful discussion . this research has made use of public suzaku data obtained through the data archives and transmission system ( darts ) , provided by the institute of space and astronautical science ( isas ) at japan aerospace exploration agency ( jaxa ) , public chandra data obtained through the high energy astrophysics science archive research center ( heasarc ) at nasa / goddard space flight center . for data reduction , we used the software provided by the high energy astrophysics science archive research center ( heasarc ) at nasa / goddard space flight center and chandara x - ray center ( cxc ) at harvard - smithsoniann center for astrophysics . k.e . acknowledges ms . akiko sato for helping us illustrate our model and producing a beautiful artwork .

our spectral model is composed of three continuum components ; ( 1 ) a direct power - law component , ( 2 ) a heavily absorbed power - law component by mildly ionized intervening matter , and ( 3 ) a cold disk reflection component far from the black hole with moderate solid - angle ( ) accompanying a narrow fluorescent iron line . the first two components are affected by the surrounding highly ionized thin absorber with and . the observed flux and spectral variations are mostly explained by variation of the geometrical partial covering fraction of the central source from 0 ( uncovered ) to.63 by the intervening ionized clouds in the line of sight . the ionized iron k - edge of the heavily absorbed component explains most of the seemingly broad line - like feature , a well - known spectral characteristic of mcg-6 - 30 - 15 .

we propose a simple spectral model for the seyfert 1 galaxy mcg-6 - 30 - 15 that can explain most of the 1 40 kev spectral variation by change of the partial covering fraction , similar to the one proposed by miller et al . ( 2008 ) . our spectral model is composed of three continuum components ; ( 1 ) a direct power - law component , ( 2 ) a heavily absorbed power - law component by mildly ionized intervening matter , and ( 3 ) a cold disk reflection component far from the black hole with moderate solid - angle ( ) accompanying a narrow fluorescent iron line . the first two components are affected by the surrounding highly ionized thin absorber with and . the heavy absorber in the second component is fragmented into many clouds , each of which is composed of radial zones with different ionization states and column densities , the main body ( , ) , the envelope ( , ) and presumably a completely opaque core . these parameters of the ionized absorbers , as well as the intrinsic spectral shape of the x - ray source , are unchanged at all . the central x - ray source is moderately extended , and its luminosity is not significantly variable . the observed flux and spectral variations are mostly explained by variation of the geometrical partial covering fraction of the central source from 0 ( uncovered ) to.63 by the intervening ionized clouds in the line of sight . the ionized iron k - edge of the heavily absorbed component explains most of the seemingly broad line - like feature , a well - known spectral characteristic of mcg-6 - 30 - 15 . the direct component and the absorbed component anti - correlate , cancelling their variations each other , so that the fractional spectral variation becomes the minimum at the iron energy band ; another observational characteristic of mcg-6 - 30 - 15 is thus explained .

1009.4033

i

modern lattice qcd simulations are mostly based on direct evaluation of the path integral of the theory . such approach , while being very general and efficient for many applications , suffers from a number of problems , most notable of which are the sign problem at finite chemical potential , critical slowing down at small quark masses and large finite - volume effects as well as small signal - to - noise ratio in the analysis of excited states . these problems are inherent to standard monte - carlo simulations and can not be efficiently solved by simply increasing the computation power , since the required computing time quickly increases ( in the worst cases , exponentially ) with the required precision . such situation makes it tempting to devise alternative simulation algorithms for non - abelian lattice gauge theories . one of the efficient alternative numerical methods is the so - called diagrammatic monte - carlo , a method based on stochastic summation of all the terms in the strong- or weak - coupling expansion of the observable of interest @xcite . such a method in some cases allows one to reduce or avoid completely the sign problem in the original path integral , and does not suffer from finite - volume effects . furthermore , one can construct algorithms which yield particular correlation functions in terms of probability distributions of some random variables , which greatly facilitates the analysis of excited states @xcite . this is the idea of the `` worm '' algorithm by prokofev and svistunov @xcite , in which the probability distribution of the positions @xmath2 , @xmath3 of `` head '' and the `` tail '' of the worm yields the two - point green function @xmath4 . diagrammatic monte - carlo and the `` worm '' algorithm have been successfully applied to a number of statistical models with discrete symmetry groups such as the ising model , the xy model and unitary fermi gas and showed practically no critical slowing down near quantum phase transitions . however , application of such methods to lattice field theories with continuous field variables ( such as two - dimensional @xmath1 and @xmath5 sigma - models , abelian gauge theories and the @xmath6 theory ) resulted so far in quite complicated and model - dependent algorithms @xcite . a generalization of such algorithms to @xmath7 sigma - models or to non - abelian gauge theories is still not found . these algorithms are in essence based on the strong - coupling expansion , and while their applicability is not limited by the strong - coupling regime , one can expect that algorithms based on the weak - coupling expansion might show better performance near the continuum limit . typically , the weak - coupling expansion in such lattice theories is either quite complicated or non - convergent . up to now , divergent behavior of the weak - coupling perturbative expansions strongly limits the applicability of diagrammatic monte - carlo to field theories with continuous field variables . in a recent paper @xcite a method was proposed to construct convergent series which approximate the non - analytic path integrals with desired precision . this method , however , is difficult to generalize to physically interesting field theories such as non - abelian lattice gauge theories . another way to obtain convergent series while preserving important physical properties of the theory is to sum over diagrams with certain topology only . this corresponds to the large-@xmath0 limit in quantum field theories and matrix models , that is , the limit of infinite dimensionality of an internal symmetry group , such as @xmath1 or @xmath7 . for such theories , each feynman diagram acquires a factor @xmath8 , where @xmath9 is the euler character of this diagram @xcite . in the limit @xmath10 , the contribution of planar diagrams with @xmath11 dominates , and the sum over all planar diagrams typically has a finite convergence radius @xcite . in this paper we describe a stochastic method for summing over all planar diagrams in large-@xmath0 quantum field theories . the method is based on stochastic solution of schwinger - dyson equations , so that the correlators of field variables are obtained as stationary probability distributions of certain random variables . in this way we implement the idea of importance sampling , so that numerically small observables correspond to unlikely events . these probability distributions are sampled by the so - called nonlinear random processes . in contrast to conventional markov chains , stationary probability distributions of such random processes satisfy nonlinear equations , and hence they can be called `` nonlinear random processes '' or `` nonlinear markov chains '' in the terminology of @xcite . factorization of single - trace operators in the large-@xmath0 limit of quantum field theories corresponds to the phenomena of `` chaos propagation '' in random processes @xcite . while in the diagrammatic monte - carlo and in the `` worm '' algorithm the diagrams are stored in computer memory as a whole and are updated in such a way that the detailed balance condition is satisfied at each step , the method described in this paper works only with external lines . in contrast to the standard metropolis algorithm , one should not know explicitly the weight of each diagram , and the transition probabilities do not satisfy any detailed balance condition . unlike the quite popular `` numerical functional methods '' in continuum gauge theories ( see @xcite for a review ) , the proposed method does not require any truncation of the hierarchy of schwinger - dyson equations , and work only with singlet operators w.r.t . the internal symmetry group . another distinct feature is that the computational complexity of the method does not depend on @xmath0 , while the standard monte - carlo , the functional methods and the `` worm '' algorithm all require infinite computational resources in the limit @xmath10 . this feature might be advantageous for numerical checks of the predictions of the holographic models which are dual to large-@xmath0 quantum field theories @xcite . in section [ sec : sdeq_general ] we analyze the general structure of schwinger - dyson equations in large-@xmath0 quantum field theories on the example of a scalar matrix - valued field theory . when large-@xmath0 factorization is taken into account , schwinger - dyson equations become nonlinear equations with infinitely many unknowns . in section [ sec : recursive_process ] we describe nonlinear random processes of recursive type @xcite which can be used to stochastically solve such equations . in section [ sec : sds_stochastic_solution ] we apply such random processes to solve schwinger - dyson equations in several large-@xmath0 theories . in subsection [ subsec : phi4_general ] we consider the scalar matrix - valued field theory , for which the perturbative expansion yields the conventional feynman diagrams in momentum space . in subsection [ subsec : matrix_model ] this solution is compared with the exact solution of the simplest quantum field theory in zero dimensions , that is , the hermitian matrix model @xcite . the convergence of such solution and the strength of the sign problem is discussed . in subsection [ subsec : weingarten ] we consider the weingarten model @xcite and demonstrate how the proposed method can be used to simulate random surfaces on the hypercubic lattice . in this case , our method reproduces an ensemble of open , rather than closed , random surfaces , with critical behavior which is quite different from those of the closed planar random surfaces . since the structure of schwinger - dyson equations in the weingarten model is similar to the loop equations in large-@xmath0 non - abelian lattice gauge theories @xcite , studying this model might be helpful for further extensions of the present approach to non - abelian gauge theories . while the method described in section [ sec : recursive_process ] works well for non - compact field variables , for field theories with compact field variables , such as nonlinear sigma - models or non - abelian lattice gauge theories , a straightforward stochastic interpretation of schwinger - dyson equations is only possible in the strong coupling limit . in the weak - coupling limit one expects the field correlators to contain both the perturbative part in the coupling constant @xmath12 as well as nonperturbative corrections of the form @xmath13 with some constant @xmath14 . moreover , perturbative expansion in powers of @xmath12 typically results in asymptotic series , and nonperturbative corrections appear as a result of resummation of such series @xcite . in section [ sec : rps_with_mem ] we show how such nonperturbative corrections can be taken into account by a further relaxation of the markov property of the random process . the basic idea is to absorb the divergent part of the series into a self - consistent redefinition of the expansion parameter . these redefined parameters play the role of nonperturbative `` condensates '' @xcite . it turns out that the redefined expansion parameters can be estimated with increasing precision from the previous history of the random process which solves the schwinger - dyson equations , thus leading to the emergence of the `` memory '' of the random process . the approach of the redefined parameters to their self - consistent values is reminiscent somehow of the renormalization - group flow @xcite . such dependence on the previous history makes the random process essentially non - markovian , so that the stationary probability distribution also satisfies some nonlinear equation . we illustrate this idea on the example of @xmath1 sigma - model in two dimensions , which is equivalent to a bosonic random walk with a self - consistent mass . random process which simulates this model has the `` memory '' but no `` recursive '' structure . presumably , in order to sum up both perturbative and non - perturbative corrections which arise in non - abelian lattice gauge theories or @xmath15 sigma - models , one should devise the `` recursive '' nonlinear random process ( which would sum up perturbative corrections ) with memory ( which would generate nonperturbative quantities in a renormalization - group - like way ) . finally , in the concluding section we summarize the present work and discuss its extension to non - abelian lattice gauge theories in the limit of large @xmath0 .

we propose a stochastic method for solving schwinger - dyson equations in large- quantum field theories . expectation values of single - trace operators are sampled by stationary probability distributions of the so - called nonlinear random processes . we illustrate the method on the examples of the matrix - valued scalar field theory and the weingarten model of random planar surfaces on the lattice . for theories with compact field variables , such as sigma - models or non - abelian lattice gauge theories , one can absorb the divergences into a self - consistent redefinition of expansion parameters . we illustrate this idea on the example of two - dimensional sigma - model .

we propose a stochastic method for solving schwinger - dyson equations in large- quantum field theories . expectation values of single - trace operators are sampled by stationary probability distributions of the so - called nonlinear random processes . the set of all histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators . we illustrate the method on the examples of the matrix - valued scalar field theory and the weingarten model of random planar surfaces on the lattice . for theories with compact field variables , such as sigma - models or non - abelian lattice gauge theories , the method does not converge in the physically most interesting weak - coupling limit . in this case one can absorb the divergences into a self - consistent redefinition of expansion parameters . stochastic solution of the self - consistency conditions can be implemented as a `` memory '' of the random process , so that some parameters of the process are estimated from its previous history . we illustrate this idea on the example of two - dimensional sigma - model . extension to non - abelian lattice gauge theories is discussed .

1005.0708

i

we have proposed a model of quasi - degenerate neutrinos which predicts the neutrinoless double beta decay mass observable to be approximately equal to the neutrino mass scale @xmath16 , thereby allowing its determination approximately independently of unknown majorana phases . in general such quasi - degenerate neutrino masses may be naturally realised if there exists a non - abelian family symmetry with real triplet representations that enforces an additional contribution to the neutrino mass matrix proportional to the unit matrix , hence determining the neutrino mass scale . in our model , the additional contribution was generated by a type ii seesaw , or , alternatively , by another type i seesaw contribution from an additional triplet representation of right - handed neutrinos ( or neutrino messenger fields ) . in addition , the standard type i seesaw contribution determines the neutrino mixing angles . although such a mechanism ( called a `` type ii upgrade '' in @xcite ) has been known for some time , the model in this paper is the first of its kind to combine this mechanism with tri - bimaximal mixing arising from @xmath2 family symmetry together with a @xmath18 susy gut . the susy @xmath0 model considered here has several attractive features . the full renormalisable superpotential for the coupling of matter to flavons , messenger fields and higgs fields is specified , and only discrete auxiliary symmetries are introduced , rather than the more common continuous abelian symmetry that is typically invoked in such models . in the considered model , the neutrino mass scale can either originate from the induced vacuum expectation value of a @xmath196 triplet contained in a fifteen - dimensional representation of @xmath18 , or from an additional contribution to the neutrino mass operator induced by @xmath18 singlet messenger fields in the triplet representation of @xmath2 . since the type i seesaw contribution involves very hierarchical additional neutrino mass contributions , responsible for the tiny mass splittings between the quasi - degenerate neutrinos , we use the constrained sequential dominance mechanism which is well suited for achieving such strongly hierarchical contributions . in such a model the neutrino flavour symmetry associated with tri - bimaximal mixing is achieved indirectly from the family symmetry , given the assumed vacuum alignment . we have included renormalisation group corrections to the mixing angles and shown that they are under control for small values of @xmath26 in our framework and do not significantly modify the leptonic mixing angles . we have therefore considered small values of @xmath26 throughout our study . the model has several interesting phenomenological features which emerge from our numerical fit to the quark and lepton masses and quark mixing . in addition to @xmath23-@xmath24 unification that may be viable for small @xmath26 , the model realises the gut scale relation @xmath197 proposed in @xcite , which is favourable for small values of @xmath26 . in the quark sector , we observe that the correct @xmath126 ( corresponding to the right unitarity triangle with @xmath3 ) can be realised for the simple ansatz in eq . . we remark that this simple ansatz leads to an interesting alternative texture ( different from @xcite ) that gives rise to a right - angled unitarity triangle with @xmath198 . for the leptonic mixing angles and cp phases we find @xmath168 , @xmath199 , @xmath200 and @xmath4 . the leptonic mixing angles satisfy the `` lepton mixing sum rule '' proposed in @xcite with only small theoretical errors since the 1 - 3 mixing in the charged lepton mass matrix is very small and the 2 - 3 mixing vanishes . the majorana cp phases are small for quasi - degenerate neutrino masses via a large additional contribution proportional to the unit matrix , as expected , and the model thus predicts the neutrinoless double beta decay mass observable to be approximately equal to the neutrino mass scale , or lightest neutrino mass , i.e. @xmath201 . in conclusion , if neutrinoless double beta decay were observed in the near future then this would herald another neutrino revolution in which neutrino masses would be quasi - degenerate . amongst the many possible models of quasi - degenerate neutrinos , the model with an additional contribution to neutrino mass matrix proportional to the unit matrix , as considered here , are distinguished by their prediction of that the neutrinoless double beta decay mass observable is approximately equal to the neutrino mass scale @xmath16 . we have proposed the first realistic model of this kind involving @xmath2 and susy @xmath18 guts . the @xmath2 family symmetry has the dual effect of enforcing on the one hand quasi - degeneracy via the additional unit matrix contribution to the neutrino mass matrix , and on the other hand tri - bimaximal mixing via the type i seesaw mechanism and constrained sequential dominance . a numerical fit to quark masses and mixing angles reveals that a simple ansatz describing quark cp violation with @xmath3 also leads to the leptonic phase @xmath4 . in such models the absolute neutrino masses could be directly measurable by experiment quite soon .

we propose a supersymmetric model of quasi - degenerate neutrinos which predicts the effective neutrino mass relevant for neutrinoless double beta decay to be proportional to the neutrino mass scale , thereby allowing its determination approximately independently of unknown majorana phases . such a natural quasi - degeneracy is achieved by using family symmetry ( as an example of a non - abelian family symmetry with real triplet representations ) to enforce a contribution to the neutrino mass matrix proportional to the identity .

we propose a supersymmetric model of quasi - degenerate neutrinos which predicts the effective neutrino mass relevant for neutrinoless double beta decay to be proportional to the neutrino mass scale , thereby allowing its determination approximately independently of unknown majorana phases . such a natural quasi - degeneracy is achieved by using family symmetry ( as an example of a non - abelian family symmetry with real triplet representations ) to enforce a contribution to the neutrino mass matrix proportional to the identity . tri - bimaximal neutrino mixing as well as quark cp violation with and a leptonic cp phase arise from the breaking of the family symmetry by the vacuum expectation values of four `` flavon '' fields pointing in specific postulated directions in flavour space . mpp-2010 - 52 + * measurable neutrino mass scale in * + s. antusch , stephen f. king , m. spinrath , + _ max - planck - institut fr physik ( werner - heisenberg - institut ) , _ _ fhringer ring 6 , d-80805 mnchen , germany _ _ school of physics and astronomy , university of southampton , _ _ so17 1bj southampton , united kingdom _

1401.6949

i

the physics of topological defects , such as vortices , becomes especially intriguing at the interface between coexisting , topologically distinct phases of a macroscopically coherent system . due to different broken symmetries on either side , a defect can not perforate the interface unchanged . instead it must either terminate , or continuously connect across the boundary to an object representing a different topology . this situation arises , for example , at the interface between the @xmath0 and @xmath1 phases of superfluid liquid @xmath2he @xcite , at interfaces between regions of different vacua in theories of the early universe @xcite , in the physics of branes in superstring theory @xcite , and in exotic superconductivity @xcite . the parallels @xcite between cosmological objects and defects in superfluids prompted the suggestion that analogues of cosmological phenomena can be studied in the laboratory @xcite , for example the formation of defects in phase transitions @xcite or properties of cosmic vortons ( superconducting cosmic strings @xcite ) @xcite . current experimental techniques in atomic physics allow accurate measurements and precise control and manipulation of ultracold atomic gases by finely tuning electromagnetic fields . in spinor bose - einstein condensates ( becs ) , where the atoms retain their spin degree of freedom , experiments have demonstrated controlled preparation of coreless vortices and analogous non - singular textures formed by the nematic axis @xcite . vortex nucleation in phase transitions @xcite and dynamical formation of spin textures @xcite have also been experimentally observed . simultaneously there has been a rapidly increasing theoretical interest in the wide variety of vortices , point defects and particle - like textures in two - component ( pseudospin-@xmath3 ) @xcite , as well as spin-1 @xcite and spin-@xmath4 @xcite becs . this development brings multi - component systems of ultracold atoms to the forefront as candidate laboratories where properties of a variety of field - theoretical solitons ( see for exampel @xcite ) may be studied . we have previously suggested @xcite that spatially non - uniform manipulation of scattering lengths by optical or microwave - induced feshbach resonances can be used to study the physics of topological interfaces in ultracold atomic gases with spin degree of freedom . an example is the spinor becs , which exhibit distinct phases of the ground - state manifold . in the simplest case of a spin-1 bec there are two phases , polar and fm , and the sign of the spin - dependent interaction determines which phase is energetically favourable . we proposed that a combination of ( microwave or optical ) feshbach resonances and spatially - dependent ac - stark shifts can be used to enforce different signs of this interaction in different spatial regions of the same spin-1 bec , establishing a coherent interface between the phases . within this system , we formulated spinor wave functions corresponding to defect combinations that can be phase imprinted using existing techniques . by numerical simulation we found examples of energetically stable interface - crossing defects and complex core deformations , such as the formation of an arch - shaped half - quantum vortex on the interface . in addition , defects at an energetically established boundary in a two - component bec , where in one region the two components are miscible and in the other immiscible , have recently been studied in becs in @xcite . here we propose to employ precise spatial engineering of the zeeman shifts to create topologically dissimilar regions within a spinor bec , providing an experimentally simple route for studying defects and textures at the emerging topological interface . the ground state of the spinor bec generally depends on the linear and quadratic energy shifts of the zeeman levels . in the case of the spin-1 bec , the zeeman shift can cause the condensate to adopt the fm phase even when the polar phase is favoured by the interactions , and vice versa @xcite . in particular , we demonstrate that a stable , coherent , topologically non - trivial interface between fm and polar phases of a spin-1 bec can be established through spatially non - uniform linear or quadratic zeeman shifts . uniform ground - state solutions exist , for both polar and fm interaction regimes , that follow the variation of the zeeman shift ; the corresponding wave functions continuously interpolate between the polar and fm phases . we then analytically construct defect states that continuously connect defects and textures representing the topology of the fm and polar phases , such that the connection is provided directly by the spatial dependence of the zeeman energy shifts . we show that the modulation of the zeeman splitting allows the preparation of a rich family of interface - crossing defect solutions , with various combinations of singular ( integer and half - quantum ) and non - singular vortices , point defects , and terminating vortices . by numerical simulation , we determine the stability properties of the constructed solutions and determine their energy - minimizing core structures . in the polar interaction regime , the interface is established by a varying linear zeeman shift . examples of energetically stable interface - perforating defect configurations in a rotating trap include a singly quantized fm vortex line continuously connecting to a singly quantized polar vortex whose core splits into a pair of half - quantum vortices , as well as a polar vortex that terminates at the interface . for a bec in the fm interaction regime , a spatially varying quadratic energy shift is used to establish the interface between the polar and fm phases . we find an energetically stable , singular fm vortex that terminates at the interface . moreover , non - singular , coreless vortices in the fm phase become energetically favourable , and we find energetically stable structures where the coreless vortex continuously connects to a singly quantized vortex on the polar side of the interface . the unusual property of the singly quantized polar vortex in this configuration is the axially symmetric stable vortex core , in which the line singularity is filled with atoms in the fm phase , and the core is not split into a pair of half - quantum vortices . the existence of stable core structures of different symmetries in atomic spinor becs is reminiscent of the rich vortex core symmetries encountered in superfluid liquid @xmath2he @xcite . for example , the core of a singular @xmath1-phase vortex may analogously retain a non - zero superfluid density by filling with the @xmath0 phase , either with an axially symmetric core @xcite or by breaking the axial symmetry when forming a two - fold symmetric split core @xcite . in the case of both fm and polar interactions we also find stable core structures of singular fm vortex lines terminating on a point defect in the polar phase . such a point defect is analogous to the t hooft - polyakov monopole @xcite and the combined defect configuration of the terminating vortex line and the point defect is closely related to boojums that can exist in superfluid liquid @xmath2he @xcite . the core of the point defect minimizes its energy by deforming into a half - quantum line defect connecting at both ends to the interface . as the point defect , or the ` alice arch ' line defect , does not couple to the trap rotation , the defect experiences a trivial instability with respect to drifting out of the atom cloud as a result of the density gradient of the harmonic trap ( the order parameter bending energy of defects and textures generally favours lower atom densities ) , but can be otherwise stable . such an instability could be overcome by creating a local density minimum close to the trap centre by an additional optical potential @xcite . the interface physics with the zeeman shifts provides several promising experimental scenarios . accurate tuning of zeeman shifts has been experimentally demonstrated in ultracold atoms @xcite , and also applied to the study of spin textures @xcite . on the other hand , the control of multiple interfaces and their time - dependence could open up avenues for emulating complex cosmological phenomena in the laboratory . for instance , in superfluid liquid @xmath2he @xcite or in a two - component bec system @xcite it has been proposed that colliding interfaces or phase boundaries could mimic cosmic defect formation . in a spin-1 bec we could envisage , for instance , the following set - up : a disc of polar phase is created in an otherwise fm condensate by locally increasing zeeman shift . the two parallel fm - polar interfaces can then be interpreted as analogues of string - theoretical @xmath5-branes and anti - branes arising in theories of brane inflation @xcite . removing the local zeeman shift causes the interfaces to collapse , simulating defect formation in brane annihilation scenarios . similar experiments have been performed with colliding superfluid @xmath2he @xmath0-@xmath1 interfaces @xcite , where , however , observation of defects is more difficult .

we propose to use spatial control of the zeeman energy shifts in an ultracold atomic gas to engineer an interface between topologically distinct regions . this provides an experimentally accessible means for studying the interface physics of topological defects and textures . using the spin-1 bose - einstein condensate as an example , we find spinor wave functions that represent defects and textures continuously connecting across the interface between polar and ferromagnetic regions induced by spatially varying zeeman shifts . by numerical energy - minimization we characterize the defect core structures and determine the energetic stability .

we propose to use spatial control of the zeeman energy shifts in an ultracold atomic gas to engineer an interface between topologically distinct regions . this provides an experimentally accessible means for studying the interface physics of topological defects and textures . using the spin-1 bose - einstein condensate as an example , we find spinor wave functions that represent defects and textures continuously connecting across the interface between polar and ferromagnetic regions induced by spatially varying zeeman shifts . by numerical energy - minimization we characterize the defect core structures and determine the energetic stability . the techniques proposed could potentially be used in the laboratory to emulate complex interface physics arising , e.g. , in cosmological and condensed - matter contexts in both uniform and lattice systems .

math9812106

i

let @xmath0 be an affine kac - moody algebra , @xmath1 a @xmath2-submodule of a finite direct sum @xmath3 of irreducible integrable highest weight @xmath4-modules , and @xmath5 the limit of the demazure operator for an element @xmath6 of the weyl group as @xmath7 . the main theorem of this paper gives sufficient conditions on @xmath1 so that the formula @xmath8 holds , where @xmath9 is the character of @xmath1 . when @xmath1 is the one - dimensional @xmath2-module generated by the dominant integral weight @xmath10 then is the weyl - kac character formula . the above result is well - known when @xmath1 is a union of demazure modules for any kac - moody algebra @xmath0 . let @xmath11 be the derived subalgebra of @xmath0 . consider the @xmath11-module @xmath1 given by a tensor product of finite - dimensional @xmath12-modules that admit a crystal of level at most @xmath13 , with the one - dimensional subspace generated by a highest weight vector of an irreducible integrable highest weight @xmath12-module of level @xmath13 . such modules @xmath1 can be given the structure of a @xmath2-module and as such , satisfy the above conditions . then a special case of is a bosonic formula for the @xmath14-enumeration of level - restricted inhomogeneous paths by the energy function . in type @xmath15 this formula was conjectured in @xcite , stated there as a @xmath14-analogue of the goodman - wenzl straightening algorithm for outer tensor products of irreducible modules over the type @xmath16 hecke algebra at a root of unity @xcite . in the isotypic component of the vacuum , the bosonic formula coincides with half of the bose - fermi conjecture in ( * ? ? ? * ( 9.2 ) ) . the authors would like to thank nantel bergeron , omar foda , masaki kashiwara , atsuo kuniba , masato okado , jean - yves thibon , and ole warnaar for helpful discussions .

we prove a bosonic formula for the generating function of level - restricted paths for the infinite families of affine kac - moody algebras . in affine type a this yields an expression for the level - restricted generalized kostka polynomials . supported by the `` stichting fundamenteel onderzoek der materie '' . ] partially supported by nsf grant dms-9800941 . ]

we prove a bosonic formula for the generating function of level - restricted paths for the infinite families of affine kac - moody algebras . in affine type a this yields an expression for the level - restricted generalized kostka polynomials . supported by the `` stichting fundamenteel onderzoek der materie '' . ] partially supported by nsf grant dms-9800941 . ]

1004.2002

i

in discussing steady flows which are supersonic in the entrance section of a duct and then become subsonic , r. courant and k. o. friedrichs wrote in their classical monograph _ supersonic flow and shock waves _ @xcite that _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ @xmath7 we know in general that this assumption ( the flow is continuous ) is not tenable and that we must consider flows involving shocks . it is a question of great importance to know under what circumstances a steady flow involving shocks is uniquely determined by the boundary conditions at the entrance , and when further conditions at the exit are appropriate . " _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ this paper is exactly devoted to showing that , for the two - dimensional steady complete compressible euler system , with given uniform upstream supersonic flows , under certain reasonable conditions of the downstream of the subsonic flows , in the class of piecewise @xmath0 functions , the uniqueness of the following three important flow patterns in gas dynamics : * the transonic normal shock in a two dimensional straight duct with finite or infinite length , after fixing a point the shock - front passing through ( see figure 1 ) ; + * the transonic oblique shocks attached to an infinite wedge against the uniform supersonic flow ( see figure 2 ) ; + * a flat mach configuration involving three shocks and a contact discontinuity , where one shock is supersonic , and another two are transonic , with the contact line separating two subsonic regions , after fixing a point @xmath8 where the four discontinuities intersect ( see figure 3 ) . these flow patterns have been constructed in ( * ? ? ? * , pp.332 - 333 ) by using shock polar , under the assumptions that the shock - fronts ( contact line ) are straight lines , and the subsonic flows behind the shock - fronts are also uniform i.e. , the solution is piecewise constant ( see 2 below ) . the uniqueness results we obtain in this work indicate that under certain conditions of the downstream subsonic flows , these assumptions may be relaxed to that the flow fields are only piecewise continuously differentiable then for given uniform upcoming supersonic flows , the transonic shock - fronts ( and the contact line appeared in the mach configuration ) must be straight lines and the subsonic flows behind them must be uniform . from mathematical point of view , since the steady euler system for subsonic flows is of elliptic - hyperbolic composite - mixed type , these are all results on uniqueness of solutions of free boundary value problems of a nonlinear system of mixed type , with the transonic shock - fronts and contact line being the free boundaries . ( 300 , 200)(0,0 ) ( 0,0 ) and zero attacking angle in uniform supersonic flows.,title="fig : " ] ( 133,92)@xmath9 ( 133,83)@xmath9 ( 300 , 200)(0,0 ) ( 0,0 ) is a supersonic shock lying in the quadrant @xmath10 , @xmath11 are transonic shocks lying in quadrant @xmath12 respectively , and @xmath13 is a contact line . they are all straight lines . the flow field is piecewise constant.,title="fig : " ] ( 77,65)@xmath14 ( 40,75)@xmath15 ( -10,100 ) ( 100,145)@xmath16 ( 70,155 ) ( 133,75)@xmath17 ( 150,100 ) ( 133,30)@xmath18 ( 150,0 ) ( 85,180)@xmath19 ( 235,75)@xmath20 ( 25,165)@xmath21 ( 90,-5)@xmath22 ( 190,170)@xmath23 ( 220,20)@xmath24 these special while important flow patterns have been the focus of research for many years , since the pioneering work on transonic shocks in ducts by g .- chen , m. feldman @xcite for the potential flow equation , and s. chen @xcite for the euler system . in a series of papers @xcite , g .- q . chen and m. feldman established the stability of transonic shocks in finitely long or infinitely long duct with square sections or arbitrary sections , under various conditions at the exit of the duct . z. xin and h. yin studied similar problems but employed different methods @xcite . for the euler system , h. yuan showed in @xcite various stability and instability results by using lagrangian coordinates introduced by s. chen in @xcite and characteristic decomposition technique @xcite . chen , j. chen and m. feldman also introduced the method of stream function in lagrangian coordinates by which the euler system can be written as a single second order equation to study the stability , local uniqueness and asymptotic behavior of transonic shocks in infinite ducts for the euler system . z. xin , h. yin and their collaborators also studied the problem of stability of transonic shock in nozzles for the steady euler system , see @xcite . for the study of stability of oblique transonic shocks attached to a wedge in supersonic flow , there are papers of s. chen , b. fang @xcite , e. h. kim @xcite , and h. yin , c. zhou @xcite . both the potential flow equation and the complete euler system were used as models and the authors showed stability under suitable downstream conditions . for the mach configurations , one has to use the euler system since there is a contact discontinuity . s. chen firstly studied the stability of a mach configuration under perturbations of upcoming supersonic flow , for the steady euler flow and pesudo - steady euler flow @xcite . later on he and b. fang also showed the stability of a wave pattern of regular reflection - refraction of shocks upon an interface @xcite , which is similar to a mach configuration . comparing to stability , the progress on the study of uniqueness is rather slow . for potential flows , g .- q . chen and h. yuan @xcite proved the transonic shock in a two - dimensional or three - dimensional straight duct is unique modulo a translation . l. liu showed uniqueness of subsonic potential flow in various domains @xcite , see also @xcite . by proposition 3.1 in @xcite , in two - dimensional case , many of the uniqueness results on subsonic flows also hold for the euler system , since under appropriate boundary conditions , the flow is in itself irrotational , i.e. , governed by the potential flow equation . however , to our knowledge , there is no any result on global uniqueness of transonic shocks for the complete euler system before . in this paper , we are going to establish the global uniqueness , for the complete euler system , of the three flow patterns we previously mentioned . it turns out that the method of maximum principles employed in @xcite for potential flow also works for euler flow , but the point is that one should consider now the extreme values of pressure @xmath4 and slope of the flow angle @xmath5 , with @xmath25 the velocity component of the flow along @xmath26 axis , respectively . in @xcite , h. yuan has shown that @xmath4 and @xmath27 satisfy a first order elliptic system for subsonic flow . then as in @xcite , one needs to show if there are nontrivial extremes of @xmath4 ( or @xmath27 ) on the shock - front @xmath28 , there would be contradictions by a hopf - type boundary point lemma . it is here we need to utilize some nice properties of the rankine - hugoniot conditions particularly , a rather simple curve called @xmath29 shock polar ( see figure 4 ) , which shows the relation between @xmath4 and @xmath27 behind the shock - front . we recommend @xcite for detailed computations of these relations . this paper is organized as follows . in 2 , we formulate the above mentioned physical problems ( flow patterns ) and state rigorously our results , theorem [ thm1]theorem [ thm6 ] . we also introduce briefly the @xmath29 shock polar for the comfort of those readers not familiar with this subject . then we prove in 3 the uniqueness of transonic shocks in straight ducts ( theorem [ thm1]theorem [ thm2 ] ) , and in 4 , the uniqueness of oblique transonic shocks attached to an infinite wedge ( theorem [ thm3]theorem [ thm5 ] ) . theorem [ thm6 ] , on the uniqueness of the mach configuration studied by s. chen @xcite , is established in 5 .

we prove that for the two - dimensional steady complete compressible euler system , with given uniform upcoming supersonic flows , the following three fundamental flow patterns ( special solutions ) in gas dynamics involving transonic shocks are all unique in the class of piecewise smooth functions , under appropriate conditions on the downstream subsonic flows : the normal transonic shocks in a straight duct with finite or infinite length , after fixing a point the shock - front passing through ; the oblique transonic shocks attached to an infinite wedge ; a flat mach configuration containing one supersonic shock , two transonic shocks , and a contact discontinuity , after fixing the point the four discontinuities intersect . these special solutions are constructed traditionally under the assumption that they are piecewise constant , and they have played important roles in the studies of mathematical gas dynamics . our results show that the assumption of piecewise constant can be replaced by some more weaker assumptions on the downstream subsonic flows , which are sufficient to uniquely determine these special solutions . mathematically , these are uniqueness results on solutions of free boundary problems of a quasi - linear system of elliptic - hyperbolic composite - mixed type in bounded or unbounded planar domains , without any assumptions on smallness . the proof relies on an elliptic system of pressure and the tangent of the flow angle obtained by decomposition of the euler system in lagrangian coordinates , and a newly developed method for the estimate that is independent of the free boundaries , by combining the maximum principles of elliptic equations , and careful analysis of shock polar applied on the ( maybe curved ) shock - fronts .

we prove that for the two - dimensional steady complete compressible euler system , with given uniform upcoming supersonic flows , the following three fundamental flow patterns ( special solutions ) in gas dynamics involving transonic shocks are all unique in the class of piecewise smooth functions , under appropriate conditions on the downstream subsonic flows : the normal transonic shocks in a straight duct with finite or infinite length , after fixing a point the shock - front passing through ; the oblique transonic shocks attached to an infinite wedge ; a flat mach configuration containing one supersonic shock , two transonic shocks , and a contact discontinuity , after fixing the point the four discontinuities intersect . these special solutions are constructed traditionally under the assumption that they are piecewise constant , and they have played important roles in the studies of mathematical gas dynamics . our results show that the assumption of piecewise constant can be replaced by some more weaker assumptions on the downstream subsonic flows , which are sufficient to uniquely determine these special solutions . mathematically , these are uniqueness results on solutions of free boundary problems of a quasi - linear system of elliptic - hyperbolic composite - mixed type in bounded or unbounded planar domains , without any assumptions on smallness . the proof relies on an elliptic system of pressure and the tangent of the flow angle obtained by decomposition of the euler system in lagrangian coordinates , and a newly developed method for the estimate that is independent of the free boundaries , by combining the maximum principles of elliptic equations , and careful analysis of shock polar applied on the ( maybe curved ) shock - fronts .

1408.3502

i

an important part of a mathematical setting of probability theory can be considered as a special case of quantum theoretic kinematics . this can be seen most clearly when quantum theoretic kinematics is reformulated in algebraic terms , with quantum states defined as normal positive ( or normalised ) functionals over @xmath0-algebras ( see e.g. @xcite for an overview ) . the borel steinhaus kolmogorov measure theoretic approach to foundations of probability theory is then recovered precisely from commutative @xmath0-algebras and quantum states over them . ) . ] however , both quantum theory and probability theory are equipped with additional structures , which describe possible mappings of probabilities or quantum states . can these prescriptions of information dynamics also be directly related to each other ? in particular , there are various considerations @xcite of von neumann s and lders rules @xcite as noncommutative _ analogues _ of the bayes laplace rule @xcite . it is tempting to ask whether this analogy could be turned to something more definite , both conceptually and mathematically . the main motivation for this paper is a series of results @xcite showing that both bayes laplace and jeffrey s rules ( as well as some other rules @xcite ) can be derived as special cases of the constrained minimisation of various information distances on probabilistic models ( in section [ bayes.section ] we review briefly some of these results ) . this has led us to conjecture @xcite that lders rules may be special cases of constrained maximisation of a quantum relative entropy . in section [ vn.lu.section ] we prove that the weak lders rule of quantum state change due to `` nonselective quantum measurement '' is a special case of quantum entropic projection , provided by the minimisation of the araki distance subject to a specific set of constraints . we also introduce a quantum analogue of jeffrey s rule and derive it as another special case of constrained araki distance minimisation . these are the two main results of this paper . in addition , we show that the strong lders rule of quantum state change due to `` selective quantum measurement '' can be obtained from these results as the limiting case of quantum jeffrey s rule or by regularised araki distance minimisation . in section [ transition.correlation.section ] we show that both weak lders rule and strong von neumann s rule ( which is the same as strong lders rule for pure states ) are also quantum entropic projections for a different quantum distance functional . with an exception of a derivation of a quantum jeffrey s rule , our results hold for arbitrary @xmath0-algebras , so they are applicable in quantum field theoretic and relativistic quantum information problems . these results extend earlier considerations of lders rules as _ analogues _ of the bayes laplace rule with a novel mathematical and conceptual content : all these rules are special cases of the constrained relative entropic inference . in this sense , ` quantum bayesianism ' can be considered a branch of ` quantum relative entropism ' . a discussion of this issue is provided in section [ discussion.section ] . + * history of the problem . * an inference based on minimisation of quantum distance on quantum models was first proposed by herbut @xcite . he derived the weak lders rule from a constrained minimisation of norm distance in the hilbert schmidt operator space . unfortunately , his work has been left unnoticed by all works cited below . several years later marchand and collaborators @xcite used bures distance @xcite ( which is metrical ) , and argued that its constrained minimisation should be considered as a description of the change of state of information _ due to _ `` quantum measurement '' described by a specific form of a coarse graining map @xcite ( conditioned upon a subset of an operator algebra , and predual to a specific form of noncommutative conditional expectation @xcite ) . independently of this body of work , in @xcite it was proposed to use the constrained minimisation of the wgkl distance of probabilities arising from traces of density operators to derive the post - measurement quantum state . the rules of inferential change of quantum states based on a constrained minimisation of other metrical distances on quantum models were later reconsidered by other authors @xcite and some derivations of the strong von neumann rule were obtained ( see section [ transition.correlation.section ] ) . the reinterpretation of von neumann s and lders rules for `` quantum measurement '' as principles of inductive inference conditioned on specific information , and analogous to the bayes laplace rule , was proposed at about the same time by bub @xcite ( however , it can be claimed @xcite , that already von neumann was aware of the possibility of such interpretation ) . these two lines of thought were ( implicitly ) joined in hadjisavvas @xcite postulate that a quantum state change due to acquisition of data ( e.g. in a measurement ) should be provided by means of constrained minimisation of the jmgk distance , as well as in donald s @xcite postulate that a description of `` quantum measurement '' , understood as an inductive inference , should be provided by means of constrained minimisation of the araki distance . at least for injective @xmath0-algebras @xmath1 . ] donald stressed also that this procedure @xcite , where @xmath2 is the constraint set . however , he provided no derivation of any of lders rules ( nor any other `` quantum measurement '' rules ) from this procedure . independently of the above works , warmuth @xcite used constrained minimisation of umegaki s distance to derive a generalisation of the bayes laplace rule to the case of density operators , with conditional probabilities replaced by covariance matrices . this generalisation has not reproduced lders rules . our derivation of lders rule is not only the first such result obtained for umegaki s and araki s distances , but also first result of this type obtained for any nonsymmetric quantum information distance . all results for quantum jeffrey s rule are new . see also a closely related paper @xcite , where the analogous results for weak and strong lders rules are derived using another technique ( based on differentiation , as opposed to generalised pythagorean theorem ) . , where @xmath3 are rank @xmath4 projectors , minimises the umegaki distance @xmath5 . this is a special case of our result for the weak lders rule . the generalisation to our result is stated without proof in @xcite . ]

we prove that the standard quantum mechanical description of a quantum state change due to measurement , given by lders rules , is a special case of the constrained maximisation of a quantum relative entropy functional . laplace rule as a special case of the constrained maximisation of relative entropy . the proof is provided for the umegaki relative entropy of density operators over a hilbert space as well as for the araki relative entropy of normal states over a-algebra . we also introduce a quantum analogue of jeffrey s rule , derive it in the same way as above , and discuss the meaning of these results for quantum bayesianism . * lders and quantum jeffrey s rules as entropic projections * + + ryszard pawe kostecki + + perimeter institute for theoretical physics , 31 caroline street north , n2l 2y5 waterloo , ontario , canada + institute for theoretical physics , department of physics , university of warsaw , hoa 69 , 00 - 681 warszawa , poland + ` ryszard.kostecki@fuw.edu.pl ` + + august 15 , 2014

we prove that the standard quantum mechanical description of a quantum state change due to measurement , given by lders rules , is a special case of the constrained maximisation of a quantum relative entropy functional . this result is a quantum analogue of the derivation of the bayes laplace rule as a special case of the constrained maximisation of relative entropy . the proof is provided for the umegaki relative entropy of density operators over a hilbert space as well as for the araki relative entropy of normal states over a-algebra . we also introduce a quantum analogue of jeffrey s rule , derive it in the same way as above , and discuss the meaning of these results for quantum bayesianism . * lders and quantum jeffrey s rules as entropic projections * + + ryszard pawe kostecki + + perimeter institute for theoretical physics , 31 caroline street north , n2l 2y5 waterloo , ontario , canada + institute for theoretical physics , department of physics , university of warsaw , hoa 69 , 00 - 681 warszawa , poland + ` ryszard.kostecki@fuw.edu.pl ` + + august 15 , 2014

1307.0017

i

upcoming galaxy cluster surveys from the millimeter to the x - ray wavelengths have the potential to identify thousands to hundreds of thousands of groups and clusters @xcite . these large cluster samples will be used to constrain the cosmological parameters which govern the growth of structure in our universe @xcite . regardless of the luminous tracer used to infer the underlying dark matter distribution ( e.g. , normal galaxies , emission - line galaxies , luminous red galaxies , quasi - stellar objects , galaxy clusters ) , our ability to constrain the cosmological parameters depends on the accuracy and precision of the mass . unlike most galaxies , the masses of galaxy clusters can be directly inferred via the observational signature of the gravitational potential ( or its derivative ) . in fact , clusters are the only object for which current technology enable three physically independent mass estimation techniques : via the dynamics of the member galaxies , via the hot gas in the intra - cluster medium , and via gravitational lensing . these three techniques provide a vital cross - check on the mass estimation techniques , assuming one can quantify the statistical precision and accuracy of the cluster mass estimates themselves . cosmological n - body and hydrodynamic simulations play a new and important role in characterizing the statistical and systematic uncertainties on cluster mass estimates @xcite . there has been excellent recent progress on the important step of utilizing realistic mock astronomical observations based on ideal simulations @xcite . our primary goal is to utilize a diverse suite of semi - analytic galaxy catalogs to study how well a realistic spectroscopic program can constrain the dynamical masses of galaxy clusters in the low redshift universe . we quantify our results based on the scatter and bias of the `` observed '' dynamical mass when compared to the halo masses m@xmath10 , which refers to the mass within a radius of @xmath11 . when inferring the dynamical masses of clusters , we require an accurate measurement of the galaxy peculiar velocities . with their total dispersion , their dispersion profiles , and/or their escape velocity profile , we can infer cluster masses based on the virial theorem , the jeans relation for a collision - less fluid , or the caustic technique . to first order , galaxies dynamically respond to the influence of the newtonian gravitational potential , regardless of their luminosities , shapes , colors , or star - formation histories . yet galaxies traveling within a cluster environment are likely to have had one or more localized and short - lived gravitational interaction over its lifetime . this `` dynamical friction '' alters the total cluster velocity distribution away from its simple newtonian expectations , an effect that needs to be captured by the semi - analytic galaxies . in this work , we use sub - halo catalogs as well as a suite of semi - analytic mock galaxy catalogs , to explore how sensitive dynamical masses are to different prescriptions of this dynamical friction . given the above context and the state of both cosmological simulations and semi - analytic galaxy formation , the question as to whether these mock galaxies capture the true velocity distribution of real galaxies in clusters is still unanswered . however , the current simulated data now contain a wide variety of options for how galaxies are pasted into the clusters . more - so , these semi - analytic techniques create mock galaxy clusters which very closely resemble the observed universe in many respects @xcite . while the semi - analytic galaxy catalogs are not fully simulated universes , they do provide us with an opportunity to assess how well our theories and algorithms could do under realistic observational conditions ( e.g. , non - ideal target selection ) . in this study , we focus on how different tracers in the n - body simulations ( e.g. sub - halos or semi - analytic galaxies ) allow us to observe the gravitational potential and measure the projected escape velocity to infer the cluster mass . this technique is analogous to applying the jeans equation , except that the cluster observable is the radial escape velocity as opposed to the velocity dispersion and that the escape velocity maps directly to the gravitational potential , whereas the jeans analysis maps to its derivative . these differences are subtle but important . regardless , both the jean s technique and the caustic technique posit that the radius / velocity _ phase - space _ does indeed map directly to the gravitational potential and through some simplifying assumptions , ultimately to the gravitational mass . our primary goal is to present the statistical characterization ( accuracy and precision ) of caustic inferred halos masses , as well as study the effects of survey strategy when planning spectroscopic follow - up . in section 2 we discuss the caustic technique in detail and apply this technique in section 3 on n - body simulations using the underlying particles , the sub - halos , as well as on the semi - analytic mock galaxy catalogs . using the galaxy catalogs , we incorporate realistic targeting scenarios and show the effects on the measured bias and scatter .

we quantify the expected observed statistical and systematic uncertainties of the escape velocity as a measure of the gravitational potential and total mass of galaxy clusters . we focus our attention on low redshift ( z ) clusters , where large and deep spectroscopic datasets currently exist . utilizing a suite of millennium simulation semi - analytic galaxy catalogs ,

we quantify the expected observed statistical and systematic uncertainties of the escape velocity as a measure of the gravitational potential and total mass of galaxy clusters . we focus our attention on low redshift ( z ) clusters , where large and deep spectroscopic datasets currently exist . utilizing a suite of millennium simulation semi - analytic galaxy catalogs , we find that the dynamical mass , as traced by either the virial relation or the escape velocity , is robust to variations in how dynamical friction is applied to `` orphan '' galaxies in the mock catalogs ( i.e. , those galaxies whose dark matter halos have fallen below the resolution limit ) . we find that the caustic technique recovers the known halo masses ( ) with a third less scatter compared to the virial masses . the bias we measure increases quickly as the number of galaxies used decreases . for n , the scatter in the escape velocity mass is dominated by projections along the line - of - sight . algorithmic uncertainties from the determination of the projected escape velocity profile are negligible . we quantify how target selection based on magnitude , color , and projected radial separation can induce small additional biases into the escape velocity masses . using , the caustic technique has a per cluster scatter in of and bias for clusters with masses at .

1307.0017

m

under newtonian dynamics , the escape velocity is related to the gravitational potential of the system , @xmath12 if the dynamics of the system are controlled by the gravitational potential , tracers which have not escaped the potential well should exist in a well - defined region of @xmath13 phase space , where @xmath14 is the physical or projected radius from the center of the cluster and @xmath15 is the peculiar 3-dimensional velocity or projected 1-dimensional velocity respectively relative to the bulk cluster motion . the edge of this region in @xmath13 space within which bound tracers are allowed to exist defines the escape velocity , @xmath16 . in figure 1 , we show an example halo from the millennium simulation where we identify the actual gravitational potential of the dark matter @xmath17 ( red lines ) and the iso - density contour which traces the escape velocity profile of the halo ( blue lines ) . in the left panel , the velocities and radii are 3-dimensional and in spherical coordinates while in the right panel they are projected along one line - of - sight . the surface that defines the density edge in the @xmath13 phase space is an iso - density contour that follows @xmath16 and therefore @xmath18 . in observed data , we identify the projected @xmath16 surface by applying standard kernel density estimation techniques to the dynamical tracers in the @xmath13 phase - space . the observed tracers have inherent observational uncertainties in both the radial and velocity directions . in this work , we focus on low - redshift sdss - like observations with spectroscopic precision of @xmath19 or @xmath20 in normalized coordinates and astrometric precision of @xmath21 . therefore , our kernel must be non - symmetric to account for the factor of ten difference in the two dimensions of the phase - space . @xcite showed that such axis weighting does not have a large effect on the mass profile determination , something that we confirm in this work . we use a fixed multi - dimensional gaussian kernel with a width in the @xmath14 and @xmath15 directions that independently adapt to the sampling according to ( silverman 1998 ) @xmath22 where @xmath23 is the number of dynamical tracers in the total phase - space and @xmath24 is the dispersion in the radial and velocity dimensions . equation [ eq : kernel ] minimizes the mean integrated squared error of the density estimate , which is the sum of the square of the statistical bias and the variance , also known as the statistical risk @xcite ) . while @xcite adopt an adaptive kernel technique , we will show that a standard fixed kernel recovers the cluster mass estimates with low scatter and bias . @xcite assert that any realistic models of galaxy clusters exhibit escape velocity profiles that at no point exceed @xmath25 where @xmath26 . if an iso - density contour breaks this limit along its surface , the @xmath16 value is replaced with a new value that yields @xmath25 . here , we follow the prescription used in @xcite which invoke a looser constraint of @xmath27 rather than @xmath26 . this allows the algorithm to remove very drastic changes in @xmath28 , but does not overly restrict the iso - density contour values . once the iso - density contours are determined we must choose which surface corresponds to the escape velocity . however , here we follow the standard procedure of assuming that the data are for time - averaged , self - gravitating , isolated clusters in a steady state . as described in @xcite , virialization means that the average system kinetic energy is half of the average system potential energy ( ke = @xmath29pe and @xmath30 ) within the virial radius @xmath31 . in combination with equation [ eq : escape ] this leads to @xmath32 equation [ eq : vesc_sigmav ] is defined for three dimensional measurements of the velocities . @xcite test this virialization condition in the millennium simulation and find it to hold when the system average energies are calculated near the virial radius . in real data we only observe the projected line - of - sight component of both the velocity dispersion and the escape velocity . there could exist some level of anisotropy in the velocity vectors : for example the radial and non - radial components of the velocity are not equal : @xmath33 . this is parameterized by the anisotropy parameter @xmath34 . by assuming that the escape velocity profile we measure in projection @xmath35 , where @xmath36 is where the 3-dimensional radius @xmath14 equals the projected radius @xmath37 , @xcite show that @xmath38 and as in @xcite , we define the projection correction term : @xmath39 recalling that equation [ eq : vesc_sigmav ] is for the three - dimensional velocities , it can be re - written in terms of the observed projected quantities ( i.e. , the projected radii @xmath40 and the line - of - sight velocities of the galaxies ) : @xmath41 we calculate the velocity dispersion @xmath42 ( hereafter labeled @xmath43 ) using a robust median - weighted technique on galaxies within the projected radius that has @xmath44 ( i.e. , @xmath11 ) , which is @xmath45 . interlopers are removed via a shifting - gapper technique described in [ sec : interloper_removal ] . we then choose the iso - density contour that satisfies equation [ eq : vesc_sigmav_proj ] . there is some uncertainty in the determination of this surface , which we quantify in [ sec : results_los ] . we note that we always use the same tracers when calculating the dispersions and the phase - space density ideally , we could use the escape velocity profile , which we assume to be the potential profile through equation [ eq : escape ] , to estimate a mass by using the poisson equation @xmath46 or some variation to arrive at the mass profile . however , this ideal scenario involves the challenge of taking derivatives of a noisy estimate of @xmath47 . instead , @xcite introduce an alternative estimation through the partial mass differential equation @xmath48 . invoking equation [ eq : escape ] , we may rewrite this differential as : @xmath49 and integrate to arrive at : @xmath50 after identifying the iso - density contour that describes the projected @xmath51 , we now have an estimate for @xmath18 by using equation [ eq : escape ] and @xmath52 and our equation now becomes : @xmath53 where @xmath54 @xcite claim that @xmath55 is roughly constant as a function of radius from 1 - 3@xmath11 as calibrated against simulations . for instance , @xcite find @xmath56 and @xcite find @xmath57 . we use a constant value calibrated against the millennium simulations to be @xmath58 and discuss the implications of both the assumption of a constant as well as its calibration in section [ sec : discussion ] . for a variation of the caustic technique that does not require this calibration , see @xcite . @xcite show that the velocity dispersion of a dark matter halo obeys a very tight virial relationship when compared with the critical dark matter mass @xmath1 of the form : @xmath59 where @xmath60 is the 1d velocity dispersion of the dark matter , or more precisely the 3d velocity dispersion divided by the @xmath61 . for the millennium simulation , we use the normalization @xmath62 km / s and slope @xmath63 . @xcite find these to be consistent between different cosmological simulations . the scatter in @xmath64 at fixed @xmath1 from the n - body simulations for equation [ eq : evrard_rel ] is @xmath65 . with slope @xmath29 , this inherent scatter implies a mass scatter from the virial relation to be @xmath66 . however , this amount of scatter only applies when the 3d velocity dispersion is known , which is never the case in the observed universe . @xcite show that the real scatter in mass as measured from the line - of - sight velocity dispersion is closer to @xmath67 when 100 red - sequence galaxies are used . this huge increase in scatter stems mostly from the projection of the galaxies and their velocities along the line - of - sight . @xcite use the @xcite semi - analytic galaxy catalogs but they do not use the @xcite calibration . instead , they re - calibrate the slope and amplitude of equation [ eq : evrard_rel ] using the 3-dimensional information of the _ galaxies _ as opposed to the particles . @xcite also calibrate their measured scatter in velocity and mass against a specific set of 100 red - sequence galaxies within the 3d virial radius of each halo . in the former case , the slope and amplitude will differ from the dark matter if the galaxies are dynamically biased with respect to the dark matter . in the latter case , relationships for the scatter ( e.g. , as a function of the number of observed galaxies ) become meaningless for larger samples ( and it is quite common to have clusters with more than 100 observed galaxies in their @xmath13 phase space ) . in this work , we use the virial - mass relationship from @xcite . this is an important distinction , because the different semi - analytic galaxy catalogs can each have inherent dynamical biases between the dark matter and the galaxies that we would otherwise not detect . similarly , the scatter in the measured line - of - sight velocity dispersions are determined against the particle velocity dispersions . this is also important , in that the observed line - of - sight scatter in the velocity dispersions and masses can be compared between the different semi - analytic galaxy catalogs . we select 100 halos from the millennium simulation to perform this study . while the halos are not chosen on the basis of any specific physical characteristics , our sample aims for fairly even mass sampling over @xmath68 . the average mass @xmath69 and the average critical radius @xmath70mpc . we then use four semi - analytic catalogs @xcite created using the millennium simulation along with the identified subhalos within each halo to test the caustic technique in section [ sec : results ] . @xcite suggest that in its most basic form , a theory of galaxy formation is a set of rules motivated by physical processes which transforms a halo mass function into an observed galaxy luminosity function . in fact , most semi - analytic techniques ( which define the rule - set ) judge their success primarily by comparing to published galaxy luminosity functions . in this work , we are equally concerned with how well those galaxies trace the underlying radial velocity phase - space , which we use to measure the escape velocity of halos and their gravitational potentials . galaxies in the semi - analytic algorithms are first identified at the location of collapsed sub - structure within halos . these are nominally the sub - halos and algorithms like subfind @xcite which have been shown to work well to identify all of the sub - structure in n - body simulations ( see also @xcite ) . once identified , these sub - halos trace the positions and velocities of the galaxy population . rules are put in place to define when and how a burst of activity ( e.g. star - formation / nuclear ) occurs . these sub - halos can grow in total mass ( and luminosity ) by accreting gas ( or a model for gas ) , other particles , and other sub - halos through merging . it is the merging and other dynamical interactions which are responsible for altering the radial velocity phase - space and thus affecting our ability to use dynamical tracers for the halo mass . at any given redshift ( or snapshot output of an n - body simulation ) , the sub - halos which have survived a merger up to that point would not be good tracers of the halo radial velocity phase - space ( see also figure [ fig : mvsm ] ) . this is because at the resolution of the millennium simulation , the sub - halos in simulations are easier to destroy compared to galaxies in the real universe , which are much more compact and gravitationally bound . so while an interaction might destroy a sub - halo , there is no reason to think it would destroy a galaxy . in modern semi - analytic techniques , decisions ( or a rule set ) must be defined to decide what to do with a `` galaxy '' after its sub - halo is no longer identified in a snapshot . the most common approach is to identify the most - bound particle in the sub - halo before it was destroyed and follow it as a surviving galaxy through future snapshots ( i.e. , to lower redshifts ) . these are sometimes called `` orphans '' as they are semi - analytic galaxies that have lost their dark matter halos . the above rule does not happen in reality : the evolution of the position and velocity of a galaxy can not be determined from a single particle . so a technique is applied to define statistically how long a galaxy might survive before it is ripped apart in a merger ( i.e. , the merging time due to dynamical friction ) : @xmath71 where @xmath72 is the circular velocity for a mass in a gravitational potential defined by an isothermal sphere at radius @xmath73 of the sub - halo and the masses of the halo and the sub - halo are @xmath74 and @xmath75 respectively @xcite , and @xmath76 is a coefficient needed to reproduce observed luminosity functions at the luminous end @xcite . in this rule - set , a clock is started when a galaxy s sub - halo is destroyed . the surviving galaxy is merged with its nearest galaxy or sub - halo after this time - scale has expired . when the final merging happens , the galaxy is destroyed and its stars , gas , and dark matter are distributed in various ways ( i.e. , it is a rule - set in the semi - analytic algorithm ) . however , this statistical rule - set only defines _ when _ a dark matter orphaned galaxy is destroyed , not how . for instance , the particle which represents the galaxy is no longer actually merging or changing its orbit due to dynamical interactions outside the normal particle - particle interactions . this would require a new rule - set . the above description is complicated and there are numerous ways in which a semi - analytic techniques can implement dynamical events in the lifetime of a simulated galaxy . this is why we will investigate the effects on the caustic masses from different implementations of halo dynamics in the semi - analytic galaxy catalogs . in this analysis we start with all of the semi - analytic galaxies within a 60h@xmath77mpc - length 3-dimensional box around each halo center . we then sub - select the n brightest galaxies ( where n = 100,50,25 , etc ) within a projected radius in these volumes to create the halo radius / velocity phase - space diagrams along one or more lines - of - sight . these volumes place limits on the projected phase - space velocities that are @xmath78km / s relative to the halo velocity centroids . since the typical escape velocities are @xmath79km / s , these volumes are large enough to incorporate realistic projection effects ( see figure [ fig : caustics ] ) . with projection , interlopers ( non - member foreground / background galaxies ) can play a large role in affect both the measured phase - space density as well as the line - of - sight velocity dispersion . therefore , an effort must be made to systematically remove the interlopers from each line - of - sight projection . many methods have been devised to identify and remove interloper galaxies from a sample around a halo . these include color - based @xcite , @xmath80-clipping , gapper @xcite , and phase - space selection methods @xcite . in this study , we do not try and optimize any particular method , but rather choose one in existence that returns a minimal bias for velocity dispersion and mass at large sampling . we limit ourselves by testing only a few basic interloper removal techniques , and compare their relative biases and resulting scatter . in figure [ fig : interlop ] we compare three common techniques to measure velocity dispersions against the underlying dark matter . the first technique is to apply a simple upper / lower bound in velocity space ( @xmath81 km / s ) . the second is to iteratively remove outliers via sigma clipping ( @xmath82 ) . the third is called a shifting - gapper , where we work in the full phase - space and identify velocity gaps as a function of radius as indicators of interloping sub - structure . this shifting - gapper technique is similar to what is applied in @xcite . galaxies are sorted into bins as a function of radius while keeping the number in each bin constant at @xmath83 . when odd multiples of 25 are used , the last radial bin may have less than 25 galaxies . in each bin , the galaxies are sorted by their peculiar velocity and a f - pseudosigma " @xcite is calculated and used as the velocity gap to remove perceived interlopers . the calculation of f - pseudosigma is an iterative process that we stop if less than 5 galaxies remain in a bin or if f - pseudosigma @xmath84 km / s . in all cases , the final interloper - cleaned velocity dispersion is calculated using a robust bi - weighted estimator , which we confirm is always less biased than a simple standard deviation @xcite . when applying only a simple velocity boundary , the dispersions are biased high and the scatter is large ( for @xmath85 ) . however , both the sigma clipping and the shifting - gapper techniques do better and equally well in recovering unbiased velocity dispersions ( see also @xcite ) . the shifting - gapper does a better job at reducing the scatter at all values of n@xmath86 . this is because the technique utilizes the 2-dimensional phase - space data as opposed to the one - dimensional velocity distributions . as such , the shifting - gapper can identify sub - structure in the phase - space which sigma clipping can not . clusters with poor sampling @xmath87 , have dispersions that are biased low . throughout the rest of this work we apply the shifting - gapper technique to measure velocity dispersions .

we find that the dynamical mass , as traced by either the virial relation or the escape velocity , is robust to variations in how dynamical friction is applied to `` orphan '' galaxies in the mock catalogs ( i.e. , those galaxies whose dark matter halos have fallen below the resolution limit ) . the bias we measure increases quickly as the number of galaxies used decreases . for n , the scatter in the escape velocity mass is dominated by projections along the line - of - sight . algorithmic uncertainties from the determination of the projected escape velocity profile are negligible .

we quantify the expected observed statistical and systematic uncertainties of the escape velocity as a measure of the gravitational potential and total mass of galaxy clusters . we focus our attention on low redshift ( z ) clusters , where large and deep spectroscopic datasets currently exist . utilizing a suite of millennium simulation semi - analytic galaxy catalogs , we find that the dynamical mass , as traced by either the virial relation or the escape velocity , is robust to variations in how dynamical friction is applied to `` orphan '' galaxies in the mock catalogs ( i.e. , those galaxies whose dark matter halos have fallen below the resolution limit ) . we find that the caustic technique recovers the known halo masses ( ) with a third less scatter compared to the virial masses . the bias we measure increases quickly as the number of galaxies used decreases . for n , the scatter in the escape velocity mass is dominated by projections along the line - of - sight . algorithmic uncertainties from the determination of the projected escape velocity profile are negligible . we quantify how target selection based on magnitude , color , and projected radial separation can induce small additional biases into the escape velocity masses . using , the caustic technique has a per cluster scatter in of and bias for clusters with masses at .

1307.0017

c

with the availability of large and complete spectroscopic surveys like the sloan digital sky survey ( * ? ? ? * sdss ) and gama ( galaxy mass and assembly gama ) @xcite , highly multiplexed multi - object optical spectroscopy on 8 m class telescopes ( imacs @xcite , vimos @xcite , deimos @xcite ) , and the latest generation of multi - object near - infrared spectrographs ( mmirs @xcite , flamingos 2 @xcite , mosfire @xcite ) , we can measure galaxy large numbers of galaxy velocities in clusters from @xmath127 to @xmath128 . and just as we can use three different observables to infer the masses of clusters ( see section [ sec : intro ] ) , we can use the galaxy velocities in three different ways to infer dynamical mass ( e.g. , via virial scaling , the jean s equation , and the escape velocity ) . the questions then are how well do these different dynamical techniques work under realistic observing conditions and how do they compare . here , we compare the virial relation via the velocity dispersion @xcite and the escape velocity mass inferred from the caustic technique @xcite . we examine four different semi - analytic mock galaxy catalogs , as well as the sub - halos and the particles in the millennium simulation . the measured scatter and bias in the inferred dynamical masses are quantified in tables 1 - 5 . the level of scatter and bias varies by only a few percent between most of the different semi - analytic tracers . the exception is for the @xcite galaxies , which sometimes differ by slightly more than the 1@xmath80 errors on the bias estimates . in one sense , this robustness is not surprising , since the majority of galaxies in the semi - analytics are attached to sub - halos , which are the same for each of the mock galaxy catalogs . however , there are a variety of rules which are applied to the `` orphan '' population ( see section [ sec : methods_data ] ) . for the satellite population , these orphan galaxies are quite common at low stellar masses , while the exact fraction depends on the semi - analytic rule - set . in the semi - analytic catalogs studied here , the fraction of @xmath129 brightest galaxies that are orphans ranges from 50% ( bower ) to 25% ( guo ) . consider some of the differences in the orphan population between the @xcite semi - analytics compared to @xcite , @xcite , and @xcite : the bower sample uses a merger tree that differed in how friend - of - friend groups were defined , how spuriously linked halos were handled , how independent halos were identified , and how descendants of halos were tracked through time ; the bower sample includes the sub - halo orbital energy and angular momentum when calculating the merging timescale of the orphans ; the @xcite semi - analytics go one step further by modeling the orbital decay of the orphans before they are destroyed . these algorithmic differences manifest as variations in the spatial distribution of the satellites within the halos . the de lucia semi - analytic galaxies have much flatter density profiles within the virial radius when compared to the @xcite galaxies @xcite . since the @xmath13 phase - space is different between the semi - analytics , one might expect that the caustic technique ( which is based on the phase - space density ) would also differ significantly . however , this is not the case and even when the orphan fraction and radial densities differ by factors of two or more , the caustic masses vary by @xmath130 . we interpret this lack of difference between the different semi - analytic techniques as a measure of the robustness of the technique to large systematic variations in the @xmath13 velocity distribution function . the one exception to this robustness is for the sub - halo population where we detect large biases in the velocity dispersion compared to the dark matter . since the caustic mass is calibrated using the velocity dispersion , this bias carries through into a bias in both the virial mass and the caustic mass . we attribute this to how poorly the sub - halos trace the @xmath13 phase - space within halos in simulations with resolution similar to the millennium simulation ( see also @xcite ) . one could ask whether the semi - analytic techniques have converged in their representation of the @xmath13 phase - space inside clusters , as represented by the fraction of orphan galaxies . @xcite have shown that at higher resolutions , galaxies are no longer orphaned from sub - halos . instead , a new `` crisis '' of sub - halo over - abundance presents itself . @xcite also show that this crisis is averted through rule - sets analogous to the ones used at lower resolution . in other words , instead of following the most - bound particle of a destroyed sub - halo , one attaches semi - analytic galaxies only to those sub - halos that previously achieved some minimal mass threshold before entering the cluster . the velocity dispersion of these semi - analytic galaxies is unbiased with respect to the dark matter , which is what we already find here . while none of these semi - analytic prescriptions is how nature places galaxies into halos , we have established that the virial relation and the caustic technique are robust to variations in their rule - sets . this baseline allows for a comparison of the absolute levels of the inferred mass biases and scatters between the virial and the caustic techniques . for a fixed number of tracers projected to lie within @xmath131 of the clusters , the scatter in the caustic mass @xmath90 at fixed @xmath91 is about 1/3 smaller than @xmath132 . in other words , at fixed n , the caustic technique is a more precise estimate of the true halo mass compared to the virial relation . the growth of the mass scatter as @xmath107 decreases is the same for the two techniques . as with the virial relation and the velocity dispersion , the dominant component of the scatter in the caustic mass is from the line - of - sight variations in the observed velocity dispersion and phase - space density ( see also @xcite ; @xcite ) . uncertainties in @xmath88 induced from the sampling of the phase space do not contribute unless n@xmath133 , below which they quickly grow to be a dominant component . in figure [ fig : bias_vs_n ] we show the strong dependence of the bias on the number of tracers used in the mass calculation . @xcite suggest that this was due to dynamical friction , since we ( as they ) explicitly restrict the sub - samples to the brightest galaxies . however at fixed n , large variations in the brightness distribution of the galaxies has only a small affect on the observed bias . the same can be said for color selection ( see figure [ fig : red_bias_vs_red ] ) . thus while velocity segregation from sub - sampling plays a role , it is minimal compared to the number of galaxies used in the mass determination . this holds for both the virial masses as well as the caustic masses . put simply , if a targeting algorithm requires a trade - off between number and color , number wins . regardless of how biases are introduced into the velocity distributions ( e.g. , through number , brightness , or color ) the caustic mass is less affected than the virial mass . the trends in the biases for the virial and caustics masses are similar . the exception is when radial selection constraints are applied . we find that the velocity dispersion is more susceptible to incompletenesses in the core sampling while the caustic technique is more susceptible to incompletenesses in the cluster outskirts . the former trend can be understood from a dynamically cold population of galaxies which dominates the dispersion measurement at low sampling . the latter is also a sampling issue , where the iso - density contour gets lost in the background for low sampling in the cluster outskirts . finally , we note that the implementation of the caustic technique utilizes a step which calibrates to simulations ( see @xmath134 in equation [ eq : caustic_final ] ) . this is no different than the virial calibration ( equation [ eq : evrard_rel ] ) . @xcite find @xmath56 and @xcite find @xmath57 , which corresponds to a systematic uncertainty of 30% in mass . this is larger than any biases we detect from sample selection . one explanation the difference in the value for @xmath134 is in how @xcite and @xcite define their mock galaxy catalogs : the former used only halos ( with ten particles or more ) while the latter used only particles to define galaxies . since sub - halos in n - body simulations are biased tracers of the dark matter velocity dispersions , the calibration factor and caustic masses will also be biased ( see figure [ fig : bias_vs_n ] middle and right panels ) . we test this hypothesis by re - calibrating @xmath134 using the millennium simulation sub - halos alone . the high halo velocity dispersions of the sub - halos require a lower calibration factor than from the dark matter . we find @xmath56 , identical to what is used in @xcite , who note that their own halo velocity dispersions are biased with respect to the dark matter in their simulations . @xcite explicitly used dark matter particle positions and velocities to define their galaxies and calibrate @xmath134 . the semi - analytics we use lie in between these two extremes , which explains why we find @xmath135 . @xcite notes that @xmath134 is not constant with radius in simulations and that the caustic mass profiles can over - estimate the mass within @xmath136 , where velocity anisotropies become smaller . likewise , @xcite compare caustic - derived and weak - lensing - derived mass profiles and find disagreement within @xmath137 , as expected from the anisotropy profiles in simulations . in this work , we are not measuring mass profiles but instead the integrated masses of the clusters out to @xmath11 . as shown in @xcite , unbiased halo masses require an appropriate measure of @xmath138 from equation [ eq : caustic_final ] , which is what we do to achieve unbiased caustic masses for the @xcite semi - analytic galaxies . this is without question a tuning step which carries with it a certain level of additional systematic uncertainty . it is very unlikely that the radius - velocity phase - space of galaxies in the universe is represented by the sub - halo population in n - body simulations ( regardless of resolution ) . current observational constraints on the bias between the galaxy and dark matter velocity dispersions are measured indirectly ( e.g. , @xcite ) and find it to be @xmath139 when a multitude of independent cosmological priors are leveraged . from the current simulation and observational work , it is not likely that @xmath56 , which corresponds to a galaxy / dark matter velocity bias of 10% in a @xmath140cdm simulation ( see table 2 sub - halos ) . if galaxies and dark matter have dispersions that are unbiased with respect to each other , the caustic masses ( integrated to @xmath11 ) would be low by @xmath14120% using @xmath56 @xcite . ideally , the simulation calibration factor can be dropped entirely , and in @xcite we present a revised derivation of the caustic technique that relies only on the observable parameters : the nfw density scale parameter , @xmath142 , and @xmath143 and their statistical and systematic uncertainties .

we find that the caustic technique recovers the known halo masses ( ) with a third less scatter compared to the virial masses . we quantify how target selection based on magnitude , color , and projected radial separation can induce small additional biases into the escape velocity masses . using , the caustic technique has a per cluster scatter in of and bias for clusters with masses at .

we quantify the expected observed statistical and systematic uncertainties of the escape velocity as a measure of the gravitational potential and total mass of galaxy clusters . we focus our attention on low redshift ( z ) clusters , where large and deep spectroscopic datasets currently exist . utilizing a suite of millennium simulation semi - analytic galaxy catalogs , we find that the dynamical mass , as traced by either the virial relation or the escape velocity , is robust to variations in how dynamical friction is applied to `` orphan '' galaxies in the mock catalogs ( i.e. , those galaxies whose dark matter halos have fallen below the resolution limit ) . we find that the caustic technique recovers the known halo masses ( ) with a third less scatter compared to the virial masses . the bias we measure increases quickly as the number of galaxies used decreases . for n , the scatter in the escape velocity mass is dominated by projections along the line - of - sight . algorithmic uncertainties from the determination of the projected escape velocity profile are negligible . we quantify how target selection based on magnitude , color , and projected radial separation can induce small additional biases into the escape velocity masses . using , the caustic technique has a per cluster scatter in of and bias for clusters with masses at .

astro-ph0303141

i

the high resolution of the has enabled astronomers to study the low - luminosity x - ray source populations in globular clusters in great detail . combined x - ray , radio , and optical _ hubble space telescope _ ( ) studies of the globular cluster 47 tucanae have revealed quiescent low - mass x - ray binaries ( qlmxbs ) that have not experienced x - ray outbursts in the history of x - ray astronomy , cataclysmic variables ( cvs ) as x - ray luminous as any known in the field , flaring behavior from coronally active stellar binary systems , and predominantly thermal x - ray emission from millisecond pulsars ( msps ) ( grindlay et al . 2001a , 2002 ) . similar populations have been uncovered in the globular clusters ngc 6397 ( grindlay et al . 2001b ) , ngc 6752 ( pooley et al . 2002a ) , and @xmath6 cen ( rutledge et al . 2001 , cool , haggard & carlin 2002 ) , while the luminosities and broad x - ray spectral types of these sources have allowed classification of sources in the more obscured cluster ngc 6440 ( pooley et al . 2002b ) and m28 ( becker et al . 2003 ) . the globular cluster terzan 5 contains a known transient lmxb , exo 1745 - 248 , which was first detected in a bursting state by _ hakucho _ ( makishima et al . 1981 ) , and has been irregularly active since then ( johnston et al . 1995 and refs . therein ) . exo 1745 - 248 is one of the few luminous globular cluster lmxbs not analyzed by sidoli et al . ( 2001 ; hereafter spo01 ) or parmar et al . ( 2001 ) , who identify spectral distinctions between normal and ultracompact lmxbs . ultracompact lmxbs , defined as having periods less than 1 hour , are thought to possess a degenerate helium white dwarf secondary . deutsch et al . ( 2000 ) remark upon the overabundance of ultracompact lmxbs in globular clusters , and speculate that the short periods may be due to dynamical effects in globular clusters . terzan 5 also contains two identified msps , with many additional msps probably making up the extended steep - spectrum radio source at the cluster core ( lyne et al . 2000 ; fruchter & goss 2000 ) . terzan 5 s high central density and large mass make it a rich target for studies of binary systems , but its high reddening and severe crowding make optical and even infrared observations extremely difficult . the deepest infrared survey of terzan 5 was performed with the nicmos camera by cohn et al . ( 2002 ; hereafter clg02 ) . the extreme reddening indicates that the cluster parameters are best determined in the infrared . nicmos observations produced the first cmds of terzan 5 to reach the main - sequence turnoff ( clg02 ; see also ortolani et al . therefore we utilize the new cluster parameters derived by clg02 in our analysis , particularly the reddening , distance , core radius , and radial star - count profiles . the attempt by edmonds et al . ( 2001 , hereafter egc01 ) to identify exo 1745 - 248 and the eclipsing msp through time - series variability analysis and color information did not uncover any promising candidates due to the crowding and overlapping airy profiles , although it did identify two truly variable stars , one of which was shown to be an rr lyrae variable . this paper is organized as follows . section 2.1 describes the observations we used . section 2.2 explains our methods for detecting sources and performing an astrometric correction based upon identification of serendipitous sources . section 2.3 describes our search for an infrared counterpart for exo 1745 - 248 , extending the work of egc01 using our position . section 2.4 classifies the faint x - ray sources , and quantifies our detection incompleteness ( due to the outburst of exo 1745 - 248 ) . section 2.5 attempts simple spectral fits to the faint sources , while section 2.6 examines the simultaneous and spectra of exo 1745 - 248 . section 3.1 compares our spectral analysis of exo 1745 - 248 to other observations of lmxbs . section 3.2 recalculates the central density and collision frequency of terzan 5 , while section 4 summarizes our conclusions .

the previously known transient low - mass x - ray binary ( lmxb ) exo 1745 - 248 in the cluster entered a rare high state during our august 2000 observation , complicating the analysis . their x - ray colors and luminosities , and spectral fitting , indicate that five of them are probably cataclysmic variables , and four are likely quiescent lmxbs containing neutron stars . nicmos images .

we report a acis - i observation of the dense globular cluster terzan 5 . the previously known transient low - mass x - ray binary ( lmxb ) exo 1745 - 248 in the cluster entered a rare high state during our august 2000 observation , complicating the analysis . nevertheless nine additional sources clearly associated with the cluster are also detected , ranging from down to ergs s . their x - ray colors and luminosities , and spectral fitting , indicate that five of them are probably cataclysmic variables , and four are likely quiescent lmxbs containing neutron stars . we estimate the total number of sources between and ergs s as by the use of artificial point source tests , and note that the numbers of x - ray sources are similar to those detected in ngc 6440 . the improved x - ray position allowed us to identify a plausible infrared counterpart to exo 1745 - 248 on our 1998 _ hubble space telescope _ nicmos images . this blue star ( f110w=18.48 , f187w=17.30 ) lies within 0.2 of the boresighted lmxb position . simultaneous _ rossi x - ray timing explorer _ ( ) spectra , combined with the spectrum , indicate that exo 1745 - 248 is an ultracompact binary system , and show a strong broad 6.55 kev iron line and an 8 kev smeared reflection edge .

astro-ph0107534

r

using the values for the geometrical factors just discussed , the 8 mr upper limit for the h@xmath0 flux , and values of @xmath79 and @xmath80 from equation ( [ phi_ex_calc ] ) we obtain values for the one sided ionizing flux of @xmath100 for the low , fiducial and high values of the geometrical correction factor @xmath99 . the first two of these are within the range inferred by @xcite , while the third is about a factor of two lower , though it should be remembered that our surface brightness value is an upper limit . expressing the radiation field as @xmath101 , we obtain @xmath102 , where @xmath103 is planck s constant and @xmath0 is the spectral index . assuming the srgpf value for the spectral index of @xmath104 , the corresponding upper limits for the mean intensity at the lyman limit are @xmath105 . the local unshielded metagalactic photoionization rate is calculated from this as @xmath106 , which yields @xmath107 , where @xmath108 has the dimensions s@xmath5 . had we adopted a different spectral index ( e.g. , 1.0 ) the corresponding numbers for our fiducial value of @xmath96 of @xmath76 , @xmath109 and log@xmath110 would be @xmath111 , @xmath112 and @xmath113 , respectively . if our possible detection at 4 mr should ultimately be confirmed , the actual values would of course all be lower by a factor of two . a review of recent attempts to detect , or set limits on , the intensity of the ionizing background may be found in srgpf . some of these are summarized in their table 1 . it should be noted however that in the paper by @xcite , their definition of @xmath76 is in terms of the ionizing specific intensity , not the flux . they also assume a value for @xmath79 of 1.0 , so their numbers in their table 2 can not be compared directly with ours . their upper limit on the h@xmath0 surface brightness from hi 1225@xmath101 sw is about 65mr . the h@xmath0 surface brightness limit of vwrh ( 20mr ) is the lowest surface brightness limit we are aware of prior to the current work , which is about 2.5 times higher than our new upper limit . our use of different assumptions about the values of @xmath79 and @xmath80 and the range of the projection factors considered here ( vwrh assumed a face on slab ) results in our current value for @xmath76 which ranges between about 2.5 to 10 times lower than that quoted in vwrh . [ [ comparison - with - estimates - of - agn - and - hot - star - contributions - to - the - background ] ] comparison with estimates of agn and hot star contributions to the background ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ a recent careful analysis of the contributions expected from both agns and hot stars to the ionizing background has also been carried out in srgpf as well as estimation of the uncertainties in these estimates . in principle , these contributions are directly observable independent of cosmological parameters , but of course local h i prevents radiation near the lyman limit from penetrating into the disk of the galaxy along essentially all lines of sight from the sun . in practice , according to srgpf , the two largest uncertainties in the estimate of the contributions from the agns are the uv luminosity functions for the agns and the assessment of the amount of attenuation from the cumulative absorption of intervening h i between ourselves and the agns . for the contributions from hot young stars embedded in galaxies the luminosity function of ionizing radiation is also somewhat uncertain , but the dominant uncertainty in this case is the fraction @xmath115 of ionizing photons which escape the galaxy . srgpf thus characterize this fraction as a free parameter but favor a value of order 5% , and for this contribution quote if we examine the various combinations of the `` best '' , `` upper '' and `` lower '' 1@xmath67 estimates in srgpf we find that our largest value ( for the face on projection ) is compatible for all but the largest of these combinations . for our fiducial value of the projection factor , our limit is compatible with , but slightly lower than , the sum of the two `` best '' contributions . the range of our upper limits on the inferred z @xmath12 0 photoionization rate of log @xmath118 may be compared with that inferred from very recent numerical simulations of the ly@xmath0 forest by @xcite . the recent advances in both computing power and numerical simulation techniques have produced results for the uncondensed gas giving rise to the ly@xmath0 forest which reproduce with impressive faithfulness the observed properties of the ly@xmath0 absorption lines over the entire range of observed redshifts from @xmath119 to @xmath71 . assuming a specific cosmological model , it is possible to infer , at any epoch , the value of the ionizing flux which can be compared with empirical determinations such as the one we have presented above . the basic argument is as follows : a complete specification of the cosmological parameters ( e.g. , @xmath120 , @xmath121 , @xmath122 , the h / he ratio , and , e.g. an lcdm initial perturbation model ) completely specifies the total baryon density at any redshift , and , in principle the course of the entire process of gas condensation . the simulations thus yield estimates of the actual density of hydrogen nuclei at any point in the spatial grid and at any redshift , along with the velocity field of that material , and thus the local column density of hydrogen nuclei . comparing these simulations with the observed values of the frequency of the h i absorption lines one can then infer the required fraction of hydrogen nuclei which are neutral and thus the h i photoionization rate , @xmath108 . @xcite deduce a value of @xmath123 at a mean redshift of 0.17 , and a rough extrapolation of this estimate to zero redshift yields a value of about @xmath124 , which is compatible with our range of upper limits . of course there are considerable uncertainties in the simulations themselves , in addition to the basic cosmological parameters , but these are most severe for the highest density regions where the relatively rare higher column density h i systems are formed . with further improvements in the sensitivity of the h@xmath0measurements , improved data on the density of the low redshift ly@xmath0 forestline density , and refinements in the simulations themselves , it will be possible to impose a constraint on the combination of the cosmological parameters which are involved in the @xcite estimate , especially those that yield the present epoch baryon density . as our detailed discussion of the reduction procedures and our final spectra make clear , there are certainly uncertainties in our fitted value for the h@xmath0 surface brightness and its upper limit . however , the uncertainty in the geometry of hi 1225@xmath101 sw also introduces an additional major uncertainty . there is also the possibility that our ( implicit ) assumption that the h i gas has a projected filling factor near unity is wrong . suppose in fact the h i gas in the cloud has already undergone significant fragmentation on scales much smaller than the 21 cm resolution , with each `` cloudlet '' having h i column densities substantially higher than that inferred under the assumption that no such small scale structure exists . this implies a corresponding reduction in the actual solid angle subtended by the high column density fragmented gas . in such circumstances the surface brightness of h@xmath0from each little cloudlet would be only slightly increased from that expected in the absence of fragmentation , however the total h@xmath0 flux would be reduced by the projected area filling factor , and the true value of the photoionization value would be higher than that we have inferred . we consider this scenario rather unlikely since one would expect star formation to be underway in at least some portions of the structure if such gas fragmentation had already occurred to such an extent . it is also possible that the tidal interaction between the ne and sw components has produced filamentary or clumpy hi structure as sometimes seen in higher linear resolution observations of tidally interacting galaxies . we have also considered the possibility of significant amounts of internal extinction of h@xmath0 in the sw component by dust . even for a normal dust / gas ratio , for @xmath125 @xmath4 the extinction is negligible ; however , for the peak observed column density of @xmath126 @xmath4 in the 40 resolution map of @xcite , the emission in that direction could be attenuated to 75% of the extinction - free value . however , most of the 6590.4 ring lies toward regions of the target where the column density is much lower ( see figure [ wcce_image ] ) , with a median column density of @xmath127 @xmath4 . in any case , a normal dust / gas ratio in a cloud in which no star formation seems to have occurred seems unlikely . it would be useful to reobserve the sw component of hi 1225@xmath101 with improved sensitivity in order to see if h@xmath0 at the level of @xmath124 mr is really present . however , the ambiguity in the geometry of hi 1225@xmath101 sw remains a difficuly . it would be very interesting for numerical simulations of interacting galaxies to be run to see if the morphology and velocity fields of the entire hi 1225@xmath101 complex can be understood , and this may shed some light on the correct geometry . beyond the issue of the geometry however , investigation of the initial conditions and subsequent evolution of the rare large isolated h i clouds such as hi 1225@xmath101 in which little or no star formation has taken place would seem a worthwhile program . in any event , it will be important to observe with increased sensitivity several other suitable targets , since although the sw hi 1225@xmath101component has some features which make it an attractive target , the [ ] galactic emission and the uncertain geometry make a definitive determination of the background flux problematic . the expert assistance of bill kunkel and oscar duhalde in resolving technical problems at the telescope is gratefully acknowledged . rjw thanks romeel dav for helpful discussions on the ly@xmath0 forestsimulations and don osterbrock and tom slanger for enlightening discussions and data concerning the night sky spectrum . snv and sv acknowledge support from nsf ast-9529167 . finally , we acknowledge the helpful comments of the referee , p. maloney , in particular for pointing out the dynamical objection to the @xcite geometrical model .

we report a new fabry - perot search for h emission from the intergalactic cloud hi 1225 in an attempt to measure the low redshift ionizing background radiation . conversion of this limit to limits on the strength of the ionizing background requires knowledge of the ratio of the projected to total surface area of this cloud , which is uncertain . we discuss the plausible range of this ratio , and within this range find that the strength of the ionizing backround is in the lower range of , but consistent with , previous observational and theoretical estimates .

we report a new fabry - perot search for h emission from the intergalactic cloud hi 1225 in an attempt to measure the low redshift ionizing background radiation . we set a new upper limit on h emission of 8 mr ( ergs s arcsec ) . conversion of this limit to limits on the strength of the ionizing background requires knowledge of the ratio of the projected to total surface area of this cloud , which is uncertain . we discuss the plausible range of this ratio , and within this range find that the strength of the ionizing backround is in the lower range of , but consistent with , previous observational and theoretical estimates .

astro-ph0309103

i

the mass ratio distribution of binaries provides one of the few diagnostics for testing models of binary formation ( for recent reviews , see clarke 2001 ; tohline 2002 ; halbwachs et al . however , the use of the mass ratio distribution in spectroscopic binaries ( sbs ) has been limited because , in most studies , only the primary spectrum is detected . without the secondary radial velocities , the mass ratio of a spectroscopic binary can not be measured . detection of the secondary spectrum is difficult because most radial velocity observations are made in visible light , where the luminosity of stars less massive than @xmath4 is a strong function of the mass ( e.g. , carney et al . 1994 , hereafter cl94 ) . as a result , the measured secondary / primary mass ratios , @xmath0 , are clustered close to 1 . to overcome this bias astronomers have applied powerful statistical techniques to samples of single and double - lined spectroscopic binaries ( sb1s and sb2s ) , in order to derive the mass ratio distribution down to mass ratios as low as @xmath5 ( e.g. , halbwachs 1987 ; heacox 1995 ) . however , because of the missing information on the mass ratios of the binaries , the resolution ability of the statistical techniques is limited , and they can only derive the gross features of the distribution . this might be the reason why the results of such analyses still differ and a consensus on the underlying distribution has not been reached . goldberg , mazeh & latham ( 2003 , hereafter g03 ) studied 129 binaries identified in the carney & latham high - proper - motion sample ( cl94 ) , which consisted of a large fraction of halo stars . their sample of binaries included 25 sb2s . g03 found a rise in the distribution as the mass ratio decreases to @xmath6 , a drop at @xmath7 , and a small peak at @xmath8 . halbwachs et al . ( 2003 ) considered a well - defined sample of 27 binaries within the nearby f7 to k stars , together with 25 binaries found in the open clusters of pleiades and praesepe . their sample of 52 binaries consisted of 15 sb2s , for which the mass ratios were directly derived , another 9 binaries with mass ratios estimated from astrometric data ( udry et al . 2003 ) , and an additional 7 cluster binaries with mass ratios estimated from their photometric properties . halbwachs et al . found a mass ratio distribution with two peaks : a broad , shallow , peak between @xmath9 and @xmath10 , and a sharp , high , peak at @xmath11 . the latter appears only in the distribution of the short period binaries , with periods shorter than 50 days . evidently , even the most recent studies do not agree on the true mass ratio distribution . it is therefore desirable to derive the mass ratio distribution with minimal need for statistical tools . to accomplish this we need a large , well defined sample of binaries dominated by sb2s with mass ratios measured over as large a range as possible . our approach to the detection of main - sequence and pre@xmath12main - sequence ( pms ) sb2s is to observe with high resolution , infrared ( ir ) spectroscopy sb1s that were previously identified and measured with visible light ( mazeh et al . 2002 ; prato et al.2002a , b ) . because the secondaries in sb1s are cool , the secondary to primary light ratio is greater in the ir than in visible band , favoring their detection in the ir . one result of this approach is the smallest mass ratio ever measured dynamically in a pms sb , @xmath13 , in the ntts 160905@xmath121859 system ( prato et al.2002a ) . to compile as complete and large as possible a sample for study , we chose to use a subsample of the sbs in the carney & latham study of 1464 high - proper - motion , nearby , late g and early k , main - sequence stars ( cl94 ) . systematic , long term radial velocity monitoring of these stars in visible light has identified 171 sb1s and 34 sb2s ( latham et al . 2002 , hereafter l02 ; goldberg et al . 2002 , hereafter g02 ) . out of these , we focused on 51 sb1s , turning 32 systems into sb2s . the composition of our sample is described in 2 , the observations in 3 , the analysis in 4 , and the measured and derived mass ratio distribution in 5 . we compare our results with previous studies in 6 , discuss our results in 7 and conclude the discussion in 8 .

we report infrared spectroscopic observations of a large , well - defined sample of main - sequence , single - lined spectroscopic binaries in order to detect the secondaries and derive the mass ratio distribution of short - period binaries . the sample consists of 51 galactic disk spectroscopic binaries found in the carney & latham high - proper - motion survey , with primary masses in the range of 0.60.85 . our infrared observations detect the secondaries in 32 systems , two of which have mass ratios , , as low as . together with 11 systems previously identified as double - lined binaries by visible light spectroscopy , we have a complete sample of 62 binaries , out of which 43 are double - lined .

we report infrared spectroscopic observations of a large , well - defined sample of main - sequence , single - lined spectroscopic binaries in order to detect the secondaries and derive the mass ratio distribution of short - period binaries . the sample consists of 51 galactic disk spectroscopic binaries found in the carney & latham high - proper - motion survey , with primary masses in the range of 0.60.85 . our infrared observations detect the secondaries in 32 systems , two of which have mass ratios , , as low as . together with 11 systems previously identified as double - lined binaries by visible light spectroscopy , we have a complete sample of 62 binaries , out of which 43 are double - lined . the mass ratio distribution is approximately constant over the range to 0.3 . the distribution appears to rise at lower values , but the uncertainties are sufficiently large that we can not rule out a distribution that remains constant . the mass distribution derived for the secondaries in our sample , and that of the extra - solar planets , apparently represent two distinct populations .

0707.1700

i

our understanding of the nature of the intergalactic medium ( igm ) and its evolution as traced by the absorption features observed in the sightlines towards luminous objects like quasars , has benefitted tremendously within the past few years both from observational and theoretical advances . high - resolution studies of the lyman @xmath0 forest have been extended to very low column densities due to high - resolution echelle spectrographs on powerful 8 m class telescopes like hires ( keck ) and uves ( vlt ) @xcite . at the same time , theoretical models incorporating gas dynamics , radiative cooling , and photoionisation , have been developed that can reproduce the majority of the observed properties of the quasar absorption spectra @xcite . in this picture , baryonic gas can be encountered in a wide variety of physical conditions . within the lyman @xmath0 forest , at least at high redshift where the forest is the main repository for baryons , most of the gas resides in relatively cool ( t@xmath3 k ) low - to - medium overdensity structures that are not in dynamical or thermal equilibrium and are mostly governed by photoionisation . + the igm is expected to be highly ionised with a neutral fraction of hydrogen f ( ) @xmath4 to @xmath5 . in such a medium , metals are also highly ionised . thus , oxygen , as the most abundant intergalactic metal , may exist in the state . since the 1032/1038 doublet is observable from ground - based telescopes for redshifts beyond z@xmath6 2.0 , these transitions constitute a primary tool for studying the characteristics of the metals in the igm at high redshift . the density of the igm is sufficiently low as to allow the production of by photoionisation from the intergalactic uv and soft x - ray radiation field @xcite . indeed , absorbers seen towards higher redshifts can usually be modelled by structures that are photoionised @xcite . + due to the different wavebands required for detections at different redshifts and the strong evolution of the lyman forest , a variety of different techniques and observational strategies have to be applied for finding and identifying absorbers . detection of the 1032/1038 doublet from ground based telescopes is only possible beyond redshifts of @xmath72.0 due to the 3000 atmospheric cutoff , and thus studies of the absorber statistics below this threshold need to rely on space - based instruments . @xcite conducted the first systematic survey of absorbers at z @xmath8 1.0 , employing fos on hst to study a sample of 11 qsos , and found 12 suitable candidates of which 9 were expected to be real , thus establishing that the number density per redshift interval of these absorbers is similar to , if not greater than , that for and absorbers at the same redshift . + towards higher redshifts , despite the advantange of shifting the lines into the range for ground - based instruments , the ever increasing density of the lyman forest renders unambigious identifications of absorbers in its midst more difficult than detections made longward of the lyman @xmath0 forest . thus , most studies have relied upon high - resolution and high - signal - to - noise ratio spectra . around redshifts of z @xmath8 2.0 - 3.0 , a variety of surveys find evidence for a population of absorbers residing in low to medium overdense regions , mostly photoionised by the ambient extragalactic radiation field @xcite . the metal enrichment of the igm inferred by theses surveys ranges from @xmath9 to @xmath10 of the solar value for structures around the mean density of the universe at @xmath11 2.0 . using uves spectra for 2 lensed quasar systems , @xcite find size constraints for such intervening absorbers with lower boundaries on the kpc scale , where no or only very little variation in different lines of sights are seen this is broadly consistent with other studies of binary qso sightline inferring correlation lengths of the absorbers up to several tens of kpc @xcite . + an interesting method to statistically infer the abundance from measuring the mean optical depth associated with all pixels of the lyman @xmath0 forest with similar optical depths , was pioneered by @xcite . the authors find a general correlation of @xmath12 with @xmath13 when @xmath14 1.0 . this method was applied to by @xcite , @xcite and recently @xcite who assert the existence of in gas where the optical depth is as low as 0.1 . there is , however , some ambiguity in the interpretation of the results of such statistical pixel - to - pixel correlations . for an extensive discussion of the method see @xcite , and @xcite for a critical analysis of the results . + the mechanism for enriching the igm with metals to the level inferred by these surveys remains somewhat unclear , yet there are at least good candidates : early and wide - spread dissemination of metals by population iii star formation on pre - galactic structures at very high redshifts @xcite or winds and superwinds from starbursts within galaxies at later stages @xcite . for the latter mechanism , driving these winds out of the dense environments into the low density igm remains a crucial point of contention , and a variety of methods have been suggested ranging from supernovae @xcite , to ejection by mergers @xcite , or photoevaporation @xcite . + table 1 gives an overview of different surveys for direct detection in a variety of environments and over a wide redshift range . @xcite find 6 different systems and a further 8 potential , but blended , candidates in a single object ( hs0747 + 4259 ) at 1.46 @xmath15 1.81 , deriving a redshift path density of @xmath16 13 . @xcite analyse 230 lyman @xmath0 forest lines with a hydrogen column density n@xmath17 @xmath18 , for 7 qsos with @xmath19 2.6 , and retrieve a total of about 50 accompanying systems with secure identifications . using the capabilities of vlt and uves within the large programme : the cosmic evolution of the igm , @xcite survey 10 bright qso at 2.1 @xmath20 2.8 , and find 136 candidates with 12.7 @xmath21 14.6 in 51 systems . @xcite focus on two z@xmath22 = 2 qsos and hydrogen absorbers with log n@xmath23 14.0 . they identify 7 individual lines in 2 intervening systems in one case , and find 13 individual lines in 10 intervening systems in the other . @xcite study the frequency of absorbers associated with 35 damped and sub - damped lyman @xmath0 systems , and report 12 detections of which 9 are intervening . @xcite present 10 intervening absorbers seen towards two lensed qso pairs at a median redshift of z@xmath24 = 2.3 . our sample , residing at z@xmath25 , therefore greatly increases the redshift range of known absorbers at high redshifts . it will allow us to test expectation based upon photoionisation models like the ones presented in @xcite , thereby possibly constraining the physical conditions of the igm and the metagalactic uv / x - ray background at high - redshifts . + in this paper , we have decided to apply a direct pixel - by - pixel search for signatures of strong 1032/1038 features seen in the spectra of sdss qsos . this is , to our knowledge , the first systematic survey at high redshifts ( 2.7 @xmath205.0 ) at low resolution ( r@xmath81800 ) and low signal - to - noise ratio . we demonstrate that there is a redshift window of opportunity where the density of the lyman forest is not yet too high to obliterate the hope for finding and identifying relatively narrow metal absorbers , and that the pathlength covered by the combined sdss sample is high enough to expect finding a reasonable number of such absorbers given conservative assumptions about the metallicity of the igm , the abundance of due to photoionisation and the average signal - to - noise ratio of the qso data sample . + what type of absorbers do we expect to detect via such a direct search without a priori selecting on other transitions ? if a sightline passes through a galaxy , and if there are analogues to local examples surveyed early by @xcite and @xcite for highly ionised metals in absorption , we anticipate to detect in such cases mixed with in the gas phase inside that galaxy , like in the disk of our galaxy . furthermore , a recent , thorough examination of fuse spectra @xcite revealed the occurence of local absorbers in almost all of the more than 100 sightlines probed by extragalactic background objects , indicating a large covering fraction when a sightline passes the galaxy . while the majority of these absorbers are probably located within the galaxy @xcite , especially the high - velocity ( relative to the local standard of rest ) traces a variety of different environments and phenomena , most likely including warm / hot gas interaction in an extended galactic corona and even truly intergalactic gas within the local group @xcite . as an aside , the gas residing in the background agn host galaxy is subject to a strong uv radiation field by the central engine itself , and thus might contain more than normal galaxies . and while we are per se not interested in such absorbers for the study of intergalactic gas , we have included intrinsic absorbers , as they are being found with our algorithm as well . + from hydrodynamic simulations @xcite assert , however , that the majority of detectable lines with rest frame equivalent widths ew@xmath26 do _ not _ reside in virialised regions like galaxies , groups and clusters , but trace intergalactic gas at only moderate overdensities ( @xmath810 - 40 ) . although their estimated redshift path density of about 5 such absorbers per redshift of unity drops rapidly by a factor of at least ten when increasing the equivalent width limit to 0.35 , even that lower rate of incidence allows us to detect an appreciable number of such strong intergalactic absorbers , owing to the large redshift path length probed by the collective sdss agn sample . + to summarise , we expect to detect the signals of absorbers in a variety of environments . while this first step of finding rests upon a blind doublet search plus an alignment with lyman @xmath0 and @xmath27 lines , in order to ensure high purity of the candidate sample , we may then , in a future effort , use independent line detections of different ions to better characterise the physical stae and potentially the nature of the absorbers found here . because there are a variety of possible origins of the ovi gas , including outflows , intervening galaxies , and the contribution of the agn host galaxy , this next step is needed to arrive at a sample of igm absorbers . there is evidence for a population of absorbers that contain little , if any detectable hydrogen , as pointed out by @xcite , and it is clear that our search algorithm presented here can not detect those . however , as we anticipate the need for high - resolution follow - up of our candidates in order to confirm their nature , we might then be able to learn about this oxygen - rich subset ( type 0 of @xcite ) of absorbers as well . + the paper is organised as follows : section [ prelim ] details our preliminary analyses of whether the signal - to - noise ratio of the sdss spectra and the density of the lyman forest enables our search program . in section [ agn_sample ] we present our sdss qso sample selection , and section [ search_strategy ] gives an overview of the search algorithms we applied . before we summarise and conclude in section [ summary ] , we present the results of our search in section [ candidate_list ] . the search method developed here can be easly tailored to a variety of different ionic species . we stress that follow - up observations of the candidates we retrieve with high s / n and high resolution is neccessary to determine the reliability of our search algorithm by determining the nature of the features we detect . + throughout this study we use a cosmology with h@xmath28=71 km s@xmath29mpc@xmath29 , @xmath30 = 0.27 and @xmath31=0.73 . abundances are given by number relative to hydrogen , and vacuum wavelength are being used , if not otherwise noted .

we report the results of a systematic search for signatures of metal lines in quasar spectra of the sloan digital sky survey ( sdss ) data release 3(dr3 ) , focusing on finding intervening absorbers via detection of their doublet . here in addition , we compare our findings with simulations of the lyman forest in order to estimate the detectability of doublets over various redshift intervals . this sample is further subdivided into 3 groups according to the likelihood of being real and the potential for follow - up observation of the candidate . 69 of these reside at a velocity separation 5000 km / s from the qso , and can therefore be classified tentatively as intervening absorbers . this sample increases the number of known absorbers at redshifts beyond z 2.7 substantially .

we report the results of a systematic search for signatures of metal lines in quasar spectra of the sloan digital sky survey ( sdss ) data release 3(dr3 ) , focusing on finding intervening absorbers via detection of their doublet . here we present the search algorithm , and criteria for distinguishing candidates from spurious lyman forest lines . in addition , we compare our findings with simulations of the lyman forest in order to estimate the detectability of doublets over various redshift intervals . we have obtained a sample of 1756 doublet candidates with rest - frame equivalent width 0.05 in 855 agn spectra ( out of 3702 objects with redshifts in the accessible range for detection ) . this sample is further subdivided into 3 groups according to the likelihood of being real and the potential for follow - up observation of the candidate . the group with the cleanest and most secure candidates is comprised of 145 candidates . 69 of these reside at a velocity separation 5000 km / s from the qso , and can therefore be classified tentatively as intervening absorbers . most of these absorbers have not been picked up by earlier , automated qso absorption line detection algorithms . this sample increases the number of known absorbers at redshifts beyond z 2.7 substantially .

1609.02078

c

a detailed characterization of the thickness dependence of dzyaloshinskii - moriya interaction ( dmi ) and spin - orbit torques ( sots ) in pt@xmath0co(t)@xmath0alo@xmath1 was obtained by mean of two different experimental techniques : current - induced domain wall motion and second - harmonic hall measurements . the sign and strength of the dmi are extracted by measuring the domain wall motion stopping fields . a negative dmi , corresponding to the presence of left - handed homo - chiral dws , is observed to decrease in strength with an increasing co thickness . this confirms that the dmi originates from the pt@xmath0co interface and its measured effective strength decreases for thicker ferromagnetic layers . the extracted dmi strengths are in agreement with values reported in previous current - induced dw motion studies on similar materials stacks , however they are quantitatively different from the values extracted for the very same sample by brillouin light scattering ( bls ) measurements . the dmi values presented here are about a factor 3 smaller than the values extracted by bls . this quantitative disagreement highlights that care has to be taken when comparing the results of the two techniques and the differences possibly originate from the different length scales and physical processes probed in the two experiments . + from the analysis of the dw motion using a collective - coordinates model we extracted the driving sot - field , while the symmetry and magnitude of both damping - like and field - like sot - fields acting on a magnetic single domain state were extracted by @xmath11 hall measurements . the effective damping - like sot - field driving the dw motion is observed to increase with an increasing ferromagnetic layer thickness up to @xmath117 nm . from the @xmath11 measurements both effective fields acting on the homogeneous spin structure are found to initially increase up to a co thickness of about 1.3 nm , and then to decrease with a further increase of the ferromagnetic thickness . the differences in the thickness dependence of the effective fields obtained by the two techniques can have different origins : the non - ability of the 1d - model to capture the real dynamics of the dw internal magnetization during its motion , or the different parts of the polar angle dependence of the torques probed in the two experiments . + the similar non - monotonic thickness dependence observed for the damping - like and field - like effective fields suggests a possible common origin for the two fields : the spin - hall effect in the pt bottom layer . in this scenario , the final effective fields are defined by the transverse spin diffusion length in co , which is expected to be around 1.2 nm . accordingly , for co thicknesses smaller than the transverse spin diffusion length the effective fields are observed to increase , while for co thicknesses larger than the spin diffusion length the effective fields are observed to decrease . however , while qualitatively the behavior fits a dominating she origin we can not rule out additional effects that affect the two torques similarly leading to a similar thickness dependence . finally , the qualitatively different thickness dependence of dmi and sots shows that both effects clearly do not have a common origin in our investigated system .

we report the thickness dependence of dzyaloshinskii - moriya interaction ( dmi ) and spin - orbit torques ( sots ) in ptco(t)alo , studied by current - induced domain wall ( dw ) motion and second - harmonic experiments . from the dw motion study , is found to initially increase and then saturate with an increasing ferromagnetic thickness , while the effective sot - fields acting on a saturated magnetic state exhibit a non - monotonic behavior with increasing co - thickness .

we report the thickness dependence of dzyaloshinskii - moriya interaction ( dmi ) and spin - orbit torques ( sots ) in ptco(t)alo , studied by current - induced domain wall ( dw ) motion and second - harmonic experiments . from the dw motion study , a monotonous decay of the effective dmi strength with an increasing co thickness is observed , in agreement with a dmi originating at the ptco interface . the study of the ferromagnetic thickness dependence of spin - orbit torques reveals a more complex behavior . the effective sot - field driving the dw motion is found to initially increase and then saturate with an increasing ferromagnetic thickness , while the effective sot - fields acting on a saturated magnetic state exhibit a non - monotonic behavior with increasing co - thickness . the observed thickness dependence suggests the spin - hall effect in pt as the main origin of the sots , with the measured sot amplitudes resulting from the interplay between the varying thickness and the transverse spin diffusion length of the co layer .

1106.3042

c

let us summarize our main results . the detailed analysis of the reflection - and - transmission problem for the dirac electrons demonstrates essential differences from the conventional schrdinger case , due to the role of the berry phase . the reflection coefficient turns out to be nonanalytic function of the transverse momentum @xmath228 vanishing as @xmath361 at @xmath413 . we have presented a complete treatment of the chiral tunneling for both single and bilayer graphene in terms of a classical phase space . this gives a natural explanation of complete transmission of normally incident wave for single layer and its exponentially damped transmission in bilayer . we have also demonstrated that , for the case of nonsymmetric n - p - n junction in single layer graphene , there is total transmission for the normal incidence only , and other maxima are suppressed . our numerical studies show that for the case of bilayer there are always magic angles with total transmission .

peculiarities of the chiral tunneling are naturally explained in terms of classical phase space . in a one - dimensional geometry we have also demonstrated that , for the case of asymmetric n - p - n junction in single layer graphene , there is total transmission for normal incidence only , side resonances are suppressed .

we review chiral ( klein ) tunneling in single - layer and bilayer graphene and present its semiclassical theory , including the berry phase and the maslov index . peculiarities of the chiral tunneling are naturally explained in terms of classical phase space . in a one - dimensional geometry we reduced the original dirac equation , describing the dynamics of charge carriers in the single layer graphene , to an effective schrdinger equation with a complex potential . this allowed us to study tunneling in details and obtain analytic formulas . our predictions are compared with numerical results . we have also demonstrated that , for the case of asymmetric n - p - n junction in single layer graphene , there is total transmission for normal incidence only , side resonances are suppressed .

0901.2070

i

the task of determining good trading strategies is a fundamental problem in mathematical finance . a typical approach to this problem aims at finding the trading strategy that maximizes , for example , the final expected utility , which is defined as a deterministic , concave , and increasing function @xmath5 of the final wealth . there are , however , many applications where a utility function has to change with the underlying securities , or more generally , with the source of randomness ( say a brownian motion ) . for example , in the so - called _ optimal partial replication _ of a contingent claim , introduced by fllmer and leukert @xcite , one tries to find the trading strategy that best replicates the claim @xmath6 under a budget constraint . in particular , when the market is incomplete , it is often more beneficial to allow certain degree of shortfall " in order to reduce the super hedging cost " , a threshold for the minimum initial wealth so that super - hedging is feasible ( see , e.g. , @xcite and @xcite for more details ) . mathematically , such a shortfall risk could be measured by the expected loss @xmath7,\ ] ] where @xmath8 is the loss function " , a convex increasing function that incorporates the investor s attitude towards the shortfall @xmath9 , and the value process @xmath10 is subject to the constraint @xmath11 . such a problem can then be formulated as a utility maximization problem with a bounded _ state - dependent utility _ , in which the utility function is defined by ( cf . @xcite ) : @xmath12 in general , we can define a _ state - dependent utility _ as a function @xmath13 such that @xmath14 is a utility function for each @xmath15 . the utility maximization problem is then defined as @xmath16 : \ ; v\;{\rm is}\;{\rm admissible}\;{\rm and } \ ; v_{0}\leq{}z \right\},\ ] ] where the supreme is taken over all wealth processes @xmath17 generated by admissible trading strategies ( see section [ finmodelsect ] for a precise definition ) . the existence and essential uniqueness of the solution to the problem ( [ primalproblemreal ] ) was proved in @xcite for a general semimartingale price model using a convex duality method , built on a celebrated bipolar theorem by kramkov and schachermayer @xcite . however , this approach does not seem to shed any light on how to compute , in a feasible manner , the optimal trading strategy . this is partly due to the generality of the problem considered there . in this paper we shall consider the market model in which the price is driven by a lvy process , and we propose a more manageable dual problem with a specific domain . we should note that our method can be extended to handle more general jump - diffusion models driven by even additive processes . the problem of utility maximization can be traced back to merton @xcite-@xcite . in a brownian - driven market model , karatzas et . @xcite developed a program , known as the _ convex duality method _ , that has become one of the most powerful methods , yet relatively explicit and simple , to analyze optimal portfolio problems in non - markovian markets . they prove that the marginal utility of the optimum final wealth is proportional to the risk - neutral local martingale that minimizes a dual " problem , defined as another optimization problem with the objective function being the legendre - fenchel - type transformation of the original utility function . to be more precise , consider a minimization problem @xmath18 , \qquad y>0,\ ] ] where @xmath19 , the so - called _ dual domain or class _ , consists of ( risk - neutral ) exponential local martingales , and @xmath20 stands for the _ convex dual function _ of @xmath21 . the idea is first to find , for any @xmath22 , a minimizer @xmath23 of ( [ dualprob0 ] ) , which in turn induces a potential " optimal terminal wealth @xmath24 in the sense that the so - called weak duality relation @xmath25\ ] ] holds . if one can further show that for some @xmath26 , there exists an admissible portfolio @xmath27 such that @xmath28 , then clearly equality holds in ( [ wd ] ) ( a property typically called _ strong duality _ ) , and @xmath27 solves the original problem . customarily , finding the optimal portfolio @xmath27 relies on a variational problem for the dual value function and the existence of the minimizer @xmath29 utilizes the particular form of the market model and some general properties of the utility function . more recently , the convex duality method was further extended to a general `` jump - diffusion '' market by kunita @xcite building on an exponential representation for _ positive _ local supermartingales as well as a variational equality for the dual problem . to ensure the attainability of the dual problem , it is required that the utility function satisfies the same conditions as @xcite ( one of which is unboundedness ) , and that the dual domain @xmath19 contain all positive `` risk - neutral '' local supermartingales . the main purpose of this paper is to further extend the seminal approach of @xcite to the case of _ state - dependent , bounded _ utility functions . for simplicity , we will be contented with a market with only one stock , whose jumps are driven by a lvy process @xmath30 , but our analysis can be readily extended to more general jump - diffusion multidimensional models such as the one considered in @xcite . we should emphasize that the boundedness and potential non - differentiability of the utility function causes some technical subtleties . for example , the dual optimal process can be @xmath31 with positive probability , thus the representation theorem of kunita does not apply anymore . to get around these difficulties we shall reconsider the dual problem over an arbitrary subclass . using an exponential representation for nonnegative supermartingales due to fllmer and kramkov @xcite , we show how to construct suitable explicit dual classes associated with certain classes of semimartingales that are closed under mery s topology . to work with this last condition , we prove a closure property for integrals with respect to poisson random measures , a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to mmin @xcite . it is also worth mentioning that part of our approach relies on the fundamental characterization of contingent claims that are super - replicable ( see @xcite and @xcite ) , while that of fllmer and leukert @xcite ( see also xu @xcite ) was based on the bipolar theorem of @xcite . we feel that the convex duality approach of @xcite that we develop in this paper offers several advantages . the proofs are more direct and the dual problem might be more suitable for computational purposes since the dual class enjoys an `` explicit '' description and `` parametrization '' . in the case that ( i ) the jumps of the price process @xmath32 are driven by the superposition of finitely - many shot - noise poisson processes or that ( ii ) @xmath2 , we are even able to show that the dual solution is a risk - neutral local martingale . we would like to remark that some of our results in section [ convdualsect ] below may look similar to those in ( * ? ? * chapter 3 ) , but there are essential differences . for example , the model in @xcite exhibits only finite - jump activity , while our model allows general jumps . also , @xcite allows only downward price jumps , an assumption that seems to be crucial for the approach there , which was based on the existence of the solutions to certain stochastic differential equations ( see , e.g. , ( * ? ? ? * lemma 3.3 , proposition 3.4 ) ) . we should point out that our approach is also valid for general additive processes , including the time - inhomogeneous cases considered in @xcite . we present an argument in ( ii ) of section [ fnlrmrkssect ] to justify this point . the paper is organized as follows . in section [ finmodelsect ] we introduce the financial model , along with some basic terminology that will be used throughout the paper . the convex duality method is revised in section [ convdualsect ] , where a potential optimal final wealth satisfying ( [ wd ] ) is constructed . an explicit description of a dual class for which equality in ( [ wd ] ) holds is presented in section [ specdualclsssect ] , along with some interesting simple characterizations of the dual optimum . in particular , as it was mentioned earlier , we prove that under certain conditions in the structure of the jumps , the dual optimum is actually a local martingale and we also provide an explicit characterization of the admissible trading strategies . in section [ rplcbltysect ] we show that the potential optimal final wealth is attained by an admissible trading strategy , as the last step for proving the existence of an optimal portfolio . finally , we give some concluding remarks in section [ fnlrmrkssect ] . some necessary fundamental theoretical results behind our approach are collected in appendix [ covclsssect ] , such as the exponential representation for nonnegative supermartingales of fllmer and kramkov @xcite and the closure property for integrals with respect to poisson random measures that was previously mentioned .

we revisit merton s portfolio optimization problem under boun - ded state - dependent utility functions , in a market driven by a lvy process extending results by karatzas et . al . result we prove a _ closure property _ for integrals with respect to poisson random measures , a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to mmin . in the case that ( i ) the lvy measure of is atomic with a finite number of atoms or that ( ii ) for a process and a deterministic function , we explicitly characterize the admissible trading strategies and show that the dual solution is a risk - neutral local martingale .

we revisit merton s portfolio optimization problem under boun - ded state - dependent utility functions , in a market driven by a lvy process extending results by karatzas et . al . and kunita . the problem is solved using a _ dual variational problem _ as it is customarily done for non - markovian models . one of the main features here is that the domain of the _ dual problem _ enjoys an explicit `` parametrization '' , built on a _ multiplicative optional decomposition _ for nonnegative supermartingales due to fllmer and kramkov . as a key step in obtaining the representation result we prove a _ closure property _ for integrals with respect to poisson random measures , a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to mmin . in the case that ( i ) the lvy measure of is atomic with a finite number of atoms or that ( ii ) for a process and a deterministic function , we explicitly characterize the admissible trading strategies and show that the dual solution is a risk - neutral local martingale .

1606.05292

c

the white dwarf mass distributions from the 20 pc and sdss samples were first studied by designing monte carlo simulations with fixed standard astrophysical constraints . the good qualitative agreement between simulations and observations in figs . [ fg : f1 ] and [ fg : f4 ] confirms that the local white dwarf population is consistent with our basic knowledge of stellar and galactic evolution . we have then systematically studied the uncertainties on the input parameters of the simulations . our results suggest that given our current knowledge of stellar and galactic evolution , we can only predict the mean mass and mass dispersion of observed samples within @xmath510% . additionally , we find that the relative number of high - mass white dwarfs ( @xmath0 @xmath7 ) can only be predicted within a factor of @xmath51.5 . the main uncertainties are the assumed ifmr and the imf , followed by the sfh , the scale height variation of the galactic disk as a function total stellar age , and binaries . other biases lead to moderate changes , such as effects from missing magnetic white dwarfs ( sdss sample ) , incompleteness ( 20 pc sample ) , white dwarf model atmospheres and evolution tracks , and core composition . finally , we find that observational errors lead to fairly small uncertainties on the mean properties and high - mass fraction . from the same local white dwarf sample as the one studied in this work , @xcite have successfully extracted the local sfh in the last 10 gyr . we have verified that if we observe our monte carlo simulation @xmath101 with added observational errors , we can recover the input sfh from @xcite to a high precision with the technique described in that work . our present study does not lessen the significance of this recent determination of the sfh in the solar neighborhood . we demonstrate instead that it is difficult to extract the imf from the same sample . the first reason for this behaviour is that @xcite have used a direct method employing both the mass and cooling age of individual white dwarfs . in the present case , we consider the mass distribution integrated over all ages . the second reason why it is difficult to constrain the imf is that the imfr leads to similar effects on the mass distribution . finally , biases owing to binary populations and incompleteness directly impact the mass distributions , while @xcite have demonstrated that it does not lead to significant systematic effects on the sfh . we find that our simulations overpredict the fraction of massive white dwarfs by a factor of @xmath51.5 for both the 20 pc and sdss samples . this interpretation is consistent with earlier monte carlo simulations of similar populations ( see , e.g. , * ? ? ? this result suggests a single star imf that is significantly steeper than salpeter for the galactic disk . however , if we account for all uncertainties , a salpeter imf is not ruled out . we note that this result differs from the common view that there is an observed excess of massive white dwarfs when representing the peak in the mass distributions with a gaussian function ( see , e.g. , * ? ? ? we do not challenge this fact but only the astrophysical interpretation . our calculations suggest that gaussian functions are a poor substitute to realistic simulations including stellar and galactic evolution when attempting to understand the nature of high - mass white dwarfs . _ gaia _ will soon provide precise parallaxes for all white dwarfs studied in this work . this will supply precise independent masses leading to a better understanding of the observed mass distributions . _ gaia _ will also provide a much better picture of the completeness of the samples . for the sdss sample in particular , this includes the identification of double degenerates and the determination of precise masses for all subtypes including magnetic white dwarfs . by identifying a much larger 40 pc sample with the help of _ gaia _ and spectroscopic follow - ups , it will be possible to improve our understanding of the local sfh and kinematics as a function of age and mass . for instance , it will be possible to study the mass distribution for subsamples in total age , reducing the uncertainties due to galactic evolution effects . nevertheless , it could remain a challenge to disentangle the effects from the imf and ifmr on the mass distribution even with the _ gaia _ data , although many more white dwarfs in clusters and common proper motion pairs will be discovered allowing to improve the ifmr . our study will be useful to re - assess all uncertainties in the _ gaia _ era . little is known about the fraction of white dwarfs that are the product of mergers ( wd+wd , wd+rg , or rg+rg , where rg stands for red giant ) in the solar neighborhood . @xcite have analysed the kinematics of massive sdss white dwarfs and demonstrated that they have the characteristics of a young singly - evolved population . from multi - epoch spectroscopy of sdss white dwarfs , @xcite have calculated the wd+wd merger rate to be around @xmath102 yr@xmath103 . binary population synthesis models predict merger rates that are about twice as large @xcite . for the last 10 gyr , this leads to approximately one merger product in our main sdss subsample in the range @xmath23 ( k ) @xmath68 22,000 . on the other hand , this does not include stars that have merged before both of them became white dwarfs ( wd+rg or rg+rg ) , which could account for a larger fraction . however , there is little evidence that a merging process involving red giants would favour the production of white dwarfs that are more massive than the average @xcite . on the other hand , early investigations of the white dwarf mass distribution have identified a high - mass peak or so - called bump around 0.8 @xmath7 @xcite , and proposed a merger population as a possible cause . more recently , @xcite and @xcite have also suggested that the high - mass peak is likely due to mergers . however , these studies are not based on extensive simulations of stellar populations , which for instance @xcite are cautious to mention . nevertheless , @xcite suggests that mergers account for @xmath53% of the 20 pc sample . this is much larger than the observed wd+wd merger rate . from the simulations performed in this work , we can suggest a number of alternatives to explain features in the field white dwarf mass distribution . first of all , our standard set of simulations already predict too many massive white dwarfs . hence there is no need to invoke mergers to explain even the most massive ( non - magnetic ) white dwarfs in the current samples . this applies to the sdss mass distribution at all temperatures according to table [ fg : t2 ] . furthermore , even our standard simulations have a bump around 0.8 @xmath7 , and this is most easily seen when we neglect observational errors in fig . [ fg : f10 ] . this feature is in fact due to the two - piece polynomial fit to the ifmr of @xcite . it is not present when using any linear ifmr . we do not claim that it is a real astrophysical feature of the ifmr even though our parameterisation was motivated by theoretical imfrs @xcite . it merely demonstrates that current constraints on single star evolution and the ifmr do not rule out the presence of a high - mass peak . finally , there are number of biases that impact the field white dwarf mass distribution , the combination of which could cause the high - mass peak . we conclude that no evidence of wd+wd mergers can be found in the field white dwarf mass distribution .

each of these input ingredients has a moderate effect on the predicted mass distributions , and we must also take into account biases owing to unidentified faint objects ( 20 pc sample ) , as well as unknown masses for magnetic white dwarfs and spectroscopic calibration issues ( sdss sample ) . nevertheless , we find that fixed standard assumptions for the above parameters result in predicted mean masses that are in good qualitative agreement with the observed values . it suggests that derived masses for both studied samples are consistent with our current knowledge of stellar and galactic evolution . our simulations overpredict by 40 - 50% the number of massive white dwarfs ( for both surveys , although we can not exclude a salpeter imf when we account for all biases . furthermore , we find no evidence of a population of double white dwarf mergers in the observed mass distributions .

we revisit the properties and astrophysical implications of the field white dwarf mass distribution in preparation of _ gaia _ applications . our study is based on the two samples with the best established completeness and most precise atmospheric parameters , the volume - complete survey within 20 pc and the sloan digital sky survey ( sdss ) magnitude - limited sample . we explore the modelling of the observed mass distributions with monte carlo simulations , but find that it is difficult to constrain independently the initial mass function ( imf ) , the initial - to - final - mass relation ( ifmr ) , the stellar formation history ( sfh ) , the variation of the galactic disk vertical scale height as a function of stellar age , and binary evolution . each of these input ingredients has a moderate effect on the predicted mass distributions , and we must also take into account biases owing to unidentified faint objects ( 20 pc sample ) , as well as unknown masses for magnetic white dwarfs and spectroscopic calibration issues ( sdss sample ) . nevertheless , we find that fixed standard assumptions for the above parameters result in predicted mean masses that are in good qualitative agreement with the observed values . it suggests that derived masses for both studied samples are consistent with our current knowledge of stellar and galactic evolution . our simulations overpredict by 40 - 50% the number of massive white dwarfs ( for both surveys , although we can not exclude a salpeter imf when we account for all biases . furthermore , we find no evidence of a population of double white dwarf mergers in the observed mass distributions . [ firstpage ] white dwarfs galaxy : disk galaxy : stellar content galaxy : evolution solar neighborhood

0910.3924

i

a precise understanding of the origin of observed neutrino masses and mixing is one of the major goals of particle physics right now . a simple paradigm for understanding the smallness of the masses is the seesaw mechanism @xcite where one introduces three standard model ( sm ) singlet right - handed ( rh ) neutrinos with majorana masses @xmath4 , which mix with left - handed ( lh ) ones via the yukawa coupling @xmath5 . the resulting formula for light neutrino masses is given by @xmath6 , where @xmath7 is the dirac neutrino mass . since the sm does not restrict the majorana mass @xmath4 , we could choose this to be much larger than the weak scale thereby providing a natural way to understand the tiny neutrino masses . this is called the type i seesaw . there are several variations of this mechanism where one replaces the rh neutrino by either a sm triplet higgs field ( type ii seesaw ) @xcite or sm triplet of fermions ( called type iii seesaw ) @xcite . a great deal of attention has been devoted to testing these ideas . as far as the type i seesaw is concerned , the prospects of testing this depends on the scale @xmath4 as well as any associated physics that comes with it at that scale . it can be accessible to current and future collider experiments if the scale is not far above a tev . a different way to test the type i seesaw mechanism follows from the observation that this mechanism involves the mixing of the lh neutrinos with sm singlet heavy neutrinos as a result of which there would in general be violation of unitarity of the pontecorvo - maki - nakagawa - sakata ( pmns ) mixing matrix that describes only the mixing of the three light neutrinos . one could contemplate searching for such effects in oscillation experiments @xcite . however , in the type i seesaw case , the resulting mixing effects are of order @xmath8 and since neutrino masses are in the sub - ev range , such non - unitarity effects are too small to be observable for generic high scale seesaw models . this would also be true with tev mass rh neutrinos unless there are cancellations to get small neutrino masses from large dirac masses using symmetries ( see for example cases with @xcite ) . we note that the non - unitarity effects are also there in the type iii seesaw case but not in the type ii case even though they have other interesting effects such as lfv processes @xcite . since the testability of seesaw is intimately related to the magnitude of the seesaw scale , a key question of interest is whether there could be any theoretical guidelines for the seesaw scale . in such a case , the searches for seesaw effects in experiments could then be used to test the nature of physics beyond the standard model . it is well - known that @xcite the simplest grand unified theory ( gut ) realizations of the seesaw mechanism are based on the @xmath0 group which automatically predicts the existence of the rh neutrinos ( along with the sm fermions ) required by the seesaw mechanism . an advantage of gut embedding of the seesaw mechanism is that the constraints of gut symmetry tends to relate the dirac neutrino mass @xmath7 to the charged fermion masses thereby making a prediction for the seesaw scale @xmath4 from observations . for type i seesaw gut embedding , typical values for the @xmath4 are very high ( in the range of @xmath9 - @xmath10 gev ) . this makes both the collider as well as non - unitarity probes of seesaw impossible . the key feature that leads to such restrictions in type i seesaw case is the close link between the @xmath11 breaking rh neutrino mass and the smallness of the lh neutrino masses . a completely different realization of the seesaw mechanism is the so - called inverse seesaw mechanism @xcite , where instead of one set of three sm singlet fermions , one introduces two sets of them @xmath12 ( @xmath13 ) . in the context of @xmath0 models , since one of the two sets can be identified with the sm singlet neutrino in the @xmath0 * 16 * -representation containing matter , the others would have to be a separate set of three @xmath0 singlet fermions . due to the existence of the second set of singlet fermions ( and perhaps additional gauge symmetries e.g. @xmath0 ) , the neutrino mass formula in these models has the form @xmath14 where @xmath15 breaks the lepton number . because of the presence of this new mass scale in this theory , the seesaw scale @xmath4 can be very close to a tev even for `` large '' dirac masses . this makes the tests of this possibility in colliders much more feasible . in fact it has recently been argued that @xcite the inverse seesaw scenario can also lead to non - negligible non - unitarity effects which can be accessible at the future long - baseline neutrino oscillation experiments . there are also significant lepton flavor violation ( lfv ) effects in these models as noted many years ago in ref . these possibilities have generated a great deal of interest in the inverse seesaw models in recent days @xcite . our effort in this paper focuses on possible grand unification of inverse seesaw models . similar unification studies have been performed in ref . @xcite , but they have not addressed the non - unitarity issues . an interesting question is whether such models are necessarily compatible with grand unification when the seesaw scale is in the tev range and if so what kind of non - unitarity effects they predict . we find that it is indeed possible to embed the tev scale inverse seesaw models within a simple @xmath0 framework consistent with gauge coupling unification and realistic fermion masses . the @xmath0 symmetry helps to reduce the number of parameters in the inverse seesaw matrix , once we require degeneracy of the tev scale rh neutrinos to have successful resonant leptogenesis . within this set of assumptions , we present our expectations for the non - unitarity effects as well as consequences for lepton flavor violation which are in the testable range in future experiments . this paper is organized as follows : in section 2 , we describe the general framework of the inverse seesaw model and its embedding into a generic supersymmetric @xmath0 theory . in section 3 , we analyze the non - unitarity predictions of the inverse seesaw model . in section 4 , we investigate a specific @xmath0 breaking chain and obtain the gauge coupling unification with tev scale left - right symmetry with unification scale consistent with proton decay bounds . in section 5 , we analyze the renormalization group ( rg ) evolution of the yukawa couplings and obtain the running masses for quarks and leptons at the unification scale to check that our model leads to realistic fermion masses . in section 6 , we determine the dirac neutrino mass matrix using the results of section 5 . in section 7 , we study the implication of our model on non - unitarity effects and its phenomenological consequences . a brief summary of the results is presented in section 8 . in appendix a , we have given the expressions for the masses of the @xmath0 higgs multiplets in our model , and in appendix b , we have derived the rg equations for the quark and lepton masses and the ckm mixing elements in the context of a supersymmetric left - right model .

we show that a tev scale inverse seesaw model for neutrino masses can be realized within the framework of a supersymmetric model consistent with gauge coupling unification and observed neutrino masses and mixing . we present our expectations for non - unitarity effects in the leptonic mixing matrix some of which are observable at future neutrino factories as well as the next generation searches for lepton flavor violating processes such as . umd - pp-09 - 055 + october , 2009 * tev scale inverse seesaw in so(10 ) and leptonic non - unitarity effects * +

we show that a tev scale inverse seesaw model for neutrino masses can be realized within the framework of a supersymmetric model consistent with gauge coupling unification and observed neutrino masses and mixing . we present our expectations for non - unitarity effects in the leptonic mixing matrix some of which are observable at future neutrino factories as well as the next generation searches for lepton flavor violating processes such as . the model has tev scale and bosons which are accessible at the large hadron collider . umd - pp-09 - 055 + october , 2009 * tev scale inverse seesaw in so(10 ) and leptonic non - unitarity effects * +

1402.3347

i

electronic relaxation rates contain important information about the excitations in a metallic system . the single - particle relaxation rate , @xmath1 , determines the lifetime of quasi - particles as well as the thermal conductivity @xmath2 ; the transport relaxation rate , @xmath3 , the electrical conductivity via the drude formula @xmath4 . here @xmath5 and @xmath6 are the conduction electron effective mass and number density , respectively , @xmath7 is the fermi velocity , and @xmath8 is the specific heat . there are various contributions to these relaxation rates , including those from the scattering of electrons by propagating , or particle - like , excitations . for instance , the coupling of longitudinal phonons to conduction electrons leads to the well - known bloch @xmath9-behavior of the electrical resistivity ; the corresponding effect in the single - particle relaxation rate is a @xmath10-law.@xcite in magnetically ordered phases , the coupling of the conduction electrons to any magnetic goldstone modes contributes to the relaxation rates . in isotropic heisenberg ferromagnets , the goldstone modes are the ferromagnons with a frequency - momentum relation @xmath11 . they have been found to contribute a @xmath0 term to the transport relaxation rate.@xcite in helimagnets,@xcite which have a helically modulated magnetic ground state , the corresponding goldstone mode ( the helimagnon ) has been shown to lead to a term in the electrical resistivity that is proportional to @xmath12 in the low - temperature limit.@xcite in antiferromagnets , the corresponding contribution is known to be proportional to @xmath10.@xcite these results all hold for three - dimensional systems , which is the only physical dimension in which long - range magnetic order exists . for later reference we note , however , that the various power laws quoted above are dimensionality dependent . for instance , in a generic dimension @xmath13 the contribution from ferromagnons to the resistivity is proportional to @xmath14 . in addition to the scattering by propagating excitations , there are contributions to the transport coefficients due to excitations with a continuous spectrum . the best known example is the one due to the coulomb interaction between the electrons . in simple metals it leads to a @xmath0 contribution to both the single - particle rate and the transport rate , i.e. , a lower power than the phonon contribution . however , since the relevant energy scale is the fermi energy @xmath15 or fermi temperature @xmath16 ( we use units such that @xmath17 ) , which is much larger than the debye temperature , this dominates the phonon contribution only at very low temperatures.@xcite in metals that display ferromagnetism the latter statement is not necessarily true , due to fermi surfaces that consist of multiple sheets , and the issue of both the temperature dependence and the prefactor of the coulomb contribution to the electrical resistivity is complicated . these are old questions@xcite that recently have been revisited in the context of quantum criticality and exotic metals.@xcite another example is the scattering of electrons in ferromagnets by both longitudinal magnetization fluctuations and the so - called stoner excitations in the transverse channel.@xcite the latter are dissipative , non - hydrodynamic transverse excitations in addition to the propagating spin waves . in a random - phase approximation , the contribution to the resistivity from these dissipative excitations , both longitudinal and transverse , was shown in ref . to result in a @xmath0 behavior with a prefactor that is inversely proportional to the magnetization . this is qualitatively the same behavior these authors found for the scattering by magnons , and it agrees roughly with the trend observed in fe , co , and ni.@xcite as we will see , this conclusion , as far as the magnons is concerned , is true only in a temperature window , but not at asymptotically low temperature . it should be stressed , however , that this similarity is somewhat accidental and approximation dependent even in the regime where it holds . for instance , the power law of the magnon contribution is dimensionality dependent , as mentioned above , while the contribution from the dissipative excitations is not . also , the prefactor of the former is essentially determined by the dispersion relation of the magnons , which is governed by very general principles , whereas the latter is dependent on many non - universal details . nevertheless , the fact that various contributions of very different nature to the relaxation rates show a @xmath0 temperature dependence makes the interpretation of the experimentally observed @xmath0 behavior of the electrical resistivity in many ferromagnetic materials difficult.@xcite at the same time , the electrical resistivity is a basic physical property that is very useful , for instance , for tracking and identifying magnetic phase transitions,@xcite and establishing its behavior in the ferromagnetic phase as a benchmark is important . in this paper we focus on the magnon contribution to the relaxation rates in ferromagnets and show that for this process the established result is qualitatively incorrect at asymptotically low temperatures ; instead of a @xmath0 temperature dependence , the magnon contributions to both the electrical resistivity and the thermal resistivity display an exponential behavior . a problem with the established ferromagnetic result was first noted in ref . , which showed that the results for the helimagnetic and ferromagnetic cases are not mutually consistent : if one considers the ferromagnetic limit of the helimagnetic ground state , by letting the wavelength of the helix go to infinity , one finds that the leading contribution to the relaxation rate , which would yield a power law , vanishes . what is left behind is an exponential behavior of the form@xcite 1/ _ ( t^2/)(-t_0/t ) , [ eq:1.1 ] where the temperature scale @xmath18 depends on the conduction band splitting or `` stoner gap '' @xmath19 or , equivalently , the magnetization,@xcite and on the fermi energy @xmath15 . this result is surprising , given that the relaxation rates due to magnetic goldstone modes in both helimagnets and antiferromagnets show a power - law behavior . the purpose of this paper is to discuss this problem , and to elaborate on the brief remarks that were given in appendix d of ref . . we will show that the asymptotic low - temperature behavior of both the transport relaxation rates due to magnons is indeed exponential of the form shown in eq . ( [ eq:1.1 ] ) , with @xmath20 with @xmath21 the spin - wave stiffness , which itself depends on @xmath19 , and @xmath22 and @xmath15 the fermi wave number and fermi energy , respectively . this result holds in an asymptotic regime defined by @xmath23 . however , in a sizable pre - asymptotic temperature window given by @xmath24 one recovers the @xmath0 behavior found previously . the reason for the exponential asymptotic result is the fact that , in a ferromagnet , the goldstone modes are purely transverse , and therefore couple only quasi - particles in different stoner bands . the effective electron - electron - interaction due to ferromagnon exchange therefore describes purely inter - stoner - band scattering , which leads to an activated process . in contrast , in helimagnets and antiferromagnets there is an intra - stoner - band coupling which leads to a power law . this vanishes as the characteristic wave number of the magnetic order goes to zero in the ferromagnetic limit . these results are valid for all metallic ferromagnets , whether or not the magnetism is caused by the conduction electrons themselves or by localized electrons in a different band . we will refer to such systems as `` itinerant ferromagnets '' and `` localized - moment ferromagnetes '' , respectively . in the main body of the paper we will consider a very general model that does not depend on which of these two cases is realized , and that uses only very general properties of ferromagnets that follow from symmetry arguments . a more specific stoner - type model for the case of itinerant ferromagnets is considered in an appendix . this paper is organized as follows . in sec . [ sec : ii ] we derive an effective action that describes an effective electron - electron interaction due to the exchange of ferromagnons . the effective action is valid for calculating relaxation rates to first order in the magnon propagator , and it holds for both itinerant and localized - moment ferromagnets . in sec . [ sec : iii ] we use this model to calculate the single - particle relaxation time , and in sec . [ sec : iv ] we calculate the transport relaxation time , and hence the electrical conductivity , by evaluating the pertinent kubo formula in an approximation that is equivalent to the boltzmann equation . in sec . [ sec : v ] we discuss our results . in appendix a we recall the stoner - moriya mean - field treatment of itinerant ferromagnets . in appendix b we recall the cases of electron - electron and electron - phonon scattering in non - magnetic metals , and cast them in a language that illustrates why our general method works even in the case of itinerant ferromagnets .

we show that the magnon - exchange contribution to the single - particle and transport relaxation rates in ferromagnetic metals , which determine the thermal and electrical conductivity , respectively , at asymptotically low temperature does not obey a power law as previously thought , but rather shows an exponential temperature dependence . we motivate and derive a very general effective theory for metallic magnets that we then use to derive these results . comparisons with existing experiments are discussed , and predictions for future experiments at low temperatures are made .

we show that the magnon - exchange contribution to the single - particle and transport relaxation rates in ferromagnetic metals , which determine the thermal and electrical conductivity , respectively , at asymptotically low temperature does not obey a power law as previously thought , but rather shows an exponential temperature dependence . the reason is the splitting of the conduction band that inevitably results from a nonzero magnetization . at higher temperatures there is a sizable temperature window where the transport rate shows a temperature dependence , in accord with prior results . this window is separated from the asymptotic regime by a temperature scale that is estimated to range from tens of mk to tens of k for typical ferromagnets . we motivate and derive a very general effective theory for metallic magnets that we then use to derive these results . comparisons with existing experiments are discussed , and predictions for future experiments at low temperatures are made .

1402.3347

c

to summarize our results , we have presented a very general theory of electron relaxation due to the exchange of magnons in metallic ferromagnets . the theory is valid for both itinerant ferromagnets , where the magnetization is due to the conduction electrons themselves , and for localized - moment ferromagnets , where the magnetization is due to localized spins in a different band . we have found that at asymptotically low temperatures , below a temperature scale @xmath18 , both the single - particle relaxation rate and the transport relaxation rate are exponentially small . this behavior carries over to the magnon - exchange contributions to the thermal and electrical resistivities , which are determined by these respective rates . the exponential temperature dependence is a direct consequence of the split conduction band in a metallic ferromagnet . in a preasymptotic temperature regime @xmath87 , with @xmath67 close to the exchange splitting , we recover the @xmath0 behavior of the transport rate that was found in ref . . the single - particle rate is proportional to @xmath99 in this regime . for @xmath135 the two rates both show a linear temperature dependence . we start our discussion of these results by recalling the physical reason for the exponential dependence at low temperatures . -0 mm is the stoner gap , and @xmath136 is the exchange splitting . @xmath137 and @xmath138 are the smallest and largest transferrable wave numbers , respectively . see the text for more explanation.,title="fig:",width=321 ] figure [ fig:3 ] schematically shows the split conduction band ( a ) , and the densities of states for the up ( + ) and down ( - ) spin electrons ( b ) , for the case of a spherical fermi surface . since the magnons couple only electrons with opposite spin , the smallest transferrable wave number is @xmath139 . given the magnon dispersion relation , @xmath140 , this translates into a smallest transferrable energy @xmath141 , and since the magnon stiffness coefficient @xmath21 is itself roughly proportional to @xmath136 , we have @xmath142 . for temperatures @xmath23 the relaxation rates will thus show activated behavior with an activation energy @xmath18 . the exponential behavior is multiplied by a power law that can not be captured by elementary arguments . the largest momentum transfer is given by @xmath143 , and the corresponding largest energy transfer is @xmath144 . @xmath67 is the fundamental magnetic energy scale , analogous to the debye temperature @xmath145 in the case of electron - phonon coupling . @xmath18 has no analog in the electron - phonon problem . for @xmath146 the transport - relaxation rate is small compared to the single - particle rate by a factor of @xmath147 . this is analogous to the electron - phonon case , where the corresponding factor is @xmath148 . the difference between our results and those of ueda and moriya , ref . , can be traced to the fact that these authors neglected the exchange splitting in the final stages of their calculation . as a result , they obtained a @xmath0 behavior of the transport relaxation rate at low temperatures , which in fact is valid only for temperatures larger than @xmath18 . note that this discrepancy pertains to the magnon or spin - wave contribution to the electrical resistivity only . the contributions from dissipative excitations , which we have not discussed , have been found to be unaffected by the exchange splitting and proportional to @xmath0 even at asymptotically low temperatures.@xcite for the power - law behavior at @xmath149 the quadratic spectrum of the magnons is important , and also the coupling of the electrons to the magnetic fluctuations . comparing with the case of helical magnets,@xcite we notice one important difference with respect to the latter . in either case the goldstone mode is a phase fluctuation , but in the ferromagnon case the electron spin density couples directly to the phase , whereas in the helimagnon case the coupling is to the gradient of the phase . this is because in the helimagnon case the dominant low-@xmath99 contribution to the scattering rates comes from intra - stoner - band scattering . within a given band , the phase itself has no physical meaning , and the coupling therefore involves a gradient . in the ferromagnetic case , on the other hand , we deal with inter - stoner - band scattering . the coupling therefore effectively is to the difference of two phases , which does have a physical meaning . we note in passing that this latter notion also manifests itself in a spin josephson effect , see ref . . we now turn to estimates of the values of @xmath67 and @xmath18 . to get an idea about the order of magnitude of these temperature scales , let us first consider the fictitious case of simple ( i.e. , single - conduction - band ) metals with magnetic properties as in the classic `` high - temperature '' ferromagnets nickel , cobalt , and iron . the values of the exchange splitting in these materials , as determined by photoemission , are @xmath150 ev , @xmath151 ev , and @xmath152 ev , respectively.@xcite values for the spin - stiffness coefficient @xmath21 in mev@xmath153 obtained from neutron scattering are @xmath154 for ni , @xmath155 for co , and @xmath156 for fe.@xcite with a generic value @xmath157 for the fermi wave number , and @xmath158 k for the fermi energy , eqs . ( [ eq:2.16 ] ) and ( [ eq:2.17 ] ) yield @xmath159 k for these materials , and @xmath160 mk for ni , @xmath161 k for co , and @xmath162 k for fe . estimates of the ratio @xmath70 using the relation ( [ eq:2.18b ] ) yields similar results . notice that the prefactor @xmath163 in eq . ( [ eq:4.18 ] ) is of order unity , so the prefactor of the @xmath0 behavior of the resistivity is larger than the fermi - liquid @xmath0 contribution ( see eq . ( [ eq : b.7 ] ) ) by roughly a factor of @xmath164 in a single - band model . also of interest are weak ferromagnets , such as mnsi,@xcite or ni@xmath165al , where @xmath166 mev@xmath153 ( mnsi)@xcite and @xmath167 mev@xmath153 ( ni@xmath165al),@xcite respectively . the magnetic moments , @xmath168 per formula unit for mnsi,@xcite and @xmath169 for ni@xmath165al,@xcite are about two thirds and one third , respectively , of that of ni . given the observed near - linear correlation between the magnetic moment and the exchange splitting,@xcite this suggests @xmath170 ev for mnsi,@xcite , and @xmath171 ev for ni@xmath165al . if we use again @xmath157 and @xmath158 k , this yields @xmath172 k and @xmath173 mk for mnsi , and @xmath174 k and @xmath175 mk for ni@xmath165al . in reality , all of these materials are transition metals , or compounds containing transition metals , with a complicated band structure and fermi surfaces that consist of multiple sheets . one consequence of this is that the electron - electron scattering contribution to the electrical resistivity is likely much larger than a single - band model would imply , and it has been suggested that it makes the largest contribution to the observed @xmath0 behavior at low temperatures.@xcite the reason is that different band edges have different distances from the common chemical potential , which in effect leads to different fermi temperatures . depending on whether or not the various scattering processes flip the electron spin , and whether or not they couple different sheets of the fermi surface , the relaxation rates or the relaxation times may be additive , which leads a complicated structure of the overall resistivity . in addition , there are the contributions from the dissipative spin excitations , which also are proportional to @xmath0.@xcite as a result , the low - temperature transport rate in fe , ni , and co is about 100 times larger than one would expect from the coulomb contribution in a single - band model with a single fermi temperature of about @xmath176k.@xcite @xmath67 , on the other hand , is largely unaffected by a complicated band structure : it is given by @xmath21 times the largest possible momentum transfer squared , see sec . [ subsec : ii.c ] , and in a good metal the latter is on the order of @xmath177 , with @xmath55 the lattice constant , which is close to the value of @xmath178 for a single spherical fermi surface that yields the same electron density . the estimates of the temperature scale @xmath67 , which is the magnetic analog of the debye temperature for phonons , given above are therefore model independent and depend only on the experimentally measured spin stiffness coefficient . as a result , we expect the magnon contribution to the electrical resistivity in fe , ni , and co at temperatures @xmath179 to be about an order of magnitude _ less _ than the combined contribution from the coulomb interaction and the dissipative magnetic excitations . in mnsi and ni@xmath165al @xmath67 is much lower and the magnon scattering is accordingly stronger . however , the observed prefactors of the @xmath0 term in the resistivity of mnsi and ni@xmath165al are orders of magnitude larger than even the ones in fe , ni , and co , and the same is true for the weak ferromagnet zrzn@xmath180.@xcite the prefactor @xmath163 in eq . ( [ eq:4.18 ] ) is expected to be of @xmath125 not just in model calculations , but also in real materials , since both @xmath181 and @xmath67 correlated roughly with the magnetization . given the above discussion of the relatively narrow range of plausible values of @xmath67 , we conclude that the experimental value of the prefactor of the @xmath0 term in the electrical resistivity of weak ferromagnets can not possibly be explained by electron - magnon scattering . we emphasize again , however , that these considerations do not take into account the scattering of electrons by dissipative magnetization fluctuations , which lead to a @xmath0 contribution to the resistivity even at low temperatures and whose prefactor is not as universal as that of the magnon - exchange contribution . a corresponding statement holds for the coulomb contribution . for @xmath18 the influence of the band structure is more complicated . consider the effective potential given by eqs . ( [ eq:3.4b ] - [ eq:3.4d ] ) . if the up - spin and down - spin electrons , respectively , belong to different bands with different effective masses , then there will be a lower cutoff for the frequency @xmath110 even in the limit of a vanishing stoner gap , @xmath85 . for magnon - exchange scattering between electrons in stoner - subbands of the same band , on the other hand , the structure of the calculations in secs . [ sec : iii ] and [ sec : iv ] is unchanged . we therefore expect different values of @xmath18 for the various scattering processes that involve electrons on different sheets of the fermi surface . the following picture now emerges . with decreasing temperature , contributions to the magnon - exchange part of the electronic scattering rate will sequentially freeze out as the temperature drops below a sequence of temperature scales @xmath18 . rough estimates for the lowest of these temperature scales have been given above ; estimating the higher ones requires a detailed analysis of the band structure . below this lowest @xmath18 the magnon contribution to both the transport rate and the single - particle rate will be exponentially small , leaving the coulomb contribution and the one from dissipative magnetization fluctuations as the most obvious candidates for a @xmath0 behavior . experimentally , this is expected to manifest itself in a distinct temperature dependence of the prefactor of the @xmath0 term in the electrical resistivity . it is desirable for the relevant temperature scales to be small enough that phonon contributions are negligible . in that respect , fe , ni , and co are not ideal . in mnsi , the helical nature of the magnetic phase is expected to manifest itself on the temperature scale given by @xmath18 . this leaves ni@xmath165al , or other true weak ferromagnets as the most promising candidates for observing this consequence of the exchange splitting in a metallic ferromagnet . we stress , however , that according to the above discussion the magnon contribution to the electrical resistivity in weak ferromagnets is likely dwarfed by other contributions . another possible effect of a complicated band structure is that there may be points or lines in reciprocal space where the two stoner band cross . this will weaken the exponential suppression of the relaxation rates , but the weakening will depend on the nature of the crossing . we finally mention that the interplay of quenched disorder with the scattering processes discussed above constitutes an interesting problem that is likely important for a quantitative understanding of real materials . for fairly strong disorder , @xmath182 with @xmath183 the elastic scattering time , the theory of ref . applies and it is easy to see that there is no exponential suppression of the magnon contribution to the relaxation rates at low temperature . a complete discussion of disorder effects constitutes a separate problem . we thank achim rosch for discussions . this work was supported by the nsf under grants number dmr-09 - 01952 and dmr-09 - 01907 . part of this work was performed at the aspen center for physics and supported by the nsf under grant number phys-1066293 .

the reason is the splitting of the conduction band that inevitably results from a nonzero magnetization . at higher temperatures there is a sizable temperature window where the transport rate shows a temperature dependence , in accord with prior results . this window is separated from the asymptotic regime by a temperature scale that is estimated to range from tens of mk to tens of k for typical ferromagnets .

we show that the magnon - exchange contribution to the single - particle and transport relaxation rates in ferromagnetic metals , which determine the thermal and electrical conductivity , respectively , at asymptotically low temperature does not obey a power law as previously thought , but rather shows an exponential temperature dependence . the reason is the splitting of the conduction band that inevitably results from a nonzero magnetization . at higher temperatures there is a sizable temperature window where the transport rate shows a temperature dependence , in accord with prior results . this window is separated from the asymptotic regime by a temperature scale that is estimated to range from tens of mk to tens of k for typical ferromagnets . we motivate and derive a very general effective theory for metallic magnets that we then use to derive these results . comparisons with existing experiments are discussed , and predictions for future experiments at low temperatures are made .

hep-th0701075

c

in this paper we studied a general class of symmetries relating partition functions of a family of classical spin models which generalises the ising model and z(2 ) lattice gauge theory . we interpreted these theories algebraically in terms of the structure constants of a vector space @xmath0 equipped with algebra and coalgebra structures , using a formalism reminiscent from topological quantum field theories , and proved that to any change of basis of @xmath0 there is an associated symmetry between these models . the well known kramers and wannier dualities of @xcite were shown to be special cases of this formalism . we studied these dualities on two- and three - dimensional triangulations , extending results known for the case of square and cubic lattices . in addition , a new class of continuous symmetry transformations involving generalised z(2 ) gauge theories in two dimensions was developed . in two dimensions , we found the following results . it is well known that pure gauge theories in two dimensions are exactly soluble . as a simple application of our formalism , we have described a change of basis of @xmath0 which trivialises the theory and yields a solution for the partition function which is valid for any triangulation . the duality of the 2d higgs - gauge to the ising model coupled to a magnetic field was studied on general triangulations . explicit expressions for the relation between the partition functions on general lattices were given , in terms of simple combinatorial factors such as the number of links and faces in the lattice . we also proved the existence of new symmetries relating the z(2 ) higgs - gauge theory to a generalised model described by three coupling constants , which describe a plaquette interaction , a magnetic field term , and an additional ising interaction . the new symmetry transformations describe continuous transformations of these coupling constants . in three dimensions , we studied the duality from the z(2 ) pure gauge theory to the 3d ising model on finite triangulations . we derived explicit expressions for the coefficients which relate the partition functions , in a manner which is valid for general triangulations . the expression depends on the topology of the lattice only through simple combinatorial properties , namely , the number of faces and links of the lattice . we also considered a modified z(2 ) higgs - gauge theory on finite triangulations , for which the higgs coupling @xmath129 is variable along the lattice , being proportional to the number @xmath21 of faces meeting at the link @xmath27 , @xmath310 . this theory was found to be dual to an ising model with a variable inverse temperature , coupled to a magnetic field , and to an additional field which describes an area - dependent energy term in the action . the method we have used to develop these symmetries can be applied to any theory which admits an algebraic interpretation similar to the one given in @xcite for the case of z(2 ) pure gauge theory on triangulations . whether this is the case of more realistic gauge theories is an interesting question . in particular , it is natural to conjecture that dualities in z(n ) gauge theories can be formulated in a similar fashion . the extension to continuous gauge groups also deserves investigation . the mathematical prescriptions we have used do not pose any obstruction for the application to the case of non - commutative gauge groups . duality relations are difficult to be formulated in this case , and our prescriptions might be of help in the study of this subject .

the theories are interpreted algebraically in terms of the structure constants of a bidimensional vector space with algebra and coalgebra structures , and it is shown that for any change of basis in there is a related symmetry between such models . the classical kramers and wannier dualities are described as special cases of these transformations .

we study a class of duality transformations in generalised z(2 ) gauge theories and ising models on two- and three - dimensional compact lattices . the theories are interpreted algebraically in terms of the structure constants of a bidimensional vector space with algebra and coalgebra structures , and it is shown that for any change of basis in there is a related symmetry between such models . the classical kramers and wannier dualities are described as special cases of these transformations . we derive explicit expressions for the relation between partition functions on general finite triangulations for these cases , extending results known for square and cubic lattices in the thermodynamical limit . a class of symmetry transformations in which the gauge coupling changes continuously is also studied in two dimensions .

0709.2926

i

we start with an informal description of the model we study in this paper . particles live in @xmath4 and evolve in discrete time . at each time , every particle is substituted by ( possibly more than one ) offspring which are placed in neighboring sites , independently of the other particles . the rules of offspring generation depend only on the location of the particle . the collection of those rules ( so - called the _ environment _ ) is itself random , it is chosen randomly before starting the process , and then it is kept fixed during all the subsequent evolution of the particle system . this model considered in this paper was introduced in @xcite . the random environment here affects both branching and transition mechanisms , and ( as opposed to the models of @xcite ) the _ immediate _ descendants of a particle are not supposed to be independent . in @xcite we proved a dichotomy for recurrence / transience , depending only on the support of the environmental law , and we gave sufficient conditions for recurrence and transience . in the recurrent case , the tails of the hitting times are studied and a shape theorem is obtained in a preliminary form . the recurrence / transience classification was later completed in @xcite . we refer also to @xcite for other work related to branching random walks in random environment . now , let us look at the subject of this paper from a different angle . for @xmath5 , let @xmath6 be the transition probabilities from @xmath7 to its nearest neighbors , and @xmath8 . consistently with the notation introduced later in this section , we denote by @xmath9 the collection of coefficients @xmath10 ( as explained below , @xmath11 stands for the mean offspring in @xmath7 ) , and by @xmath12 the corresponding discrete markov operator , @xmath13.\ ] ] in this paper we will study for @xmath14 the solution @xmath15 of the equation @xmath16 it is easily checked , for instance by the discrete feynman - kac formula , that the solution @xmath17 is given by the expectation @xmath18 of the number @xmath19 of particles in @xmath20 at time @xmath21 in a discrete - time branching random walk starting from a single individual located at site @xmath7 at time 0 . the evolution rule of this branching random walk is that particles at @xmath7 branch with an average of @xmath11 children which then move independently to a neighboring site randomly chosen from @xmath6 . we will be interested in the case where the coefficients @xmath22 are given by a stationary and finitely dependent random field . the model has other possible formulations . in the case of continuous time , the above equation becomes the parabolic partial differential equation @xmath23 with @xmath24 the branching rate . in our case the mean number of offspring is greater than or equal to @xmath25 and bounded from above , or , equivalently , @xmath24 is nonnegative and bounded . in the case where @xmath6 are the simple random walk transition probabilities @xmath26 , so that @xmath27 is the standard laplace operator , this equation is known as the parabolic anderson problem , and has also continuous - space versions , see @xcite and @xcite . these models have motivated a huge scientific activity , with particular interest on localization and intermittency ( e.g. @xcite ) and survival analysis @xcite , leading to fine pictures in the different cases of bounded or unbounded @xmath28 s . we stress that the markov operator @xmath12 is random in the present paper , a case that seems not to have been studied so far . moreover , @xmath12 is non symmetric , this makes the model non - reversible with a possibly large drift , and prevents the use of a spectral theory as in the above references . the present paper represents a step towards the understanding of the equation ( [ eq : discrete_anderson ] ) . we will prove that the solution @xmath17 behaves like @xmath29 as @xmath30 ( see remark [ rem_complete_shape ] where we comment on the function @xmath31 ) . we will even get into the finer study of the population size @xmath32 itself , and we prove the same asymptotics under the assumption that particles can not die . hence , the growth of the population is rather smooth at the coarse scale @xmath33 . the occurrence of shape theorems and local growth rate goes back at least to @xcite and @xcite for branching random walks , and to @xcite in random environment . in fact , our model is slightly more general than described above . as mentioned in the beginning of this section , the branching and the displacement may be dependent . also , the environment that we consider is not necessarily independent , but we allow for a finite range dependence . we believe that the results extend to more general dependence , but considering this case would require an important additional technical work . * the model . * we now describe the model , keeping the notations of @xcite whenever possible . let @xmath34 and @xmath35-s be the coordinate vectors of @xmath4 . we use the notation @xmath36 for @xmath37 ( or @xmath38 ) . define the distance between two sets @xmath39 ( or @xmath40 ) by @xmath41 fix a finite set @xmath42 such that @xmath43 for all @xmath44 . define @xmath45 and for @xmath46 put @xmath47 ; note that @xmath48 for all @xmath46 . furthermore , let @xmath49 be the set of all probability measures @xmath50 on @xmath51 : @xmath52 then , suppose that @xmath53 is a stationary ergodic random field , and denote by @xmath54 the probability and expectation with respect to @xmath22 . throughout this paper we suppose that this field is also _ finitely dependent _ , that is , the following condition holds : * condition i. * there exists a positive number @xmath55 such that for any two sets @xmath40 with @xmath56 the following holds : the sigma - algebra generated by @xmath57 is independent under @xmath58 from the sigma - algebra generated by @xmath59 . note that @xmath60 corresponds to the case of independent identically distributed environment . the collection @xmath61 is called _ the environment_. given the environment @xmath22 , the evolution of the process is described in the following way : start with one particle at some fixed site of @xmath4 . at each integer time the particles branch independently using the following mechanism : for a particle at site @xmath38 , a random element @xmath62 is chosen with probability @xmath63 , and then the particle is substituted by @xmath64 particles in @xmath65 for all @xmath66 . note that the population never gets extinct , since every individual has at least one direct descendant . for the process starting from one particle at @xmath7 , let us denote by @xmath67 the number of particles in @xmath68 at time @xmath21 . define the random variable @xmath69 i.e. , @xmath70 is the total number of particles at moment @xmath21 for the process starting from @xmath7 . we denote by @xmath71 the ( so - called quenched " ) probability and expectation for the process starting from @xmath7 in the fixed environment @xmath22 . we use the notation @xmath72 = { { \mathbb e}}\,{{\mathtt p}_{\omega}}^x[\,\cdot\,]$ ] for the annealed law of the branching random walk in random environment , and @xmath73 for the corresponding expectation . also , sometimes we use the symbols @xmath74 without the corresponding superscripts when it can create no confusion ( e.g. when the starting point of the process is indicated elsewhere ) . throughout this paper , and often without recalling it explicitly , we suppose that the two conditions below are fulfilled : * condition b. * @xmath75>0.\ ] ] * condition ue . * for some @xmath76 , @xmath77 = 1.\ ] ] condition b ensures that the model can not be reduced to random walk without branching , and condition ue is a natural uniform ellipticity condition which ensures that the walk is really @xmath0-dimensional . in this paper , the weaker ellipticity condition e of @xcite will usually not be enough for our purposes . in fact , we believe that most of our results do not generally hold if one only assumes condition e. for technical reasons we need also the following two conditions : * condition d. * there exists a positive constant @xmath78 such that the expectation of the total number of the immediate descendants of any particle is at most @xmath78 , i.e. , @xmath79=1 $ ] . * condition a. * there exist @xmath80 with @xmath81 even and @xmath82 such that @xmath83>0 $ ] . we refer to condition a as the `` aperiodicity condition '' because , without it , the process starting from the origin would live on even sites at even times , and on odd sites at odd times . if ( with @xmath84 of condition a ) a site @xmath68 is such that @xmath85 , we say that this site is an _ aperiodic _ site , and when @xmath86 , we say that this site is @xmath87-aperiodic . we briefly mention that suitably adjusted versions of all our results are also true without condition a ; the proofs are either the same or even simpler , since we do not have to care about searching for the aperiodic sites , e.g. the proofs of theorems [ t_shape_reach ] and [ t_complete_shape ] . [ rem : usuel ] a particular case of the model considered here is the usual construction of the branching random walk , that was already mentioned in the beginning of this paper : for each @xmath7 , specify the transition probabilities @xmath88 , @xmath66 , and branching probabilities @xmath89 , @xmath90 . a particle in @xmath7 is first substituted by @xmath91 particles with probability @xmath89 , then each of the offspring jumps independently to @xmath65 with probability @xmath88 . the pairs @xmath92 are chosen according to some i.i.d . field on @xmath4 . in our notations , @xmath93 is a mixture of multinomial distributions on @xmath94 : @xmath95 * statement of the results . * all through the paper , we will assume the above five conditions . following @xcite , we define the notions of transience and recurrence : [ def_rec ] for the particular realization of the random environment @xmath22 , the branching random walk is called recurrent if @xmath96=1.\ ] ] otherwise , the branching random walk is called transient . the following result is a consequence of propositions 1.2 , 1.3 , and theorem 1.6 of @xcite , and also theorem 3.2 of @xcite ; in section [ s_ind_rw ] , we comment about the validity of ( i ) and ( ii ) below in the non - i.i.d . case @xmath97 . [ rec / tr ] we have either : * for @xmath58-almost all @xmath22 , the branching random walk is recurrent , in which case @xmath98=1 $ ] for all @xmath38 , or : * for @xmath58-almost all @xmath22 , the branching random walk is transient , in which case @xmath98=0 $ ] for all @xmath38 . the classification criterion : in the case of an i.i.d . environment , i.e. , @xmath60 , the branching random walk in random environment is transient if and only if there exist @xmath99 and @xmath100 such that @xmath58-almost surely we have @xmath101 where @xmath102 is the mean number of particles sent to @xmath66 by one particle at the origin . it is interesting to observe that , in the case of an i.i.d . environment , one has a simple explicit criterion of transience / recurrence for the branching random walk in random environment ; however , for the many - dimensional random walk _ without branching _ in random environment the problem of finding such a criterion is still far from being solved . in @xcite one can find more evidence that branching makes random walks in random environment `` simpler '' ; see , for instance , the results about the tails of first hitting times . now , we are ready to formulate the main results of this paper . in what follows , for any @xmath103 , @xmath104 is the closure of @xmath105 , and @xmath106 is the interior of @xmath105 . first , we obtain a shape result about the sites that _ can _ contain a particle at time @xmath21 . [ t_shape_reach ] there exists a compact convex set @xmath107 such that for any @xmath108 , for almost all @xmath22 there exists @xmath109 such that @xmath110 = 1\ ] ] and @xmath111 < 1 \qquad \text { for all } x\in{{\mathbb z}}^d\cap ( 1-{\varepsilon})mf\ ] ] for all @xmath112 . next , we characterize the ( quenched ) mean local number of particles . [ t_local_size ] there exists a convex downwards , continuous function @xmath113 such that for any closed @xmath114 @xmath115 as @xmath116 . the function @xmath31 is called the local growth exponent for the branching random walk . denote @xmath117 ; by the convexity of @xmath31 , the set @xmath118 is compact and convex . all through , convex functions will mean convex downwards . [ t_rec_trans ] the branching random walk in random environment is recurrent if and only if @xmath119 . note that the border case @xmath120 is transient . note also that , from the property ( [ sup_beta>0 ] ) below , one obtains that @xmath119 if and only if @xmath121 . thus , given @xmath118 , one can determine whether the branching random walk is recurrent or transient . the next result does not only tell us , similarly to theorem 1.10 of @xcite , where the particles are located at time @xmath21 , but it also gives an important information about the local size of the population . [ t_complete_shape ] for any closed @xmath122 , @xmath123 as @xmath116 , a.s . [ rem_complete_shape ] ( equivalence of models . ) the local growth exponent @xmath31 is defined by ( [ shape_exp ] ) . by definition it only depends on the quenched expectation of the number of particles , and further , only on the mean number @xmath124 of particles sent in one step to @xmath68 by one particle at the origin . indeed , @xmath125 where @xmath126 is the environment shifted by @xmath127 , and where the sum ranges over all sequences @xmath128 with @xmath129 . in particular , for any mapping @xmath130 from @xmath49 to itself such that @xmath131 for all @xmath132 , the two branching random walks in the environments @xmath22 and @xmath133 are equivalent , in the sense that they have the same local behavior at the logarithmic scale . fine details of the branching and displacement do not matter , under the above five conditions . moreover , for results that only concern the expected number of particles ( such as theorem [ t_local_size ] ) we really do not need the assumption that any particle produces at least one offspring ; this can be substituted by a weaker assumption @xmath134 @xmath58-a.s . finally , we formulate a result about the total size of the population : [ t_total_size ] the function @xmath31 has the property @xmath135 for the total size of the population @xmath136 , it holds that @xmath137 a.s . , as @xmath116 . note that , by ( [ sup_beta>0 ] ) , @xmath138 , and @xmath139 by convexity . from theorems [ t_local_size ] and [ t_complete_shape ] it follows that for @xmath58-almost all @xmath22 , for any @xmath108 @xmath140&=1.\end{aligned}\ ] ] as opposed to theorem 1.10 of @xcite , here we prove this result both in transient and recurrent cases . [ ex1 ] * ( constant branching ) * more information can be obtained in the particular case when there exists a constant @xmath141 such that @xmath142 in this case , the expected size of the population is @xmath143 . this is the case for instance when @xmath144 does not depend on @xmath50 , and then the branching random walk is equivalent to a tree - indexed markov chain ( since in this case we can suppose also that the immediate descendants jump independently , and the offspring distribution does not depend on the site , cf . remark [ rem_complete_shape ] ) . in the general case , we can define the transitions @xmath145 ( recall that @xmath146 only depends on @xmath147 ) , and consider the random walk in random environment @xmath148 with transition probabilities @xmath149=p^{\omega_x}(y)$ ] for @xmath150 . we see here that @xmath151 , and therefore , by theorem [ t_local_size ] , @xmath152\big]\ ] ] with @xmath153 $ ] the integer part of @xmath154 ( coordinatewise ) . the limit can be expressed in terms of the quenched large deviation rate function @xmath155 , which have been studied in the nestling case in @xcite and in complete generality in @xcite : it holds that @xmath156 these references are for i.i.d . environment and estimate the probability of sets in the scale @xmath21 instead of the probability of points , but one can see that they apply to our discussion here . this example shows that the convex function @xmath31 is not necessarily strictly convex . indeed , it is known that the rate function has a flat horizontal part if the random walk in random environment is nestling with a non - zero speed @xmath157 , in which case @xmath158 for @xmath159 in the whole interval with endpoints @xmath160 and @xmath157 . finally , it is straightforward to see from the nearest neighbor jumps case , that the shapes @xmath161 and @xmath118 may have `` facets '' , i.e. , flat parts on their boundaries ( cf . e.g. example 7 of @xcite ) .

we study branching random walks in random environment on the-dimensional square lattice , . in this model , the environment has finite range dependence , and the population size can not decrease . the limiting shape of this set is compact and convex , and the local size is given by a concave growth exponent . also , we obtain the law of large numbers for the logarithm of the total number of particles in the process . + * short title : * branching random walks in random environment + * keywords : * shape theorem , subadditive ergodic theorem , transience , growth exponent , population size + * ams 2000 subject classifications : * primary 60k37 ; secondary 60j80 , 82d30 universit paris 7 , ufr de mathmatiques , case 7012 , 2 , place jussieu , f75251 paris cedex 05 , france e - mail : ` comets@math.jussieu.fr ` , url : ` http://www.proba.jussieu.fr/\simcomets ` instituto de matemtica e estatstica , universidade de so paulo , rua do mato 1010 , cep 05508090 , so paulo sp , brasil e - mail : ` popov@ime.usp.br ` , url : ` http://www.ime.usp.br/\simpopov `

we study branching random walks in random environment on the-dimensional square lattice , . in this model , the environment has finite range dependence , and the population size can not decrease . we prove limit theorems ( laws of large numbers ) for the set of lattice sites which are visited up to a large time as well as for the local size of the population . the limiting shape of this set is compact and convex , and the local size is given by a concave growth exponent . also , we obtain the law of large numbers for the logarithm of the total number of particles in the process . + * short title : * branching random walks in random environment + * keywords : * shape theorem , subadditive ergodic theorem , transience , growth exponent , population size + * ams 2000 subject classifications : * primary 60k37 ; secondary 60j80 , 82d30 universit paris 7 , ufr de mathmatiques , case 7012 , 2 , place jussieu , f75251 paris cedex 05 , france e - mail : ` comets@math.jussieu.fr ` , url : ` http://www.proba.jussieu.fr/\simcomets ` instituto de matemtica e estatstica , universidade de so paulo , rua do mato 1010 , cep 05508090 , so paulo sp , brasil e - mail : ` popov@ime.usp.br ` , url : ` http://www.ime.usp.br/\simpopov `

cond-mat0508309

m

in this section we summarize the key elements of our cartesian - representation method for evaluating the hydrodynamic friction and mobility matrices in a suspension confined between two parallel walls . we also outline our asymptotic results , which rely on expansion of the far field flow into a hele shaw basis . the asymptotic results apply for sufficiently large interparticle separations . a detailed description of our technique is presented in @xcite and in @xcite . shaw basis and its relation to the spherical basis @xcite used in our analysis @xcite is summarized in appendices [ appendix on hele shaw basis ] and [ transformation between the hele shaw and spherical basis sets ] . in our approach , the effect of the suspended particles on the surrounding fluid is represented in terms of the induced - force distributions on the particle surfaces @xmath37 where @xmath38 and @xmath39 . by definition of the induced force , the flow field @xmath40 is identical to the velocity field in the presence of the particles @xcite . here @xmath41 is the green s function for the stokes flow in the wall - bounded system , @xmath42 is the oseen tensor ( free - space green s function ) , and @xmath43 describes the flow reflected from the walls . for a system of particles moving with the translational and angular velocities @xmath9 and @xmath10 in the external flow @xmath44 , the induced - force distribution ( [ induced forces ] ) can be obtained from the boundary - integral equation of the form @xmath45({{\bf r } } ) + \sum_{j=1}^n\int [ ( 1-\delta_{ij}){{\bf t}}_0({{\bf r}}-{{\bf r}}')\phantom{,}}\nonumber\\ & & \rule{0pt}{0pt}+{{\bf t}}'({{\bf r}},{{\bf r } } ' ) ] { \,\mbox{\boldmath{$\cdot$}}\,}{{\bf f}}_j({{\bf r}}'){{\,\mathrm d}}{{\bf r } } ' = { { \bf v}}_i^{\rm rb}({{\bf r}})-{{{\bf v}}^{\rm ext}}({{\bf r}}),\nonumber\\ & & \rule{150pt}{0pt}{{\bf r}}\in s_i,\end{aligned}\ ] ] where the rigid - body velocity field @xmath46 and the external flow field @xmath47 are evaluated on the surface @xmath48 of particle @xmath6 . in the boundary - integral equation ( [ boundary - integral equation for induced - force density ] ) , @xmath49 denotes the one - particle scattering operator , which is defined by the relation @xmath50 where @xmath51 is the velocity incident to particle @xmath6 . for specific particle models , explicit expressions for the operator @xmath49 are known @xcite . the force and torque acting on particle @xmath6 can be evaluated from the induced - force distribution using the integrals @xmath52 the friction matrix ( [ resistance formula for fixed particles ] ) can be computed by solving the boundary equation ( [ boundary - integral equation for induced - force density ] ) with the external flow @xmath44 in the form ( [ parabolic flow ] ) and no rigid - body motion , @xmath53 . similarly , the translational rotational friction matrix is obtained by solving ( [ boundary - integral equation for induced - force density ] ) with a nonzero rigid - body motion ( [ rigid - body velocity of drop i ] ) and no external flow , @xmath54 . in our approach , the boundary - integral equation ( [ boundary - integral equation for induced - force density ] ) is solved after transforming it into a linear matrix equation . the transformation is achieved by projecting ( [ boundary - integral equation for induced - force density ] ) onto a spherical basis of stokes flows . we use here the multipolar representation introduced by cichocki _ @xcite , but we apply a different normalization to emphasize full symmetry of the problem @xcite . accordingly , the induced - force distributions at the surfaces of particles @xmath55 are expanded using the basis set of multipolar force distributions @xmath56 . similarly , the flows incoming to each particle are expanded into the nonsingular basis set of stokes flows @xmath57 . here @xmath58 and @xmath59 are the angular and azimuthal spherical - harmonics orders , and @xmath60 characterizes the type of the flow . explicit definitions of the basis sets @xmath61 and @xmath62 ( as well as their counterparts @xmath63 and @xmath64 that correspond to singular stokes flows ) are given in @xcite . in order to obtain the multipolar representation of the boundary - integral equation ( [ boundary - integral equation for induced - force density ] ) , we apply the multipolar expansion @xmath65 to the induced - force density ( [ induced forces ] ) . the external flow relative to the particle motion is similarly expanded , @xmath66 inserting these expansions into eq . ( [ boundary - integral equation for induced - force density ] ) yields a linear equation of the form @xmath67 where the matrix @xmath68 can be decomposed as @xmath69 the first term on the right side of the above expression corresponds to the single - particle scattering operator @xmath70 in equation ( [ boundary - integral equation for induced - force density ] ) ; the second one to the integral operator with the kernel @xmath71 , and the third one to the integral operator with the kernel @xmath72 . explicit expressions for the first two terms were derived by felderhof and his collaborators @xcite some time ago . quadrature relations @xcite and asymptotic formulas @xcite for the wall contribution @xmath73 were recently derived by our group ( as discussed in sec . [ cartesian representation ] below ) . in order to evaluate the resistance tensors @xmath21 and @xmath22 for immobile particles in poiseuille flow , eq . ( [ induced force equations ] ) is solved with the right - hand side corresponding to the velocity field ( [ parabolic flow ] ) . the resulting induced - force multipolar distributions ( [ induced force in terms of multipoles ] ) are projected onto the total force and torque using expressions ( [ force and torque ] ) . the solution can be conveniently expressed in terms of the grand friction matrix @xmath74 which is inverse to the grand mobility matrix @xmath75 with the elements given by eq . ( [ grand mobility matrix ] ) . as shown in @xcite , the translational rotational friction matrix @xmath30 ( @xmath29 ) is given by the relation @xmath76 here @xmath77 are the elements of the grand friction matrix ( [ grand mobility and grand friction ] ) , and @xmath78 are the elements of projection matrices onto the subspace of translational ( @xmath79 , @xmath80 ) and rotational ( @xmath79 , @xmath81 ) rigid - body motions . explicit expressions for these matrices are listed in appendix b of ref .. the resistance coefficients @xmath82 ( @xmath36 ) are given by a relation analogous to ( [ usual physical friction and grand friction ] ) , @xmath83 where @xmath84 are the elements of the matrix representing the orthogonal projection onto the subspace of pressure - driven flows ( [ parabolic flow ] ) . relation ( [ friction coeff and grand friction ] ) and explicit expressions for the matrix @xmath84 are derive in appendix [ projection matrix y ] . we note that , unlike eq . ( [ usual physical friction and grand friction ] ) , relation ( [ friction coeff and grand friction ] ) involves summation over the particles . this summation is needed because the external parabolic flow ( [ parabolic flow ] ) is applied to all particles in the system . to determine the resistance coefficients ( [ usual physical friction and grand friction ] ) and ( [ friction coeff and grand friction ] ) , the matrix ( [ grand mobility matrix ] ) in the force - multipole equation ( [ induced force equations ] ) has to be first evaluated . explicit expressions for the single - particle scattering matrix @xmath85 and the free - space contribution @xmath86 are known @xcite . to evaluate the wall contribution @xmath73 to the matrix ( [ grand mobility matrix ] ) we employ our recently developed cartesian - representation method @xcite . for sufficiently large interparticle separations appropriate asymptotic expressions @xcite can also be used . as explained in @xcite , the cartesian - representation method relies on transformations between the spherical basis sets of stokes flows @xmath87 and the cartesian basis sets @xmath88 ( where * k * is a lateral wave vector ) . according to the discussion in sec.[friction and mobility of spheres in parabolic flow ] , the multipolar spherical sets @xmath87 correspond to an expansion of the velocity field into spherical harmonics . due to symmetry , the matrix @xmath89 , describing interaction of the flow field with a spherical particle , is thus diagonal in the spherical - harmonics orders @xmath58 and @xmath59 . the cartesian basis sets correspond to an expansion of the velocity field into lateral fourier modes . in the cartesian representation the matrix @xmath90 that describes interaction of the flow with a wall is diagonal in the wave vector @xmath91 . this diagonal structure of the scattering matrices @xmath89 and @xmath90 yields a significant simplification of the problem . to express our results in a compact form , we introduce a matrix notation in the three - dimensional linear space with the components corresponding to the indices @xmath60 that identify the tensorial character of the basis flow fields @xmath87 . in this notation , a column vector with components @xmath92 is denoted by @xmath93 , and a matrix with elements @xmath94 is denoted by @xmath95 . accordingly , the column vectors associated with the coefficients @xmath96 and @xmath97 are represented by @xmath98 and @xmath99 , and the two - wall green s matrix with the elements @xmath100 is represented by . we will also use @xmath101 , @xmath102 and @xmath103 matrices composed of @xmath104 blocks , as indicated below . our result for the wall green s matrix @xmath73 can be expressed in terms of the following fourier integral @xmath105 where @xmath106 is the projection of the vector @xmath107 onto the @xmath16@xmath108 plane , and @xmath109 is the corresponding two - dimensional wave vector . the matrix @xmath110 in the above expression depends on the wall separation @xmath4 and the vertical coordinates @xmath111 and @xmath112 of the points @xmath6 and @xmath113 ( measured with respect to the position of the lower wall ) . this matrix is a product of several simple matrices , @xmath114 where @xmath115 is the fluid viscosity . the component matrices @xmath116^\dagger= \left [ \begin{array}{c } { { { \mathsf}t}_{\rm cs}^{+-}}({{\bf k}},lm ) \\\\ { { { \mathsf}t}_{\rm cs}^{--}}({{\bf k}},lm ) \end{array } \right]\ ] ] describe the transformations between the spherical ( @xmath117 ) and cartesian ( @xmath118 ) basis fields . the superscripts @xmath119 refer to the singular and nonsingular basis fields for the spherical basis , and the fields that exponentially grow ( @xmath120 ) or decay ( @xmath121 ) in the vertical direction @xmath122 for the cartesian basis . the matrices ( [ two wall transformation matrices ] ) consist of two @xmath104 blocks corresponding to the lower and the upper wall , respectively . next , the matrices @xmath123^\dagger= \left [ \begin{array}{cc } { { \tilde{{\mathsf}s}}_{\rm c}^{++}}(kz_{{{\rm l}}s})&0 \\\\ 0&{{\tilde{{\mathsf}s}}_{\rm c}^{--}}(kz_{{{\rm u}}s } ) \end{array } \right]\ ] ] correspond to the propagation of the cartesian flow - field components between the point @xmath124 and the lower ( @xmath125 ) and upper ( @xmath126 ) walls . here @xmath127 and @xmath128 are the relative vertical coordinates of the point @xmath129 with respect to the walls . finally , the matrix @xmath130^{-1},\ ] ] describes scattering of the cartesian flow components from the walls . the @xmath104 matrices @xmath131 represent scattering of the flow from a single wall , and the matrices @xmath132 and @xmath133 show the propagation of the flow field between the walls during the multiple - reflection process . the structure of the expressions ( [ expression for two wall g fourier integral])([two wall z matrix ] ) is schematically represented in fig . [ schematic ] . the explicit expressions for the component matrices ( [ expression for two wall g integrand])([two wall z matrix ] ) are listed in appendix [ expressions for component matrices ] . we note that due to symmetries of the transformation and displacement matrices and the symmetry @xmath134^\dagger\ ] ] of the two - wall scattering matrix , the lorentz symmetry of the two - wall green s matrix ( [ expression for two wall g fourier integral ] ) is explicit . ) . the vectors @xmath135 and @xmath136 represent the relative position of the particle @xmath137 and the lower ( @xmath138 ) or upper ( @xmath139 wall . ] the exact cartesian representation ( [ expression for two wall g fourier integral])([two wall z matrix ] ) of the wall contribution to the green s matrix @xmath73 involves a two - dimensional fourier integral , which has to be evaluated numerically . however , for sufficiently large interparticle separations the calculation can be greatly simplified by using the far - field asymptotic expressions derived in @xcite . below we summarize this result . the derivation of the asymptotic expressions for the green s matrix @xmath140 relies on the observation that for large lateral interparticle distances , @xmath141 , the disturbance flow scattered from the particles assumes the hele shaw ( i.e. , lubrication ) form . accordingly , the the far - field disturbance flow @xmath142 is driven by a two - dimensional harmonic pressure field @xmath143 , @xmath144 the pressure @xmath143 is independent of the vertical variable @xmath122 and satisfies the two - dimensional laplace s equation @xmath145 where @xmath146 is the lateral position with respect to the particle , and @xmath147 is the two - dimensional gradient operator with respect to the lateral coordinates . the result ( [ hele - shaw flow ] ) can be obtained using a lubrication expansion of the stokes equations in the small parameter @xmath148 ( where @xmath149 ) . to obtain the asymptotic expression for the green s matrix @xmath150 we use the results listed in appendices [ appendix on hele shaw basis ] and [ transformation between the hele shaw and spherical basis sets ] . accordingly , the asymptotic flow produced by a force multipole ( [ force multipole ] ) centered at the position of particle @xmath113 is expressed in terms of the hele shaw basis ( [ hele - shaw basis velocity fields ] ) using relation ( [ expression for multipolar asymptotic field in hele - shaw basis ] ) . the resulting hele shaw multipolar flow is translated to the position of particle @xmath6 using the displacement formula ( [ displacement theorem for hele - shaw fields ] ) . finally the hele shaw field is transformed back into the spherical basis using relation ( [ expansion of hele - shaw basis field into spherical basis ] ) . the above procedure @xcite yields a compact expression of the form @xmath151 where the component matrices @xmath152 and @xmath153 are given by eqs . ( [ expression for scalar displacement matrix ] ) and ( [ condition for nonzero elements of c matrix])([coefficient a ] ) . as explained in @xcite , the correction @xmath154 to the asymptotic result ( [ asymptotic green s matrix elements ] ) decays exponentially with the lateral interparticle distance @xmath155 on the lengthscale @xmath4 . typically , the asymptotic approximation @xmath156 yields accurate results for @xmath157 . l@cccccccc + @xmath158&&0.999&0.995&0.990&0.950&0.900&0.500&0.200 + 1.1&&&&&&0.641&0.583&0.286 + 1.01&&&&0.418&0.498&0.520&0.401&0.188 + 1.007&&&&0.415&0.483&0.502&0.382&0.179 + 1.005&&&0.376&0.409&0.469&0.486&0.366&0.171 + 1.001&&0.304&0.350&0.368&0.409&0.419&0.306&0.141 l@ccccc@ccc + @xmath158&&0.999&0.995&0.990&0.950&0.900&0.500&0.200 + 1.1&&&&&&0.0197&0.723&1.189 + 1.01&&&&5.14e-4&0.101&0.177&0.620&0.903 + 1.007&&&&0.0159&0.109&0.181&0.600&0.866 + 1.005&&&1.95e-4&0.0269&0.115&0.184&0.582&0.834 + 1.001&&2.34e-5&0.0362&0.0556&0.127&0.183&0.504&0.705 in order to determine the resistance matrices ( [ usual physical friction and grand friction ] ) and ( [ friction coeff and grand friction ] ) , the induced - force - multipole equation ( [ induced force equations ] ) is solved with the matrix ( [ grand mobility matrix ] ) evaluated using known results @xcite for @xmath85 and @xmath86 , and our cartesian representation ( [ expression for two wall g fourier integral ] ) for @xmath73 . for sufficiently large interparticle distances a simpler relation ( [ asymptotic green s matrix elements ] ) may be be used instead . after the friction matrices have been obtained , the mobility matrix ( [ mobility formula for freely suspended particles ] ) can be calculated from expressions ( [ relation between parabolic - flow resistance and mobility ] ) and ( [ mobility and resistance are inverse to each other ] ) . to accelerate numerical convergence of the fourier integral in ( [ expression for two wall g fourier integral ] ) ( especially , when both particles @xmath6 and @xmath113 are close to a single wall ) , the integrand ( [ expression for two wall g integrand ] ) is decomposed into two single - wall contributions @xmath159 and @xmath160 and the correction term @xmath161 the single wall contributions can be integrated analytically @xcite . moreover , as shown in @xcite , the correction term @xmath162 is easier to integrate numerically than the original highly oscillatory integrand @xmath163 . as in other numerical algorithms based on a multipolar expansion of stokes flow @xcite the force - multipole equation ( [ induced force equations ] ) is truncated at a given multipolar order @xmath164 before it is solved numerically . to accelerate the convergence of the approximation with @xmath165 we employ the standard lubrication correction @xcite on the friction - matrix level . we closely follow the implementation of the method described in @xcite ( for a single wall problem ) . accordingly , the translational rotational friction matrix @xmath166 ( @xmath29 ) is represented as a combination @xmath167 of the two - particle superposition contribution in free space @xmath168 , the single - particle / single - wall superposition contribution @xmath169 , and the remainder @xmath170 . the superposition contributions @xmath168 and @xmath171 are determined very accurately using the power - series expansions of the friction matrix in the inverse interparticle separation and the inverse distance between the particle and wall , respectively . the remainder @xmath170 , evaluated as a difference between the multipolar expansion of the full friction matrix and the superposition contributions , converges with @xmath165 much faster than the full friction matrix @xmath172 itself . in the present implementation of our method , the linear equation ( [ grand mobility matrix ] ) is solved by matrix inversion . thus , the numerical cost of the calculation scales as @xmath173 with the number of particles @xmath0 . ( numerical cost of this order is typical of unaccelerated stokesian - dynamics algorithms . ) we note , however , that the pppm or fast - multipole acceleration techniques @xcite can naturally be used in our cartesian - representation algorithm we will return to this problem in our future publications .

we have examined the crossover between several far - field asymptotic regimes corresponding to different relations between the particle separation and the distances of the particles from the walls . therefore , the far - field contributions must be included in any reliable algorithm for evaluating many - particle hydrodynamic interactions in the parallel - wall geometry .

we study hydrodynamic interactions of spherical particles in incident poiseuille flow in a channel with infinite planar walls . the particles are suspended in a newtonian fluid , and creeping - flow conditions are assumed . numerical results , obtained using our highly accurate cartesian - representation algorithm [ physica a xxx , * xx * , 2005 ] , are presented for a single sphere , two spheres , and arrays of many spheres . we consider the motion of freely suspended particles as well as the forces and torques acting on particles adsorbed at a wall . we find that the pair hydrodynamic interactions in this wall - bounded system have a complex dependence on the lateral interparticle distance due to the combined effects of the dissipation in the gap between the particle surfaces and the backflow associated with the presence of the walls . for immobile particle pairs we have examined the crossover between several far - field asymptotic regimes corresponding to different relations between the particle separation and the distances of the particles from the walls . we have also shown that the cumulative effect of the far - field flow substantially influences the force distribution in arrays of immobile spheres . therefore , the far - field contributions must be included in any reliable algorithm for evaluating many - particle hydrodynamic interactions in the parallel - wall geometry .

cond-mat0508309

r

we now present some characteristic examples of single- and many - particle results . we consider both the motion of freely suspended particles in the external flow ( [ parabolic flow ] ) and forces and torques on fixed particles subjected to this flow . the results for an isolated particle are obtained with the truncation at the multipolar order @xmath174 , which yields accuracy better than 0.1% . for two - particle and multi - particle systems we use @xmath175 and @xmath176 , respectively . the corresponding accuracy is of the order of 1% . motion of a single particle in a parabolic flow between two planar walls was recently considered by staben _ _ @xcite and by jones @xcite ( see also much earlier results by ganatos _ we thus give here only limited results for this system . in tables [ table of linear velocity ] and [ table of angular velocity ] we list a set of our highly accurate results for the linear and angular velocities ( [ mobility formula for freely suspended particles ] ) of a force- and torque - free particle in the parabolic flow ( [ parabolic flow ] ) . the linear velocity @xmath177 is normalized by the magnitude of the parabolic flow @xmath14 , and the angular velocity @xmath178 by @xmath179 . only the @xmath16 component of the linear velocity and the @xmath108 component of the angular velocity are given because all the other components vanish by symmetry . in order to verify our results and test the accuracy of the calculations reported in @xcite , the velocities @xmath180 and @xmath181 are given for a subset of configurations represented in tables i and ii of @xcite . we also present some additional results for tight configurations with @xmath182 . we find that our results are in good agreement ( up to three digits ) with those reported in @xcite for @xmath183 , where @xmath184 is the position of the particle center measured from the lower wall . for smaller gaps between the wall and the particle the discrepancies are about @xmath185 . an exception is the rotational velocity in the tightest configuration reported in @xcite ( i.e. , @xmath186 and @xmath187 ) , where the error is @xmath188 . we expect that these discrepancies stem from inaccuracies of the boundary - integral calculations in @xcite the convergence tests we have performed indicate that the accuracy of our results is better than @xmath189 . we also note that our results agree with those of jones @xcite and with our earlier results of a multiple - reflection method @xcite . a sample of characteristic results for the translational and rotational velocities @xmath9 and @xmath10 ( i=1,2 ) of two force- and torque - free particles in the parabolic flow ( [ parabolic flow ] ) are presented in figures [ x - h2.0-z1.0][y - h2.0-z0.67 ] . the linear and angular velocities are normalized in these plots by @xmath190 and @xmath191 , respectively . the results are plotted versus the lateral particle distance @xmath192 for a moderate channel width @xmath193 in figs . [ x - h2.0-z1.0 ] and [ y - h2.0-z1.0 ] the particle @xmath194 is in the center position @xmath195 , and in fig . [ x - h2.0-z0.67 ] and [ y - h2.0-z0.67 ] it is in the off - center position @xmath196 . the results are given for several vertical positions @xmath197 of particle @xmath198 . ( we recall that @xmath89 denotes the distance of particle @xmath199 from the lower wall . ) in figs . [ x - h2.0-z1.0 ] and [ x - h2.0-z0.67 ] the particle pair is oriented in the longitudinal direction @xmath16 and in figs . [ y - h2.0-z1.0 ] and [ y - h2.0-z0.67 ] in the transverse direction @xmath108 with respect to the flow . we note that @xmath200 for the longitudinal configuration and @xmath201 for the transverse configuration , by symmetry . the results in figs . [ x - h2.0-z1.0][y - h2.0-z0.67 ] indicate that the effect of mutual particle interactions is small if both particles are at the same vertical position in the channel . the effect is the largest if one of the particles is near the channel center and the other close to a wall . the results also reveal a different behavior in the near - field and far field regions , as discussed below . [ [ near - contact motion ] ] near - contact and intermediate region + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + the results in figs . [ x - h2.0-z1.0][y - h2.0-z0.67 ] indicate that the dependence of the linear and rotational particle velocities on the interparticle distance is much more complicated in the wall - bounded system than in free space . this complex behavior stems from the competition between the tangential and normal lubrication forces and backflow effects associated with the velocity field scattered from the walls . for near - contact particle configurations @xmath202 ( where @xmath203 is the dimensionless gap between the particle surfaces , and @xmath204 ) the particle dynamics is strongly influenced by the lubrication forces . the normal relative particle motion is arrested by the @xmath205 normal lubrication force at the dimensionless gap @xmath206 of several percent . the relative tangential and rolling motions are opposed by much weaker @xmath207 lubrication forces . these motions are thus still quite substantial for @xmath208 and vanish only for nonphysically small gaps . a decrease in the relative tangential and rotational particle motion at small interparticle distances results in an increased overall dissipation , which may cause a decrease of the horizontal particle velocities even in symmetric particle configurations with @xmath209 or @xmath210 ( cf . , the results for @xmath211 and @xmath212 in fig . [ x - h2.0-z0.67 ] ) . we note that a pair of touching particles in a transverse configuration ( figs . [ y - h2.0-z1.0 ] and [ y - h2.0-z0.67 ] ) does not move , in general , as a rigid body , because there is no lubrication resistance to the relative particle rotation around the axis connecting their centers . in some cases the normal and tangential lubrication forces have an opposite effect on a given velocity component . this produces sharp kinks in some curves at near - contact positions ( e.g. , @xmath213 and @xmath214 for @xmath215 in fig . [ x - h2.0-z0.67 ] ) . an additional change of sign of particle velocities relative to the velocities at infinite interparticle separations @xmath216 may occur due to a backflow associated with scattering of the flow from the walls . due to a combination of the lubrication and back - flow effects , the @xmath122 component of the particle velocities changes sign twice for some longitudinal configurations . [ [ intermediate and far field behavior ] ] far - field region + + + + + + + + + + + + + + + + as discussed in sec . [ far - field form ] , for large lateral interparticle distances , the hydrodynamic interactions in a wall - bounded system are determined by the far - field form of the disturbance flow scattered from the particles . the scattered flow has the hele shaw form described by eqs . ( [ hele - shaw flow ] ) and ( [ 2d laplace for hele - shaw pressure ] ) . we recall that the asymptotic form of the flow field is approached exponentially on the lengthscale @xmath4 . taking into account the symmetry of the problem we find that the far - field disturbance velocity produced by a particle in external flow ( [ parabolic flow ] ) is given by equation ( [ hele - shaw flow ] ) with the pressure of the form @xmath217 where @xmath218 is the polar angle between the lateral position vector @xmath219 and the flow direction @xmath15 . to the leading order in the multiple scattering expansion , relations ( [ hele - shaw flow ] ) and ( [ solution for hele - shaw pressure ] ) determine thus the far - field form of the hydrodynamic resistance and mobility functions for a pair of particles in the external parabolic flow . in particular , eqs . ( [ hele - shaw flow ] ) and ( [ solution for hele - shaw pressure ] ) indicate that the flow @xmath142 has only lateral components . it follows that the @xmath122 components of the translational and rotational particle velocities ( [ freely suspended particles ] ) vanish in the far - field regime . this behavior is clearly seen in figs . [ x - h2.0-z1.0][y - h2.0-z0.67 ] , where these velocity components approach zero exponentially . next , the disturbance field ( [ hele - shaw flow ] ) with the pressure given by eq . ( [ solution for hele - shaw pressure ] ) behaves as @xmath220 thus the linear and angular lateral velocities shown in figs.[x - h2.0-z1.0][y - h2.0-z0.67 ] approach the one - particle asymptotic values as @xmath221 . the result ( [ scattered flow decay 2wb ] ) should be contrasted with the behavior @xmath222 in free space and @xmath223 in the presence of a single wall ( where we assume that @xmath224 ) . according to eqs . ( [ scattered flow decay 2wb])([scattered flow decay 1wb ] ) , the decay of the far - field flow in the presence of one or two walls is faster than the corresponding decay in free space , because the walls absorb momentum , and thus they slow the fluid down . on the other hand , the decay of the flow field ( [ scattered flow decay 2wb ] ) in the two - wall system is slower than the decay ( [ scattered flow decay 1wb ] ) in the presence of a single wall . this behavior stems from fluid - volume conservation constraint . in the system confined by a single wall the fluid displaced by the particle primarily flows above the particle , far from the wall , where it encounters small resistance . in contrast , in the presence of two walls , the flow is limited to the quasi - two - dimensional region ; hence , it has a longer range . since the total flux associated with the quasi - two - dimensional flow ( [ scattered flow decay 2wb ] ) vanishes for @xmath225 , the fluid velocity must form a backflow pattern , unlike the behavior in the unbounded three - dimensional space . the backflow , described by the dipolar velocity field ( [ hele - shaw flow ] ) and ( [ solution for hele - shaw pressure ] ) , results in an enhancement of relative particle motion for the transverse orientation of the particle pair ( as seen for some particle configurations in the top panels of figs.[y - h2.0-z1.0 ] and [ y - h2.0-z0.67 ] ) . we note that an analogous behavior was discussed by cui _ @xcite in their study of pair diffusion in a confined , quasi - two - dimensional colloidal suspension . similar effect was also independently described in our recent papers @xcite . ) versus interparticle distance @xmath226 normalized by the particle diameter @xmath227 for a pair of particles in longitudinal orientation . wall separation @xmath228 ( solid line ) , @xmath229 ( long - dashed lines ) , @xmath230 ( short - dashed lines ) , @xmath231 ( dotted lines ) . the top three lines correspond to particles in the center plane @xmath232 , and the bottom three to particles in the near - wall configuration @xmath233 . for @xmath228 ( middle line ) the center and near - wall configurations coincide . ] , except that for the transverse orientation of the particle pair . the top panel corresponds to particles in the center plane @xmath232 , and the bottom panel to particles in the near - wall configuration @xmath233 . ] the far - field disturbance flow , discussed above , affects not only the velocities of freely suspended particles , but also the hydrodynamic resistance force ( [ resistance formula for fixed particles ] ) acting on immobile particles in the external flow ( [ parabolic flow ] ) . figures [ ff - lng ] and [ ff - trn ] illustrate the crossover of the resistance force between the three regimes corresponding to the disturbance flows of the form given by equations ( [ scattered flow decay 2wb])([scattered flow decay 1wb ] ) . to emphasize the behavior of the force in the far - field regime , the results are shown for the @xmath16 component , @xmath234 , of the rescaled force perturbation @xmath235 where @xmath236 with @xmath237 denoting the stokes resistance force , and @xmath238 representing the value of the force @xmath239 for @xmath216 . in figs . [ ff - lng ] and [ ff - trn ] force perturbation @xmath234 is plotted versus the lateral particle separation @xmath226 for two particles at the same vertical position @xmath240 . in one configuration , the particles are at the center plane @xmath241 and in the other one they are close to the lower wall , @xmath242 the results are shown for several different wall separations . since the particles are at the same vertical position , the force @xmath243 is independent of the particle index @xmath6 . [ ff - lng ] represents the results for the longitudinal orientation of the particle pair , @xmath244 , and fig.[ff - trn ] the results for the transverse orientation @xmath245 . the force perturbation ( [ rescaled force perturbation ] ) for the longitudinal orientation is positive . it is shown on the logarithmic scale to emphasize the algebraic asymptotic behavior . for the transverse orientation the perturbation force in the wall - bounded systems changes sign due to the backflow effects discussed in sec . [ particle velocities ] . the results are thus plotted on a linear scale in two separate panels for the center ( top panel ) and the near - wall ( bottom panel ) configurations . the results shown in figs . [ ff - lng ] and [ ff - trn ] clearly demonstrate the crossover between different regimes corresponding to the far - field disturbance velocity fields of the form ( [ scattered flow decay 2wb])([scattered flow decay 1wb ] ) . for very large wall separations @xmath246 and the center particle position ( [ two particles in centerplane ] ) the rescaled force perturbation ( [ rescaled force perturbation ] ) behaves as @xmath247 , which indicates that @xmath248 , in agreement with the estimate ( [ scattered flow decay infty space ] ) of the disturbance - flow magnitude in free space . for the near - wall position ( [ two particles close to wall ] ) and the longitudinal orientation of the particle pair we find @xmath249 , consistently with the estimate ( [ scattered flow decay 1wb ] ) . in contrast , @xmath250 in the transverse case , due to an additional cancellation of the far - field contributions . for finite wall separations the force perturbation crosses over from the above - described behavior in the regime @xmath251 to the behavior @xmath252 ( i.e. , @xmath253 ) for @xmath141 , in agreement with eq . ( [ scattered flow decay 2wb ] ) . typically , the far - field behavior @xmath254 is observed already for @xmath255 . in this section we examine the influence of the walls on the hydrodynamic interactions in confined multi - particle systems . we focus on collective phenomena that involve cumulative effects of the far - field flow ( [ scattered flow decay 2wb ] ) . as shown in our recent studies of particle motion in quiescent fluid @xcite , the backflow associated with the dipolar form ( [ hele - shaw flow ] ) and ( [ solution for hele - shaw pressure ] ) of the far - field velocity may produce a strong , positive feedback resulting in large magnitudes of induced forces . in such cases the far - field flow dominates the behavior of the system . below we examine similar phenomena for particles in the imposed parabolic flow . first we analyze the effect of confinement on the motion of rigid linear arrays of touching spheres . in earlier papers @xcite , we have shown that the behavior of such arrays in quiescent fluid is strongly affected by the walls . in particular we have demonstrated that , unlike in free space , the hydrodynamic resistance force in channels with @xmath182 depends significantly on the orientation of the array with respect to its velocity . if the orientation of the array , moving along the channel , is parallel to the velocity , the resistance force evaluated per one sphere decreases with the length of the array . in contrast , for the transverse orientation the resistance force per particle increases nearly linearly with the array length . this increase results from the pressure buildup associated with the positive - feedback backflow effects . the motion of linear arrays of spheres in the imposed parabolic flow ( [ parabolic flow ] ) is illustrated in fig . [ lng - trn - mid ] and [ lng - trn - tch ] . the arrays are parallel to the walls and are oriented either in the longitudinal direction @xmath16 or the transverse direction @xmath108 . figure [ lng - trn - mid ] presents the translational velocity of arrays with different length , placed in the mid - plane @xmath256 . the results are given for several channel widths @xmath4 . figure [ lng - trn - tch ] shows linear and angular velocities of arrays at different vertical positions in the channel . the linear velocities are non - dimensionalized by the local velocity of the imposed flow @xmath257 and the angular velocities by the local share rate @xmath258 evaluated at the position @xmath184 of the array center . for the mid - plane position @xmath256 , @xmath259 is identical to the amplitude @xmath14 of the imposed flow ( [ parabolic flow ] ) . the results in fig . [ lng - trn - mid ] indicate that the normalized velocity of an array @xmath260 is smaller in channels with smaller width . this behavior stems primarily from the increased dissipation in the gaps between the particles and the channel walls . the decrease of the mobility is strongest for long arrays in longitudinal orientation the far - field disturbance flow produced by each of the particles opposes the motion of the array in this case . for the transverse orientation , the scattered flow acts in the direction of the external flow ; due to the cooperative feedback effects longer arrays move faster than the shorter ones . in narrow channels with @xmath182 , very long chains in transverse orientation translate with the velocity that is close to the average velocity of the unperturbed fluid . a set of results for short ( @xmath261 ) and a long ( @xmath262 ) linear arrays at off - center positions in channels with different width is presented in fig . [ lng - trn - tch ] . the configurations are parametrized by the normalized distances of the particle surfaces from the lower and upper walls , @xmath263 the translational and rotational velocities are shown for arrays at two vertical positions @xmath264 and @xmath265 , and they are plotted versus the distance @xmath266 . the results in the upper panels of fig . [ lng - trn - tch ] indicate that the translational velocity of an array at a fixed distance from the lower wall diminishes rapidly with the decreasing @xmath267 due to the @xmath268 lubrication resistance associated with the interaction with the upper wall . in the case of the longitudinal orientation of the chain , the translational and rotational velocities saturate at @xmath269 . in contrast , for the transverse orientation , the effect of the upper wall on the translational velocity of the array has a much longer range , especially for the larger value of the chain length @xmath0 . moreover , the effect of the upper wall is more pronounced for @xmath264 than for @xmath270 . these observations are consistent with the backflow mechanisms discussed above . lower panels of fig . [ lng - trn - tch ] represent the normalized angular velocity @xmath271 of the arrays . we note that the angular velocity itself changes sign for @xmath272 ; however , the normalized quantities shown in fig . [ lng - trn - tch ] are positive , due to the corresponding change of sign of the local share rate ( [ shear rate at center of particle ] ) . for the longitudinal orientation of the chain the angular velocity is several orders of magnitude smaller than the angular velocity in the transverse case . this strong effect can easily be explained in terms of particle wall lubrication forces . the rotation of the chain oriented perpendicularly to the flow is governed by the @xmath273 lubrication resistance . the rotation of the chain oriented parallel to the flow involves motion of individual particles towards the wall and away from it , and thus the lubrication forces are much stronger @xmath274 . ( as labeled ) . the spheres are depicted by solid circles . the lateral forces are represented by the line segments , and the normal forces by dashed ( force away from the wall ) or dotted ( towards the wall ) circles . a line segment ( circle ) of the length ( radius ) equal to the particle radius @xmath275 represents a force of magnitude @xmath276 , where @xmath259 is the local fluid velocity ( [ velocity at center of particle ] ) . ] , except that the results are for the hydrodynamic torque . a line segment ( circle ) of the length ( radius ) equal to the particle radius @xmath275 represents a torque of magnitude @xmath277 . ] except that the results are for loosely packed arrays of spheres . ] in figs . [ grid - force][grid - force - loose ] the results are presented for the hydrodynamic friction forces and torques on individual particles in arrays of spheres adsorbed on one of the walls in a parallel - wall channel . understanding of such forces is important in an analysis of the removal of colloidal particles from a wall by an applied flow @xcite . moreover , our results provide a further illustration of hydrodynamic phenomena associated with the far - field form of the disturbance velocity field produced by the particles . figures [ grid - force ] and [ grid - torque ] show forces and torques acting on individual particles in closely packed arrays of touching spheres . arrays that are loosely packed are considered in fig.[grid - force - loose ] . the results are given for a single sphere , linear arrays of spheres , and hexagonal arrays of spheres . the horizontal components of the forces and torques are represented by line segments and the normal components by the dashed ( orientation away from the wall ) and dotted ( towards the wall ) circles . the forces are scaled by @xmath278 and the torques by @xmath279 , where @xmath259 is the local fluid velocity ( [ velocity at center of particle ] ) . the lengths of the line segments and the radii of the circles are proportional to the magnitude of the represented quantity . the results presented in fig . [ grid - force ] indicate that the lateral drag force on a single particle only weakly depends on the channel width , while the forces on particles in linear arrays vary almost by a factor of five when the wall separation @xmath4 changes from @xmath280 to infinity . similarly strong dependence of the forces on the channel width is observed for the two - dimensional arrays of spheres . the hydrodynamic drag forces are the largest for linear arrays of spheres in narrow channels of the width only slightly bigger than the particle diameter ( cf . , the top panel of fig . [ grid - force ] ) . the large forces are associated with the pressure buildup in front of the array @xcite . as explained in sec . [ dynamics of polymer ] , the pressure buildup involves interaction of the flow with both walls in an essentially non - additive manner . thus , as shown in @xcite , this effect is not captured by the usual approximation based on a superposition of two single - wall contributions . the results for two - dimensional arrays of spheres involve significant screening effects resulting from mutual particle interactions . accordingly , the lateral forces acting on individual spheres in two - dimensional arrays are smaller than in the corresponding linear - array systems . the forces on the first and last row of particles are larger than the forces on particles near the center of the array . this effect is most pronounced for large wall separations @xmath4in narrow channels the relative force differences are smaller due to the quasi - two - dimensional character of the flow . our results for the vertical forces indicate that their magnitude is much smaller than the magnitude of the lateral forces . indeed , the only significant vertical forces exist on the first and last rows of particles in two - dimensional arrays . the maximal value of these forces occurs for @xmath281 . when the channel width is smaller , the upper wall suppresses the vertical flow . on the other hand , when the gap between the top wall and the spheres is too large , the volume of fluid deflected by the array is distributed over the larger space , and the vertical flow becomes weaker . we note that there are no vertical forces on particles in linear arrays because of the flow - reversal symmetry . the behavior of the torque exerted on the particles by the fluid is illustrated in fig . [ grid - torque ] . characteristic features of the torque distribution can be explained using arguments similar to the ones given above . for example , the lateral torques are the largest for @xmath281 , for the same reason as the corresponding behavior of the normal force . our results indicate that the vertical component of the torque is significant only for particles at the edges of the arrays , especially for small values of @xmath4 . figure [ grid - force - loose ] shows plots of forces on the spheres in loosely packed arrays of spheres . for linear arrays , the lateral forces are relatively small even for @xmath282 because the flow can pass through the inter - particle gaps without building up a substantial pressure drop . moreover , the forces on particles in different positions in such arrays are of approximately equal magnitude . for the two - dimensional loosely packed arrays the lateral forces are larger than for the closely - packed case , which indicates that the screening effects are smaller .

numerical results , obtained using our highly accurate cartesian - representation algorithm [ physica a xxx , * xx * , 2005 ] , are presented for a single sphere , two spheres , and arrays of many spheres . we consider the motion of freely suspended particles as well as the forces and torques acting on particles adsorbed at a wall . we find that the pair hydrodynamic interactions in this wall - bounded system have a complex dependence on the lateral interparticle distance due to the combined effects of the dissipation in the gap between the particle surfaces and the backflow associated with the presence of the walls . for immobile particle pairs we have also shown that the cumulative effect of the far - field flow substantially influences the force distribution in arrays of immobile spheres .

we study hydrodynamic interactions of spherical particles in incident poiseuille flow in a channel with infinite planar walls . the particles are suspended in a newtonian fluid , and creeping - flow conditions are assumed . numerical results , obtained using our highly accurate cartesian - representation algorithm [ physica a xxx , * xx * , 2005 ] , are presented for a single sphere , two spheres , and arrays of many spheres . we consider the motion of freely suspended particles as well as the forces and torques acting on particles adsorbed at a wall . we find that the pair hydrodynamic interactions in this wall - bounded system have a complex dependence on the lateral interparticle distance due to the combined effects of the dissipation in the gap between the particle surfaces and the backflow associated with the presence of the walls . for immobile particle pairs we have examined the crossover between several far - field asymptotic regimes corresponding to different relations between the particle separation and the distances of the particles from the walls . we have also shown that the cumulative effect of the far - field flow substantially influences the force distribution in arrays of immobile spheres . therefore , the far - field contributions must be included in any reliable algorithm for evaluating many - particle hydrodynamic interactions in the parallel - wall geometry .

1302.6037

i

since the work of a. connes and d.k kreimer ( see @xcite , @xcite ) in perturbative quantum field theory ( pqft ) , it has been possible to have a purely algebraic interpretation of some renormalization schemes , as the birkhoff decomposition of regularized characters ( with values in a commutative algebra of laurent series ) , that is of elements of the group of algebra morphisms from a graded commutative hopf algebra to the the algebra of laurent series ( see @xcite , @xcite ) . many graded commutative hopf algebras ( shuffle , quasi shuffle , tree ) do appear in this framework and , surprisingly , the same objects ( groups of characters on hopf algebras ) arise in the study of analytic dynamical systems ( see for example @xcite ) , where changes of coordinates can be computed as elements either of the group of formal identity - tangent diffeomorphisms ( namely characters over the fa di bruno hopf algebra ) or of some subgroup that corresponds to characters over a combinatorial hopf algebra of trees or words ( using mould calculus , see @xcite , @xcite ) . such interactions should allow to enrich each domain with the ideas of the other and some steps have already been done in this direction ( see @xcite or @xcite ) . the origin of this paper comes from the observation that , in pqft , the need for renormalization comes from the ill - definedness of some character on a hopf algebra , which , after dimensional regularization , is replaced by a character with values in an algebra of laurent series . the attempted character is then obtained with the help of the birkhoff decomposition . the same phenomenon occur in dynamical systems , in the study of normal forms of vector fields ( when the the change of coordinates that should linearize the vector field is ill - defined ) . apart from some remarks in the literature ( see for example @xcite ) , there does not seem that renormalization schemes have been used to compute , for example , normal forms . we shall explain in this paper in an abstract algebraic context a common framework to pqft and dynamical systems how the ideas developed in pqft ( dimensional regularization , birkhoff decomposition ... ) provide a way to compute normal forms as well as other objects that play a crude role in dynamics . in the next section , we briefly recall the definition of complete graded lie algebras and their link with commutative hopf algebras . we define then in section [ secder ] graded derivations on lie algebras and their associated logarithmic derivative . under some invertibilty condition on such derivations , we define the inverse of such logarithmic derivative ( see also section [ secovin ] ) that generalizes the @xmath1@xmath0 correspondence between a lie algebra and its lie group . whenever such a derivation is not invertible , the theory of dynamical systems ( see appendix [ secds ] ) , provide , in the framework of lie algebra , a way to study these logarithmic derivatives , using @xmath2-conjugacy and `` normal '' forms ( see section [ secnoninv ] ) . there are surprising similarities with the need for renormalization in pqft , the same ideas regularization and birkhoff decomposition provide a new method to compute normal forms ( section [ norenor ] ) and the analogy goes even further , see section [ secmore ] , since such notions as the locality of counter terms or the choice among several `` renormalization schemes '' also appear here .

we study in this paper logarithmic derivatives associated to derivations on graded complete lie algebra , as well as the existence of inverses . these logarithmic derivatives , when invertible , generalize the correspondence between a lie algebra and its lie group . surprisingly , one can adopt the same ideas as in pqft with fruitful results such as new constructions of normal forms with the help of the birkhoff decomposition . the analogy goes even further ( locality of counter terms , choice of a renormalization scheme ) and shall lead to more interactions between dynamical systems and quantum field theory .

we study in this paper logarithmic derivatives associated to derivations on graded complete lie algebra , as well as the existence of inverses . these logarithmic derivatives , when invertible , generalize the correspondence between a lie algebra and its lie group . such correspondences occur naturally in the study of dynamical systems when dealing with the linearization of vector fields and the non linearizability of a resonant vector fields corresponds to the non invertibility of a logarithmic derivative and to the existence of normal forms . these concepts , stemming from the theory of dynamical systems , can be rephrased in the abstract setting of lie algebra and the same difficulties as in perturbative quantum field theory ( pqft ) arise here . surprisingly , one can adopt the same ideas as in pqft with fruitful results such as new constructions of normal forms with the help of the birkhoff decomposition . the analogy goes even further ( locality of counter terms , choice of a renormalization scheme ) and shall lead to more interactions between dynamical systems and quantum field theory .

1110.6565

i

recently , much attention has been paid to rhythms of the brain @xcite . coherence of neural oscillations may be used for efficient sensory and cognitive processing ( e.g. , feature integration , selective attention , working memory , and decision making ) @xcite . this kind of neural coherence is also correlated with pathological rhythms associated with neural diseases ( e.g. , epileptic seizures and tremors in the parkinson s disease ) @xcite . here , we are interested in these coherent brain rhythms . a brain circuit is composed of a few types of excitatory principal cells and diverse types of inhibitory interneurons . interneuron diversity increases the computational power of principal cells @xcite . effect of chemical synapses on coherent brain rhythms has been much investigated in neural systems composed of excitatory and/or inhibitory neurons @xcite . historically , recurrent excitation between principal cells is the conventional coherence mechanism @xcite . however , when the decay time of the synaptic interaction is enough long , mutual inhibition between interneurons ( rather than excitation ) may synchronize individual neural firings @xcite . by providing a coherent oscillatory output to the principal cells , interneuronal networks play the role of the backbones ( i.e. , pacemakers ) of many brain rhythms such as the thalamocortical spindle rhythms @xcite and the fast gamma rhythms in the hippocampus and the neocortex @xcite . when the feedback between the excitatory and the inhibitory populations is strong , neural coherence occurs via the `` cross - talk '' between the two populations @xcite . in these computational studies of neural coherence , different types of network architectures have been considered @xcite ; all - to - all networks where every neuron is coupled to every other neuron , sparse random networks where synaptic connections are sparse , and complex networks such as small - world networks ( with predominantly local connections and rare long - distance connections ) @xcite and scale - free networks ( with a few percent of hub neurons with an exceptionally large number of connections ) @xcite . neurons in the neural system exhibit a variety of morphological and physiological properties . however , close to threshold , this remarkable richness may be grouped broadly into two basic types of excitability , often referred to as type i and type ii @xcite . when the strength of a constant input current passes a threshold , type - i neurons can fire at arbitrarily low frequencies and they can smoothly encode the strength of the input into the output firing frequency . in contrast , type - ii neurons have a non - zero minimum frequency of firing and they fire in a narrow frequency band which is relatively insensitive to changes in the strength of the applied current . different types of excitability occur because neurons have different bifurcations of resting and spiking states @xcite . for the type i neurons , oscillations emerge via a saddle - node bifurcation on an invariant circle . as the bifurcation parameter ( i.e. , strength of the injected current ) passes a threshold , the stable and the unstable fixed points coalesce and then disappear , leaving a large - amplitude stable periodic orbit . this is a global bifurcation and the frequency of the global loop can be arbitrarily small . on the other hand , for type - ii neurons a transition from a resting state to a periodically spiking state occurs through a hopf bifurcations with a finite non - zero firing frequency . according to their bifurcations , neurons may also be classified into integrators and resonators @xcite . type - i neurons act as integrators without subthreshold oscillations , and they prefer high - frequency input : the higher the frequency of the input , the sooner they fire . in contrast , type - ii neurons exhibit damped subthreshold oscillations and act as resonators : they prefer oscillatory input with the same frequency as that of damped oscillations . according to their excitability type , neurons make distinctly different responses to stimuli which have important implications for their distinct roles in generating population rhythms @xcite . in this paper , we study inhibitory coherence ( i.e. , collective coherence by synaptic inhibition ) in an ensemble of globally - coupled type - i neurons . neural models exhibiting the type-1 excitability include the connor model for the crab leg axons @xcite , the wang - buzsaki model for inhibitory interneurons @xcite , the hindmarsh - rose model @xcite , and the morris - lecar ( ml ) model @xcite under some circumstances . in section [ sec : he ] , we describe the biological conductance - based ml neuron model with voltage - gated ion channels . the ml neurons ( used in our study ) exhibit the type - i excitability , and they interact via inhibitory gabaergic synapses whose activity increases fast and decays slowly . inhibitory coherence ( which is our main concern ) is particularly important because it plays a significant role in integration of sensory and cognitive information ; for example , impaired inhibitory coherence is believed to be associated with schizophrenia and attention deficit disorder @xcite . hence , it is important to understand mechanisms for the emergence of inhibitory coherence . many works exploring mechanisms of neural coherence were done in neural systems composed of spontaneously firing ( i.e. , self - oscillating ) suprathreshold neurons ( above the threshold ) @xcite . for this case , neural coherence occurs via cooperation of regular firings of suprathreshold neurons . unlike the suprathreshold case , subthreshold neurons ( below the threshold ) can not fire spontaneously without noise ; they can fire only with the help of noise . stochastic excitatory coherence ( i.e. , collective coherence between noise - induced spikings by synaptic excitation ) was observed in a population of excitatory subthreshold neurons @xcite . due to the stochastic excitatory coherence , synaptic current , injected into each individual neuron , becomes temporally coherent . hence , temporal coherence resonance of an individual subthreshold neuron in the network may be enhanced . furthermore , stochastic inhibitory coherence ( i.e. , collective coherence between noise - induced spikings by synaptic inhibition ) was also investigated in a population of inhibitory subthreshold ml neurons exhibiting the type - ii excitability @xcite . weak stochastic inhibitory coherence was thus found to appear via cooperation of individual irregular oscillations ( i.e. , a regular small - amplitude ensemble - averaged oscillation emerges from sparsely synchronized neurons discharging irregularly at lower rates than the network oscillation ) . these sparsely synchronized neural oscillations have been intensively investigated in other types of neural networks @xcite and they are believed to be associated with cortical rhythms in cognition [ e.g. ultrafast rhythm ( 100 - 200 hz ) , gamma rhythm ( 30 - 100 hz ) and beta rhythm ( 15 - 30 hz ) ] with irregular and sparse neural discharges @xcite . in contrast to the case of subthreshold type - ii ml neurons , no stochastic inhibitory coherence is observed in a homogeneous population of subthreshold type - i ml neurons . hence , subthreshold type - i integrator neurons ( without subthreshold oscillations ) seem to be much more difficult to synchronize by inhibition than subthreshold type - ii resonator neurons ( exhibiting subthreshold oscillations ) . to take into consideration the effect of ( spontaneously firing ) suprathreshold neurons on the inhibitory coherence , we consider a heterogeneous inhibitory ensemble of subthreshold and suprathreshold type - i ml neurons . heterogeneity ( or diversity ) has been found to make constructive effects on collective coherence in various physical , biological , neural , and social systems @xcite . in section [ sec : ic ] , we investigate heterogeneity - induced inhibitory coherence by increasing the fraction of suprathreshold neurons @xmath0 in the whole population . as @xmath0 passes a threshold value @xmath1 suprathreshold neurons begin to synchronize and they play the role of coherent inhibitors for the emergence of inhibitory coherence in the whole heterogeneous population . thus , for @xmath3 the ensemble - averaged global potential @xmath4 exhibits a regular small - amplitude oscillation . for this coherent case , individual suprathreshold neurons exhibit intermittent spikings phase - locked to @xmath4 at random multiples of the period of @xmath4 . due to the stochastic spike skipping of suprathreshold neurons , the interspike interval ( isi ) histogram has multiple peaks and partial occupation occurs in the raster plot of neural spikes . in addition to the coherent intermittent spikings , coherent subthreshold ( small - amplitude ) hopping oscillations also appear in the individual potentials of suprathreshold neurons . thus , sparsely synchronized suprathreshold neurons exhibit coherent mixed - mode oscillations with two well - separated frequencies , a fast subthreshold hopping frequency imposed by the collective network oscillation and a lower firing frequency of individual suprathreshold neurons . by virtue of their coherent inhibition sparsely synchronized suprathreshold neurons suppress noisy activities of subthreshold neurons . thus , only coherent fast subthreshold hopping oscillations ( without spikings ) appear in the individual potentials of subthreshold neurons . we also characterize this heterogeneity - induced inhibitory coherence in terms of `` statistical - mechanical '' spike - based and correlation - based measures , and find that the degree of inhibitory coherence increases as @xmath0 is increased from @xmath1 . in a real brain , each neuron is coupled to only a certain number of neurons which is much smaller than the total number of neurons . the effect of sparseness of synaptic connectivity on the inhibitory coherence is briefly discussed by varying the average number of synaptic inputs per neuron @xmath5 in a random network . emergence of inhibitory coherence is thus found to persist until @xmath5 is larger than a threshold value @xmath6 . we also confirm the universality of the heterogeneity - induced inhibitory coherence in a population of canonical type - i quadratic integrate - and - fire neurons @xcite . this kind of heterogeneity - induced weak inhibitory coherence might be associated with cortical rhythms with stochastic and sparse neural discharges which contribute to cognitive functions in the cerebral cortex ( e.g. , information integration , working memory , and selective attention ) @xcite . finally , a summary is given in section [ sec : sum ] .

we study inhibitory coherence ( i.e. , collective coherence by synaptic inhibition ) in an ensemble of globally - coupled type - i neurons which can fire at arbitrarily low frequencies . heterogeneity - induced inhibitory coherence is investigated in a heterogeneous ensemble of subthreshold and suprathreshold neurons . as passes a threshold , suprathreshold neurons begin to synchronize and play the role of coherent inhibitors for the emergence of inhibitory coherence . thus , regularly - oscillating ensemble - averaged global potential appears for . for this coherent case suprathreshold neurons exhibit coherent mixed - mode oscillations with a fast subthreshold ( small - amplitude ) hopping frequency and a lower spiking frequency . by virtue of their coherent inhibition , sparsely synchronized suprathreshold neurons suppress noisy activities of subthreshold neurons . thus , only coherent subthreshold hoppings appear in the individual potentials of subthreshold neurons . we also characterize the inhibitory coherence in terms of the `` statistical - mechanical '' spike - based and correlation - based measures and find that the degree of inhibitory coherence increases with increasing for .

we study inhibitory coherence ( i.e. , collective coherence by synaptic inhibition ) in an ensemble of globally - coupled type - i neurons which can fire at arbitrarily low frequencies . no inhibitory coherence is observed in a homogeneous ensemble composed of only subthreshold neurons ( which can not fire spontaneously without noise ) . by increasing the fraction of ( spontaneously firing ) suprathreshold neurons , heterogeneity - induced inhibitory coherence is investigated in a heterogeneous ensemble of subthreshold and suprathreshold neurons . as passes a threshold , suprathreshold neurons begin to synchronize and play the role of coherent inhibitors for the emergence of inhibitory coherence . thus , regularly - oscillating ensemble - averaged global potential appears for . for this coherent case suprathreshold neurons exhibit coherent mixed - mode oscillations with a fast subthreshold ( small - amplitude ) hopping frequency and a lower spiking frequency . by virtue of their coherent inhibition , sparsely synchronized suprathreshold neurons suppress noisy activities of subthreshold neurons . thus , only coherent subthreshold hoppings appear in the individual potentials of subthreshold neurons . we also characterize the inhibitory coherence in terms of the `` statistical - mechanical '' spike - based and correlation - based measures and find that the degree of inhibitory coherence increases with increasing for . finally , effect of sparse randomness of synaptic connectivity on the inhibitory coherence and universality of the heterogeneity - induced inhibitory coherence are briefly discussed .

gr-qc0509113

c

we have obtained a number of general results . we have studied warped product @xmath0 spacetimes ( theorem 3.1 ) . we have presented the canonical form for the kundt @xmath0 metric ( theorem 4.1 ) , and studied higher dimensional kundt spacetimes in some detail . in sections 3 & 5 we have constructed higher dimensional examples of @xmath0 spacetimes that arise as warped products and that belong to the kundt class . in the appendices we shall present all of the 3-dimensional @xmath1 metrics , explicitly construct the metrics in the 4-dimensional @xmath0 spacetimes , and we shall establish the canonical higher dimensional @xmath1 metric . motivated by our results and examples we propose the following conjectures : a spacetime is @xmath0 iff there exists a null frame in which the riemann tensor and its derivatives can be brought into one of the following forms : either 1 . the riemann tensor and its derivatives are constant , in which case we have a locally homogeneous space , or 2 . the riemann tensor and its derivatives are of boost order zero with constant boost weight zero components at each order . this implies that riemann tensor is of type ii or less . whereas the proof of the ` if ' direction is trivial , the ` only if ' part is significantly more difficult and would require considering second order curvature invariants . we also point out that if we relax @xmath0 to @xmath0@xmath257 then in ( 1 ) we must now include all 1-curvature homogeneous spacetimes as well , since these naturally imply @xmath0@xmath257 and are not necessarily homogeneous spaces . assuming that the above conjecture is correct and that there exists such a preferred null frame , then if a spacetime is @xmath0 , then the spacetime is either locally homogeneous or belongs to the higher dimensional kundt @xmath0 class . finally , we have that if a spacetime is @xmath0 , then it can be constructed from locally homogeneous spaces and @xmath1 spacetimes . this construction can be done by means of fibering , warping and tensor sums . from the results above and these conjectures , it is plausible that for @xmath0 spacetimes that are not locally homogeneous , the weyl type is @xmath2 , @xmath3 , @xmath4 or @xmath5 , and that all boost weight zero terms are constant . we intend to study the general validity of these conjectures in future work . the relationship to curvature homogeneous spacetimes is addressed in @xcite . support for these conjectures in the 4d case is discussed in the next section .

we obtain a number of general results in arbitrary dimensions . we study and construct warped product spacetimes and higher - dimensional kundt spacetimes . we show how these spacetimes can be constructed from locally homogeneous spaces and spacetimes . in particular , it is plausible that for spacetimes that are not locally homogeneous the weyl type is , , or , with any boost weight zero components being constant .

we study lorentzian spacetimes for which all scalar invariants constructed from the riemann tensor and its covariant derivatives are constant ( spacetimes ) . we obtain a number of general results in arbitrary dimensions . we study and construct warped product spacetimes and higher - dimensional kundt spacetimes . we show how these spacetimes can be constructed from locally homogeneous spaces and spacetimes . the results suggest a number of conjectures . in particular , it is plausible that for spacetimes that are not locally homogeneous the weyl type is , , or , with any boost weight zero components being constant . we then consider the four - dimensional spacetimes in more detail . we show that there are severe constraints on these spacetimes , and we argue that it is plausible that they are either locally homogeneous or that the spacetime necessarily belongs to the kundt class of spacetimes , all of which are constructed . the four - dimensional results lend support to the conjectures in higher dimensions .

1601.00273

c

in this paper we have examined the tripartite entanglement dynamics when each party is entangled with other parties initially , but they locally interact with their own markovian or non - markovian environment . first , we have considered three ghz - type initial states @xmath186 , @xmath187 , and @xmath188 . all states are lu to each other . it turns out that the ghz symmetry of the initial states is broken due to the effect of environment . we have computed the corresponding @xmath0-tangles analytically at arbitrary time @xmath61 in eqs . ( [ ghz-1-pi-2 ] ) , ( [ ghz-2-pi-2 ] ) , and ( [ ghz-3-pi-2 ] ) . it was shown that while the esd phenomenon occurs for type i , the entanglement dynamics for the remaining types exhibits an exponential decay in the markovian regime . in the non - markovian regime the @xmath0-tangles completely vanish when @xmath189 \hspace{.3 cm } ( n = 1 , 2 , \cdots)$ ] and @xmath115 . as shown in fig . 3 the revival phenomenon of entanglement occurs after complete disappearance of entanglement . based on the analytical results it was shown that while the robustness order against the effect of reservoir is @xmath69 , @xmath133 , @xmath134 for large @xmath88 region , this order is reversed for small @xmath88 region . dependence of concurrences eq.([bipartite1 ] ) and eq . ( [ bipartite2 ] ) when @xmath170 . ( a ) in this figure we choose @xmath89 . this shows that while bipartite entanglement dynamics for type i ( red line ) decays exponentially with the half - life rule , that for type ii ( blue line ) exhibits an esd . ( b ) in this figure we choose @xmath90 . although both entanglements decay in time , the decay rate for type ii ( blue line ) is much faster than that for type i ( red line).,title="fig:",height=188 ] dependence of concurrences eq.([bipartite1 ] ) and eq . ( [ bipartite2 ] ) when @xmath170 . ( a ) in this figure we choose @xmath89 . this shows that while bipartite entanglement dynamics for type i ( red line ) decays exponentially with the half - life rule , that for type ii ( blue line ) exhibits an esd . ( b ) in this figure we choose @xmath90 . although both entanglements decay in time , the decay rate for type ii ( blue line ) is much faster than that for type i ( red line).,title="fig:",height=188 ] we also have examined the tripartite entanglement dynamics for two w - type initial states @xmath190 and @xmath191 with @xmath146 . like ghz - type initial states they are lu to each other . for initial @xmath161 state the @xmath0-tangle is analytically computed in eq . ( [ w-1-pi-3 ] ) . since , however , @xmath169 propagates to higher - rank state with the lapse of time , the analytic computation is impossible except few special cases . thus , we have computed the @xmath0-tangle analytically for special case @xmath170 . in fig . 4 and fig . 5 it was shown that @xmath161 is more robust than @xmath169 against the markovian and non - markovian environments . the bipartite entanglements measured by the concurrence@xcite for @xmath147 and @xmath163 are @xmath192 and @xmath193 \nonumber \\ & & { \cal c}^{ii}_{ac } ( t ) = 2 p_t^2 \max \left[0 , |a c| -|b| \sqrt{(1 - p_t^2 ) ( 1 - b^2 p_t^2 ) } \right ] \\ \nonumber & & { \cal c}^{ii}_{bc } ( t ) = 2 p_t^2 \max \left[0 , |a b| - |c| \sqrt{(1 - p_t^2 ) ( 1 - c^2 p_t^2 ) } \right ] . \end{aligned}\ ] ] one can show @xmath194 in the entire range of time like a tripartite entanglement regardless of markovian or non - markovian environment . the @xmath87-dependence of the concurrences is plotted in fig . 6 as red line for type i and blue line for type ii when ( a ) markovian ( @xmath89 ) and ( b ) non - markovian ( @xmath90 ) environments are introduced . 6(a ) shows that while the entanglement for type i exhibits an exponential decay with the half - life rule , that for type ii exhibits an esd . for non - markovian case the decay rate for type ii is much faster than that for type i although both exhibit a revival phenomenon of entanglement . it is of interest to study the effect of non - markovian environment when the initial state is a rank-@xmath195 mixture @xmath196 where @xmath197 and @xmath198 . the residual entanglement of @xmath199 is known as @xmath200 where @xmath201{2}}{3 + 4 \sqrt[3]{2 } } = 0.626851\cdots \hspace{1.0 cm } p_1 = \frac{1}{2 } + \frac{3 \sqrt{465}}{310 } = 0.70868\cdots \\ \nonumber & & g_i ( p ) = p^2 - \frac{8 \sqrt{6}}{9 } \sqrt{p ( 1 - p)^3 } \hspace{1.0 cm } g_{ii}(p ) = 1 - ( 1 - p ) \left(\frac{3}{2 } + \frac{1}{18 } \sqrt{465 } \right).\end{aligned}\ ] ] it is interesting , at least for us , how the non - markovian environment modifies coffman - kundu - wootters inequality @xmath202 \geq { \cal c}(\rho_{ab})^2 + { \cal c}(\rho_{ac})^2 $ ] in this model . similar issue was discussed in ref . @xcite . since we have derived the @xmath0-tangles analytically , we tried to find the entanglement invariants@xcite , which was originally found in four - qubit system . in our three - qubit systems we can not find any invariants it is of interest to examine the entanglement invariants in the higher - qubit and qudit systems . 99 m. a. nielsen and i. l. chuang , _ quantum computation and quantum information _ ( cambridge university press , cambridge , england , 2000 ) . r. horodecki , p. horodecki , m. horodecki , and k. horodecki , _ quantum entanglement _ , * 81 * ( 2009 ) 865 [ quant - ph/0702225 ] and references therein . c. h. bennett , g. brassard , c. crepeau , r. jozsa , a. peres , and w. k. wootters , _ teleporting an unknown quantum state via dual classical and einstein - podolsky - rosen channles _ , phys.rev * 70 * ( 1993 ) 1895 . c. h. bennett and s. j. wiesner , _ communication via one- and two - particle operators on einstein - podolsky - rosen states _ , * 69 * ( 1992 ) 2881 . v. scarani , s. lblisdir , n. gisin , and a. acin , _ quantum cloning _ , * 77 * ( 2005 ) 1225 [ quant - ph/0511088 ] and references therein . a. k. ekert , _ quantum cryptography based on bell s theorem _ , * 67 * ( 1991 ) 661 . c. kollmitzer and m. pivk , applied quantum cryptography ( springer , heidelberg , germany , 2010 ) . t. d. ladd , f. jelezko , r. laflamme , y. nakamura , c. monroe , and j. l. obrien , _ quantum computers _ , nature , * 464 * ( 2010 ) 45 [ arxiv:1009.2267 ( quant - ph ) ] . g. vidal , _ efficient classical simulation of slightly entangled quantum computations _ * 91 * ( 2003 ) 147902 [ quant - ph/0301063 ] . breuer and f. petruccione , _ the theory of open quantum systems _ ( oxford university press , oxford , new york , 2002 ) . w. h. zurek , _ decoherence , einselection , and the quantum origins of the classical _ , rev . mod . * 75 * ( 2003 ) 715 [ quant - ph/0105127 ] . t. yu and j. h. eberly , _ phonon decoherence of quantum entanglement : robust and fragile states _ , * b 66 * ( 2002 ) 193306 [ quant - ph/0209037 ] . c. simon and j. kempe , _ robustness of multiparty entanglement _ , phys . rev . * a 65 * ( 2002 ) 052327 [ quant - ph/0109102 ] . w. dr and h. j. briegel , _ stability of macroscopic entanglement under decoherence _ , lett . * 92 * ( 2004 ) 180403 [ quant - ph/0307180 ] . t. yu and j. h. eberly , _ finite - time disentanglement via spontaneous emission _ , * 93 * ( 2004 ) 140404 [ quant - ph/0404161 ] . t. yu and j. h. eberly , _ sudden death of entanglement : classical noise effects _ , opt . commun . * 264 * ( 2006 ) 393 [ quant - ph/0602196 ] . t. yu and j. h. eberly , _ quantum open system theory : bipartite aspects_. phys . * 97 * ( 2006 ) 140403 [ quant - ph/0603256 ] t. yu and j. h. eberly , _ sudden death of entanglement _ , science , * 323 * ( 2009 ) 598 [ arxiv:0910.1396 ( quant - ph ) ] . et al _ , _ environment - induced sudden death of entanglement _ , science * 316 * ( 2007 ) 579 [ quant - ph/0701184 ] . j. laurat , k. s. choi , h. deng , c. w. chou , and h. j. kimble , _ heralded entanglement between atomic ensembles : preparation , decoherence , and scaling _ , physics . * 99 * ( 2007 ) 180504 [ arxiv:0706.0528 ( quant - ph ) ] . c. e. lpez , g. romero , f. lastra , e. solano , and j. c. retamal , _ sudden birth versus sudden death of entanglement in multipartite systems _ , * 101 * ( 2008 ) 080503 [ arxiv:0802.1825 ( quant - ph ) ] . b. bellomo , r. lo franco , and g. compagno , _ non - markovian effects on the dynamics of entanglement _ , phys . * 99 * ( 2007 ) 160502 [ arxiv:0804.2377 ( quant - ph ) ] . s. hill and w. k. wootters , _ entanglement of a pair of quantum bits _ , * 78 * ( 1997 ) 5022 [ quant - ph/9703041 ; w. k. wootters , _ entanglement of formation of an arbitrary state of two qubits _ , * 80 * ( 1998 ) 2245 [ quant - ph/9709029 ] . breuer , e. -m . laine , and j. piilo , _ measure for the degree of non - markovian behavior of quantum processes in open systems _ * 103 * ( 2009 ) 210401 [ arxiv:0908.0238 ( quant - ph ) ] . b. vacchini , a. smirne , e. -m . laine , j. piilo , and h. -p . breuer , _ markovian and non - markovian dynamics in quantum and classical systems _ , new j. phys . * 13 * ( 2011 ) 093004 [ arxiv:1106.0138 ( quant - ph ) ] . d. chruciski , a. kossakowski , and a. rivas , _ measures of non - markovianity : divisibility versus backflow of information _ , phys . rev . * a 83 * ( 2011 ) 052128 [ arxiv:1102.4318 ( quant - ph ) ] . a. rivas , s. f. huelga , and m. b. plenio , _ quantum non - markovianity : characterization , quantification and detection _ * 77 * ( 2014 ) 094001 [ arxiv:1405.0303 ( quant - ph ) ] . m. j. w. hall , j. d. cresser , l. li , and e. andersson _ canonical form of master equations and characterization of non - markovianity _ , phys . rev . * a 89 * ( 2014 ) 042120 [ arxiv:1009.0845 ( quant - ph ) ] . kim , h .-m . li , and b. -k . zhao , _ genuinetripartite entanglement dynamics and transfer in a triple jaynes - cummings model _ , int * 55 * ( 2016 ) 241 . m. ynac , t. yu , and j. h. eberly , _ pairwise concurrence dynamics : a four - qubit model _ , j. phys . b : at . mol . * 40 * ( 2007 ) 545 [ quant - ph/0701111 ] . d. m. greenberger , m. horne , and a. zeilinger , _ bell s theorem , quantum theory , and conceptions of the universe _ , edited by m. kafatos ( kluwer , dordrecht , 1989 ) . w. dr , g. vidal , and j. i. cirac , _ three qubits can be entangled in two inequivalent ways _ , phys * a62 * ( 2000 ) 062314 [ quant - ph/0005115 ] . v. coffman , j. kundu , and w. k. wootters , _ distributed entanglement _ , phys . rev . * a 61 * ( 2000 ) 052306 [ quant - ph/9907047 ] . y. u. ou and h. fan , _ monogamy inequality in terms of negativity for three - qubit states _ , phys . rev . * a75 * ( 2007 ) 062308 [ quant - ph/0702127 ] . c. h. bennett , d. p. divincenzo , j. a. smokin , and w. k. wootters , _ mixed - state entanglement and quantum error correction _ , phys . rev . * a 54 * ( 1996 ) 3824 [ quant - ph/9604024 ] . a. uhlmann , _ fidelity and concurrence of conjugate states _ , phys . rev . * a 62 * ( 2000 ) 032307 [ quant - ph/9909060 ] . r. lohmayer , a. osterloh , j. siewert , and a. uhlmann , _ entangled three - qubit states without concurrence and three - tangle _ , phys . lett . * 97 * ( 2006 ) 260502 [ quant - ph/0606071 ] ; c. eltschka , a. osterloh , j. siewert , and a. uhlmann , _ three - tangle for mixtures of generalized ghz and generalized w states _ , new j. phys . * 10 * ( 2008 ) 043014 [ arxiv:0711.4477 ( quant - ph ) ] ; e. jung , m. r. hwang , d. k. park , and j. w. son , _ three - tangle for rank-@xmath203 mixed states : mixture of greenberger - horne - zeilinger , w and flipped w states _ , phys . rev . * a 79 * ( 2009 ) 024306 [ arxiv:0810.5403 ( quant - ph ) ] ; e. jung , d. k. park , and j. w. son , _ three - tangle does not properly quantify tripartite entanglement for greenberger - horne - zeilinger - type state _ rev . * a 80 * ( 2009 ) 010301(r ) [ arxiv:0901.2620 ( quant - ph ) ] ; e. jung , m. r. hwang , d. k. park , and s. tamaryan , _ three - party entanglement in tripartite teleportation scheme through noisy channels _ , quant . inf . comp . * 10 * ( 2010 ) 0377 [ arxiv:0904.2807 ( quant - ph ) ] . c. eltschka and j. siewert , _ entanglement of three - qubit greenberger - horne - zeilinger - symmetric states _ , phys . * 108 * ( 2012 ) 020502 [ arxiv:1304.6095 ( quant - ph ) ] . j. siewert and c. eltschka , _ quantifying tripartite entanglement of three - qubit generalized werner states _ * 108 * ( 2012 ) 230502 . g. vidal and r. f. werner , _ computable measure of entanglement _ , phys . rev . * a65 * ( 2002 ) 032314 [ quant - ph/0102117 ] . b. m. garraway , _ nonperturbative decay of an atomic system in a cavity _ , phys . rev . * a55 * ( 1997 ) 2290 . s. maniscalco and f. petruccione , _ non - markovian dynamics of a qubit _ , phys . rev . * a73 * ( 2006 ) 012111 [ quant - ph/0509208 ] . k. kraus , _ states , effect , and operations : fundamental notions in quantum theory _ ( springer - verlag , berlin , 1983 ) . a. c. s. costa , r. m. angelo , and m. w. beims , _ monogamy and backflow of mutual information in non - markovian thermal baths _ , phys . rev . * a 90 * ( 2014 ) 012322 [ arxiv:1404.6433 ( quant - ph ) ] .

we study on the tripartite entanglement dynamics when each party is initially entangled with other parties , but they locally interact with their own markovian or non - markovian environment . the corresponding-tangles , one of the tripartite entanglement measure , are analytically computed at arbitrary time . for markovian case while the tripartite entanglement for type i exhibits an entanglement sudden death , the dynamics for the remaining cases decays normally in time with the half - life rule . for non - markovian case the revival phenomenon of entanglement occurs after complete disappearance of entanglement . we also consider two w - type initial states . for both cases the-tangles are analytically derived .

we study on the tripartite entanglement dynamics when each party is initially entangled with other parties , but they locally interact with their own markovian or non - markovian environment . first , we consider three ghz - type initial states , all of which have ghz symmetry provided that the parameters are chosen appropriately . however , this symmetry is broken due to the effect of environment . the corresponding-tangles , one of the tripartite entanglement measure , are analytically computed at arbitrary time . for markovian case while the tripartite entanglement for type i exhibits an entanglement sudden death , the dynamics for the remaining cases decays normally in time with the half - life rule . for non - markovian case the revival phenomenon of entanglement occurs after complete disappearance of entanglement . we also consider two w - type initial states . for both cases the-tangles are analytically derived . the revival phenomenon also occurs in this case . on the analytical ground the robustness or fragility issue against the effect of environment is examined for both ghz - type and w - type initial states .

1106.5533

i

understanding the rates and the structure of multi - jet production in hadron hadron collisions is of primary importance for new physics searches . production of high transverse momentum jets is a hard process which implies a head - on collision of qcd partons quarks and/or gluons from the small - distance wave functions of initial hadrons . cross section of a hard collision is small compared with the size of hadron , @xmath6 , with @xmath5 the scale related to transverse momenta of the produced jets , @xmath7 . therefore , typically it is two partons that experience a hard collision in a given event . a large angle scattering of these two partons produces two ( or more ) final state partons that manifest themselves as hadron large transverse momentum jets . at the same time , one can not exclude a possibility that more than one pair of partons happen to collide in a given event , giving rise to a multi - jet event . a possibility of a double hard collision becomes more important with increase of the energy of the collision where scattering off small @xmath8 partons which have much higher densities becomes possible . in recent years multiparton collisions have attracted close attention . following the pioneering work of refs . @xcite , a large number of related theoretical papers appeared @xcite , based on the parton model and geometrical picture in the impact parameter space . more recently , this topic has been intensively discussed in view of the lhc program @xcite . monte carlo event generators that produce multiple parton collisions are being developed @xcite ; theoretical papers exploring properties of double parton distributions and discussing their qcd evolution have appeared @xcite . in our view , however , important elements of qcd that are necessary for theoretical understanding of the multiple hard interactions issue have not yet been properly taken into account by above - mentioned intuitive approaches . the problem is , sort of , educational : both the probabilistic picture , the mc generator technology is based upon , and the familiar feynman diagram technique , when used in the momentum space , prove to be inadequate for careful analysis and understanding of the physics of multiple collisions . from experience gained by treating standard ( single ) hard processes , one became used to a motto that a large momentum transfer scale @xmath5 ensures the dominance of small distances , @xmath9 , in a process under consideration . with the multiple collisions under focus , however , one has to distinguish two space - time scales : that of _ localization _ of the parton participating in a hard interaction , @xmath10 , and that of _ transverse separation _ , @xmath11 , between the two hard collision vertices . the latter can be large , of the order of the hadron size , even for large @xmath5 . in order to be able to trace the relative distance between the partons , one has to use the mixed longitudinal momentum impact parameter representation which , in the momentum language , reduces to introduction of a mismatch between the transverse momentum of the parton in the amplitude and that of the same parton in the amplitude conjugated . another unusual feature of the multiple collision analysis that may look confusing at the first sight is the fact that even at the tree level _ the amplitude _ describing the double hard interaction process contains additional integrations over longitudinal momentum components ; more precisely over the difference of the ( large ) light - cone momentum components of the two partons originating from the same incident hadron ( see section [ subsec : pt34 ] ) . in the previous short publication @xcite we have considered production of two pairs of _ nearly back - to - back _ jets resulting from simultaneous hard collisions of two partons from the wave function of one incident hadron with two partons from the other hadron ( `` four - to - four '' processes ) . as we have shown , this necessitates introduction of a new object a generalized double parton distribution , @xmath3gpd , that depends on a new transverse momentum parameter @xmath12 conjugate to the relative distance between the two partons in the hadron wave function . generalized double parton distributions provide a natural framework for incorporating longitudinal and transverse correlations between partons in the hadron wave function at the @xmath13 scale , and for tracing the perturbative @xmath5-evolution of the correlations . the corresponding 4-jet cross section can be expressed in terms of @xmath3gpd s as follows [ eq:1 ] & = & d_a(x_1,x_2 ; ) d_b(x_3,x_4;- ) . the factor on the second line has dimension of inverse area : = , [ b3 ] where @xmath14 are the corresponding one - parton distributions . the ratio of the product of two single - inclusive cross sections and the double - inclusive cross section ( @xmath15 ) is often referred to in the literature as `` an effective cross section '' @xmath16 . we prefer , however , not to look at this quantity as a cross section , since it reflects transversal area of parton overlap as well as longitudinal correlations of the partons . at the same time , it has little to do with the measure of the strength of the interaction , which is what `` cross section '' represents . in a two - parton collision , scattered partons form two nearly back - to - back jets , while additional jets ( should there be any ) tend to be softer and to align with the directions of initial and final partons , because of collinear enhancements due to radiative nature of secondary partons . such will be typical characteristics of a _ 4-jet event _ , in particular . on the other hand , four jets produced as a result of a _ double hard collision _ of two parton pairs would , on the contrary , form _ two pairs _ of _ nearly back - to - back _ jets . this kinematical preference is in stark contrast with `` hedgehog - like '' configurations of four jets stemming from a single collision and can be used in order to single out double hard collisions experimentally . such experimental studies were recently carried out by the cdf and d0 collaborations who have studied production of three jets + photon @xcite . the analysis of the data performed in @xcite using information about generalized parton distribution ( gpds ) obtained from the study of hard exclusive processes at hera has found that observed @xmath17 rates were a factor @xmath18 higher than the expected rates based on a naive model that neglected correlations between partons in the transverse plane . the use of @xmath3gpd allows one to incorporate such correlations and predict their @xmath5 evolution . on the theory side , the back - to - back enhancement has been discussed , at tree level , in a number of studies of various channels ( see , for example , discussion of the 2 jets+@xmath19 in @xcite and references therein ) . in the present paper we study perturbative radiative effects in the _ differential _ 4-jet distribution in the back - to - back kinematics and derive the expression for the corresponding cross section in the leading logarithmic collinear approximation . it takes into account qcd evolution of the generalized double parton distributions as well as effects due to multiple soft gluon radiation , and turns out to be a direct generalization of the known `` ddt formula '' for back - to - back production of two large transverse momentum particles in hadron collisions @xcite . we also discuss and treat new specific correlations between transverse momenta of jets due to 3-parton interactions producing 4 jets,``three - to - four '' . such processes are induced by perturbative splitting of a parton from one of the hadrons , the offspring of which enter double hard collision with two partons from the wave function of the second hadron . the hard scale of this parton splitting is determined by transverse momentum imbalances of pairs of jets , @xmath20 , @xmath21 , and exhibits specific collinear enhancement in the kinematical region where two jet imbalances practically compensate one another , @xmath22 . consistently taking into account three - to - four parton process solves a longstanding problem of double counting in treating multi - parton interactions . discussion of the 2-parton distribution has a long history . it is commonly defined in the momentum space as a 2-particle inclusive quantity depending on two parton momenta , see @xcite . being related to ( the imaginary part of ) a certain _ forward _ scattering amplitude , it therefore disregards impact parameter space geometry of the interaction . exploring properties of 2-parton distributions so defined , an approach to the study of the multiple jet production has been recently suggested in ref . the reason why this approach has faced difficulties , @xcite , and did not solve , in our view , the problem of systematic pqcd analysis of 4-jet production is clear : it did not incorporate effects due to variations of the transverse separation between the partons information encoded by @xmath3gpd s but not by the 2-parton momentum distributions . the @xmath3gpd s were recently used in ref . @xcite for intuitive description of the total 4-jet production cross section . however , the differential distributions were not discussed in that paper , and not all relevant pqcd contributions were included , so that our results are different from the ones obtained in @xcite . the paper is organized as follows . in section [ ptanalysis ] we recall the main ingredients of the perturbative analysis based on selection of maximally collinear enhanced contributions in all orders . in section [ sec : eveq ] we present the evolution equation for generalized two - parton distributions . section [ sec : pt ] is devoted to the perturbative analysis of small - distance correlations between partons . the main result of the paper the differential distribution of 4-jet production in the back - to - back kinematics is formulated in section [ sec:4324 ] , and the total cross section of two - dijet production is described in section [ total ] . conclusions and outlook are presented in section [ conclude ] .

we study production of two pairs of jets in hadron hadron collisions in view of extracting contribution of _ double hard interactions _ of three and four partons ( , ) . such interactions , in spite of being power suppressed at the level of the total cross section , become comparable with the standard hard collisions of two partons , , in the _ back - to - back kinematics _ when the transverse momentum imbalances of two pairing jets are relatively small . we express differential and total cross sections for two - dijet production in double parton collisions through the generalized two - parton distributions ,gpds , that contain large - distance two - parton correlations of non - perturbative origin as well as small - distance correlations due to parton evolution . we demonstrate that the mechanism , being of the same order in as the process , turns out to be _ geometrically enhanced _ compared to the latter and should contribute significantly to 4-jet production .

we study production of two pairs of jets in hadron hadron collisions in view of extracting contribution of _ double hard interactions _ of three and four partons ( , ) . such interactions , in spite of being power suppressed at the level of the total cross section , become comparable with the standard hard collisions of two partons , , in the _ back - to - back kinematics _ when the transverse momentum imbalances of two pairing jets are relatively small . we express differential and total cross sections for two - dijet production in double parton collisions through the generalized two - parton distributions ,gpds , that contain large - distance two - parton correlations of non - perturbative origin as well as small - distance correlations due to parton evolution . we find that these large- and small - distance correlations participate in different manner in 4-jet production , and treat them in the leading logarithmic approximation of pqcd that resums collinear logarithms in all orders . a special emphasis is given to double hard interaction processes that occur as an interplay between large- and short - distance parton correlations and were not taken into consideration by approaches inspired by the parton model picture . we demonstrate that the mechanism , being of the same order in as the process , turns out to be _ geometrically enhanced _ compared to the latter and should contribute significantly to 4-jet production . the framework developed here takes into systematic consideration perturbative evolution ofgpds . it can be used as a basis for future analysis of nlo corrections to multi - parton interactions ( mpi ) at lhc and tevatron colliders , in particular for improving evaluation of qcd backgrounds to new physics searches .

1106.5533

c

in this work we aimed at generalization of the qcd factorization theorem to multiple parton interactions in hadron hadron collisions . such generalization is necessary for carrying out systematic studies both theoretical and experimental of the parton correlations inside hadrons , and allows one to incorporate in a model independent way higher order pqcd effects . in the small-@xmath8 domain , generalization of the mpi analysis presented here may be looked upon as realization of the gribov pomeron calculus , with exact account of energy - momentum conservation . we considered four jet production and have shown that double hard parton collisions play a significant role in the _ back - to - back kinematics_. this kinematics one selects by demanding the transverse momentum imbalances of two pairs of jets , @xmath186 and @xmath187 , to be much smaller than the overall hard scale of the scattering process : @xmath188 . we were able to analyze and calculate corresponding differential spectra and total cross sections with account of all collinear enhanced pqcd radiative effects giving rise to sudakov form factors and to scaling violations in one - parton and _ generalized double parton distributions _ , @xmath189gpds , that have been introduced in @xcite . our main results are eqs . for the differential distribution and eq . for the total cross section of 4-jet production in the back - to - back kinematics . they are derived in the leading logarithmic ( collinear ) approximation . the formalism developed here provides the framework , and a starting point , for systematic calculation of nll and nlo corrections that may be needed for more careful account of the mpi effects at lhc . in particular , in the present study we did not hunt for single logarithmic corrections due to _ large - angle soft gluon radiation_. these ( formally subleading but potentially important ) logarithmic effects depend on details of the color transfers in hard parton scattering processes . they should be treated together with a delicate question of algorithmic determination of transverse momenta of the hadron jets . the corresponding study @xcite exists for the single hard scattering case , @xmath190 , and provides a solid base for analogous treatment of large - angle gluon radiation in double parton collision processes . we demonstrated that , in addition to the qcd - improved parton model picture of 4-parton collisions , pqcd also reserves an important place to 3-parton collisions producing four jets . such @xmath0 transitions are the novel hard double scattering processes that are systematically treated in this work for the first time . @xmath0 parton process appears when a parton from one colliding hadron splits into two partons that enter into double hard interaction with two partons from the ( non - perturbative ) wave function of the second hadron . perturbative parton splitting occurs at relatively small impact parameters , while the relative impact parameter distance between two hard vertices in a @xmath1 collision can be as large as the transverse size of the hadron . parametrically , @xmath0 and @xmath1 subprocesses are comparable ( they are of the same order in @xmath4 and have similar structure of the back - to - back enhancement ) . at the same time , the difference in geometry of the interaction processes results in a _ numerical enhancement _ of @xmath0 with respect to @xmath1 subprocess ( by a numerical factor of 45 ) . as a result , @xmath0 transitions should contribute significantly to 4-jet production , even if they happen to constitute formally a small correction to a @xmath3gpd . it is important to stress that the processes where one parton splits perturbatively into two in _ both colliding hadrons _ do not contribute to the 2-dijet production , since the corresponding differential distribution lacks the necessary back - to - back double pole enhancement @xmath191 . in fact , such configurations represent a one - loop correction to the @xmath2 jet production mechanism and as such belong to the class of the standard single hard interaction processes rather than to mpi . this result of @xcite has been later confirmed in refs . the role of @xmath0 parton subprocesses is twofold . when the perturbative splitting occurs at momentum scales smaller than the pair jet imbalances @xmath128 ( that is , `` deep inside the dglap ladder '' ) , such contributions exhibit the same two - pole enhanced structure as the conventional @xmath1 transitions already discussed in @xcite : @xmath192 the corresponding differential distribution is a direct generalization of the `` ddt formula '' @xcite containing derivatives over transverse momentum imbalances , with eq . describing @xmath1 collisions and eq . a crosstalk between large- and small - distance two - parton correlators . at the same time , the parton splitting may occur just at the scale @xmath128 and produce two partons that , without any further evolution , interact with two partons from the wave function of the second hadron . such eventuality also has a necessary back - to - back enhancement but of a different structure : @xmath193 such contributions are absent in the parton model . they can not be represented as the product of two @xmath3gpds and must be taken into account separately , see eq . . a detailed numerical investigation of these contributions will be presented elsewhere @xcite . formulas derived in this work can be used to address various aspects of the lhc physics . our results are directly applicable to the case of double drell yan processes at lhc . in particular they can be applied to the recently observed production of heavy quarkonia at the lhc @xcite . the formalism developed in the present paper should help to improve the accuracy of the prediction of qcd backgrounds in searches for new physics . it also can be used for further studies of the nucleon structure , in particular of the short - range non - perturbative inter - parton correlations in the nucleon and the nuclei , for the study of the higher twist contributions that are unavailable in the conventional dis processes , etc . in addition , it would be interesting to extend the formalism developed here to investigate qcd medium effects that manifest themselves in @xmath194 collisions in recent experiments at cern . on the experimental side , observation of the parton splitting processes discussed in this paper will give the first direct evidence of an interplay between large- and short - distance qcd correlations in hard processes . to achieve this goal one has to look for enhancement of 4-jet production in the kinematical region of jet transverse momenta @xmath195

we find that these large- and small - distance correlations participate in different manner in 4-jet production , and treat them in the leading logarithmic approximation of pqcd that resums collinear logarithms in all orders . the framework developed here takes into systematic consideration perturbative evolution ofgpds . it can be used as a basis for future analysis of nlo corrections to multi - parton interactions ( mpi ) at lhc and tevatron colliders , in particular for improving evaluation of qcd backgrounds to new physics searches .

we study production of two pairs of jets in hadron hadron collisions in view of extracting contribution of _ double hard interactions _ of three and four partons ( , ) . such interactions , in spite of being power suppressed at the level of the total cross section , become comparable with the standard hard collisions of two partons , , in the _ back - to - back kinematics _ when the transverse momentum imbalances of two pairing jets are relatively small . we express differential and total cross sections for two - dijet production in double parton collisions through the generalized two - parton distributions ,gpds , that contain large - distance two - parton correlations of non - perturbative origin as well as small - distance correlations due to parton evolution . we find that these large- and small - distance correlations participate in different manner in 4-jet production , and treat them in the leading logarithmic approximation of pqcd that resums collinear logarithms in all orders . a special emphasis is given to double hard interaction processes that occur as an interplay between large- and short - distance parton correlations and were not taken into consideration by approaches inspired by the parton model picture . we demonstrate that the mechanism , being of the same order in as the process , turns out to be _ geometrically enhanced _ compared to the latter and should contribute significantly to 4-jet production . the framework developed here takes into systematic consideration perturbative evolution ofgpds . it can be used as a basis for future analysis of nlo corrections to multi - parton interactions ( mpi ) at lhc and tevatron colliders , in particular for improving evaluation of qcd backgrounds to new physics searches .

0804.4447

i

classical cellular automata have become a standard modeling tool for complex phenomena . with their discrete time step and their intrinsically high degree of parallelization they are ideally suited for models of diverse phenomena as coffee percolation , highway traffic and oil extraction from porous media . as an abstract computational model cellular automata can simulate turing machines , and even explicit simple automata such as conway s life game have been shown to support universal computation @xcite . on the quantum side , the interest in cellular automata stems from their implementation in optical lattices and arrays of optical microtraps . however , the theory of quantum cellular automata ( qcas ) is still in its early stage . since each cell may influence several others , the dynamics is subject to a `` no - cloning '' constraint , leading to a non - trivial interplay between the conditions of locality and unitarity . it is therefore helpful to have some class of qcas , which can be analyzed in great detail , and which can serve as a testing ground for general ideas about qcas . this paper is concerned with such an analysis , namely of the special class of clifford quantum cellular automata ( cqcas ) , in which the elementary time step is given by a `` clifford gate '' , meaning that it takes tensor products of pauli matrices to tensor products of other pauli matrices . in the theory of gate model computation , and for the one - way quantum computation model , a detailed analysis of what can be done with clifford operations alone turned out to be very useful , even though as the downside of allowing an efficient classical description such gates alone do not allow universal quantum computation . by analogy it is therefore clear that cqcas do not comprise the full complexity of qcas . what one can hope to get , however , is an interesting class of cellular automata , and some tools for understanding this class in great detail . a similar analysis has been done with gaussian quantum cellular automata @xcite , e.g. the qca describes a chain of harmonic oscillators with nearest neighbor couplings . for all these qcas the hilbert space of one elementary cell is infinite dimensional , and the qca maps phase space translations , also referred to as weyl operators , to phase space translations . in our approach we use elementary cells with a finite number of levels , which corresponds to replacing the continuous phase space by a discrete space . by definition , a cellular automaton is a lattice system , which consists of many subsystems ( called `` cells '' ) labeled by a point lattice in space . for simplicity , we will always take the lattice as @xmath2 , the integer cubic lattice in @xmath3 space dimensions , where we discuss periodic boundary conditions , and hence toroidal lattices ] . the cell systems in the classical case may have states like `` occupied '' and `` empty '' . in the quantum case , they will be @xmath4-state quantum systems , for some finite @xmath4 . in either case the group of lattice translations ( `` shifts '' ) is a symmetry of the system . the dynamics will be given by a discrete global time step , or global `` transition rule '' assumed to have the following three properties : * _ translation invariance _ : the time step commutes with the lattice translation symmetries . * _ reversibility _ : there is an inverse rule . for a finite quantum system this would mean unitary dynamics . for the infinite lattice system this will be stated algebraically below . * _ locality _ , or `` finite propagation speed '' : the state of each cell after one step can be computed from the state in a fixed finite region around the cell . these assumption define the class of reversible qcas @xcite . the locality and reversibility conditions are best phrased in the heisenberg picture : if @xmath5 denotes some observable of the system , its expectation after one time step starting from the initial state @xmath6 will be @xmath7 for a suitable observable @xmath8 , where by @xmath9 we denote the expectation of @xmath5 in the state @xmath6 . the transformation @xmath10 is what we will call the _ global rule _ of the automaton . then reversibility ( together with complete positivity , which is required of any dynamical map ) implies that @xmath11 is a homomorphism of the observable algebra of the whole system : @xmath11 is linear , @xmath12 , and @xmath13 . locality means that an observable @xmath14 localized at some lattice point @xmath15 ( i.e. , an observable of the cell at @xmath16 ) will be mapped to an observable localized in the region @xmath17 . that is , @xmath18 will be in the tensor product of the cell algebras belonging to the sites @xmath19 with @xmath20 . by translation invariance this set @xmath21 , called the _ neighborhood scheme _ of the automaton is independent of @xmath16 . the global transition rule @xmath11 is a map on an infinite dimensional space , and hence not readily specified explicitly . however , by using the basic properties of qcas one can see that it suffices to know just a few local data , associated with the region @xmath21 , in order to reconstruct @xmath11 uniquely . suppose we know @xmath18 for every observable @xmath14 in some basic cell @xmath16 . then by translation invariance we know the analogous transformation for _ any _ cell . moreover , since every local observable can expanded in products of one - cell observables , and because @xmath11 is a homomorphism , we can compute @xmath11 for any local observable . so the restriction @xmath22 of @xmath11 to the observables of a single cell @xmath16 can be called the _ local rule _ of the automaton . we can also decide by a finite set of equations , whether a proposed local rule actually belongs to a well - defined global rule : clearly @xmath22 must be a homomorphism . the only further condition one has to check is that the images of observables @xmath14 and @xmath23 localized in the cells indicated also commute , i.e. , @xmath24 , whenever @xmath25 . this is necessary , because @xmath14 and @xmath23 commute , and a moment s reflection shows that this is also sufficient for uniquely reconstructing the images of arbitrary observables under @xmath11 . the commutation conditions on the local rule are trivially satisfied when @xmath16 and @xmath26 are sufficiently far apart , when @xmath17 and @xmath27 are disjoint . hence only finitely many conditions need to be checked . for special classes , the job of specifying a qca via its local rule can be reduced still further , which is where the clifford condition comes in . let us assume now that we have a qubit system , so the local cell dimension is @xmath28 . for each local cell we thus have a basis for the observables , consisting of the identity and the three pauli matrices , which we denote by @xmath29 and @xmath30 . by @xmath31 etc . we denote the corresponding pauli matrix belonging to the cell @xmath16 . finite tensor products of pauli matrices belonging to different sites , perhaps with a sign @xmath32 will be referred to as _ pauli products_. these form a group , called the pauli group . then a _ clifford quantum cellular automaton _ ( cqca for short ) is defined by the condition * _ clifford condition _ : if @xmath5 is any multiple of a pauli product , so is @xmath8 . clearly , this is equivalent to the property that one - cell pauli operators are taken to pauli products , which simplifies the local rule . moreover , it suffices to specify @xmath33 and @xmath34 for some @xmath16 , because we can compute @xmath35 via the homomorphism property . hence a cqca is defined in terms of just two pauli products . [ example-0 ] for the one - dimensional lattice ( @xmath36 ) , consider the relations @xmath37 let us verify that all requirements for a local rule are satisfied . to begin with each of the expressions on the right hand side , as a product of pauli matrices , is hermitian with square one . these are all the required conditions related to just a single line , and are satisfied for any pauli product with a sign @xmath38 . next we have to verify the anti - commutation relation arising from applying a homomorphism @xmath11 to the anti - commutation relation @xmath39 . indeed , @xmath40 . hence the definition @xmath41 again produces a hermitian operator with square @xmath42 , and the local rule is a homomorphism @xmath22 into the algebra on the sites @xmath17 with @xmath43 . finally , we have to check the commutation rules for the images of observables from neighboring sites . for example , we have @xmath44=-[z_x , z_x\otimes x_{x+1}\otimes z_{x+2}]=0 $ ] , and similarly @xmath45=0 $ ] . perhaps the only non - trivial relation to check is @xmath46 = [ z_{x-1}\otimes x_x\otimes z_{x+1},z_{x}\otimes x_{x+1}\otimes z_{x+2 } ] = 0,\ ] ] which holds because the factors on sites @xmath16 and @xmath47 both _ anti-_commute . in principle , we would also have to check the existence of an inverse for the automaton , which is actually given by @xmath48 and @xmath49 , but as was shown in @xcite , this already follows from the homomorphism property . it is clear from this example that the search for cqcas is now a combinatorial problem . we can first look for _ self commuting _ pauli products , i.e. , pauli products , which commute with all translates of itself . only these can appear on the right hand side of local rules . one can then check , for any pair @xmath50 of such products , whether they anti - commute , while all proper translates of @xmath51 commute with @xmath52 . in fact , we began our investigation by running this simple search program . we found , for example , that while there is a rich variety of self - commuting pauli products only reflection symmetric products could appear in a local rule . this will indeed be shown in full generality below . commuting sets of pauli products also play a central role in the problem of determining so - called stabilizer states : these are pure states , which can be characterized by eigenvalue equations for pauli products or , equivalently , by the condition that certain pauli products have expectation @xmath38 . it is easy to check that pauli products which simultaneously have sharp expectations @xmath38 must commute . now for the infinite lattice systems it is natural to ask which pauli products @xmath5 have the property that there is a unique pure state @xmath6 of the infinite system , which has expectation 1 for @xmath5 and all its translates . as the simplest example , let us take @xmath53 , so we ask for states with @xmath54 for all @xmath15 . clearly , this defines the `` all spins up '' state , which is an infinite product state . a slightly more complex example uses the stabilizer operators @xmath55 , which singles out the one - dimensional _ cluster state _ , whose higher dimensional analogs are used as the entanglement resource for universal one - way quantum computing @xcite . showing that these eigenvalue equations define a unique state of the infinite lattice is now very easy , by using the cellular automaton ( [ example - rule ] ) : since this automaton maps @xmath56 to the required stabilizer operator , all existence and uniqueness problems for such a state are mapped to the corresponding trivial questions for the stabilizer operator @xmath56 . in other words , self - commuting pauli products of the form @xmath57 for some cqca @xmath11 characterize a unique translation invariant cluster state . we will show later that ( at least in one dimension ) the converse is also true , so that there is a very close connection between stabilizer states and clifford cellular automata . the definition of cqcas given above applies only to qubit systems . however , all our results are also valid for higher dimensional cells , particular cells of prime dimension @xmath4 . the role of the pauli operators @xmath58 and @xmath30 is then taken by the cyclic shift on @xmath59 , and the multiplication by a phase , i.e. @xmath60 where all ket labels @xmath61 are taken modulo @xmath4 . products of these operators are called _ weyl operators _ , and the appropriate definition of cqcas requires that @xmath33 and @xmath34 are both tensor products of weyl operators . the necessary preliminaries on the pauli group and clifford operations in this extended setting , and the background concerning infinite lattice systems are provided in subsection [ sec-2 - 1 ] . in order to utilize the translation symmetry one would like to use fourier transform techniques . however , in the discrete structures an integral with complex phases makes no sense . it turns out , however , that a `` generating function '' technique does nearly as well . the analogue of the fourier transform is then a laurent - polynomial in an indeterminate variable , i.e. , a polynomial with coefficients in the field @xmath62 with both positive and negative powers . the salient facts about this structure will be provided in subsection [ sec-2 - 3 ] . the description in terms of laurent polynomials can also be adapted to lattices with periodic boundary conditions . this will be described in section [ sec - periodic ] . in order to discuss general clifford quantum cellular automata , that is , for arbitrary lattice and single cell dimension , we introduce in section [ sec-2 ] the necessary mathematical tools . we first review the concept of discrete weyl systems and ( infinite ) tensor products of them , thereby characterizing the underlying `` phase space '' . we show that clifford qcas can be completely characterized in terms of classical symplectic cellular automata . we also introduce our fourier transform techniques and study the structure of isotropic subspaces , because these play an essential role for the characterization of symplectic cellular automata and translationally invariant stabilizer states . in section [ sec-3 ] we will state our main results . we show that symplectic cellular automata can be identified with two - by - two matrices , which have laurent - polynomials as matrix elements . we will find that the determinant of this matrix must be one and that the polynomials must be reflection invariant . in the one - dimensional case we state that every translationally invariant stabilizer state can be prepared out of a product state by a single cqca step . furthermore , we also specify the generators of all 1d qcas . finally , we show in section [ sec - periodic ] that the close connection between translationally invariant stabilizer states and cqcas also holds in the case of periodic boundary conditions even in every lattice dimension .

we study reversible quantum cellular automata with the restriction that these are also clifford operations . this means that tensor products of pauli operators ( or discrete weyl operators ) are mapped to tensor products of pauli operators . we characterize these symplectic cellular automata and find that all possible local rules must be , up to some global shift , reflection invariant with respect to the origin . in the one dimensional case we also find that every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single clifford cellular automaton timestep , thereby characterizing these class of stabilizer states , and we show that all 1d clifford quantum cellular automata are generated by a few elementary operations . we also show that the correspondence between translationally invariant stabilizer states and translationally invariant clifford operations holds for periodic boundary conditions . ' '' '' * on the structure of clifford quantum cellular automata * dirk - m . schlingemann , holger vogts and reinhard f. werner ' '' '' 1 . isi foundation , quantum information theory unit + viale s. severo 65 + 10133 torino , italy [ aff-1 ] 2 . institut fr mathematische physik +

we study reversible quantum cellular automata with the restriction that these are also clifford operations . this means that tensor products of pauli operators ( or discrete weyl operators ) are mapped to tensor products of pauli operators . therefore clifford quantum cellular automata are induced by symplectic cellular automata in phase space . we characterize these symplectic cellular automata and find that all possible local rules must be , up to some global shift , reflection invariant with respect to the origin . in the one dimensional case we also find that every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single clifford cellular automaton timestep , thereby characterizing these class of stabilizer states , and we show that all 1d clifford quantum cellular automata are generated by a few elementary operations . we also show that the correspondence between translationally invariant stabilizer states and translationally invariant clifford operations holds for periodic boundary conditions . ' '' '' * on the structure of clifford quantum cellular automata * dirk - m . schlingemann , holger vogts and reinhard f. werner ' '' '' 1 . isi foundation , quantum information theory unit + viale s. severo 65 + 10133 torino , italy [ aff-1 ] 2 . institut fr mathematische physik + technische universitt braunschweig + mendelssohnstrae 3 + 38106 braunschweig , germany [ aff-2 ]

1008.2724

i

currently , the concept of slow - roll inflation is widely accepted by cosmologists , due to many precise observations , such as the wilkinson microwave anisotropy probe ( wmap)@xcite . we can explain all observations simply , using single field slow - roll inflation . however , future observations might detect non - standard signals , which will be evidence for a non - standard inflationary theory . the energy scale of inflation is considered to be very high compared to current experimental scale . thus , we can say that a new inflationary theory might contain information with regard to high energy physics , such as a superstring theory . therefore it is important to study theories beyond standard single field slow - roll inflation . one of candidates for a modified inflationary model is inflation with the gauss - bonnet and chern - simons corrections . these are the only two meaningful combinations of second order curvature terms , as a low energy effective theory@xcite , and can also be derived from some superstring models@xcite . cosmology with the gauss - bonnet term can affect background evolution and result in a non - singular cosmological model@xcite or other interesting solutions@xcite . in inflation with the chern - simons term , primordial gravitational waves are circularly polarized@xcite , which is considered as an interesting target for some future observations@xcite . many authors studied gauss - bonnet and chern - simons modified inflation . however , _ slow - roll _ inflation with the gauss - bonnet terms is not much studied , except in the papers@xcite . taking current observations into consideration , slow - roll inflation is the most plausible paradigm for inflation . therefore investigating slow - roll inflation with the gauss - bonnet and chern - simons corrections is an important subject . we have studied this topic in the previous paper@xcite . in this paper , we re - formalize slow - roll inflation in gravity with the gauss - bonnet and chern - simons corrections . we derive formulas for the observables , namely the scalar spectral index @xmath7 , the tensor spectral index @xmath8 , the tensor - to - scalar ratio @xmath9 and the circular polarization ratio @xmath10 , in our inflationary model . the gauss - bonnet term violates the consistency relation @xmath0 . we show if this violation is observationally confirmed , the derivative of the gauss - bonnet coupling function at the observation scale , namely the cosmic microwave background ( cmb ) scale , is fixed . we study the two typical cases , blue and scale invariant spectra of tensor modes . because blue and scale invariant mean @xmath1 and @xmath2 , respectively , these cases strongly violate this consistency relation . if these are confirmed in future observations , the gauss - bonnet coupling function must be @xmath3 , at the cmb scale . of course , even if no such effects are observed in future , we can get the constraint @xmath11 , at least . however , it is unclear whether these interesting cases are consistent with current observations . therefore , we perform calculations in some concrete examples . we show new - inflation - type potential with symmetry breaking scale of @xmath4 leads to an observationally consistent blue spectrum ; potential with flat region in @xmath12 leads to a consistent scale invariant spectrum . in both cases , the almost constant @xmath13 is required . the chern - simons term leads to circular polarization of gravitational waves . we show if this circular polarization is detected , we can fix the derivative of the chern - simons coupling function , at the cmb scale . it might be @xmath6 . therefore , the value of the gauss - bonnet and chern - simons coupling functions at the cmb scale will be fixed , or constrained , with future observations . we organize this paper as follows : in section ii , the action we considered is shown and slow - roll inflation in this action is studied , calculations of perturbations in slow - roll inflation is in section iii , interesting features of our model are mentioned in section iv , and section v is for conclusion .

we study slow - roll inflation with the gauss - bonnet and chern - simons corrections . we obtain general formulas for the observables : spectral indices , tensor - to - scalar ratio and circular polarization of gravitational waves . the gauss - bonnet term violates the consistency relation . particularly , blue spectrum and scale invariant spectrum of tensor modes are possible . these cases require the gauss - bonnet coupling function of . thus , with future observations , we can fix or constrain the value of these coupling functions , at the cmb scale .

we study slow - roll inflation with the gauss - bonnet and chern - simons corrections . we obtain general formulas for the observables : spectral indices , tensor - to - scalar ratio and circular polarization of gravitational waves . the gauss - bonnet term violates the consistency relation . particularly , blue spectrum and scale invariant spectrum of tensor modes are possible . these cases require the gauss - bonnet coupling function of . we use examples to show new - inflation - type potential with symmetry breaking scale and potential with flat region in lead to observationally consistent blue and scale invariant spectra , respectively . hence , these interesting cases can actually be realized . the chern - simons term produce circularly polarized tensor modes . we show an observation of these signals supports existence of the chern - simons coupling function of . thus , with future observations , we can fix or constrain the value of these coupling functions , at the cmb scale .

1008.2724

c

in this paper , we studied slow - roll inflation with the gauss - bonnet and chern - simons corrections . we defined three slow - roll parameters , while we used five parameters in the previous paper@xcite . we derived expressions for the scalar spectral index @xmath7 , the tensor spectral index @xmath8 , the tensor - to - scalar ratio @xmath9 and the circular polarization ratio @xmath10 by using these parameters . we showed that in our model , the consistency relation @xmath0 is not automatically satisfied . if this violation is observationally confirmed , we can determine the derivative of the gauss - bonnet coupling function @xmath13 at the cmb scale . in our model , even both blue and scale invariant spectra of gravitational waves can be realized . because blue and scale invariant mean @xmath1 and @xmath384 , respectively , these cases violate this consistency relation strongly . therefore these are the key for confirming our model in future observations . we showed that if either a blue spectrum or a scale invariant one is observed , it supports existence of the gauss - bonnet coupling function of @xmath350 at the cmb scale . we checked whether or not these blue and scale invariant spectra are consistent with current observations . for this purpose , we used concrete examples . we showed that new - inflation - type potential with @xmath4 symmetry breaking scale and potential with flat region in @xmath12 might result in observationally consistent blue and scale invariant spectra , respectively . an almost linear form of the gauss - bonnet coupling function is appropriate in both cases . these tell us that the detection of a blue or scale invariant spectrum of tensor modes can be actually expected with future observations . we also showed that if circular polarization of gravitational waves is detected , the derivative of the chern - simons coupling @xmath201 must be on the order of @xmath222 . thus , we can say that existence of gravitational higher coupling terms in a inflationary model will be confirmed , or at least constrained , with future experiments . these higher curvature terms are expected to appear in non - gaussian part of perturbations . therefore , calculating non - gaussianity in our model is important future work . s. kawai and j. soda , arxiv : gr - qc/9906046 . s. kawai and j. soda , phys . b * 460 * , 41 ( 1999 ) [ arxiv : gr - qc/9903017 ] . j. c. hwang and h. noh , phys . d * 61 * , 043511 ( 2000 ) [ arxiv : astro - ph/9909480 ] . c. cartier , j. c. hwang and e. j. copeland , phys . d * 64 * , 103504 ( 2001 ) [ arxiv : astro - ph/0106197 ] . s. kawai , m. a. sakagami and j. soda , phys . b * 437 * , 284 ( 1998 ) [ arxiv : gr - qc/9802033 ] . j. soda , m. a. sakagami and s. kawai , arxiv : gr - qc/9807056 . s. kawai , m. a. sakagami and j. soda , arxiv : gr - qc/9901065 . m. gasperini , phys . rev . d * 56 * , 4815 ( 1997 ) [ arxiv : gr - qc/9704045 ] . c. cartier , e. j. copeland and m. gasperini , nucl . b * 607 * , 406 ( 2001 ) [ arxiv : gr - qc/0101019 ] . b. m. leith and i. p. neupane , jcap * 0705 * , 019 ( 2007 ) [ arxiv : hep - th/0702002 ] . z. k. guo , n. ohta and s. tsujikawa , phys . d * 75 * , 023520 ( 2007 ) , [ arxiv : hep - th/0610336 ] . a. lue , l. m. wang and m. kamionkowski , phys . * 83 * , 1506 ( 1999 ) [ arxiv : astro - ph/9812088 ] . k. choi , j. c. hwang and k. w. hwang , phys . d * 61 * , 084026 ( 2000 ) [ arxiv : hep - ph/9907244 ] . s. alexander and j. martin , phys . d * 71 * , 063526 ( 2005 ) [ arxiv : hep - th/0410230 ] . d. h. lyth , c. quimbay and y. rodriguez , jhep * 0503 * , 016 ( 2005 ) [ arxiv : hep - th/0501153 ] . m. satoh , s. kanno and j. soda , phys . d * 77 * , 023526 ( 2008 ) , arxiv:0706.3585[astro - ph ] . s. saito , k. ichiki and a. taruya , jcap * 0709 * , 002 ( 2007 ) , arxiv:0705.3701 [ astro - ph ] . n. seto , phys . lett . * 97 * , 151101 ( 2006 ) [ arxiv : astro - ph/0609504 ] . n. seto and a. taruya , phys . lett . * 99 * , 121101 ( 2007 ) , arxiv:0707.0535 [ astro - ph ] . s. weinberg , phys . d * 77 * , 123541 ( 2008 ) , arxiv:0804.4291[hep - th ] . m. satoh and j. soda , jcap * 0809 * , 019 ( 2008 ) , arxiv:0806.4594[astro - ph ] . z. k. guo and d. j. schwarz , phys . d * 81 * , 123520 ( 2010 ) , arxiv:1001.1897[hep - th ] . v. f. mukhanov and a. vikman , jcap * 0602 * , 004 ( 2006 ) [ arxiv : astro - ph/0512066 ] . d. h. lyth , phys . 78 * , 1861 ( 1997 ) [ arxiv : hep - ph/9606387 ] .

we use examples to show new - inflation - type potential with symmetry breaking scale and potential with flat region in lead to observationally consistent blue and scale invariant spectra , respectively . we show an observation of these signals supports existence of the chern - simons coupling function of .

we study slow - roll inflation with the gauss - bonnet and chern - simons corrections . we obtain general formulas for the observables : spectral indices , tensor - to - scalar ratio and circular polarization of gravitational waves . the gauss - bonnet term violates the consistency relation . particularly , blue spectrum and scale invariant spectrum of tensor modes are possible . these cases require the gauss - bonnet coupling function of . we use examples to show new - inflation - type potential with symmetry breaking scale and potential with flat region in lead to observationally consistent blue and scale invariant spectra , respectively . hence , these interesting cases can actually be realized . the chern - simons term produce circularly polarized tensor modes . we show an observation of these signals supports existence of the chern - simons coupling function of . thus , with future observations , we can fix or constrain the value of these coupling functions , at the cmb scale .

1501.02889

i

current cellular communication systems operate in half - duplex ( hd ) mode by transmitting and receiving either at different time slots or over different frequency bands . the system is designed in such a way that the downlink ( dl ) and uplink ( ul ) traffics are structurally separated by time division duplexing ( tdd ) or frequency division duplexing ( fdd ) . the advantage of such design principle is that it avoids the high - powered self - interference that is generated during simultaneous transmission and reception . recent results @xcite , however , have demonstrated the feasibility of _ full - duplex _ ( fd ) wireless communication by suppressing or cancelling self - interference in the rf and baseband level . various practical designs to realize self - interference cancellation have been proposed in the literature , including adding additional antennas @xcite , adding auxiliary transmit rf chains @xcite or auxiliary receive rf chains @xcite , using polarization @xcite , employing balun circuits @xcite , and many more . for more details , see @xcite and the references therein . by enabling simultaneous transmission and reception , fd radio is expected to double the spectral efficiency of current hd systems @xcite , and is considered as one of the key technologies for next generation communication systems . evidently , in situations where the base station ( bs ) and the user simultaneously transmit bidirectionally as shown in figure [ fig : first ] , enabling fd doubles the overall spectral efficiency . this point - to - point bidirectional communication example , however , is just one instance of how a fd cellular system will function . in some practical cases , the system may have to support hd users which do not have fd radio due to extra hardware burden on mobile devices . in such case , the fd bs can simultaneously communicate with two sets of users , one receiving dl data from the bs and the other transmitting ul data to the bs ( figure [ fig : second ] ) . in another configuration shown in figure [ fig : third ] , for instance , when the bs has many more antennas compared to each user , the fd bs may wish to simultaneously communicate with multiple fd users using multi - user multiple - input and multiple - output ( mimo ) techniques . since the bs is simultaneously transmitting and receiving , there is potential to double the overall spectral efficiency compared to the conventional hd only systems . however , the configurations shown in figures [ fig : second ] and [ fig : third ] induce a new source of interference that does not arise in hd only networks . in figure [ fig : second ] , since user 1 is transmitting to the bs while user 2 is receiving from the bs , the transmission from user 1 causes interference to user 2 . similarly , in figure [ fig : third ] , the ul transmission of the users causes interference to the dl reception to each other . in cases where this type of interference is strong and proper interference mitigation techniques are not applied , the gain of having fd radios can be severely limited even when self - interference is completely removed . to manage inter - user interference and fully utilize wireless spectrum with fd operation , in this paper we employ signal space _ interference alignment _ ( ia ) schemes optimized for fd networks including the cases in figure 1 . initially proposed by the seminar works in @xcite , ia is a coding technique that efficiently deals with interference and is known to achieve the optimal dof for various interference networks @xcite . especially , it is shown that ia can be successfully applied to mitigate interference in various cellular networks , such as two - cell cellular networks @xcite and multiantenna ul dl cellular networks @xcite . furthermore , the idea of ia can also be applied to the ( multi - user ) bidirectional cellular network with ergodic phase fading @xcite , in which the achievable scheme is based on the ergodic ia scheme proposed in @xcite . motivated by the aforementioned previous works related to ia , we propose the optimal transmission schemes that attain the optimal sum dofs for two configurations : 1 ) a cellular network with a multiantenna fd bs and hd users ( figure [ fig : second ] ) ; 2 ) a cellular network with a multiantenna fd bs and fd users ( figure [ fig : third ] ) . the key idea of the proposed schemes is to carefully allocate the ul and dl information streams using ia and beamforming techniques . the ul data is sent to the bs using ia such that the inter - user interference is confined within a tolerated number of signal dimensions , while the bs transmits in the remaining signal dimensions via zero - forcing beamforming for the dl transmission . with the proposed schemes , our primary goal is to answer whether if fd operation can still double the overall spectral efficiency even in the presence of inter - user interference . we answer this question by providing matching upper bounds with the proposed achievable schemes , completely characterising the sum dofs of the considered networks . as a consequence of the result , even in the presence of inter - user interference , we show that the overall dof can approach the two - fold gain over hd only networks when the number of users becomes large as compared to the number of antennas at the bs . we further provide the dof gain of the fd systems by considering various configurations ( see sections iii and vi . ) . in @xcite , cadambe and jafar proposed a novel interference management technique called _ interference alignment _ ( ia ) , which achieves the optimal sum dof of @xmath0 for the @xmath1-user interference channel ( ic ) with time - varying channel coefficients . in addition , for the case in which all channel coefficients are constant , motahari et al . @xcite proposed a different type of ia scheme based on number - theoretic properties of rational and irrational numbers and showed that the optimal dof of @xmath0 is also achievable . later , alternative methods of aligning interference in the finite signal - to - noise regime has been also proposed in @xcite . the concept of ia has been successfully adapted to various network environments , e.g. , see @xcite and the references therein . the dof of cellular networks has been first studied by suh and tse for both ul and dl environments , where inter - cell interference exists @xcite . it was shown that , for two - cell networks having @xmath1 users in each cell , the sum dof of @xmath2 is achievable for both ul and dl . thus , multiple users at each cell are beneficial for improving the dof of cellular networks . these models were further extended to more general cases in terms of the number of users and the number of antennas at each bs @xcite . in addition , recently , the dof of the multiantenna ul dl cellular network consisting of dl and ul cells has been studied in @xcite . for a cellular network with fd operation in the absence of self - interference , the dof of the ( multi - user ) bidirectional case has been studied in @xcite for ergodic phase fading setting . the rest of this paper is organized as follows . in section ii , we describe the network model and the sum dof metric considered in this paper . in section iii , we present the main results of the paper and intuitively explain how fd operation can increase the dof . in sections iv and v , we provide the achievability and converse proofs of the main theorems , respectively . in section vi , we discuss the impacts of self - interference and scheduling on the dof . finally , we conclude in section vii . * notations * : we will use boldface lowercase letters to denote vectors and boldface uppercase letters to denote matrices . throughout the paper , @xmath3 $ ] denotes @xmath4 , @xmath5 denotes the @xmath6 all - zero vector , and @xmath7 denotes the @xmath8 identity matrix . for a real value @xmath9 , @xmath10 denotes @xmath11 . for a set of vectors @xmath12 , @xmath13 denotes the vector space spanned by the vectors in @xmath12 . for a vector @xmath14 , @xmath15 means that @xmath14 is orthogonal with all vectors in @xmath13 . for a set of matrices @xmath16 , @xmath17 denotes the block diagonal matrix consisting of @xmath16 .

we establish the dof gain by enabling fd operation in various configurations . as a consequence of the result , we show that the dof can approach the two - fold gain over the hd systems when the number of users becomes large enough as compared to the number of antennas at the bs . cellular network , degrees of freedom , full duplex , interference alignment , multiantenna technique .

we study the _ degrees of freedom ( dof ) _ of cellular networks in which a _ full duplex ( fd ) base station ( bs ) _ equipped with multiple transmit and receive antennas communicates with multiple mobile users . we consider two different scenarios . in the first scenario , we study the case when _ half duplex ( hd ) users _ , partitioned to either the uplink ( ul ) set or the downlink ( dl ) set , simultaneously communicate with the fd bs . in the second scenario , we study the case when _ fd users _ simultaneously communicate ul and dl data with the fd bs . unlike conventional hd only systems , inter - user interference ( within the cell ) may severely limit the dof , and must be carefully taken into account . with the goal of providing theoretical guidelines for designing such fd systems , we completely characterize the sum dof of each of the two different fd cellular networks by developing an achievable scheme and obtaining a matching upper bound . the key idea of the proposed scheme is to carefully allocate ul and dl information streams using interference alignment and beamforming techniques . by comparing the dofs of the considered fd systems with those of the conventional hd systems , we establish the dof gain by enabling fd operation in various configurations . as a consequence of the result , we show that the dof can approach the two - fold gain over the hd systems when the number of users becomes large enough as compared to the number of antennas at the bs . cellular network , degrees of freedom , full duplex , interference alignment , multiantenna technique .

1501.02889

c

in this paper , we have studied the sum dofs of cellular networks with a multiantenna fd bs and hd mobile users and with a multiantenna fd bs and fd mobile users . for our main contribution , we have completely characterized the sum dofs of these networks . to be specific , for achievability , the key idea was to fully utilize the intended signal dimensions by minimizing the inter - user interference dimensions via ia for the ul transmission and by minimizing the intra - cell interference dimensions via multiantenna nulling for the dl transmission . for converse , we have provided a matching upper bound that shows the optimality of the proposed scheme . as a consequence of the result , we have shown that even when inter - user interference exists , fd operation at the bs can double the sum dof over the hd only networks when the number of users becomes large enough as compared to the number of antennas at the bs , for both the fd - bs hd - user cellular network and the fd - bs fd - user cellular network . our work can be extended to several interesting directions : ( 1 ) extending to multi - cell scenarios in which inter - cell interference exists ; ( 2 ) extending to the case in which mobile users have multiple antennas ; ( 3 ) extending to the cases in which channel state information at transmitters ( csit ) is not available or delayed . j. i. choi , m. jain , k. srinivasan , p. levis , and s. katti , `` achieving single channel , full duplex wireless communication , '' in _ proc . 16th annual international conference on mobile computing , networking , and communications ( mobicom ) _ , new york , ny , aug . 2010 . e. aryafar , m. a. khojastepour , k. sundaresan , s. rangarajan , and m. chiang , `` midu : enabling mimo full duplex , '' in _ proc . 18th annual international conference on mobile computing , networking , and communications ( mobicom ) _ , istanbul , turkey , aug . 2012 . m. duarte and a. sabharwal , `` full - duplex wireless communications using off - the - shelf radios : feasibility and first results , '' in _ proc . asilomar conference on signals , systems and computers _ , pacific grove , ca , nov . 2010 . m. jainy , j. i. choi , t. m. kim , d. bharadia , s. seth , k. srinivasan , p. levis , s. katti , and p. sinha , `` practical , real - time , full duplex wireless , '' in _ proc . 17th annual international conference on mobile computing , networking , and communications ( mobicom ) _ , las vegas , nv , sep . 2011 . s. hong , j. brand , j. choi , m. jain , j. mehlman , s. katti , and p. levis , `` applications of self - interference cancellation in 5 g and beyond , '' _ ieee communications magazine _ , vol . 52 , pp . 114121 , feb . 2014 . m. a. maddah - ali , a. s. motahari , and a. k. khandani , `` communication over mimo x channels : interference alignment , decomposition , and performance analysis , '' _ ieee trans . inf . theory _ 34573470 , aug . 2008 . v. s. annapureddy , a. el gamal , and v. v. veeravalli , `` degrees of freedom of interference channels with comp transmission and reception , '' _ ieee trans . inf . theory _ , 57405760 , sep . 2012 . t. gou , s. a. jafar , c. wang , s .- w . jeon , and s .- y . chung , `` aligned interference neutralization and the degrees of freedom of the @xmath259 interference channel , '' _ ieee trans . inf . theory _ 43814395 , jul . 2012 . w. shin , n. lee , j .- b . kim , c. shin , and k. jang , `` on the design of interference alignment scheme for two - cell mimo interfering broadcast channels , '' _ ieee trans . wireless commun . _ , vol . 437442 , feb .

we study the _ degrees of freedom ( dof ) _ of cellular networks in which a _ full duplex ( fd ) base station ( bs ) _ equipped with multiple transmit and receive antennas communicates with multiple mobile users . we study the case when _ half duplex ( hd ) users _ , partitioned to either the uplink ( ul ) set or the downlink ( dl ) set , simultaneously communicate with the fd bs . in the second scenario ,

we study the _ degrees of freedom ( dof ) _ of cellular networks in which a _ full duplex ( fd ) base station ( bs ) _ equipped with multiple transmit and receive antennas communicates with multiple mobile users . we consider two different scenarios . in the first scenario , we study the case when _ half duplex ( hd ) users _ , partitioned to either the uplink ( ul ) set or the downlink ( dl ) set , simultaneously communicate with the fd bs . in the second scenario , we study the case when _ fd users _ simultaneously communicate ul and dl data with the fd bs . unlike conventional hd only systems , inter - user interference ( within the cell ) may severely limit the dof , and must be carefully taken into account . with the goal of providing theoretical guidelines for designing such fd systems , we completely characterize the sum dof of each of the two different fd cellular networks by developing an achievable scheme and obtaining a matching upper bound . the key idea of the proposed scheme is to carefully allocate ul and dl information streams using interference alignment and beamforming techniques . by comparing the dofs of the considered fd systems with those of the conventional hd systems , we establish the dof gain by enabling fd operation in various configurations . as a consequence of the result , we show that the dof can approach the two - fold gain over the hd systems when the number of users becomes large enough as compared to the number of antennas at the bs . cellular network , degrees of freedom , full duplex , interference alignment , multiantenna technique .

1406.4958

i

graphons have been introduced as limit objects of convergent sequences of dense simple graphs , and many aspects of graphs can be extended to graphons . the goal of this paper is to describe a natural way to extend the notion of graph automorphisms to graphons . our notion of automorphism group satisfies the natural requirement that it is invariant under weak isomorphism of graphons . ( weakly isomorphic graphons represent the limit objects of the same convergent graph sequences . ) thus our study of the automorphisms of graphons fits well into graph limit theory . in this paper we heavily use the topological aspects of graph limit theory developed in @xcite . it was shown in @xcite that every graphon has two `` canonical '' representations on metric spaces , which we call , informally , the _ neighborhood metric _ and the _ @xmath1-neighborhood metric_. these metric spaces depend only on the weak isomorphism class of the graphon . ( in @xcite , these are called the `` neighborhood metric '' and the `` similarity metric '' . ) the neighborhood metric space is simpler to define and work with , but it is not compact in general ; the @xmath1-neighborhood metric space is compact . the automorphism group acts on each of these as a subgroup of isometries . it is a rather straightforward consequence of the compactness of the @xmath1-neighborhood metric that the automorphism group is always a compact topological group ( theorem [ thm : aut - comp ] ) . this fact is also closely related to ( and could be derived from ) a theorem of vershik and habck @xcite on the compactness of isometry groups of multivariate functions . as a consequence we prove that for node - transitive graphons the neighborhood metric is also compact . the space of graphons ( with weakly isomorphic graphons identified ) is compact in a natural topology ( defined by the `` cut distance '' ) . another result of this paper is that the set of node - transitive graphons is closed , and hence compact , in this topology . as we will see , graph limit theory restricted to this closed set gives rise to a rather interesting limit theory for functions on groups . such a theory was initiated in @xcite , and it was a crucial component of the limit approach to higher order fourier analysis ( see @xcite ) . we give a characterization of the orbits of the automorphism group on @xmath0-tuples of points . this generalizes results in @xcite from finite graphs to graphons , as well as the characterization of weak isomorphism of graphons by borgs , chayes and lovsz @xcite . we use this characterization to connect the topic of graph algebras with group theory . as an application , we give a group theoretic description of the graph algebras defined by finite rank graphons . it follows from our results that the limit of a convergent sequence of finite graphs , each having a node - transitive automorphism group , is a node - transitive graphon . however , the relationship between the automorphism groups of the finite graphs and that of the limit graphon is more involved .

we study the automorphism group of graphons ( graph limits ) . we prove that after an appropriate `` standardization '' of the graphon , the automorphism group is compact . furthermore , we characterize the orbits of the automorphism group on-tuples of points . among applications we study the graph algebras defined by finite rank graphons and the space of node - transitive graphons .

we study the automorphism group of graphons ( graph limits ) . we prove that after an appropriate `` standardization '' of the graphon , the automorphism group is compact . furthermore , we characterize the orbits of the automorphism group on-tuples of points . among applications we study the graph algebras defined by finite rank graphons and the space of node - transitive graphons .

1106.1447

i

[ [ section ] ] _ graph hypersurfaces _ are hypersurfaces of projective space associated with the parametric formulation of feynman integrals in scalar quantum field theories . the study of their geometry was prompted by certain conjectures concerning the appearance of multiple zeta values in the results of computation of feynman amplitudes , and has been the object of intense investigation ( see e.g. , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , and many others ) . in this paper we study chern classes of graph hypersurfaces , from the point of view of deletion - contraction and multiple - edge formulas . [ [ section-1 ] ] ` algebro - geometric feynman rules ' are invariants of graphs which only depend on the isomorphism class of the corresponding hypersurfaces , and have controlled behavior with respect to unions . ( this definition of course captures only a very small portion of the quantum field theory feynman rules ; it would be very interesting to have examples of algebro - geometric feynman rules mirroring more faithfully their physical counterparts . ) matilde marcolli and the author note in @xcite that the classes of graph hypersurfaces in the grothendieck ring of varieties satisfy this basic requirement ; grothendieck classes of graph hypersurfaces have been studied rather thoroughly , given their relevance to the conjectures mentioned above . in the same paper we produced a different example of algebro - geometric feynman rules , with values in @xmath0 $ ] , based on the _ chern classes _ of graph hypersurfaces . the definition of this polynomial invariant @xmath1 will be recalled below ; its main interest lies in the fact that it carries intersection - theoretic information about the singularities of graph hypersurfaces . for example , the ( push - forward to projective space of the ) segre class of the singularity subscheme of a hypersurface may be recovered from the polynomial feynman rules . the milnor number of the hypersurface ( in its natural generalization to arbitrary hypersurfaces as defined by parusiski , @xcite ) is but one piece of the information carried by @xmath1 . the fact that the invariant satisfies the basic requirements of algebro - geometric feynman rules is proved in @xcite , theorem 3.6 , and is substantially less straightforward than the corresponding fact for grothendieck classes . grothendieck classes of graph hypersurfaces also satisfy a ` deletion - contraction ' relation : this fact has been pointed out by several authors , see e.g. , @xcite , @xcite , @xcite . the purpose of this article is to examine deletion - contraction relations for chern classes of graph hypersurfaces , in terms of the polynomial feynman rules mentioned above . as in @xcite , it is natural to expect the situation for chern classes to be substantially subtler than for classes in the grothendieck ring , and in fact our first guess concerning a double - edge formula for chern classes , based on somewhat extensive evidence computed for small graphs , turns out to be _ incorrect _ as stated in conjecture 6.1 in @xcite . nevertheless , we will be able to show here that these invariants do satisfy the expected general structure underlying multiple - edge formulas examined in @xcite . [ [ section-2 ] ] the _ graph hypersurface _ associated with a graph @xmath2 is the zero - set of the polynomial @xmath3 where @xmath4 ranges over the maximal spanning forests of @xmath2 . this is a homogeneous polynomial in variables @xmath5 corresponding to the edges @xmath6 of @xmath2 , and its zero set may be viewed in @xmath7 or @xmath8 , depending on the context . graph hypersurfaces are singular in all but the simplest cases , and in this article ( as in @xcite ) we employ the theory of _ chern - schwartz - macpherson _ ( csm ) classes . csm classes are defined for arbitrary varieties , and agree with the ordinary ( total homology ) chern class of the tangent bundle when evaluated on nonsingular varieties . the reader may refer to 2.2 - 3 of @xcite for a quick summary of this theory , which has a long and well - documented history . csm classes can be viewed as a generalization of the topological euler characteristic : indeed , the degree of the csm class of a variety _ is _ its euler characteristic , and to some extent csm classes maintain the same additive and multiplicative behavior of the euler characteristic . in this respect they are similar in flavor to the grothendieck class . they also offer a direct measure of ` how singular ' a variety is , by comparison with other characteristic classes of singular varieties , see e.g. 2.2 in @xcite and references therein . csm classes are in fact defined for _ constructible functions _ on a variety ( @xcite ) , and what we call the csm class of @xmath9 is the class @xmath10 of the constant function @xmath11 . as our objects of study are hypersurfaces of projective space , we view csm classes as elements of the chow group of projective space , i.e. , as polynomials in the hyperplane class . the polynomial feynman rules mentioned above are closely related to the csm class of the _ complement _ of a graph hypersurface @xmath12 : if a graph @xmath2 with @xmath13 edges is not a forest , then the polynomial feynman rules @xmath1 are determined by the relation @xmath14\quad,\ ] ] where @xmath15 denotes the hyperplane class ; see prop . 3.7 in @xcite . [ [ section-3 ] ] in graph theory , _ deletion - contraction _ formulas express invariants for a graph @xmath2 directly in terms of invariants for the ` deletion ' graph @xmath16 obtained by removing an edge @xmath6 , and the ` contraction ' graph @xmath17 obtained by contracting the same edge . _ tutte - grothendieck _ invariants are the most general invariants with controlled behavior with respect to deletion - contraction ; an impressive list of important graph invariants are of this kind , ranging from chromatic polynomials to partition functions for potts models . in fact , these invariants may be viewed as ` feynman rules ' in a sense closely related to the one adopted in @xcite , see prop . 2.2 in @xcite . in @xcite we show that the invariant arising from the grothendieck class satisfies a weak form of deletion - contraction ( which involves ` non - combinatorial ' terms ) ; and that enough of this structure is preserved to trigger combinatorial ` multiple - edge ' formulas . more precisely , let @xmath18 $ ] denote the grothendieck class of the complement of the affine graph hypersurface , and denote by @xmath19 the graph obtained by doubling the edge @xmath6 in @xmath2 . if @xmath6 is neither a bridge nor a looping edge , then ( @xcite , proposition 5.2 ) @xmath20 where @xmath21 is the class of @xmath22 . note that ( * ) holds without further requirements on @xmath6 . ( simpler formulas hold in case @xmath6 is a bridge or a looping edge . ) [ [ section-4 ] ] as we will show in this paper , the situation concerning the polynomial invariant @xmath1 recalled above is somewhat different . as in the case of the grothendieck class , this invariant does not satisfy on the nose a deletion - contraction relation ( this was already observed in @xcite , prop . 3.2 ) . unlike in the case of the invariant @xmath23 , however , even a weaker non - combinatorial form of deletion - contraction only holds under special hypotheses on the edge @xmath6 . the main result of this article is the determination of conditions on a pair @xmath24 such that a sufficiently strong deletion - contraction relation ( and corresponding consequences , such as multiple - edge formulas ) holds for the edge @xmath6 of @xmath2 . these conditions are presented in [ condis ] ; somewhat surprisingly , they appear to hold for ` many ' graphs . one of them can be formulated as follows . assume that @xmath6 is neither a bridge nor a looping edge of @xmath2 . we may consider the polynomial @xmath25 for the deletion @xmath16 . the condition is then that @xmath26 _ belongs to the jacobian ideal of @xmath25 . _ the smallest counterexample to this requirement appears to be the graph with respect to the vertical edge . we find it surprising that this condition is satisfied as often as it is . the second condition is more technical . see [ condis ] for a discussion of both conditions . once a ( weak ) deletion - contraction formula is available , one should expect combinatorial multiple - edge formulas to hold . and indeed , we will prove the following analogue of ( * ) for the chern class feynman rules : [ double ] if the conditions on @xmath27 mentioned above are satisfied , then @xmath28 this is the formula that was proposed in @xcite , conjecture 6.1 , on the basis of many examples computed explicitly in @xcite . however , the additional conditions on @xmath27 had not been identified at the time ; the formula proposed in _ loc . _ for the class of a triangle with doubled edges is incorrect , and will be corrected here in example [ doubletriangex ] . [ [ section-5 ] ] as mentioned above , we do not have a sharp combinatorial characterization on @xmath27 ensuring that the technical hypotheses needed for theorem [ double ] are satisfied . however , there is one important case in which we are able to prove that these conditions are indeed satisfied : the conditions hold if @xmath6 is itself a multiple edge , i.e. , if the endpoints of @xmath6 are adjacent in @xmath16 . thus , theorem [ double ] implies that the polynomial feynman rules satisfy essentially the same recursive structure for multiple - edge formulas that is studied in general in @xcite , 6 . if @xmath6 is neither a bridge nor a looping edge of @xmath2 , then @xmath29 in a sense , this recursion is ` nicer ' than the corresponding one for grothendieck classes ( see the comments following lemma [ recurs ] ) . [ [ section-6 ] ] this paper is organized as follows . in [ condis ] we state precisely the technical conditions mentioned above , in the case of graph hypersurfaces , providing a few simple examples to illustrate them . this is also done in the hope that others may identify sharp combinatorial versions of these conditions . we prove ( lemma [ mainlemma ] ) that the conditions hold for @xmath24 if @xmath6 has parallel edges in @xmath2 , and describe one class of examples in which the conditions do not ( both ) hold . in [ generals ] we discuss a formula for the csm class of a transversal intersection , needed for the application to graph hypersurfaces presented here ; this section can be read independently of the rest of the paper . in [ particulars ] we apply these formulas to the case of graph hypersurfaces , obtaining the deletion - contraction relation ( theorem [ delconthm ] ) . in [ multedges ] we apply this relation to obtain multiple - edge formulas as mentioned above ( theorem [ goodform ] , lemma [ recurs ] ) . in [ speci ] we describe a different and more ` geometric ' ( but in practice less applicable ) approach to the main deletion - contraction formula , using _ verdier s specialization . _ _ acknowledgment . _ i thank matilde marcolli for stimulating my interest in graph hypersurfaces through our previous joint work , and for the hospitality at caltech , where this paper was written . i also thank don zagier for a conversation concerning a technical point in [ multedges ] .

we study the behavior of the chern classes of graph hypersurfaces under the operation of deletion - contraction of an edge of the corresponding graph . this leads to recursions for the chern classes of graph hypersurfaces for graphs obtained by adding parallel edges to a given ( regular ) edge . analogous results for the case of grothendieck classes of graph hypersurfaces were obtained in . both grothendieck classes and chern classes were used to define ` algebro - geometric ' feynman rules in . the results in this paper provide further evidence that the polynomial feynman rule defined in terms of the chern - schwartz - macpherson class of a graph hypersurface reflects closely the combinatorics of the corresponding graph . the key to the proof of the main result is a more general formula for the chern - schwartz - macpherson class of a transversal intersection ( see [ generals ] ) , which may be of independent interest . we also describe a more geometric approach , using the apparatus of ` verdier specialization ' .

we study the behavior of the chern classes of graph hypersurfaces under the operation of deletion - contraction of an edge of the corresponding graph . we obtain an explicit formula when the edge satisfies two technical conditions , and prove that both these conditions hold when the edge is multiple in the graph . this leads to recursions for the chern classes of graph hypersurfaces for graphs obtained by adding parallel edges to a given ( regular ) edge . analogous results for the case of grothendieck classes of graph hypersurfaces were obtained in . both grothendieck classes and chern classes were used to define ` algebro - geometric ' feynman rules in . the results in this paper provide further evidence that the polynomial feynman rule defined in terms of the chern - schwartz - macpherson class of a graph hypersurface reflects closely the combinatorics of the corresponding graph . the key to the proof of the main result is a more general formula for the chern - schwartz - macpherson class of a transversal intersection ( see [ generals ] ) , which may be of independent interest . we also describe a more geometric approach , using the apparatus of ` verdier specialization ' .

1504.03917

i

the discrimination between a finite number of quantum states , prepared with given prior probabilities , is essential for many tasks in quantum information and quantum cryptography . since nonorthogonal states can not be distinguished perfectly , discrimination strategies have been developed which are optimal with respect to various figures of merit . based on the outcome of a measurement , in these strategies a guess is made about the actual state of the quantum system . several strategies admit a certain probability , or rate , @xmath2 , of inconclusive results , where the measurement outcomes do not allow to infer the state . in the strategy of minimum - error discrimination @xcite inconclusive results are not permitted , and the overall probability @xmath3 of making a wrong guess is minimized with @xmath4 , which corresponds to maximizing the overall probability @xmath5 of getting a correct result . apart from studying some general features of the optimal measurement @xcite , in the beginning mainly the minimum - error discrimination of states obeying certain symmetry properties or of two mixed states was investigated , see e. g. @xcite . the minimum - error discrimination of more than two states that are arbitrary has gained renewed interest only recently @xcite . generalizing the concept of minimum - error discrimination , an optimal discrimination strategy has been studied which maximizes the total rate of correct results , @xmath5 , with a fixed rate @xmath2 of inconclusive results @xcite . this strategy also maximizes the relative rate @xmath6 for the fixed value @xmath2 , that is it yields the maximum achievable fraction of correct results referred to all conclusive results , which in most cases is larger for @xmath7 than for @xmath8 necessary and sufficient operator conditions for the optimal measurement have been derived @xcite , and it was shown @xcite that under certain conditions the strategy for maximizing @xmath5 with a fixed rate @xmath2 contains the optimal strategies for unambiguous discrimination @xcite or for discrimination with maximum confidence @xcite as limiting cases for sufficiently large values of @xmath2 . moreover , it was found @xcite that when the maximum of @xmath5 is known as a function of the fixed value @xmath2 , then from this function one can also obtain the maximum of @xmath5 in another optimal discrimination strategy where the error probability is fixed @xcite . optimal discrimination with a fixed rate @xmath2 has been also investigated for a modified optimization problem where in contrast to the usual assumption the prior probabilities of the states are unknown @xcite . solutions for optimal state discrimination with a fixed rate @xmath2 of inconclusive results and with given prior probabilities of the states have been recently derived in three independent papers : starting from the operator equations for the optimality conditions , in ref . @xcite we obtained analytical solutions for the discrimination of symmetric states and of two states occurring with arbitrary prior probabilities , where the two states are either pure or belong to a certain class of mixed qubit states . in refs . @xcite and @xcite the respective authors showed that the optimization problem with fixed @xmath2 can be solved by reducing it to a resulting minimum - error problem the solution of which is known and to an additional optimization . they derived analytical solutions for discriminating between two pure states occurring with arbitrary prior probabilities and between the trine states @xcite , and also for the discrimination of geometrically uniform states @xcite . the present paper goes beyond these previous investigations in several respects . based on the ideas of our earlier work @xcite we study general properties of the optimal measurement for discriminating with fixed @xmath2 between @xmath0 arbitrary qudit states in a @xmath1-dimensional hilbert space . specializing on the case @xmath9 , we develop a method for treating the optimal discrimination with fixed @xmath2 between @xmath0 arbitrary qubit states , occurring with arbitrary prior probabilities . in contrast to the previous papers @xcite we take into account that often the optimal measurement is not unique , which means that the maximal probability of correct results with fixed @xmath2 can be obtained by a number of different measurements . in the special case @xmath4 , where the problem corresponds to minimum - error discrimination , our method differs from the approaches developed previously for treating the minimum - error discrimination of @xmath0 arbitrary qubit states @xcite . we obtain explicit analytical results for several problems that have not been solved before , mostly for the discrimination with fixed @xmath2 between qubit states which posses a certain partial symmetry , but also for discriminating @xmath0 equiprobable qubit states and for the discrimination between a pure state and a uniformly mixed state in a @xmath1-dimensional hilbert space . the paper is organized as follows . in sec . ii we start by considering the optimal discrimination with fixed @xmath2 for @xmath0 qudit states . after this we specialize on the discrimination of @xmath0 qubit states in a two - dimensional hilbert space and develop a method for solving the problem . sec . iii is devoted to the discrimination of @xmath0 partially symmetric qubit states . we conclude the paper in sec . iv with discussing the relation of our method to previous studies of the minimum - error discrimination of arbitrary qubit states and with a brief summary of results . the detailed derivations referring to sec . iii are presented in the appendix .

we develop a method to determine an optimal measurement for discriminating arbitrary qubit states , taking into account that often the optimal measurement is not unique and the maximum probability of correct results can be achieved by several different measurements . analytical results are derived for a number of examples , mostly for the discrimination between qubit states which possess a partial symmetry , but also for discriminating equiprobable qubit states and for the dicrimination between a pure and a uniformly mixed state in dimensions . in the special case where the fixed rate of inconclusive results is equal to zero , our method provides a treatment for the minimum - error discrimination of arbitrary qubit states which differs from previous approaches .

we study the discrimination of mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value . after considering the discrimination of states in a-dimensional hilbert space , we focus on the discrimination of qubit states . we develop a method to determine an optimal measurement for discriminating arbitrary qubit states , taking into account that often the optimal measurement is not unique and the maximum probability of correct results can be achieved by several different measurements . analytical results are derived for a number of examples , mostly for the discrimination between qubit states which possess a partial symmetry , but also for discriminating equiprobable qubit states and for the dicrimination between a pure and a uniformly mixed state in dimensions . in the special case where the fixed rate of inconclusive results is equal to zero , our method provides a treatment for the minimum - error discrimination of arbitrary qubit states which differs from previous approaches .

1504.03917

c

before concluding the paper , we briefly discuss the relation of our method to previous investigations of the minimum - error discrimination of arbitrary qubit states , where @xmath4 . from eq . ( [ perp ] ) we obtain the representation @xmath392 @xmath393 , where due to eq . ( [ compl1 ] ) for minimum - error discrimination the condition @xmath394 has to be satisfied with non - negative values of @xmath175 . upon eliminating the operator @xmath24 , we obtain from the first equality in eq . ( [ mx ] ) for any pair of states the equation @xmath395 ( @xmath396 ) . ( [ my ] ) has been recently derived in an alternative way @xcite , and has been applied to study the minimum - error discrimination of qubit states using a geometric formulation @xcite . in contrast to this , in our method , which refers to the general case @xmath397 , the operator @xmath24 is not eliminated . rather , our approach essentially rests on determining @xmath24 and is therefore for @xmath4 related to the treatments of minimum - error discrimination in refs . @xcite,@xcite and @xcite . in this paper we investigated the discrimination of @xmath0 mixed quantum states by an optimal measurement that yields the maximum probability of correct results , @xmath32 , while the probability of inconclusive results is fixed at a given value @xmath397 . for the discrimination of qudit states in a @xmath1-dimensional hilbert space , we discussed the general properties of the optimal measurement . moreover , we derived the analytical solution for optimally discriminating with fixed @xmath2 between a uniformly mixed and a pure qudit state . in the main part of the paper we specialized on the optimal discrimination of qubit states in a two - dimensional hilbert space and developed a general method to obtain the solution . we studied the special case where the prior probabilities of the qubit states are equal , and we also treated the discrimination between four or less arbitrary qubit states with fixed @xmath2 . as an illustrative application of our method , we derived explicit analytical results for discriminating qubit states which posses a partial symmetry . we emphasize that apart from determining @xmath32 , our method also allows to consider the various possible realizations of the optimal measurement for a given discrimination problem . in particular , we found that for discriminating @xmath0 symmetric qubit states the maximum probability of correct results with fixed @xmath2 can be for instance also achieved by a measurement where only three of the states are guessed to occur when @xmath0 is odd , and only two of the states when @xmath0 is even , instead of guessing all @xmath0 states . note added : after submitting this work a related paper @xcite appeared .

we study the discrimination of mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value . after considering the discrimination of states in a-dimensional hilbert space , we focus on the discrimination of qubit states .

we study the discrimination of mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value . after considering the discrimination of states in a-dimensional hilbert space , we focus on the discrimination of qubit states . we develop a method to determine an optimal measurement for discriminating arbitrary qubit states , taking into account that often the optimal measurement is not unique and the maximum probability of correct results can be achieved by several different measurements . analytical results are derived for a number of examples , mostly for the discrimination between qubit states which possess a partial symmetry , but also for discriminating equiprobable qubit states and for the dicrimination between a pure and a uniformly mixed state in dimensions . in the special case where the fixed rate of inconclusive results is equal to zero , our method provides a treatment for the minimum - error discrimination of arbitrary qubit states which differs from previous approaches .

1410.0139

i

the last decades have witnessed a surge in research activities in the physical properties of biopolymers , such as double - stranded dna ( dsdna ) , filamental actin ( f - actin ) and microtubules . semiflexibility is a common feature they share ; as they preserve mechanical rigidity over a range , characterized by the persistence length @xmath3 , along their contour . ( e.g. , for a dsdna , f - actin and microtubules , @xmath4 nm @xcite , @xmath5 m @xcite and @xmath6 mm @xcite respectively . ) mechanical properties of semiflexible polymers are well - captured by the kratky - porod wormlike chain ( wlc ) model @xcite , wherein the chain conformation is described by an inextensible and differentiable curve . in general , the stretching modulus for semiflexible polymers is far greater than their bending modulus , i.e. , the chains are effectively inextensible at the length for which the persistence length is relevant . the wlc model @xcite , its subsequent modifications @xcite , and recent analyses @xcite have been very successful in describing static / mechanical properties of dsdna , such as its force - extension curve and the radial distribution function of its end - to - end distance . for the study of dynamics , the wlc model needs to be extended . this is done by a langevin - like description of sideways excursions of the wlc . the contour length of the polymer is constrained in the original wlc model , and lagrangian multipliers of a varying degree of sophistication need to be implemented in order to enforce a contour length that is either strictly fixed @xcite , or fixed on average @xcite . this enforcement allows for the calculation of many dynamical quantities theoretically . it also makes it difficult to deal with motion along the wlc s contour @xcite , which become relevant , e.g. , in crowded conditions . in this context , we note that the standard interpretation of the `` stored lengths '' for semiflexible polymers are their ( transverse ) thermal undulations @xcite ( which are penalized ) . although this interpretation is consistent with the dynamics of stored lengths @xcite , and allows one to intuitively conceptualize chain tension along the contour , the interplay between local extensibility and dynamics remains somewhat problematic , unlike in bead - spring models . in order to circumvent some of the difficulties , in a recent paper ( hereafter referred to as paper i ) @xcite two of us recently introduced a bead - spring model for extensible semiflexible polymers in hamiltonian formulation , in the absence of hydrodynamic interactions . in this paper we use this bead - spring model to study the dynamics of polymer chains which are shorter than or of the order of the persistence length . in particular , we have in mind the simulation of the dynamics of crosslinked networks of semiflexible polymers such as actin@xcite ; first making the network configurations continuous , and then discretizing them again , seems a bit indirect ; we prefer to work with a discrete model right from the start . paper i focused on dsdna and matched the model to its force extension curve in terms of two parameters , @xmath0 and @xmath1 . in comparison to its groundstate value , the bead - spring hamiltonian is approximated in the first order by the hessian that is quadratic in the bead positions . the eigenmodes of the hessian provide the longitudinal ( stretching ) and transverse ( bending ) eigenmodes of the polymer , and the corresponding eigenvalues for the stretching ( longitudinal ) and the bending ( transverse ) modes , indexed by @xmath7 ( @xmath8 ) , were shown to scale as @xmath9 and @xmath10 respectively for small @xmath7 . these are the characteristic signatures of semiflexible polymers @xcite . in this paper , also focused on dsdna , we exploit the knowledge on these modes to theoretically obtain some interesting dynamical quantities , such as ( i ) the end - to - end vector autocorrelation function , ( ii ) the correlation function of a bond vector in the middle of the chain , and ( iii ) the mean - squared displacement ( msd ) of a tagged bead . in the linear regime , where the modes can be taken as independent , our ( analytical ) mode sum results for the above quantities ( i - iii ) are the following . the end - to - end vector autocorrelation function for the chain decays in time as a stretched exponential with an exponent @xmath11 , crossing over to pure exponential decay at the terminal time @xmath12 ; this exponent is partially shared with that of the wlc @xcite . the autocorrelation of the orientation of the middlemost bond vector decays in time in a similar manner , but with an exponent @xmath13 ; this property , too , is partially shared with the wlc @xcite . the mean - square displacement ( msd ) of the middle bead shows anomalous diffusion with an exponent @xmath11 until time @xmath14 , beyond which its motion becomes diffusive ; this property has been reported for the wlc @xcite , as well from experiments @xcite . the full dynamics of semiflexible polymers in our model is obviously nonlinear , and we also perform simulations of the full dynamics for chains . we find that for dsdna the mode sums agree remarkably well with the numerical values obtained from simulations . this does not however mean that the nonlinearities are not present . indeed , we find that the msd of the longitudinal component of the end - to - end vector showcases strong nonlinear effects in the polymer dynamics , and we identify an effective @xmath2 power - law regime in its time - dependence . we show that the nonlinear effects in the msd of the longitudinal component of the end - to - end vector increase with increasing length for dsdna ; nevertheless , in comparison to the full mean - square displacement of the end - to - end vector the nonlinear effects remain small at all times . it is in this sense we state that the linearized dynamics suffices for dsdna fragments that are shorter than or comparable to the persistence length . from the results above , which are expanded further in the paper in great detail , we hope that confidence can build up on our model . the results are trivially extended to other semiflexible polymers as long as the model parameter values are matched to the experimental ones , as demonstrated in paper i. the structure of this paper is as follows . given that the model was described in a fair amount of detail in paper i , we first briefly introduce the model and describe its key characteristics ( specially those that are needed for the calculations presented in this paper ) in sec . [ sec2 ] . in sec . [ sec3 ] we elaborate on the ( linearized ) polymer dynamics , and in sec . [ sec4 ] we analytically determine ( and verify by simulations ) the behavior of the autocorrelation function of the end - to - end vector of the chain , that of a bond vector at the middle of the chain , and the msd of a tagged bead in terms of the mode sums . we dedicate sec . [ sec5 ] to separating the longitudinal and transverse components of dynamical quantities , and sec . [ sec6 ] to nonlinear aspects of the full polymer dynamics , specially the msd of the longitudinal component of the end - to - end vector . we finish the paper in sec . [ sec7 ] with a comparison of our results with those of the wlc model .

we study the dynamical properties of semiflexible polymers with a recently introduced bead - spring model . we focus on double - stranded dna ( dsdna ) . the two parameters of the model , and , are chosen to match its experimental force - extension curve . in comparison to its groundstate value , the bead - spring hamiltonian is approximated in the first order by the hessian that is quadratic in the bead positions . the eigenmodes of the hessian provide the longitudinal ( stretching ) and transverse ( bending ) eigenmodes of the polymer , and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers . at the hessian approximation of the hamiltonian , we also perform simulations with the full dynamics of the model . the simulations yield numerical values of the correlations functions ( i - iii ) that agree very well with the analytical expressions for the linearized dynamics . this does not however mean that the nonlinearities are not present . nevertheless , in comparison to the full mean - square displacement of the end - to - end vector the nonlinear effects remain small at all times it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsdna fragments that are shorter than or comparable to the persistence length . our results are consistent with those of the wormlike chain ( wlc ) model , the commonly used descriptive tool of semiflexible polymers .

we study the dynamical properties of semiflexible polymers with a recently introduced bead - spring model . we focus on double - stranded dna ( dsdna ) . the two parameters of the model , and , are chosen to match its experimental force - extension curve . in comparison to its groundstate value , the bead - spring hamiltonian is approximated in the first order by the hessian that is quadratic in the bead positions . the eigenmodes of the hessian provide the longitudinal ( stretching ) and transverse ( bending ) eigenmodes of the polymer , and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers . at the hessian approximation of the hamiltonian , the polymer dynamics is linear . using the longitudinal and transverse eigenmodes , for the linearized problem , we obtain analytical expressions of ( i ) the autocorrelation function of the end - to - end vector , ( ii ) the autocorrelation function of a bond ( i.e. , a spring , or a tangent ) vector at the middle of the chain , and ( iii ) the mean - square displacement of a tagged bead in the middle of the chain , as sum over the contributions from the modes the so - called `` mode sums '' . we also perform simulations with the full dynamics of the model . the simulations yield numerical values of the correlations functions ( i - iii ) that agree very well with the analytical expressions for the linearized dynamics . this does not however mean that the nonlinearities are not present . in fact , we also study the mean - square displacement of the longitudinal component of the end - to - end vector that showcases strong nonlinear effects in the polymer dynamics , and we identify at least an effective power - law regime in its time - dependence . nevertheless , in comparison to the full mean - square displacement of the end - to - end vector the nonlinear effects remain small at all times it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsdna fragments that are shorter than or comparable to the persistence length . our results are consistent with those of the wormlike chain ( wlc ) model , the commonly used descriptive tool of semiflexible polymers .

astro-ph0107189

i

the determination of the pregalactic , or primordial , helium abundance by mass @xmath0 is paramount for the study of cosmology , the physics of elementary particles , and the chemical evolution of galaxies . in this paper we present a new determination of @xmath0 based on observations of the metal - poor extragalactic h regions ngc 346 , i zw 18 , ngc 2363 , haro 29 , and sbs 0335052 . this determination is compared with those carried out by other authors . a preliminary account on the results for i zw 18 and ngc 2363 is presented elsewhere @xcite . there are three problems affecting the @xmath0 determination that need to be further analyzed : @xmath6 ) the temperature structure , @xmath7 ) the ionization structure , and @xmath8 ) the collisional excitation of the hydrogen lines . this paper will be mainly concerned with the effect of the temperature structure of the nebulae on the helium line intensities . in a future paper we will discuss in more detail the problem of the collisional excitation of the hydrogen lines @xcite . the most accurate @xmath0 values in the literature have been derived under the assumption of no contribution to the hydrogen balmer lines due to collisional excitation , we will refer to these determinations in this paper as @xmath0(nhc ) and to those that include the hydrogen collisional effect as @xmath0(+hc ) . due to the collisional contribution to the balmer line intensities the @xmath0(nhc ) determinations are lower limits to the @xmath0(+hc ) value . there are several pieces of evidence indicating that @xmath1(he ) is smaller than @xmath1(o ): @xmath6 ) observations of ngc 346 [ hereinafter paper i ] pei00z , @xmath7 ) photoionization models of giant extragalactic h regions @xcite , @xmath8 ) in photoionization models @xmath1(o ) is smaller than @xmath1(o ) for objects with @xmath1(o ) higher than 12,360 k @xcite , and a considerable fraction of the he lines originates in the o@xmath3 zone . this small difference is significative because it lowers the he@xmath3/h@xmath3 determination . by combining the observed he lines it is found that @xmath1(he ) and @xmath9(he ) are coupled in the sense that a lower @xmath1 implies a higher @xmath9 reducing the he@xmath3/h@xmath3 determination ( see paper i ) . another problem that has to be considered to determine very accurate he / h values of a given h region is its ionization structure . the total he / h value is given by : @xmath10 for objects of low degree of ionization it is necessary to consider the presence of he@xmath11 inside the h@xmath3 zone , while for objects of high degree of ionization it is necessary to consider the possible presence of h@xmath11 inside the he@xmath3 zone . for objects of low degree of ionization @xmath12 might be larger than 1.00 , while for objects of high degree of ionization @xmath13 might be smaller than 1.00 . this problem has been discussed by many authors ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? each h region is different and a good photoionization model is needed to estimate an @xmath12 of very high accuracy . in this paper we will assume that the h regions are chemically homogeneous . in section 2 we will adapt the @xmath14 and @xmath15 formalism introduced by @xcite to relate @xmath1(o ) and @xmath1(o ) with @xmath1(he ) , the full mathematical treatment is presented in the appendix . in section 3 we will rediscuss the @xmath16 determination of ngc 346 , the most luminous h region in the smc , carried out in paper i. in sections 4 to 7 we redetermine the he@xmath3/h@xmath3 values for i zw 18 , ngc 2363 , haro 29 , and sbs 0335052 , based on the observations of @xcite and @xcite and on photoionization models for these objects . these four objects were selected from their sample based on the following criteria : the two objects with the lowest heavy element abundances and the two objects with the smallest observational errors @xcite . we derive he@xmath3/h@xmath3 , @xmath9(he ) , @xmath1(he ) , and @xmath17(3889 ) self - consistently based on all the observed he line intensities , with the exception of those strongly affected by underlying absorption . by combining the he@xmath3/h@xmath3 values of these four objects with that of ngc 346 we derive a new @xmath0(nhc ) in section 8 . the collisional contribution to the balmer lines is estimated in section 9 . the discussion and conclusions are presented in sections 10 and 11 .

we call this determination(nhc ) because the collisional contribution to the balmer line intensities has not been taken into account . all the recent determinations in the literature have not taken into account the collisional contribution to the balmer line intensities . by considering the collisional contribution to the balmer line intensities of these five objects we derive that(+hc) .

we study the effect that the temperature structure has on the determination of the primordial helium abundance , . we provide an equation linking(o ) , the temperature derived from the [ o ] lines , and(he ) , the temperature of the he i lines , both for h regions with o only and for h regions where a fraction of o is present . by means of(he ) , which is always smaller than(o ) , we derive the helium abundances of 5 objects with low and very low metallicity ( ngc 346 , ngc 2363 , haro 29 , sbs 0335052 , and i zw 18 ) ; these objects were selected from the literature because they include the 3 low metallicity objects with the best line determinations and the 2 objects with the lowest metallicity . from these abundances we obtain that(nhc ) , a value 0.0088 lower than that derived by using(o ) . we call this determination(nhc ) because the collisional contribution to the balmer line intensities has not been taken into account . all the recent determinations in the literature have not taken into account the collisional contribution to the balmer line intensities . by considering the collisional contribution to the balmer line intensities of these five objects we derive that(+hc) .

astro-ph0107189

c

the brightest extragalactic h regions with temperatures in the 14,000 to 16,000 k range might be the best objects to determine @xmath0 . the reasons are the following : @xmath6 ) there are many of these objects available and the brightest of them are brighter than the metal - poorest objects known which implies that the errors in the line intensity ratios will be smaller , and @xmath7 ) the effect of collisional excitation of the balmer lines is considerably smaller than for the metal - poorer objects ( those with temperatures in the 18,000 to 22,000 k range ) reducing the error in the @xmath16 determination due to this effect . on the other hand the correction to the @xmath16 determination to obtain @xmath0 based on objects with temperatures in the 14,000 to 16,000 k range increases the error in the @xmath0 determination , but in general the size of this error is expected to be smaller than those introduced in the previous paragraph because the correction is small and can be obtained with high accuracy under the assumption that @xmath163 ( see paper i ) . from chemical evolution models it is found that changes in @xmath154 are small even in the presence of a very strong burst of star formation @xcite ; moreover these objects seem to have been forming stars over periods of at least 1 to 2 gyr implying that most of their oxygen formed before the present burst , as in the case of haro 29 ( e.g. * ? ? ? * ) , and consequently that the expected changes in @xmath154 due to bursts are very small . the @xmath0(nhc ) value derived by us is significantly smaller than the value derived by @xcite , from the @xmath16 o / h linear regression for a sample of 45 bcgs , and by @xcite , from the average for the two most metal deficient galaxies known ( i zw 18 and sbs 0335052 ) , that amount to @xmath164 and @xmath165 respectively . our @xmath66(he ) determinations , that we prefer , produce @xmath16 values that are about 0.007 smaller than those derived by @xcite and @xcite , a small but significative difference , as we will see below . it should be noted that the abundances for ngc 2363 , sbs 0335052 , haro 29 , and i zw 18 obtained by both groups are based on the same observations . from photoionization models computed with cloudy we estimate that @xmath1(he ) , the temperature that should be used to determine the helium abundance , should be at least 5% smaller than @xmath1(o ) . moreover , if in addition to photoionization there is additional energy injected to the h region the difference between @xmath1(o ) and @xmath1(he ) might be even larger . figure [ feta ] shows the helium , deuterium , and lithium abundances predicted by standard big bang nucleosynthesis computations with three light neutrino species for different values of @xmath166 , the baryon to photon ratio @xcite , also in this figure we present observational abundance determinations of these elements . the implications of this figure for the determination of @xmath167 , the baryon content of the universe , are presented in table [ tbar ] .

we provide an equation linking(o ) , the temperature derived from the [ o ] lines , and(he ) , the temperature of the he i lines , both for h regions with o only and for h regions where a fraction of o is present . by means of(he ) , which is always smaller than(o ) , we derive the helium abundances of 5 objects with low and very low metallicity ( ngc 346 , ngc 2363 , haro 29 , sbs 0335052 , and i zw 18 ) ; these objects were selected from the literature because they include the 3 low metallicity objects with the best line determinations and the 2 objects with the lowest metallicity . from these abundances

we study the effect that the temperature structure has on the determination of the primordial helium abundance , . we provide an equation linking(o ) , the temperature derived from the [ o ] lines , and(he ) , the temperature of the he i lines , both for h regions with o only and for h regions where a fraction of o is present . by means of(he ) , which is always smaller than(o ) , we derive the helium abundances of 5 objects with low and very low metallicity ( ngc 346 , ngc 2363 , haro 29 , sbs 0335052 , and i zw 18 ) ; these objects were selected from the literature because they include the 3 low metallicity objects with the best line determinations and the 2 objects with the lowest metallicity . from these abundances we obtain that(nhc ) , a value 0.0088 lower than that derived by using(o ) . we call this determination(nhc ) because the collisional contribution to the balmer line intensities has not been taken into account . all the recent determinations in the literature have not taken into account the collisional contribution to the balmer line intensities . by considering the collisional contribution to the balmer line intensities of these five objects we derive that(+hc) .

0706.2004

i

semiconductor superlattices ( sls ) are nanostructures made from alternating layers of two different semiconductor materials , usually with very similar lattice constants , for example gaas and ( alga)as @xcite . due to the different energy band gaps of the two materials , the conduction band edge of an ideal superlattice is periodically modulated . typically , a sl made by molecular beam epitaxy contains 10 - 100 quantum wells in series , which are coupled by tunnel barriers . this periodic potential leads to the formation of energy bands , known as `` minibands '' , for electron motion perpendicular to the layers @xcite . a voltage applied to ohmic contacts at the two ends of the sl generates an electric field , @xmath0 , perpendicular to the plane of the layers ( see fig . [ schema ] ) , which causes charge to flow through the device . the current - voltage characteristics of sls are usually highly nonlinear due to a variety of quantum mechanical effects including resonant tunneling , the formation of wannier - stark energy level ladders , and the occurrence of bloch oscillations @xcite , whose frequency is proportional to the spatial period , @xmath1 , of the sl and , also , to @xmath2 . in natural crystals , @xmath1 is so small ( @xmath3 nm ) that bloch oscillations do not occur because the bloch frequency is much less than the electron scattering rate . but in sls , @xmath1 and the corresponding bloch frequency can be large enough for the electrons to perform bloch oscillations , which then play a key role in both the dc and high - frequency charge transport processes . the onset of bloch oscillations localizes the electrons , thus causing their drift ( average ) velocity to decrease as the electric field increases . this negative differential velocity can induce high - frequency collective oscillations of the conduction electrons within the sl layers @xcite , making sls attractive for the generation and detection of electromagnetic radiation in the ghz to thz frequency range @xcite . , which lies in the @xmath4 plane at an angle @xmath5 to the sl ( @xmath6 ) axis . the lower arrow shows direction of the electric field , @xmath0 , applied perpendicular to the plane of the layers and anti - parallel to the @xmath6 axis . ] the occurrence of negative differential velocity for electrons in sls has also led to fundamentally new regimes of charge transport involving deterministic chaos , characterized by complex irregular electron dynamics @xcite . understanding the effects of chaos on the current - voltage characteristics , @xmath7 , and high - frequency electromagnetic properties of sls is an emerging research area at the interface between nonlinear dynamics and condensed matter physics . in most previous studies , chaos in sls was identified in the cooperative motion of interacting electrons in either periodically driven @xcite or undriven sls @xcite . recent theoretical and experimental work has revealed that the single - particle trajectories and collective behavior of electrons moving through the lowest miniband of a biased sl with a tilted magnetic field have unique properties @xcite . for example , the electrons exhibit an unusual type of hamiltonian chaos , known as `` non - kam '' chaos @xcite , which does not obey the kolmogorov - arnold - moser ( kam ) theorem and provides a sensitive new mechanism for controlling electron transport . remarkably , the effective classical hamiltonian for the electron motion in a sl has an intrinsically quantum - mechanical origin as it depends explicitly on the energy versus wavevector dispersion relation of the miniband @xcite . analysis of hamilton s equations reveals that the stochastic electron motion switches on abruptly when the field parameters satisfy certain resonance conditions , described in detail below . the onset of chaos delocalizes the electrons by imprinting an intricate mesh of conduction channels ( known as a `` stochastic web '' ) in phase space , which produces large resonant enhancement of the electron velocity and current flow measured in experiment @xcite . this phase - space patterning provides a fundamentally new concept for controlling electrical conductance @xcite and operates even at room temperature @xcite . in the absence of dissipation , the resonant delocalization of the conduction electrons would produce a series of delta - function peaks in the @xmath7 curves . but in real sls , the resonances are broadened because the electrons scatter both elastically @xcite , due mainly to roughness at the interfaces between the tunnel barriers and quantum wells and to ionized donor atoms , and inelastically via the emission and absorption of phonons . when calculating the transport characteristics of the sls , the effect of scattering on the electron dynamics must be taken into account in order to obtain @xmath7curves that agree with experiment . in our previous theoretical work @xcite , we incorporated electron scattering in the following phenomenological way . first , we calculated the electron trajectories by solving hamilton s equations for the system , assuming @xmath8 scattering . next , we used these trajectories to determine the average electron velocity from a simple kinetic formula in which scattering appears _ a posteriori _ as an exponential damping term whose decay rate depends on the elastic and inelastic relaxation times . in this paper , we investigate whether the striking electron resonance effects and phase space patterning predicted by our earlier collision - free hamiltonian model of the electron dynamics persist when scattering is included _ a priori _ in the equations of motion . we find that when the scattering is described in this way , it creates far richer electron dynamics than expected from our previous hamiltonian analysis . in particular , scattering makes the system highly sensitive to changes in the control parameters ( electric and magnetic fields ) , which induce complex bifurcation sequences characterized by alternating windows of stability and chaos . counter - intuitively , dissipation also enhances the resonant delocalization of the semiclassical trajectories by creating attractors that drive the electrons rapidly through the sl . the regimes of dissipative chaos that we have identified have a pronounced effect on the velocity - field characteristics of the miniband electrons and provide mechanisms for controlling sl magnetotransport by exploiting complex nonlinear dynamics . the structure of the paper is as follows . in section ii , we introduce the semiclassical equations of motion for a miniband electron in a tilted magnetic field and show how scattering is included _ a priori _ in those equations . in section iii , we show that scattering dramatically changes the electron trajectories and phase space structure of the system by creating attractors corresponding to periodic orbits that extend through the whole sl . in section iv , we present a detailed analysis of the stability of the electron orbits . section v explores the complex series of resonances that scattering induces in the electron dynamics and elucidates the effect of these resonances on the electron velocity and experimentally - measured electrical current . finally , in section vi , we summarize our results and draw conclusions .

, we showed that although the applied fields are stationary , they act like a thz plane wave , which strongly couples the bloch and cyclotron motion of electrons within the lowest miniband . as a consequence , the electrons exhibit a unique type of hamiltonian chaos , which creates an intricate mesh of conduction channels ( a stochastic web ) in phase space , leading to a large resonant increase in the current flow at critical values of the applied voltage . this phase - space patterning provides a sensitive mechanism for controlling electrical resistance . in this paper , we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term . we demonstrate that even in the presence of dissipation , deterministic chaos plays an important role in the electron transport process . we identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories . in particular , for fixed values of the control parameters several distinct stable regimes can coexist , each corresponding to different initial conditions . we show that this multistability has clear , experimentally - observable , signatures in the electron transport characteristics .

we study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis . in previous work , we showed that although the applied fields are stationary , they act like a thz plane wave , which strongly couples the bloch and cyclotron motion of electrons within the lowest miniband . as a consequence , the electrons exhibit a unique type of hamiltonian chaos , which creates an intricate mesh of conduction channels ( a stochastic web ) in phase space , leading to a large resonant increase in the current flow at critical values of the applied voltage . this phase - space patterning provides a sensitive mechanism for controlling electrical resistance . in this paper , we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term . we demonstrate that even in the presence of dissipation , deterministic chaos plays an important role in the electron transport process . we identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories . when the bloch and cyclotron frequencies are commensurate , complex multistability phenomena occur in the system . in particular , for fixed values of the control parameters several distinct stable regimes can coexist , each corresponding to different initial conditions . we show that this multistability has clear , experimentally - observable , signatures in the electron transport characteristics .

1102.0857

i

tidal interactions are important in determining the fate of short - period extrasolar planets and the spins of their host stars . the extent of the spin - orbit evolution that results from tides depends on the dissipative properties of the star and planet . these are usually parametrized by a dimensionless quality factor for each body , which is an inverse measure of the dissipation . this is usually defined to be proportional to the ratio of the maximum energy stored in a tidal oscillation to the energy dissipated over one cycle ( e.g. @xcite ) . in principal the modified quality factor by @xmath1 , where @xmath2 is the second - order potential love number of the body . ] @xmath3 depends on tidal frequency , the internal structure of the body , and the amplitude of the tidal forcing . unfortunately , the mechanisms of dissipation that contribute to @xmath3 are poorly understood . to simplify this difficult problem , nearly all studies neglect any amplitude dependence of the dissipation ( except , for example @xcite ) . such studies already exhibit a complicated dependence of @xmath3 on the tidal frequency ( e.g @xcite ; @xcite ; @xcite , hereafter ol04 ; @xcite , hereafter ol07 ; @xcite ) , and the internal structure of the body ( e.g ol07 ; @xcite ) . in this paper we extend the work of @xcite ( hereafter bo10 ) to study an important nonlinear dissipation mechanism in solar - type stars . we can decompose the tidal response of a fluid body , which in this paper we take to mean a solar - type star , into an equilibrium and a dynamical tide , defined such that the total displacement is the sum of these two displacements , i.e , that @xmath4 . the equilibrium tide is a quasi - hydrostatic bulge defined by @xmath5 in stratified regions ( @xcite ) , where @xmath6 is the tidal gravitational potential experienced by the body and @xmath7 is the gravitational acceleration . the total displacement is not well described by eqs . [ eqmtideeqns ] in convective regions ( @xcite , hereafter gd98 ; @xcite , hereafter t98 ; olo4 ) . this is because in a barotropic flow ( with adiabatic stratification ) vorticity is conserved , so we must have @xmath8 , whereas @xmath9 , in general . the presence of a convection zone ( hereafter cz ) thus implies that a dynamical tide must exist . the dynamical tide @xmath10 is defined as the residual response that results from the equilibrium tide not being the exact ( linearised ) solution to the problem , when the tidal frequency is nonzero . the equations governing the adiabatic equilibrium and dynamical tides in linear theory are @xmath11 from which it is clear that the dynamical tide is not forced directly by the tidal potential , only by the inertial terms in the equation of motion . dynamical tides in radiation zones of solar - type stars take the form of internal ( inertia- ) gravity waves ( igws ) , which have frequencies below the buoyancy ( or brunt - visl ) frequency @xmath12 . these have previously been proposed to contribute to @xmath3 for early - type stars ( e.g. @xcite ) , where they are damped at the surface by radiative diffusion . it has also been proposed that these waves could synchronise the spin of the star with the orbit ( in this case of a close - binary perturber ) from the outside in @xcite . in bo10 , we considered a nonlinear mechanism of tidal dissipation in solar - type stars ( with radiative cores ) , extending an idea by gd98 . the consequences of this mechanism are similar to @xcite , except that the star is synchronised with the orbit from the inside out . a short - period planet excites igws at the top of the rz of a solar - type star , where @xmath12 increases from zero with distance into the rz from the cz / rz interface . there is thus a location at which @xmath13 , with @xmath14 being the planetary orbital period , at which igws ( which have frequencies less than @xmath12 ) are efficiently excited . these waves propagate downwards into the radiation zone ( hereafter rz ) , until they reach the centre of the star , where they are geometrically focused and can become nonlinear . if their amplitudes are sufficiently large , convective overturning occurs , and the wave breaks . this has consequences for the tidal torque , and the stellar @xmath3 . in this paper we study this mechanism , primarily using three - dimensional numerical simulations . in bo10 , we derived a boussinesq - type system of equations that is relevant for describing the dynamics of igws approaching the centre of a solar - type star . we then performed numerical simulations , solving these equations in two dimensional cylindrical geometry . in this paper we extend these simulations to three dimensions , in spherical geometry , and confirm that the most important results of bo10 are not affected by this extension . we first derive a linear wave solution , which represents the waves excited by planets on short - period orbits as they approach the central @xmath15 of the star , within which @xmath16 and @xmath17 . a weakly nonlinear analysis confirms that this solution is not exact , though the reflection of ingoing waves is close to perfect for moderate amplitude waves . we present the numerical setup and the analysis of the simulation results . we then discuss the launching region at the top of the rz , and the possible effects of magnetic fields on the problem . together with bo10 , we provide a possible explanation for the survival of all short - period extrasolar planets observed thus far , which will be tested by ongoing observational studies , such as wasp and kepler .

we first derive a linear wave solution , which is not exact in 3d ; however , the reflection of ingoing waves from the centre is close to perfect for moderate amplitude waves . [ firstpage ] planetary systems stars : rotation binaries : close hydrodynamics waves instabilities

we study the fate of internal gravity waves approaching the centre of an initially non - rotating solar - type star , by performing three - dimensional numerical simulations using a boussinesq - type model . these waves are excited at the top of the radiation zone by the tidal forcing of a short - period planet on a circular , coplanar orbit . this extends previous work done in two dimensions by barker & ogilvie . we first derive a linear wave solution , which is not exact in 3d ; however , the reflection of ingoing waves from the centre is close to perfect for moderate amplitude waves . waves with sufficient amplitude to cause isentropic overturning break , and deposit their angular momentum near the centre . this forms a critical layer , at which the angular velocity of the flow matches the orbital angular frequency of the planet . this efficiently absorbs ingoing waves , and spins up the star from the inside out , while the planet spirals into the star . we also perform numerical integrations to determine the linearised adiabatic tidal response throughout the star , in a wide range of solar - type stellar models with masses in the range , throughout their main sequence lifetimes . the aim is to study the influence of the launching region for these waves at the top of the radiation zone in more detail , and to determine the accuracy of a semi - analytic approximation for the tidal torque on the star , that was derived under the assumption that all ingoing wave angular momentum is absorbed in a critical layer . the main conclusions of this work are that this nonlinear mechanism of tidal dissipation could provide an explanation for the survival of all short - period extrasolar planets observed around fgk stars , while it predicts the destruction of more massive planets . this work provides further support for the model outlined in a previous paper by barker & ogilvie , and makes predictions that will be tested by ongoing observational studies , such as wasp and kepler . [ firstpage ] planetary systems stars : rotation binaries : close hydrodynamics waves instabilities

1102.0857

c

in this paper , we have presented the results of a set of 3d simulations of igws approaching the centre of a solar - type star . the aim of this work is to determine the importance of a nonlinear mechanism of tidal dissipation in solar - type stars , first proposed by gd98 , continuing the investigation of bo10 . we have confirmed that the main results of bo10 are unaffected by the extension to 3d by performing numerical hydrodynamical simulations , using a boussinesq - type model solved with a pseudospectral method . we first derived a linear wave solution in 3d , and found that nonlinearities do not vanish for this wave , unlike the 2d solution , which is exact . nevertheless , these waves are found to reflect approximately perfectly for moderate - amplitudes , a result which we have qualitatively confirmed in numerical simulations of moderate - amplitude tidal forcing . the general picture for high - amplitude forcing is that igws break within the innermost wavelengths of a star , if they reach the centre with sufficient amplitude to overturn the stratification . if this occurs , they form a critical layer , which we have confirmed from the simulations efficiently absorbs ingoing wave angular momentum . this results in the star being spun up to the orbital angular frequency of the planet , from the inside out . this could be very important to the survival of massive planets in short - period orbits around solar - type stars . one noticeable difference in 3d is that the absorption of @xmath74 ingoing waves results in the formation of latitudinal differential rotation . this is perpetually reinforced by critical layer absorption . instabilities may act on this rotation profile , which could homogenise the horizontal angular momentum distribution . these include shear instabilities , which can be linear @xcite or nonlinear instabilities , that set in at a critical reynolds number @xcite . these have growth times comparable to the tidal period , and could transfer angular momentum latitudinally . there are also doubly diffusive instabilities ( @xcite ; @xcite ) , or magnetic instabilities , such as the magnetorotational instability @xcite . however , these mechanisms are unlikely to be able to prevent the critical layer absorption , and thus prevent the tidal engulfment of a short - period planet . in these simulations we artificially forced waves at the top of the computational domain . in reality , the waves are launched at the top of the rz . in this paper we also solved the linearised equations for the adiabatic tidal response , in order to study the influence of the launching region in more detail . we provide an expression for the energy flux eq . [ besselenergyflux ] , which has been checked to agree very well with the numerically computed energy flux for all orbits for which this effect is potentially important , and in a wide range of solar - type stellar models . we then presented the breaking criterion that must be satisfied for the waves to break , slightly refining bo10 . finally , in [ qandexplanation ] we presented the tidal @xmath3 that results from this process , together with a breaking criterion that determines when these waves break . this allowed us to outline a possible explanation for the survival of all short - period extrasolar planets , that is not in conflict with current observations , and makes predictions which will be tested by ongoing observational studies such as wasp and kepler . as in bo10 , our simulations do not show any instabilities that act on the waves when they have insufficient amplitude to overturn the stratification . this result suggests that to obtain any efficient tidal dissipation , the waves must have sufficient amplitude to satisfy eq . [ breakingcriterion ] , so that they overturn the stratification . however , it may be that weaker parametric instabilities operate for waves with lower amplitudes ( suggested by gd98 ) . a detailed stability analysis of the 2d exact wave solution written down in bo10 is ongoing , and should shed light on this matter . in our explanation in the previous section , we ignored the potential effects of the evolution of either the stellar eigenfrequencies or the tidal frequency , that could result in a passage through a resonance with a global mode of oscillation . if this occurs , and simple estimates suggest that this is very likely at least once in the lifetime of a system , then the waves may break , even if the amplitude of the tide is small before the passage through resonance . future work is required to study this problem in detail . the simulations performed in this paper used a boussinesq - type model , which is only valid in the central @xmath228 by radius of a solar - type star . for future work , it is possible to perform simulations using an anelastic code , which could take into account the radial variation in stellar properties throughout the whole rz ( e.g. @xcite ) . we have also neglected the rotation ( or possible differential rotation ) of the rz , which is reasonable since we are considering the waves excited by short - period planets in slowly rotating stars . however , the inclusion of rotation ( and differential rotation ) would certainly be interesting to study for more rapidly rotating stars . one consequence could be that the latitudinal differential rotation observed in the simulations in 3d may be enhanced by rotation , because inertia - gravity waves can be confined in the equatorial regions . in addition , we have so far considered a planet on a circular , coplanar orbit . since many planets have been observed with eccentric or inclined orbits , this makes a study of the circularisation and potential spin - orbit alignment through wave breaking and the resulting critical layer absorption , seem an attractive avenue of future research .

this extends previous work done in two dimensions by barker & ogilvie . this work provides further support for the model outlined in a previous paper by barker & ogilvie , and makes predictions that will be tested by ongoing observational studies , such as wasp and kepler .

we study the fate of internal gravity waves approaching the centre of an initially non - rotating solar - type star , by performing three - dimensional numerical simulations using a boussinesq - type model . these waves are excited at the top of the radiation zone by the tidal forcing of a short - period planet on a circular , coplanar orbit . this extends previous work done in two dimensions by barker & ogilvie . we first derive a linear wave solution , which is not exact in 3d ; however , the reflection of ingoing waves from the centre is close to perfect for moderate amplitude waves . waves with sufficient amplitude to cause isentropic overturning break , and deposit their angular momentum near the centre . this forms a critical layer , at which the angular velocity of the flow matches the orbital angular frequency of the planet . this efficiently absorbs ingoing waves , and spins up the star from the inside out , while the planet spirals into the star . we also perform numerical integrations to determine the linearised adiabatic tidal response throughout the star , in a wide range of solar - type stellar models with masses in the range , throughout their main sequence lifetimes . the aim is to study the influence of the launching region for these waves at the top of the radiation zone in more detail , and to determine the accuracy of a semi - analytic approximation for the tidal torque on the star , that was derived under the assumption that all ingoing wave angular momentum is absorbed in a critical layer . the main conclusions of this work are that this nonlinear mechanism of tidal dissipation could provide an explanation for the survival of all short - period extrasolar planets observed around fgk stars , while it predicts the destruction of more massive planets . this work provides further support for the model outlined in a previous paper by barker & ogilvie , and makes predictions that will be tested by ongoing observational studies , such as wasp and kepler . [ firstpage ] planetary systems stars : rotation binaries : close hydrodynamics waves instabilities

astro-ph0608375

r

in general , the simulations evolve as described in paper i and in sec . [ sec : quali ] . as an illustration , figs.[fig : anim_256_edgeon ] and [ fig : anim_256_faceon ] show selected snapshots of run l256@xmath380.17 viewed edge - on and face - on , respectively . in the electronic version of the paper , these figures are also available as full - length animations . the times indicated in the frames are in the code s internal unit , @xmath92 myr . the animation shows that the gas at the collision site begins to undergo a phase transition to the cold phase ( the cnm ) at roughly one cooling time after the collision @xcite , becoming much denser and colder . because this gas is in equilibrium with the total ( thermal+ram ) pressure of the inflow , the density overshoots far beyond that of standard cnm , well into the realm of molecular gas , with mean densities of several hundred @xmath15 and temperatures of a few tens of kelvins . this implies a much lower jeans mass than that in the conditions of the initial wnm and quickly the cloud s mass exceeds its jeans mass . defining the `` cloud '' as the material with @xmath93 , the cloud s mass becomes larger than its mean jeans mass at @xmath94 myr in runs with @xmath23 pc and at @xmath95 myr in the run with @xmath42 pc , at which times the mean density in the dense gas is @xmath96 , the mean temperature is @xmath97 k , the jeans mass is @xmath98 , and the free - fall time is @xmath99 myr , where @xmath73 is the local sound speed . for comparison , the total mass in the two cylinders , which contain the material that initially builds up the cloud , is @xmath33 in the runs with @xmath23 pc , and @xmath100 in the run with @xmath42 pc . thus , the cloud eventually becomes much more massive than its mean jeans mass . for example , in run l256@xmath380.17 at @xmath101 myr , the ( mass - weighted ) mean density of the dense gas is @xmath102 , the mean temperature is @xmath103 k , and @xmath104 . these values imply a mean effective jeans mass @xmath105 , while at that time the cloud contains @xmath106 . note that the cloud+sink mass might exceed the mass in the inflows , since ambient material surrounding the cylinder is dragged along with the flow , effectively increasing the amount of gas in the inflow ( see below ) . the animations show that global collapse does indeed occur , although at significantly later times than when the cloud s mass becomes larger than the jeans mass , probably reflecting the role of turbulence as an opposing agent to the collapse . indeed , the clouds in the 128-pc boxes begin global contraction at @xmath107 myr , while the cloud in the 256-pc box , with more than twice the inflow duration , begins contracting at @xmath108 myr . figure [ fig : multi_evo ] ( _ top _ panel ) shows the evolution of the cloud s mass in run l256@xmath380.17 , together with the mass in collapsed objects ( sinks ) , to be discussed further in [ sec : energy_sf ] . it is clearly seen that the _ cloud s mass is not constant , but rather evolves in time_. gas at cloud densities first appears after 2 myr of evolution , and the cloud s mass increases monotonically until @xmath109 myr , at which time it reaches a maximum value @xmath110 . after this time , it begins to decrease because of the rapid conversion of gas to stars . by the end of the simulation , the total mass in stars plus dense gas is almost three times the initial mass in the inflows . in practice , the inflows last longer than the simple estimate @xmath111 would indicate , and involve more mass than the mass initially within the cylinders . this is due to the fact that , as the cylinders begin advancing , they leave large voids behind them that have the double effect of slowing down the tails of the inflows and of dragging the surrounding gas behind the cylinders . for @xmath112 , @xmath113 myr for runs with @xmath114 pc ( l128@xmath380.24 and l128@xmath380.66 ) , and @xmath115 myr for the run with @xmath116 pc ( l256@xmath380.17 ) . instead , in the first two runs , the inflow actually lasts @xmath117 myr , while in the latter run it lasts @xmath118 myr . this can be observed in the animation of fig.[fig : anim_256_edgeon ] , in which the velocity field arrows clearly show the gradual decay of the inflows , and their longer duration compared to the simple linear estimate . our simulations do not include any feedback from the stellar objects , while this process is probably essential for the energy balance and possibly the destruction of the cloud ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? thus , the simulations can not be safely considered realistic after their stellar content would likely disrupt the cloud . we now present an _ a posteriori _ estimation of the time at which this occurs . @xcite have suggested that the maximum number of ob stars that the cloud can support at any time is given by the number of h ii regions required to completely ionize the cloud . in particular , they found that the maximum number of massive stars that can be formed within a molecular cloud is @xmath119 where @xmath120 is the mass of the cloud , in units of 4 @xmath121 , @xmath122 is the number density in units of 3 cm3 , @xmath123 is the photoionizing flux from the massive stars , in units of s1 , @xmath124 is the isothermal sound speed in units of 15 @xmath5 , and @xmath125 is a characteristic ob star main sequence lifetime , in units of 7 yr . however , as @xcite pointed out , clouds are more efficiently destroyed by stars at the cloud edge because the lower external pressure ensures that the ionized gas expands rapidly away from the cloud , driving a fast ionization front into the dense material . thus , in this case , these authors find that the maximum number of ob stars that the molecular cloud can support is given by : @xmath126 in order to determine the time at which the mc in our simulation has formed a sufficient number of stars to disrupt it , we proceed as follows . since the individual sink particles in the simulations in general correspond to clusters rather than to single stars , we can not use the sink particle masses directly . instead , for each temporal output of our simualtion , we fit a standard initial mass function @xcite to the total mass in sink particles at that time , to obtain the the `` real '' distribution of stellar masses in the simulation at that time . we then use table 1 of @xcite , which gives the ionizing flux as a function of stellar mass , to estimate the flux associated to each mass bin , and then integrate over all relevant masses to obtain the total @xmath123 . now , from eqs . ( [ eq : franco4insidestars ] ) or ( [ eq : franco4edgestars ] ) one can solve for @xmath120 as a function of @xmath127 , to find the minimum cloud mass that survives the ionizing radiation from the existing ob stars in the simulation . when this minimum surviving mass is larger than the actual cloud mass , we expect that the cloud will be disrupted . since we define the `` cloud '' as the gas with densities above 50@xmath15 , we take @xmath128 . also , for simplicity we assume @xmath129 . for run l256@xmath380.17 , fig . [ fig : cloud_disrup ] shows the evolution of the cloud s mass together with the minimum disrupted cloud mass under the two estimates , eqs.([eq : franco4insidestars ] ) and ( [ eq : franco4edgestars ] ) . we see that the cloud is expected to be disrupted at @xmath130 with either estimate . at this time the mass in sinks is @xmath131 and the cloud s mass is @xmath132 , so that the star formation efficiency ( sfe ) up to this time has been @xmath133 this number is still larger than observational estimates for cloud complexes @xcite , and suggests that additional physical processes , such as longer inflow durations ( [ sec : eff_infl_sigma ] ) or magnetic fields ( [ sec : caveats ] ) may be necessary to further reduce the sfe . we conclude from this section that after @xmath134 myr run l256@xmath380.17 is probably not realistic anymore , as far as the evolution of a real mc is concerned , and we thus restrict most of our subsequent discussions to times earlier than that , except when later times may be illustrative of some physical process . self - consistent inclusion of stellar feedback in the simulations , similarly to the studies of @xcite and @xcite , to investigate the final stages of mc evolution will be the subject of future work . the collision also generates turbulence in the dense gas , and so the cloud can be considered to be in a driven turbulent regime while the inflows persist , and in a decaying regime after the inflows subside , although the transition from driven to decaying is smooth , rather than abrupt , since the inflows subside gradually , as explained above . figure [ fig : multi_evo ] ( _ bottom _ panel ) shows the evolution of the velocity dispersion @xmath135 for the dense gas along each of the three coordinate axes for run l256@xmath380.17 . during the first 10 myr of the cloud s existence ( @xmath136 myr ) @xmath137 , although it is interesting to note that the turbulence appears to be anisotropic , with @xmath138 first increasing and then decreasing . it reaches a maximum of more than twice as large ( @xmath139 ) as that of @xmath140 and @xmath141 at @xmath142 myr , reflecting the fact that the inflows are directed along this direction . this suggests that the generation of transverse turbulent motions is not 100% efficient . of course , this effect is probably exaggerated by our choice of perfectly anti - parallel colliding streams . clouds formed by obliquely colliding streams are likely to have more isotropic levels of turbulence . after @xmath143 myr , @xmath138 begins to decrease , reflecting the weakening of the inflows , settling at @xmath144 by @xmath145 myr . at this time , @xmath140 and @xmath141 begin to increase , reflecting the global collapse of the cloud on the @xmath146 plane , while @xmath138 remains nearly stationary , unaffected by the global planar collapse , until @xmath147 myr , at which time it also begins to increase . this coincides with the onset of star formation , and probably reflects the local , small - scale , isotropic collapse events forming individual collapsed objects . an important consideration for understanding the production of local collapse events is the distribution of the density and temperature as the cloud evolves . this is shown in fig.[fig : hists ] , where the normalized mass - weighted histograms of density ( _ left _ panel ) and of temperature ( _ right _ panel ) are shown at times 4 , 8 , 12 , 14 , 16 , and 20 myr for run l256@xmath380.17 . it can be seen that a cold phase already exists at @xmath148 myr , although at this time the cloud s conditions do not greatly exceed those of the standard cnm , meaning that turbulence is only building up in the cloud at this stage , at which the simulation resembles a two - phase medium . at @xmath149 myr , the density maxima and temperature minima have shifted to more extreme values , which persist up to @xmath150 myr , indicating that the density and temperature fluctuations are predominantly created by the supersonic turbulence in the cloud @xcite . however , by @xmath151 myr , the density and temperature extrema are seen to be again moving towards more extreme values , and this trend persists throughout the rest of the simulation , indicating that gravitational collapse has taken over the evolution of the density fluctuations ( see also [ sec : energy_sf ] ) . it thus appears that in this particular simulation , the turbulent density fluctuations act as simply as seeds for the subsequent growth of the fluctuations by gravitational instability , as proposed by @xcite . however , both in that paper as in the present study , the global turbulence is already decaying , and by definition it can not then continue competing with self - gravity . minimally , a fundamental role of turbulence , even in this decaying state , must be to create _ nonlinear _ density fluctuations , of much larger amplitudes than would be created by thermal instability alone , which can collapse in shorter times than the whole cloud ( cf . [ sec : energy_sf ] and [ sec : implications ] ) . in any case , simulations in which the inflow lasts beyond the onset of collapse would be desirable , but unfortunately , as mentioned in [ sec : eff_infl_sigma ] , we have not found it feasible to attempt them with the present code and computational resources , and such a study must await a different numerical scheme and physical setup . figure [ fig : multi_evo2 ] ( _ top _ panel ) shows the evolution of the kinetic ( @xmath1 ) and thermal ( @xmath152 ) energies within a cylinder of length 16 pc and radius 32 pc centered at the middle point of the numerical box , together with the evolution of the ( absolute value of the ) gravitational energy ( @xmath2 ) for the entire simulation box . this cylinder contains most of the cloud s mass thoughout the simulation , although it also contains sizable amounts of interspersed wnm . figure [ fig : multi_evo2 ] ( _ bottom _ panel ) , on the other hand , shows the evolution of the same energies but with @xmath1 and @xmath152 calculated for the dense gas only . the gravitational energy is shown for the entire box because of the practical difficulty to evaluate it only for the cloud s mass , although we expect the latter to dominate the global gravitational energy when the cloud has become very massive . indeed , we observe that @xmath2 at late times is very large and dominates the other forms of energy . a brief period of positive values of @xmath2 is observed for @xmath153 myr , which can be understood as follows : because the boundary conditions are periodic , poisson s equation for the gravitational potential is actually modified to have the density fluctuation @xmath154 as its source . this is standard fare in cosmological simulations ( see , e.g. , * ? ? ? * ; * ? ? ? moreover , gravity is a long - range force , and so large - scale features tend to dominate @xmath0 . thus , during the early epochs of the simulation , when the cloud is beginning to be assembled , the dominant density features are the voids left behind by the cylinders because they are large , while the cloud is small and not very massive . however , once the cloud becomes sufficiently massive , and the voids have been smoothed out , the cloud dominates @xmath0 . the period of positive @xmath0 is omitted from both panels of fig . [ fig : multi_evo2 ] . comparison of the energy plots ( figs . [ fig : multi_evo2 ] _ top _ and _ bottom _ ) with the evolution of the gas and sink masses ( fig.[fig : multi_evo ] _ top _ ) and the animations shows some very important points . first and foremost , the cloud is never in virial equilibrium over its entire evolution . instead , we can identify three main stages of evolution . first , over the period @xmath155 myr , @xmath2 increases monotonically , transiting from being negligible compared to @xmath1 and @xmath152 to becoming larger than either one of them . the exact time at which this occurs depends on what system is being considered . it occurs at @xmath156 myr when only the energies in the dense gas are considered , while it occurs at @xmath147 myr when the entire cylinder , which includes substantial amounts of warm gas , is considered . since global gravitational contraction starts at @xmath157 myr , it appears that the true balance is bracketed by the estimates based on the full cylinder volume and on the dense gas , though closer to the latter . thus , over the interval @xmath158 myr , the increase in @xmath2 is driven mostly by the cooling and compression of the gas . second , from @xmath157 myr to @xmath159 myr , @xmath2 continues to increase ( @xmath0 becomes more negative ) , but now driven by the global collapse of the cloud . over this period , we see that @xmath1 for the dense gas ( fig . [ fig : multi_evo2 ] , _ bottom _ panel ) closely follows @xmath2 , approximately satisfying the condition @xmath160 we see that in this case , _ this condition is a signature of collapse , not of gravitational equilibrium _ , even though it lasts for nearly 12 myr . the maintenance of this equipartition arises from the fact that the cloud is converting gravitational potential energy into kinetic energy , but is replenishing the former by the collapse itself . note that we have cautioned in [ sec : cloud_disrup ] that our simulations may not be realistic after @xmath134 myr , because by that time the stellar energy feedback may be sufficient to revert the global collapse and disperse the cloud , but even in that case the cloud will have evolved out of equilibrium up to that point . finally , after @xmath161 myr , the gravitational and kinetic turbulent energies saturate and begin to vary in approximate synchronicity . although this late stage may not be representative of actual mcs , it is important to understand what is happening in the simulation . the near constancy of @xmath2 and @xmath1 could naively be interpreted as a final state of near virial equilibrium . however , inspection of the animations shows otherwise . at @xmath161 myr , the main body of the cloud is completing its global collapse , and the mass in stars is beginning to exceed the mass in dense gas , which is itself decreasing . so , at this point , the gravitational energy is beginning to be dominated by the stars , rather than by the gas . moreover , the face - on animation ( fig.[fig : anim_256_faceon ] ) shows that at this time ( @xmath162 in code units , shown in the animations ) the star cluster is beginning to re - expand , after having reached maximum compression . this leads to the decrease of @xmath2 between @xmath163 and @xmath164 myr . meanwhile , @xmath1 , which is dominated by the dense gas , decreases because the dense gas is being exhausted . nevertheless , the outer `` chaff '' of the dense gas , mostly in the form of radial filaments , is continuing to fall onto the collapsed cloud . this leads to a new increase in both energies , as this is a secondary collapse . this situation repeats itself at @xmath165 myr ( @xmath166 in code units ) after the secondary collapse ends and its second - generation star cluster begins to expand away . the end of each collapse and the re - expansion of the clusters is marked by kinks in the graph of @xmath167 _ versus _ time in fig . [ fig : multi_evo ] ( _ top _ ) , indicating a decrease in the star formation rate . it is important to recall as well that the condition given by eq . ( [ eq : equip ] ) is not sufficient for virial equilibrium . the necessary and sufficient condition for this is that the second time derivative of the moment of inertia of the cloud be zero , and eq . ( [ eq : equip ] ) can not guarantee this , as many other terms enter the full virial balance of the cloud @xcite . thus , the observed closeness of @xmath2 and @xmath1 in actual molecular clouds must exclusively be considered an indication of near equipartition and probably of collapse , but not of virial equilibrium ( see also * ? ? ? thus , rather than evolving in near virial equilibrium , _ the cloud evolves far from equilibrium_. @xmath2 starts out from essentially zero and increases monotonically until it catches up with the thermal and kinetic energies . from that time on , gravity dominates the energy balance , leading to collapse , which in turn causes a near equipartition between @xmath2 and @xmath1 , although both energies continue to vary systematically . finally , figure [ fig : multi_evo ] ( _ top _ ) also shows that star formation begins at @xmath168 myr , roughly 5 myr after global contraction of the cloud has begun . yet , the star - forming local collapse events proceed much more rapidly than the global collapse of the cloud . this indicates that the turbulence in the cloud has created _ nonlinear _ density fluctuations , whose local free - fall time is shorter than that of the whole cloud . in particular , the mass in stars increases from zero to @xmath169% of the cloud s mass in @xmath170 myr ( from @xmath171 to @xmath172 myr ) . the main conclusions from this section are that a ) the cloud evolves far from equilibrium all the way from its inception through its final collapse ; b ) as soon as @xmath0 dominates the dynamics , the cloud develops equipartition indicative of the collapse , not of equilibrium , and c ) star formation is rapid in comparison with the evolution and collapse of the whole cloud . in previous papers @xcite , it has been argued that the star formation efficiency is a sensitive function of whether the turbulence in the cloud is in a driven or in a decaying regime . our system is driven at first , and gradually transits to a decaying regime , as pointed out in [ sec : turb ] . in all of the runs in this paper , global cloud contraction and the subsequent star formation occur after the inflows have weakened substantially ( @xmath173 ) . the main motivation behind run l256@xmath380.17 was precisely to model an inflow of as long a duration as possible , to approximate the case of a driven cloud , although this goal was not completely achieved . for example , @xcite suggest accumulation lengths of up to 400 pc . runs with even larger boxes ( e.g. , 512 pc ) would be desirable , but they are either prohibitely expensive , or have an excessively poor mass resolution . in addition , vertical stratification effects would have to be considered . this will require a transition to the code gadget2 , which allows for non - cubic boundary conditions and/or inflow boundary conditions , a task we defer to a subsequent paper . nevertheless , comparison of the runs with different inflow lengths does shed light on the effect of a longer driving duration . the cloud in run l256@xmath380.17 , whose inflow has @xmath116 pc and lasts @xmath174 myr ( although it begins weakening at @xmath175 myr ) , begins contracting at @xmath108 myr and begins forming stars at @xmath176 myr , while both runs with @xmath177 pc , for which the inflow lasts 11 myr ( begins weakening at @xmath178 myr ) , start to contract at @xmath107 myr ( recall that the inflows have the same density and velocity in all runs ) . run l128@xmath380.24 begins forming stars at @xmath179 myr , and run l128@xmath380.66 does so at @xmath180 myr . these results clearly suggest that a longer inflow duration delays the onset of both global collapse and star formation , in spite of the fact that the cloud formed by it is more massive . this is attributable to the fact that the turbulence in the cloud is continuously driven by the inflow . this is verified by comparing the three components of the velocity dispersion for runs l256@xmath380.17 and l128@xmath380.24 , respectively shown in fig.[fig : multi_evo ] ( _ bottom _ ) and fig . [ fig : veldisp_run18 ] . both runs show an initial transient peak in @xmath138 ending at @xmath181 myr . however , after this transient , @xmath138 in run l256@xmath380.17 increases again , reaching a maximum of @xmath182 , and decreasing afterwards , until it nearly stabilizes at a value @xmath144 at @xmath183 myr . during this time interval , @xmath184 . instead , in run l128@xmath380.24 , @xmath138 does not increase again after the initial transient , and remains at a much more moderate level of @xmath185 , while @xmath186 . clearly , the turbulence level is significantly higher in the longer - inflow run . note that the delay in the onset of global collapse and of local star formation can not be attributed to the amplitude of the initial velocity fluctuations in the inflow , since runs l128@xmath380.24 and l256@xmath380.17 , which have comparable amplitudes , differ substantially in these times , while runs l128@xmath380.24 and l128@xmath380.66 begin global contraction at almost the same time and differ by only @xmath169% in the time at which they begin forming stars , in spite of one having more than twice the velocity fluctuation amplitude of the other . this leaves the inflow duration as the sole cause of delay of both the global and local collapses . the initial conditions in our simulations are assumed to consist exclusively of atomic gas . however , the final density and temperature conditions are typical of molecular clouds , so molecule formation must occur somewhere along the way in the evolution of the clouds . one important shortcoming of our simulations is that they can not distinguish between atomic and molecular gas , as no chemistry is included . thus , we can not directly tell from the simulations how long does it take for star formation to begin after molecular gas forms . we can , nevertheless , measure the column density of the dense gas in star - forming regions , and compare it to the estimates for self - shielding given by @xcite and @xcite , under solar galactocentric conditions of the background uv field . the former authors find a threshold column desity for self - shielding of @xmath187 , while the latter authors quote values @xmath188 12@xmath189 from @xcite and @xcite . so , we take a reference value of @xmath190 . for comparison , in table [ tab : coldens_sf ] we report the column densities of the dense gas in the first four regions of star formation in run l256@xmath380.17 at the time immediately before they begin forming stars . we see that the column densities fall in the range 0.52 @xmath191 , suggesting that star formation _ locally _ occurs nearly simultaneously with the conversion of the gas from atomic to molecular . moreover , we can compare the time at which we expect the bulk of the cloud to become molecular ( i.e. , the time at which the mean column density in the cloud is reaching @xmath192 ) with the time at which star formation begins in the cloud . a lower limit for the time at which the mean column density in the cloud equals @xmath192 is given by @xmath193 where @xmath194 and @xmath8 have been defined in [ sec : params ] . this estimate is a lower limit because , as mentioned in [ sec : mass ] , @xmath8 is not constant , but actually decreases in time . for @xmath195 , we obtain @xmath196 myr , suggesting that the bulk of the cloud is still expected to be predominantly atomic by the time star formation is beginning . together , these simple estimates suggest that stars form roughly simultaneously with the conversion of gas from atomic to molecular , with the local star forming regions being more advanced in the conversion process than the bulk of the cloud . in turn , this suggests that our model cloud would be observed as a collection of predominantly molecular clumps immersed in a large , predominantly atomic , substrate . this suggestion is consistent with recent observations that substantial amounts of atomic gas coexist with the molecular phase in mcs @xcite , with perhaps even warm gas mixed in @xcite . of course , a more conclusive confirmation of these estimates must await simulations in which the chemistry and radiative transfer are properly taken care of .

simultaneously , the turbulent , nonlinear density fluctuations induce fast , local collapse events . the simulations show that : a ) the clouds are _ not _ in a state of equilibrium . instead , they undergo secular evolution . during the early stages of the evolution , their mass and gravitational energy increase steadily , while the turbulent energy reaches a plateau . c ) longer inflow durations delay the onset of global and local collapse , by maintaining a higher turbulent velocity dispersion in the cloud over longer times . the mc formation mechanism discussed here naturally explains the apparent `` virialized '' state of mcs and the ubiquitous presence of hi halos around them .

we study the formation of giant dense cloud complexes and of stars within them by means of sph numerical simulations of the collision of gas streams ( `` inflows '' ) in the warm neutral medium ( wnm ) at moderately supersonic velocities . the collisions cause compression , cooling and turbulence generation in the gas , forming a cloud that then becomes self - gravitating and begins to collapse globally . simultaneously , the turbulent , nonlinear density fluctuations induce fast , local collapse events . the simulations show that : a ) the clouds are _ not _ in a state of equilibrium . instead , they undergo secular evolution . during the early stages of the evolution , their mass and gravitational energy increase steadily , while the turbulent energy reaches a plateau . b ) when becomes comparable to , global collapse begins , causing a simultaneous increase in and that maintains a near - equipartition condition . c ) longer inflow durations delay the onset of global and local collapse , by maintaining a higher turbulent velocity dispersion in the cloud over longer times . d ) the star formation rate is large from the beginning , without any period of slow and accelerating star formation . e ) the column densities of the local star - forming clumps are very similar to reported values of the column density required for molecule formation , suggesting that locally molecular gas and star formation occur nearly simultaneously . the mc formation mechanism discussed here naturally explains the apparent `` virialized '' state of mcs and the ubiquitous presence of hi halos around them . also , within their assumptions , our simulations support the scenario of rapid star formation _ after _ mcs are formed , although long ( 15 myr ) accumulation periods do occur during which the clouds build up their gravitational energy , and which are expected to be spent in the atomic phase .

astro-ph0608375

c

the results presented in [ sec : results ] provide general support to the scenario outlined in @xcite . the clouds in our simulations are never in a state of virial equilibrium before they convert most of their mass into stars . instead , they are in a continuously evolving state , initially obtaining their mass and turbulence simultaneously as they form out of the compression and cooling of diffuse warm gas ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the gas initially has negligible self - gravity compared to its thermal support , but it quickly becomes super - jeans because of the compression , the cooling , and the mass increase of the dense gas , until its self - gravitating energy eventually becomes comparable with the sum of its thermal and turbulent energies , at which point it begins to undergo global collapse . after this time , gravity becomes the main driver of the large - scale motions in these ( semi- ) decaying simulations , causing a near - equipartition , @xmath3 , which however is indicative of _ collapse _ , not equilibrium . the nonlinear density fluctuations induced by the turbulence collapse faster than the whole cloud , as they have shorter free - fall times , and star formation proceeds vigorously before global collapse is completed . this result is in contrast with the standard notion that _ linear _ density fluctuations can not lead to fragmentation because the fastest growing mode of gravitational instability in a nearly uniform medium is an overall contraction of the whole medium @xcite . thus , a crucial role of the turbulence in the medium is to create _ nonlinear _ density fluctuations that have shorter free - fall times than the entire cloud . these results bring back the scenario of global cloud collapse proposed by @xcite , but with a twist that avoids the criticism of @xcite , namely that mcs could not be in global collapse because the star formation rate would be exceedingly high . our simulations suggest that mcs may be undergoing global gravitational contraction , but the efficiency is reduced because local collapse events , which involve only a fraction of the total cloud mass , proceed faster than the global collapse . once a sufficiently large number of stars have formed , their energy feedback may partially or completely halt the collapse . further reduction may be provided by supercritical magnetic fields @xcite . this scenario is consistent with the recent proposal of @xcite that the orion a cloud may be undergoing gravitational collapse on large scales . the fact that the cloud s mass is not constant is equivalent to the property that the locus of a lagrangian boundary of the cloud defined ( by means of a threshold density ) at any given time does not remain at the cloud s boundary as time progresses , but instead it is later incorporated into the interior of the cloud . this implies that the cloud does not always consist of the same set of fluid parcels , and that in a virial balance analysis of the cloud , there is non - zero flux of the physical variables through eulerian boundaries defined at any given time @xcite . it is important to note that the star formation rate ( given by the slope of the mass in sinks _ versus _ time in fig.[fig : multi_evo ] [ _ top _ ] ) is large from the start , and we observe no long period of slow , accelerating star formation , contrary to the suggestion of @xcite that star formation accelerates in time . problems with this suggestion have been discussed by @xcite , and , within the framework of their assumptions and limitations , our simulations do not confirm it . an important question is whether this result will persist when magnetic fields are included . it is possible that during the early stages of the cloud s evolution , it may behave under magnetically subcritical conditions , giving very low star formation rates ( sfrs ) , and then transit into a supercritical regime , with higher sfrs ( [ sec : accum_dist ] ) . the clouds in our simulations do spend a long latency period between the beginning of the compressive motion that creates the cloud and the time at which they begin forming stars ( @xmath7 1417 myr in the three runs we have considered ) . however , this long period is most probably spent in the atomic phase , since the column densities of the star - forming regions in the simulations are comparable to those required for molecule formation @xcite . more specifically , have found that the timescale for co molecule formation is essentially that required for reaching a dust extinction of @xmath197 . note also that during this time , the formation of h@xmath198 can be fast within density peaks ( cores ) , even if most of the mass of the cloud is still in the low - density regime @xcite . thus , the concept of `` rapid '' star formation refers to the time elapsed between the appearance of a ( co ) molecular cloud and the onset star formation , as well as to the _ rate _ of the star formation process itself . note that the latency period is in fact by definition of the order of the crossing time of the entire large - scale compressive wave , in agreement with observational evidence @xcite . the formation of gmcs by an accumulation process such as the one modeled here has two important additional implications . first , because the process starts with lower - density gas ( the wnm in our simulations ) that is compressed by some external agent , gmcs , which are the `` tip of the iceberg '' of the density distribution , are expected to have in general hi envelopes , which would constitute the corresponding `` body of the iceberg '' . this gas would include transition material traversing the unstable phase between the warm to the cold phases , which would appear to have a nearly isobaric behavior @xcite , in agreement with the conclusion reached by @xcite from observations of hi envelopes of mcs . such envelopes are routinely observed ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * see also the combined hi and co maps of blitz & rosolowsky 2004 ) . weaker compressions than we have modeled may produce mostly thin cnm sheets , with little or no molecular gas , as discussed in @xcite . second , this scenario of molecular cloud formation implies that the mass - to - flux ratio of the cloud is a variable quantity as the cloud evolves . this ratio is equivalent to the ratio of column density to magnetic field strength @xcite , with the critical colum density given by @xmath199~{{\rm ~cm}^{-2}}$ ] . although in principle under ideal mhd conditions the criticality of a magnetic flux tube involves _ all _ of the mass contained within it , in practice it is only the mass in the dense gas phase that matters , because the diffuse gas is not significantly self - gravitating at the size scales of mc complexes . as pointed out by @xcite , the above value of the dense gas column density for magnetic criticality is very close to that required for molecule formation ( eq . ) and for gravitational binding ( eq . ) , and therefore , the cloud is expected to become magnetically supercritical nearly at the same time it is becoming molecular and self - gravitating . our simulations are limited in a number of aspects . first and foremost , as already mentioned in [ sec : sinks ] , one major shortcoming of our simulations is the absence of feedback from the stellar objects onto the cloud . this is certainly an unrealistic feature . second , our clouds are in a regime of turbulence decay after the inflows have subsided . this may or may not be an unrealistic feature , and rather it may represent a fraction of the population of clouds . finally , we have neglected magnetic fields altogether , due to the non - existence of suitable sph algorithms including mhd for the problem of fully developed turbulent flows . all of these limitations tend to exaggerate the sfe in our simulations , as the turbulence within them is not replenished by either a continuing flow or by stellar energy feedback . it is possible that a continued inflow ( and therefore a sustained turbulence level ) could prevent global collapse altogether , with only local collapse events happening randomly , although certainly the inflows can not last indefinitely . thus , it would appear that global collapse is inescapable . however , once star formation begins , the stellar energy feedback is likely to either be able to halt the global collapse and disperse the cloud @xcite or else maintain it in rough equilibrium ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? thus , two important questions to address in future papers are , one , what is the evolution like when star formation begins before the inflows subside . it is likely that this case will have much smaller sfes . two , whether the stellar energy feedback tends to disperse the clouds , or else to maintain them in rough equilibrium . observationally , star clusters older than 510 myr tend to be already devoid of gas @xcite , suggesting that the effect is more disruptive than equilibrating . finally , our simulations have neglected the magnetic field . as discussed in [ sec : quali ] , this is not a crucial omission if gmcs are in general magnetically supercritical , since the supercritical case is qualitatively equivalent to the nonmagnetic case , with the only difference being that it behaves as if it were less massive than a non - magnetic cloud of the same mass @xcite . thus , we consider that our models are still representative of the large - scale evolution up to the early times of star formation in supercritical clouds . the main difference is expected to be that magnetized , supercritical clouds should have lower sfes than nonmagnetic ones @xcite . on the other hand , the evolution of subcritical clouds will certainly differ from the models presented here , because they will have no global tendency to collapse . at any rate , it is necessary to perform simulations of the full process in the presence of magnetic fields . this will presumably require the usage of amr techniques incorporating the analogue of sink particles and stellar feedback , and will be pursued in future papers .

the collisions cause compression , cooling and turbulence generation in the gas , forming a cloud that then becomes self - gravitating and begins to collapse globally . b ) when becomes comparable to , global collapse begins , causing a simultaneous increase in and that maintains a near - equipartition condition . d ) the star formation rate is large from the beginning , without any period of slow and accelerating star formation . e ) the column densities of the local star - forming clumps are very similar to reported values of the column density required for molecule formation , suggesting that locally molecular gas and star formation occur nearly simultaneously .

we study the formation of giant dense cloud complexes and of stars within them by means of sph numerical simulations of the collision of gas streams ( `` inflows '' ) in the warm neutral medium ( wnm ) at moderately supersonic velocities . the collisions cause compression , cooling and turbulence generation in the gas , forming a cloud that then becomes self - gravitating and begins to collapse globally . simultaneously , the turbulent , nonlinear density fluctuations induce fast , local collapse events . the simulations show that : a ) the clouds are _ not _ in a state of equilibrium . instead , they undergo secular evolution . during the early stages of the evolution , their mass and gravitational energy increase steadily , while the turbulent energy reaches a plateau . b ) when becomes comparable to , global collapse begins , causing a simultaneous increase in and that maintains a near - equipartition condition . c ) longer inflow durations delay the onset of global and local collapse , by maintaining a higher turbulent velocity dispersion in the cloud over longer times . d ) the star formation rate is large from the beginning , without any period of slow and accelerating star formation . e ) the column densities of the local star - forming clumps are very similar to reported values of the column density required for molecule formation , suggesting that locally molecular gas and star formation occur nearly simultaneously . the mc formation mechanism discussed here naturally explains the apparent `` virialized '' state of mcs and the ubiquitous presence of hi halos around them . also , within their assumptions , our simulations support the scenario of rapid star formation _ after _ mcs are formed , although long ( 15 myr ) accumulation periods do occur during which the clouds build up their gravitational energy , and which are expected to be spent in the atomic phase .

astro-ph0608375

i

in this paper we have presented a suite of numerical simulations designed to investigate jointly the formation of molecular clouds ( mcs ) and of stars within them . the simulations use an sph scheme including self - gravity , sink particles and cooling leading to thermal bistability . magnetic fields are neglected . the simulations describe the collision of oppositely - directed gas streams ( `` inflows '' ) in the warm neutral medium ( wnm ) at moderately supersonic velocities ( each with a velocity of @xmath200 , or a mach number of 1.22 in the unperturbed wnm ) . three simulations were considered , varying the length of the inflow and the amplitude of the initial velocity fluctuations in the gas . the collisions trigger a transition to the cold phase in the gas , and simultaneously generate turbulence in the resulting `` cloud '' , defined as the gas at densities @xmath93 . the inflows secularly weaken in time , and so does the turbulence level in the cloud , implying that the turbulence in the clouds gradually transits from being continuously driven to being in a decaying regime . the cooling and the mass gain of the dense gas eventually cause the cloud to contain a large number of jeans masses at the mean conditions . moreover , because the cloud is supersonically turbulent , locally the density can be much larger , with a correspondingly lower jeans mass and shorter free - fall times than those of the whole cloud . thus , by the time the inflows have almost subsided , the cloud engages in global gravitational collapse , but shortly thereafter it begins to produce numerous local collapse events that occur on much smaller timescales because of the larger densities , so that by the time the global collapse of the cloud is completed , it has converted most of its mass to collapsed objects ( sink particles ) . the sinks in general represent star clusters , due to the limited mass resolution and lack of modeling of opacity - limited fragmentation ( e.g. * ? ? ? our simulations can only be considered reliable up to the time when the mass in collapsed objects ( sinks ) implies a high enough number of massive stars that they would disrupt the cloud . nevertheless , the evolution up to that point shows a number of relevant results : \1 . the clouds are never in virial equilibrium during this period . instead , they continually evolve , increasing their mass and self - gravitating energy , until the latter becomes comparable or larger than the thermal and kinetic energies . some @xmath201 myr after global contraction began , star formation begins . \2 . in spite of not being in equilibrium , the near - equipartition condition @xmath3 is approximately satisfied as soon as @xmath2 becomes comparable to @xmath1 , because of the gravitational contraction of the cloud , with both quantities increasing simultaneously . this occurs long before the onset of star formation . this fact can explain the observed state of apparent virialization of gmcs . the near equipartition is a signature of global gravitational collapse , not equilibrium , and suggests a return to goldreich & kwan s ( 1974 ) scenario of global gravitational contraction in mcs . however , the criticism by @xcite , namely that an excessively large star formation should result through this process , is avoided in part because the nonlinear turbulent density fluctuations collapse earlier than the whole cloud , involving only a fraction of the total mass , and in part because as soon as the stars form they probably contribute to dispersing the cloud , or at least halting its global collapse . further reduction of the sfe may occur in the presence of supercritical magnetic fields . \5 . the star formation rate , measured by the slope of the mass in stars _ versus _ time , is large from the beginning . within the framework , assumptions and limitations of our simulations , no long period of slow , accelerating star formation is observed . longer inflow durations maintain larger turbulent velocity dispersions in the clouds and delay the onset of both global and local collapse . instead , larger amplitudes of the initial velocity fluctuations have little effect in delaying the collapse . the latter effect can be attributed to the fact that the turbulence is already dissipating in the clouds by the time global collapse begins . \7 . a long period ( @xmath20217 myr ) of `` dormancy '' does occur between the time when the cloud begins to form and the time when star formation begins . nevertheless , it is likely that most of this time is spent with the gas being in atomic form , since the column density of star forming regions in our simulations are comparable to values required for molecular gas formation , as reported in the literature . thus , our simulations support the notion that star formation occurs almost simultaneously with the formation of molecular gas , under local ism conditions . we conclude that our simulations support the scenario of rapid star formation after molecular gas has formed , involving accumulations of gas from distances of a few hundred parsecs @xcite , while simultaneously requiring timescales of the order of the crossing time across the largest scales involved @xcite , and in a systematically out - of - equilibrium fashion @xcite . however , the evidence will have to be made more compelling as additional physical processes , such as longer - duration inflows , stellar feedback , magnetic fields and chemistry are included . we thankfully acknowledge useful comments from lee hartmann and chris mckee , and the help of luis ballesteros - paredes with postprocessing of the computer animations . this work has received financial support from crya - unam ; from conacyt grants 36571-e and 47366-f to e. v .- s . , and unam - papiit grant 110606 ; and from the emmy noether program of the german science foundation ( dfg ) under grant kl1358/1 to r.s.k . and a.k.j . the simulations were performed in the cluster at crya - unam acquired with grant 36571-e . this work has made extensive use of nasa s ads and lanl s astro - ph abstract services . ballesteros - paredes , j. , klessen , r. s. , mac low , m .- m . , vzquez - semadeni , e. 2006 , in protostars and planets v , eds . b. reipurth , d. jewitt , k. keil ( tucson : univ . of arizona press ) , in press ( astro - ph/0603357 ) blitz , l. , fukui , y. , kawamura , a. , leroy , a. , mizuno , n. , & rosolowsky , e. , 2006 , in protostars and planets v , eds . b. reipurth , d. jewitt , k. keil ( tucson : univ . of arizona press ) , in press ( astro - ph/0602600 ) bonnell , i. 2005 , in massive star birth : a crossroads of astrophysics , iau symposium 227 , eds . r. cesaroni , r. , m. felli , e. churchwell . and m. walmsley , ( cambridge : cambridge university press , 2005 . ) , p.266 crapsi , a. , devries , c. h. , huard , t. l. , lee , j .- e . , myers , p. c. , ridge , n. a. , bourke , t. l. , evans , n. j. , ii , jrgensen , j. k. , kauffmann , j. , lee , c. w. , shirley , y. l. , young , c. h. 2005 , a&a , 439 , 1023 shadmehri , m. , vzquez - semadeni , e. & ballesteros - paredes , j. 2002 , in seeing through the dust : the detection of hi and the exploration of the ism in galaxies , ed . a. r. taylor , t. l. landecker , and a. g. willis . ( san francisco : astronomical society of the pacific ) , p.190 ccccccccccc l128@xmath380.24 & 128 & 48 & 9.20 & 1.22 & 0.24 & @xmath203 & @xmath204 & 0.04 + l128@xmath380.66 & 128 & 48 & 9.20 & 1.22 & 0.66 & @xmath203 & @xmath204 & 0.04 + l256@xmath380.17 & 256 & 112 & 9.20 & 1.22 & 0.17 & @xmath205 & @xmath206 & 0.16 +

we study the formation of giant dense cloud complexes and of stars within them by means of sph numerical simulations of the collision of gas streams ( `` inflows '' ) in the warm neutral medium ( wnm ) at moderately supersonic velocities . also , within their assumptions , our simulations support the scenario of rapid star formation _ after _ mcs are formed , although long ( 15 myr ) accumulation periods do occur during which the clouds build up their gravitational energy , and which are expected to be spent in the atomic phase .

we study the formation of giant dense cloud complexes and of stars within them by means of sph numerical simulations of the collision of gas streams ( `` inflows '' ) in the warm neutral medium ( wnm ) at moderately supersonic velocities . the collisions cause compression , cooling and turbulence generation in the gas , forming a cloud that then becomes self - gravitating and begins to collapse globally . simultaneously , the turbulent , nonlinear density fluctuations induce fast , local collapse events . the simulations show that : a ) the clouds are _ not _ in a state of equilibrium . instead , they undergo secular evolution . during the early stages of the evolution , their mass and gravitational energy increase steadily , while the turbulent energy reaches a plateau . b ) when becomes comparable to , global collapse begins , causing a simultaneous increase in and that maintains a near - equipartition condition . c ) longer inflow durations delay the onset of global and local collapse , by maintaining a higher turbulent velocity dispersion in the cloud over longer times . d ) the star formation rate is large from the beginning , without any period of slow and accelerating star formation . e ) the column densities of the local star - forming clumps are very similar to reported values of the column density required for molecule formation , suggesting that locally molecular gas and star formation occur nearly simultaneously . the mc formation mechanism discussed here naturally explains the apparent `` virialized '' state of mcs and the ubiquitous presence of hi halos around them . also , within their assumptions , our simulations support the scenario of rapid star formation _ after _ mcs are formed , although long ( 15 myr ) accumulation periods do occur during which the clouds build up their gravitational energy , and which are expected to be spent in the atomic phase .

1005.3240

i

we have discussed the general phenomenology of neutrinoless double beta decay ( @xmath0 decay ) in different types of seesaw models . in particular , we have focused on the contributions of the extra degrees of freedom in different mass regimes without assuming preference to a particular mass scale . in order to do this , we computed the nuclear matrix element ( nme ) involved in the decay amplitudes as function of the mass of the mediating field , detailing all the assumptions performed in each step and estimating the final error due to the approximations taken to be at most 30 % for light neutrinos and around 40 % for heavy neutrinos . the results of this computation are publicly available at ref . @xcite . in particular , the behaviour of the nme is found to be that which can be expected from the propagator @xmath267 , where @xmath268 mev@xmath269 is the typical momentum transfer between the nucleons . thus , the nmes are essentially constant for @xmath270 mev ( light regime ) and decrease as @xmath271 for @xmath272 mev ( heavy regime ) . the transition region around 100 mev is smooth and no significantly new phenomenology takes place at this regime . in our discussion we have seen that , for the type - i seesaw , a number of possibilities exist . in the case where all the masses of the extra fermion singlets are in the heavy regime , the contribution of these states to @xmath0 decay is negligible and difficult to constrain directly . however , the contribution from the light left handed neutrinos can be rewritten in terms of the masses and mixings of the heavy states , which results in quite stringent bounds on their mixings . on the contrary , if the extra fermion singlet states are instead in the light regime , a gim - like cancellation with the left handed neutrino contributions occurs . in this situation , neutrinos are majorana particles , but the @xmath0 decay rate becomes unobservable , being suppressed by at least six orders of magnitude if the mass of the extra states is below 1 mev . thus , considering the extra states alone and neglecting the sm neutrino contribution will result in bounds on their mixings which are generally too strong . such bounds only apply when considering extra contributions to neutrino masses beyond the light extra states in order to prevent the cancellation from taking place . dirac neutrinos , where the majorana mass term of the extra fermion states is zero , are a special case of the situation with only light extra states . in this scenario , the right and left handed states are exactly degenerate and the cancellation is exact . if there are extra states in both the light and heavy regimes , then the main contribution to the @xmath0 transition could come from the light extra states , although some fine - tuning is necessary . as such , this could be a way to reconcile a large @xmath0 decay rate ( _ e.g. _ , the heidelberg - moscow claim ) with more stringent cosmological bounds with a mild cancellation of about 50 % . as for the other types of seesaws , current bounds from accelerator experiments place the extra degrees of freedom in the heavy regime . this effectively reduces the situation to that which appears for the type - i seesaw with only heavy extra states . however , in mixed seesaw models , the situation can instead resemble that of the type - i with states in both regimes and thus be used to reconcile large @xmath0 decay rates with cosmological bounds . in conclusion , the contribution to @xmath0 decay from the light active neutrinos can be forecasted by combining present and future neutrino oscillation data on the neutrino mixing and mass hierarchy with probes of the absolute neutrino mass scale such as cosmology . these predictions can be compared to future @xmath0 decay searches so as to gain information on the origin and nature of the neutrino masses . in this comparison , we can distinguish the following scenarios : * * the @xmath1 process is observed to be in agreement with the forecasted rates . * this indicates that the light active neutrinos dominate the @xmath0 decay rate . since new degrees of freedom are in any event required to give the light neutrinos majorana masses , this implies that there is necessarily new physics above the nuclear scale , so that its contribution is suppressed . * * the @xmath1 process is observed to be smaller than the forecasted rates . * this means that there is a partial cancellation between the active and extra neutrino contributions . sterile neutrinos around the nuclear scale are then necessary . a higher mass would imply too big a suppression through their nme to show any sizable cancellation , while too small masses would make the gim - like cancellation exact . * * the @xmath1 process is observed to be larger than the forecasted rates . * in this situation the light active neutrinos can not dominate the @xmath0 decay rate . extra sterile neutrinos , lighter or around the nuclear scale , could have a significant contribution and reconcile the observations . however , the gim - like cancellation between both contributions has to be avoided . this implies either a cancellation between extra neutrinos both above and below the nuclear scale ( see sec . [ sec : heavylight ] ) or between the extra neutrinos and a type - ii or iii seesaw contribution ( see sec . [ sec : mix ] ) . this is the case that would correspond to a confirmation of the heidelberg - moscow claim . * * the @xmath1 process is not observed but was forecasted . * while this could imply that neutrinos are dirac and not majorana particles , it can also be the case that neutrinos are majorana but extra sterile neutrinos below the nuclear scale are present . thus , the gim - like cancellation takes place and the @xmath0 decay rate becomes unobservable . * * the @xmath1 process is not observed and was not forecasted . * this is the most pessimistic scenario since it is impossible to draw any conclusion on the nature and origin of neutrino masses . we are specially indebted to andrea donini for carefully reading through this paper and providing valuable comments . we also acknowledge very interesting and fruitful discussions with carla biggio , belen gavela , pilar hernandez , alessandro mirizzi , ann nelson , alfredo poves and achim schwenk . this work was supported by the european union through the european commission marie curie actions framework programme 7 intra - european fellowship : neutrino evolution [ m.b . ] and the european commission framework programme 07 design study euro@xmath273 , project 212372 [ j.l.p ] ; the spanish ministry of education and science through the cup consolider - ingenio 2010 , project csd2008 - 0037 [ j.l.p . ] and grants fpa2009 - 09017 [ j.l.p ] and fpa2009 - 13377 [ j.m . ] ; the dfg through cluster of excellence `` origin and structure of the universe '' [ e.f.m . ] and grant sfb 634 [ j.m . ] ; the helmholtz association through the helmholtz alliance program , contract ha216/emmi `` extremes of density and temperature : cosmic matter in the laboratory '' [ j.m . ] ; and the comunidad autnoma de madrid through project hephacos - cm ( s2009esp-1473 ) [ j.l.p . , j.m .

we study the general phenomenology of neutrinoless double beta decay in seesaw models . in particular , we focus on the dependence of the neutrinoless double beta decay rate on the mass of the extra states introduced to account for the majorana masses of light neutrinos . for this purpose , we compute the nuclear matrix elements as functions of the mass of the mediating fermions and estimate the associated uncertainties . in particular , the decay rate is reduced by at least six orders of magnitude for masses of the extra states below 1 mev in absence of extra contributions .

we study the general phenomenology of neutrinoless double beta decay in seesaw models . in particular , we focus on the dependence of the neutrinoless double beta decay rate on the mass of the extra states introduced to account for the majorana masses of light neutrinos . for this purpose , we compute the nuclear matrix elements as functions of the mass of the mediating fermions and estimate the associated uncertainties . we then discuss what can be inferred on the seesaw model parameters in the different mass regimes and clarify how the contribution of the light neutrinos should always be taken into account when deriving bounds on the extra parameters . conversely , the extra states can also have a significant impact , canceling the standard model neutrino contribution for masses lighter than the nuclear scale and leading to unobservable neutrinoless double beta decay amplitudes even if neutrinos are majorana particles . in particular , the decay rate is reduced by at least six orders of magnitude for masses of the extra states below 1 mev in absence of extra contributions . we also discuss how seesaw models could reconcile large rates of neutrinoless double beta decay with more stringent cosmological bounds on neutrino masses .

astro-ph0112531

i

gravitational lensing has proven to be an exceptional tool for studying a diverse set of astrophysical phenomena . its utility is due , at least in part , to the fact it operates in a number of qualitatively different regimes . the term strong lensing , or macrolensing , is usually applied when a distant source ( typically cosmological ) is lensed into multiple , resolved images by an intervening mass , such as a foreground cluster or a galaxy . weak lensing is used to refer to the case when multiple images are not created , and the gravitational field of the intervening matter serves only to slightly distort the image of the source . for most applications of both strong and weak lensing , the source , lens , and observer can be considered static . the term microlensing is often used to describe the case when multiple images are created , but are not resolved . typically the separation of the images created by a gravitational microlens are of order the einstein ring radius , @xmath0 here @xmath1 is the mass of the lens , @xmath2 is defined by , @xmath3 , and @xmath4 , @xmath5 , and @xmath6 are the distances between the observer - source , observer - lens , and lens - source , respectively . in cosmological contexts , angular diameter distances should be used . when @xmath7 is less than the resolution , individual images in general can not be distinguished . due to the small scale of @xmath7 , it is typically not a good approximation to assume that the source , lens , and observer are static . therefore the lensing properties can be expected to change on timescales of order the einstein ring crossing time , @xmath8 where @xmath9 is the transverse speed of the lens relative to the observer - source line - of - sight . the standard observables in gravitational microlensing are therefore the time rate of change of the total magnification and center - of - light ( centroid ) of all the microimages . there are two different regimes where microlensing has been discussed : quasar microlensing @xcite and microlensing in the local group @xcite . in the local group , gravitational microlensing occurs whenever a massive , compact object passes close to our line of sight to a more distant star . microlensing was originally suggested as a method to detect baryonic dark matter in the halo of our galaxy @xcite , but has been developed and applied as an important tool in studying a number of astrophysical topics , including the stellar mass function @xcite , extrasolar planets @xcite , stellar atmospheres @xcite , and stellar multiplicity @xcite . the only microlensing effect currently observable is the magnification of the background source as function of time . this is because , for typical distances in the local group , the angular einstein ring radius is @xmath10 and therefore too small to be resolved with current instruments . the timescale for a microlensing event is @xmath11 . in general , it is much easier to determine the center - of - light of an image than it is to resolve it . thus future interferometers , such as the _ space interferometry mission ( sim ) _ , although still not able to resolve separations of @xmath12 , should be able to measure the centroid of all the images to much better than this , perhaps even down to @xmath13 in the case of _ sim_. such accuracy is sufficient to easily detect the motion of the centroid of the images created in a microlensing event , which is also of order @xmath7 . this regime is typically referred to as astrometric microlensing , as opposed to photometric microlensing when only the total magnification is observable . astrometric microlensing has a number of important applications . by combining ground - based photometry of microlensing events with photometry and astrometry from an astrometric satellite on an earth - like orbit , the masses of microlenses can routinely be measured @xcite , allowing for the determination of the compact object mass function in the bulge , including stellar remnants @xcite . astrometric information alone allows for the precise ( few % ) measurement of the masses of nearby stars @xcite . finally , for a subset of events , it will be possible to obtain precision measurements of angular diameters of stars in the galactic bulge using astrometric information @xcite . binary microlenses have proven to be enormously useful in photometric microlensing studies . this is primarily because binary lenses exhibit caustics : closed curves on which the mapping from the lens plane to light source plane becomes critical , and the point - source magnification becomes formally infinite . regions near caustics exhibit large , rapidly changing ( with respect to source position ) magnification , and are therefore useful not only for providing a large source flux , but also high angular resolution . however , binary lenses have also proven to be difficult to study both theoretically and observationally . this is partially because the lens equation , which describes the mapping from the lens plane to the light source plane , is equivalent to a fifth - order complex polynomial in the source position @xcite , and therefore is not analytically solvable in general . furthermore , care must be taken when considering finite source effects near caustics due to the divergent magnification . however , considerable progress can be made when one realizes that the smooth arcs ( away from cusps ) of caustics that arise in nearly equal - mass binary lenses are well approximated as simple linear fold catastrophes , which have generic , simple , and most importantly , _ analytic _ behavior . thus the caustics of binary lenses can be analyzed analytically or semi - analytically without reference to the global ( and non - analytic ) topology of the general binary lens . in particular , a simple equation for the magnification of a source near a fold exists @xcite , which has been used in a number of important applications including binary - lens fitting @xcite , stellar atmospheres @xcite , and caustic - crossing predictions @xcite . in contrast to the astrometric behavior of single lenses , which is analytic and has been quite well studied @xcite , there have been only a few preliminary studies of the astrometric properties of binary gravitational lenses @xcite . it is known that astrometric binary - lens curves exhibit complex behavior , including instantaneous @xmath14 jumps in the image centroid trajectory that occur when a point source crosses a binary - lens caustic and two highly - magnified images appear in a position unrelated to the position of the centroid of the other three binary - lens images . the generic behavior of these centroid jumps , or how they are altered by finite source effects , is not understood . as is the case for photometric microlensing , the astrometric behavior of binary lenses will likely prove quite useful for several applications . the usefulness of binary lenses is primarily related to the complex image centroid trajectories and the large centroid jumps . although , in general , these properties do not allow one to measure any additional parameters over the single lens case ; they do allow one to measure these parameters much more easily . in particular , @xcite have shown that lens mass measurements can be made to a given accuracy with 1 - 3 orders of magnitude fewer photons with caustic - crossing binary - lens events than with single lens events , thus greatly reducing the resources required to achieve one of the primary proposed science goals of astrometric microlensing . caustic crossing binary - lens events are also enormously useful for measuring the angular radii of microlensing source stars in the bulge , for two reasons . first , the expected ratio of binary - to - single lens events for which the source star is resolved is a factor of @xmath15 for giant sources and @xmath16 for main sequence sources . furthermore , the large and complex centroid shifts expected for caustic - crossing binary - lens events makes the requisite astrometric measurements easier . @xcite have shown that , by combining accurate ground - based photometry with a handful of precise astrometric measurements , caustic - crossing binary - lens events should yield @xmath17 stellar radius measurements with reasonable expenditure of resources . thus , given the importance of caustic crossing binary - lens events , an analytic study of the generic behavior of astrometric microlensing near folds would prove quite useful . in quasar microlensing , the separate macroimages of a quasar that is multiply - imaged by a intervening galaxy or cluster also feel the combined , non - linear effect of individual point masses ( i.e. stars ) in the macrolensing object that are near the macroimage position . the individual macroimages are in fact composed of many , unresolved microimages with separations of order the einstein radius of a @xmath18 object at cosmological distances , @xmath19 . the typical timescale for the source to cross an angle of @xmath7 is @xmath20 ; however microlensing light curves should show structure on much smaller timescales due to the combined effects of many individual microlenses . since it was first discussed by @xcite , cosmological microlensing has been studied theoretically by numerous authors ( see @xcite and references therein ) , and detected in at least two systems ( q2237 + 0305 , @xcite , b1600 + 434 , @xcite ) . observations have been used to place constraints on , e.g. , the size of the emitting region of quasars @xcite and the mass function of microlenses @xcite . quasar microlensing differs markedly from microlensing in the local group in that the surface mass density in units of the critical density for lensing ( the `` optical depth '' ) is of order unity , rather than @xmath21 for the local group . in the high optical depth regime the lensing effects of the individual microlenses add nonlinearly , resulting in a complex caustic network . due to this nonlinear behavior and the large number of lenses typically involved , calculation of the observable properties of such a lensing system is difficult and time consuming . although in the high optical depth regime the caustics often exhibit considerably more complicated global behavior than the caustics of binary lenses in the local group , it is still the case that the smooth arcs ( away from cusps ) of the caustics are locally well - approximated by generic fold catastrophes . this fact , combined with a simple formula for the magnification near folds , has been exploited by numerous authors to quickly and efficiently calculate various observable properties of quasar microlensing @xcite . the observable effects of quasar microlensing have been limited to the relative magnifications of the various macroimages as a function of time . as with local group microlensing , astrometric effects should also be present . the centroid of the individual macroimages should vary as a function of time , particularly when new images are created or destroyed when the source crosses a caustic . this effect has been studied by @xcite and @xcite . in particular , @xcite predict that magnitude of the centroid shift for the q2237 + 0305 system ( apparent magnitude @xmath22 ) can be as large as @xmath23 , and thus potentially observable with _ sim_. they also note that the magnitude of the centroid shift is often correlated with the magnitude of the change in total magnification . the analytic results presented in this paper may prove useful for this application . here we study the generic , local behavior of microlensing near fold catastrophes . in 2 we present an analytic study of the photometric and astrometric behavior near folds . we begin with the equations that describe the mapping near a fold caustic in 2.1 , and use these to derive the behavior of a point source near a fold . we extend this analysis to finite sources in 2.2 , and limb - darkened sources in 2.3 . in 2.4 we show how and when our generic parabolic fold form reduces to the more familiar linear caustic . in 2.5 we use our analytic results to derive some generic results about the astrometric behavior near folds . we verify the applicability of our results in 3 by numerically calculating the photometric and astrometric behavior of one well - observed binary - lens event . we find excellent agreement with our analytic formulae . finally , we summarize and conclude in 4 . our goal is to provide a thorough , comprehensive study of gravitational microlensing near fold caustics . although our study is interesting in its own right , the primary utility of the results presented here is their potential application to the topics mentioned in the previous paragraphs . a prescription for how specifically our results can be applied to these topics is beyond the scope of this paper , but we will make general comments along these lines over the course of the paper , and more specific comments in 2.5 . we are currently preparing a complementary , similarly detailed study of microlensing near cusps . combined with this study , we will have a reasonably thorough and complete understanding of the local behavior of microlensing observables near all stable gravitational lensing singularities . we note that some of the results derived here , particularly the results on the photometric behavior near folds , have been presented elsewhere ( see , e.g. @xcite , @xcite , and @xcite ) . we include those results here for the sake of completeness .

we show how this form reduces to the more familiar linear caustic , which lenses a nearby source into two images which have equal magnification , opposite parity , and are equidistant from the critical curve . in this case # 1equation ( [ # 1 ] ) # 1eq . [ # 1 ]

we study the local behavior of gravitational lensing near fold catastrophes . using a generic form for the lensing map near a fold , we determine the observable properties of the lensed images , focusing on the case when the individual images are unresolved , i.e. , microlensing . allowing for images not associated with the fold , we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic . we show how this form reduces to the more familiar linear caustic , which lenses a nearby source into two images which have equal magnification , opposite parity , and are equidistant from the critical curve . in this case , the simplicity and high degree of symmetry allows for the derivation of semi - analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles . we use our results to derive some basic properties of astrometric microlensing near folds , in particular we predict for finite sources with uniform and limb darkening profiles , the detailed shape of the astrometric curve as the source crosses a fold . we find that the astrometric effects of limb darkening will be difficult to detect with the currently planned accuracy of the _ space interferometry mission ( sim ) _ for galactic bulge sources ; however , this also implies that astrometric measurements of other parameters , such as the size of the source , should not be compromised by an unknown amount of limb darkening . we verify our results by numerically calculating the expected astrometric shift for the photometrically well - covered galactic binary lensing event ogle-1999-bul-23 , finding excellent agreement with our analytic expressions . our results can be applied to any lensing system with fold caustics , including galactic binary lenses and quasar microlensing . # 1equation ( [ # 1 ] ) # 1eq . [ # 1 ]

astro-ph0112531

i

we have presented a detailed study of gravitational lensing near fold catastrophes , concentrating on the regime where the individual images are unresolved , i.e. microlensing . by taylor expanding the scalar potential @xmath29 in the neighborhood of a fold up to third order in the image position , one can obtain a generic form for the lensing map near a fold . beginning with this mapping , we derive the local lensing properties of a source in the vicinity of the fold caustic . approximating the critical curve by its tangent line at the origin , we find that the caustic is locally a parabola . on one side of the parabola , the fold lenses a nearby source into two images ; on the other side of the parabola , there are no images . we derive the image positions and magnifications as a function of the position of the source . we find that the magnifications of the two images are equal , and recover the well - known result that the magnification is inversely proportional to the square root of the distance to the caustic . we show how this holds for parabolic caustics ( as well as linear caustics ) , provided that the ` vertical ' distance from the caustic is used . assuming a rectilinear source trajectory , and allowing for the existence of slowly- and smoothly - varying images not associated with the fold caustic , we derive analytic expressions for the total magnification and image centroid ( center - of - light ) as a function of time . we then consider how the photometric and astrometric behavior is altered in the presence of a finite source size . we derive semi - analytic expressions for the magnification and centroid as a function of time for both a uniform source , and limb - darkened source . along the way we derived expressions that can be used to evaluate the photometric and astrometric behavior near a fold for a source with arbitrary surface brightness profile . we then show how and under what conditions the generic parabolic fold reduces to the more familiar linear fold . we derive simplified expressions for the individual and total image positions and magnifications near a linear fold . we used some of our analytic results to derive a few generic properties of microlensing near folds . in particular , we derive and evaluate expressions for the magnitude of the centroid jump that occurs when a finite source crosses a fold relative to the point source jump , and the magnitude of the effect of limb darkening on both the photometric and astrometric behavior . notably , we predict , for galactic bulge lensing events , the shape of the centroid due to finite sources with uniform and limb darkening surface brightness profiles . we also find for galactic bulge lensing that the effect of limb darkening on the image centroid near a fold is quite similar to the uniform source case , making the limb darkening effect difficult to detect by the currently planned accuracy for the instrumentation of _ we discussed how our formulae can be used to fit both photometric and astrometric data sets near fold caustic crossings and thus used to derive such properties as the angular size of the source and the microlensing parallax . finally , we numerically calculate expected astrometric behavior of the photometrically well - observed galactic bulge binary lensing event @xcite , finding excellent agreement with our analytic predictions . caustics are ubiquitous in gravitational lenses , and the most common type of caustic is the fold . caustics play an especially important role in microlensing , as the rapid time variability of the total image magnification allows the possibility of detailed studies of the source and lens . in the future , we can expect that time - series photometric measurements will be supplemented by time - series _ astrometric _ measurements of the center - of - light of microlens systems . this paper presents the most thorough and comprehensive study of the photometric and astrometric behavior of gravitational microlensing near fold caustics to date . the results should prove useful to those studying microlens systems with caustics : the analytic expressions derived here can be used to fit fold caustic crossings observed both photometrically and astrometrically , gain some insight into more complicated numerical studies , and establish predictions for the feasibility of future observations . we would like to thank the referee , eric agol , for several helpful suggestions that led to a much improved manuscript . b.s.g . was supported in part by nasa through a hubble fellowship grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas5 - 26555 . a.o.p . was supported in part by an alfred p. sloan research fellowship and nsf career grant dms-98 - 96274 .

we study the local behavior of gravitational lensing near fold catastrophes . using a generic form for the lensing map near a fold , we determine the observable properties of the lensed images , focusing on the case when the individual images are unresolved , i.e. , microlensing . allowing for images not associated with the fold , we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic . , the simplicity and high degree of symmetry allows for the derivation of semi - analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles . we use our results to derive some basic properties of astrometric microlensing near folds , in particular we predict for finite sources with uniform and limb darkening profiles , the detailed shape of the astrometric curve as the source crosses a fold . we verify our results by numerically calculating the expected astrometric shift for the photometrically well - covered galactic binary lensing event ogle-1999-bul-23 , finding excellent agreement with our analytic expressions . our results can be applied to any lensing system with fold caustics , including galactic binary lenses and quasar microlensing .

we study the local behavior of gravitational lensing near fold catastrophes . using a generic form for the lensing map near a fold , we determine the observable properties of the lensed images , focusing on the case when the individual images are unresolved , i.e. , microlensing . allowing for images not associated with the fold , we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic . we show how this form reduces to the more familiar linear caustic , which lenses a nearby source into two images which have equal magnification , opposite parity , and are equidistant from the critical curve . in this case , the simplicity and high degree of symmetry allows for the derivation of semi - analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles . we use our results to derive some basic properties of astrometric microlensing near folds , in particular we predict for finite sources with uniform and limb darkening profiles , the detailed shape of the astrometric curve as the source crosses a fold . we find that the astrometric effects of limb darkening will be difficult to detect with the currently planned accuracy of the _ space interferometry mission ( sim ) _ for galactic bulge sources ; however , this also implies that astrometric measurements of other parameters , such as the size of the source , should not be compromised by an unknown amount of limb darkening . we verify our results by numerically calculating the expected astrometric shift for the photometrically well - covered galactic binary lensing event ogle-1999-bul-23 , finding excellent agreement with our analytic expressions . our results can be applied to any lensing system with fold caustics , including galactic binary lenses and quasar microlensing . # 1equation ( [ # 1 ] ) # 1eq . [ # 1 ]

cond-mat0211024

i

in recent years , there has been great interest in the shot noise in mesoscopic systems @xcite , because it contains additional information about correlations , which is not contained , e.g. , in the linear response conductance . the shot noise is characterized by the fano factor @xmath0 , the dimensionless ratio of the zero - frequency noise power @xmath1 to the average current @xmath2 . while it assumes the poissonian value @xmath3 in the absence of correlations , it becomes suppressed or enhanced when correlations set in as e.g. imposed by the pauli principle or due to interaction effects . in the present paper we study the shot noise of the cotunneling @xcite current . we consider the transport through a quantum - dot system ( qds ) in the coulomb blockade ( cb ) regime , in which the quantization of charge on the qds leads to a suppression of the sequential tunneling current except under certain resonant conditions . we consider the transport away from these resonances and study the next - order contribution to the current . this suppression can be interpreted @xcite as being a result of the natural correlations imposed by charge conservation . ] ( see fig . [ energies ] ) . we find that in the weak cotunneling regime , i.e. when the cotunneling rate @xmath4 is small compared to the intrinsic relaxation rate @xmath5 of the qds to its equilibrium state due to the coupling to the environment , @xmath6 , the zero - frequency noise takes on its poissonian value , as first obtained for a special case in @xcite . this result is generalized here , and we find a universal relation between noise and current for the qds in the first nonvanishing order in the tunneling perturbation . because of the universal character of this result eq . ( [ db - fdt ] ) we call it the nonequilibrium fluctuation - dissipation theorem ( fdt ) @xcite in analogy with linear response theory . one might expect however that the cotunneling , being a two - particle process , may lead to strong correlations in the shot noise and to the deviation of the fano factor from its poissonian value @xmath3 . we show in sec . [ super - poissonian ] that this is indeed the case for the regime of strong cotunneling , @xmath6 . specifically , for a two - level qds we predict giant ( divergent ) super - poissonian noise @xcite ( see sec . [ degenerate ] ) : the qds goes into an unstable mode where it switches between states 1 and 2 with ( generally ) different currents . in sec . [ dd - system ] we consider the transport through a double - dot ( dd ) system as an example to illustrate this effect ( see eq . ( [ dd - noise ] ) and fig . [ double - d ] ) . the fano factor turns out to be a periodic function of the magnetic flux through the dd leading to an aharonov - bohm effect in the noise @xcite . in the case of weak cotunneling we concentrate on the average current through the dd and find that it shows aharonov - bohm oscillations , which are a two - particle effect sensitive to spin entanglement . finally , in sec . [ continuum ] we discuss the cotunneling through large qds with a continuum spectrum . in this case the correlations in the cotunneling current described above do not play an essential role . in the regime of low bias , elastic cotunneling dominates transport,@xcite and thus the noise is poissonian . in the opposite case of large bias , the transport is governed by inelastic cotunneling , and in sec . [ continuum ] we study heating effects which are relevant in this regime .

we study the noise of the cotunneling current through one or several tunnel - coupled quantum dots in the coulomb blockade regime . we prove a non - equilibrium fluctuation - dissipation theorem which leads to a universal expression for the noise - to - current ratio ( fano factor ) . the transport through a double - dot ( dd ) system shows an aharonov - bohm effect both in noise and current . in the case of cotunneling through a qds with a continuous energy spectrum

we study the noise of the cotunneling current through one or several tunnel - coupled quantum dots in the coulomb blockade regime . the various regimes of weak and strong , elastic and inelastic cotunneling are analyzed for quantum - dot systems ( qds ) with few - level , nearly - degenerate , and continuous electronic spectra . in the case of weak cotunneling we prove a non - equilibrium fluctuation - dissipation theorem which leads to a universal expression for the noise - to - current ratio ( fano factor ) . the noise of strong inelastic cotunneling can be super - poissonian due to switching between qds states carrying currents of different strengths . the transport through a double - dot ( dd ) system shows an aharonov - bohm effect both in noise and current . in the case of cotunneling through a qds with a continuous energy spectrum the fano factor is very close to one .

cond-mat0211024

c

here we give a short summary of our results . in sec . [ fdt - double ] , we have derived the non - equilibrium fdt , i.e. the universal relation ( [ db - fdt ] ) between the current and the noise , for qds in the weak cotunneling regime . taking the limit @xmath358 , we show that the noise is poissonian , i.e. @xmath3 . in sec . [ super - poissonian ] , we present the results of the microscopic theory of strong cotunneling , ref . @xcite : the master equation , eq . ( [ mastereq ] ) , the average current , eq . ( [ avcurrent ] ) , and the current correlators , eqs . ( [ ndnoise ] ) and ( [ correlator - delta - s ] ) , for a qds system coupled to leads in the strong cotunneling regime @xmath95 at small frequencies , @xmath359 . in contrast to sequential tunneling , where shot noise is either poissonian ( @xmath3 ) or suppressed due to charge conservation ( @xmath360 ) , we find that the noise in the inelastic cotunneling regime can be super - poissonian ( @xmath361 ) , with a correction being as large as the poissonian noise itself . in the regime of elastic cotunneling @xmath3 . while the amount of super - poissonian noise is merely estimated at the end of sec . [ super - poissonian ] , the noise of the cotunneling current is calculated for the special case of a qds with nearly degenerate states , i.e. @xmath362 , in sec . [ degenerate ] , where we apply our results from sec . [ super - poissonian ] . the general solution eq . ( [ result01 ] ) is further analyzed for two nearly degenerate levels , with the result eq . ( [ two - noise ] ) . more information is gained in the specific case of a dd coupled to leads considered in sec . [ dd - system ] , where we determine the average current eqs . ( [ current4]-[factor1 ] ) and noise eqs . ( [ noise2]-[noise3 ] ) in the weak cotunneling regime and the correlation correction to noise eq . ( [ dd - noise ] ) in the strong cotunneling regime as a function of frequency , bias , and the aharonov - bohm phase threading the tunneling loop , finding signatures of the aharonov - bohm effect and of the quantum entanglement . finally , in sec . [ continuum ] , another important situation is studied in detail , the cotunneling through a qds with a continuous energy spectrum , @xmath363 . here , the correlation between tunneling events plays a minor role as a source of super - poissonian noise , which is now caused by heating effects opening the possibility for tunneling events in the reverse direction and thus to an enhanced noise power . in eq . ( [ f - continuum ] ) , we express the fano factor @xmath364 in the continuum case in terms of the dimensionless numbers @xmath365 , defined in eq . ( [ cpm ] ) , which depend on the electronic distribution function @xmath301 in the qds ( in this regime , a description on the single - electron level is appropriate ) . the current eq . ( [ i - continuum ] ) is expressed in terms of the prefactor @xmath304 , eq . ( [ prefactor ] ) . both @xmath364 and @xmath304 are then calculated for different regimes . for weak cotunneling , we immediately find @xmath3 , as anticipated earlier , while for strong cotunneling we distinguish the two regimes of cold ( @xmath312 ) and hot ( @xmath313 ) electrons . for both regimes we find that the fano factor is very close to one , while @xmath304 is given in fig . [ coldhot ] . this work has been partially supported by the swiss national science foundation .

the various regimes of weak and strong , elastic and inelastic cotunneling are analyzed for quantum - dot systems ( qds ) with few - level , nearly - degenerate , and continuous electronic spectra . in the case of weak cotunneling the noise of strong inelastic cotunneling can be super - poissonian due to switching between qds states carrying currents of different strengths . the fano factor is very close to one .

we study the noise of the cotunneling current through one or several tunnel - coupled quantum dots in the coulomb blockade regime . the various regimes of weak and strong , elastic and inelastic cotunneling are analyzed for quantum - dot systems ( qds ) with few - level , nearly - degenerate , and continuous electronic spectra . in the case of weak cotunneling we prove a non - equilibrium fluctuation - dissipation theorem which leads to a universal expression for the noise - to - current ratio ( fano factor ) . the noise of strong inelastic cotunneling can be super - poissonian due to switching between qds states carrying currents of different strengths . the transport through a double - dot ( dd ) system shows an aharonov - bohm effect both in noise and current . in the case of cotunneling through a qds with a continuous energy spectrum the fano factor is very close to one .

hep-ph0508166

i

the @xmath0 ( @xmath6 ) one - loop structure has been considerably studied in the literature not just because it may constitute a mechanism through which physics beyond the fermi scale may show up , but also due to some theoretical issues concerning its dependence on the gauge - fixing scheme . it turns out that the conventional gauge - fixing procedures give rise to ill - behaved off - shell green functions that may display inadequate properties such as a nontrivial dependence on the gauge - fixing parameter , an increase larger than the one observed in physical amplitudes at high energies , and the appearance of unphysical thresholds . the on - shell green functions can represent physical amplitudes as they are independent on the gauge - fixing procedure , such as occurs with the static electromagnetic properties of the @xmath7 boson @xcite , but gauge independence is lost if at least one external particle becomes virtual . although off - shell green functions are generally gauge dependent , the @xmath8-matrix elements to which they contribute must be gauge independent . this is the case of the off - shell @xmath0 vertex , which is just a piece of some physical process such as the @xmath9 and @xmath10 reactions . nonetheless , it would be interesting if one was able to study the sensitivity to radiative corrections of the @xmath0 coupling , and other sm couplings as well , without invoking some particular @xmath8-matrix element . the concepts of gauge invariance and gauge independence are two essential ingredients of gauge systems , though the former is not necessarily present at the quantum level . while gauge invariance plays a central role when defining the classical action of the system , once the latter is quantized one must invariably invoke an appropriate gauge - fixing procedure to define a nondegenerate action , which means that gauge invariance is to be broken explicitly . the resultant action is not gauge invariant , though it is invariant under brst symmetry @xcite . as a consequence , the green functions derived from this action can not satisfy simple ( qed - like ) ward identities , but they do satisfy more elaborate slavnov - taylor identities that are dictated by brst symmetry . also , green functions contain much unphysical information that is removed provided a physical observable is considered . contrary to green functions , which are highly dependent on the gauge - fixing procedure , physical amplitudes have no such dependence , thereby being gauge independent . there are thus some subtle mechanisms that conspire to produce nontrivial cancelations between the green functions defining a physical observable . it is clear that a nonconventional quantization scheme must be applied in order to generate gauge - invariant green functions , which in turn can be obtained from a gauge - invariant quantum action @xmath11 . in this respect , the background - field - method ( bfm ) @xcite is meant to construct manifest gauge - invariant quantum actions from which well - behaved green functions satisfying simple ward identities can be derived . this method , implemented at the level of generating functionals , relies on the decomposition of the gauge fields into two parts : the quantum field @xmath12 and the background ( classical ) field @xmath13 , i.e. @xmath14 . in the generating functional only the quantum fields are integrated out , whereas the background fields are treated as sources . this means that only the quantum fields can circulate inside the loops . this method allows one to introduce a gauge - fixing procedure for the quantum fields without spoiling the gauge invariance of the quantum action with respect to the classical fields . although it is necessary to define a gauge - fixing procedure for both the quantum and the classical fields in order to define @xmath8-matrix elements , only a gauge - fixing scheme for the quantum gauge fields is required to define general off - shell green functions . the quantum action is invariant under ordinary gauge transformations of the classical fields , while the quantum fields transform as the adjoint representation of the group in consideration . in other words , the so constructed action @xmath15 $ ] is degenerate with respect to the background fields but nondegenerate with respect to the quantum fields . the green functions derived from the quantum action @xmath16 $ ] are gauge invariant in the sense that they satisfy simple ward identities , but it is worth stressing that they are still dependent on the gauge parameter @xmath17 that characterizes the gauge - fixing scheme used for the quantum fields , and so there is no gauge independence . the bfm has proved useful in many applications @xcite , simplifying both technically and conceptually the calculation of radiative corrections . as already mentioned , green functions arising from a conventional quantum action ( a brst - invariant but gauge - noninvariant one ) contain a lot of unphysical information that is removed once they are inserted into some physical observable . some of this unwanted information can be removed at the level of the generating functional through the bfm formalism , which allows one to construct a gauge - invariant quantum action from which gauge - invariant green functions can be obtained . although the resultant green functions satisfy simple ward identities , they are not gauge independent . thus far there is still no known mechanism yielding both gauge - invariant and gauge - independent green functions directly from the generating functional , although there is already a diagrammatic method meant for this purpose , the so - called pinch technique ( pt ) @xcite . this method relies on constructing well - behaved green functions by combining some individual contributions from self - energies , vertex , and box diagrams , which usually appear in physical processes . in general , the feynman rules used in this diagrammatic approach are derived from a conventional effective action , though those derived from the bfm have also been used for a deeper study of the method self - consistence @xcite . although the pt was first introduced for the study of pure yang - mills theories at the one - loop level @xcite , it has already been applied to theories with spontaneous symmetry breaking ( ssb ) @xcite , including the study of self - energies @xcite and trilinear vertices @xcite involving the electroweak gauge bosons . a complete calculation of the one - loop contribution to the @xmath0 vertex from the electroweak bosons was presented in refs . @xcite : it was intended to show that the vertex functions satisfy a simple ward identity , which establishes a relationship between this vertex and the @xmath7 self - energy . more specifically , ref . @xcite discusses the gauge independence of the form factors associated with the @xmath18 vertex for off - shell photon and on - shell @xmath7 bosons . afterwards , an important connection between the pt and the bfm was established @xcite at the one - loop level by showing that the green functions calculated via the bfm feynman rules coincide with those obtained through the pt for the specific value @xmath19 . more recently , the pt was extended to the two - loop level in the context of both the yang - mills @xcite and the electroweak sectors @xcite , and the one - loop connection to the bfm was established too . a step toward a nondiagrammatic formulation of the pt via the powerful batalin - vilkovisky quantization method @xcite was presented in ref . this framework was used to generalize the pt at any order of perturbation theory @xcite , and it was meant to show that the link between the pt green functions and those obtained via the bfm along with the feynman - thooft gauge remains at all orders of perturbation theory @xcite . the reason for such a link remains a puzzle , though it is worth noting that the feynman - thooft gauge yields no unphysical thresholds . establishing such a connection at any order of perturbation theory is very important for practical purposes because one can simply use the bfm feynman - thooft gauge ( bfmfg ) to calculate gauge - independent off - shell amplitudes , which happens to be much less cumbersome than the use of the pt . although in conventional quantization schemes the quantum action of the theory is not gauge invariant , it is still possible to introduce gauge invariance with respect to a subgroup of such a theory . this scheme is particulary useful when the quantum fluctuations of the gauge fields associated with this subgroup are deemed negligible . for instance , it would be interesting to assess the virtual effects of the heavy physics lying beyond the fermi scale on the sm green functions in a @xmath3-covariant manner , in which case it is only necessary to introduce a quantization scheme for the heavy fields since the sm fields would only appear as external legs . this is indeed the philosophy behind the effective lagrangian approach widely used in the context of the electroweak theory , where it is assumed that the new physics effects must respect the @xmath3 symmetry . in a specific theory beyond the sm , a @xmath3-invariant effective lagrangian can be constructed by introducing a @xmath3-covariant gauge - fixing procedure for the heavy gauge bosons in order to integrate them out in the generating functional . in analogy with the bfm , the gauge - fixing procedure for the heavy gauge fields must involve the @xmath3-covariant derivative given in the representation in which the heavy fields transform under this group . this is the reason why such gauges , which were first introduced by fujikawa in the context of the sm @xcite , are called nonlinear or covariant gauges . in this case , the @xmath7 propagator is defined in a covariant way under the electromagnetic @xmath20 group , so the vertex functions associated with the @xmath18 interaction and the @xmath7 self - energy satisfy a simple ward identity . the most general renormalizable structure of this gauge - fixing procedure has been discussed from the brst - symmetry standpoint in @xcite , and a discussion about the difficulties on implementing the faddeev - popov method ( fpm ) has been presented too @xcite . this gauge - fixing procedure has proved a valuable tool in radiative corrections as it simplifies considerably the loop calculations @xcite . the method has also been used to quantize yang - mills theories without ssb @xcite . we will show below that , within some specific models , it is possible to use a nonlinear gauge to parametrize in an @xmath3-invariant way the impact of new physics on the sm green functions . in particular , we will show that it is possible to use this class of gauges to estimate the one - loop effects of new heavy gauge bosons on the @xmath0 vertex . we are interested in the sensitivity of the @xmath0 vertex to the new heavy gauge bosons predicted by the so - called minimal @xmath21 model @xcite , which is based on the @xmath22 gauge group . apart from predicting signals of new physics at the tev scale , this model introduces unique features that have been the focus of great interest recently @xcite such as a possible approach to the solution of the family replication problem . in this model , the lepton spectrum is the same as the sm one , but it is accommodated in @xmath23 antitriplets ; the quark sector is also arranged in the fundamental representation of this group , which requires the introduction of three new quarks . in order to endow all the particles with mass , a higgs sector composed by three triplets and one sextet of @xmath23 is required , though only one of the triplets is needed to break down @xmath24 into @xmath3 at the new physics scale @xmath25 . in the first stage of ssb , there emerge singly and doubly charged gauge bosons in a doublet of the @xmath26 group , as well as a new neutral boson @xmath27 . the new charged gauge bosons were dubbed bileptons because they carry two units of lepton number . the three exotic quarks and a cp even higgs boson do not couple to the @xmath7 gauge boson since they emerge as singlets of @xmath26 , and get their mass at the @xmath28 scale . thus , at this scale , the @xmath18 and @xmath29 vertices can only receive contributions from the bileptons . the fact that the @xmath26 group is totally embedded in @xmath23 gives rise to unusual couplings between the bileptons and the sm gauge fields , which arise via the electroweak covariant derivative since the bileptons transform as the fundamental representation of @xmath26 . it turns out that these couplings do not involve any mixing angle and are similar both in strength and lorentz structure to those couplings existing between the sm gauge bosons themselves , as opposed to the gauge bosons appearing in other sm extensions . our main goal is to estimate , in a @xmath3-invariant way , the sensitivity of the @xmath0 vertex to the bileptons . to this end , we introduce a @xmath3-covariant gauge - fixing procedure for the bileptons , which leads to an invariant quantum action . we will show below that the resulting @xmath18 and @xmath29 green functions are gauge invariant and satisfy simple ward identities . another feature worthwhile to emphasize is that the fpm fails when it is attempted to be used in conjunction with this class of gauges : the resultant theory is not renormalizable @xcite . instead of using this method , we will present a discussion based on brst symmetry @xcite , which is a powerful formalism adequate not only to quantize yang - mills theories with broader gauge - fixing procedures , as the nonlinear ones , but also to quantize more general gauge systems . as we will see below , our quantization scheme incorporates the main ingredient of the bfm , namely , the gauge invariance of the quantum action , which turns loop calculations into a somewhat simple task . the rest of the paper has been organized as follows . in sec . [ model ] a brief description of the minimal @xmath21 model is presented . particular emphasis is given to the yang - mills sector . [ gauge ] a @xmath3-covariant gauge - fixing procedure for the bileptons is presented along with a discussion on the advantages of using the brst formalism instead of the fpm . [ cal ] is devoted to present the one - loop amplitudes for the @xmath18 and @xmath29 vertices , whereas in secs . [ dis ] and [ con ] we discuss our results and present the conclusions .

we study the one - loop sensitivity of the ( ) vertex to the new massive gauge bosons predicted by the minimal model , which have unusual couplings to the standard model ( sm ) gauge bosons . a gauge - fixing procedure covariant under the group was introduced for these new gauge bosons ( dubbed bileptons ) in order to generate gauge - invariant green functions . the similarities between this procedure and the nonconventional quantization scheme of the background field method are discussed .

we study the one - loop sensitivity of the ( ) vertex to the new massive gauge bosons predicted by the minimal model , which have unusual couplings to the standard model ( sm ) gauge bosons . a gauge - fixing procedure covariant under the group was introduced for these new gauge bosons ( dubbed bileptons ) in order to generate gauge - invariant green functions . the similarities between this procedure and the nonconventional quantization scheme of the background field method are discussed . it is found that , for relatively light bileptons , with a mass ranging from to , the radiative corrections to the form factors associated with the vertex can be of the same order of magnitude than the sm one . in the case of heavier bileptons , their contribution is smaller by about one and two orders of magnitude than their sm counterpart .

1501.07693

i

branching brownian motion ( bbm ) is a well - known model that finds applications in several areas of science including physics , mathematics and biology . bbm arises naturally in the context of systems where new particles are generated at each time step such as models of evolution , epidemiology , population growth and nuclear reactions , and now has a long history @xcite . in addition , bbm has also been widely used in theoretical physics where it has been studied in the context of reaction - diffusion models , disordered systems amongst others @xcite . bbm is also an important model in probability theory as it combines the long - studied diffusive motion with the random branching mechanism of galton - watson trees @xcite . in this paper we are interested in one dimensional bbm . the process begins with a single particle at the position @xmath21 at time @xmath22 . the dynamics proceeds in continuous time , where in a small time interval @xmath23 , each particle splits into two independent particles with probability @xmath24 , dies with with probability @xmath25 , and with the remaining probability @xmath26 performs a brownian motion on a line with a diffusion constant @xmath3 . a realization of the dynamics of such a process is shown in fig . [ walk_picture ] . , where @xmath7 and @xmath8 are the maximum and minimum displacements of the process up to a certain time @xmath2 respectively . ] in a given realization of this bbm process , there are in general @xmath27 particles present in the system at a particular time @xmath2 . the parameters @xmath5 and @xmath4 in this bbm model define three regimes with different properties . the number of particles @xmath28 is a random variable whose statistics depends on @xmath4 and @xmath5 . when the rate of birth is greater than the death rate ( @xmath29 ) , the _ supercritical _ phase , the process is explosive and the average number of particles in the system grows exponentially with time @xmath30 . in contrast , when the birth rate is smaller than the death rate ( @xmath31 ) , the _ subcritical _ phase , the process eventually dies and , on an average , there are no particles present in the system as @xmath32 . at the critical point @xmath33 , the system is characterized by a fluctuating number of particles with @xmath34 at all times @xmath2 . if one takes a snapshot of the system at a given time @xmath2 , the spatial positions of the existing particles happen to be strongly correlated , since the particles are linked by their common genealogy . one important object that has been extensively studied is the order statistics of these particles , i.e. , the statistics of the position @xmath35 of say the @xmath36-th rightmost particle at time @xmath2 , where the particle positions on the line are ordered as @xmath37 @xcite . another related interesting quantity is the gap @xmath38 between the @xmath36-th and @xmath39-th particle at time @xmath2 . most of these studies have thus focused on extreme value questions at a given time @xmath2 . however , there are other interesting extreme value observables that concern the history of the process over the entire time interval @xmath40 $ ] . for instance , one can consider the global maximum , @xmath41 $ ] which represents the maximum of all the particle positions _ up to _ time @xmath2 . this has the simple interpretation as the maximum displacement of the entire process up to time @xmath2 ( see fig . [ walk_picture ] ) . this global maximum has appeared in a variety of applications including the spread of gene populations @xcite and the propagation of animal epidemics in two dimensions @xcite . similarly the global minimum @xmath42 $ ] is another interesting quantity that , by symmetry , has the same marginal probability distribution function ( pdf ) as @xmath43 . the marginal pdf of @xmath7 has been studied extensively for the supercritical @xcite , critical and the subcritical phases @xcite . while the marginal distributions of @xmath7 , and hence that of @xmath44 , are well studied , much less is known about the correlation between these two random variables . in this paper , we study the joint pdf of @xmath7 and @xmath8 . in the supercritical phase , this joint pdf is always time dependent , and is hard to compute analytically . however , in this case , @xmath7 and @xmath8 get separated from each other ballistically in time and hence become uncorrelated at late times . in contrast , in the critical and subcritical phases ( @xmath6 ) , we show that the joint pdf reaches a limiting stationary form at late times , which we compute analytically . moreover , for @xmath45 , our exact results for the stationary joint pdf demonstrate that this correlation between @xmath7 and @xmath8 remains finite even in the stationary state . the joint pdf of @xmath7 and @xmath8 has the following interesting physical application . for instance , in the context of epidemic spreads , it is important to characterize the spatial extent over which the epidemic has propagated up to time @xmath2 . this is clearly measured by the span @xmath46 of the process up to time @xmath2 ( see fig . [ walk_picture ] ) @xcite . evidently , to compute the distribution of @xmath47 , we need to know the joint pdf of @xmath7 and @xmath8 . in this paper we also compute analytically the stationary pdf of the span @xmath47 in the critical ( @xmath48 ) and the subcritical ( @xmath49 ) cases . our exact results demonstrate that the correlation between @xmath7 and @xmath8 is also manifest in the stationary span pdf . the rest of the paper is organized as follows . in section ii , we define the model precisely and summarize our main results . in section iii we derive an exact evolution equation for the joint distribution of @xmath7 and @xmath8 . in section iv we derive the stationary joint pdf of @xmath7 and @xmath8 for the critical ( @xmath48 ) and the subcritical ( @xmath49 ) cases . in section v we compute the stationary pdf of the span and extract its asymptotic behaviors analytically . in section vi we compare our analytical predictions with monte carlo simulations . finally , we conclude with a discussion in section vii . some details of computations are relegated to the appendices .

we study the one dimensional branching brownian motion starting at the origin and investigate the correlation between the rightmost ( ) and leftmost ( ) visited sites up to time . at each time step the existing particles in the system either diffuse ( with diffusion constant ) , die ( with rate ) or split into two particles ( with rate ) . we show that at large time , the joint probability distribution function ( pdf ) of the two extreme points becomes stationary . , we show that the span distribution decays exponentially as for large spans , where is a non - trivial function of which we compute exactly . finally we verify our results via direct monte carlo simulations .

we study the one dimensional branching brownian motion starting at the origin and investigate the correlation between the rightmost ( ) and leftmost ( ) visited sites up to time . at each time step the existing particles in the system either diffuse ( with diffusion constant ) , die ( with rate ) or split into two particles ( with rate ) . we focus on the regime where these two extreme values and are strongly correlated . we show that at large time , the joint probability distribution function ( pdf ) of the two extreme points becomes stationary . our exact results for demonstrate that the correlation between and is nonzero , even in the stationary state . from this joint pdf , we compute exactly the stationary pdf of the ( dimensionless ) span , which is the distance between the rightmost and leftmost visited sites . this span distribution is characterized by a linear behavior for small spans , with . in the critical case ( ) this distribution has a non - trivial power law tail for large spans . on the other hand , in the subcritical case ( ) , we show that the span distribution decays exponentially as for large spans , where is a non - trivial function of which we compute exactly . we show that these asymptotic behaviors carry the signatures of the correlation between and . finally we verify our results via direct monte carlo simulations .

1501.07693

c

in summary , we have obtained exact results for the stationary joint pdf @xmath72 of the dimensionless maximal displacements @xmath321 and @xmath55 _ up to time @xmath2 _ for the one - dimensional bbm in the critical ( @xmath230 ) and subcritical cases ( @xmath322 ) ( see figs . [ walk_picture ] and [ fig : cartoon ] ) . in both cases we found that the correlation between @xmath58 and @xmath81 remain nonzero , even in the stationary state . from this joint pdf we have computed exactly the pdf @xmath11 of the ( dimensionless ) span , @xmath323 , which provides an estimate of the spatial extent of the process . we demonstrated that @xmath11 carries the signatures of the correlation between the two extreme displacements @xmath58 and @xmath81 , which can be seen for instance in the asymptotic behaviors of @xmath11 both for small and large arguments ( [ pzeta_asympt_critical ] , [ pzeta_asympt_subcritical ] ) . the span is an interesting physical observable associated with bbm , which has several potential applications , for example in the context of epidemic spreads @xcite . moreover , our results are also interesting from the general point of view of extreme value statistics ( evs ) of strongly correlated variables . it was indeed recently demonstrated that random walks and brownian motion ( see e.g. , refs . @xcite for recent studies ) are interesting laboratories to test the effects of correlations on evs , beyond the well known case of independent and identical random variables @xcite . in that respect , the results for the one - dimensional bbm obtained in the present paper constitute an interesting instance of a strongly correlated multi - particle system where the correlation between extreme values can be computed analytically . in this paper we have restricted ourselves to computing the span distribution for the critical ( @xmath48 ) and subcritical cases ( @xmath49 ) . the computation was feasible because the span distribution becomes stationary at late times @xmath2 in these cases . in contrast , in the supercritical case ( @xmath60 ) the span distribution will always be time dependent and it would be interesting to compute this distribution exactly . the recent developments @xcite in the supercritical case may shed some light on this outstanding problem . it would also be interesting to extend these calculations to branching processes where the particles can split into @xmath324 particles at each time step , which can be treated using the techniques developed in our paper .

we focus on the regime where these two extreme values and are strongly correlated . our exact results for demonstrate that the correlation between and is nonzero , even in the stationary state . from this joint pdf , we compute exactly the stationary pdf of the ( dimensionless ) span , which is the distance between the rightmost and leftmost visited sites . this span distribution is characterized by a linear behavior for small spans , with . in the critical case ( )

we study the one dimensional branching brownian motion starting at the origin and investigate the correlation between the rightmost ( ) and leftmost ( ) visited sites up to time . at each time step the existing particles in the system either diffuse ( with diffusion constant ) , die ( with rate ) or split into two particles ( with rate ) . we focus on the regime where these two extreme values and are strongly correlated . we show that at large time , the joint probability distribution function ( pdf ) of the two extreme points becomes stationary . our exact results for demonstrate that the correlation between and is nonzero , even in the stationary state . from this joint pdf , we compute exactly the stationary pdf of the ( dimensionless ) span , which is the distance between the rightmost and leftmost visited sites . this span distribution is characterized by a linear behavior for small spans , with . in the critical case ( ) this distribution has a non - trivial power law tail for large spans . on the other hand , in the subcritical case ( ) , we show that the span distribution decays exponentially as for large spans , where is a non - trivial function of which we compute exactly . we show that these asymptotic behaviors carry the signatures of the correlation between and . finally we verify our results via direct monte carlo simulations .

hep-ph0507096

i

according to the inflationary scenario , the universe at early times expands quasi - exponentially in a vacuum - like state without entropy or particles . during this stage of inflation , all energy is contained in a classical slowly moving inflaton field @xmath1 . the fundamental lagrangian @xmath2 contains the inflaton part with the potential @xmath3 and other fields which give subdominant contributions to gravity . in chaotic inflationary models , soon after the end of inflation the almost homogeneous inflaton field @xmath4 coherently oscillates with a very large amplitude of the order of the planck mass around the minimum of its potential . due to the interactions of other fields with the inflaton in @xmath5 , the inflaton field decays and transfers all of its energy to relativistic particles . if the creation of particles is sufficiently slow ( for instance , if the inflaton is coupled only gravitationally to the matter fields ) the decay products simultaneously interact with each other and come to a state of thermal equilibrium at the reheating temperature @xmath6 . this gradual reheating can be treated with the perturbative theory of particle creation and thermalization as long as the couplings are sufficiently small @xcite . however , the particle production from a coherently oscillating inflaton for a wide range of couplings occurs in a non - perturbative regime of parametric excitation @xcite . this picture , with variation in its details , is extended to other inflationary models . for instance , in hybrid inflation inflaton decay proceeds via a tachyonic instability of the inhomogeneous modes which accompany the symmetry breaking @xcite . one consistent feature of preheating non - perturbative copius particle production immediately after inflation is that the process occurs far away from thermal equilibrium . the energy of the inflaton zero mode is transferred to particles in an out - of - equilibrium state with very large occupation numbers within a very short time interval of about @xmath0 sec , which can be much shorter than the time needed for relaxation towards thermal equilibrium . one can expect the initial conditions for many parameters of the subsequent cosmological thermal history to be settled during or around preheating . it is often thought that the details of the transition between inflation and the hot radiation dominant stage are not relevant , except for the so - called reheating temperature @xmath6 , the temperature of the ultra - relativistic plasma at the time when it reaches thermal equilibrium . definitely , this is an important parameter of the early universe . however , a precise understanding of how thermal equilibrium is reached is crucial since partial thermal distributions can be responsible for cosmological baryo / leptogenesis , the possible creation of dangreous cosmological relics , etc . the out - of - equilibrium character of preheating opens the possibility for equally relevant phenomena associated with non - equilibrium physics , including phase transitions , non - thermal production of heavy particles , etc . precise knowledge of the expansion of the universe @xmath7 is also required to connect a physical wavelength of the observed cosmological perturbation , @xmath8 , to the number of e - foldings @xmath9 at which that wavelength exited the horizon during inflation . finally , we can have an alternative mechanism of generation of ( almost ) scale free adiabatic metric perturbations from preheating , based on spatial modulation of couplings @xcite . small spatial fluctuations in the couplings lead to small fluctuations of the rates of physical processes , which in turn generate adiabatic perturbations of the energy density and of the metric . analyzing the details of this mechanism require precise knowledge of the evolution of the equation of state ( eos ) . to understand the early post - inflationary period we have to understand the dynamics of interacting fields in an out - of - equilibrium state with large occupation numbers evolving towards a state of ultimate thermal equilibrium . this is a complicated problem of non - equilibrium quantum field theory , which is by itself a very interesting topic . the theory of the transition from inflation to thermalization has been investigated with fully non - linear numerical lattice simulations plus different techniques of classical field dynamics @xcite . classical field dynamics is adequate as long as occupation numbers of field excitations are large . there has also been progress in understanding out - of - equilibrium qft dynamics in @xmath10 sigma models beyond the hartree approximation @xcite , taking into account crucial effects of rescattering after preheating @xcite . from all of these methods , the following picture emerges . immediately after preheating , either from parametric resonance or tachyonic , one or more bose fields are excited in an out - of - equlibrium state with large occupation number . backreaction of these fields terminates their production . interaction ( rescattering ) of these modes between each other , and with the remaining inflaton field after the first stage of preheating is violent and non - perturbative . during this very short stage a large amount of entropy is generated , chaotic ( turbulent ) wave dynamics is established , and the fields not directly excited during preheating get excited in out - of - equilibrium states due to rescattering ; residual inflaton oscillations are still present . a next , longer stage then takes place , characterized by lower ( but still large ) occupation numbers such that rescattering is perturbative , and the occupation spectra gradually move towards a saturated state by cascading towards ultra - violet ( uv ) and infra - red ( ir ) modes ( in the spirit of kolmogorov wave turbulence ) . the last and the longest stage will be the stage of proper thermalization , when the distributions evolve towards thermal equilibrium . quantum physics is important at the end of this stage , when the occupation numbers are small and the classical approximation breaks down . one may say that reheating is completed when this last , longest stage is completed , and its timing defines @xmath6 and @xmath11 . in this paper we suggest a new look at the transition between inflation and thermalization . we focus on calculation and understanding of the effective equation of state @xmath12 throughout all of these stages after inflation . we use numerical lattice simulations @xcite to calculate @xmath13 in the simple chaotic model with a quadratic potential and a simple four - legs interaction @xmath14 . in particular , we notice that @xmath13 approaches ( but does not necessarily reach ) the equilibrium radiation - dominated value @xmath15 while the fields are far from ultimate thermal equilibrium . we compare this with the analysis of @xcite , devoted to thermalization of the @xmath16 sigma model in minkowski spacetime . in that case , the equation of state was found to evolve sharply towards @xmath17 long before thermalization completes , which prompted the authors of @xcite to describe the state of the system as a pre - thermalized state . although we also see a somewhat similar effect , the expansion of the universe and the presence of a residual massive inflaton component , prevent the equation of state from being exactly the one of radiation at this very early stage . moreover , we enphasize that the exact microphysics of the system is described by a turbulent state , which is still very far from a thermalized one . ( this difference can be important when discussing the cosmological effects of decay products , as for instance production of dangerous relics from nonthermal distributions . ) indeed , our simulations show that the occupation numbers of excited infra - red modes evolve towards a steady state , related to turbulence of classical interacting waves . the plan of the paper is the following : in section [ sec : model ] we describe preheating in a simple chaotic inflationary model . in section [ sec : numerics ] we present the results of lattice simulations for time - dependent variables , including the equation of state @xmath18 during different stages of preheating , occupation numbers and fluctuations . in section [ sec : implementations ] we discuss some immediate applications of our results for cosmology . we consider the application of the eos evolution to modulated cosmological fluctuations and to the @xmath19 formula . we note several qualitatively important issues in the dynamics of thermalization . the interaction @xmath20 describes ( at the perturbative level ) scattering between inflaton quanta , rather than inflaton decay . scattering between massive @xmath1 soon becomes inefficient , and does not lead to a complete depletion of the inflaton , which eventually ends up dominating over the light degrees of freedom @xmath21 . this problem is automatically avoided if three - legs bosonic interactions @xmath22 are also present . we illustrate this with an example motivated by supersymmetry . we also discuss the rapid saturation of the ir modes excited during preheating , which occurs long before the ultimate thermal equilibrium ( of all modes ) is reached . one consequence of the excitation of infrared modes is that it can lead to an overproduction of gravitinos or of other dangerous gravitational relics . this generation is different from direct nonperturbative production during preheating @xcite . instead , it is analogous to the perturbative thermal production first considered in @xcite . the main difference with @xcite is that we compute the production right after the first preheating stage , and not only after thermalization has completed @xcite . although the distributions formed at preheating / rescattering are far from thermal , the high particle occupation numbers can lead to a significant generation of gravitinos . the above results are summarized in section [ sec : summary ] .

the energy in the homogeneous inflaton is exponentially rapidly transfered into highly occupied out - of - equilibrium inhomogeneous modes , which subsequently evolve towards equilibrium . the infrared modes excited during preheating evolve towards a saturated distribution long before thermalization completes . we also highlight the effects of three - legs inflaton interactions on the dynamics of preheating and thermalization in an expanding universe .

we study the out - of - equilibrium nonlinear dynamics of fields after post - inflationary preheating . during preheating , the energy in the homogeneous inflaton is exponentially rapidly transfered into highly occupied out - of - equilibrium inhomogeneous modes , which subsequently evolve towards equilibrium . the infrared modes excited during preheating evolve towards a saturated distribution long before thermalization completes . we compute the equation of state during and immediately after preheating . it rapidly evolves towards radiation domination long before the actual thermal equilibrium is established . the exact time of this transition is a non - monotonic function of the coupling between the inflaton and the decay products , and it varies only very weakly ( around s ) as this coupling changes over several orders of magnitude . this result is applied to refine the relation between the number of efoldings n and the physical wavelength of perturbations generated during inflation . we also discuss the implications for the theory of modulated perturbations from preheating . we finally argue that many questions of the thermal history of the universe should be addressed in terms of pre - thermalization , illustrating this point with a calculation of perturbative production of gravitinos immediately after chaotic inflation . we also highlight the effects of three - legs inflaton interactions on the dynamics of preheating and thermalization in an expanding universe .

hep-ph0507096

r

in the simple model discussed so far , with the interaction term @xmath145 , the decay of the inflaton @xmath1 is not complete . indeed , such a term mediates scatterings between inflaton quanta , rather than single particle decay . once @xmath1 is diluted by the expansion of the universe , the scatterings become inefficient , and the number of inflaton quanta remain practically constant . this poses a problem because in order to reach the stage of radiation domination we need to have complete decay of the inflaton . the simplest way to have a complete decay is to consider three legs interactions . for instance , we can replace ( [ int ] ) by @xmath146 where @xmath36 is a mass dimension parameter , which breaks the @xmath147 symmetry . for @xmath148 , the trilinear term produced by this interaction is irrelevant and the inflaton decay occurs as described above . however , when @xmath1 is decreased by the expansion of the universe , the trilinear interaction becomes dominant , leading to a complete inflaton decay . we can avoid discussing the introduction of the scale @xmath36 by considering a yukawa interaction of the inflaton with some fermions @xmath149 . by itself , this interaction has interesting consequences for preheating , as discussed e.g. in @xcite . when both fermionic and bosonic interactions are present , preheating into bosons is typically much more efficient , since the one into fermions is reduced by pauli blocking . however , once the interactions become perturbative , the trilinear @xmath150 decay will eventually dominate over the @xmath151 scattering . three - legs interactions arise very naturally in susy theories . indeed , consider the simple superpotential @xmath152 the corresponding scalar field potential contains three - legs as well as four - legs plus self - interaction terms @xmath153 ( neglecting the imaginary parts of the fields ) . the four - legs interaction dominates over the three - legs one as long as @xmath154 . for reasonable values of @xmath36 , this happens during the first stages of preheating . eventually , the amplitude of @xmath1 decreases due to the expansion of the universe , and the trinlinear interaction dominates , resulting in a complete decay of the massive inflaton . hence , considering a supersymmetric theory automatically introduces trilinear vertices among the scalars . it also allows for stronger couplings between the inflaton and other fields , without spoiling the flatness of the inflaton potential , as we have discussed in sec . [ sec : model ] . the precise history of the expansion of the universe @xmath7 is important for connecting the physical wavelength @xmath155 of the cosmological perturbations we observe to the number of efoldings @xmath9 at which the perturbation was generated ( left the horizon ) during inflation . according to the general lore @xcite , one has [ efold ] n(k ) = 62 - ln + , where @xmath156 is the inverse size of the present cosmological horizon and @xmath157 is defined by the physics after inflation : = -ln + - , [ deltadef ] where @xmath158 is the energy density at the end of reheating , @xmath159 is the value of the inflaton potential at the moment when the mode with the comoving wave number @xmath117 exits the horizon at inflation and finally @xmath160 is the value at the end of inflation . the last term in the right hand side of eq . ( [ deltadef ] ) is related to reheating , specifically that it is not an instantaneous process . it is typically computed under the assumption that the universe is matter dominated ( by the coherent oscillations of the inflaton ) all throughout reheating , and that it ( instantaneously ) becomes radiation dominated at the end of the reheating stage . as we have seen , this is not what happens . indeed , a better definition of the last term in @xmath157 is @xmath161 where @xmath162 is the scale factor at the moment after reheating at which the eos reaches its value at radiation dominance . as we have been discussing , this moment can occur while the distributions of particles are very far from thermal , shortly after the end of preheating . this amounts to taking @xmath163 , rather than @xmath164 , where @xmath165 is the value of the scale factor at the end of reheating under the common assumption that perturbative reheating occurs entirely within a regime of matter domination , with @xmath166 . in this situation one has @xmath167 at the end of matter domination , and the corresponding value of the scale factor @xmath168 can be estimated as @xmath169 . hence , for a preheating scenario with a very wide range of values of the coupling @xmath170 , the first term of ( [ deltadef ] ) can be fixed to @xmath171 this result holds for a wide class of inflationary models , and for many different types of preheating . one of the most important parameters in physics of the early universe is the highest temperature of the hot plasma after the inflaton field decays and transfer its energy into radiation . , defined at the moment when the thermal bath starts dominating . ] this is traditionally called the reheating temperature @xmath6 . as we have seen in many previous papers and above in this paper , ultimate thermal equilibrium is preceeded by several stages . let us distinguish four of them : * preheating , with the duration @xmath172 , * a short violent stage at the end of preheating when non - linearity and non - perturbative effects are dominant ; chaos is onset , erasing the details of the initial conditions , on a timescale @xmath173 , * the stage of turbulence of classical fields , with the saturated spectrum cascading both towards uv and ir modes with duration @xmath174 , longer than the two previous stages , * the last stage of proper qft thermalization , with particle fusion / offshell processes ; it is characterized by the timescale @xmath175 , much longer than the previous ones . traditionally the beginning of the thermal history is related to the moment @xmath175 , which may be very long ; as a result of redshift , the reheating temperature can be rather low . let us reconsider this attitude . while the question of when the ultimate thermal equilibrium will be established and to which value of @xmath6 it corresponds is still very interesting , we will argue that important physics which constrains the model of inflation and interactions takes place long before full thermal equilibrium is completed . indeed , figures [ fig : phinkwk][fig : phispl ] show that the modes at physically interesting scales , up to @xmath176 tens of @xmath177 gev , are quickly excited towards a saturated distribution . this raises several subtle and interesting questions . usually , the relativistic particles embedded in the thermal bath are brought into thermal equilibrium after the relaxation time @xmath178 , where @xmath36 is the cross section of the processes relevant for thermalization , and @xmath179 is the number density of particles . this estimate works in the diluted gas approximation . indeed , consider the vertex @xmath22 , leading to inflaton decay into quanta of @xmath21 . the particle number density enters in the collisional integral in the combination @xmath180 ( @xmath181 is the momentum of the inflaton quantum , while @xmath182 are the momenta of the two quanta of @xmath21 entering in the process ) . the above estimate for the thermalization timescale assumes that the inverse process @xmath183 ( described by the second term in ( [ collfactor ] ) ) is irrelevant , and that all the occupation numbers are much smaller than one , so that @xmath184 . in particular , this last assumption is not valid until the very end of the thermalization stage . therefore , for large @xmath66 we expect that particles are dragged into effective thermal equilibrium faster , due to the stimulated interaction . we have observed this fact also in previous numerical lattice simulations @xcite . another relevant effect , already discussed above , is that large fluctuations of fields can contribute to the effective masses of particles , which can become effectively heavy . this leads to the blocking of some processes which may lead to a faster thermalization , until fields fluctuations are diluted by the expansion . finally , a very relevant question is the one of particle production from the nonthermal but highly excited distributions . in particular , one should verify that dangerous relics are not overproduced at this stage . to see this , let us discuss gravitino production from the decay products of the inflaton . in models where supersymmetry is broken gravitationally , only a very small number of gravitinos can be tolerated , @xmath185 ( the exact value being dependent on the gravitino mass ) @xcite . the typical approach is to compute the production of gravitinos only after the thermal bath has formed . the dominant processes are @xmath186 scatterings with only one gravitino as outgoing particle ( and , hence , only one gravitationally suppressed vertex , while the other vertex is typically a gauge interaction ) . the rate of gravitino production follows from the boltzman equation @xmath187 where @xmath188 is the abundance of the ( mssm ) degrees of freedom in the thermal bath , and where the average cross section is of the order @xmath189 , where @xmath190 is a gauge structure constant . the right hand side decreases very rapidly with time , and the production at the highest possible temperature ( that is , at @xmath6 ) dominates . hence , only the production in the first hubble time is relevant , and the final result can be estimated as @xmath191 where @xmath192 is the hubble parameter at @xmath193 . this leads to the gravitino abundance @xmath194 and to the well known bound @xmath195 on the reheating temperature . this standard computation of gravitinos generated from the thermal bath neglects all the production which may have taken place during the thermalization stage . the underlying idea is that , during reheating , most of the energy is in the inflaton condensate , where the quanta ( loosely speaking ) do not have momentum , and hence can not scatter to produce gravitinos . while this may be true for a slow ( perturbative ) inflaton decay , this is certainly not the case for preheating / rescattering , where the distributions of the decay products form right after the end of inflation . these distibutions may be responsible for significant gravitino production , even before complete thermalization has taken place @xcite . the computation is now more difficult than in the thermal case @xcite . first of all , unlike the thermal computation , the result is expected to be model dependent . second , turbulent nonlinear processes are dominant right after preheating , so that it is possible that processes including more vertices give a sizeable contribution to the amount of gravitinos produced . however , we can obtain a conservative estimate by considering only @xmath186 tree level processes also in this case . for definiteness , let us take the model ( [ pot ] ) , ( [ int ] ) , with @xmath196 ( the value that we have studied above ) , and assume that the @xmath21 field produced at rescattering has a trilinear vertex with its femionic superpartner @xmath197 and another fermion @xmath198 . for instance , this could be a gaugino , if @xmath21 has gauge interactions . however , let us consider here a generic vertex with coupling constant @xmath199 and the interaction @xmath200 , mediated by the fermionic partner of @xmath21 . ( as a technical point , we consider production of transversal gravitinos , since the nature of the longitudinal component changes with time ) . we are interested in evaluating the production at the time @xmath201 , when the ( physical ) number density of quanta of @xmath21 is maximal . we first discuss whether the process we are considering is kinematically allowed . at the time @xmath202 , the non - gravitational vertex provides an effective mass for fermions of the order ( see fig . [ fig : fluc ] ) . @xmath203 the distributions of @xmath21 obtained from the lattice have a typical comoving momenum of the order of @xmath204 , which , at the time @xmath205 , corresponds to the physical momentum @xmath206 . hence , if @xmath207 , most of the quanta of @xmath21 will be able to produce gravitinos through the process we are considering . for higher values ( for example , if the second vertex is a gauge interaction ) , only the few quanta of @xmath21 with very high momenta can contribute to the production , so that this process is significantly suppressed . however , as the universe expands , @xmath208 decreases as @xmath209 , while the physical momenta @xmath210 decrease less . therefore , more and more quanta will have a sufficiently high momentum to produce a @xmath211 pair . indeed , since thermalization proceeds through particle fusion it has the effect of both increasing the typical momenta of the distributions and of decreasing the effective masses . ] for simplicity , @xmath212 is assumed in the following discussion ; we do not expect that the following conclusions will significantly change if a stronger coupling is considered . by proceeding as in the thermal case , we can estimate the number of gravitinos produced in the first hubble time after @xmath213 . ( again , the numerical values are taken from the lattice results ; @xmath214 denotes the physical number density of the @xmath21 quanta at the time @xmath213 . ) @xmath215 for sufficiently high @xmath216 , this value is actually incorrect , since it exceeds pauli blocking . assuming that the whole pauli sphere up to physical momentum @xmath217 is filled gives @xmath218 the number density of produced gravitinos is then the smaller between eqs . ( [ n321 ] ) and ( [ n322 ] ) , according to the value of @xmath219 . in the following , we assume @xmath220 , so that pauli blocking is reached and the number density of gravitinos is given by eq . ( [ n322 ] ) . the gravitino abundance is obtained by dividing the gravitino number density by the entropy . at the time @xmath202 , the distributions of the decay products are far from thermal ( being concentrated in the ir ) , so that their entropy is smaller than that of a thermal bath with the same energy . the entropy density can be computed from the lattice simulations to be approximately @xmath221 at this stage @xcite . however , the ( comoving ) entropy is expected to increase due to thermalization . if we convert the actual particle distribution instanteneously into the thermal distribution , the entropy would reach the maximal value @xmath222 allowed by energy conservation . the difference between the actual entropy density and @xmath223 gives rise to the dilution of the gravitino abundance during thermalization . ( further sources of dilution require extensions of the minimal model . ) therefore , the conservative estimate for the gravitino abundance is obtained by dividing the gravitino number density by @xmath224 where @xmath225 is the ( physical ) background energy density at the time @xmath202 . hence , the ratio @xmath226 is about @xmath227 orders of magnitude higher than the allowed limit . this is a serious concern , which has to be addressed in the model building of inflation . it can be resolved by introduction of extra radical assumptions . for instance , this gravitino abundance can be decreased by an entropy dilution . this happens if a massive species @xmath126 is produced at reheating , and it dominates the energy density of the universe for some time . when it decays , it leads to a significant amount of entropy , which dilutes the particle pieces produced directly at the inflaton decay . concretely , the entropy dilution leads to the decrease of the gravitino abundance @xmath228 . supposing that the universe is matter dominated between the times @xmath229 and @xmath230 , the ratio @xmath231 is decreasing as @xmath232 ( @xmath233 being the scale factor at the time @xmath234 ) . this entropy dilution could also occur through a secondary stage of inflation @xcite . in the specific toy model we have considered , a decrease of six orders of magnitude does not seem to be realistic , so that the production of gravitinos in this model appears to be a serious concern . however , it is important to remember that the result ( [ granont ] ) is very sensitive to the specific model considered , and that a case by case calculation is necessary . one of the motivations for studying the eos after preheating is related to the theory of modulated cosmological fluctuations . we briefly review the idea as it was presented in @xcite , and discuss the implications of our findings on the evolution of the eos for this mechanism . we leave the explicit calculations for subsequent publication . suppose that the coupling @xmath37 depends on some modulus field @xmath235 , ( as is typical in string theory ) @xmath236 during inflation the modulus field @xmath235 can be light , with a mass smaller than the hubble parameter during inflation @xmath237 gev . then , large scale fluctuations @xmath238 with an almost scale free spectrum are inevitably generated from inflation . the wavelength of fluctuations exceeds the size of the causal patch @xmath239 . as we have discussed above , the eos varies very quickly already at the beginning of the thermalization stage . the variation is a non monotonic function of the coupling @xmath240 , see for instance figs . [ fig : w1 ] and [ fig : tran ] . due to the large scale spatial fluctuations of the coupling @xmath241 , the change in the eos proceeds with a slight time shift in different hubble patches . this results in the generation of ( almost ) scale free scalar metric cosmological perturbations . to perform accurate calculations of the amplitude of modulated fluctuations , one needs to know the exact character of the transition from inflaton field to radiation . in the simplified picture of perturbative reheating , when the inflaton energy decays exponentially as @xmath242 , calculations of modulated fluctuations @xcite are based on linearization of the inflaton decay rate @xmath243 , which is linearly dependent on the coupling @xmath37 . however , as we have remarked , the decay of the inflaton field is typically more complicated , and the transition towards rd occurs very quickly ( well before thermalization completes ) . in addition , we stress that the time of the transition is a non monotonic function of @xmath37 . finally , although we focused only on the direct coupling of the inflaton to matter , the details of thermalization ( and of the evolution of the eos ) depend on the other interactions among the decay products ; the strength of these interactions are likely to be dependent on some modulus field as well , and they can also modulate cosmological perturbations . all these features have to be taken into account for precision computations of modulated fluctuations .

the exact time of this transition is a non - monotonic function of the coupling between the inflaton and the decay products , and it varies only very weakly ( around s ) as this coupling changes over several orders of magnitude . we finally argue that many questions of the thermal history of the universe should be addressed in terms of pre - thermalization , illustrating this point with a calculation of perturbative production of gravitinos immediately after chaotic inflation .

we study the out - of - equilibrium nonlinear dynamics of fields after post - inflationary preheating . during preheating , the energy in the homogeneous inflaton is exponentially rapidly transfered into highly occupied out - of - equilibrium inhomogeneous modes , which subsequently evolve towards equilibrium . the infrared modes excited during preheating evolve towards a saturated distribution long before thermalization completes . we compute the equation of state during and immediately after preheating . it rapidly evolves towards radiation domination long before the actual thermal equilibrium is established . the exact time of this transition is a non - monotonic function of the coupling between the inflaton and the decay products , and it varies only very weakly ( around s ) as this coupling changes over several orders of magnitude . this result is applied to refine the relation between the number of efoldings n and the physical wavelength of perturbations generated during inflation . we also discuss the implications for the theory of modulated perturbations from preheating . we finally argue that many questions of the thermal history of the universe should be addressed in terms of pre - thermalization , illustrating this point with a calculation of perturbative production of gravitinos immediately after chaotic inflation . we also highlight the effects of three - legs inflaton interactions on the dynamics of preheating and thermalization in an expanding universe .

hep-ph0507096

i

in this paper we studied the out - of - equilibrium nonlinear dynamics of the fields during and after preheating . this continues earlier works in @xcite . we use lattice numerical simulations of fully non - linear dynamics of interacting classical fields . in this investigation , we computed the evolution of the equation of state during preheating and the early thermalization stage . immediately after inflation , the eos is the one corresponding to inflaton domination . for a massive inflaton , we have matter domination , characterized by @xmath244 . after a very short time , the inflaton transfers its energy into inhomogeneous modes . at the first stage ( preheating ) inhomogeneous field fluctuations are copiously produced in the regime of parametric resonance . then the modes rescatter to redistribute the energy by cascading in the phase space . this process of classical wave turbulence can be rather long . this leads to a final stage , where the occupation numbers are small and the classical approximation breaks down . thermalization finishes when the quantum fields reach the ultimate thermal equilibrium . if all the participating fields are light , the final thermalized state corresponds to an eos of radiation , with @xmath245 . the transition between the matter and radiation dominated eos is hence typically supposed to occur on a ( relatively ) very long timescale . what we found in our numerical simulations is very different from this naive expectation . in fact , the eos jumps from matter domination to ( almost ) radiation domination immediately after the first stage of preheating , i.e. in a couple dozen inflaton oscillations ( @xmath87 sec each ) , long before thermal equilibrium has been established . in other words , the macroscopic eos is close to the one of radiation domination , while the microscopic state is far from thermal . this result is similar to the conclusion of @xcite regarding @xmath10 theory in flat spacetime . the sharp change of the eos we observed can be very conveniently related to the moment of energy transfer from the inflaton to the inhomogeneous radiation . as we mentioned , it is a very fast process , as is well - known from the theory of preheating , which takes place in only about @xmath0 sec . moreover , the time at which the transition occurs depends only weakly on the coupling @xmath37 between the inflaton and the other fields . the exact dependance is non - monotonic , and the transition time oscillates around @xmath246 sec ( as set by preheating ) for a very wide range of couplings . this result is drastically different from perturbative inflaton decay , where the transition timing is proportional to the coupling . \i ) the first is related to the generation of modulated cosmological fluctuations from preheating . it is conceivable @xcite that the strength of the inflaton interactions with its decay products is a function of some moduli fields as expected in string theory . fluctuations of the light moduli ( with mass smaller than @xmath247 gev ) are inevitably generated during inflation . this results in spatial variations of the couplings at large scales , well beyond the size of the causal ( hubble ) patch at the end of inflation . hence , the transition from inflation to radiation domination occurs at slightly diffferent times in different hubble patches , giving rise to scalar metric fluctuations . to calculate metric fluctuations from modulated perturbations , one needs to know the exact evolution of the eos , from the matter domination ( inflaton ) to the radiation domination ( light decay products ) stage . we found that the transition of the eos occurs sharply in a step - like manner . therefore one can introduce a time - like ( but spatially rippled ) hypersurface which divides two cosmological regimes , with @xmath244 and @xmath248 . metric fluctuations can be calculated using gr matching conditions across this hypersurface , similar to how it was done to calculate modulated fluctuations in hybrid inflation @xcite . \ii ) the second application of the eos history is related to the formula which links the number of efoldings during inflation @xmath9 and the present day physical wavelengths of fluctuations in terms of the logs of their momenta @xmath249 . indeed , the cosmological evolution of the scale factor @xmath250 is ultimately defined by the eos . refining the @xmath19 relation is mandatory to put precise observational constraints on inflationary models . in this paper we notice that a ( practically ) immediate transition from inflation to radiation domination is a common feature of inflationary models with preheating , either parametric resonance or tachyonic ones . equation ( [ deltadef ] ) , with our result ( [ finalrat ] ) , refines the @xmath19 relation . \iii ) the next note is related to the model building of inflaton interactions . in the majority of papers discussing inflaton decay , interactions with bosons are considered in the form of four - legs vertices of the type @xmath14 . these interactions are the dominant ones at the early stages of preheating , when the amplitude of the inflaton is large . ( we do not consider here nonrenormalizable interactions , which if present could be more important . ) however , they do not lead to a complete inflaton decay . a complete decay requires vertices with only one inflaton , as the yukawa interaction @xmath251 wih fermions , or the three - legs bosonic interaction @xmath252 ( where @xmath36 is a mass scale ) . as we have argued , these trilinear interactions are very natural in supersymmetric models . supersymmetry has the additional advantage of protecting the flatness of the inflaton potential from too large radiative corrections , which arise from the coupling of the inflaton to the light degrees of freedom . \iv ) finally , the early evolution of the light degrees of freedom from the decay of the inflaton can have very important consequences for the generation of particles far from thermal equilibrium . a particularly relevant application is the possible ( over)production of gravitinos from the decay products of the inflaton . although this is a perturbative generation , it can be very effective , since it occurs at very early times . traditionally , the limit @xmath253 is due to gravitinos produced only after the @xmath21 quanta have thermalized . however , a nonthermal distribution can also be responsible for gravitino overproduction @xcite . these inflaton decay products arise very rapidly , with an energy density much higher than @xmath254 ; although their initial distribution is far from thermal , we have seen that they can be responsible for a significant gravitino production , which in some cases exceeds by several orders magnitude the allowed bound . clearly , this is a less universal bound than the standard one , since it depends on the details of how the thermal bath is produced . ( for instance , the gravitino abundance can be diluted by entropy release during thermalization . ) in addition , the gravitino problem is avoided altogether if the gravitino mass is significantly smaller ( as in gauge mediated supersymmetry breaking ) or larger ( as in the simplest versions of the kklt model @xcite ) than the electroweak scale . still , this possible production must be addressed in many inflationary models . * acknowledgements*. we thank j. berges , j.f . dufaux , a. linde , a. mazumdar , and i. tkachev for useful discussions . gf and mp thank cita for its warm hospitality during different stages of this work . lk was supported by ciar and nserc . mp was supported in part by the doe grant de - fg02 - 94er40823 . r. allahverdi , phys . d * 62 * , 063509 ( 2000 ) [ arxiv : hep - ph/0004035 ] ; s. davidson and s. sarkar , jhep * 0011 * , 012 ( 2000 ) [ arxiv : hep - ph/0009078 ] ; r. allahverdi and m. drees , phys . d * 66 * , 063513 ( 2002 ) [ arxiv : hep - ph/0205246 ] . g. n. felder , j. garcia - bellido , p. b. greene , l. kofman , a. d. linde and i. tkachev , phys . lett . * 87 * , 011601 ( 2001 ) [ arxiv : hep - ph/0012142 ] ; g. n. felder , l. kofman and a. d. linde , phys . d * 64 * , 123517 ( 2001 ) [ arxiv : hep - th/0106179 ] . r. kallosh , l. kofman , a. d. linde and a. van proeyen , phys . d * 61 * ( 2000 ) 103503 [ arxiv : hep - th/9907124 ] , class . * 17 * ( 2000 ) 4269 [ arxiv : hep - th/0006179 ] ; g. f. giudice , a. riotto , and i. tkachev jhep * 9908 * ( 1999 ) 009 [ arxiv : hep - ph/9907510 ] , jhep * 9911 * ( 1999 ) 036 [ arxiv : hep - ph/9911302 ] ; h. p. nilles , m. peloso and l. sorbo , phys . rev . lett . * 87 * ( 2001 ) 051302 [ arxiv : hep - ph/0102264 ] , jhep * 0104 * ( 2001 ) 004 [ arxiv : hep - th/0103202 ] . j. ellis , a. linde and d. nanopoulos , phys . lett . * 118b * , 59 ( 1982 ) ; l.m . krauss , nucl . b227 * , 556 ( 1983 ) ; d. nanopoulos , k. olive and m. srednicki , phys . lett . * 127b * , 30 ( 1983 ) ; m. yu . khlopov and a. linde , phys . 138b * , 265 ( 1984 ) ; j. ellis , j. kim and d. nanopoulos , phys . lett . * 145b * , 181 ( 1984 ) ; j. ellis , g.b . gelmini , j.l . lopez , d.v . nanopoulos , and s. sarkar , nucl . b373 * , 399 ( 1992 ) ; m. kawasaki and t. moroi , progr . theor . phys . * 93 * , 879 ( 1995 ) . j. baacke , k. heitmann and c. patzold , phys . d * 58 * , 125013 ( 1998 ) [ arxiv : hep - ph/9806205 ] ; p. b. greene and l. kofman , phys . b * 448 * , 6 ( 1999 ) [ arxiv : hep - ph/9807339 ] ; g. f. giudice , m. peloso , a. riotto and i. tkachev , jhep * 9908 * , 014 ( 1999 ) [ arxiv : hep - ph/9905242 ] . p. b. greene and l. kofman , phys . d * 62 * , 123516 ( 2000 ) [ arxiv : hep - ph/0003018 ] . m. peloso and l. sorbo , jhep * 0005 * , 016 ( 2000 ) [ arxiv : hep - ph/0003045 ] . l. boubekeur , s. davidson , m. peloso and l. sorbo , phys . d * 67 * , 043515 ( 2003 ) [ arxiv : hep - ph/0209256 ] . for the entropy density we used the formula @xmath255 $ ] . see for example r. h. brandenberger , t. prokopec and v. mukhanov , phys . d * 48 * , 2443 ( 1993 ) [ arxiv : gr - qc/9208009 ] . d. h. lyth and e. d. stewart , phys . lett . * 75 * , 201 ( 1995 ) [ arxiv : hep - ph/9502417 ] ; l. kofman , a. d. linde and a. a. starobinsky , phys . lett . * 76 * , 1011 ( 1996 ) [ arxiv : hep - th/9510119 ] ; g. n. felder , l. kofman , a. d. linde and i. tkachev , jhep * 0008 * , 010 ( 2000 ) [ arxiv : hep - ph/0004024 ] .

we study the out - of - equilibrium nonlinear dynamics of fields after post - inflationary preheating . during preheating , we compute the equation of state during and immediately after preheating . it rapidly evolves towards radiation domination long before the actual thermal equilibrium is established . this result is applied to refine the relation between the number of efoldings n and the physical wavelength of perturbations generated during inflation .

we study the out - of - equilibrium nonlinear dynamics of fields after post - inflationary preheating . during preheating , the energy in the homogeneous inflaton is exponentially rapidly transfered into highly occupied out - of - equilibrium inhomogeneous modes , which subsequently evolve towards equilibrium . the infrared modes excited during preheating evolve towards a saturated distribution long before thermalization completes . we compute the equation of state during and immediately after preheating . it rapidly evolves towards radiation domination long before the actual thermal equilibrium is established . the exact time of this transition is a non - monotonic function of the coupling between the inflaton and the decay products , and it varies only very weakly ( around s ) as this coupling changes over several orders of magnitude . this result is applied to refine the relation between the number of efoldings n and the physical wavelength of perturbations generated during inflation . we also discuss the implications for the theory of modulated perturbations from preheating . we finally argue that many questions of the thermal history of the universe should be addressed in terms of pre - thermalization , illustrating this point with a calculation of perturbative production of gravitinos immediately after chaotic inflation . we also highlight the effects of three - legs inflaton interactions on the dynamics of preheating and thermalization in an expanding universe .

cond-mat0007358

i

the phase behavior of fluid mixtures in confined geometry has attracted abiding interest over many decades.@xcite the preferential interactions at the surfaces give rise to an enrichment of one component at the surface . in a semi - infinite system at phase coexistence , the thickness of this enrichment layer diverges at the wetting transition.@xcite upon approaching the wetting transition temperature from below the thickness of the enrichment layer might increase continuously ( second order wetting ) or jump from a microscopically thin layer to a macroscopic layer at the ( first order ) transition . this latter case is by far the most common experimentally . if the transition is of first order a continuation of the singularity persists also slightly above the wetting transition temperature . at a chemical potential ( partial pressure ) of the preferred species , which is smaller than the coexistence value ( undersaturation ) , a thin and a thick enrichment layer coexist . upon following this coexistence line ( prewetting ) to higher temperatures we decrease the difference in the enrichment layers of the coexisting phases and encounter a prewetting critical point . if a symmetric binary mixture is confined into a film with antisymmetric boundaries , i.e. , the upper surface attracts one species with exactly the same strength than the lower surface attracts the other species , no phase transition will occur close to the bulk critical point . upon decreasing the temperature the enrichment layers at both surfaces gradually develop and stabilize an @xmath3 interface in the center of the film ( `` soft mode '' phase ) . it is only close to the wetting transition temperature that the symmetry is spontaneously broken and the @xmath3 interface is localized close to one surface . this interface localization delocalization transition@xcite and the anomalous fluctuations of the delocalized @xmath3 interface in the `` soft mode '' phase have attracted recent interest@xcite and experimental realizations in terms of polymeric systems have been investigated.@xcite the application of experimental techniques ( e.g. , nuclear reaction analysis or neutron reflectometry ) is facilitated by the large length scale of the enrichment layers , which is determined by the molecules end - to - end distance @xmath4 . the macromolecular architecture also allows a successful comparison to the results of the mean field theory . the free energy cost of an @xmath3 interface @xmath5 on the length scale @xmath4 increases with chain length ; a fact that reduces the effect of interface fluctuation on the phase diagram for very long chains . the extended fractal shape of the polymers leads to a strong interdigitation of different molecules . the large number of neighbors with which a molecule interacts strongly suppresses composition fluctuations and imparts mean field behavior to the phase diagram except for the ultimate vicinity of the critical point . in the following we consider a symmetric binary polymer mixture confined into a thin film with antisymmetric boundaries and study how the wetting transition in the semi - infinite geometry affects the phase stability in a film . we employ self - consistent field calculations@xcite to calculate the phase diagram as a function of the incompatibility , the short range surface interactions , and the film thickness . our paper is arranged as follows : in the next section we describe the self - consistent field technique.@xcite then we present the phase behavior in a thin film with antisymmetric boundaries . for thick films or strong surface fields the phase diagram contains two critical points , corresponding to the prewetting critical points of each surface . interfacial profiles between the coexisting , laterally segregated phases are discussed , and the interfacial and line tensions are analyzed . the paper closes with a summary and a discussion of fluctuation effects .

we study the phase behavior of a symmetric binary polymer blend which is confined into a thin film . antisymmetric boundaries , where one surface attracts the component with the same strength than the opposite surface attracts the component , are applied . the phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition . the behavior close to the tricritical point , which separates phase diagrams with one and two critical points , is studied in the framework of a ginzburg two - dimensional profiles of the interface between the laterally coexisting phases are calculated , and the interfacial and line tensions analyzed .

we study the phase behavior of a symmetric binary polymer blend which is confined into a thin film . the film surfaces interact with the monomers via short range potentials . we calculate the phase behavior within the self - consistent field theory of gaussian chains . over a wide range of parameters we find strong first order wetting transitions for the semi infinite system , and the interplay between the wetting / prewetting behavior and the phase diagram in confined geometry is investigated . antisymmetric boundaries , where one surface attracts the component with the same strength than the opposite surface attracts the component , are applied . the phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition . for very thin films or weak surface fields one finds a single critical point at . for thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions . only below a triple point there is a single two phase coexistence region . when we increase the film thickness the two coexistence regions become the prewetting lines of the semi infinite system , while the triple temperature converges towards the wetting transition temperature from above . the behavior close to the tricritical point , which separates phase diagrams with one and two critical points , is studied in the framework of a ginzburg landau ansatz . two - dimensional profiles of the interface between the laterally coexisting phases are calculated , and the interfacial and line tensions analyzed . the effect of fluctuations and corrections to the self - consistent field theory are discussed . + pacs : 05.70-h , 68.45-gd , 83.80-es epsf

cond-mat0007358

r

coexistence between different phases occurs if the two phases have the same semi - grandcanonical energy at fixed temperature @xmath90 and exchange potential @xmath38 . since the bulk is symmetric with respect to exchanging @xmath91 , phase coexistence occurs at @xmath92 and the phase diagram is given implicitly by eq.([eqn : mu ] ) . the critical temperature is given by @xmath93 . of course , the scf theory yields a parabolic shape of the binodal close to the critical point , because it is a mean field theory . the location of the wetting transition can be determined via the young equation.@xcite the @xmath0 component wets the surface , if @xmath94 , where @xmath95 denotes the @xmath3 interface tension between the coexisting bulk phases , and @xmath96 and @xmath97 denote the excess surface free energies per unit area of a surface in contact with the @xmath0rich or @xmath1rich phase , respectively . in the strong segregation limit ( ssl ) , i.e. , @xmath98 , the @xmath3 interface tension takes the form:@xcite @xmath99 the excess surface free energy of a surface in contact with the @xmath0rich phase has two contributions . on the one hand the polymer conformations are restricted due to the presence of the surface and the decay of the density profile in the vicinity of the wall . since the @xmath0 and @xmath1 polymers have identical architecture this conformational entropy contribution to the excess surface free energy is , however , the same for the two species and does not enter into the difference @xmath100.@xcite on the other hand , the surface fields @xmath27 and @xmath28 give rise to a contribution to the excess surface free energy . if the surface is completely covered by the @xmath0 component , this contribution amounts to : @xmath101 the contribution of a surface covered by the @xmath1 component has the opposite sign . if the wetting transition occurs at high incompatibility it will be of first order . in this case the enrichment layer in the non wet state is negligible small . monte carlo simulations show that this is a good approximation.@xcite the young equation@xcite yields for the strength of the surface field at the wetting transition : @xmath102 if the integrated monomer - wall interaction @xmath103 which is the experimentally relevant quantity does not depend on the chain length @xmath21 , the left hand side of the equation will be large and the wetting transition in the binary polymer blend will occur in the strong segregation limit , i.e. , @xmath104 . this is in contrast to the behavior of mixtures of small molecules , where the cahn argument@xcite suggests that the wetting transition occurs close to the critical point . if the wetting transition is first order a prewetting lines emanates from the coexistence curve above the wetting transition temperature . along this line a thin and a thick enrichment layer coexist at undersaturation . for short range forces the prewetting line approaches the bulk coexistence curve linearly @xmath105.@xcite upon increasing the temperature , the difference in the thickness of the enrichment layers decreases and the prewetting line ends in a prewetting critical point . this prewetting behavior is pertinent to the phase behavior in thin films . only for very weak surface fields the wetting transition occurs close to the critical point . in this limit polymers exhibit a behavior similar to small molecules and the wetting behavior has been studied within the square gradient approximation.@xcite the latter assumes that the concentration varies slowly on the length scale @xmath4 . in this approximation the dependence of the bare surface free energy on the composition at the wall plays a central role . in our model , both the surface fields and the `` missing neighbor '' effect due to the decay of the monomer density at the wall give rise to a composition dependence of the bare surface free energy . @xmath106 where @xmath107 denotes the composition at the surface . other contributions to the bare surface free energy ( e.g. , terms proportional to the gradient of the composition at the surface ) are omitted . from this we identify the coefficients @xmath108 and @xmath109 . one central result of the square gradient theory is that wetting transitions close to the critical point are of second order and occur at @xmath110 ( a detailed derivation of this equation in the framework of the square gradient approximation can be found in ref@xcite ) . using the parameters of our model we rewrite this result in the form : @xmath111 for arbitrary strength of the surface fields we expect the variable @xmath112 to be a function of @xmath113 and the above equations describe the limit @xmath89 and @xmath114 . rather than focusing on the detailed composition profile across the enrichment layers at the surface much qualitative insight into the wetting behavior and the interface localization delocalization transition can be gained from characterizing the profile only by the distance @xmath115 between the wall and the @xmath3 interface . the dependence of the free energy per unit area the effective @xmath3 interface potential @xmath116 on the distance @xmath115 determines the wetting behavior . the short range surface fields distort the profile in the vicinity of the wall and give rise to an effective interaction which decays exponentially with the distance @xmath115 between the wall and the @xmath3 interface . qualitatively , the effective interface potential @xmath117 in the semi infinite system can be expanded in the form@xcite @xmath118 this expression retains only the lowest powers of @xmath119 , which are necessary to bring about the salient features of the wetting behavior . we neglect the temperature dependence of the coefficients @xmath120 and @xmath64 . @xmath121 denotes the length scale of the interaction between the surface and the @xmath3 interface ( cf . below ) . in principle , the numerical values of the coefficients can be obtained from fitting the results of our scf calculation to the equation above , but we can not offer analytical expression for the coefficients in the framework of the scft . in the following we discuss the qualitative behavior which arises from an effective interface potential of type ( [ eqn : eih ] ) . if the coefficient @xmath120 is negative the wetting transition is of second order and occurs when the coefficient @xmath122 changes its sign . following parry and evans@xcite we obtain the effective interface potential @xmath123 in a thin film by superimposing the interactions originating from each individual wall ; @xmath124 . the qualitative form of the potential is shown in the inset of fig.[fig : ginz](*a * ) , where the parameter @xmath125 is proportional to the distance of the interface from the center of the film . the values of @xmath126 correspond to various temperatures . a second order wetting transition gives rise to a second order interface localization delocalization transition . above the transition a single @xmath3 interface parallel to the surfaces is stable , the system is in the one phase region . below the transition , the system phase separates laterally into a phases where the @xmath3 interface is located close to the right or the left surface , respectively . the transition is of second order , i.e. , the composition difference between the coexisting phases increases continously . the transition temperature approaches rapidly the wetting transition temperature of the semi infinite system from below as we increase the film thickness . if the coefficient @xmath120 is positive , the form of @xmath117 leads to a first order wetting transition in the semi infinite system where a thin layer of thickness @xmath127 coexists with a macroscopically thick enrichment layer at @xmath128 . the prewetting critical point is located at @xmath129 and @xmath130 . the superposition of interactions between the @xmath3 interface and the opposing walls yields the effective interface potential in a thin film . the qualitative shape of the potential is shown in fig.[fig : ginz ] ( * a * ) schematically , while panel ( * b * ) presents the results of the scf calculations for @xmath80and @xmath131 . at low temperature we find phase coexistence between two laterally segregated phases . upon increasing the temperature we encounter a triple point at which these two phases , where the @xmath3 interface is located close to the right or the left surface , respectively , coexist with third phase , where the @xmath3 interface is delocalized at the center of the film . the location of the triple point ( @xmath132 and @xmath133 ) is given by the conditions @xmath134 and @xmath135 . for large film thickness this yields : @xmath136 ; i.e. , as the film thickness is increased the triple temperature converges exponentially fast to the temperature of the first order wetting transition of the semi infinite system from above . above this triple point there are two coexistence regions which each correspond to the prewetting coexistence of the semi infinite system . at @xmath137 we find the coexistence of a thick and a thin enrichment layer of the @xmath0 species at the @xmath0attracting surface and at @xmath138 a similar coexistence at the opposite surface . the two coexistence regions end in critical points close to the prewetting critical temperature of the semi infinite system . this first order interface localization delocalization behavior is the analogon of the first order wetting behavior of the semi infinite system . the different coexisting phases and their semi grandcanonical free energy @xmath69 are presented in fig.[fig : gfree ] for @xmath80 and @xmath139 . below the triple point @xmath140 the phases are well segregated . the monomer density profiles of the @xmath0component are depicted on the left side . upon following the coexistence curve to higher temperatures @xmath69 decreases . at the triple temperature , these two phases coexist with a third phase in which the interface is delocalized in the middle of the film . from there onwards , there are two coexistence regions at positive and negative values of the exchange potential @xmath38 . profiles of the two phases of the @xmath0poor coexisting region are presented on the right side . they consist of a thin ( upper right inset of fig.[fig : gfree ] ) and a thin ( lower right inset ) enrichment layer of the @xmath0 component at the surface that favors @xmath0 . for our strictly antisymmetric system , the concentration corresponding to the triple point always is exactly @xmath141 due to the symmetry . this has an interesting consequence if one cools a mixture at @xmath142 : while in the bulk this mixture would undergo a second order phase separation ( critical unmixing at @xmath143 , @xmath144 ) , one finds a single first order unmixing transition at @xmath145 . for asymmetric compositions , however , enrichment layers form gradually at a wall close to the bulk critical temperature . this stabilizes an @xmath3 interface , which runs parallel to the surfaces . the interface is located close to one surface ; its position is given by the composition of the system . close to the prewetting critical point , the enrichment layer may phase separate laterally into a thick and a thin enrichment layer . upon further cooling , we encounter a second phase transition where the thickness of the thick enrichment layer become comparable to the film thickness , i.e. , two almost completely segregated phases coexist . previous monte carlo simulations@xcite yield evidence that the interaction range @xmath146 in eq.([eqn : eih ] ) is determined by the bulk correlation length @xmath147 for large distances between the @xmath3 interface and the surface . this is in accord with the expectation that the @xmath3 interface profile in the outer wing is characterized by the length scale @xmath147 , which measures the decay of composition fluctuations in the bulk , rather than @xmath148 , which characterizes the slope of the @xmath3 interface profile at the center of the interface . this is further corroborated by our scf calculations . for two temperatures @xmath149 and @xmath150 above the critical temperature we have measured the free energy density @xmath151 as a function of the composition @xmath152 for various film thicknesses . around @xmath142 the free energy density can be expanded in the form @xmath153 . this yields for the effective @xmath3 interface potential @xmath154 . above the critical temperature we can estimate the effective range @xmath146 of the interaction according to @xmath155 . in fig.[fig : range ] we plot @xmath156 _ vs. _ the film thickness @xmath11 . for large film thicknesses the data exhibit an exponential dependence on the film thickness . upon increasing the temperature the interaction increases as the surfaces repel the @xmath3 interface stronger . for large @xmath11 the interaction range is compatible with @xmath157 , where we have used the behavior of the correlation length at strong segregation . for small @xmath11 , i.e. , distances between the @xmath3 interface and the surface which are not very much larger than the interfacial width @xmath158 , the interaction decays somewhat faster @xmath159 . at these intermediate distances a rather complicated interaction has been predicted.@xcite upon varying the sign of the coefficient @xmath120 we alter the order of the interface localization delocalization transition . at the tricritical point the order of the transition changes . for small values of @xmath120 we make a phenomenological ginzburg - landau ansatz for the effective interface potential @xmath160 in terms of the ( not normalized ) order parameter @xmath161 . for antisymmetric surface fields the effective interface potential is invariant under the transformations @xmath91 and must be an even function of @xmath162 . we assume the simplest ansatz which allows for three phase coexistence : @xmath163 the coefficients of this landau expansion ( [ eqn : landau ] ) can be derived from an effective interface hamiltonian ( [ eqn : eih ] ) : @xmath164 and @xmath165 , where @xmath166 denotes the @xmath7th derivative of the wall interface potential at the center of the film . this effective interface potential is depicted in fig.[fig : ginz](*a * ) . for @xmath167 ( inset ) the coefficient in front of the fourth order term @xmath168 is positive and we find a single second order phase transition at @xmath169 , @xmath170 , and @xmath171 . the case @xmath172 corresponds to a first order interface localization delocalization transition . for @xmath173 there is a three phase coexistence , at which the order parameter of the coexisting phases takes the values @xmath174 and @xmath175 . of course , the landau expansion is only appropriate for small @xmath176 . the parameter @xmath126 characterizes the temperature difference to this triple point . above the triple temperature , we find two coexistence regions and , eventually , we encounter two critical points at @xmath177 and order parameters @xmath178 . the critical chemical potential @xmath179 is given by @xmath180 . @xmath181 marks the tricritical transition ; the three coexisting phases collapse to a single one with order parameter @xmath182 . the critical and triple temperature coincide likewise . the fourth order coefficient in the ginzburg landau ansatz vanishes and the binodals close to the critical temperature open like @xmath183 with @xmath184 rather than with @xmath185 ( in mean field approximation ) . the qualitative features of this scenario are confirmed by the scf calculations . results for film thickness @xmath186 are presented in fig.[fig : d0.9a ] . panel ( * a * ) presents the phase diagram for various strength of the surface fields as a function of temperature and composition . for weak surface fields @xmath187 the interface localization delocalization transition is of second order and we obtain phase diagrams with one critical point at @xmath2 upon increasing the strength of the surface fields the critical point shifts to lower temperatures . around @xmath188 the binodal become flatter and are compatible with an exponent @xmath184 . in accordance with the ginzburg landau ansatz this marks the tricritical transition . at stronger surface fields we obtain phase diagrams with two critical points , which correspond to the prewetting critical points of the first order wetting transition in the semi infinite system . when we increase @xmath187 further , the two critical points , which are located symmetrically around @xmath142 , gradually move to lower temperatures , and higher or lower @xmath0 concentration , respectively . moreover , the temperature distance between the critical points and the triple point increases . fig.[fig : d0.9a](*b * ) depicts the behavior in terms of temperature and chemical potential difference . for second order interface localization delocalization transitions the coexistence chemical potential is @xmath92 by virtue of the symmetry with respect to exchanging @xmath91 . the same holds true for first order transitions below the triple point . at the triple point , however , the coexistence curve bifurcates into two symmetrical branches , which correspond to the prewetting lines of the semi infinite system . these lines end at critical points . upon increasing the strength of the surface fields the two critical points move to lower temperatures and larger absolute values of @xmath38 . to make closer connection to the ginzburg landau ansatz , we assume that the parameter @xmath176 , which drives the transition between the two types of phase diagrams , varies as a function of the surface field @xmath187 . then the ginzburg landau ansatz predicts that the quantities @xmath189 . this is tested in fig.[fig : crit ] . indeed , our scf calculations confirm that these quantities exhibit a very similar dependence on the surface field close to the transition . moreover , we estimate the critical value of the surface field to be @xmath190 . the corresponding power laws for the location of the critical points in the vicinity of tricriticality are also displayed in the figs.[fig : d0.9a](*a * ) and ( * b * ) . additionally , the inset of fig.[fig : crit ] shows that the binodals are characterized by an exponent @xmath184 at this tricritical value of the surface field . this provides strong evidence that the ginzburg landau ansatz captures the salient features of the tricritical transition . square gradient calculations@xcite and recent monte carlo simulations@xcite of the ising model indicate that the interface localization delocalization transition can be second order in thin films ( @xmath191 ) , even if the wetting transition is first order . within our ginzburg landau ansatz this finding can be rationalized as follows : close to the tricritical point the coefficient @xmath192 is small and the temperature of the triple point is given by the condition @xmath193 or @xmath194 . at the tricritical film thickness @xmath195 the coefficient @xmath196 changes its sign . neglecting terms of order @xmath197 we obtain : @xmath198 . if the semi infinite system exhibits a first order wetting transition the coefficients @xmath120 and @xmath64 are positive . hence , for large @xmath8 the coefficient @xmath176 is positive and leads to a first order interface localization delocalization transition . if the film width @xmath8 becomes comparable to the correlation length @xmath146 , however , the second term might drive the coefficient @xmath176 negative upon decreasing the film thickness . this is further explored in our scf calculations . in fig.[fig : thick](*a * ) we present the phase diagrams as a function of the film thickness at @xmath199 . for large film thickness @xmath200 , we find a first order interface localization delocalization transition . upon decreasing the film thickness the two critical points move to lower temperatures and closer to the symmetry axis . @xmath201 corresponds to the tricritical transition : there is only a single critical point but the binodals are describable by the exponent @xmath184 . upon further decreasing @xmath8 the critical temperature increases and the binodals assume parabolical shape . the corresponding coexistence curves are shown in fig.[fig : thick](*b * ) . the mechanism is most clearly visible in the effective @xmath3 interface potential @xmath202 , which is presented in fig.[fig : thick](*c * ) for @xmath203 as a function of the distance @xmath204 between the surface and the @xmath3 interface . for the largest film thickness @xmath205 @xmath123 is to a good approximation the effective potential of the nearest surface @xmath206 . @xmath203 corresponds to a temperature above the wetting ( triple ) transition but below the ( prewetting ) critical temperature of the thick film . each surface repels the @xmath3 interface and there is a shoulder in the effective interaction around @xmath207 . qualitatively , the scf calculations confirm that @xmath123 is the linear superposition of the interactions with each surface . when we decrease the film thickness larger values of @xmath115 become unfavorable , because the more the interface moves away from one surface the more it experiences the repulsion from the opposite surface . this results in a minimum of @xmath123 close to each surface . the shape of @xmath123 corresponds to a temperature below the triple point , i.e. , the interface is localized at one or the other surface . this shows that the triple temperature increases when we decrease the film thickness . the first order character of the transition is associated with the shoulder of @xmath206 around @xmath208 . obviously , this feature of @xmath123 disappears when the film thickness @xmath11 is of the order @xmath209 and we find second order transitions for smaller film thicknesses . this thickness dependence implies that the value @xmath210 obtained from the phase diagram of rather thin films @xmath186 is not a reliable approximation of the strength of the surface fields at which a tricritical wetting transition in the semi infinite system occurs . we have attempted to locate the strength of the surface fields at which the binodals are describable by the exponent @xmath184 as a function of the film thickness @xmath11 . the results of this procedure are collected in fig.[fig : thick](*d * ) . as we increase @xmath11 the surface fields at which the tricritical transition occurs decreases and the transition temperature approaches the critical point . for film thickness much larger than the range of interaction @xmath146 between the surface and the @xmath3 interface we expect a thin film to behave similar as a semi infinite system . close to the critical point , however , the range of interaction @xmath211 between the surface and the @xmath3 interface increases . therefore we anticipate very pronounced finite size effects even for film thicknesses which exceed the end to end distance @xmath4 by far . these difficulties prevent us from reliably estimating the tricritical wetting transition of the semi infinite system or comparing our calculations to the prediction ( [ eqn:2nd ] ) of the square gradient approximation.@xcite from the behavior at film thickness @xmath212 we conclude that critical wetting transitions in the semi infinite systems occur only for @xmath213 and @xmath214 in our model . qualitatively this is in agreement with scf calculations of carmesin and noolandi@xcite and monte carlo simulations@xcite which find only first order wetting transitions , except for the ultimate vicinity of the critical point which has not been investigated . the effective interface potential also determines the composition profiles across an interface between the laterally coexisting phases . at low temperatures the coexisting phases are almost completely segregated , i.e. , the thickness of the enrichment layers of the minority components are small . in this case the interface between the coexisting phases is planar and makes an angle @xmath215 with the surface . the contact angle @xmath215 is given by the young equation : @xmath216 the width @xmath158 of the interface between the coexisting phases is given by @xmath217 , where @xmath218 denotes the distance of the @xmath3 interface from the center of the film in each phase . at a second order interface localization delocalization transition the contact angle decreases linearly with the distance from the transition temperature @xmath126 and the composition difference between the coexisting phases vanishes like @xmath219 . hence , the width of the interface between the coexisting phases diverges like @xmath220 where @xmath221 is the mean field exponent for the correlation length upon approaching the critical point . close to a first order interface localization delocalization transition the effective interface potential exhibits more structure and this will modify the shape of the interface . within the mean field approximation the shape of the interface will minimize the effective interface free energy . approximating the @xmath3 interface profile as a sharp kink at the position @xmath115 we obtain for the free energy the effective interface hamiltonian:@xcite @xmath222}{k_bt } = \int { \rm d}y{\rm d}z\ ; \left\ { \sigma_{ab } \left(\sqrt{1 + \left(\frac{{\rm d}l}{{\rm d}y}\right)^2}-1 \right ) + g(l ) \right\ } \approx l \int { \rm d}y\ ; \left\ { \frac{\sigma_{ab}}{2 } \left(\frac{{\rm d}l}{{\rm d}y}\right)^2 + g(l ) \right\ } \label{eqn : h}\ ] ] where we have assumed that the position @xmath115 of the @xmath3 interface depends only on one lateral coordinate @xmath223 . the last approximation is valid if the angle between the interface and the surface is small . this is justified in the vicinity of the wetting transition , but the approximation breaks down at low temperatures , where the interface runs almost perpendicular to the surfaces . this effective interface hamiltonian yields the euler lagrange equation : @xmath224 which can be interpreted as the trajectory @xmath115 of a particle in the potential @xmath225 . to obtain a qualitative insight we extract the effective interface potential from the one dimensional scf calculations @xmath226 at @xmath227 . typical shapes of the interface between the coexisting phases for a film thickness @xmath80 are presented in fig.[fig : prof ] . far below the triple temperature the interface is planar and makes an angle @xmath215 with the surfaces . slightly below the triple temperature , however , the interfacial profile becomes @xmath228shaped , i.e. , the angle between the interface and the surface is larger in the vicinity of the surface than at the center of the film . note that the lateral interfacial width can exceed the film thickness by far in the vicinity of the triple temperature . the flatter portion in the center of the film is a consequence of the metastability of the third phase with composition @xmath142 or the additional local minima in @xmath123 , respectively . upon approaching the triple temperature the interfacial width becomes larger and the central portion of the profiles becomes flatter and more extended . this central portion might be conceived as a microscopic layer of the metastable delocalized phase ( @xmath142 ) , which completely wets the interface between the @xmath0-rich and @xmath1rich phase at the triple point . in the semi infinite system the interfacial tension varies smoothly upon rising the temperature through the wetting transition temperature . the excess free energy of the interface approaching the surface the line tension @xmath229 varies rapidly close the wetting transition . employing an effective interface hamiltonian of the form ( [ eqn : h ] ) , indekeu@xcite has obtained a simple expression for the line tension @xmath229 . @xmath230 where @xmath231 is the position of the minimum of @xmath117 close to the surface and @xmath232 . this formula has been applied to analyze recent experiments.@xcite the behavior of the line tension close to the wetting transition depends on the order of the transition and the range of the monomer wall interaction . for short range forces the line tension @xmath229 reaches a finite positive value at the wetting transition temperature , while it is negative far below the wetting temperature . the effective interface hamiltonian captures only the qualitative behavior . monte carlo simulations and scf calculations have shown that the properties of the @xmath3 interface depend on the distance @xmath115 from the surface . this gives rise to a position dependence of the tension@xcite and width of the @xmath3 interface.@xcite a more detailed description of the interface is provided by the two dimension composition profiles in fig.[fig : profs ] . due to the choice of basis functions the profiles are periodic in @xmath223 direction and only half the system is shown . in qualitative agreement with the considerations above , the interface between the @xmath0rich and @xmath1rich phases runs straight across the film at low temperatures ( @xmath233 and @xmath234 ) . the contact angle at @xmath235 is about @xmath236 . upon increasing the temperature the contact angle between the surface and the interface decreases and the interface becomes @xmath228shaped in the vicinity of the triple point . the scf calculations also reveal that the interface becomes broader when we increase the temperature . moreover , the width of the interface is broader in the vicinity of the surfaces than in the middle of the film . this effect is due to the reduction of the monomer density in the vicinity of the surface , which imparts a reduced effective incompatibility ( `` missing neighbor effect '' ) on the surface region . a similar effects has been observed in confined systems containing copolymers@xcite this effect gives rise to a negative contribution to the line tension when the interface approaches the surface . we decompose the free energy of systems containing two interfaces between an @xmath0rich and a @xmath1rich phase into bulk , surface and line contributions : @xmath237 note that the surface fields and the entropy loss of the chains at the surfaces give rise to a thickness dependence of the bulk free energy density @xmath238 . varying both @xmath9 and @xmath11 we have estimated the coefficients in our scf calculations and the results are displayed in fig.[fig : line ] . qualitatively similar to the behavior at a first order wetting transition the line tension changes its sign from negative to positive upon approaching the triple point temperature from below . the coefficient @xmath239 decreases as we approach the triple point . to a first approximation one would expect a behavior of the form @xmath240 . the data are also compared to indekeu s formula ( [ eqn : ind ] ) . in order to apply the formula to thin films , we extend the integration only to the middle of the film and we shift the constant @xmath241 accordingly to @xmath242 in the dimensionless units of the scf calculations we obtain : @xmath243 this approximation for a thin film gives a reasonable estimate for the temperature dependence and the order of magnitude of the line tension ; however , the value of the lines tension in a thin film is systematically underestimated . when we apply the above approximation to thicker films the value of the line tension increases . if we use the film thickness @xmath205 instead of @xmath80 the approximation yields @xmath244 instead of @xmath245 . unfortunately , we are unable to extend our scf calculations to larger film thicknesses . in addition to the finite film thickness there are other effects which might upset the comparison between the scf calculations and the effective hamiltonian description : it is unclear how accurate the identification of the effective interface potential via @xmath246 is . this identification of the interface position via the absorbed amount is a good approximation for large distances between the surface and the @xmath3 interface . in this case , the composition profile across the @xmath3 interface is well describable by the interfacial profile between the coexisting bulk phases . if the @xmath3 interface is close to the surface , however , the profile becomes strongly distorted ( cf . fig.[fig : gfree ] ) and the definition of the interface position @xmath115 is somewhat ambiguous , but this is exactly the region which gives the dominant contribution to the line tension . moreover there are non local contributions to the free energy , e.g. , due to the conformational entropy . the polymers change their conformation as to fill the wedge shaped volume between the surface and the @xmath3 interface . this differ from the behavior close to a surface or an @xmath3 interface and gives rise to a contribution to the line tension , which is only partially described by the effective interface hamiltonian .

we calculate the phase behavior within the self - consistent field theory of gaussian chains . over a wide range of parameters when we increase the film thickness the two coexistence regions become the prewetting lines of the semi infinite system , while the triple temperature converges towards the wetting transition temperature from above . landau ansatz .

we study the phase behavior of a symmetric binary polymer blend which is confined into a thin film . the film surfaces interact with the monomers via short range potentials . we calculate the phase behavior within the self - consistent field theory of gaussian chains . over a wide range of parameters we find strong first order wetting transitions for the semi infinite system , and the interplay between the wetting / prewetting behavior and the phase diagram in confined geometry is investigated . antisymmetric boundaries , where one surface attracts the component with the same strength than the opposite surface attracts the component , are applied . the phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition . for very thin films or weak surface fields one finds a single critical point at . for thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions . only below a triple point there is a single two phase coexistence region . when we increase the film thickness the two coexistence regions become the prewetting lines of the semi infinite system , while the triple temperature converges towards the wetting transition temperature from above . the behavior close to the tricritical point , which separates phase diagrams with one and two critical points , is studied in the framework of a ginzburg landau ansatz . two - dimensional profiles of the interface between the laterally coexisting phases are calculated , and the interfacial and line tensions analyzed . the effect of fluctuations and corrections to the self - consistent field theory are discussed . + pacs : 05.70-h , 68.45-gd , 83.80-es epsf

cond-mat0007358

i

we have calculated the phase diagram of a symmetric polymer mixture confined to a thin film in mean field approximation . the left surface attracts the @xmath0 component with the same strength than the right surface the @xmath1 component of the mixture . the calculations reveal a rich interplay between the phase behavior in confined geometry and the wetting behavior of the semi infinite system . if the wetting transition of the semi infinite system is second order so is the interface localization delocalization transition in a thin film.@xcite at stronger surface fields the wetting transition in the semi infinite system is first order and this gives rise to a first order interface localization delocalization transition in a thick film . the phase diagram in a thin film exhibits two critical points symmetric around @xmath142 . these correspond to the prewetting critical points of the semi infinite system . at lower temperatures we encounter a triple point at which an @xmath0rich phase , a phase where the @xmath3 interface is located in the center of the film , and a @xmath1rich phase coexist . this triple temperature converges from above to the wetting temperature as we increase the film thickness . below the triple temperature there is a single coexistence region between an @xmath0rich and a @xmath1rich phase . the interplay between the prewetting behavior and the phase diagram in a thin film has been considered for symmetric surface fields ( capillary condensation),@xcite but to the best of our knowledge phase diagrams with two critical points far below the bulk critical temperatures in films with antisymmetric surface fields have neither been discussed analytically@xcite nor observed in experiments or simulations . as we shall discuss below , we do not expect corrections to the mean field calculations to alter our conclusions qualitatively and we hope our predictions to be confirmed by experiments or simulations . qualitatively , the interplay between the prewetting behavior and the phase diagram in a film with antisymmetric boundaries is not specific to polymer blends but is rather characteristic of all binary mixtures . symmetric polymer mixtures might , however , be especially suitable model systems for exploring these effects experimentally and we hope our detailed calculations to provide some guidance . the existence of the triple point also influences the shape of the interface between the laterally segregated , coexisting phases . at low temperatures the interfaces runs straight across the film and the angle between the interface and the surface is given by the macroscopic contact angle . upon approaching the triple point from below , however , the profiles becomes s shaped with a flatter portion at the center of the film . this signals the metastability of the third delocalized phase with composition @xmath142 . at the triple point the delocalized phase completely wets the interface between the @xmath0rich and @xmath1rich phase . upon approaching the triple temperature from below the line tension changes sign from negative to positive . the properties of the interface between the coexisting phases are in qualitative agreement with the results on an effective hamiltonian description . in thin films the interface localization delocalization transition might be of second order even though the wetting transition is of first order . this has been predicted in the framework of a square gradient approach by swift _ et al._,@xcite and is in accord with simulations of the ising model.@xcite a similar behavior is found in our self - consistent field calculations for polymer blends . for our model second order wetting transitions are restricted to the ultimate vicinity of the critical point of the bulk while second order interface localization delocalization transitions can be observed far below the bulk critical temperature for film thickness comparable to the end to end distance @xmath4 . this leads us to anticipate very strong finite film thickness effects close to a second order wetting transition even for film thicknesses which exceed @xmath4 by far . of course , our self - consistent field calculations neglect fluctuations . in the vicinity of the critical point we rather expect 2d ising critical behavior with much flatter binodals than the parabolic binodals of the mean field universality class . the ginzburg criterion ensures , however , that these composition fluctuations are only important in the ultimate vicinity of the critical point @xmath247 , where the reduced chain length @xmath248 measures the degree of interdigitation . as we increase @xmath249 the relative temperature distance from the critical point for which these composition fluctuations are important decreases . for small and intermediate chain lengths an interesting interplay between mean field , 3d ising and 2d ising critical behavior is anticipated . in the limit of large interdigitation , however , we expect composition fluctuations to be only of minor importance for most part of the phase diagram . moreover , the interface profiles in the self - consistent field calculations are ideally flat , i.e. , there are no capillary waves of the interfaces . the importance of these fluctuations is not restricted to the vicinity of critical points . on the one hand , capillary waves lead to a broadening of profiles across the interface . the `` internal '' @xmath3 interfaces run parallel to the surfaces and the effective interaction between the @xmath3 interface and the surface imparts a long wavelength cut off @xmath250 to the spectrum of capillary waves . hence , the interfacial width does not grow unbound as we increase the lateral system size , but still the self - consistent field calculations might severely underestimate the width of the `` internal '' @xmath3 interfaces.@xcite within a convolution approximation the apparent width @xmath251 of the @xmath3 interface , which is observed in experiments or simulations , is related to the intrinsic width @xmath252 in the scf calculations via : @xmath253 where we have used the temperature dependence of the interfacial tension and width for strong segregation to obtain the last expression.@xcite @xmath1 is a short length cut off for the capillary wave spectrum . analytical calculations and recent monte carlo simulations show that @xmath1 tends to @xmath254@xcite or @xmath255,@xcite respectively , in the strong segregation limit . even though the second term in the above equation is only of the order @xmath256 the increase of the apparent interfacial width due to capillary waves typically is of the order of the intrinsic width for experimentally relevant chain lengths.@xcite on the other hand , capillary waves renormalize the effective interaction between the surface and the @xmath3 interface . for instance , the effective interaction range @xmath146 is increased to @xmath257 , where the capillary parameter@xcite @xmath258 measures the strength of fluctuation effects and decreases like @xmath259 . at weak segregation @xmath260 and @xmath261 and the capillary parameter increases like @xmath262^{-1/2}$ ] . in the ultimate vicinity of the critical point the mean field theory breaks down and we expect a crossover to a constant value.@xcite the divergence of @xmath263 upon approaching the critical point is cut off around @xmath264 , in accord with the ginzburg criterium for the crossover from mean field to ising critical behavior . in the strong segregation limit the correlation length @xmath147 approaches the temperature independent limit @xmath265 and the capillary parameter scales like @xmath266 $ ] . conformational changes are incompletely described by our self - consistent field calculations . within the gaussian chain model the lateral extension @xmath267 of a molecule parallel to the surfaces remains always unperturbed , i.e. , it is independent of the local composition , the distance between the molecules and the surface , and the film thickness . experiments and monte carlo simulations , however , do reveal a dependence of the lateral chain extension on the parameters above . partially , some of these effects can be rationalized as follows : if the film thickness is very thin the lateral chain extension @xmath267 has to increase as to restore a constant monomer density . this increase of the lateral chain extensions occurs if @xmath268 or @xmath269 . under these conditions the chains are quasi two dimensional and the density of monomers belonging to the same chain inside the coil volume is not small . @xcite an @xmath0chain in a @xmath1rich environment shrinks as to exchange energetically unfavorable intermolecular contacts with contacts along the same chain . by reducing its size it increases the density of its own monomers inside the coil volume . the energy gain upon shrinking is counterbalanced by the loss of conformational entropy . scaling arguments , monte carlo simulations and scf calculations@xcite yield for the relative reduction of a minority chain in the strong segregation limit : @xmath270 . in the limit of infinite interdigitation @xmath271 the above correction to the scf calculations become small . however , even for experimentally relevant chain lengths finite @xmath87effects might give rise to sizable corrections to the scf calculations ( e.g. , broadening of the apparent width of @xmath3 interfaces by capillary waves ) . besides finite @xmath87effects there are other corrections which are not captured by the scf calculations and which remain important even in the limit of infinite interdigitation . the finite compressibility of the polymeric fluid , for instance , gives rise to packing effects at the surfaces . the monomer density profile in the vicinity of the wall is determined by an intricate interplay between equation of state effects , loss of conformational entropy , fluid like packing effects and surface fields . these effects are not included in the scf calculations of gaussian chains , but require a detailed consideration of the molecular architecture and fluid like packing structure . however , we do not expect these effects to change our conclusions qualitatively . likewise , it is difficult to find an experimental realization of a symmetric mixture confined into a film with antisymmetric boundaries . the effects of deviations from perfectly antisymmetric surfaces and the crossover between capillary condensation ( for strictly symmetric boundary fields ) to interface localization delocalization has been explored in the framework of our model.@xcite this study shows that phase diagrams with two critical points also occur for nearly antisymmetric surface fields . the stronger the order of the wetting transition ( the more extended the prewetting line ) the more stable is the topology of the phase diagram against small deviations from perfect antisymmetry . 99 r. evans , j.phys.cond.matter * 2 * , 8989 ( 1990 ) . a.o . parry , j.phys.condens.matter * 8 * , 10761 ( 1996 ) . cahn , j.chem.phys . * 66 * , 3667 ( 1977 ) . m. schick , liquids at interfaces , les houches , session xlviii , j. charvolin , j.f . joanny , and j. zinn - justin ( eds ) , elsevier , amsterdam ( 1990 ) . s. dietrich , phase transitions and critical phenomena , vol 12 , c. domb and j. lebowitz ( eds ) academic press , london ( 1988 ) . sullivan , m.m . telo da gamma , fluid interfacial phenomena , c.a . croxton , new york , wiley ( 1986 ) . de gennes , wetting statics and dynamics , rev.mod.phys . * 57 * , 827 ( 1985 ) . f. brochard wyart and p .- g . de gennes , acad.sci . paris * 297 * , 223 ( 1983 ) . a.o . parry and r. evans , phys.rev.lett . * 64 * , 439 ( 1990 ) , physica * a 181 * , 250 ( 1992 ) . swift , a.l . owczarek , and j.o . indekeu , europhys.lett . * 14 * , 475 ( 1991 ) . k. binder , d.p . landau , and a.m. ferrenberg , phys.rev.lett . * 74 * , 298 ( 1995 ) ; phys.rev . * e 51 * , 2823 ( 1995 ) . albano , k. binder , d.w . heermann , and w. paul , surf.sci . * 233 * , 151 ( 1989 ) . indekeu , a.l . owczarek , and m.r . swift , phys.rev.lett . * 66 * , 2174 ( 1991 ) . a.o . parry and r. evans , phys.rev.lett . * 66 * , 2175 ( 1991 ) . j. rogiers and j.o . indekeu , europhys.lett . * 24 * , 21 ( 1993 ) . e. carlon and a. drzewinski , phys.rev.lett . * 79 * , 1591 ( 1997 ) . t. kerle , j. klein , and k. binder , phys.rev.lett . * 77 * , 1318 ( 1996 ) , europ . j. b*7 * , 401 ( 1999 ) . m. sferrazza , m. heppenstall butler , r. cubitt , d. bucknall , j. webster , r.a.l . jones , phys.rev.lett . * 81 * , 5173 ( 1998 ) ; m. sferrazza , c. xiao , r.a.l . jones , g.d . bucknall , j. webster , j. penfold , phys.rev.lett . * 78 * , 3693 ( 1997 ) . a. werner , f. schmid , m. mller , and k. binder , j.chem.phys . * 107 * , 8175 ( 1997 ) . a. budkowski , adv . polymer sci . * 148 * , 1 ( 1999 ) . k. binder , adv . polymer sci . * 138 * , 1 ( 1999 ) . e. helfand and y. tagami , j.chem.phys . * 56 * , 3592 ( 1972 ) . j. noolandi and k.m . hong , macromolecules * 14 * , 727 ( 1981 ) . l. schlangen , f.a.m . leermakers , and l.k . koopal , j.chem.soc.faraday trans . * 92 * , 579 ( 1996 ) . matsen , j.chem.phys . * 106 * , 7781 ( 1997 ) . t. geisinger , m. mller , and k. binder , j.chem.phys . * 111 * , 5241 and 5251 ( 1999 ) . m. mller , k. binder , and e.v . albano , physica * a 279 * , 188 ( 2000 ) . m. mller , k. binder , and e.v . albano , europhys.lett . * 50 * ( jun , 15 ) ( 2000 ) . m. mller , macromolecules * 31 * , 9044 ( 1998 ) . m. mller , macromol . theory simul . ( feature article ) * 8 * , 343 ( 1999 ) . t. young , philos.trans.r.soc . ( london ) * 5 * , 65 ( 1805 ) . semenov , j.phys . ii ( france ) * 6 * , 1759 ( 1996 ) . m. mller and k. binder , macromolecules * 31 * , 8323 ( 1998 ) . e.h . hauge and m. schick , * b 27 * , 4788 ( 1983 ) . i. schmidt and k. binder , j.physique * 46 * , 1631 ( 1985 ) . h. nakanishi and p. pincus , j.chem.phys . * 79 * , 997 ( 1983 ) . a.m. ferrenberg , d.p . landau , and k. binder , phys.rev . * e 58 * , 3353 ( 1998 ) . i. carmesin and j. noolandi , macromolecules * 22 * , 1689 ( 1989 ) . huse , w. van saarloos , and j.d . weeks , phys.rev . * b 32 * , 233 ( 1985 ) . indekeu , physica * a 183 * , 439 ( 1992 ) ; j.o . indekeu , int.j.mod.phys . * b 8 * , 309 ( 1994 ) . wang , s. betelu , and b.m . law , phys.rev.lett . * 83 * , 3677 ( 1999 ) . fisher and h. nakanishi , j.chem.phys . * 75 * , 5857 ( 1981 ) . h. nakanishi and m.e . fisher , j.chem.phys . * 78 * , 3279 ( 1983 ) . d. nicolaides and r. evans , phys.rev . * b 39 * , 9336 ( 1989 ) . r. evans and u. marini bettolo marconi , phys . rev * a 32 * , 3817 ( 1985 ) . semenov , macromolecules * 26 * , 6617 ( 1993 ) ; _ ibid _ * 27 * , 2732 ( 1994 ) . a. werner , f. schmid , m. mller , and k. binder , phys.rev . * e 59 * , 728 ( 1999 ) . shull , a.m. mayes , and t.p . russell , macromolecules * 26 * , 3939 ( 1993 ) . d.s . fisher and d.a . huse , phys.rev . * b 32 * , 247 ( 1985 ) . fisher and h. wen , phys.rev.lett . * 68 * , 3645 ( 1992 ) . however , a non vanishing stiffness of the molecule gives rise to an additional change in the lateral extension @xmath267 close to the film surface . this orientation effects is not describable in the gaussian chain model and persists also for thick films . , , and as a function of the surface field . in agreement with the ginzburg landau ansatz all quantities show the same dependence on the parameter . the dashed line is only a guide to the eye . the location of the critical surface field is indicated . . the inset display the behavior of the binodals for @xmath273 . the curve corresponds to the scf calculations , while the dashed line indicates the with . ( * a * ) phase diagram for @xmath131 and various film thicknesses @xmath8 . for @xmath205 and @xmath274 the interface localization delocalization transition is first order , @xmath275 corresponds to a tricritical transition , while the transition is second order for @xmath276 . ( * b * ) phase diagram as a function of temperature and chemical potential for the same parameters than in ( * a * ) . ( * c * ) effective interface potential @xmath277 at @xmath278 as a function of the film thickness @xmath8 for @xmath203 . ( * d * ) surface field ( circles ) and temperature ( squares ) of the tricritical transition as a function of the film thickness @xmath8 .

we find strong first order wetting transitions for the semi infinite system , and the interplay between the wetting / prewetting behavior and the phase diagram in confined geometry is investigated . for very thin films or weak surface fields one finds a single critical point at . for thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions . only below a triple point there is a single two phase coexistence region . the effect of fluctuations and corrections to the self - consistent field theory are discussed .

we study the phase behavior of a symmetric binary polymer blend which is confined into a thin film . the film surfaces interact with the monomers via short range potentials . we calculate the phase behavior within the self - consistent field theory of gaussian chains . over a wide range of parameters we find strong first order wetting transitions for the semi infinite system , and the interplay between the wetting / prewetting behavior and the phase diagram in confined geometry is investigated . antisymmetric boundaries , where one surface attracts the component with the same strength than the opposite surface attracts the component , are applied . the phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition . for very thin films or weak surface fields one finds a single critical point at . for thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions . only below a triple point there is a single two phase coexistence region . when we increase the film thickness the two coexistence regions become the prewetting lines of the semi infinite system , while the triple temperature converges towards the wetting transition temperature from above . the behavior close to the tricritical point , which separates phase diagrams with one and two critical points , is studied in the framework of a ginzburg landau ansatz . two - dimensional profiles of the interface between the laterally coexisting phases are calculated , and the interfacial and line tensions analyzed . the effect of fluctuations and corrections to the self - consistent field theory are discussed . + pacs : 05.70-h , 68.45-gd , 83.80-es epsf

1010.6036

i

geometric representation of graphs is a beautiful area where combinatorial optimization , graph theory and semidefinite optimization meet and connect with many other research areas . in this paper , we start by studying geometric representations of graphs where each node is mapped to a point on a hypersphere so that each edge has unit length and the radius of the hypersphere is minimum . lovsz @xcite proved that this graph invariant is related to the lovsz theta number of the complement of the graph via a simple but nonlinear equation . we show that this tight relationship leads to min - max theorems and to a `` dictionary '' to translate existing results about the theta function and its variants to the hypersphere representation setting and vice versa . based on our approach , we derive a weighted version of the hypersphere number of a graph and deduce related min - max theorems . our viewpoint allows us to make new connections , strengthen some facts and correct some inaccuracies in the literature . after observing that the hypersphere number of a graph is equal to the radius of the smallest euclidean ball containing a unit - distance representation of the graph , we propose generalizations of the underlying optimization problems . given a graph , the generalized optimization problem seeks the smallest ellipsoid of given shape which contains a unit - distance representation of the graph . we finally show that at this end of the new spectrum of unit - distance representations , arbitrary positive semidefinite forms describing the shapes of the ellipsoids yield np - hard geometric representation problems .

we derive and prove min - max theorems . this framework allows us to derive a weighted version of the hypersphere number of a graph and a related min - max theorem . then , we connect to sandwich theorems via graph homomorphisms . we present and study a generalization of the hypersphere number of a graph and the related optimization problems . the generalized problem involves finding the smallest ellipsoid of a given shape which contains a unit - distance representation of the graph . we prove that arbitrary positive semidefinite forms describing the ellipsoids yield np - hard problems .

we study the relationship between unit - distance representations and lovsz theta number of graphs , originally established by lovsz . we derive and prove min - max theorems . this framework allows us to derive a weighted version of the hypersphere number of a graph and a related min - max theorem . then , we connect to sandwich theorems via graph homomorphisms . we present and study a generalization of the hypersphere number of a graph and the related optimization problems . the generalized problem involves finding the smallest ellipsoid of a given shape which contains a unit - distance representation of the graph . we prove that arbitrary positive semidefinite forms describing the ellipsoids yield np - hard problems .

1610.03695

i

in this paper , we have investigated the statics and dynamics of a compressible bilayer vesicle . first we have calculated a free energy matrix in terms of linear perturbations in local curvature and local densities . calculating the eigenvalues of the free energy matrix , we performed the stability analysis by varying the curvature - density coupling parameter @xmath127 , and the lipid density difference between the two monolayers @xmath120 . as a result , we identified two different instabilities : one affecting the small-@xmath123 modes and the other influencing the large-@xmath123 modes . onsager s variational principle offers an universal framework for obtaining the dynamical equations for soft matter , and it has been used to derive the dynamical equations of the compressible bilayer vesicle . the dynamical matrix @xmath223 in eq . ( [ eq : full_dynamical_matrix ] ) gives the relaxation rates for a vesicle whose inside and outside fluids are characterized by different viscosities . the three relaxation modes are coupled to each other as a consequence of the bilayer and spherical structure of the vesicle . assuming that one of the relaxation modes is much faster than the other two , we derived the dynamical equation for the slower modes in eq . ( [ eq : reduced_dynamical_matrix ] ) . we focused on the effect of viscosity contrast @xmath260 on the relaxation rates , and found that it linearly shifts the cross - over @xmath123 mode between the bending and the slipping relaxations [ see eq . ( [ crossovermode ] ) ] . as @xmath225 is increased , the relaxation rate of the bending mode decreases , while that of the slipping mode remains almost unaffected . for parameter values close to the unstable region , some of the relaxation modes are dramatically reduced . for example , as they approach the region of large-@xmath123 instability , we find an unusual behavior of the relaxation rate as shown in fig . [ fig : unstable_dynamics](b ) . although the viscosity contrast in vesicles and rbcs has been discussed in some experiments @xcite , we have derived here the exact relaxation rates of a compressible bilayer vesicle for an arbitrary @xmath225-value . in experiments , a commonly encountered case is where the inside viscosity is slightly larger than the outside @xmath298 , for which the bending mode is slowed down and cross - over mode @xmath274 becomes larger . for even larger viscosity contrast ( @xmath299 ) , the relaxation is entirely dominated by the bending mode . for @xmath300 , on the other hand , @xmath274 does not depend on @xmath225 and the relaxation rate of the bending modes is slightly increased . our result clearly shows that the viscosity contrast significantly affects the dynamical behavior of vesicles . in the present work , the vesicle stability was analyzed in terms of the curvature - density coupling parameter @xmath127 , and the lipid density difference between the monolayers @xmath120 . whereas the large-@xmath123 instability is induced only by @xmath127 , the small-@xmath123 instability could be triggered by changing either @xmath127 or @xmath120 . since the large-@xmath123 instability corresponds to small wavelength deformations , it leads to the stabilization of small buds or tube - like deformations . for parameter ranges close to the yellow region in fig . [ fig : stability ] , we predict that the small-@xmath123 modes slow down significantly . although it would be experimentally challenging , the control of the number of lipids in each monolayers enables the change of the parameter @xmath120 . extending the work by schneider _ et al . _ @xcite , milner and safran derived the bending relaxation rate in vesicles and microemulsion droplets @xcite . in their work , however , the membrane was assumed to be an incompressible 2d sheet immersed in fluids having the same viscosity on either side of the membrane . this case is equivalent to a bilayer that moves together as a single entity with no difference in the number of molecules in the upper and lower leaflets , i.e. @xmath99 . the bending relaxation rate obtained by milner and safran corresponds to a limiting case of eq . ( [ eq : limit1 ] ) when @xmath242 . the slipping relaxation rates for planar bilayers was originally discussed by seifert and langer who included the dissipation due to inter - monolayer friction @xcite . as mentioned before , all the results obtained for the planar membrane case can be reproduced from our results by setting @xmath301 ( @xmath302 being a wavenumber ) and taking the limit of @xmath277 . comparing the free energy employed by seifert and langer @xcite , we see that the bending rigidity @xmath55 in eq . ( [ eq : freeenergy ] ) corresponds to the renormalized bending rigidity @xmath303 in their free energy . moreover , the coupling parameter @xmath56 in eq . ( [ eq : freeenergy ] ) can be interpreted as the quantity @xmath304 in ref . @xcite , where @xmath258 is the distance between the bilayer midsurface and the neutral surface in one of the monolayers . the effective thickness of the membrane can be controlled either by changing the length of the lipid tails , or by attaching a layer of other molecules or polymers . for example , rbcs have a network of spectrin proteins attached on the cytosolic side which might effectively alter the membrane thickness . in general , the parameter @xmath56 can be regarded as the coupling strength between the composition of the adsorbed molecule and the local curvature @xcite . it is worthwhile to mention that , even though we have discussed only the case when the vesicle size is @xmath244 @xmath117 m , our results can be readily used to predict the relaxation behavior of vesicles of other sizes , provided that the parameters @xmath305 , @xmath306 , @xmath127 , and @xmath230 are scaled appropriately . for smaller vesicles such as @xmath307 @xmath117 m , the physically relevant @xmath123-range is reduced , and even small changes in viscosity contrast significantly affects the relaxation behavior . vesicles in biological systems usually belong to this size range . the effects of surface tension on the relaxation dynamics of membranes were investigated in some of the previous works @xcite . in general , the surface tension makes the small-@xmath123 relaxation of the bending mode faster . _ studied the dynamics of fluid membranes with general curved shapes , not restricted to a quasi - spherical vesicle and also a membrane with free or internal boundaries @xcite . they also accounted for the 2d viscosity of the membrane monolayers , which has been neglected in our work . based on the previous results , we expect that including the membrane 2d viscosity will slow down the large-@xmath123 slipping relaxation modes @xcite . as a future work , it is interesting to consider the situation where the internal material is a viscoelastic fluid as investigated in the experiment @xcite . although , the viscoelasticity of the membrane itself has been taken into account by some of the previous works @xcite , the viscoelasticity of the fluid inside has not yet been studied . one can expect that the existence of different timescales due to the viscoelasticity of the inner fluid will make the dynamics of the vesicle much richer @xcite . t.v.s.k . thanks tokyo metropolitan university for the support provided through the co - tutorial program . s.k . acknowledges support from the grant - in - aid for scientific research on innovative areas _ fluctuation and structure _ " ( grant no . 25103010 ) from the ministry of education , culture , sports , science , and technology of japan , the grant - in - aid for scientific research ( c ) ( grant no . 15k05250 ) from the japan society for the promotion of science ( jsps ) .

first we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers . considering the bulk fluid viscosity and the inter - monolayer friction as the dissipation sources , we next employ onsager s variational principle to derive the coupled equations both for the membrane and the bulk fluid . the three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle . most importantly , a higher fluid viscosity inside the vesicle shifts the cross - over mode between the bending and the slipping to a larger value . as the vesicle parameters approach toward the unstable regions , the relaxation dynamics is dramatically slowed down , and the corresponding mode structure changes significantly . in some limiting cases , our general result reduces to the previously obtained relaxation rates .

we study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium . first we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers . two types of instabilities are identified : a small wavelength instability and a larger wavelength instability . considering the bulk fluid viscosity and the inter - monolayer friction as the dissipation sources , we next employ onsager s variational principle to derive the coupled equations both for the membrane and the bulk fluid . the three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle . most importantly , a higher fluid viscosity inside the vesicle shifts the cross - over mode between the bending and the slipping to a larger value . as the vesicle parameters approach toward the unstable regions , the relaxation dynamics is dramatically slowed down , and the corresponding mode structure changes significantly . in some limiting cases , our general result reduces to the previously obtained relaxation rates .

1212.3823

i

to illustrate the main ideas , we first consider a random polynomial in the special case @xmath108 . as mentioned in the introduction , in this case both the zero dimensional volume and the number of connected components coincide . for simplicity of notation we will denote their expectation by : @xmath109 in view of the generalization to higher dimensions , we will give two proofs that @xmath110 . the first one is based on techniques coming from _ integral geometry _ and will produce an exact result ; this proof will generalize to any number of variables producing again an exact result . the second is based on the _ barrier method _ introduced by nazarov and sodin ; it will produce only an approximate result but has the advantage that it generalizes to higher dimensions . we notice that in the case @xmath108 , a real random polynomial is just a trigonometric polynomial with either only even or only odd terms ( depending on whether @xmath2 is even or odd ) . the first proof is obtained following the ideas of @xcite . recall that if we have functions @xmath111 defined on the real line we can consider the random function : @xmath112 then if the coefficients are independently distributed , the expected number of zeros of @xmath1 on the interval @xmath113 $ ] is given by the formula : @xmath114$}\}=\frac{1}{\pi}\int_a^b\| \dot{\gamma}(t ) \|dt,\ ] ] where @xmath115 is the projection of the curve @xmath116 on the unit sphere @xmath117 ( we refer the reader to the beautiful paper @xcite for this and related topics ) . we note that ( [ expintgeom ] ) is proved using a special case of the _ kinematic formula _ from integral geometry . in our case @xmath113=[0 , 2\pi]$ ] and if @xmath2 is even , @xmath118 the curve @xmath119 is given by : @xmath120 and its norm in @xmath121 is constant and equals @xmath122 in particular we have : @xmath123 the norm of @xmath124 is @xmath125 which easily simplifies to : @xmath126 a similar calculation in the case @xmath2 is odd gives the exact same result . we are now in the position to use formula ( [ expintgeom ] ) and we obtain that the expected number of zeros of @xmath1 on @xmath127 $ ] is @xmath128 . thus , the number @xmath129 of expected zeros on the _ real projective line _ is : @xmath130 notice that this is an exact result and gives the asymptotic @xmath131 in this section we only prove that @xmath132 for @xmath2 large enough ; the inequality @xmath133 follows from the fundamental theorem of algebra . the proof is centered around the function described in the following claim whose proof is deferred until the end . there exist numerical constants @xmath134 and @xmath135 such that , for each sufficiently large @xmath2 and each @xmath136 there is a homogeneous polynomial @xmath137 of degree @xmath2 and @xmath16-norm one satisfying : @xmath138 once a point @xmath20 in @xmath17 is fixed , we can decompose @xmath139 where @xmath140 is a gaussian random variable with variance @xmath141 , and @xmath142 is in the orthogonal complement to @xmath143 in @xmath15 . we choose a new gaussian random variable @xmath144 independent of @xmath140 and of @xmath142 with variance @xmath141 , and set : @xmath145 by construction the random functions @xmath146 and @xmath147 have the same distribution as @xmath1 . we notice that we can write : @xmath148 next we apply the following claim to @xmath146 and @xmath147 . there exists a constant @xmath149 such that @xmath150 for every @xmath20 in @xmath151 we also defer the proof of this claim in favor of first seeing how it is used . let us recall that markov s inequality for a positive random variable @xmath152 reads @xmath153 . if we apply such inequality to @xmath154 , because of the previous claim we can find a constant @xmath155 such that : @xmath156 where @xmath134 is provided by the _ existence of the barrier _ claim . the event that @xmath157 and @xmath158 are each simultaneously _ at most _ @xmath155 is an intersection of four events each of which is complementary to the one of the above . thus the probability of their intersection satisfies : @xmath159 we note that these four events are not mutually independent , but this is not needed in the line above . now consider the event @xmath160 that @xmath161 and @xmath162 . if @xmath160 occurs then @xmath1 has a zero ; in the current situation we only need to use one of the two boundary points of an interval centered at @xmath20 . ] on @xmath17 between @xmath20 and @xmath163 . the event @xmath160 happens provided that : ( i ) @xmath164 and ( ii ) @xmath165 evaluated at at @xmath20 and @xmath163 are each bounded in absolute value by @xmath155 . note that ( i ) and ( ii ) are independent , and we have just checked above that ( ii ) happens with probability at least @xmath166 . moreover , @xmath167 for some constant @xmath168 , since @xmath169 has variance @xmath170 . it remains to choose @xmath171 disjoint intervals in @xmath17 each of length @xmath172 . each of them contains a zero of @xmath1 with probability at least @xmath173 and hence : @xmath174 as desired . we will choose our barrier in such a way that the barrier @xmath143 centered at some point @xmath136 is obtained just by precomposing @xmath175 with a rotation that moves the point @xmath176 to @xmath20 , so we only need to define @xmath175 which we do by normalizing the function : @xmath177 notice that @xmath178 is a polynomial of degree @xmath2 , since the denominator divides the numerator . ( @xmath178 is a projectivized chebychev polynomial of the second kind ) . + we have : @xmath179 say by de lhopital s rule with @xmath180 , and for all @xmath2 sufficiently large , we also have @xmath181 thus it suffices to show that the norm of @xmath178 is on the order of @xmath38 as @xmath182 , for then we will obtain the desired properties for @xmath183 ( the normalization of @xmath178 ) . it is easy to show that @xmath184 thus the function @xmath185 has the desired properties with @xmath186 and @xmath187 . let us choose a new orthonormal basis @xmath188 so that all basis elements except @xmath189 vanish at @xmath20 . to see that it is possible to do this , first notice that the subspace @xmath190 of homogeneous polynomials of degree @xmath2 vanishing at @xmath20 has codimension one inside @xmath15 . thus , to get the desired orthonormal basis , we may first orthonormalize a basis for @xmath190 , then take its orthogonal complement @xmath191 which consists of just one function . once normalized , this function gives the basis element @xmath189 . writing our random polynomial in terms of this basis , we have @xmath192 using again the standard basis @xmath193 , the fact that @xmath189 is a normalized trigonometric polynomial of degree @xmath2 means that @xmath194 where we have also used the triangle inequality and the discrete cauchy - schwarz inequality . combining this with the above , @xmath195 which implies that @xmath196 is bounded by a constant ( the gaussian random variable @xmath197 has variance of constant order , and therefore so has the expectation of its modulus ) .

+ we do not restrict ourselves to the random homogeneous case and we consider more generally random polynomials belonging to a window of eigenspaces of the laplacian on the sphere proving that the same asymptotic holds . as for the volume properties we prove that : both equations ( [ bettiabstract ] ) and ( [ volumeabstract ] ) exhibit expectation of maximal order in light of milnor s bound and the bound

we study the statistics of the number of connected components and the volume of a random real algebraic hypersurface in defined by a homogeneous polynomial of degree in the _ real fubini - study _ ensemble . we prove that for the expectation of the number of connected components : the asymptotic being in for fixed . + we do not restrict ourselves to the random homogeneous case and we consider more generally random polynomials belonging to a window of eigenspaces of the laplacian on the sphere proving that the same asymptotic holds . as for the volume properties we prove that : both equations ( [ bettiabstract ] ) and ( [ volumeabstract ] ) exhibit expectation of maximal order in light of milnor s bound and the bound

1108.3559

i

magnetic nanoparticles are of great interest because of their nanoscale physical properties and many current and potential applications . these applications range from high - density storage media@xcite and spintronic devices@xcite to biomedical applications like drug delivery , cell separation , cancer treatment and many others ( for a review , see refs . ) . since the physical properties of nanoparticles play a decisive role in all these applications , their study is of fundamental importance . in particular , for high - density storage media , e.g. , bit - patterned media@xcite where each nanoparticle is a carrier of information , the thermal stability of a given direction ( or magnitude ) of the nanoparticle magnetic moment is one of the most important problems . the reason is that under thermal fluctuations the magnetic moment can be randomly switched to a new state leading to the loss of information . in the case of ferromagnetic nanoparticles , the fluctuation dynamics of the nanoparticle magnetic moment can be described by the stochastic landau - lifshitz equation . if the noise term in this equation is approximated by the gaussian white noise , then the probability density of the magnetic moment satisfies the fokker - planck equation whose properties are well known.@xcite this approach , introduced by brown@xcite almost five decades ago , has become an important tool in the study of stochastic magnetic dynamics ( see ref . and references therein ) . to characterize the thermal stability in the case of uniaxial nanoparticles , it is often enough to determine the lifetimes of the nanoparticle magnetic moment in the up " and down " states . in the above approach , the lifetime in a given state is usually interpreted as the relaxation time . however , from a theoretical point of view , the lifetime is reasonable to associate with the mean first - passage time ( mfpt ) , i.e. , average time that a random process dwells in a prescribed state . an additional advantageous feature of this definition of the lifetime is that the mfpt method is mathematically well developed.@xcite this approach was first applied to study the magnetic relaxation in systems of noninteracting@xcite and dipolar interacting@xcite nanoparticles subjected to a constant magnetic field . in general , the lifetime depends on both intrinsic properties of nanoparticles and external magnetic fields . the case when the external fields contain a rotating magnetic field applied perpendicular to the easy axes of nanoparticles has a particular interest . on the one hand , this is because the rotating field plays a key role in the microwave - assisted switching@xcite and , on the other hand , because the corresponding dynamical equations ( without accounting the thermal fluctuations ) can often be solved analytically.@xcite specifically , it has been shown@xcite ( see also ref . ) that the rotating field can induce two types of the stable precessional modes of the magnetic moment , namely , the periodic ( p ) and quasi - periodic ( q ) modes . under certain conditions,@xcite one mode can exist in the up state of the magnetic moment and the other in the down state . the thermal fluctuations make the random transitions between these modes possible , and the problem of the lifetime of the p and q modes appears . some aspects of this problem have already been considered previously in the context of magnetic relaxation and induced magnetization.@xcite but the dependence of the lifetime on the parameters of the rotating field has not been studied systematically . at the same time , the effect of strong dependence of the lifetime on the rotating field frequency , which is expected to exist in the vicinity of the larmor frequency , could be important for applications . therefore , in this paper we present a detailed analytical and numerical analysis of the above mentioned problem . the paper is organized as follows . in sec . [ life ] , we describe the model and define the lifetime of both the p and q modes . here we also derive the boundary conditions and transformation properties of the lifetime . in sec . [ anres ] , we develop an analytical method for calculating the frequency dependence of the lifetime of the p mode in the case of high anisotropy barrier . our numerical results obtained by the simulation of the deterministic and stochastic landau - lifshitz equations are presented in sec . [ numres ] . specifically , the features of the p and q modes at zero temperature are studied in sec . [ prec ] and the effects of thermal fluctuations are considered in sec . [ simulat ] . finally , in sec . [ con ] we summarize our findings .

an analytical method for determining the lifetime of the p mode in the case of high anisotropy barrier and small amplitudes of the rotating field is developed within the fokker - planck formalism . in general case we show analytically and numerically that the lifetime is a nonmonotonic function of the rotating field frequency which , depending on the direction of field rotation , has either a pronounced maximum or a deep minimum near the larmor frequency .

we study the thermal stability of the periodic ( p ) and quasi - periodic ( q ) precessional modes of the nanoparticle magnetic moment induced by a rotating magnetic field . an analytical method for determining the lifetime of the p mode in the case of high anisotropy barrier and small amplitudes of the rotating field is developed within the fokker - planck formalism . in general case , the thermal stability of both p and q modes is investigated by numerical simulation of the stochastic landau - lifshitz equation . we show analytically and numerically that the lifetime is a nonmonotonic function of the rotating field frequency which , depending on the direction of field rotation , has either a pronounced maximum or a deep minimum near the larmor frequency .

1108.3559

c

we have studied in detail the thermal stability of the precessional modes of the nanoparticle magnetic moment induced by the rotating magnetic field whose plane of rotation is perpendicular to the easy axis of the nanoparticle . if the direction of field rotation and the direction of the natural precession of the magnetic moment are opposite , i.e. , if the condition @xmath325 holds , then only periodic ( p ) stable mode is induced by this field . in contrast , if the above mentioned directions coincide , i.e. , if @xmath250 , then the magnetic moment exhibits a much more complicated behavior . the numerical solution of the deterministic landau - lifshitz equation in the long - time limit has shown that , depending on the rotating field amplitude and frequency , in this case the magnetic moment can be in one of two p modes , in the quasi - periodic ( q ) mode , or even be unstable . these results obtained in the absence of thermal fluctuations have been collected in the diagram shown in fig . 1 . if the amplitude and frequency of the rotating field are chosen so that a stable precessional mode exists in both up ( @xmath459 ) and down ( @xmath493 ) states of the magnetic moment , then the thermal fluctuations can cause transitions between these modes . one of the most important parameters characterizing these transitions is the lifetime of a given mode . since it can be naturally associated with the mean first - passage time for the magnetic moment , we have used the fokker - planck formalism to define this quantity and calculate its properties . in particular , we have determined the boundary conditions and transformation properties of the lifetime and have developed an analytical method for finding its frequency dependence in the case of high anisotropy barrier and small amplitudes of the rotating field . using this method , it has been shown that the rotating field ( a ) slightly decreases ( if @xmath250 ) or increases ( if @xmath494 ) the lifetime of the p mode at large frequencies and ( b ) strongly decreases it ( if @xmath250 ) in the vicinity of the larmor frequency . we have also established that at zero frequency the lifetime is always less than in the limit of large frequencies . these analytical findings for the lifetime of the p mode have been confirmed by our numerical simulations of the stochastic landau - lifshitz equation . moreover , the numerical simulations of this equation for not too small amplitudes of the rotating field permitted us to solve the problem of the lifetime of the q mode . since in this case the precession angle is a periodic function of time which can cross the anisotropy barrier , the solution of this problem is of particular interest . it has turned out that , although the precessional angle depends on time , the lifetime of the q mode practically does not depend on this time , i.e. , on the precession angle . we have also verified this result by calculating the lifetime from the first - passage time distributions that correspond to different values of the precession angle .

we study the thermal stability of the periodic ( p ) and quasi - periodic ( q ) precessional modes of the nanoparticle magnetic moment induced by a rotating magnetic field . , the thermal stability of both p and q modes is investigated by numerical simulation of the stochastic landau - lifshitz equation .

we study the thermal stability of the periodic ( p ) and quasi - periodic ( q ) precessional modes of the nanoparticle magnetic moment induced by a rotating magnetic field . an analytical method for determining the lifetime of the p mode in the case of high anisotropy barrier and small amplitudes of the rotating field is developed within the fokker - planck formalism . in general case , the thermal stability of both p and q modes is investigated by numerical simulation of the stochastic landau - lifshitz equation . we show analytically and numerically that the lifetime is a nonmonotonic function of the rotating field frequency which , depending on the direction of field rotation , has either a pronounced maximum or a deep minimum near the larmor frequency .

quant-ph9808065

i

in quantum communication , qubits @xcite are sent across quantum channels that connect distant nodes of a quantum network . in general , these quantum channels are noisy and therefore limit the fidelity of the transmission . a bottleneck for quantum communication is the scaling of the probability of transmission errors with the length of the channels connecting the nodes . different from classical ( digital ) communication , the signals " in quantum communication consist of single qubits which may be entangled . owing to fundamental principles , these qubits can not be cloned @xcite nor amplified @xcite without destroying the essential quantum feature . this fact limits the maximum distance between the nodes to a few multiples of the absorption length ( or the coherence length ) of the channel , and poses a severe restriction on any practical application . for example , in recent experiments on quantum cryptography @xcite , single photons are sent through optical fibers with a given absorption and depolarization length . this has two effects : @xmath0 to transmit a photon without absorption , the number of trials scales exponentially with @xmath1 ; @xmath2 even when a photon arrives , the fidelity of the transmitted state decreases exponentially with @xmath1 . in the experiment , the distance between the nodes is therefore presently limited by a few multiples of the absorption length of the fiber @xcite . in the context of fault - tolerant quantum computing @xcite , knill and laflamme @xcite have discussed an important scheme that allows , in principle , to transmit a qubit over arbitrarily long distances with a polynomial overhead in the resources . their method requires to encode a single qubit into a concatenated quantum code ( i.e. an entangled state of a large number of qubits ) and to operate on this code repeatedly while it is propagated through the channel . the tolerable error probabilities for transmission are less than @xmath3 , whereas for local operations they are less than @xmath4 . this seems to be outside the range of any practical implementation in the near future . a crucial figure for any experiment will be the number of particles that can be manipulated locally in a coherent fashion , together with the precision with which such local manipulations can be realized . for instance , even when the number of particles scales only polynomially with the length of the channel , a polynomially large number may still be far too large for any practical implementation . a central tool in the theory of quantum information , specifically for quantum communication is entanglement purification @xcite . it allows , in principle , to create maximally entangled states of particles at different locations even if the channel that connects those locations is noisy @xcite . these entangled particles can then be used for faithful teleportation @xcite or secure quantum cryptography @xcite . it seems therefore natural to use this method as an ingredient for a quantum repeater . furthermore , it allows highly efficient two - way protocols which can not be realized with quantum error correction procedures . if a noisy quantum channel is much longer than its coherence length , one can not directly employ standard purification schemes . these schemes first create an ensemble of low fidelity epr pairs across the channel , and then purify / distill a few perfect epr pairs out of the ensemble . this , however , requires a minimum fidelity @xmath5 of the initial pairs to operate with , which can not be achieved as the length @xmath1 of the channel increases . in this paper , we treat the problem of a quantum repeater based on the method of entanglement purification . the idea of such a repeater is to divide a long quantum channel into shorter segments , which are purified separately , before they are connected . connecting two segments of a channel means here to build up quantum correlations across the compound channel from correlations that exist across the individual segments . this can be done by entanglement swapping , or teleportation of entanglement . a quantum repeater must therefore combine the methods of entanglement purfication and teleportation . although the combination of these methods should , in principle , allow to create entanglement over arbitrary distances , it is another question how much this `` costs '' in terms of resources needed for purification . resources means here the number of low fidelity epr pairs that have to be provided for purification of each channel segment . this quantity is related to the number of particles that have to be manipulated locally ( at the connection points between the segments ) in a coherent fashion . if the resources grow too fast with the length of the channel , not much will be gained by the whole procedure . a further important quantity is the error tolerance for the local operations . in every real situation , the local operations applied to one or more particles , will bear some imperfections . since such operations are the building blocks for any entanglement purification protocol , their imperfections will limit the maximum attainable fidelity for an epr pair and the efficiency of the protocol . in the context of the quantum repeater , a maximum fidelity @xmath6 corresponds to a residual amount of noise for each segment . when the segments are connected , this noise accumulates . to give a realistic treatment of the quantum repeater , we will therefore first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations . the general conditions under which standard purification protocols can be used in the presence of errors have been studied by giedke _ this includes , in particular , thresholds and lower bounds for the attainable fidelities . for a generic class of stochastic errors , one can give explicit representations of the imperfect operations in terms of completely positive maps and/or povms @xcite . in terms of these maps , we derive recursion formulas for the fidelities , which generalize the results given by bennett _ _ @xcite and by deutsch _ _ @xcite . from these results , we estimate that , for a generic class of errors , standard entanglement purifcation protocols work even for error probabilities of the order of a few per cent . in the context of long distance communication , we develop a purification procedure that combines the standard protocols with quantum teleportation in a certain way to be specified . this purification procedure allows quantum communication via noisy channels of arbitrary length . since it explicitly exploits two - way classical communication @xcite , our procedure is much more efficient for quantum communication than protocols based on quantum error correction @xcite . specifically , this solution of the quantum repeater tolerates errors on the per - cent level ; it requires a polynomial overhead in time and an overhead in local resources that grows only logarithmically with the length of the channel . the paper is organized as follows : in sec . [ error ] we introduce a generic error model to describe imperfect local operations such as noisy 1 bit and 2 bit operations and imperfect measurements . with the aid of these models , we revisit in sec . [ secelements ] the basic elements of quantum communication purfication and teleportation . this discussion includes results for the maximum attainable fidelities and the working conditions of the standard protocols under the condition of noisy local operations . after this discussion , in sec . [ secqrep ] , we are ready to attack the quantum repeater problem itself . our solution combines the methods of entanglement purification and entanglement swapping into a single ( meta- ) protocol , which we call nested entanglement purification . this protocol allows to distribute entanglement with a given fidelity across arbitrary long distances , even when local operations are imperfect . it requires an overhead in local resources that grows polynomially with the length of the channel . a modification of this protocol works with resources that grow only logarithmically with the length of the channel ( while the build - up time grows polynomially ) .

it is however possible to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping . this method can be much more efficient than schemes based on quantum error correction , as it makes explicit use of two - way classical communication . , we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations . we then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the per - cent level . it requires a polynomial overhead in time , and an overhead in local resources that grows only logarithmically with the length of the channel . # 1

we study the use of entanglement purification for quantum communication over long distances . for distances much longer than the coherence length of a corresponding noisy quantum channel , the fidelity of transmission is usually so low that standard purification methods are not applicable . it is however possible to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping . this method can be much more efficient than schemes based on quantum error correction , as it makes explicit use of two - way classical communication . an important question is how the noise , introduced by imperfect local operations ( that constitute the protocols of purification and the entanglement swapping ) , accumulates in such a compound channel , and how it can be kept below a certain noise level . to treat this problem , we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations . we then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the per - cent level . it requires a polynomial overhead in time , and an overhead in local resources that grows only logarithmically with the length of the channel . # 1

1202.3207

r

the measurements of the resistivity noise were performed with the sample , the structure of which is presented in fig . [ fig : structure ] . parameters of this sample are as follows : mn content is 0.35 ml , and it corresponds to @xmath250 cm@xmath96 surface concentration ; the thickness of the spacer separating mn @xmath0-layer and the qw is 3 nm ; indium concentration in the ga@xmath7in@xmath6as qw @xmath252=0.17 and so its depth is about 70 mev ; the hole density @xmath1 and their mobility @xmath253 in qw are @xmath254 cm@xmath96 ( 77 k ) or @xmath255 cm@xmath96 ( 5 k ) and 2370 @xmath256/v@xmath257s ( 77 k ) or 3400 @xmath256/v@xmath257s ( 5 k ) , respectively . as it was shown ref . , this sample is close to the metal - insulator transition of the percolation type having high enough value of resistance @xmath258 k@xmath259 and @xmath260 . the temperature dependence of its resistivity can be fitted to the arrhenius law with an activation energy @xmath261 k. ferromagnetic ordering is established for this sample through observations of the anomalous hall effect and resistivity anomaly ( peak at the temperature dependence of the resistance ) . the direct magnetic measurements for samples from the same set show magnetic hysteresis even for samples with smaller mn content . @xcite the temperature corresponding to the onset of strong ferromagnetic correlations for this sample was found to be about 30 k as measured by the resistivity anomaly . as it was shown previously @xcite , the mn @xmath0-layer consists of fm droplets affecting the magnetic state in the qw giving rise to a set of metallic fm droplets , which is responsible for metal - insulator transition . so , there are two characteristic temperatures : first that corresponds to the fm ordering inside droplets and the second related to the formation of the long - range fm state in the sample , which can be treated as a kind of the `` fm percolation transition '' . the characteristic temperature found from the resistive anomaly corresponds to the second case . at this temperature magnetic correlations became significant . the data ( see fig . [ fig : freq - dep ] ) on the frequency dependence of noise show @xmath262 ( @xmath263 ) as a function of frequency for a number of temperatures ( mostly below the resistivity peak ) . the noise is non - monotonous at all these temperatures , and especially so at lower temperatures . the curves at higher temperatures suggest more than one relaxation time while the low temperature data indicates a single relaxation time . ( color online ) plots of the measured frequency dependence of @xmath262 for various values of the temperature . ] the data in fig . [ fig : freq - dep ] correspond to temperatures well below the resistivity anomaly . this is the regime where ferromagnetic correlations are significant . note that the resistivity noise amplitude decreases with increase of temperature for the high frequency as well as the low - frequency limits . thus , we try power - law fits in the low- and high - frequency range away from the peak in the resistivity noise ( see fig . [ fig : freq - dep-4k ] ) . this behavior is consistent with both the magnetic and charge fluctuation models . we will discuss the temperature dependence of resistivity noise later in sec . [ sub : temperature - dependence ] . we consider power - law fits at the low- and high - frequency ends . at high frequencies , we find ( see fig . [ fig : freq - dep-4k ] ) for example for the @xmath264 data , @xmath265 which should be contrasted with a @xmath266 decrease expected for a lorentzian . at low frequencies , one can find a fit to @xmath267 or @xmath268 the former would be consistent with a lorentzian ( no conserved order parameter ) while the logarithmic behavior in the latter can arise from model b dynamics ( conserved order parameter ) . ( color online ) frequency dependence of noise at @xmath264 ( solid curve ) together with fits to the low and high frequency regimes . at the low - frequency end , the dashed curve and the dotted curve are fits to @xmath269 and @xmath270 respectively . at the high - frequency end , the fit is to @xmath271 by analyzing the long - time behavior of @xmath272 we find that the agreement is better with model b dynamics . [ fig : griffiths4.4k ] shows the time dependence of the resistivity autocorrelation function numerically obtained by a discrete fourier transform of the frequency data . the long - time behavior shows a good fit to @xmath273 for disordered rkky ferromagnets , one expects @xmath274 while for the double exchange case , @xmath275 we found that fits to exponential relaxation , @xmath276 or a griffiths relaxation , @xmath277 are not as good as the power - law fits . the @xmath203 power - law relaxation supports the case of the rkky ferromagnet . ( color online ) plot showing the long time dependence of the resistivity autocorrelation function @xmath278 extracted from the resistivity noise data at @xmath279 ( solid curve ) together with fits to a power - law time dependence with logarithmic corrections . the dashed curve is a fit to @xmath280 while the dot - dashed curve is a fit to @xmath281 in two dimensions , @xmath282 behavior is expected for a disordered rkky ferromagnet ( see eq . ) and @xmath283 for double exchange ferromagnets ( see eq . ) . the logarithmic time dependence indicates @xmath284 noise contributions . the fit to the rkky model is better than to the double exchange . ] time traces of resistivity fluctuations showing distinct telegraph - like switching at low temperatures . at temperatures higher than around 20k , the telegraph - like switching is not so prominent . ] in fig . [ fig : telegraph - noise ] , the time traces of resistivity fluctuations are shown , while the main stable contribution to the resistivity is subtracted . note that the time traces of the resistivity show distinct telegraph - like switching at low temperature . this switching is not so prominent once the temperature exceeds about 200 k : this is near to but below the temperature , at which one observes the anomalous peak in the resistivity and noise . the advent of telegraph - like switching can be understood if the magnetic model has uniaxial symmetry instead of complete rotational symmetry . this is possible given the planar geometry of the structure . nevertheless , at the moment we are unable to say whether at still longer times , the autocorrelation relaxation will remain a power law or become exponential . the logarithmic term indicates @xmath284 noise , possibly from other mechanisms . figure [ fig : temp - dep ] shows the temperature dependence of the resistivity noise at two difference frequencies . the temperature range shown in in the figure corresponds to the low frequency regime for both @xmath285 and @xmath286 hz . this can be deduced from fig . [ fig : freq - dep ] where the crossover frequency ( between the low- and high - frequency regimes ) for @xmath287 k is around 200 hz , and the data in fig . [ fig : temp - dep ] are taken at @xmath288 k. we analyze the temperature dependence in the context of the magnetic and charge fluctuation models we have developed above . for models a and b as well as for the griffiths picture , the temperature dependence of the normalized resistivity noise is directly related to the temperature dependence of the magnetic correlation length @xmath289 as well as the coefficients @xmath175 ( model a ) and @xmath290 ( model b ) . in all cases , @xmath291 we do not yet know the contribution to @xmath175 and @xmath290 from the change of hole resistivity with temperature . suppose the holes in the quantum well do contribute to @xmath175 and @xmath292 in this case , as the temperature is reduced , @xmath175 and @xmath290 can show a decrease mirroring the resistivity , and that it has an anomaly when the correlation length becomes comparable with the inter - droplet separation . ( color online ) temperature dependence of the resistivity noise @xmath293 measured at @xmath285 hz ( solid curve ) and @xmath286 hz ( dashed curve ) . ] for models a and b in the low - frequency regime , in accordance with eqs . and , we fit the temperature dependence data in fig . [ fig : temp - dep ] to @xmath294 where @xmath295 is a constant . the exponential temperature dependence of @xmath159 and @xmath138 together with the scatter in the data makes it difficult to extract the sub - leading power - laws and logarithms ; thus , we do not attempt to distinguish models a and b here . for the charge fluctuation model , following eq . , we tried fitting the data to @xmath296 where @xmath297 is a constant . we consider @xmath3 and @xmath298 as fitting parameters . we could not obtain a satisfactory fit for the charge fluctuation result for any positive value of @xmath299 ( color online ) temperature dependence of the resistivity noise @xmath293 for @xmath286 hz ( dots ) and a fit ( solid curve ) to our model of magnetic fluctuations , @xmath300 the fit corresponds to @xmath301 k. the model does not take into account changes in the damping parameters @xmath175 or @xmath290 across the resistivity anomaly . ] [ fig : tempdep - fit ] shows the resistivity noise data for @xmath286 hz and a fit to our model of magnetic fluctuations . possible variation of @xmath175 or @xmath290 across the resistivity anomaly is not taken into account in the fit . from this fitting we have got @xmath301 k that by two times exceeds the temperature of the resistance anomaly and maximum of @xmath293 versus temperature , while it is in a good agreement with @xmath302 k , which was found from fitting of the resistivity temperature dependence . @xcite that additionally proves the earlier result that there are two characteristic temperatures in such systems : the local curie temperature at which ferromagnetic ordering occurs inside the magnetic droplets and the global curie temperature of the long - range ferromagnetic ordering establishment at the scale of the whole sample `` magnetic percolation transition '' .

we study theoretically and experimentally the frequency and temperature dependence of resistivity noise in semiconductor heterostructures-doped by mn . the resistivity noise is observed to be non - monotonous as a function of frequency . as a function of temperature , the noise increases by two orders of magnitude for a resistivity increase of about 50% . we find that the resistivity noise in these structures is well described by a disordered rkky ferromagnet model dynamics with a conserved order parameter .

we study theoretically and experimentally the frequency and temperature dependence of resistivity noise in semiconductor heterostructures-doped by mn . the resistivity noise is observed to be non - monotonous as a function of frequency . as a function of temperature , the noise increases by two orders of magnitude for a resistivity increase of about 50% . we study two possible sources of resistivity noise dynamic spin fluctuations and charge fluctuations , and find that dynamic spin fluctuations are more relevant for the observed noise data . the frequency and temperature dependence of resistivity noise provide important information on the nature of the magnetic interactions . in particular , we show how noise measurements can help resolve a long standing debate on whether the mn - doped gaas is a- zener / ruderman - kittel - kasuya - yosida ( rkky ) or double exchange ferromagnet . our analysis includes the effect of different kinds of disorder such as spin - glass type of interactions and a site - dilution type of disorder . we find that the resistivity noise in these structures is well described by a disordered rkky ferromagnet model dynamics with a conserved order parameter .

gr-qc0510075

i

gr is a classical field theory for 10 independent variables the components of metric tensor @xmath0 . it is well known , however , that some problems inside and beyond einstein s gravity require a richer set of 16 independent variables the components of the coframe ( aka reper , vierbein , ... ) . in the following issues of gravity , the coframe is not only a useful tool but often can not even be replaced by the standard metric variable : * hamiltonian formulation @xcite,@xcite ; * positive energy proofs @xcite ; * fermions on a curved manifold @xcite,@xcite ; * supergravity @xcite ; * loop quantum gravity @xcite , @xcite . absolute ( teleparallel ) frame / coframe variables were introduced in physics by einstein in 1928 with an aim of a unification of gravitational and electromagnetic fields ( for classical references , see @xcite ) . in gr description , the additional six degrees of freedom do not have a physical sense and treated as a type of a gauge symmetry of the metric tensor . it was already noticed by einstein , that 16 reper components can not be completely equivalent to 10 components of the metric tensor . indeed , the supergravity and the loop quantum gravity models apparently can be formulated only in term of vierbein . so , it is natural to study which geometric structure can be constructed from the vierbein ( frame / coframe ) variables and which field models can be related to this geometry . this is a subject of the current paper . the frame field @xmath1 and its dual , the coframe field @xmath2 , have a well defined geometrical sense . in particular , even been considered as independent physical fields , they provide a special ( absolute ) reference basis . for the bases , @xmath3 , fixed at a point , the construction gives an invariant meaning to the components of a tensor , thus it emerges in violation of the rotational and lorentz invariance @xcite . however , when the _ global _ ( rigid ) lorentz transformations of the absolute basis fields are acceptable , the frame components of a tensor are transformed merely by the lorentz transformation law . thus , some interrelation between the lorentz invariant field theories and the diffeomorphism invariant gravity emerges . when the absolute basis field is restricted to a point , the lorentz invariance requires to consider it not alone but as a member of a class of equivalent bases . the equivalence relation for this class is provided by a group @xmath4 of transformations @xmath5 , which has to include local physics symmetries , i.e. , the rotations and the boosts . when we are dealing with the absolute basis fields on a manifold , the relation between the frames at different points is not governed by the constrains of local physics . consequently , three principally different possibilities are open : \(i ) _ riemannian geometry . _ the frames at distinct points are not related to one another at all , i.e. the dependence of the elements of the group @xmath4 on a point is absolutely arbitrary . it is possible only if the corresponding geometry , i.e the metric and the connection , respect the arbitrary transformations of the frame field . the unique connections with this property is the _ levi - civita connection _ of riemannian geometry . this case is realized in the standard gr when it is formulated in an arbitrary non - holonomic frame . the frame / coframe fields are not physical in this case and only play a role of a useful reference tool . they can be replaced even by holonomic bases generated by local coordinates . \(ii ) _ teleparallel geometry . _ another limiting case emerges when the frames in distinct points are strongly connected to one another . it means that when a frame in an arbitrary point is rotated in a certain angle , the frames at distant points immediately rotated in the same angle . the unique connection with this property is the flat _ weitzenbck connection . _ although the scalar curvature is zero for such a connection , the action functional can be constructed from the torsion tensor . it is natural to require this action functional to be invariant only under global transformations of the basis field . the analysis of this model shows that it has not spherical symmetric solutions with newtonian behavior at infinity . as a result , this absolute teleparallel gravity model is not physical . \(iii ) _ gauge geometry . _ besides the two limiting cases given above , there is a family of geometries with the field of frame rotations satisfying some system of differential equations . the basic geometrical quantities , metric and connection , have to be invariant under local transformations of the frame field satisfied these equations . in this construction , the frame field does not emerge explicitly , so we will refer to the corresponding geometrical structure as a _ gauge coframe geometry_. in alternative gravity models ( see @xcite @xcite and the reference given therein ) , the frame variable appears as an independent physical field . in the first order approximation @xcite , the coframe field is separated to a sum of two independent fields - a metric field and an antisymmetric field of the rang two . the same separation emerges in the lagrangian , in the field equation and also in the energy - momentum tensor . in the current paper we show that a geometrical and physical interpretation of the antisymmetric part can be prolongated in the higher order approximations . our main result is : in the viable coframe models , alternative to gr , the additional degrees of freedom can be interpreted as a new dynamical field which behavior in the first order approximation is described by the vacuum maxwell - type system . the aim of this paper is to derive the mentioned coframe gauge geometrical structure and its possible applications to classical fields . the paper is organized as followed . in section 2 , we construct a most general class of connections which are linear in the first order derivatives of the coframe field . this six - parametric family involves the levi - civita and the weitzenbck connections as special limiting cases . we also identify the sub - families of torsion - free and metric compatible connections . in section 3 , the behavior of the coframe connections under local @xmath6 transformations of the coframe is considered . besides the levi - civita and the weitzenbck connections , we identify a sub - family of gauge invariant connections . the corresponding constraints compose a system of 8 first order partial differential equation for six independent entries of a @xmath6 matrix . this situation is very similar to the standard maxwell system of eight field equations for six independent components of the electromagnetic field . in section 4 , we derive the same system of constrains from a different ( physical ) point of view . we require a most general quadratic coframe lagrangian to be invariant under @xmath6 transformations of the coframe . the gauge invariant lagrangians turn out to be in a correspondence with the known viable coframe models having the schwarzschild solution . in section 5 , we study the first order approximation to the system of the constrains . on a flat manifold , this system coincides with the vacuum maxwell equations . on a curved manifold , it turns out to be a system of covariant maxwell - type equations when the covariant derivatives are considered relative to the weitzenbck connections . in section 6 , we derive an exact spherical symmetric solution to our system of constrains . we also compare our model with the standard description of interaction between gravitational and electromagnetic fields . in contrast to the standard einstein - maxwell system , our model predicts mass dependence in the coulomb - type law . we derive the exact expression of the corresponding correction term . in section 7 , we give an outlook of the proposed alternative model and discuss how ( and if ) the additional degrees of freedom can be related to the ordinary electromagnetic field . we use the greek indices @xmath7 to identify the specific vector fields of the frame @xmath1 and the specific 1-forms of the coframe @xmath2 . the roman indices @xmath8 refer to local coordinates . summation from 0 to 3 is understood over repeated indices of both types ( einstein s summation convention ) . two types of indices and basically different . in particular , they can not be summed ( contracted ) in the expressions @xmath9 or @xmath10 . the lorentz metric is used with the sign agreement @xmath11 . the spatial indices are denoted as @xmath12 . we denote the coefficients of connection as @xmath13 and @xmath14 . such notation is useful for the exterior form representation . in order to go back to the ordinary tensorial notations @xmath15 , it is enough to move the last index to the first position . the symmetrization and antisymmetrization operators are used in the normalized form , i.e. , @xmath16 and @xmath17}= ( 1/{p!})(a_{i_1\cdots i_p}- \cdots)$ ]

we study which geometric structure can be constructed from the vierbein ( frame / coframe ) variables and which field models can be related to this geometry . the coframe field models , alternative to gr , are known as viable models for gravity , since they have the schwarzschild solution . this system is similar to the vacuum maxwell system and even coincides with it on a flat manifold . exact spherical symmetric solution for our dynamical field is derived .

we study which geometric structure can be constructed from the vierbein ( frame / coframe ) variables and which field models can be related to this geometry . the coframe field models , alternative to gr , are known as viable models for gravity , since they have the schwarzschild solution . since the local lorentz invariance is violated , a physical interpretation of additional six degrees of freedom is required . the geometry of such models is usually given by two different connections the levi - civita symmetric and metric - compatible connection and the weitzenbck flat connection . we construct a general family of linear connections of the same type , which includes two connections above as special limiting cases . we show that for dynamical propagation of six additional degrees of freedom it is necessary for the gauge field of infinitesimal transformations ( antisymmetric tensor ) to satisfy the system of two first order differential equations . this system is similar to the vacuum maxwell system and even coincides with it on a flat manifold . the corresponding `` maxwell - compatible connections '' are derived . alternatively , we derive the same maxwell - type system as a symmetry conditions of the viable models lagrangian . consequently we derive a nontrivial decomposition of the coframe field to the pure metric field plus a dynamical field of infinitesimal lorentz rotations . exact spherical symmetric solution for our dynamical field is derived . it is bounded near the schwarzschild radius . further off , the solution is close to the coulomb field .

1607.00795

i

yang baxter deformations provide a systematic way to study integrable deformations of non - linear sigma models in two dimensions . this method was invented by klimcik for principal chiral models based on the modified classical yang baxter equation ( mcybe ) @xcite . it was generalized to the symmetric coset case in @xcite and the homogeneous cybe case in @xcite . it is very interesting to consider some applications of yang baxter deformations in the context of the ads / cft correspondence @xcite . the green - schwarz action of type iib superstring on @xmath0 was constructed by metsaev and tseytlin in terms of the supercoset @xcite @xmath4 this supercoset has a @xmath5-grading , generalizing the @xmath6-grading of the symmetric cosets . hence the @xmath0 superstring exhibits classical integrability in the sense of kinematic integrability @xcite ( for nice reviews , see @xcite ) . the first application of yang baxter deformation to the @xmath0 superstring was carried out by delduc , magro and vicedo @xcite . the classical action was constructed with a classical @xmath1-matrix of drinfeld - jimbo type @xcite and the associated symmetry algebra is a @xmath7-deformation of @xmath8 . this specific example is often called @xmath9-deformation . the metric and ns - ns two - form were subsequently computed by performing a coset construction for the bosonic element @xcite . after that , some works were done towards constructing the full background by directly solving the equations of motion of type iib supergravity @xcite . this strategy was preferred simply because of the technical difficulty of the supercoset construction . in the end , arutyunov , borsato and frolov accomplished doing the supercoset construction and the full background was determined @xcite ( for a good review , see @xcite ) . a remarkable point is that the resulting background does not satisfy the equations of motion of type iib supergravity . however , the situation is not hopeless . the ten - dimensional background is related to the full solution of the usual type iib supergravity via t - dualities up to the linear dependence of the dilaton @xcite . the world - sheet theory is not weyl invariant but still scale invariant , _ i.e. _ , the world - sheet beta function does not vanish but is given by a total derivative . from the viewpoint of the spacetime , this result indicates that the on - shell condition of type iib supergravity is weakened to a generalized set of the equations . in fact , the generalized equations of type iib supergravity were proposed in @xcite and the background obtained in @xcite is a solution of the generalized equations . for a more general argument on the relation between the @xmath10-symmetry of the @xmath9-deformed @xmath0 superstring and the generalized equations , see @xcite . other examples of yang baxter deformations of the @xmath0 superstring are based on the homogeneous cybe @xcite . in comparison to the mcybe case , there are some advantages . one of them is that one can perform partial deformations of @xmath0 , i.e. , only ads@xmath11 or only @xmath12 can be deformed . this class of yang baxter deformations includes well - known examples such as gravity duals of non - commutative gauge theories @xcite , the gamma - deformations of @xmath12 @xcite , and schrdinger spacetimes @xcite . in a series of works @xcite , the associated classical @xmath1-matrices were identified with these backgrounds , flat spacetime and pp - wave , see @xcite . for short summaries , see @xcite . ] . in a remarkable advance , the supercoset construction has been performed in @xcite and now the full background can be obtained for arbitrary classical @xmath1-matrices . for abelian classical @xmath1-matrices , the r - r sector and dilaton have been confirmed for well - known backgrounds and it seems likely that yang baxter deformations work well @xcite . however , for non - abelian classical @xmath1-matrices , the associated backgrounds do not in general satisfy the equations of motion of type iib supergravity @xcite . an interesting question here is whether deformed backgrounds for non - abelian classical @xmath1-matrices satisfy the generalized equations of motion or not . this question can be answered if the deformed string theory is supposed to be the canonical action of the green - schwarz string @xcite . this assumption however has to be confirmed by a separate analysis and it is still an open problem . a confirmation was also given in @xcite based on scaling limits of the @xmath9-deformed ads@xmath13 . it may also be intriguing to study `` t - dualized '' backgrounds related to non - abelian classical @xmath1-matrices and consider their physical interpretation . we use quotation marks for t - dualities involving solutions to the generalized sugra equations , where the usual buscher rules have to be supplemented with a prescription for the behavior of the dilaton @xcite . in this paper , we consider yang baxter deformations of the @xmath0 superstring with the homogeneous cybe and focus on some examples of non - abelian classical @xmath1-matrix . we derive the associated backgrounds explicitly and show that all of the resulting backgrounds satisfy the generalized equations . for some of them , `` t - dualized '' backgrounds are derived by adding a linear coordinate dependence to the dilaton and these satisfy the usual type iib supergravity equations . remarkably , some of the `` t - dualized '' backgrounds are locally t - dual to the undeformed @xmath0 via appropriate coordinate transformations , though it does not seem that this is always the case . at least in cases where the undeformed @xmath0 background can be reproduced , the classical integrability of the `` t - dualized '' background is manifest . this paper is organized as follows . section [ sec : yang - baxter - deformed ] introduces yang baxter deformations of the @xmath0 superstring based on the homogeneous cybe and gives an outline of the supercoset construction . in section [ sec : generalized - type - iib ] , we briefly introduce the generalized type iib supergravity equations of motion . in section [ sec : examples ] , we study six examples of non - abelian classical @xmath1-matrices and the associated full backgrounds . for four of them , `` t - dualized '' backgrounds , which are solutions of the usual type iib supergravity , are found . then , three of the `` t - dualized '' backgrounds are shown to be locally equivalent to the undeformed @xmath0 . section [ sec : conclusions ] is devoted to conclusion and discussion .

, the current understanding is that abelian classical-matrices give rise to solutions of type iib supergravity , while non - abelian classical-matrices lead to solutions of the generalized supergravity equations . we examine here some examples of non - abelian classical-matrices and derive the associated backgrounds explicitly . all of the resulting backgrounds satisfy the generalized equations . for some of them , we derive `` t - dualized '' backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type iib supergravity equations . remarkably , some of the `` t - dualized '' backgrounds are locally identical to undeformed after an appropriate coordinate transformation , but this seems not to be generally the case . * generalized type iib supergravity equations + and non - abelian classical-matrices * + domenico orlando , susanne reffert , + jun - ichi sakamoto , and kentaroh yoshida _institute for theoretical physics , albert einstein center for fundamental physics , university of bern , sidlerstrasse 5 , ch-3012 bern , switzerland _ +_department of physics , kyoto university , +

we study yang baxter deformations of the superstring with non - abelian classical-matrices which satisfy the homogeneous classical yang baxter equation ( cybe ) . by performing a supercoset construction , we can get deformed backgrounds . while this is a new area of research , the current understanding is that abelian classical-matrices give rise to solutions of type iib supergravity , while non - abelian classical-matrices lead to solutions of the generalized supergravity equations . we examine here some examples of non - abelian classical-matrices and derive the associated backgrounds explicitly . all of the resulting backgrounds satisfy the generalized equations . for some of them , we derive `` t - dualized '' backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type iib supergravity equations . remarkably , some of the `` t - dualized '' backgrounds are locally identical to undeformed after an appropriate coordinate transformation , but this seems not to be generally the case . * generalized type iib supergravity equations + and non - abelian classical-matrices * + domenico orlando , susanne reffert , + jun - ichi sakamoto , and kentaroh yoshida _institute for theoretical physics , albert einstein center for fundamental physics , university of bern , sidlerstrasse 5 , ch-3012 bern , switzerland _ +_department of physics , kyoto university , + kitashirakawa oiwake - cho , kyoto 606 - 8502 , japan _

astro-ph0110275

m

the two - dimensional luminosity distribution observed in most galaxies most often displays a high degree of azimuthal symmetry . this justifies the use of one - dimensional radial surface brightness profiles in describing the radial stellar surface density distribution . such profiles are then decomposed into constituent photometric components ( de vaucouleurs 1958 , de vaucouleurs and simien 1986 , kent 1986 , de jong and van der kruit 1994 ) . this profile is extracted from the galaxy image in many ways , but most often by computing mean flux density in elliptical annuli having the shape and orientation of the faint surface brightness , outer isophotes . parameterizing this profile , with a concentration index , will produce a measurement that correlates well with bulge - to - disk ratio and hence with hubble type . local departures from this overall radial symmetry in the form of high spatial frequency components ( arms , bars , rings ) form the basis for additional criteria to visual galaxy classification systems like the rhs . a method which quantitatively describes departures from azimuthal symmetry in galaxy images would seem to be a rich starting place for developing a machine automated classification system , either of the supervised learning variety ( odewahn 1992 , weir 1995 ) or the unsupervised variety ( mahonen 1995 ) . towards this end , we have adapted a moments - based image analysis technique ( odewahn 1989 ) to fit fourier components to fixed - grid azimuthal profiles in elliptical annuli to reconstruct galaxy images . one may think of this step as an optimized data compression technique for reducing the dimensionality of our ultimate pattern classification problem : the recognition and characterization of morphological features in galaxies . the technique of fourier decomposition presented here is used to quantify the two dimensional luminosity distributions of galaxies . similar approaches have been used to study the shapes of isophotes in elliptical galaxies by bender and mollenhoff ( 1987 ) , and applications to the luminosity distribution are described by lauer ( 1985 ) , buta ( 1987 ) , and ohta ( 1990 ) . with this methodology , we can quantify the amplitude and phase of the bar and spiral arm components in a galaxy image . this technique is very useful for modeling the bar luminosity distribution for systems in which a simple elliptical bar model was not sufficient , as was first demonstrated by elmegreen and elmegreen ( 1985 ) in describing the bar luminosity distributions exhibited by galaxies over a range of hubble types . artificial neural networks ( ann s ) are systems of weight vectors , whose component values are established through various machine learning algorithms . these systems receive information in the form of a vector ( the input pattern ) and produce as output a numerical pattern encoding a classification . they were designed to simulate groups of biological neurons and their interconnections and to mimic the ability of such systems to learn and generalize . discussion of the development and practical application of neural networks is well presented in the literature ( see mcclellan and rumelhardt 1988 ) . in astronomical applications , this technique has been applied with considerable success to the problem of star - galaxy separation by odewahn ( 1992 ) . a neural network classifier was developed storrie - lombardi ( 1992 ) to assign galaxy types on the basis of the photometric parameters supplied by the eso - lv catalog of lauberts and valentijn ( 1989 ) . applications of this method to large surveys of galaxies using photographic schmidt plate material are discussed in odewahn ( 1995 ) and naim ( 1995 ) . more recent discussions of star - galaxy separation using ann s are presented by andreon ( 2000 ) , mahonen & frantti ( 2000 ) , and and philip ( 2000 ) . an extremely thorough discussion of galaxy classification with ann methods is given by bazell ( 2000 ) . the neural network literature quoted above contains a wealth of information on the theoretical development of neural networks and the various methods used to establish the network weight values . we summarize here only the practical aspects of the ann operation and the basic equations for applying a feed - forward network . the input information , in our case the principal components formed from the fourier profiles discussed in section 3.2 , is presented to the network through a set of input nodes , referred to as the input layer . each input node is `` connected '' via an information pathway to nodes in a second layer referred to as the first hidden layer . in a repeating fashion , one may construct a network using any number of such hidden layers . for the backpropagation networks discussed here , we have used ann s with two hidden layers . the final layer of node positions , referred to as the output layer , will contain the numerical output of the network encoding the classification . this system of nodes and interconnections is analogous to the system of neurons and synapses of the brain . information is conveyed along each connection , processed at each node site , and passed along to nodes further `` upstream '' in the network . this is referred to as a feed - forward network . the information processing at each node site is performed by combining all input numerical information from upstream nodes , @xmath1 , in a weighted average of the form : @xmath2 the @xmath3 subscript refers to a summation of all nodes in the previous layer of nodes and the @xmath4 subscript refers to the node position in the present layer , i.e. the node for which we are computing an output . each time the ann produces an output pattern , it has done so by processing information from the input layer . this input information is referred to as the input pattern , and we use the @xmath5 subscript to indicate input pattern . hence , if there are 5 nodes in the previous layer ( @xmath3 ) , each node ( @xmath4 ) in the current layer will contain 5 weight values ( @xmath6 ) and a constant term , @xmath7 , which is referred to as the bias . the final nodal output is computed via the activation function , which in the case of this work is a sigmoidal function of the form : @xmath8 hence , the information passed from node @xmath4 in the current layer of consideration , when the network was presented with input pattern @xmath5 , is denoted as @xmath9 . this numerical value is subsequently passed to the forward layer along the connection lines for further network processing . the activation values computed in the output layer form the numerical output of the ann and serve to encode the classification for input pattern , @xmath5 . in order to solve for the weight and bias values of equation 1 for all nodes , one requires a set of input patterns for which the correct classification is known . this set of examples is used in an iterative fashion to establish weight values using a gradient descent algorithm known as backpropagation . in brief , backpropagation training is performed by initially assigning random values to the @xmath6 and @xmath7 terms in all nodes . each time a training pattern is presented to the ann , the activation for each node , @xmath9 , is computed . after the output layer is computed , we go backwards through the network and compute an error term which measures of the change in the network output produced by an incremental change in the node weight values . based on these error terms , all network weights are updated and the process continues for each set of training patterns . as discussed in the next section , precautions must be taken in this process to avoid problems from over - training ( simply memorizing the input pattern set as opposed to generalizing the problem ) . the goal of the present work is to develop a system that automatically detects the presence of specific types of morphological structures in galaxy images . this is clearly a more complex problem compared to the use of a few global photometric parameters to predict types , and so we desired to use an additional method of neural network classification to confirm the results of our classical backpropagation approach . philip ( 2000 ) develop a neural network based on bayes principal that assumes the clustering of attribute values ( the input parameters ) . the method considers the error produced by each training pattern presented to the network , and weights are updated on the basis of the bayesian probability associated with each attribute for a given training pattern . in this approach , the probability density of identical attribute values flattens out while attributes showing large differences from the mean get boosted in importance . this is referred to as a difference boosting neural network ( dbnn ) . we have applied this new approach as a check on our backpropagation network results , however this method has the added advantage that it trains to convergence in a much faster time than is required by classical backpropagation methods . in this paper we develop a technique that is a pre - processing step for producing input to a supervised classifier in the form of an artificial neural network ( odewahn 1997 ) . in this approach , the radial surface brightness profile of a galaxy is computed in elliptical annuli centered on the galaxy center . the rational here , valid in most cases , is that we are isolating the disk component of the galaxy and hence establishing a way of defining the equatorial plane of the system . the position , shape and orientation of these annuli are determined using classical isophotal ellipse fitting techniques . within each annulus , we compute the run of flux density with position angle , @xmath10 , in the equatorial plane of the galaxy , to form the azimuthal surface brightness profile . to describe each azimuthal profile , and reduce the dimensionality of our classification problem , each azimuthal profile is modeled by the following fourier series : @xmath11 for computational efficiency , the fourier terms are computed for each azimuthal profile using the following moment relations : @xmath12 @xmath13 @xmath14 where @xmath10 is the angle ( in the equatorial plane of the galaxy ) with respect to the photometric major axis , and m is an integer . hence , if we assume galaxy disks to be thin and suffer no internal extinction , this approach crudely removes inclination effects and allows us to compare galaxy images independent of orientation . the fourier series in this paper were computed up to m=5 . fourier amplitudes , describing the relative amplitude of each component are computed using the following expression : @xmath15 finally , a phase angle describing the angular position of the peak signal contributed by each component can be computed . we compute the phase angle of the @xmath16 component as : @xmath17 a practical application of this method to a barred spiral galaxy imaged with hst is shown in figure [ model_sample_1 ] . another example for an elliptical galaxy image which contains no high spatial frequency image structure is shown in figure [ model_sample_2 ] . through experimentation with both hst- and ground - based images , we have determined that using 17 elliptical annuli and up to @xmath18 in equation [ eq : fourier0 ] consistently reproduces the basic morphological features of most galaxy images . a considerable amount of experimentation went into determining how one should establish the radial bin intervals in this procedure . a series of tests were made using unequal linear bins that overlapped and logarithmic binning interval . we experimented with normalizing the bin radius by the effective radius , @xmath19 , so that all galaxies could be compared on more uniform spatial scale . this approach proved problematic since it produced profile scales that were highly compressed for early - type systems , a highly expanded in late - type systems . in such cases , the inner regions if the late - type galaxies , where much of the important morphological structure is present , was under - resolved . additionally , we found that measurement of the effective radius of galaxies in low resolution , low hst images can be systematically low , and using @xmath19 in this manner will introduce a substantial bias when comparing local and distant samples . in the end , we found that using equal size radial bins extending to an outer , low surface brightness optical isophote produce the most robust results for comparing morphological properties among galaxy images . it should be noted that one can justify the use of higher order fourier components for cases of high resolution galaxy images . in experiments with some of the deep palomar 60@xmath20 images described in section 3 , we found that the bars of many galaxies have a strong contrast relative to the disk , and high spatial frequency components ( up to @xmath21 ) are required to reconstruct such a sharp feature . incorporating so many spatial frequencies in a general image classifier is impractical , but one might hope to use some type of information about high frequency structure : if the inclusion of such components in the model significantly improves the model fit , then this is important information . perhaps a good number of barred galaxies can be identified if we simply search for images that require high order fourier components in the inner annuli to build a good fit model . the fourier - reconstructed images described above are comprised of radially - dependent sets of fourier amplitudes and phase angles . using 17 annuli , 6 fourier amplitudes ( including the @xmath22 term ) and the corresponding phase angles to parameterize each image , we thus describe each galaxy with a 221 element classification vector . some human classifiers have insisted that at least 10,000 resolution elements are required in a galaxy image that is to be morphologically classified ( de vaucouleurs , private communication ) . more liberally , we might consider that one should have at least a @xmath23 image of a galaxy , or 2500 pixels , to convey morphological information . hence , using the fourier description of a galaxy reduces the number of parameters describing the image information content by a factor of more than ten compared to that used by a human classifier . an input classification vector with over 100 elements is rather large for most pattern classifiers trained in the presence of noise . to distill our image parameterization further , we have chosen to characterize the radial properties of each fourier component . in other words , just as we often describe the radial surface brightness profile of a galaxy using several model parameters , so too can we describe the radial trends in each set of amplitude and phase estimates computed with equations [ eq : fourier4 ] and [ eq : fourier5 ] . the mean radial trends in both the amplitude and phase of the coefficients in equations [ eq : fourier4 ] and [ eq : fourier5 ] are shown in figures [ mfprof1 ] and [ mfprof2 ] for three types of galaxies . in these figures the mean phase or amplitude of a given fourier component is plotted on the y - axis as a function of elliptical annulus number on the x - axis . we divided a sample of 196 galaxies from section 3 into three family categories : a ( unbarred system ) , ab ( transitional systems ) , and b ( barred systems ) and computed the mean radial profiles for the amplitude and phase coefficients of the @xmath24 and @xmath25 coefficients . as noted by elmegreen and elmegreen ( 1985 ) and ohta ( 1990 ) , these are the dominant terms needed to reproduce the light distributions of most barred galaxies . in figure [ mfprof1 ] we see a clear trend among the @xmath24 and @xmath25 amplitudes : barred systems have significant power in the inner rings , ab systems have systematically lower power , and a galaxies have the lowest amount of @xmath24 and @xmath25 power in even the inner elliptical annuli . these mean profiles were computed with 71 a , 73 ab and 61 b galaxies taken from the analysis of section 4 . the 1-@xmath26 error of each point in the a - system profiles are shown in figures [ mfprof1 ] and [ mfprof2 ] , and it is clear that a single point from the profile of one galaxy will have little discriminatory power in distinguishing bar class . however , if we combine the information of the points from annuli with ring numbers between 3 and 12 , then we can expect to derive a robust estimate of whether a bar is present in the inner regions of a galaxy image . in this region of the reconstructed images , the mean fourier profiles clearly delineate the presence of a bar . in figure [ mfprof2 ] we plot the corresponding mean profiles for the @xmath24 and @xmath25 phase angles . although these profiles are less sensitive to bar presence , the phase terms will be important in distinguishing barred galaxies from purely spiral systems . in the case of a barred galaxy , the @xmath24 and @xmath25 phase angles remain fixed with ring number ( radius ) , whereas with a two - armed spiral pattern we expect to see a systematic variation of @xmath24 and @xmath25 phase angles with radius since the flux density peaks are changing their position angle smoothly as we progress outward in the radial annuli . as can be seen in figure [ mfprof2 ] we still observe a gradual progression in the trends of these phase angle profiles for the a , ab , and b galaxy sets . to summarize , the radial @xmath24 and @xmath25 amplitude and phase angle profiles of a galaxy carry important information about the nature of the 2-d structure present in a galaxy image , and specifically allow us to robustly quantify the presence of a linear bar structure . following the innovative work of han ( 1995 ) , we performed a principal component analysis ( pca ) of each set of fourier profiles for our collections of galaxies that had reliable stage and family classifications . for most fourier coefficients it was determined that 85% to 90% of the profile variance could be described with only 2 or 3 principal components . hence , using the eigenvectors determined from this analysis , we can characterize the fourier profile of a random galaxy using only 2 or 3 parameters . should we use the amplitude and phase of only the @xmath24 and @xmath25 components to characterize a galaxy , then we can parameterize the light distribution using 4 coefficients @xmath27 2 principal components @xmath28 8 parameters . such an image vector constitutes a very reasonable size for training a supervised classifier with the 100 - 200 patterns ( galaxies ) available in this work . in figures [ mfprof1 ] and [ mfprof2 ] we have divided the galaxies by family class , but these fourier - based principal components may be used to identify stage - related image traits also . in figure [ pc_demo ] we demonstrate our principal component method by showing pca - based image parameter spaces that are symbol coded by stage and family class .

the two - dimensional light distribution of a galaxy is reconstructed using fourier series fits to azimuthal profiles computed in concentric elliptical annuli centered on the galaxy . both the phase and amplitude of each fourier component have been studied as a function of radial bin number for a large collection of galaxy images using principal component analysis .

we use automated surface photometry and pattern classification techniques to morphologically classify galaxies . the two - dimensional light distribution of a galaxy is reconstructed using fourier series fits to azimuthal profiles computed in concentric elliptical annuli centered on the galaxy . both the phase and amplitude of each fourier component have been studied as a function of radial bin number for a large collection of galaxy images using principal component analysis . we find that up to 90% of the variance in many of these fourier profiles may be characterized in as few as 3 principal components and their use substantially reduces the dimensionality of the classification problem . we use supervised learning methods in the form of artificial neural networks to train galaxy classifiers that detect morphological bars at the 85 - 90% confidence level and can identify the hubble type with a scatter of 1.5 steps on the 16-step stage axis of the revised hubble system . finally , we systematically characterize the adverse effects of decreasing resolution and on the quality of morphological information predicted by these classifiers . * date of this version : * _ subject headings : _ galaxies : automated morphological classification

astro-ph0110275

m

here we describe the application of the method to a set of hst archival images . using the results of section 2 , we assembled samples of local and distant galaxies having weighted mean stage estimates and family classifications that at least two human classifiers agreed upon . we show a representative sample of these galaxies in figure [ sample_gals ] . as we shall discuss below , the criteria for building a family classifier training set had to be somewhat liberal in order to compile a usable experimental sample . for stage classification , a series of backpropagation networks using different input parameter vectors and network layer architectures were experimented with . in the case of the family classifier , we used two different types ann classifiers : a backpropagation - trained feed forward network , and a difference boosting neural network ( dbnn ) developed by philip ( 2000 ) . a set of 262 images were collected using the sample of galaxies having @xmath35 and weighted mean stage estimates from the analysis of section 3 . most galaxy classification systems provide criteria for estimating the morphological type of an edge - on system , however because we are concerned here with the analysis of two - dimensional morphological structures , we chose to exclude such high - inclination systems . an lmorpho task was used to perform automated surface photometry of each image , and then an interactive mosaic viewer was used to inspect the ellipse fit to the low surface brightness isophote in each galaxy postage stamp image . this was done to verify that no improper image processing errors occurred due to confusion from nearby images or other image defects . ten galaxy stamps were rejected in this step , the majority of these being relatively faint hst - observed galaxies that extended too close to the edge of the wfpc2 field . the human classifiers dealt well with `` masking '' such edge effects when the visual classification of section 2 was performed , however the sky fitting and surface brightness contouring routines of lmorpho were unable to properly handle such situations . future automated morphological surveys will of course have to deal more effectively with this type of error , but for the purpose of this work we chose to simply delete these galaxies from any machine classification experiments . for each of the 252 postage stamp images of well - classified galaxies remaining in our experimental sample the full set of morphologically - dependent fourier image parameters discussed in section 3 were computed with lmorpho . a series of backpropagation neural networks were trained following the procedures outlined in odewahn ( 1997 ) using 3 different types of input vector sets and 6 different network architectures . in every training case , two hidden layers of the same size were used to map n - dimension input vectors to an 8-node output layer , one node for each 2-step interval of the stage axis of the rhs . in practice , a final type was assigned for each input vector using the weighted mean value of the output node value . this allows one to assign not only the highest weight classification , but the rms scatter in this node - weighted mean value can be used to assign a classification confidence . hence , while any output pattern will result in the assignment of an estimated type , patterns where most of the output signal is carried in one major node will have a high confidence assignment , and patterns where the output pattern is distributed over many nodes will be assigned low confidence . the image parameter catalogs were collected into a single binary catalog which can be used in lmorpho to interactively generate symbol - coded parameter space plots like those shown in figures [ pars_stage ] and [ pars_family ] . with this package the user can quickly view many different parameter spaces and judge which one shows the largest degree of type separation ( whether stage or family ) by determining how well the different type - coding symbols are separated in the plot . an important feature in this graphical tool is that any point may be marked and used for a variety of uses . in one mode the user can choose to view on a real - time basis the galaxy image of any selected data point . in this way one is able to determine if a particular outlier is due to improper image processing or some truly unique morphological circumstance . in the latter case , such data are retained for use in classifier training . in the former , these patterns would be rejected from use in gathering training and testing samples . as the images used in this particular series of classification experiments were generally of high quality , fewer than 5% of the original 252 postage stamps were rejected in this manner . for only a few hundred galaxy images ( or even less than a few thousand ) this process of parameter space inspection is trivial to complete in a few minutes . finally , we made a preliminary set of ann training runs using different input parameter sets as well as subdividing the training / testing data in different subsets . through this process we uncovered an additional 28 objects that consistantly gave highly discrepant training results , the image parameter combinations for these sources were highly abnormal compared to the bulk of the data , and these sources were rejected from further experiments . this represented about 9% of our original training set , but determining the source of peculiarity for these galaxies will require a larger , more diverse collection of images for future experiments . we determined a number of useful input parameter combinations that showed good segregation by morphological type and a series of different image parameter set patterns were formulated . each type of pattern would form the input layer to an ann classifier . for clarity , we assigned a running integer value to each type of input , and we refer to this as the feature set number . we indicate the feature set number for each training exercise in column 8 of table 6 . in table [ parlist ] we summarize the lmorpho image parameters that were selected for the stage and family classifiers developed in this paper . since different image parameters are used in each classifier , we list in column 2 the feature set number for each input pattern using each image parameter . the selection of training and testing samples was carried out in the same manner for all input vector types . as summarized in table [ tbreakdown ] all galaxies were binned into the 8 type bins corresponding to the 8 nodes of the ann output layer . each such bin was divided into two sets : one for training and one for testing . one is always tempted to use more galaxies in the training sample so that the network has a larger number of patterns for generalizing the problem . one danger in backpropagation training is over - training : beyond some number of training iterations the network weights could be adjusted so as to simply memorize the training pattern sets as opposed to generalizing the mapping of input vectors to output classes . to prevent this , one should use an independent test data set to judge classifier performance . the backpropagation code in lmorpho computes classifier statistics for both a training sample and a testing sample at each user - specified iteration in which the updated ann weights are stored . in a post - training phase , each set of statistics is inspected by the code to determine the optimal training cycle . the algorithm used to isolate this iteration uses the slope and rms scatter of the correlation between the target stage prediction and the ann stage prediction . both the training and testing data sets are used . the case of over - training is detected by a progressive drop in the rms scatter for the training data with a flat or even increasing rms scatter for the test sample . an optimal training cycle is selected that minimizes the rms scatter for training data before over - training occurs . additionally , the slope of the linear regression must be close to unity within some user - specified tolerance , usually set at 20% . we summarize the results of our backpropagation training to develop fourier - based ann classifiers in table [ stageclassstats ] . the slope ( @xmath36 ) and scatter ( @xmath37 ) about a linear regression between the ann - predicted and the targeted mean hubble stage are tabulated for both the training and testing data sets for the selected optimal training epoch . additionally , as with the type comparison analysis in section 3 , we compute a scatter ( @xmath38 ) based on direct differences between the ann and target values following odewahn and de vaucouleurs ( 1993 ) . this statistic reflects more honestly the scatter to be expected for the user of such an ann - derived catalog . as expected , scatter among the training data is systematically lower than for the test data , since the error function being minimized in the backpropagation training is formed with the training data . however , the scatter derived for the test data is usually about 2-steps on the rhs stage axis , and hence very reasonable for most scientific pursuits with morphological data . in figure [ net_results ] we compare mean neural network classifier types from 3 different anns ( marked with asterisks in table [ stageclassstats ] ) to weighted mean visual types for two sets of data : the training data and the testing data . to summarize , the test data , comprised of sets of input classification parameters and their corresponding target types , were never presented to the ann classifiers during backpropagation training to establish the network weight values . as such , this data sample represents a fair comparison by which we can judge true network performance . we include in figure [ net_results ] the same correlation for the training sample . in summary , the fourier - based stage classifiers developed in this experiment clearly perform as well as a human classifier . these results are certainly encouraging if our goal is simply to estimate revised hubble types for a large number of digital images , but a more important point must be stressed . we have shown that our method of parameterizing a galaxy image preserves the information content needed to emulate the process used by a human classifier . as with the bar classification work described below , our ultimate goal will be to use such a digital image analysis to search for more direct correlations among galaxy properties and ultimately develop a more physically meaningful classification system beyond the rhs . as discussed in section 3 , the visual classifiers divided the family estimates into the three bins of the rhs : a , ab , b. the difference between each class is somewhat vague and subject to personal bias . it is not surprising that we found very few cases where all three classifier agree that a galaxy was of the ab family class . as was discussed for figure [ mfprof1 ] , the fourier profiles for ab galaxies are , in the mean , intermediate between the a and b galaxies . however , the ab galaxies show a markedly large variance which is probably due to the wide variance in ab classification criteria used by the human classifiers . the presence of such uncertainty made it impossible to train an effective 3-division stage classifier . for the present work , we approached the problem using an unambiguous set of a and b galaxies and attempted to develop a robust classifier for identifying them using the fourier - based eigenvector approach discussed in section 3 . when larger samples of morphologically classifiable galaxy images are collected , it is anticipated that a more thorough study of bar strength parameters will allow the development of a more sophisticated automated family classifier . for the present set of classification experiments we gathered images of 71 a galaxies and 61 b galaxies drawn from the analysis of section 3 . in this case , any galaxy which had family classifications that were agreed upon by at least 2 of the 3 human classifiers were adopted for use . to clarify the problem , we used only a and b classes for classifier experiments . after a series of parameter space inspections , such as those described in the stage classification section , we chose to use the first principal components of the @xmath24 and @xmath25 amplitude profiles . we found that additional discrimination was added in many cases using the first principal component of the @xmath25 phase profile and adopted this for use in the classifier input vector . it was found that including parameters that are highly correlated with bulge to disk ratio ( the principal components of the normalized flux profile ) did not add significantly to detecting the presence of a bar . this was surprising in that it is well known that bar shapes and properties are correlated with hubble stage , and hence bulge to disk ratio ( elmegreen and elmegreen 1986 ) . in future work with much larger samples of galaxies , the use of terms related to the shape of the surface brightness profile may prove useful for this reason : pattern classifiers can better interpret the meaning of morphological shape parameters like the first principal components of the @xmath24 and @xmath25 amplitude profiles if some information related to hubble stage is provided . for the present small sample of potentially useful training samples , we decided to exclude the use of surface brightness profile shape parameters for the training of a family classifier . we added two simple global image parameters that contribute information about bar presence that were independent of the fourier model approach . in determining the shape and orientation of the optimal elliptical aperture for measuring each galaxy , lmorpho computes a series of ellipse fits to progressively fainter surface brightness levels . the initial surface brightness levels are high and generally sample the bright inner region of a galaxy where the bars are found . it was found that simple parameters using these elliptical isophote parameters could be formed that gave useful information about the presence of a bar that would be independent of the image models derived with the fourier method . we define the minimum axis ratio of the series of ellipse fits to be @xmath39 , and the axis ratio of the largest ellipse ( i.e. the fit to the lowest surface brightness level ) to be @xmath40 . in general , a barred galaxy will have @xmath41 , but with the condition that the major axis length of the isophote measured for @xmath39 is significantly smaller than that measured at the isophote for @xmath40 . to discriminate this condition we formed the parameter @xmath42 , where @xmath43 is the semi - major axis length measured at @xmath39 and @xmath44 is the semi - major axis length measured at @xmath40 . additionally , we formed @xmath45 , to measure the contrast of the ellipticity variation in the galaxy image . it was found that for many galaxies , a plot with @xmath46 on the y - axis and @xmath47 on the x - axis places b galaxies in the upper left corner and a galaxies in the lower right corner . of course , there is a rather substantial overlapping zone in the low @xmath46 and low @xmath47 region of this plot . hence , while such a simple scheme can not discriminate all a , b galaxies , it can provide high weight information for some systems . simple initial ann classification experiments provided evidence that these parameters , when added to the fourier - based parameters , produced better discrimination for a , b samples and hence we included them in the training of our final family classifier . two types of family classifiers were trained with the input vector parameters shown in table [ parlist ] . first , the backpropagation network code used the previously discussed stage classifiers was used to train a network consisting of 2 hidden layers having 12 nodes each . this network mapped an 8-element input vector to a 2-node output layer . patterns with more power produced in output node 1 were classified as a , and patterns with more power produced in output node 2 were classified as b. many of the dimensions in this 8-dimensional classification space produce a good split between the a and b populations and hence the backpropagation training converged relatively quickly . as with the stage classifiers , a sample of pure test patterns was retained and used to assess network performance at each stage in the backpropagation weight update process . this procedure gives us a truly independent check on the classifier performance and an effective means of guarding against over - training . a total of 30 training epochs were used in the backpropagation training , and epoch 15 was selected as providing optimal performance with a success rate performance of 92% among training patterns and 85% among test patterns . in a second experiment the dbnn method of philip ( 2000 ) was applied to the identical training and testing patterns as for the backpropagation ann . after boosting , the training set was found to produce a 94.1% successful classification rate and the test set was found to produce a success rate of 87.5% . the performance of the dbnn classifier was found to be marginally better than the backpropagation - trained network , however a large sample of training data will be needed to assess if this improvement is significant . nevertheless , both methods produced automated family classifiers that are able to discriminate bar presence with a roughly 90% probability of success . image quality plays a crucial role in determining the extent to which morphological classification can be performed on a galaxy . a gradual decrease in image resolution and will systematically degrade the quality of morphological classifications , both by human and machine methods . with stage estimation , one might expect that we lose the ability to differentiate the bulge and disk components , making it extremely difficult to work at the early stage of the hubble sequence ( differentiate e , s0 and early spiral systems ) . at the late hubble stages , we lose many of the low surface brightness features in the out disk regions that are crucial for differentiating among the sd , sm and i m systems . with family classification , one can expect that gradual image degradation will make it impossible to detect the presence of a bar , much less characterize the properties of the bar ( see van den bergh 2001 ) . in the past , human classifiers , in particular those dealing with low resolution and low schmidt plate images ( nilson 1973 , corwin 1985 ) , have generally taken such effects into account by dropping the amount of detail in the literal type assigned to a galaxy . in other words , a system might be classified simply as `` s '' rather that `` sbc '' , if the image quality is sufficient only to differentiate the difference between early- , mid- , or late - type galaxy . such effects must be accounted for in any automated system geared towards the recognition of morphological features . one must know if there is a strong systematic bias towards , for instance , missing bar or spiral features as resolution decreases . perhaps if such effects are well understood we may hope to correct large statistical samples in some systematic way . at the very least , we must quantify the levels of low or resolution that can be tolerated before the quality of automated classifications falls below some minimum tolerance required by a given science goal . we chose to define resolution as the number of pixels in a galaxy image contained within the isophotal ellipse used to integrate the isophotal magnitude in lmorpho . this is a reasonable approach for hst images where , for most filters , each pixel approaches the resolution of the optical image . for ground based images we should use the size of the seeing disk , which is generally several times larger than the pixel size . in our present study all of the ground based images have been block averaged to produce pixel sizes that are comparable to the seeing disk and hence we can use this uniform resolution definition for all of the galaxies analyzed . as for defining the in a galaxy image we used two approaches . in the first , we simply compute the ratio of the mean signal ( above sky ) per pixel to the standard deviation of the local sky measure . in the second approach , we define the mean signal , @xmath48 , to be the zeroeth order term in the fourier series fitted to the azimuthal distribution in each model annulus , and the noise , @xmath49 , is the r.m.s . scatter about that fit . this latter approach incorporates the poisson noise associated with the detected galaxy signal and accounts for large scale structural changes across the azimuthal profile . in practice , the two methods had very different ranges , but were found to be well correlated . the method 1 approach yielded estimates in the range 100 to 1000 , and the fourier - based method produced values in the range of 3 to 20 . it was found that the early - type galaxies , having little large scale structure in their images , produced the tightest correlation between these two types of estimators . for practical reasons , we used the more easily computed method 1 values in the image classification experiments described in this section . to characterize how decreased and resolution will affect the quality of our fourier - based ann classifiers , we selected sets of galaxies having extremely high and resolution . these systems were found to be classified correctly by the stage and family classifiers discussed in the previous sections . most of these images were taken from the ground - based datasets obtained with the palomar 60@xmath20 discussed in section 3 , but a few of the highest resolution hst images were also included . for samples having well classified stage and family types , we selected galaxies with images that had at least 2000 pixels contained within the optimal elliptical aperture . these sets of images were then systematically re - sampled using an lmorpho package designed for this experiment to produce postage stamp images of galaxies having progressively lower and resolution . as this exercise was designed to study the general systematic effects of image degradation on morphological classification , no attempt was made to model the noise properties of a given detector , like wfpc2 or stis ( as in odewahn 1997 ) . for each re - sampled image , an extra component of gaussian noise was added to the original image . we modeled decreasing resolution in two ways . first , we consider the case of high sample rate with image blurring , the case typically encountered with ground - based observations of nearby galaxies . in the second , and more relevant case , we considered a low sample rate with high optical resolution , the image suffers from a high degree of pixelation . to simulate this effect , we simply block averaged the original galaxy images to a lower image sampling rate . this latter effect is well known to anyone who has classified large numbers of distant galaxies on wfpc2 images and is the one , as we will show , which dominates our ability to determine distant galaxy morphological classification . the results for the backpropagation ann stage classifiers are summarized in figure [ systematics_stage ] . for this experiment a simple success rate calculation was not appropriate . we desire to know not only whether a classifier fails to predict the correct stage estimate within some number of type bins , but in which direction a misclassification occurs . if the classifier consistently pushed stage estimates in an early ( towards e , s0 ) or a late ( toward i m ) direction then a substantial bias will be introduced in the scientific interpretation of the ann - generated morphological catalog . hence , we chose to compute the trend in type stage residuals , computed in the sense of @xmath50 , as a function of resolution and , where @xmath51 is the true galaxy type . these trends were computed using overlapping bins in resolution or , with the mean stage residual and the rms about that mean computed in each bin . a set of 1901 re - sampled images were processed with the ann classifiers discussed in section 4.2 to estimate hubble stage . in figure [ systematics_stage ] we show trends in stage residuals for three sets of target stage intervals : e - s0 , sa - sbc , and sc - im . in each case we have used overlapping x - axis bins of width 0.2 dex , and we expect to observe the degradation in classifier performance as image quality is lowered . spiral and irregular stages show a moderate trend in positive mean offset ( the ann classifies these galaxies with an earlier value ) and increased rms scatter about the mean with decreasing resolution and . of more significance , e+s0 galaxies exhibit a mean negative offset ( the ann classifies these systems to be later than the target value ) of 2 - 3 hubble steps . this occurs for even the highest resolution and highest galaxy images in our present sample . additionally , this mean offset and increasing rms scatter in t - types for the e+s0 galaxies is clearly steeper than for spiral and irregular galaxies . a variety of network architectures and input parameter vectors were experimented with in order to correct this problem . little improvement was obtained due in large part to the lack of a sufficiently large sample of images for such galaxies . as discussed in cohen ( 2001 ) , e+s0 in the field are relatively rare for 22 , and hence a very large number of hst parallel observations are needed to build up a significant image library . work is currently underway to collect such images from the many archival hst observations of moderate - redshift clusters . clusters contain not only a large number of galaxies in a single wfpc2 field , but the morphological fractions of these galaxies are skewed to the early - types . the analysis of such large samples will potentially eliminate the mean negative stage offsets observed for the e+s0 samples of figure [ systematics_stage ] , however it is doubtful that we can hope for a comparable decrease in the rms of such stage classifications in the low and resolution regimes . it is clear that images of sufficiently high quality are needed to differentiate many of the subtle structural properties of early - type galaxies , as is clear from the work of i m ( 2000 ) . the larger field size , higher quantum efficiency , and especially increased resolution of acs , compared to wfpc2 , will make this the instrument of choice on hst for identifying large samples of moderate - redshift e+s0 systems in the near future . the results for the backpropagation ann family classifier are summarized in figure [ systematics_bar ] . unlike the stage classifiers , our family classifiers predict only two states : a or b. hence , we are able to characterize the output results as success or failure cases . we therefore chose to plot the distribution of and resolution for ann - predicted classes for a sample of barred galaxies that agree with the target value and for those that fail to agree . as expected , in figure [ systematics_bar ] the success cases cluster in the high , high resolution area of the plot , and the failure cases cluster most heavily in the low and resolution region . for clarity , we also plot the success rate trends binned by and resolution . for identifying the presence of a bar , it is quite clear from these mean relations that some critical image resolution is required . for our present samples and fourier - based ann classifiers , we are unable to effectively identify barred systems at better than a 70% success rate until we obtain galaxy images with at least 1000 resolution elements ( @xmath52 3 , where @xmath52 is the number of image pixels above the isophotal threshold ) . the trend with is less steep , but a mean ( per pixel ) of around 1000 is also required to reliably identify bars . the same experiment was carried out for a sample of unbarred ( a ) galaxies with different , but expected , results . in this case , galaxies that are successfully classified as a at high and resolution generally retain that classification at low and resolution . in other words , the ann classifiers rarely turn a galaxies into b galaxies , as is true for human classifiers . in general , as we lose image resolution we begin to loose the ability to identify morphological bars , but we do not tend to contaminate b galaxy samples with misclassified a galaxies , an important point when considering the the frequency of barred systems at high redshift .

we find that up to 90% of the variance in many of these fourier profiles may be characterized in as few as 3 principal components and their use substantially reduces the dimensionality of the classification problem . we use supervised learning methods in the form of artificial neural networks to train galaxy classifiers that detect morphological bars at the 85 - 90% confidence level and can identify the hubble type with a scatter of 1.5 steps on the 16-step stage axis of the revised hubble system . finally , we systematically characterize the adverse effects of decreasing resolution and on the quality of morphological information predicted by these classifiers .

we use automated surface photometry and pattern classification techniques to morphologically classify galaxies . the two - dimensional light distribution of a galaxy is reconstructed using fourier series fits to azimuthal profiles computed in concentric elliptical annuli centered on the galaxy . both the phase and amplitude of each fourier component have been studied as a function of radial bin number for a large collection of galaxy images using principal component analysis . we find that up to 90% of the variance in many of these fourier profiles may be characterized in as few as 3 principal components and their use substantially reduces the dimensionality of the classification problem . we use supervised learning methods in the form of artificial neural networks to train galaxy classifiers that detect morphological bars at the 85 - 90% confidence level and can identify the hubble type with a scatter of 1.5 steps on the 16-step stage axis of the revised hubble system . finally , we systematically characterize the adverse effects of decreasing resolution and on the quality of morphological information predicted by these classifiers . * date of this version : * _ subject headings : _ galaxies : automated morphological classification

1103.4026

i

age estimates are required for studying the evolutionary history of star clusters . based on such age estimates , a general framework has been developed starting from formation within the dense cores of giant molecular clouds ( gmcs ) ; a stage where the young stars are completely obscured by their dusty gas cocoons ; an emerging stage where the clusters become visible in the infrared ( ir ) and then visible in the optical as stellar winds and supernovae blow away the gas and dust ; a stage where an expanding bubble of ionized gas is blown ; and later stages with no evidence of ionized gas ( e.g. , see the lada & lada 2003 review article ) . in the past , two general methods for estimating the ages of unresolved extragalactic star clusters have been used . the first requires obtaining high quality spectroscopic observations covering wavelength regions of lines which change as a function of time . examples of this approach include bica & alloin ( 1986 ) , schweizer & seitzer ( 1993 ) , whitmore ( 1999 ) , bastian et al . ( 2009 ) and wofford et al . while these spectroscopic observations typically provide high quality age determinations , they are limited to age - dating relatively small numbers of bright clusters due to constraints on the brightness of clusters that can be observed spectroscopically in a reasonable amount of time . the standard method for age - dating large numbers of extra - galactic clusters compares photometry in several broadband filters ( e.g. , _ ubvi _ ) with predictions from population synthesis models ( e.g. , chandar et al . 2010 ) . comparisons of age estimates using spectroscopic and photometric observations of the same clusters show good agreement in most cases . an early example of this is the famous searle et al . ( 1980 ) paper where they compare integrated four - filter _ ugvr _ photometry of 61 star clusters in the magellanic clouds with the strength of different spectral features ( e.g. , balmer lines , @xmath14 band , etc . ) a recent example is wofford et al . ( 2010 ) who compared ages estimated from spectral energy distribution ( sed ) fitting with those derived from uv spectroscopy for 14 young ( @xmath15 myr ) clusters in the nuclear starburst region of m83 and found that the photometric ages are within a factor of 1.4 of the spectroscopic ones . whitmore et al . ( 2010 ) find similar agreement between their photometric age estimates and the spectroscopic estimates from bastian et al . ( 2009 ) for clusters in the antennae galaxies . while generally satisfactory , both the spectroscopic and photometric techniques have limitations . it is therefore important to develop independent methods for estimating the ages of clusters , especially for cases where spectroscopic or multi - band photometric observations are not available and it is necessary to estimate ages based on morphological appearance alone . here , we develop two new methods for estimating the ages of young star clusters in nearby galaxies based on high - resolution images at optical wavelengths . the first method uses the morphology of the ionized gas and its position relative to the cluster stars , as measured from narrowband h@xmath0 emission , to estimate ages ( @xmath16 ) for clusters younger than @xmath17 myr . this method relies on the general premise that the distribution of h@xmath0 will be largely coincident with the distribution of optical light in the youngest clusters ( i.e. , @xmath10 few myr ) , will be in a small ring - like structure around the optical stellar emission in slightly older clusters where massive star winds and supernovae have had time to blow a bubble ( i.e. , @xmath18 myr ) , and will be in a larger ring - like bubble for still older clusters ( i.e. , 510 myr ) . many past observational and theoretical studies of hii regions and `` supershells '' in the milky way and nearby galaxies have laid the groundwork for this method . for example , walborn ( 2002 ; see also walborn & parker 1992 and especially walborn 2010 for related discussions ) outlined an evolutionary cluster sequence based on observed properties of several well known clusters and ob associations in the milky way with ages ranging from @xmath19 myr to @xmath5 myr . this sequence was then used to illustrate observed changes with age in the visually brightest stars , in the ionized gas and dust content , and in the existence of red supergiants . much of this sequence was based on spectroscopy of individual stars . while we are unable to make similarly detailed observations at the distance of m83 , many of the same basic correlations and underlying physical processes are relevant for the age sequence outlined in this paper . theoretically , several works have made predictions for the size evolution of an expanding hii region over time . oey & clark ( 1997 , 1998 ) model the size evolution due to mass loss and supernova - injected energy from cluster stars , and assume that expanding bubbles `` stall '' when their internal pressure equals the ambient pressure in the ism . these simulations predict a strong dependence of bubble size on both the age and mass of the central cluster . ( e.g. , weaver et al . 1977 , oey & massey 1995 , oey & garcia - segura 2004 , dopita et al . 2006a , 2006b ) . our observations of clusters in m83 reveal a strong dependence of bubble size on cluster age , and possibly a weak dependence on cluster mass , as discussed in section 6 . the second method developed in this paper uses the surface brightness fluctuations of cluster stars to estimate their ages . young clusters have strong pixel - to - pixel flux variations , due to the presence of massive , luminous stars . as a cluster ages , the bright , short - lived massive stars disappear , and these fluctuations fade in strength . this technique is especially useful in the range @xmath20100 myr , ages that can be somewhat difficult to deal with using the sed method , because the predicted integrated colors loop back on themselves . our primary target for this study is the spiral galaxy m83 . at a distance of 4.5 mpc ( corresponding to a distance modulus of @xmath21 ; thim et al . 2003 , and a pixel scale of 0.876 pc pixel@xmath22 ) , m83 , nicknamed the `` southern pinwheel , '' is the nearest massive grand - design spiral galaxy . it is a slightly barred galaxy , with a hubble type sab(s)c ( 3rc ) . in this work , we make use of observations taken with the wide - field camera 3 ( wfc3 ) , which were described in detail in dopita et al . ( 2010 ) and chandar et al . briefly , the observations are part of the early release science project 1 ( ers1 ) program 11360 ( pi : oconnell ) and were taken in august , 2009 . observations were taken in several broadband ( `` uv '' - f225w , `` u '' - f336w , `` b '' - f438w , `` v '' - f555w , `` i '' - f814w , `` j '' - f110w , and `` h '' - f160w ) , and narrowband filters ( [ oiii ] - f373n , h@xmath23 - f487n , [ oii ] f502n , h@xmath0 - f657n , [ sii ] - f673n , paschen@xmath23 - f128n , and [ feii ] - f164n ) . in the appendix we briefly investigate clusters in m51 and find that the age versus morphological category relationship derived for m83 is appropriate for this galaxy as well . this paper is organized as follows : in section 2 we outline our working scheme for an evolutionary cluster classification system based on observables at optical wavelengths . in section 3 we investigate the correlation between h@xmath0 morphology and sed age estimates while section 4 examines the correlation between the strength of surface brightness fluctuations within clusters and their ages . a catalog of smaller hii regions , apparently ionized by `` single stars , '' is presented in section 5 . we examine the effect of cluster mass on h@xmath0 bubble size in section 6 , and summarize our primary results in section 7 .

the first method uses the physical extent and morphology of h emission to estimate the ages of clusters younger than myr . this method relies on the fact that the brightest individual stars in a cluster are most prominent at ages around 10 myr , and fall below the detection limit ( i.e. , m ) for ages older than about 100 myr . the youngest clusters also have lower flux variations , hence the relationship is double valued . these two methods are the basis for a new morphological classification system which can be used to estimate the ages of star clusters based on their appearance . we compare previous age estimates of clusters in m83 determined from fitting _ _ ubvi__h measurements using predictions from stellar evolutionary models with our new morphological categories and find good agreement at the% level .

we use new wfc3 observations of the nearby grand design spiral galaxy m83 to develop two independent methods for estimating the ages of young star clusters . the first method uses the physical extent and morphology of h emission to estimate the ages of clusters younger than myr . it is based on the simple premise that the gas in very young ( few myr ) clusters is largely coincident with the cluster stars , is in a small , ring - like structure surrounding the stars in slightly older clusters since massive star winds and supernovae have had time to push out the natal gas ( e.g. , myr ) , and is in a larger ring - like bubble for still older clusters ( i.e. , myr ) . if no h is associated with a cluster it is older than myr . the second method is based on an observed relation between pixel - to - pixel flux variations within clusters and their ages . this method relies on the fact that the brightest individual stars in a cluster are most prominent at ages around 10 myr , and fall below the detection limit ( i.e. , m ) for ages older than about 100 myr . older clusters therefore have a smoother appearance and smaller pixel - to - pixel variations . the youngest clusters also have lower flux variations , hence the relationship is double valued . this degeneracy in age can be broken using other age indicators such as h morphology . these two methods are the basis for a new morphological classification system which can be used to estimate the ages of star clusters based on their appearance . we compare previous age estimates of clusters in m83 determined from fitting _ _ ubvi__h measurements using predictions from stellar evolutionary models with our new morphological categories and find good agreement at the% level . the scatter within categories is dex in for young clusters ( myr ) and dex for older ( myr ) clusters . a by - product of this study is the identification of 22 `` single - star '' hii regions in m83 , with central stars having ages myr .

1103.4026

i

we have used observations taken with the newly installed wfc3 camera on - board the _ hubble space telescope _ to develop two independent methods for age - dating young star clusters in the nearby spiral galaxy m83 . our primary results are summarized below . a working classification system , largely based on h@xmath0 morphology and pixel - to - pixel flux variations , was developed to map an observed age sequence onto a proposed sequence of cluster evolution . the underlying evolutionary picture includes the formation of dense cores in giant molecular clouds ( gmcs ) ; a stage where the young stars are completely obscured by their dust cocoon ; an emerging stage where the clusters become visible in the ir , and then in the optical as stellar winds and supernovae blow away the dust ; a stage where an expanding h@xmath0 bubble is blown and the existence of very bright young stars leads to large pixel - to - pixel flux variations ; and later stages with no evidence of h@xmath0 and diminishing pixel - to - pixel flux variations . \2 . we found that h@xmath0 morphology , i.e. , the size of the ionized gas bubble , provides a viable method for age - dating clusters in the range 110 myr . this method is based on the simple premise that the gas in very young ( @xmath2 few myr ) clusters is largely coincident with the cluster stars , is in a small , ring - like structure surrounding the stars in slightly older clusters since the winds from massive stars have had time to push out the natal gas ( e.g. , @xmath75 myr ) , and is in a larger ring - like bubble for still older clusters ( i.e. , @xmath67510 myr ) . if no h@xmath0 is associated with a cluster it is generally older than @xmath6710 myr . we first made _ qualitative _ estimates based on the classification scheme outlined above , and find that the ages of the clusters , as determined from the sed method described in chandar et al . ( 2010 ) , correlate well with the morphological categories , with a scatter of @xmath670.1 in @xmath29 within each category for the clusters with h@xmath0 emission , and a scatter of @xmath670.5 in @xmath29 for the older clusters . we then _ quantified _ this technique by correlating the measured radii of the most conspicuous h@xmath0-emitting ring or shell which appears to be physically related to the cluster with the sed ages determined in chandar et al . we found tentative evidence for a weak correlation between bubble size and cluster mass , but a larger , more objectively selected sample will be required to confirm this . we then used pixel - to - pixel flux variations to age - date clusters . this technique is based on the fact that individual stars are bright enough to be visible within clusters when they are young ( e.g. , m@xmath6 , the approximate detection level , for the brightest stars with ages @xmath10100 myr ) , leading to relatively large pixel - to - pixel variations in flux . the strength of the fluctuations peaks in clusters with ages of @xmath67510 myr , presumably because this is when the brightest stars ( e.g. , red and blue super giants ) appear . the number of luminous , evolved stars falls off for both younger and older clusters . this degeneracy in age can be broken using other age indicators such as the h@xmath0 morphology . the technique is especially useful for identifying clusters older than 100 myr . a by - product of this study was the identification of 22 `` single - star '' hii regions in m83 . by assuming that all of these objects have a similar age , and that the distribution in the two - color diagram is primarily due to reddening , we corrected for the effects of reddening and extinction . we found that this procedure moves most of the objects to a very young isochrone with an age approximately 4 myr . some of these massive stars are located far from any star - forming region , indicating that they either formed in the field or were dynamically ejected from their birthsites at very high velocities . these sshii regioins will be studied in more detail in h. kim et al . ( 2011 , in preparation ) . in the future , we will extend the classification system into the near - ir ( i.e. , categories 1 and 2 ) using our j and h observations . we will also calculate the energy budget of cluster stars and compare with physical properties of the clusters and the ism . finally , we will extend this analysis to other galaxies in the ers1 sample ( including `` low pressure '' systems such as the dwarf starburst galaxy ngc 4214 ) in order to determine whether the relationships are universal or are strongly dependent on environment . we thank zolt levay for making the color images used in figures [ fig:18plot ] and [ fig : large_image ] . this paper is based on observations taken with the nasa / esa _ hubble space telescope _ obtained at the space telescope science institute , which is operated by aura , inc . , under nasa contract nas5 - 26555 . the paper makes use of early release science observations made by the wfc3 science oversight committee . we are grateful to the director of stsci for awarding director s discretionary time for this program . r. c. is grateful for support from the nsf through career award 0847467 . this research has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , california institute of technology , under contract with nasa . the spiral galaxy m51 was originally used to perform a pilot study to test how well h@xmath0 morphology can be used to estimate cluster ages . examples of the results are included in figures [ fig : m51_ha_morph_1 ] and [ fig : m51_ha_morph_2 ] . these are similar to figure [ fig : large_image ] for m83 and show that even at twice the distance of m83 the quality of the images are comparable , and the morphological categories match sed age estimates at a similar level . a more complete analysis will be included in a future paper ( r. chandar et al . 2011 ; in preparation ) . 1&65815&204.244637&@xmath7629.8507043&@xmath766.10 & 2.57&@xmath761.35&@xmath760.12&0.24&6.52&1.1e3 & 3&2&0.082 + 2&63611&204.2426354&@xmath7629.8515924&@xmath766.42 & 2.35&@xmath761.27&0.07&0.34&6.54&2.1e3 & 3&1&0.091 + 3&41736&204.251687&@xmath7629.8640556&@xmath768.70 & 2.68&@xmath760.21&0.80&0.50&6.7&2.6e4 & 3&7&0.064 + 4&39744&204.2524132&@xmath7629.8651911&@xmath7611.03 & 2.58&@xmath761.33&0.23&0.30&6.56&1.2e5 & 3&7&0.119 + 5&49651&204.2564416&@xmath7629.8586912&@xmath767.17 & 2.50&@xmath760.38&0.68&0.50&6.48&7.1e3 & 3&3&0.063 + 6&32461&204.2880034&@xmath7629.8692326&@xmath767.67 & 2.62&@xmath761.36&0.30&0.44&6.52&8.6e3 & 3&5&0.073 + 7&53072&204.2889299&@xmath7629.8569125&@xmath766.64 & 2.61&@xmath760.93&0.56&0.50&6.48&4.2e3 & 3&4&0.076 + 8&93801&204.2795357&@xmath7629.8392001&@xmath767.10 & 2.50&@xmath761.37&0.08&0.32&6.54&3.6e3 & 3&1&0.106 + 9&50287&204.2865616&@xmath7629.8582915&@xmath767.35 & 2.66&@xmath760.54&0.69&0.50&6.70&7.4e3 & 3&6&0.072 + 10&59214&204.2818977&@xmath7629.8537395&@xmath767.56 & 2.53&@xmath761.08&0.36&0.50&6.54&9.3e3 & 3&6&0.105 + 11&24767&204.2493318&@xmath7629.8729735&@xmath766.89 & 2.32&@xmath760.46&0.70&0.50&6.56&5.1e3 & 3&7&0.096 + 12&58013&204.2475174&@xmath7629.8543366&@xmath766.49 & 2.43&@xmath761.29&0.15&0.42&6.46&5.4e3 & 3&7&0.104 + 13&52726&204.2458956&@xmath7629.8570619&@xmath768.13 & 2.78&@xmath761.50&@xmath760.06&0.26&6.42&1.2e4 & 3&7&0.130 + 14&12721&204.2908632&@xmath7629.8785688&@xmath765.98 & 2.43&@xmath761.30&0.32&0.50&6.46&4.3e3 & 3&5&0.070 + 15&19354&204.2525635&@xmath7629.8755537&@xmath766.06 & 2.83&@xmath761.39&0.27&0.44&6.44&2.5e3 & 3&7&0.065 + 16&51616&204.2799185&@xmath7629.8575701&@xmath769.31 & 2.43&@xmath761.33&@xmath760.02&0.20&6.58&1.8e4 & 4a&6&0.131 + 17&49790&204.2546965&@xmath7629.8585957&@xmath767.88 & 2.27&@xmath760.85&0.27&0.42&6.68&1.1e4 & 4a&10&0.091 + 18&17035&204.2906967&@xmath7629.8766101&@xmath767.23 & 2.24&@xmath761.48&@xmath760.16&0.00&6.70&1.8e3 & 4a&15&0.119 + 19&66897&204.2654298&@xmath7629.8502774&@xmath768.60 & 2.96&@xmath761.50&@xmath760.12&0.00&6.72&4.4e3 & 4a&20&0.134 + 20&39842&204.2520397&@xmath7629.8651314&@xmath7610.94 & 2.71&@xmath761.51&@xmath760.15&0.08&6.58&5.2e4 & 4a&13&0.086 + 21&31457&204.2855284&@xmath7629.8698283&@xmath768.83 & 2.19&@xmath761.31&@xmath760.03&0.04&6.78&8.9e3 & 4a&17&0.164 + 22&74860&204.262148&@xmath7629.8474511&@xmath768.59 & 2.67&@xmath761.43&@xmath760.14&0.00&6.78&5.5e3 & 4a&21&0.141 + 23&89929&204.2581863&@xmath7629.8412261&@xmath766.79 & 2.23&@xmath761.35&@xmath760.05&0.04&6.72&1.3e3 & 4a&17&0.118 + 24&25607&204.2492229&@xmath7629.8725982&@xmath767.85 & 2.61&@xmath760.66&0.42&0.50&6.70&1.2e4 & 4a&21&0.120 + 25&75041&204.2775285&@xmath7629.847385&@xmath767.31 & 2.24&@xmath761.61&@xmath760.15&0.12&6.52&2.7e3 & 4a&7&0.137 + 26&64462&204.2811447&@xmath7629.8512236&@xmath768.19 & 2.30&@xmath760.81&0.34&0.46&6.68&1.7e4 & 4a&7&0.121 + 27&61923&204.263904&@xmath7629.8523354&@xmath766.02 & 2.52&@xmath761.28&0.06&0.36&6.54&1.5e3 & 4a&9&0.105 + 28&21601&204.2861725&@xmath7629.8744932&@xmath769.59 & 2.27&@xmath761.48&@xmath760.12&0.00&6.74&1.5e4 & 4a&15&0.158 + 29&62771&204.2811659&@xmath7629.8519608&@xmath767.25 & 2.27&@xmath760.96&0.28&0.38&6.70&5.6e3 & 4a&16&0.130 + 30&13265&204.2547344&@xmath7629.8783208&@xmath767.64 & 2.44&@xmath761.63&@xmath760.27&0.00&6.64&2.3e3 & 4a&13&0.148 + 31&5990&204.2551409&@xmath7629.8813282&@xmath768.17 & 2.47&@xmath761.53&@xmath760.26&0.00&6.72&3.9e3 & 4a&46&0.124 + 32&67958&204.2887307&@xmath7629.8499286&@xmath769.84 & 3.20&@xmath761.35&@xmath760.04&0.02&6.78&1.1e4 & 4a&19&0.161 + 33&66054&204.2644967&@xmath7629.8506016&@xmath769.97 & 2.63&@xmath761.45&0.39&0.00&6.88&2.8e4 & 4a&49&0.127 + 34&69793&204.2694643&@xmath7629.8493238&@xmath7611.41 & 2.63&@xmath761.48&@xmath760.16&0.00&6.78&7.5e4 & 4a&25&0.136 + 35&7716&204.2816067&@xmath7629.8807039&@xmath769.17 & 2.47&@xmath761.43&0.41&0.00&6.88&1.4e4 & 4b&68&0.151 + 36&36651&204.2524088&@xmath7629.8668398&@xmath7612.17 & 3.09&@xmath761.58&@xmath760.22&0.00&6.78&1.1e5 & 4b&&0.070 + 37&35937&204.2537197&@xmath7629.8672182&@xmath7610.31 & 2.79&@xmath761.24&0.45&0.02&6.90&4.2e4 & 4b&&0.052 + 38&54268&204.2932226&@xmath7629.8563319&@xmath768.57 & 2.87&@xmath760.91&0.79&0.34&6.86&1.7e4 & 4b&32&0.108 + 39&23366&204.2529648&@xmath7629.8736403&@xmath769.39 & 2.43&@xmath761.29&@xmath760.08&0.02&6.78&1.3e4 & 4b&41&0.116 + 40&27423&204.2896066&@xmath7629.8718058&@xmath768.38 & 2.34&@xmath760.99&0.50&0.36&6.78&1.4e4 & 4b&71&0.170 + 41&78807&204.2629122&@xmath7629.8459862&@xmath769.71 & 2.46&@xmath761.55&@xmath760.23&0.00&6.78&1.6e4 & 4b&45&0.169 + 42&36729&204.2525635&@xmath7629.8667944&@xmath7612.15 & 3.08&@xmath761.45&0.00&0.00&6.74&1.0e5 & 4b&&0.073 + 43&70777&204.2607456&@xmath7629.8489709&@xmath768.18 & 2.68&@xmath761.23&0.49&0.08&6.88&6.7e3 & 4b&43&0.087 + 44&70769&204.2650559&@xmath7629.8489734&@xmath767.77 & 2.92&@xmath761.34&@xmath760.08&0.00&6.76&2.1e3 & 4b&18&0.108 + 45&37589&204.2519048&@xmath7629.8663287&@xmath7611.96 & 3.20&@xmath761.13&0.46&0.24&6.74&1.4e5 & 4b&&0.064 + 46&49893&204.2897929&@xmath7629.8585381&@xmath769.76 & 2.74&@xmath761.49&@xmath760.24&0.00&6.78&1.6e4 & 4b&48&0.189 + 47&37095&204.2523893&@xmath7629.8665896&@xmath7611.18 & 2.79&@xmath761.32&0.35&0.00&6.88&8.0e4 & 4b&&0.059 + 48&78154&204.257905&@xmath7629.8462475&@xmath768.28 & 2.76&@xmath760.86&0.18&0.00&7.86&3.4e4 & 5a&&0.080 + 49&66216&204.2897363&@xmath7629.8505371&@xmath768.87 & 2.56&@xmath760.98&0.70&0.34&6.84&2.5e4 & 5a&&0.145 + 50&76156&204.2556622&@xmath7629.8469956&@xmath7610.21 & 3.15&@xmath761.08&0.62&0.06&7.48&1.0e5 & 5a&&0.089 + 51&66123&204.2903301&@xmath7629.8505755&@xmath769.39 & 2.50&@xmath761.11&0.59&0.22&6.86&3.0e4 & 5a&&0.125 + 52&66069&204.2844254&@xmath7629.8505955&@xmath768.88 & 3.13&@xmath760.78&0.47&0.06&7.81&4.5e4 & 5a&&0.067 + 53&85836&204.2694279&@xmath7629.8431197&@xmath769.43 & 3.25&@xmath761.12&0.18&0.10&6.78&8.7e3 & 5a&&0.093 + 54&40779&204.2926898&@xmath7629.8645926&@xmath7610.17 & 3.06&@xmath760.65&0.49&0.08&7.96&2.1e5 & 5a&&0.044 + 55&30950&204.2578713&@xmath7629.8701108&@xmath7610.85 & 2.94&@xmath761.08&0.60&0.08&7.49&2.5e5 & 5a&&0.085 + 56&83925&204.2643496&@xmath7629.8439131&@xmath768.71 & 2.79&@xmath760.97&0.77&0.14&7.44&4.3e4 & 5a&&0.129 + 57&44034&204.2499199&@xmath7629.8626794&@xmath769.56 & 3.10&@xmath760.82&0.44&0.28&6.78&2.1e4 & 5b&&0.030 + 58&17159&204.2616672&@xmath7629.8765474&@xmath768.22 & 3.18&@xmath760.42&0.57&0.16&8.06&4.3e4 & 5b&&0.052 + 59&25716&204.2827697&@xmath7629.8725452&@xmath767.28 & 2.76&@xmath760.14&0.42&0.00&8.41&2.6e4 & 5b&&0.054 + 60&18032&204.2849161&@xmath7629.876142&@xmath767.72 & 2.98&@xmath760.72&0.61&0.36&6.78&5.7e3 & 5b&&0.064 + 61&74692&204.2760088&@xmath7629.8475135&@xmath766.99 & 3.17&@xmath760.04&0.70&0.50&6.74&3.3e3 & 5b&&0.075 + 62&85964&204.2565326&@xmath7629.843069&@xmath767.59 & 2.99&@xmath760.33&0.44&0.00&8.36&2.7e4 & 5b&&0.049 + 63&14748&204.2752747&@xmath7629.8776532&@xmath767.14 & 3.29&@xmath760.11&0.40&0.00&8.36&1.2e4 & 5b&&0.038 + 64&65733&204.2851579&@xmath7629.8507302&@xmath769.82 & 2.73&@xmath760.94&0.61&0.10&7.59&1.3e5 & 5b&&0.089 + 65&65479&204.2862739&@xmath7629.8508316&@xmath769.06 & 3.19&@xmath760.37&0.42&0.00&8.31&7.8e4 & 5b&&0.050 + 66&65304&204.2849235&@xmath7629.8508999&@xmath768.51 & 3.39&0.07&0.80&0.18&8.41&5.8e4 & 5b&&0.039 + 67&10114&204.2664853&@xmath7629.8796816&@xmath767.17 & 2.64&@xmath761.53&@xmath760.33&0.00&6.64&1.4e3 & 5b&&0.105 + 68&58911&204.2807662&@xmath7629.8539005&@xmath767.69 & 2.88&0.15&1.55&0.32&9.11&2.9e5 & 5b&&0.050 + 69&58363&204.2831825&@xmath7629.8541717&@xmath767.23 & 3.27&0.27&0.54&0.00&8.86&2.9e4 & 5b&&0.034 + 70&66553&204.2887134&@xmath7629.8504088&@xmath768.06 & 3.23&0.64&1.08&0.20&9.01&1.5e5 & 5b&&0.035 + 71&55591&204.2710795&@xmath7629.8556304&@xmath767.27 & 3.14&0.34&0.74&0.04&8.86&4.1e4 & 5b&&0.036 + 72&94866&204.2790178&@xmath7629.8386224&@xmath768.34 & 3.28&0.06&0.39&0.00&8.46&4.0e4 & 5b&&0.031 + 73&3113&204.2651882&@xmath7629.8828492&@xmath766.93 & 3.28&0.04&0.89&0.00&9.16&3.8e4 & 6&&0.031 + 74&12505&204.2762954&@xmath7629.8786591&@xmath766.67 & 3.26&0.44&0.97&0.00&9.06&2.2e4 & 6&&0.029 + 75&24528&204.2890323&@xmath7629.8730866&@xmath769.15 & 3.13&@xmath760.14&0.80&0.22&8.36&1.8e5 & 6&&0.040 + 76&55985&204.2695705&@xmath7629.8553997&@xmath767.97 & 2.91&0.02&1.01&0.00&9.26&2.1e5 & 6&&0.040 + 77&18044&204.2956504&@xmath7629.8761376&@xmath768.29 & 3.24&0.12&0.54&0.00&8.61&5.3e4 & 6&&0.034 + 78&54416&204.2898224&@xmath7629.8562536&@xmath768.01 & 3.15&@xmath760.37&0.91&0.38&7.96&6.1e4 & 6&&0.042 + 79&46572&204.2634717&@xmath7629.8608741&@xmath768.54 & 3.05&0.18&0.81&0.04&8.91&1.7e5 & 6&&0.058 + cccccccc 3 & @xmath77 & @xmath78 & @xmath79 & @xmath80 & @xmath81 & @xmath82 & @xmath83 + 4a & @xmath84 & @xmath85 & @xmath86 & @xmath87 & @xmath88 & @xmath89 & @xmath90 + 4b & @xmath91 & @xmath92 & @xmath93 & @xmath94 & @xmath95 & @xmath96 & @xmath97 + 5a & @xmath98 & @xmath99 & @xmath100 & @xmath101 & @xmath102 & & @xmath103 + 5b & @xmath104 & @xmath105 & @xmath106 & @xmath107 & @xmath108 & & @xmath109 + 6 & @xmath110 & @xmath111 & @xmath112 & @xmath113 & @xmath114 & & @xmath115 + 1&3550&204.2548844&@xmath7629.8825632&@xmath765.51 & 2.13&@xmath761.63&@xmath760.22&9 + 2&3916&204.2554865&@xmath7629.8823689&@xmath765.19 & 2.30&@xmath761.60&@xmath760.28&8 + 3&10373&204.2549063&@xmath7629.8795771&@xmath765.24 & 2.28&@xmath761.49&@xmath760.16&7 + 4&11098&204.2672170&@xmath7629.8792752&@xmath766.89 & 2.02&@xmath761.64&@xmath760.33&4 + 5&29250&204.2745636&@xmath7629.8709998&@xmath764.41 & 2.09&@xmath761.21&0.02&8 + 6&35101&204.2745919&@xmath7629.8676963&@xmath765.23 & 2.11&@xmath761.49&@xmath760.39&6 + 7&37778&204.2667959&@xmath7629.8662227&@xmath765.93 & 2.21&@xmath761.13&0.08&9 + 8&47544&204.2823703&@xmath7629.8602099&@xmath765.86 & 2.10&@xmath761.51&@xmath760.14&7 + 9&47772&204.2689918&@xmath7629.8600630&@xmath765.09 & 2.12&@xmath761.31&0.27&7 + 10&48660&204.2894733&@xmath7629.8594131&@xmath764.26 & 2.25&@xmath761.62&@xmath760.48&2 + 11&49679&204.2535423&@xmath7629.8586761&@xmath765.78 & 2.18&@xmath760.49&0.32&9 + 12&50923&204.2552793&@xmath7629.8579399&@xmath766.13 & 2.23&@xmath761.15&0.25&5 + 13&51301&204.2887045&@xmath7629.8577311&@xmath765.19 & 2.18&@xmath761.27&0.15&2 + 14&52904&204.2462139&@xmath7629.8569822&@xmath764.69 & 2.23&@xmath761.59&0.14&1 + 15&56031&204.2828693&@xmath7629.8553764&@xmath766.15 & 2.18&@xmath761.36&0.02&6 + 16&56485&204.2849019&@xmath7629.8551313&@xmath766.19 & 2.04&@xmath761.42&0.06&8 + 17&56492&204.2829518&@xmath7629.8551272&@xmath766.24 & 2.24&@xmath760.12&1.07&9 + 18&56937&204.2841803&@xmath7629.8548844&@xmath768.06 & 2.13&@xmath760.21&0.90&6 + 19&60624&204.2516243&@xmath7629.8530186&@xmath764.99 & 2.20&@xmath761.28&@xmath760.02&7 + 20&61345&204.2496746&@xmath7629.8526196&@xmath764.79 & 2.23&@xmath761.25&@xmath760.32&4 + 21&72114&204.2810230&@xmath7629.8485123&@xmath766.34 & 2.08&@xmath760.77&0.33&2 + 22&88339&204.2804302&@xmath7629.8420518&@xmath764.49 & 2.30&@xmath761.08&@xmath760.13&7 +

we use new wfc3 observations of the nearby grand design spiral galaxy m83 to develop two independent methods for estimating the ages of young star clusters . it is based on the simple premise that the gas in very young ( few myr ) clusters is largely coincident with the cluster stars , is in a small , ring - like structure surrounding the stars in slightly older clusters since massive star winds and supernovae have had time to push out the natal gas ( e.g. , myr ) , and is in a larger ring - like bubble for still older clusters ( i.e. , myr ) . if no h is associated with a cluster it is older than myr . the second method is based on an observed relation between pixel - to - pixel flux variations within clusters and their ages . this degeneracy in age can be broken using other age indicators such as h morphology . the scatter within categories is dex in for young clusters ( myr ) and dex for older ( myr ) clusters . a by - product of this study is the identification of 22 `` single - star '' hii regions in m83 , with central stars having ages myr .

we use new wfc3 observations of the nearby grand design spiral galaxy m83 to develop two independent methods for estimating the ages of young star clusters . the first method uses the physical extent and morphology of h emission to estimate the ages of clusters younger than myr . it is based on the simple premise that the gas in very young ( few myr ) clusters is largely coincident with the cluster stars , is in a small , ring - like structure surrounding the stars in slightly older clusters since massive star winds and supernovae have had time to push out the natal gas ( e.g. , myr ) , and is in a larger ring - like bubble for still older clusters ( i.e. , myr ) . if no h is associated with a cluster it is older than myr . the second method is based on an observed relation between pixel - to - pixel flux variations within clusters and their ages . this method relies on the fact that the brightest individual stars in a cluster are most prominent at ages around 10 myr , and fall below the detection limit ( i.e. , m ) for ages older than about 100 myr . older clusters therefore have a smoother appearance and smaller pixel - to - pixel variations . the youngest clusters also have lower flux variations , hence the relationship is double valued . this degeneracy in age can be broken using other age indicators such as h morphology . these two methods are the basis for a new morphological classification system which can be used to estimate the ages of star clusters based on their appearance . we compare previous age estimates of clusters in m83 determined from fitting _ _ ubvi__h measurements using predictions from stellar evolutionary models with our new morphological categories and find good agreement at the% level . the scatter within categories is dex in for young clusters ( myr ) and dex for older ( myr ) clusters . a by - product of this study is the identification of 22 `` single - star '' hii regions in m83 , with central stars having ages myr .

1412.0287

r

we proceed now to present our qmc results for the hubbard model ( [ hubb ] ) . we first consider static quantities and then study single- and two - particle dynamical correlation functions . vs. @xmath35 for several values of the interchain hopping @xmath5 found on a @xmath36 lattice . the inset shows the evolution of the qp gap @xmath37 on increasing @xmath5 extracted from a linear fit . , scaledwidth=45.0% ] due to the relevance of umklapp scattering in the 1d limit , the single - particle imaginary time green s function , @xmath38 , follows for large @xmath39 an exponential decay @xmath40 , where @xmath37 is the qp gap . the latter might be extracted from the uniform charge susceptibility , @xmath41 where @xmath42 is the particle number operator . at low temperatures one expects @xmath43 . in order to quantify the behavior of the qp gap upon increasing @xmath5 , we plot in fig . [ c00 ] @xmath44 vs. @xmath35 for several values of the interchain hopping . in this way , the activated behavior is reflected in the slope of the curves given by @xmath37 : a decreased negative slope signals the reduction of the magnitude of @xmath37 . a rough estimate of the qp gap @xmath37 extracted from a linear fit of the data points indicates that it does not close but shows an inflection point around @xmath45 , see the inset in fig . . found on a 16@xmath46 lattice : ( a ) @xmath47 and ( b ) @xmath2 . the inset shows the finite - size scaling of the staggered magnetic moment @xmath48 for @xmath49 at @xmath50 , @xmath51 , and @xmath52 . , title="fig:",scaledwidth=45.0% ] + found on a 16@xmath46 lattice : ( a ) @xmath47 and ( b ) @xmath2 . the inset shows the finite - size scaling of the staggered magnetic moment @xmath48 for @xmath49 at @xmath50 , @xmath51 , and @xmath52 . , title="fig:",scaledwidth=45.0% ] the existence of the inflection point is suggestive of a crossover in the origin of the charge gap . numerical evidence for this conjecture is provided in fig . [ s_t ] showing the fourier transform of equal - time spin - spin correlations , @xmath53 on the one hand , the low-@xmath54 enhancement of @xmath55 for @xmath56 in fig . [ s_t](a ) indicates the predominance of spin - spin correlations along the chains thus confirming the relevance of umklapp scattering . on the other hand , the low-@xmath54 increase of the staggered spin structure factor @xmath57 shown in fig . [ s_t](b ) suggests the formation of significant af spin correlations . to further study the spin - spin correlations , we plot in the inset of fig . [ s_t](b ) the finite - size scaling of the staggered magnetic moment , @xmath58 at @xmath49 . as is apparent , @xmath48 is consistent with a finite value _ below _ our lowest temperature @xmath59 , thus marking the effective zero - temperature regime in our finite - size systems . hence , on the basis of the static quantities , one can conclude in the @xmath60 limit the onset of a higher - dimensional insulating phase gapped out by long - range af spin fluctuations . however , a strong reduction of the qp gap @xmath37 upon increasing @xmath5 implies that for this value of the coulomb repulsion @xmath19 , the onset of the insulating state occurs at lower temperatures in comparison to the 1d mott gap . this opens up a possibility to study finite , but still low - enough to avoid dominant thermal broadening effects , temperature properties of the quasi-1d metallic state in the dimensional crossover . a response function particularly suitable for investigating transport properties in the anisotropic system such as weakly coupled 1d hubbard chains is the frequency- and polarization - dependent optical conductivity @xmath61 : it allows one to resolve a distinct behavior of the charge dynamics along @xmath62 and perpendicular @xmath0 to the chains . noting that , experimentally , the dimensionality is controlled not only by the physical or chemical pressure , which changes the ratio of the interchain transfer integral to the intrachain one , but also by the energy scale used in the measurement , the knowledge of @xmath61 offers a possibility to track the evolution of remnant aspects of the 1d physics in the high - energy part of the spectrum . finally , optical conductivity is a useful experimental @xcite and numerical @xcite response to study the interplay between the qp itineracy and the tendency towards their localization by dressing with af spin fluctuations . a real part of @xmath61 is a measure of the rate at which particle - hole pairs are created by the absorption of photons with a given frequency @xmath63 . it might be calculated from the kubo formula by looking at the qmc imaginary time current - current correlation functions , @xmath64 here , @xmath65 ( @xmath66 ) is the intrachain ( interchain ) component of the current operator : @xmath67 respectively , with @xmath68 being the @xmath69 component of the vector connecting sites @xmath70 and @xmath71 . a dimensional - crossover - driven reconstruction of electronic states as evinced by frequency - dependent intra- @xmath62 and interchain @xmath0 optical conductivities at a given temperature @xmath72 is shown in fig . [ sig_20 ] . at our smallest interchain coupling @xmath73 , both optical conductivities display solely a finite - frequency feature typical of the 1d mott insulating phase . @xcite its location @xmath74 roughly matches _ twice _ the magnitude of the single - particle gap @xmath37 , cf . [ c00 ] , thus corresponding to the particle - hole pair absorption across the lower and upper hubbard bands . while some smearing of this absorption mode becomes apparent , the peak retains its position in the weakly coupled regime with @xmath75 . it reflects the relevance of umklapp processes and indicates charge confinement to the individual chains . a further increase in @xmath5 renders umklapp scattering progressively irrelevant and the system enters a transient regime with a competing interchain single - particle tunneling . as a result , a drude - like response in @xmath62 develops around @xmath76 accompanied by a tiny zero - frequency weight in @xmath0 . still , given a nearly @xmath5-independent position of the finite - frequency absorption , the overall structure of @xmath62 is reminiscent of what is expected for a weakly doped 1d mott insulator . @xcite although there is no actual doping in the system , a non - negligible warping of the fs introduced by @xmath5 might be considered as an effective deviation from the commensurate filling of individual chains which otherwise continue to exhibit a substantial tendency to confine charge carriers reflected in a strongly reduced zero - frequency weight in @xmath0 . . the plot shows : ( a ) intra- @xmath62 and ( b ) interchain @xmath0 optical spectra found on a @xmath36 lattice at @xmath72 . from bottom to top : @xmath73 , 0.1 , 0.15 , 0.2 , 0.25 , and 0.3 . , scaledwidth=45.0% ] at larger coupling @xmath49 , a pronounced drude - like feature in @xmath0 signals the onset of a higher - dimensional metallic phase : single - particle _ interchain _ tunneling requires the recombination of fractionalized excitations characteristic of the 1d regime into electronic qps . the crossover in the effective dimensionality is not restricted to the lowest energies : a high - energy mode in @xmath62 , remnant of the 1d mott gap , is replaced by a low - frequency hump whose evolution tracks the qp energy scale @xmath37 . the hump stems from coupling between charge carriers and short - range af spin fluctuations beyond the 1d framework . a similar piling up of optical weight at finite frequency is also resolved in @xmath0 for @xmath77 and then , in contrast to @xmath62 , the hump merges with the high - frequency tail of the drude mode . we attribute this difference to a spatial anisotropy in the spin - wave velocity ; the _ smaller _ velocity associated with the _ interchain _ spin - wave - like dispersion relation renders the paramagnon decay rate into particle - hole excitations _ higher _ thus giving rise to a fl - like response in @xmath0 . . the plot shows : ( a ) intra- @xmath62 and ( b ) interchain @xmath0 optical spectra at @xmath49 ( solid ) and @xmath78 ( dashed ) . from top to bottom : @xmath50 , @xmath79 , @xmath51 , and @xmath52 . for @xmath78 , a complete optical gap develops at @xmath72 and we expect at lower temperatures qualitatively similar spectra ( not shown ) . , scaledwidth=45.0% ] inspection of the static quantities in sec . [ static ] revealed the formation of a small qp gap @xmath37 associated with the onset of the sdw state in the @xmath80 limit . it is interesting to explore the behavior of this gap as a function of temperature . thermal evolution of @xmath61 at a fixed value of the interchain coupling @xmath49 is shown in fig . [ sig_t ] . at elevated temperature @xmath50 , both intra- @xmath62 and interchain @xmath0 optical conductivities exhibit broad drude - like features exhausting most of the optical weight . this indicates a fl - like metal albeit with anisotropic transport properties due to inequivalent hopping amplitudes . as the temperature is decreased down to @xmath72 , a low - frequency depletion of optical weight separating the narrow drude - like mode from the finite - frequency hump becomes apparent . it follows from a marked enhancement of the af spin correlation length and dressing of qps with a cloud of spin fluctuations . upon further cooling , the af spin correlations extend across the entire lattice and the sdw gap opens up . we now compare the above evolution of @xmath61 with the corresponding redistribution of optical weight at a twice _ smaller _ interchain coupling @xmath78 . the low - temperature increase of the static spin structure factor @xmath55 reveals dominant 1d spin correlations in this regime , see fig . [ s_t](a ) . a pronounced 1d character of the system is also reflected in a different frequency dependence of intra- and interchain optical conductivities . this effect is particularly dramatic at @xmath50 : while a clear finite - frequency depletion of optical weight is visible in @xmath62 , only a narrow drude - like peak is resolved in @xmath0 . in spite of thermal broadening comparable with the interchain bandwidth masking partially warping of the fs , the presence of the zero - frequency mode in @xmath0 suggests that charge carriers retain their electronic qp nature . this indicates that thermal melting of the quasi-1d mott insulator induces at the _ smallest _ energy scales a crossover to the fl characteristics rather than to the ll behavior . furthermore , at the intermediate low temperature @xmath81 , the frequency range with a reduced weight in @xmath62 becomes wider thus signaling proximity to the insulating phase . a reduced mobility of charge carriers also affects @xmath0 ; here , most of the drude - like weight is transferred to a high - energy feature . finally , a complete optical gap driven by umklapp scattering develops already at @xmath72 . our next aim is to address momentum - resolved single - particle spectral properties . in particular , one would like to know ( i ) whether the quasi-1d metallic phase can be described within the fl theory , and ( ii ) topology and qp weight along the emergent fs . another interesting question is whether some spectral features in the higher - dimensional electronic structure can be traced back to those of the 1d regime . @xcite to gain insight into these issues , we compute the momentum - resolved single - particle spectral function @xmath82 which is related to the qmc imaginary time green s function @xmath83 by the spectral theorem : @xmath84 obtained at @xmath72 on : ( a ) 32-site chain with a dummy transverse momentum and ( b),(c ) @xmath36 lattice with : @xmath45 ( middle ) and @xmath85 ( bottom ) . solid line in panel ( c ) gives the paramagnetic hartee - fock band structure . , title="fig:",scaledwidth=43.0% ] + obtained at @xmath72 on : ( a ) 32-site chain with a dummy transverse momentum and ( b),(c ) @xmath36 lattice with : @xmath45 ( middle ) and @xmath85 ( bottom ) . solid line in panel ( c ) gives the paramagnetic hartee - fock band structure . , title="fig:",scaledwidth=43.0% ] + obtained at @xmath72 on : ( a ) 32-site chain with a dummy transverse momentum and ( b),(c ) @xmath36 lattice with : @xmath45 ( middle ) and @xmath85 ( bottom ) . solid line in panel ( c ) gives the paramagnetic hartee - fock band structure . , title="fig:",scaledwidth=43.0% ] the evolution of @xmath82 with increasing interchain coupling @xmath5 is summarized in fig . [ akw ] . in the 1d regime , the relevance of umklapp process generates a gap in the half - filled band at @xmath86 and the equivalent points , see fig . [ akw](a ) . at frequencies above the single - particle gap , the dispersion is approximately linear reflecting aspects of the ll theory . @xcite moreover , the spectrum significantly broadens on approaching the brillouin zone edges reminiscent of the spinon and holon branches . @xcite next , fig . [ akw](b ) provides evidence for highly incoherent single - particle dynamics in the metallic regime with @xmath45 ; a significant depletion of spectral weight at the @xmath87 momentum is accompanied by a backfolding behavior in the dispersion at @xmath88 and @xmath89 points . upon further increase in the interchain coupling strength , the spectral intensity at the @xmath87 point gradually recovers . finally , a single qp peak becomes apparent at the fermi level at @xmath85 and the low - frequency part of @xmath82 follows roughly the paramagnetic hartee - fock band structure , see fig . [ akw](c ) . another noteworthy feature is found in the inverse photoemission @xmath90 part of the spectra , i.e. , the formation of a weakly dispersive qp - like band near the @xmath91 momentum . while the flatness is reminiscent of the 1d nature of the problem , only a broad structure is resolved in the photoemission @xmath92 part around the @xmath93 point . the difference between the inverse- and photoemission parts reflects a broken particle - hole symmetry due to the finite next - nearest - neighbor hopping @xmath16 . ( solid ) and of the purely 1d case ( dashed).,scaledwidth=35.0% ] the evolution of the spectral function @xmath82 is a consequence of dramatic changes in the single - particle green s function @xmath94 . in the mott insulator , the presence of a spectral gap requires that the real part of the zero - frequency green s function @xmath95 changes sign in momentum space by going through a _ zero_. this is accomplished by the singularity in the corresponding self - energy . as one approaches the mott transition , the locus of zeros in @xmath96-space affects the topology of the emergent fs defined by zero - frequency _ poles _ of the green s function . @xcite we address this issue by examining two special momenta : ( i ) nodal @xmath87 , corresponding to a vanishing interchain kinetic energy @xmath97 , and ( ii ) an antinodal @xmath88 one , where the maximum warping of the noninteracting 1d fs occurs , see fig . [ fs ] . we focus first on the nodal @xmath87 point considered in fig . [ g_nod ] . at our smallest @xmath73 , @xmath95 has a negative slope in a broad range of frequencies around the fermi level . the imaginary part of the corresponding self - energy @xmath98 displays a diverging - like behavior on approaching the smallest matsubara frequency @xmath99 thus signaling a zero of @xmath95 , see fig . [ g_nod ] , left inset . the anomalous behavior of the self - energy stems from umklapp scattering and is responsible for a robust mott gap in the single - particle spectral function @xmath82 , right inset of fig . [ g_nod ] . at larger @xmath5 , the umklapp process becomes less effective at low - energy scales . this shrinks the frequency region with a negative slope of @xmath95 and reduces the scattering rate @xmath100 . as a result , some thermally excited single - particle states whose weight is controlled by @xmath5 become apparent at the fermi energy . finally , @xmath95 develops a positive slope at @xmath85 thus forming a pole - like structure as in the fl phase . still , a small kink at @xmath101 signals substantial qp scattering off af spin fluctuations . consequently , a broad qp - like feature is resolved in @xmath82 . at the nodal @xmath87 point . insets show the corresponding : ( left ) low - frequency dependence of the imaginary part of the self - energy and ( right ) single - particle spectral function from bottom to top : @xmath73 , 0.1 , 0.15 , 0.2 , 0.25 , and 0.3 . , scaledwidth=45.0% ] we turn now to the antinodal @xmath88 point . as shown in fig . [ g_anod ] , the zero of @xmath95 and the mott gap in the spectral function @xmath82 remain for small values of @xmath102 nearly pinned at the @xmath88 momentum . hence , at the expense of loss in the _ interchain _ kinetic energy , the interaction renders the fs warping tendency irrelevant . @xcite in contrast , at larger interchain hopping amplitude , a reduced scattering rate @xmath103 indicates that the kinetic energy gain can not be further ignored and the warping effects become discernible . indeed , vanishing @xmath104 at the @xmath88 point requires now a finite frequency @xmath90 thus approaching a pole - like behavior around @xmath105 . the latter produces a faint spectral feature in @xmath82 ; it signals backfolding of the conduction band and as such is a fingerprint of the mott gap slightly off the @xmath88 momentum . finally , the finite - frequency zero and pole - like features annihilate together and only a shallow dip in @xmath95 is resolved at @xmath45 which in turn evolves into a smooth behavior at @xmath49 . obviously , we can not resolve the fermi wave vector @xmath106 across the @xmath107 path on our discrete @xmath96-point mesh . given , however , a comparable slope of the qp energy dispersion near the antinodal @xmath88 and nodal @xmath87 points , see fig . [ akw](c ) , we expect a _ continuous _ warped fs . this should be contrasted with the isotropic two - dimensional hubbard model at half - filling where the flatness of the qp band around the @xmath91 point renormalizes locally the fermi velocity and enhances qp scattering off af spin fluctuations . as a result , the depletion of qp weight starts at different temperatures in different regions of the brillouin zone . @xcite however , this momentum - sector - selective opening of the single - particle spectral gap is suppressed by next - nearest - neighbor hopping @xmath16 . @xcite the latter shifts the flat region in the qp dispersion away from the fermi level thus providing further support for the continuous fs in the quasi-1d regime . but at the antinodal @xmath88 point . , scaledwidth=45.0% ] the evolution of the qmc green s function @xmath94 and the shape of the emergent fs are different from those concluded on the basis of the cdmft approach on the @xmath108 cluster . @xcite in cdmft , the range of af spin fluctuations is restricted to the cluster size . therefore , the evolution of the electronic structure is governed by dominant umklapp process : a finite @xmath5 shifts the _ zero _ of @xmath95 away from the @xmath109 points giving way to a finite - frequency _ pole _ from the conduction band , see fig . 5(a ) in ref . . at a critical value of @xmath5 , the latter crosses the fermi level which opens up elongated _ electron _ pockets centered around the @xmath110 momenta . at the same time , _ hole _ pockets open up at the @xmath111 points and thus a _ broken _ fs emerges with the 1d nesting wave vector @xmath91 . hence , in the absence of finite - range af spin fluctuations , this particular evolution of @xmath95 ensures the relevance of umklapp scattering and extends the stability of the mott phase away from the 1d regime . let us however point out that a larger next - nearest - neighbor hopping @xmath16 in the lattice calculations will frustrate the af spin correlations and could bring our findings in line with the cdmft results . unfortunately , this leads to a sign problem which renders qmc simulations very expensive . competing effects in strongly correlated systems often result in various energy scales which govern the population of excited states . this also holds for weakly coupled 1d hubbard chains with a half - filled band : in the regime where the interaction between spin and electronic degrees of freedom becomes relevant , both single- and two - particle processes contribute to the excited state dynamics . the energy- and momentum - resolved spin and charge structure factors help to separate these contributions which is crucial for the understanding of the low - energy dynamics . in addition , these quantities allow one to identify momentum - resolved energy scales above which spin and charge fluctuations lose their 1d nature . thus , to complement the characteristic of the emergent quasi-1d metallic phase , we consider the spin @xmath1 and charge @xmath112 dynamical structure factors defined as : @xmath113 here , @xmath114 and @xmath115 correspond to the generalized charge and spin susceptibilities . the susceptibilities can be obtained from the imaginary - time displaced two - particle correlation functions , @xmath116 where , @xmath117 with @xmath118 being the average filling level . the elementary excitations of the 1d hubbard model are bosonic collective spin and charge density oscillations with a linear dispersion in the long - wavelength limit @xmath119 . @xcite the relevance of umklapp scattering at half - filling opens up a gap for long - wavelength charge excitations while leaving the spin sector gapless , see fig . [ chain ] . the dynamical charge structure factor @xmath112 in fig . [ chain](a ) shows an overall agreement with the one obtained at a slightly smaller interaction @xmath120 using the time - dependent density matrix renormalization group method in the @xmath60 limit , see fig . 10 in ref . . above the charge gap , one finds aspects of the ll dynamics with low - lying charge excitations located at long wavelengths as well as at @xmath121 . as found in ref . , the latter carry little spectral weight and are thus more difficult to resolve in our finite - temperature qmc simulations . since the charge sector is fully gapped , the spin dynamics can be understood within a spin - only @xmath7 heisenberg chain . in this case , the spin dynamics is characterized by the two - spinon continuum of states bounded from below and above by , @xcite @xmath122 with the lowest - lying excitations carrying dominant spectral weight at low temperatures . @xcite as is apparent in fig . [ chain](b ) , for the considered value of the interaction @xmath19 , the majority of spectral weight is located at the lower bound of the continuum as in the heisenberg model . and ( b ) dynamical spin structure factor @xmath1 obtained on a 32-site chain at @xmath72 . the transverse momentum is a dummy label . , title="fig:",scaledwidth=43.0% ] + and ( b ) dynamical spin structure factor @xmath1 obtained on a 32-site chain at @xmath72 . the transverse momentum is a dummy label . , title="fig:",scaledwidth=43.0% ] + in spatial dimensions greater than one , the spinons bind together and form magnons , the goldstone modes of the broken continuous su(2 ) symmetry group . as a result , the continuum of excitations in the dynamical spin structure factor gives way to well defined spin - wave modes . @xcite the low - frequency magnons in af _ insulators _ and in the @xmath60 limit are well accounted for within the linear spin - wave theory ( lswt ) of the heisenberg model to leading @xmath123 order . @xcite this picture should break down at finite temperatures where cranking up the interchain coupling triggers the crossover to a _ metal_. let us consider first a weakly coupled regime with @xmath45 . as shown in fig . [ g_nod ] , the corresponding single - particle spectral function @xmath82 exhibits two broadened peaks separated by a region with a strongly reduced weight that we refer to as a _ pseudogap_. as is apparent , the system is at the verge of localization near the 1d mott phase . figure [ dyn15](a ) depicts the dynamical charge structure factor @xmath112 . using the continuity equation one finds that upon approaching the long - wavelength limit @xmath119 parallel ( perpendicular ) to the chains , this observable is related to the intrachain ( interchain ) real part of the optical conductivity @xmath61 , respectively : @xcite @xmath124 where @xmath125 is the @xmath69 component of the momentum transfer parallel / perpendicular to the chains . given that the intensity of charge fluctuations rapidly decreases in the long - wavelength limit , it is difficult to pin down the metallic vs. insulating nature of the system . this issue is resolved by looking at the low - frequency part of the optical conductivity @xmath61 , see fig . [ sig_20 ] . on the one hand , zero - frequency weight in the interchain optical conductivity @xmath0 indicates a metallic phase at @xmath45 . on the other hand , the smallness of this weight reveals a large degree of incoherence in the interchain transport . moreover , as shown in fig . [ g_nod ] , the imaginary part of the corresponding self - energy @xmath126 increases at low matsubara frequency contributing to the effective mass enhancement and _ reduced _ mobility of charge carriers . , and ( b ) dynamical spin structure factor @xmath1 obtained on a @xmath36 lattice with @xmath45 at @xmath72 . solid line in panel ( b ) gives the lswt dispersion eq . ( [ magnon ] ) with @xmath127 and @xmath128 . the chosen exchange couplings are fit parameters subject to the constraint of a finite magnetic order parameter in lswt consistent with the long - range af order in the system . , title="fig:",scaledwidth=43.0% ] + , and ( b ) dynamical spin structure factor @xmath1 obtained on a @xmath36 lattice with @xmath45 at @xmath72 . solid line in panel ( b ) gives the lswt dispersion eq . ( [ magnon ] ) with @xmath127 and @xmath128 . the chosen exchange couplings are fit parameters subject to the constraint of a finite magnetic order parameter in lswt consistent with the long - range af order in the system . , title="fig:",scaledwidth=43.0% ] + from this standpoint , we can analyze the magnetic excitation spectrum shown in fig . [ dyn15](b ) . the most striking difference with respect to the 1d regime is a low - frequency dispersive feature along the @xmath129 path accompanied by a broad upward dispersion along the @xmath130 direction . they are signatures of damped af spin fluctuations ( paramagnons ) which are not strong enough to gap out the fs and develop long - range af order but nevertheless can propagate an appreciable distance . to get further insight into the spin dynamics , we consider the spin @xmath7 heisenberg model with nearest neighbor interactions @xmath131 ( @xmath4 ) along the intrachain ( interchain ) bonds , respectively , extended by next - nearest neighbor interaction @xmath132 : @xmath133 as illustrated in fig . [ dyn15](b ) , the lswt dispersion relation of the heisenberg model ( [ hj ] ) , @xcite @xmath134 with two - dimensional structure factors , @xmath135 tracks the low - frequency paramagnon spectrum . clearly , the frequency region with depleted single - particle spectral weight efficiently separates the low - frequency spin - wave - like excitations from the high - frequency particle - hole excitations across the pseudogap in @xmath82 . moreover , a reduced mobility of charge carriers leads to a separation of time scales , a characteristic feature of correlated systems with complex dynamics ; @xcite charge carriers are _ localized _ on the spin time scale and thus a coherent - like precession of individual spins might still take place . consequently , despite broadening and renormalization of the paramagnon dispersion ( softening ) as compared to lswt with localized moments , an approximate heisenberg - like picture turns out to still be applicable below the single - particle pseudogap . but for @xmath85 . , title="fig:",scaledwidth=43.0% ] + but for @xmath85 . , title="fig:",scaledwidth=43.0% ] + we now examine the spin and charge responses at our largest interchain coupling @xmath85 . a closure of the pseudogap in the single - particle spectral function @xmath82 illustrated in fig . [ g_nod ] gives rise to a more pronounced gapless charge mode in the long - wavelength limit @xmath119 , see fig . [ dyn3](a ) . as follows from eq . ( [ sigma_cqw ] ) , this is in turn reflected in a marked increase in the drude - like weight shown in fig . [ sig_20 ] thus providing the evidence of an _ increased _ mobility of charge carriers . consequently , the low - frequency part of the dynamical spin structure factor @xmath1 can not anymore be interpreted solely in terms of spin - wave - like excitations assuming _ localized _ spins . @xcite our next goal is to identify these various components in the spin excitation spectrum . figure [ dyn3](b ) reveals featureless continua in @xmath1 near @xmath136 and @xmath47 momenta . it is natural to assign these incoherent excitations to the continuum of _ independent _ particle - hole pairs , a hallmark of an electron system with mobile charge carriers . indeed , in the presence of electronic qps , a _ single _ spin - flip excitation can be made at arbitrary low energy . hence , the paramagnons can not propagate without exciting unbound particle - hole pairs . the latter contribute to the charge excitation spectrum @xmath112 which features a similar continuum around @xmath136 , cf . [ dyn3](a ) . this similarity confirms that these features stem from the particle - hole bubble of dressed single - particle green s functions . @xcite less clear evidence of the particle - hole excitations in @xmath112 is found at @xmath47 : since most of the spectral weight is exhausted by a high - frequency @xmath137 charge mode , and [ dyn3 ] supports the point of view that the high - frequency features of @xmath1 and @xmath112 at @xmath85 are reminiscent of the 1d isolated - chain limit . ] it is more difficult to resolve the expected particle - hole continuum . however , we believe that a faint low - frequency mode corresponds to a lower bound of the particle - hole continuum . in contrast , the particle - hole interaction vertex remains finite near the af wave - vector @xmath2 . consequently , an excited particle and a hole are _ bound _ together in this part of the brillouin zone . this leads to low - frequency paramagnon excitations , see fig . [ dyn3](b ) . as compared to the weakly coupled regime shown in fig . [ dyn15](b ) , these paramagnons are broadened by scattering off mobile charge carriers and dissolve into a fl - like particle - hole continuum on moving away from the af wave - vector . such a _ localized _ nature of spin fluctuations in momentum space restricted to a narrow range around @xmath2 arises from _ spatial _ af spin correlations rather than from a set of mutually interacting local moments . @xcite independently of the intrinsic interest in finding fingerprints of the ll behavior at elevated temperatures , quasi-1d materials often exhibit low-@xmath54 broken - symmetry ground states . these instabilities occur at a temperature scale at which the system effectively becomes three - dimensional and long - range order can occur at low but finite temperatures . the physics associated with a thermal crossover can be studied in weakly coupled hubbard chains : for a weak interchain superexchange coupling @xmath138 , the energy difference between the broken - symmetry af ground state and excited states is small , thus facilitating their thermal population . this offers the opportunity to analyze the interaction of low - energy electronic qps with finite - range af spin fluctuations in a thermally disordered quasi-1d metal and to probe transient changes in the spin excitation spectrum intimately connected to the onset of the long - range af order in the @xmath80 regime . figure [ sqw_t ] tracks the temperature dependence of the dynamical spin structure factor @xmath1 at a fixed @xmath49 . for this value of the interchain coupling , optical spectra in fig . [ sig_t ] provide evidence of a thermal crossover from a fl - like regime at @xmath50 to the broken - symmetry sdw ground state in the effective zero - temperature limit . obtained on a @xmath36 lattice with fixed @xmath49 : ( a ) @xmath50 , ( b ) @xmath72 , and ( c ) @xmath59 . insets show the single - particle spectral function at @xmath87 ( left ) and low - frequency dependence of the imaginary part of the corresponding self - energy ( right ) . , title="fig:",scaledwidth=43.0% ] + obtained on a @xmath36 lattice with fixed @xmath49 : ( a ) @xmath50 , ( b ) @xmath72 , and ( c ) @xmath59 . insets show the single - particle spectral function at @xmath87 ( left ) and low - frequency dependence of the imaginary part of the corresponding self - energy ( right ) . , title="fig:",scaledwidth=43.0% ] + obtained on a @xmath36 lattice with fixed @xmath49 : ( a ) @xmath50 , ( b ) @xmath72 , and ( c ) @xmath59 . insets show the single - particle spectral function at @xmath87 ( left ) and low - frequency dependence of the imaginary part of the corresponding self - energy ( right ) . , title="fig:",scaledwidth=43.0% ] at elevated temperature @xmath50 , see fig . [ sqw_t](a ) , @xmath1 features solely broad continua associated with single - particle spin - flip excitations prominent features of the fl dynamics . the validity of the fl - like picture is further supported by a well defined qp peak in the single - particle spectral function @xmath82 resolved at the nodal @xmath87 point , see fig . [ sqw_t](a ) . these qp excitations are responsible for a drude - like feature in the corresponding optical conductivity shown in fig . [ sig_t ] . although a drude - like weight signals that the system remains metallic upon cooling down to @xmath72 , the single - particle dynamics becomes _ incoherent _ ; a single qp peak in @xmath82 at the @xmath87 point is replaced by two broadened peaks separated by a shallow pseudogap , see fig . [ sqw_t](b ) . this double peak structure yields a _ finite_-frequency hump in the optical spectra due to particle - hole excitations _ across _ the pseudogap , cf . [ sig_t ] . further evidence of the growing incoherence in the system is brought by the enhancement of the qp scattering rate @xmath139 , cf . insets in figs . [ sqw_t](a ) and [ sqw_t](b ) . as is apparent from the low-@xmath54 growth of the staggered spin structure factor @xmath57 depicted in fig . [ s_t](b ) , the change in the qp damping rate should be traced to the increase in the magnetic correlation length . this has a pronounced effect on the spin excitation spectrum which develops a paramagnon branch near the af wave vector , see fig . [ sqw_t](b ) . as indicated by their broad spectral width , these paramagnons have a short lifetime due to scattering off mobile charge carriers and merge into a particle - hole continuum on moving away from the @xmath2 momentum . obtained on a @xmath36 lattice with fixed @xmath49 : ( a ) @xmath50 , ( b ) @xmath72 , and ( c ) @xmath59 . , title="fig:",scaledwidth=43.0% ] + obtained on a @xmath36 lattice with fixed @xmath49 : ( a ) @xmath50 , ( b ) @xmath72 , and ( c ) @xmath59 . , title="fig:",scaledwidth=43.0% ] + obtained on a @xmath36 lattice with fixed @xmath49 : ( a ) @xmath50 , ( b ) @xmath72 , and ( c ) @xmath59 . , title="fig:",scaledwidth=43.0% ] finally , at our lowest temperature @xmath59 , a further increase in the qp damping rate @xmath140 leads to a strong depletion of single - particle spectral weight , see the inset in fig . [ sqw_t](c ) . despite some thermally excited qp states at the fermi level , a complete suppression of the drude weight in the corresponding optical conductivity shown in fig . [ sig_t ] provides clear evidence of charge localization . hence , the formation of the insulating state appears here as the outcome of a divergent qp mass rather than the disappearance of charge carriers . this insulating phase features rich spin dynamics with a pronounced frequency - dependent damping , see fig . [ sqw_t](c ) . on the one hand , we resolve at our lowest temperature @xmath59 the increase in both the magnetic intensity and stiffness of the spin - wave - like dispersion near the af wave - vector . the latter effect is similar to spin - wave stiffening found in the weakly doped two - dimensional @xmath13-@xmath131 model on reducing the hole doping and approaching the long - range af phase . @xcite moreover , a correlation - induced gap for spin excitations becomes discernible at the @xmath47 momentum . the size of this gap might be considered as a measure of the vertex correction , i.e , binding energy between an excited particle and a hole , a precursor of collective spin excitations . on the other hand , the interaction of electronic single - particle excitations with magnetic modes results in the overdamped spin dynamics at energies above the pseudogap in @xmath82 . figure [ cqw_t ] summarizes the corresponding temperature evolution of the dynamical charge structure factor @xmath112 . the intensity of the low - frequency weight in the long - wavelength limit @xmath119 progressively decreases with decreasing temperature and is completely washed out below the crossover scale marking the onset of the sdw phase . this agrees with a small gap in the optical conductivity resolved at @xmath59 , cf . [ sig_t ] . let us now discuss the relevance of our results to quasi-1d organic bechgaard - fabre salts . at ambient pressure , the fabre ( tmttf)@xmath8x salts are typically mott insulators due to a combined effect of umklapp process and dimerization leading effectively to a half - filled band . upon increasing pressure , the 1d mott phase is replaced by a higher - dimensional metal when the interchain hopping reaches the order of the mott gap . @xcite in contrast , the bechgaard ( tmtsf)@xmath8x salts are quasi-1d metals due to larger interchain hopping . it effectively warps the fs thus introducing deviation from ideal nesting properties of the 1d limit . the optical conductivity spectra of the bechgaard salts are markedly different from those of a simple metal : a narrow drude - like weight is accompanied by a finite - frequency feature exhausting most of the spectral weight . @xcite the latter is usually interpreted in terms of the remnant 1d mott gap . @xcite the drude feature survives up to arbitrarily low temperatures before being disrupted by the onset of a small sdw gap driven by the fs nesting . @xcite on the one hand , recent cdmft studies capturing only short - range af spin correlations have shown evidence of a quasi-1d metallic phase with a fs broken into pockets . @xcite as the interchain coupling was increased , a continuous fs was restored although with a substantial variation of the qp weight in the brillouin zone . a strong momentum dependence of the self - energy offers a simple framework accounting for the unusual frequency dependence of the optical conductivity in ( tmtsf)@xmath8x salts . indeed , it is natural to associate a drude - like feature ( finite - frequency absorption ) to the fs pockets ( gapped regions of the brillouin zone ) , respectively . on the other hand , our qmc simulations yield a continuous fs in the quasi-1d metallic phase . as a result , a two - component optical response follows from the depletion of single - particle spectral weight at the fermi level with a finite - frequency contribution assigned to particle - hole excitations across the pseudogap . one possible reason behind the continuous fs is that the formation of the fs pockets requires simulations in the thermodynamic limit . alternatively , it is known that the breakup of the fs into pockets appears only at sufficiently low temperatures , @xcite i.e. , possibly below the onset of the intervening sdw phase . in this respect , a larger deviation from the fs nesting , e.g. , a larger next - nearest - neighbor hopping @xmath141 , would be required to extend the region of stability of the quasi-1d metallic phase to lower temperatures . finally , we point out a strong renormalization of the qmc drude - like weight with respect to the one found in the chain - dmft studies . @xcite it stems from dressing of mobile charge carriers with a cloud of finite - range af spin fluctuations beyond the chain - dmft approximation . interestingly , a reduced qmc drude response is reminiscent of the experimental data on the ( tmtsf)@xmath8x salts with the zero - frequency mode containing a tiny @xmath142 fraction of the total optical weight .

the low - temperature behavior of the charge gap indicates a crossover between two distinct energy scales : a high - energy one - dimensional ( 1d ) mott gap due to the umklapp process and a low - energy gap which stems from long - range antiferromagnetic ( af ) spin fluctuations . away from the 1d regime and at temperature scales above the charge gap , the emergence of a zero - frequency drude - like feature in the interchain optical conductivity implies the onset of a higher - dimensional metal . in this metallic phase , enhanced quasiparticle scattering off finite - range af spin fluctuations results in incoherent single - particle dynamics . the coupling between spin and charge fluctuations is also seen in the spin dynamical structure factor displaying damped spin excitations ( paramagnons ) close to the af wave - vector and particle - hole continua near 1d momentum transfers spanning quasiparticles at the fermi surface .

we use quantum monte carlo simulations to study a finite - temperature dimensional - crossover - driven evolution of spin and charge dynamics in an anisotropic two - dimensional system of weakly coupled hubbard chains with a half - filled band . the low - temperature behavior of the charge gap indicates a crossover between two distinct energy scales : a high - energy one - dimensional ( 1d ) mott gap due to the umklapp process and a low - energy gap which stems from long - range antiferromagnetic ( af ) spin fluctuations . away from the 1d regime and at temperature scales above the charge gap , the emergence of a zero - frequency drude - like feature in the interchain optical conductivity implies the onset of a higher - dimensional metal . in this metallic phase , enhanced quasiparticle scattering off finite - range af spin fluctuations results in incoherent single - particle dynamics . the coupling between spin and charge fluctuations is also seen in the spin dynamical structure factor displaying damped spin excitations ( paramagnons ) close to the af wave - vector and particle - hole continua near 1d momentum transfers spanning quasiparticles at the fermi surface . we relate our results to the charge deconfinement in quasi-1d organic bechgaard - fabre salts .

1312.4899

i

galaxies map the distribution of the underlying dark matter field and provide invaluable information about both the nature of dark energy ( de ) and properties of gravity ( see e.g. * ? ? ? the shape of the two - point correlation function of the observed galaxy field , or of its fourier - transform the power spectrum , contains features such as baryon acoustic oscillations ( bao ) and the turn - over marking the transition between radiation dominated and matter dominated evolutionary phases @xcite . these features can be used to place tight constraints on relative abundances of different energy - density components of the universe ( radiation @xmath12 , dark matter @xmath13 , baryonic matter @xmath14 and de @xmath15 ) . presently , these ratios are measured to much higher accuracy in the cosmic microwave background ( cmb ; * ? ? ? therefore , for most cosmological models these features provide most information when used as a standard ruler . if the universe is statistically isotropic and homogeneous on large - scales , the correlation function and power spectrum should likewise be rotationally invariant . the observed two - point statistics instead exhibit a strong anisotropy with respect to the line - of sight ( los ) direction . two effects are responsible for this apparent anisotropy : the redshift - space distortions ( rsd ; * ? ? ? * ) and the alcock paczynski effect ( ap ; * ? ? ? the rsd arise in maps made from galaxies if distances are determined from measured redshifts assuming that they are only caused by the hubble flow . because of gravitational growth , the galaxies tend to infall towards high- density regions , and flow away from low - density regions , such that the clustering is enhanced in the los direction compared to the perpendicular direction . the observed redshifts thus have a component aligned with these flows . on large - scales where gravitational growth is linear , measuring the relative clustering in both los and transverse directions leads to a measurement of the logarithmic growth rate of structure @xmath16 where @xmath17 is a scale factor , @xmath18 is a measure of the amplitude of the matter power spectrum and @xmath19 is the linear growth function normalized such that @xmath20 ( see * ? ? ? * for a review of rsd ) . the magnitude of the large - scale velocity field traced by galaxies depends on the nature of gravitational interactions and measured values of @xmath21 can be used to constrain models of gravity ( see e.g. * ? ? ? galaxy clustering data measures the growth at low redshifts . combining this information with the accurate estimates of the amplitude of matter perturbations at @xmath22 provided by cmb allows for extremely strong constraints for deviations from the predictions of general relativity ( gr ) since even small changes in the growth of structure accumulate to a large offset over cosmic time ( for recent gr constraints see e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? anisotropies are also observed due to the ap effect , which stems from the fact that we need to convert observed angular positions and redshifts of galaxies to physical coordinates in order to measure clustering statistics . if the fiducial cosmology used for this mapping is different from the true cosmology this will induce anisotropies in the measured clustering pattern even in absence of rsd . angular distortions are sensitive to the offset in the angular distance @xmath23 and distortions in the los direction depend on the offset in @xmath24 . measuring the ap effect provides accurate estimates of the angular distance and hubble parameter and can be used to constrain properties of de ( see e.g. * ? ? ? measurements of both angular and radial projected scales are usually reported in terms of the volume averaged distance @xmath25^{1/3},\ ] ] and the ap - parameter @xmath26 in the absence of rsd , the measured correlation function monopole would be sensitive mostly to isotropic scale dilation through @xmath27 and the quadrupole to anisotropic scale dilation through @xmath28 . most of the information on @xmath27 usually comes from the most pronounced feature in the correlation function the position of the bao peak in the monopole . it is therefore convenient to report results in terms of @xmath29 where @xmath30 is the sound horizon at the drag epoch which sets the bao scale ( for a review of bao and ap see e.g. * ? ? ? the rsd and ap are partially degenerate but have a different scale dependence which makes their simultaneous measurement possible @xcite . specifying cosmological models of background expansion or gravity helps to further break this degeneracy ( e.g. * ? ? ? * ) . measuring correlation function in different fiducial cosmological models and fitting the rsd signal in each can help to reduce the degeneracy as well @xcite . the rsd signal within the correlation function is difficult to model because of the significant contribution from nonlinear effects and higher order contributions from galaxy bias . a number of recent studies have shown that many current rsd models result in biased estimates of the growth rate ( see e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? in our work , we use the ` streaming model'-based approach developed in @xcite that has been demonstrated to fit the monopole and quadrupole of the galaxy correlation function with better than per cent level precision to scales above @xmath31 mpc , for galaxies with bias of @xmath32 . many distance - scale and rsd measurements have previously been made using spectroscopic survey data . recent highlights include the bao measurements from the 6df galaxy redshift survey ( 6dfgrs ; * ? ? ? * ) , sloan digital sky survey ii ( sdss - ii ; * ? ? ? * ) , sdss - iii baryon oscillation spectroscopic survey ( boss ) data release 9 sample ( dr9 ; * ? ? ? * ) , wigglez survey @xcite and sdss - iii boss dr10 and dr11 samples @xcite . the rsd signal has been measured in the 6dfgrs @xcite , the sdss - ii survey @xcite , the sdss - iii boss dr9 data @xcite and vimos public extragalactic redshift survey ( vipers ; * ? ? ? simultaneous fits to rsd and ap parameters have been performed for the wigglez survey @xcite , sdss - ii data @xcite and sdss - iii boss dr9 data @xcite . the analysis presented in this paper builds upon that of @xcite , who measured the rsd and ap simultaneously in the boss cmass dr9 sample , achieving a 15 per cent measurement of growth , 2.8 per cent measurement of angular diameter distance , and 4.6 per cent measurement of the expansion rate at @xmath33 . using these estimates @xcite derived strong constraints on modified theories of gravity ( mg ) and de model parameters . in this paper we perform a similar analysis on the cmass dr11 sample , which covers roughly three times the volume of dr9 . this paper is organized as follows . in section [ sec : data ] we describe the data used in the analysis . section [ sec : measurements ] explains how the two - dimensional correlation function is estimated from the data . section [ sec : covariances ] shows how we derive the estimates of the covariance matrix for our measurements . in section [ sec : model ] we describe the theoretical model used to fit the data . section [ sec : constraints ] presents and discusses our main results the estimates of growth rate , distance - redshift relationship and the expansion rate from the measurements . section [ sec : cosmoconstraints ] uses these estimates to constrain parameters in the @xmath6 cold dark matter ( @xmath6cdm ) model assuming gr ( @xmath6cdm - gr ) and possible deviations from this standard model . we conclude and discuss our results in section [ sec : conclusions ] . our measurements require the adoption of a cosmological model in order to convert angles and redshifts into comoving distances . as in @xcite we adopt a spatially - flat @xmath6cdm cosmology with @xmath34 and @xmath35 for this purpose . for ease of comparison across analyses , we follow @xcite and also report our distance constraints relative to a model with @xmath36 , @xmath35 , and @xmath37 , for which the bao scale @xmath38 mpc .

we use the observed anisotropic clustering of galaxies in the baryon oscillation spectroscopic survey ( boss ) data release 11 cmass sample to measure the linear growth rate of structure , the hubble expansion rate and the comoving distance scale . we find , and when fitting the growth and expansion rate simultaneously .

we use the observed anisotropic clustering of galaxies in the baryon oscillation spectroscopic survey ( boss ) data release 11 cmass sample to measure the linear growth rate of structure , the hubble expansion rate and the comoving distance scale . our sample covers 8498 and encloses an effective volume of 6 at an effective redshift of . we find , and when fitting the growth and expansion rate simultaneously . when we fix the background expansion to the one predicted by spatially - flatcdm model in agreement with recent planck results , we find ( 6 per cent accuracy ) . while our measurements are generally consistent with the predictions ofcdm and general relativity , they mildly favor models in which the strength of gravitational interactions is weaker than what is predicted by general relativity . combining our measurements with recent cosmic microwave background data results in tight constraints on basic cosmological parameters and deviations from the standard cosmological model . separately varying these parameters , we find ( 8 per cent accuracy ) and ( 16 per cent accuracy ) for the effective equation of state of dark energy and the growth rate index , respectively . both constraints are in good agreement with the standard model values of and . [ firstpage ] gravitation cosmological parameters dark energy dark matter distance scale large - scale structure of universe

1312.4899

c

we have used the anisotropic clustering of galaxies in the _ boss _ dr11 data set to simultaneously constrain the growth rate , the redshift distance relationship and the expansion rate at the redshift of @xmath33 . overall , our measurements are in good agreement with the results of the _ planck _ satellite propagated to low redshifts assuming @xmath6cdm - gr . by combining our measurements of @xmath136 , @xmath27 and @xmath28 with the cmb data we were able to derive tight constraints on basic cosmological parameters and parameters describing deviations from the @xmath6cdm - gr model . we were able to constrain the curvature of universe with 0.3 per cent precision , the de eos parameter @xmath248 with 8 per cent precision and the @xmath258-index for growth with 16 per cent precision . when we vary the background expansion within @xmath6cdm predictions of the _ planck _ data we measure the growth rate ( parametrized by @xmath258 ) to be weaker but consistent within @xmath263 of gr predictions . this preference for lower values of growth rate has also been observed in other similar low - redshift measurements ( see e.g. * ? ? ? * for discussion ) . our measurement of @xmath21 follows this trend but is closer to the gr predictions compared to the dr9 results of @xcite and the dr11 measurement of @xcite . similar measurements from a lower redshift ( lowz ) sample of _ boss _ galaxies will provide a complementary measurement of the growth rate in the de - dominated redshift range of @xmath271 , which will significantly strengthen the constraining power over possible gr modifications and can potentially increase the significance of the ` low growth rate ' signal .

when we fix the background expansion to the one predicted by spatially - flatcdm model in agreement with recent planck results , we find ( 6 per cent accuracy ) . while our measurements are generally consistent with the predictions ofcdm and general relativity , they mildly favor models in which the strength of gravitational interactions is weaker than what is predicted by general relativity . combining our measurements with recent cosmic microwave background data results in tight constraints on basic cosmological parameters and deviations from the standard cosmological model . separately varying these parameters , we find ( 8 per cent accuracy ) and ( 16 per cent accuracy ) for the effective equation of state of dark energy and the growth rate index , respectively . both constraints are in good agreement with the standard model values of and .

we use the observed anisotropic clustering of galaxies in the baryon oscillation spectroscopic survey ( boss ) data release 11 cmass sample to measure the linear growth rate of structure , the hubble expansion rate and the comoving distance scale . our sample covers 8498 and encloses an effective volume of 6 at an effective redshift of . we find , and when fitting the growth and expansion rate simultaneously . when we fix the background expansion to the one predicted by spatially - flatcdm model in agreement with recent planck results , we find ( 6 per cent accuracy ) . while our measurements are generally consistent with the predictions ofcdm and general relativity , they mildly favor models in which the strength of gravitational interactions is weaker than what is predicted by general relativity . combining our measurements with recent cosmic microwave background data results in tight constraints on basic cosmological parameters and deviations from the standard cosmological model . separately varying these parameters , we find ( 8 per cent accuracy ) and ( 16 per cent accuracy ) for the effective equation of state of dark energy and the growth rate index , respectively . both constraints are in good agreement with the standard model values of and . [ firstpage ] gravitation cosmological parameters dark energy dark matter distance scale large - scale structure of universe

0902.2787

i

the identification of the progenitor stars of supernova ( sn ) explosions is one of the central problems of stellar astrophysics . in the case of core collapse supernovae ( cc sne : types ii , ib , ic , and derived subtypes ) the progenitors are known to be massive ( @xmath5 ) stars whose inner cores collapse to a neutron star or a black hole . in a few cases , it has been possible to constrain the properties of the progenitor star using pre - explosion images or the turn - off masses of compact clusters @xcite , but there are still many open issues regarding which stars lead to specific subtypes of cc sne ( for an extended discussion and a complete set of references , see * ? ? ? * ; * ? ? ? in the case of thermonuclear ( type ia ) sne , the situation is much more complex . although a co white dwarf ( wd ) in some kind of binary is almost certainly the exploding star , the exact nature of the progenitor system has never been firmly established , either theoretically or observationally ( see * ? ? ? * and references therein ) . when direct identifications are not possible , the properties of the progenitors can be constrained using the stellar populations around the exploding stars . a number of studies have done this for sne in nearby galaxies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but this approach has important limitations . first , the available information , be it photometric ( e.g. * ? ? ? * ) or spectral ( e.g. * ? ? ? * ) , is usually integrated over the entire host galaxy , although local measurements at the sn sites have been made for a small number of objects ( e.g. * ? ? ? this effectively ignores the metallicity and stellar age gradients that must be present in the host . second , even in surveys that work with complete host spectra , the stellar populations are not resolved . among other things , this means that the stellar light is weighted by luminosity , which can conceal many important properties of the stellar populations . in practice , the information that can be obtained from this kind of observations is restricted to average metallicities and ages , unless sophisticated fitting techniques are used to extract the star formation history ( sfh ) of the host ( see * ? ? ? ideally , one would want to study _ resolved _ stellar populations associated with sn progenitors . the information that can be obtained in this way is much more detailed and reliable , but it requires focusing on very nearby sne . the present work is the first in a series of papers aimed at constraining the fundamental properties of cc and ia sn progenitors in the magellanic clouds by examining the stellar populations at the locations of the supernova remnants ( snrs ) left behind by the explosions . to do this , we take advantage of the large amount of observational data accumulated on the stellar populations of the clouds , in particular the star formation history ( sfh ) maps published by @xcite for the smc and @xcite ( henceforth , hz09 ) for the lmc . to identify the sites of recent sne , we rely on the extensively observed population of snrs in the mcs @xcite . much information about the sn explosions can be extracted from the observations of snrs of both ia and cc origin @xcite , and in some cases this information can be complemented by light echoes from the sne themselves @xcite . in this first installment , we focus on the eight youngest snrs in the lmc : sn1987a , n158a , n63a , and n49 ( cc snrs ) ; 0509@xmath067.5 , 0519@xmath069.0 , n103b and dem l71 ( ia snrs ) . this paper is organized as follows . in [ sec : targets ] we describe the criteria that have led to the selection of our eight target snrs . in [ sec : sntosnr ] we review their types and the characteristics of the parent sne that can be inferred from their observational properties . in [ sec : map ] we review the fundamental details of the sfh map of the lmc presented in hz09 . in [ sec : relevance ] we discuss the relevance that the local sfh has for the properties of the sn progenitors , given our knowledge about the global sfh and the stellar dynamics of the lmc . in [ sec : sfh ] we examine the local sfhs for the target snrs , with specific comments relating each sfh to the sne that originated the snrs . in [ sec : disc ] we discuss the impact that our findings have in the context of our current understanding of cc and ia sn progenitors . finally , in [ sec : conc ] we present our conclusions and we outline some avenues for future research .

we use the star formation history map of the large magellanic cloud recently published by harris & zaritsky to study the sites of the eight smallest ( and presumably youngest ) supernova remnants in the cloud : sn 1987a , n158a , n49 , and n63a ( core collapse remnants ) , 0509.5 , 0519.0 , n103b , and dem l71 ( type ia remnants ) . we discuss these results in the context of our present understanding of core collapse and type ia supernova progenitors .

we use the star formation history map of the large magellanic cloud recently published by harris & zaritsky to study the sites of the eight smallest ( and presumably youngest ) supernova remnants in the cloud : sn 1987a , n158a , n49 , and n63a ( core collapse remnants ) , 0509.5 , 0519.0 , n103b , and dem l71 ( type ia remnants ) . the local star formation histories provide unique insights into the nature of the supernova progenitors , which we compare with the properties of the supernova explosions derived from the remnants themselves and from supernova light echoes . we find that all the core collapse supernovae that we have studied are associated with vigorous star formation in the recent past . in the case of sn 1987a , the time of the last peak of star formation ( 12 myr ) matches the lifetime of a star with the known mass of its blue supergiant progenitor ( ) . more recent peaks of star formation can lead to supernovae with more massive progenitors , which opens the possibility of a type ib / c origin for snrs n158a and n63a . stars more massive than are very scarce around snr n49 , implying that the magnetar sgr 0526 in this snr was either formed elsewhere or came from a progenitor with a mass well below the threshold suggested in the literature . three of our four ia snrs are associated with old , metal poor stellar populations . this includes snr 0509.5 , which is known to have been originated by an extremely bright type ia event , and yet is located very far away from any sites of recent star formation , in a population with a mean age of gyr . the type ia snr n103b , on the other hand , is associated with recent star formation , and might have had a relatively younger and more massive progenitor with substantial mass loss before the explosion . we discuss these results in the context of our present understanding of core collapse and type ia supernova progenitors .

astro-ph9809042

i

an ultimate goal of the study of quasar ( qso ) absorption lines is to develop a comprehensive understanding of the kinematic , chemical , and ionization conditions of gaseous structures in early epoch galaxies and to chart their cosmic evolution . for a comprehensive physical picture of any given absorption system , both high resolution spectra of a wide range of chemical and ionization species and the empirically measured properties of the associated galaxies are required . for @xmath10 , shortly following the epoch of peak star formation , the association between mg0.1emii @xmath11 absorption and galaxies is well established ( @xcite ; @xcite ) , and their kinematics , though complex and varied , are consistent with being coupled to the galaxies themselves ( @xcite ; @xcite ) . it is unfortunate , however , that for @xmath12 , the spectroscopic data of are not of uniform , high quality due to the need for large amounts of space based telescope time to observe ultraviolet wavelengths . presently , any comprehensive analyses of low redshift systems for which the low ionization species ( i.e. , , ) have been observed at high resolution with hires / keck ( see churchill , vogt , & charlton 1999b ) must incorporate low resolution fos/_hst _ spectra of the intermediate and high ionization species , especially the strong c0.1emiv @xmath13 , n0.1emv @xmath14 , and o0.1emvi @xmath15 doublets , and of several other important low ionization species . presently , it is not clear if these low resolution data can be used to place meaningful constraints on the chemical and ionization conditions of the clouds in selected absorbers . in this paper , we investigated this issue in a pilot study , since an affirmation would imply that a larger sample could be studied using existing data from the _ hst _ archive . we would then be able to address the broader implications for galaxy formation scenarios based upon the inferred metallicities , abundance patterns , and inferred relative spatial distribution of the low and high ionization absorbing gas clouds . under the assumptions of photoionization and/or collisional ionization equilibrium , we developed a technique in which it was assumed that the number of clouds and their kinematics are obtained by voigt profile decomposition of the high resolution spectra . we then used the lower resolution profiles from the fos data to place constraints on the range of chemical and ionization conditions in these clouds . we also explored the idea that the could arise in relatively low ionization clouds embedded in a higher ionization and more extended medium ( see @xcite ; @xcite ) . more specifically , we set out to answer three questions : ( 1 ) assuming the clouds measured with hires are photoionized , can we construct model clouds that are consistent with the many low and intermediate ionization species captured in the fos data ? ( 2 ) if so , are we required to infer an additional ( presumedly low density and diffuse ) component to account for higher ionization absorption from , , and ? ( 3 ) if so , can this diffuse component be made consistent with photoionized only , collisionally ionized only , or photo plus collisionally ionized gas ? for this paper , we chose the three systems at @xmath16 , @xmath3 , and @xmath4 along the line of sight toward pg @xmath5 ( @xmath17 ) because they are exceptionally rich in low , intermediate , and high ionization ultraviolet transitions ( @xcite ; @xcite ; @xcite ) . the hires / keck profiles are illustrated in figure [ fig : order28 ] . two of the systems are kinematically `` complex '' and are separated by @xmath18 . the third system is more isolated , being @xmath19 from the other two . this system is classified as a `` weak '' absorber [ defined by @xmath20 ( @xcite ) ] . the highest ionization transitions , , and , are seen to have a total kinematic spread of @xmath21 coincident with the three system seen in absorption ( @xcite ) . in the qso field , kirhakos et al . ( 1994 ) found three bright galaxies with angular separations from the quasar of 5.6 , 8.6 , and 9.0 and @xmath22 magnitudes 21.1 , 21.5 , and 22.3 , respectively . the 8.6 galaxy has detected @xmath23 with flux @xmath24 ergs s@xmath25 at @xmath26 ( @xcite ) . at this redshift , the qso galaxy impact parameters are @xmath27 , @xmath28 , and @xmath29 kpc ( @xmath30 ) . there are @xmath31 galaxies with @xmath32 within 100 of the qso ( @xcite ) . this is an overdensity by a factor of @xmath33 compared to field galaxies ( @xcite ) . thus , it is of interest to entertain the possibility of a group environment for these absorbers . in [ sec : data ] we describe the data and its analysis . in [ sec : models ] we outline our modeling technique and simplifying assumptions . a synopsis of the model results are given in [ sec : results ] . details on how the data were used to constrain the models and how various ionizing spectral energy distributions modify these models are given in appendices [ app : constraints ] and [ app : models ] . in [ sec : discussion ] , we compare and contrast the system properties , and in [ sec : onthe ] , we discuss what might be inferred about the relative spatial distribution of the low and high ionization gas . we summarize in [ sec : conclusion ] .

the chemical and ionization species covered in the fos/_hst _ spectra are , , , , , , , , , , s0.1emvi , , and , with ionization potentials ranging from 13.6 to 138 ev . a main result of this paper is that the low resolution spectra can provide meaningful _ constraints _ on the physical conditions of the clouds , including allowed ranges of cloud to cloud variations within a system . = 100000

we used hires / keck profiles ( ) of and in combination with fos/_hst _ spectra ( ) to place constraints on the physical conditions ( metallicities , ionization conditions , and multiphase distribution ) of absorbing gas in three galaxies at , , and along the line of sight to pg . the chemical and ionization species covered in the fos/_hst _ spectra are , , , , , , , , , , s0.1emvi , , and , with ionization potentials ranging from 13.6 to 138 ev . the multiple clouds exhibit complex kinematics and the , and are exceptionally strong in absorption . we assumed that the clouds are photoionized by the extra galactic background and determined the allowed ranges of their physical properties as constrained by the absorption strengths in the fos spectra . a main result of this paper is that the low resolution spectra can provide meaningful _ constraints _ on the physical conditions of the clouds , including allowed ranges of cloud to cloud variations within a system . we find that the clouds , which have a typical size of pc , give rise to the , the majority of which arises in a single , very large ( kpc ) , higher ionization cloud . however , the clouds can not account for the strong , , and absorption . we conclude that the clouds are embedded in extended ( kpc ) , highly ionized gas that gives rise to , , and ; these are multiphase absorption systems . the high ionization phases have near solar metallicity and are consistent with galactic like coronae surrounding the individual galaxies , as opposed to a very extended common `` halo '' encompassing all three galaxies . = 100000

astro-ph9809042

c

as shown in figure [ fig : vpfits ] , system a is comprised of six distinct clouds with a total velocity spread of @xmath149 and is @xmath150 from system b , which has five clouds spread over @xmath6 . system c is @xmath19 from system b and is comprised of a single , resolved cloud . in figure 3 , we show the normalized fos spectrum with simulated spectra superimposed . these low resolution data reveal that each system is rich in multiple chemical species covering a wide range of ionization potentials and that the chemical and ionization conditions differ from system to system . one motivation for our study was simply to ascertain if a multiphase medium was required to explain the strong , and absorption lines . in all three systems , we were required to postulate a higher ionization component that is not seen in absorption . we emphasize that ( 1 ) the overall cloud properties are well constrained by the data and modeling , and ( 2 ) the allowed cloud to cloud variations are constrained tightly enough that no scenario even remotely modifies the requirement for a high ionization phase to explain the data . to the accuracy afforded by the fos spectrum , each of these high ionization phases is well described by a single component with @xmath151 ( based upon simulations ) . given the large @xmath46 parameters and the range of sizes derived from the models ( table [ tab : dics ] ) , this high ionization gas is likely to have a line of sight extent of @xmath152 kpc , and thus may be a surrounding medium in which the @xmath153 kpc clouds are embedded . consider the cloud to cloud variations in system b , which is a lyman limit system . the line of sight velocity spread of the clouds is @xmath154 , which implies they are bound within a galactic potential . if the clouds are equally illuminated by the extragalactic background , then the presence of in three of the clouds ( 8 , 9 , and 11 ) implies that they are more dense , more shielded from the ionizing flux , and/or iron group enriched relative to the other two clouds ( 7 and 10 ) . this suggests that clouds 8 , 9 , and 11 may be spatially contiguous ( relatively speaking ) , in that they may share similar histories of iron group enrichment from type ia sne . in the galaxy , the association of type ia explosions with the kinematically old disk implies that some events take place at large scale heights , so there is uncertainty in how much iron rich gas is driven into galactic halos ( @xcite ) . the unique cloud in system b is cloud 10 , which gives rise to a broader absorption profile ( @xmath155 ) and has no detectable . it has a higher ionization condition and gives rise to the majority of the absorption ( see figure [ fig : stis ] ) . it also has the largest @xmath87 . models yield that it is extended ( @xmath7 kpc ) and has lower metallicity . this leads us to conservatively speculate that cloud 10 is more akin to a halo like cloud or to a so called galactic high velocity cloud . the ratio @xmath156 may be a useful indicator of the differing local environments of clouds in higher redshift systems . system c classifies as a `` weak '' absorbers , defined by @xmath20 ( @xcite ) . from a sample of thirty such systems over the redshift range @xmath157 , churchill et al . found a wide range of @xmath158 and @xmath159 , presumedly due to variations in abundance pattern and ionization conditions , including single phase and multiphase . these absorbers are sub lyman limit systems with @xmath160 and [ some with @xmath161 ( @xcite ) ] . apart from its line of sight proximity ( @xmath162 ) to system b , system a would classify as a weak absorber . the @xmath163 kinematic spread of the six clouds in system a , and the large @xmath164 ratio in the diffuse component are suggestive of lower ionization clouds moving within a high ionization galactic corona , or halo , where the ratio @xmath164 is expected to be large ( @xcite ) . is it possible that the system c cloud arises in a similar environment as the six system a clouds , but that the line of sight happens to sample only one cloud ? if so , the absorption strength in system c would be comparable to that of system a , and it is significantly weaker . for weak systems , it may be that strong , broad absorption implies a larger number of clouds with a larger kinematic spread . in figure [ fig : stis ] , we present simulated stis/_hst _ spectra with @xmath165 , two pixels per resolution element , and a signal to noise ratio of @xmath140 for the first four transitions in the lyman series , and for the , , , and profiles of systems a and b. these spectra were generated assuming voigt profiles with the properties listed in tables [ tab : pics ] and [ tab : dics ] . these model profiles can be compared directly to observed data ( from stis/_hst _ ) and thus provide a direct test of the models . we show the contributing components as smooth curves . the dotted line curves are the clouds , with their velocity centroids marked with the short ticks above the continuum . the solid curves are from the photoionized diffuse component and the dash dot curves in system a represents the collisionally ionized diffuse component . here , we emphasize the importance of the lyman series . for all three systems , the and profiles in the fos spectra were significantly broader than could be fully accounted by the obtained soley from the model clouds . however , the narrower , , and profiles were fully accounted by the in these clouds . based upon the curve of growth behavior of the lyman series , we found that the addition of a very broad ( @xmath166 ) , lower @xmath80 component naturally explained the deeper and broader and profiles , without overproducing the narrower , , and profiles ( or modifying the lyman limit break ) . such behavior of the lyman series in low resolution data is likely to be a strong indication that a broad , perhaps highly ionized diffuse component is present . in figure [ fig : stis ] , we illustrate this behavior as it would be seen in higher resolution spectra . note that the widths of and are dominated by a broad , high ionization component , whereas the higher order transition widths are dominated by the clouds . in high resolution spectra , a diffuse component gives rise to a broadened , shallow wing when the profiles are saturated ( see and in system b ) and/or suppresses the recovery of the flux to the continuum level between clouds in the profile centers ( see and in system a ) . in system a , the profiles have structure due to the lower ionization clouds . the absorption predominantly arises in the clouds , and thus closely traces the kinematics . together , these profiles are tantalizing similar to those observed by savage , sembach , & cardelli ( 1994 ) along the line of sight to hd 167756 in the galaxy . we quote , `` the sight line contains at least two types of highly ionized gas . one type gives rise to a broad profile , and the other results in a more structured profile . the profile contains contributions from both types of highly ionized gas . '' we also find similarities between the model profiles and those in the damped systems at @xmath167 toward q@xmath168 and @xmath169 toward q@xmath170 ( lu et al . 1996 , figures 2 and 3 ) . in system b , cloud 10 is clearly unique among the clouds . this cloud has the largest ionization parameter and accounts for the majority of the absorption , which was clearly constrained to arise in the clouds . since the ionization conditions of clouds 8 , 9 , and 11 were set by their measured @xmath86 , the ionization condition in cloud 10 was well constrained by the ratio @xmath171 ; there was no alternative but for cloud 10 to dominate the absorption . the point is that this cloud may arise in a spatially distinct environment and have a unique formation history from the other clouds in system b ( see [ sec : discussion ] ) . the profile is dominated by a diffuse higher ionization phase , whereas the is predominantly due to higher density clouds . some lines of sight through the galaxy also exhibit narrow profiles and broad profiles ( for examples , see @xcite ; @xcite ) . in contrast , the and profiles in the @xmath172 damped system towards q@xmath173 ( @xcite ) appear to arise in the same phase . a synthetic stis/_hst _ spectrum for system c ( not shown ) reveals a narrow profile and broad , , and profiles . the profile exhibits a slightly deep , narrow core due to the low ionization phase . however this contribution would be lost for the expected noise levels in observed data , unless this narrow component was off center by @xmath174 relative to the broad component ( within the uncertainty of our modeling such an offset is not ruled out ) .

we assumed that the clouds are photoionized by the extra galactic background and determined the allowed ranges of their physical properties as constrained by the absorption strengths in the fos spectra . we find that the clouds , which have a typical size of pc , give rise to the , the majority of which arises in a single , very large ( kpc ) , higher ionization cloud . the high ionization phases have near solar metallicity and are consistent with galactic like coronae surrounding the individual galaxies , as opposed to a very extended common `` halo '' encompassing all three galaxies .

we used hires / keck profiles ( ) of and in combination with fos/_hst _ spectra ( ) to place constraints on the physical conditions ( metallicities , ionization conditions , and multiphase distribution ) of absorbing gas in three galaxies at , , and along the line of sight to pg . the chemical and ionization species covered in the fos/_hst _ spectra are , , , , , , , , , , s0.1emvi , , and , with ionization potentials ranging from 13.6 to 138 ev . the multiple clouds exhibit complex kinematics and the , and are exceptionally strong in absorption . we assumed that the clouds are photoionized by the extra galactic background and determined the allowed ranges of their physical properties as constrained by the absorption strengths in the fos spectra . a main result of this paper is that the low resolution spectra can provide meaningful _ constraints _ on the physical conditions of the clouds , including allowed ranges of cloud to cloud variations within a system . we find that the clouds , which have a typical size of pc , give rise to the , the majority of which arises in a single , very large ( kpc ) , higher ionization cloud . however , the clouds can not account for the strong , , and absorption . we conclude that the clouds are embedded in extended ( kpc ) , highly ionized gas that gives rise to , , and ; these are multiphase absorption systems . the high ionization phases have near solar metallicity and are consistent with galactic like coronae surrounding the individual galaxies , as opposed to a very extended common `` halo '' encompassing all three galaxies . = 100000

1611.05494

i

many mathematical models of real - life processes pose challenges during numerical computations , due to their large size and complexity . model order reduction ( mor ) techniques are methods that reduce the computational complexity of numerical simulations , an overview of mor methods is provided in @xcite . mor techniques such as balanced truncation ( bt ) and singular perturbation approximation ( spa ) are methods which have been introduced in @xcite and @xcite , respectively , for linear deterministic systems @xmath0 here @xmath1 is asymptotically stable , @xmath2 , @xmath3 and @xmath4 , @xmath5 , @xmath6 are state , output and input of the system , respectively . from the gramians @xmath7 and @xmath8 which solve dual lyapunov equations @xmath9 a balancing transformation is found , which is used to project the state space of size @xmath10 to a much smaller dimensional state space ( see , e.g. @xcite ) . recently , the theory for bt and spa has been extended to stochastic linear systems of the form @xmath11 where @xmath12 , @xmath13 and @xmath14 as above , and @xmath15 and @xmath16 ( @xmath17 ) are uncorrelated scalar square integrable lvy processes with mean zero ( often @xmath18 and the special case of wiener processes are considered , see , for example , @xcite ) . in this case bt and spa require the solution of more general lyapunov equations of the form @xmath19 where @xmath20 $ ] for general lvy processes . note that @xmath21 , @xmath22 for the case of a wiener process @xcite . we refer to @xcite for a detailed theoretical and numerical treatment of balancing related mor for ( [ linsysafterdisintr ] ) . in this paper we are going to study balancing related mor for systems of the form @xmath23 where @xmath24 and @xmath25 is the @xmath26 column of @xmath27 . the processes @xmath28 are the components of a square integrable mean zero lvy process @xmath29 that takes values in @xmath30 . consequently , these components are not necessarily uncorrelated . for a general theoretical treatment of sdes with lvy noise we refer to @xcite . the setting in ( [ linsysafterdisintr2 ] ) is of particular interest in many applications . if one is interested in a large number of different realisations of the output @xmath31 ( e.g. to compute moments of the form @xmath32 $ ] ) , then one needs to solve the sde in ( [ linsysafterdisintr2 ] ) a large number of times . for a state space of high dimension this is computationally expensive . reduction of the state space dimension decreases the computational complexity when sampling the solution to ( [ linsysafterdisintr2 ] ) , as the sde can then be solved in much smaller dimensions . hence the computational costs are reduced dramatically . the linear system ( [ linsysafterdisintr2 ] ) is a problem where the control is noise . in this case the standard theory for balancing related mor applied to a deterministic system no longer applies . balanced truncation has been applied to linear systems with white noise before . the discrete time setting was discussed in @xcite . for the continuous time setting , dissipative hamiltonian systems with wiener noise were treated in @xcite , but no error bounds were provided . in this paper we consider both bt and spa model order reduction . as far as we are aware , no theory and in particular error bounds for balancing related mor have been developed for continuous time sdes with lvy noise . using theory for linear stochastic differential equations with additive lvy noise we provide a stochastic concept of reachability . this concept motivates a new formulation of the reachability gramian . we prove bounds for the error between the full and reduced system which provide criteria for truncating , e.g. criteria for a suitable size of the reduced system . we analyse both bt and spa and apply the theory directly to an application arising from a second order damped wave equation . we now consider a particular example which explains why the above setting is of practical interest . [ [ motivational - example ] ] motivational example + + + + + + + + + + + + + + + + + + + + in @xcite the lateral time - dependent displacement @xmath33 of an electricity cable impacted by wind was modeled by the following one - dimensional symbolic second order spde with lvy noise : @xmath34 for @xmath35 $ ] , @xmath36 $ ] and @xmath37 , with boundary and initial conditions @xmath38 for small @xmath39 , the output equation @xmath40 is approximately the position of the middle of the cable . in @xcite , it is shown that transforming this spde in into a first order spde and then discretising it in space , leads to a system of the form ( [ linsysafterdisintr ] ) where @xmath41 . one drawback of the approach above is , that , when the electricity cable is in steady state , the wind has no impact . a more realistic scenario , which models the wind as some form of stochastic input , is the following symbolic equation @xmath42 for @xmath35 $ ] , @xmath36 $ ] and @xmath37 , boundary and initial conditions as in ( [ eq : bcic ] ) , and @xmath16 the components of a square integrable mean zero lvy process @xmath29 that takes values in @xmath30 . in this paper , we consider a framework which covers this model . moreover we modify the output in ( [ introbspout ] ) and let @xmath43 so that both the position and velocity of the middle of the string are observed . transformation and discretisation of this spde leads to a system of the form ( [ linsysafterdisintr2 ] ) where @xmath12 is an asymptotically stable matrix , i.e. @xmath44 . this paper is set up as follows . section [ sec : balancing ] provides the theoretical tools for balancing linear sdes with additive lvy noise . we explain the theoretical concepts of reachability and observability in this setting and show how this motivates mor using bt and spa . moreover we provide theoretical error bounds for both methods . in section [ sec : wave ] we show how a wave equation driven by lvy noise can be transformed into a first order equation and then reduced to a system of the form ( [ linsysafterdisintr2 ] ) by using a spectral galerkin method . numerical results which support our theory are provided in section [ sec : numerics ] .

when solving linear stochastic differential equations numerically , usually a high order spatial discretisation is used . balanced truncation ( bt ) and singular perturbation approximation ( spa ) are well - known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity . this work considers both methods when the control is replaced by a noise term . [ [ ams - subject - classifications ] ] ams subject classifications + + + + + + + + + + + + + + + + + + + + + + + + + + + primary 93a15 , 93b40 , 93e03 , 93e30 , 60j75 . secondary 93a30 , 15a24 .

when solving linear stochastic differential equations numerically , usually a high order spatial discretisation is used . balanced truncation ( bt ) and singular perturbation approximation ( spa ) are well - known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity . this work considers both methods when the control is replaced by a noise term . we provide theoretical tools such as stochastic concepts for reachability and observability , which are necessary for balancing related model order reduction of linear stochastic differential equations with additive lvy noise . moreover , we derive error bounds for both bt and spa and provide numerical results for a specific example which support the theory . [ [ keywords ] ] keywords : + + + + + + + + + model order reduction , balanced truncation , singular perturbation approximation , stochastic systems , lvy process , gramians , lyapunov equations . [ [ ams - subject - classifications ] ] ams subject classifications + + + + + + + + + + + + + + + + + + + + + + + + + + + primary 93a15 , 93b40 , 93e03 , 93e30 , 60j75 . secondary 93a30 , 15a24 .

1312.2449

i

extreme ultraviolet ( euv ) imaging of the inner solar corona gives the most valuable information about the spatial and temporal dynamics of coronal plasma , because this spectral range corresponds to its inherent temperature range of 12 mk . the temperature sensitivity of the euv emission results in noticeable differences in coronal structures that are seen simultaneously in the euv and white - light spectral ranges during eclipses @xcite . whereas in white light the corona is routinely studied at distances from disk center ( heliocentric distance ) exceeding 2@xmath0 , in euv the corona is typically observed below 1.3@xmath0 , because ordinary euv telescopes and spectrometers have a limited field of view adapted for imaging of the solar disk with the highest possible resolution . examples of such studies can be found elsewhere ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and others ) . at distances of 1.311@xmath0 , systematic spectroscopic investigations of the coronal plasma in the selected euv lines were performed with the ultraviolet coronagraph spectrometer ( uvcs ; * ? ? ? * ) on board the _ solar and heliospheric obseratory _ ( _ soho _ ) . although this instrument observed the corona only in a scanning mode , it gave significant results in the study of properties of various coronal structures , such as active region streamers , quiescent equatorial streamers , polar coronal plumes , _ etc . * and references therein ) . in particular , it was found that plasma in solar - minimum streamers is in thermal equilibrium , with the electron , proton and ionic temperatures all at similar values between 1.1 and 1.5 mk . the first real imaging of the extended euv corona above 1.3@xmath0 at high solar activity was performed in 2002 with the spectrographic x - ray imaging telescope - spectroheliograph ( spirit ) onboard the _ complex orbital observations near - earth of activity of the sun _ ( _ coronas - f _ ) satellite in its coronagraphic mode @xcite . the telescope operated in the 175 spectral band , which comprises the resonance lines of fe ix to fe xi with excitation temperatures around 1 mk . in several dedicated coronagraphic observations , it was found that the euv corona contained elongated bright ray - like structures stretching from some active regions to distances of 23@xmath0 , with brightness 24 times greater than that of the ambient background corona . comparison has shown that coronal structures seen by spirit were different from those observed in uvcs scans observing the colder o vi line , probably due to differences in the emission mechanisms or excitation temperatures . similar structures have been detected during eclipses in visible lines generated in transitions between higher levels of the same fe ix fe x ions @xcite . recently , it was shown that these ray - like structures very likely represent coronal signatures of long living plasma outflows originating at the interfaces between active regions and mid - latitude coronal holes , and contributing to the quasi - stationary component of the slow solar wind @xcite . @xcite and @xcite have shown that outflows are associated with interchange reconnection between closed field lines of active regions and the surrounding open field lines , which introduces a pressure imbalance that drives the plasma outward . based on this conclusion , we conjecture that plasma outflows propagating along open field lines produce enhancements of density in the corona , which can be seen at the limb as bright , elongated , ray - like structures . in the work of @xcite , and in the present work , it is shown that these structures correspond spatially to streamers observed above the same active regions by white - light coronagraphs . therefore , the ray - like structures concerned can be regarded as the euv counterparts of white - light streamers , revealing inner structure that is indistinguishable in visible light . since its launch on november 2 , 2009 , regular euv observations of the corona have come from the sun watcher with active pixels and image processing ( swap ) telescope aboard the _ project for onboard autonomy 2 _ ( _ proba2 _ ) mission @xcite . this telescope has a single spectral channel at 174 , with high sensitivity to euv emission of the same fe lines as spirit . the extended corona is imaged by swap in a special off - pointing mode by co - adding several dozen consecutive frames that are obtained with a cadence of 2030 seconds . the swap telescope has important advantages in studying the corona over similar euv instruments _ e.g. _ , _ soho _ s euv imaging telescope ( eit ; * ? ? ? * ) and the _ solar dynamics observatory _ s advanced imaging assembly ( _ sdo_/aia ; * ? ? ? * ) because it has a wide field of view and low stray light , which allow one to see the corona up to 2@xmath0 and beyond . regular imaging of the sun in this off - pointing mode has shown that , even at low solar activity , the corona often displays large - scale euv structures above active regions with some rays extending up to 2@xmath0 . a photometric analysis of the swap data assists in understanding plasma conditions and the physical mechanisms of coronal euv emission , opening up the possibility of more accurately modeling these . the role of various mechanisms of euv emission in the extended corona is still not well established due to a lack of observational data on plasma densities and temperatures at these larger distances , which are needed for numerical modeling of coronal euv flux . commonly , it is supposed that the euv emission of the corona is formed only by collisional excitation ( see , e.g. , * ? ? ? * ) , which results , in particular , in widespread use of the emission - measure approach . by default , the chianti package @xcite calculates intensities of the aforementioned fe ion lines in the corona by taking into account only the collisional excitation mechanism . radiative excitation , namely photoexcitation by continuous radiation from the solar disk , is commonly considered only for visible and infra - red lines @xcite . based on analysis of the 2010 eclipse observations , @xcite determined that radiative excitation by photospheric continuum emission from the solar disk dominates the generation of the monochromatic radiation in the visible fe - ion lines at heliocentric distances as large as 3@xmath0 . these authors also compared their results with observations in the proba2/swap 174 euv channel , and remarked that collisional excitation is the only excitation process for the fe x 174 emission since the solar disk has practically no emission shortward of 1000 corresponding to the wavelength range of these fe ion lines . however , the fe ix fe xi ions in the upper corona can absorb and re - emit the strong monochromatic euv radiation of those same ions , generated lower in the corona . this emission corresponds to resonance transitions of the ions , which makes excitation and emission by resonant scattering considerably more effective than excitation by continuum radiation from much colder photosphere ( see , e.g. , * ? ? ? * ; * ? ? ? it should be noted that this efficiency depends to some degree on the matching of spectral profiles between the illuminating and scattered radiation : in particular , this matching decreases in the case of radially - moving coronal plasma , which results in the doppler dimming effect . the collisional excitation rate of a spectral line is proportional to the product of the ion and electron densities , @xmath4 , whereas the resonant radiative excitation rate is proportional to only the ion density , @xmath5 . this means that at large distances from the solar surface , where plasma density decreases by 23 orders of magnitude , the contribution of the resonant scattering in the euv emission may become comparable or even dominant . even near the limb , where the electron density is relatively high , the resonant scattering contribution to the radiance of the corona along the line of sight can produce noticeable opacity effects , such as the distortion of intensities and profiles of strong euv and x - ray spectral lines that are often used in spectroscopic diagnostics ( see , e.g. , earlier works of @xcite , @xcite , and more recent works of @xcite , @xcite , @xcite ) . relevant estimates of contributions of collisional and radiative excitation mechanisms in emission of the extended corona depend on the radial distribution of electron density , temperature and bulk velocity in coronal structures , which may be established by a detailed spectroscopic consideration of the observational data . by contrast , white light coronal emission is caused by the thomson scattering of continuum radiation from the photosphere by free electrons in the corona . the intensity of this emission is proportional to the first power of density , so this emission decreases with distance more slower than the euv emission and does not depend on plasma temperature . this paper presents the results of a photometric study of a streamer observed * in * october 2010 with the swap instrument in the 174 spectral band . on october 2021 the streamer was seen at the western limb above active region ar 11112 , stretching to distances of more than 2@xmath0 . on october 21 , the base of the streamer from the limb to a distance of 1.2@xmath0 was observed by the euv imaging spectrometer ( eis ) on board the _ hinode _ spacecraft @xcite in a coordinated eis / swap _ hinode _ observing programme ( known as hop 165 ) . on october 20 the same streamer was observed by the mauna loa mk4 coronagraph , which measured the polarization brightness , @xmath6 , in the streamer produced by the thomson scattering of photospheric continuum radiation by free coronal electrons . based on the analysis of probable excitation mechanisms , we built a forward model of the coronal emission using assumed radial distributions of electron density and temperature in the streamer and in the surrounding corona . the parameters of these distributions were then determined in a self - consistent manner , using a solution that gave the best fit of the simulated euv emission to the measured swap and eis data , as well as the best fit of the simulated white - light brightness to the @xmath6 data provided by the mk4 coronagraph . finally , we estimated the relative contribution of resonant scattering in the formation of coronal euv emission for the plasma conditions determined along the streamer . observations of the corona with swap are described in section 2 . in section 3 , we consider mechanisms of formation of the coronal euv emission in fe ion spectral lines that appear in the swap wavelength band . in section 4 , we describe physical conditions in the inner corona and basic relations for modeling the coronal euv emission . section 5 describes a determination of the model fitting parameters and comparison of the calculated emission with measurements . section 6 contains a summary and our conclusions .

wide - field euv telescopes imaging in spectral bands sensitive to 1 mk plasma on the sun often observe extended ray - like coronal structures stretching radially from active regions to distances of 1.52 , which represent the euv counterparts of white - light streamers . to explain this phenomenon , it was found that plasma in the streamer above 1.2 is nearly isothermal , with a temperature mk . we conclude that , inside the streamer , collisional excitation provided more than 90% of the observed euv emission ; whereas , in the background corona , the contribution of resonance scattering became comparable with that of collisions at .

wide - field euv telescopes imaging in spectral bands sensitive to 1 mk plasma on the sun often observe extended ray - like coronal structures stretching radially from active regions to distances of 1.52 , which represent the euv counterparts of white - light streamers . to explain this phenomenon , we investigated the properties of a streamer observed on october 2021 , 2010 by the _ proba2_/swap euv telescope together with the _ hinode_/eis spectrometer ( hop 165 ) and the mauna loa mk4 white - light coronagraph . in the swap 174 band comprising the fe ix fe xi lines , the streamer was detected to a distance of 2 . we assume that the euv emission is dominated by collisional excitation and resonant scattering of monochromatic radiation coming from the underlying corona . below 1.2 , the plasma density and temperature were derived from the _ hinode_/eis data by a line - ratio method . plasma conditions in the streamer and in the background corona above 1.2 from disk center were determined by forward - modeling the emission that best fit the observational data in both euv and white light . it was found that plasma in the streamer above 1.2 is nearly isothermal , with a temperature mk . the hydrostatic scale - height temperature determined from the evaluated density distribution was significantly higher ( 1.72.08 mk ) , which suggests the existence of outward plasma flow along the streamer . we conclude that , inside the streamer , collisional excitation provided more than 90% of the observed euv emission ; whereas , in the background corona , the contribution of resonance scattering became comparable with that of collisions at .

1312.2449

i

this paper presents the results of a photometric study of * a * streamer observed on 2021 october 2010 with the swap euv telescope in the 174 spectral band , together with the _ hinode_/eis spectrometer ( obtained in the hop 165 session ) and the mauna loa mk4 white - light coronagraph . the application of special observational modes off - pointing , summation of several dozen high - cadence images and stray - light correction have allowed us to obtain the radial distribution of euv brightness in the longest coronal ray to a distance of more than @xmath154 with acceptable signal - to - noise ratio . in order to understand the origin of the euv emission observed by swap , we considered two main mechanisms of excitation of the fe ix fe xi ion lines that contribute to the flux in the swap spectral band : collisional excitation of ions by electrons and resonant scattering of the monochromatic radiation generated in the underlying corona . the incident fluxes in these spectral lines were determined from the swap and eit images using segmentation of the structure types on the solar disk and the calculation of their component fluxes , using the chianti package . assuming a commonly used radial density distribution in the quiet equatorial corona @xcite , an estimate of the relative contributions of collisional and resonant excitation to the euv emission has shown that for the strongest fe ix 171.08 line , collisional excitation dominates up to radial distances in excess of 2.5@xmath139 . for this range of distances , the characteristic timescale for reaching ionization equilibrium between the fe ix fe xi ions is shorter than the plasma expansion timescale @xcite , indicating that thermal equilibrium is reached in the streamer plasma . the radial distributions of plasma density and temperature in both the streamer and the surrounding corona have been determined by forward - modeling their white - light and euv emission , to best fit their measured values . the selected streamer ray was modeled as a slab with constant angular divergence from the solar center , a gaussian density distribution and a constant temperature along the line - of - sight . in the first step , the plasma temperature and density distributions in the ray from the limb to the distance 1.2@xmath139 were determined from the eis euv data using fe x / fe xi and fe xii ion line ratios , respectively . the effective width of the streamer along the line of sight , in these spectral lines , has been estimated as a ratio of the measured line brightnesses to their local emission , which were calculated using chianti and the inferred plasma density and temperature . the electron density distribution along the coronal ray above the reference point , 1.2@xmath139 , was then determined by forward - modeling the k - corona emission and fitting this to the polarization brightness measured by the mk4 coronagraph . the parameters to be fitted were taken as the effective width of the streamer and density at the reference point derived from the eis data . the validity of our model is confirmed by the fact that the effective width , which is derived independently from the white - light data ( 0.139@xmath139 , or @xmath17 6.6@xmath12 relative to the center of the sun ) is in good agreement with the values obtained from the euv data ( 0.1330.145@xmath139 ) . in the following step , we performed a forward - modeling of the streamer s euv emission in the swap spectral band . a fitting of the modeled euv brightness to the swap data gave the radial dependence of the product of emission measure ( along the line of sight ) with the temperature - dependent contribution function in the given fe ion lines . using the density values already determined from mk4 data , we obtained the temperature distribution along the streamer . as a result , the forward - modeling of white - light and euv brightnesses to match the measured data from all three instruments allowed us to obtain a self - consistent solution that yielded the most probable radial distributions of density and temperature in the streamer ray and surrounding background corona . it was found that the plasma temperature in the streamer ray varied from 1.25 mk at the limb to 1.43 mk at 1.2@xmath139 , being almost constant up to a distance of 2@xmath139 . the density in the streamer ray varied from @xmath17 2@xmath8310@xmath84@xmath19 at the limb to @xmath1712@xmath8310@xmath155@xmath19 at 2@xmath0 , and in the background corona it varied from @xmath1723@xmath8310@xmath85 to 23@xmath8310@xmath156 at the distance @xmath171.7@xmath0 . it was also found that the plasma density in the streamer decreases with distance sufficiently slower than it follows from the hydrostatic model with scale - height temperature equal to the independently determined value of 1.43@xmath20.08 mk . the best - fit scale - height temperature to the obtained density distribution is found to be noticeably higher , at 1.72@xmath20.08 mk . this result could mean that the plasma in the streamer contains a non - thermal component of motion , perhaps associated with an outward plasma flow . the existence of such time - varying plasma flows is consistent with the modulation of brightness in the swap images of the streamer during solar rotation . our photometric analysis has confirmed that enhanced brightness of ray - like coronal structures in fe ix fe xi euv lines up to distances of @xmath157 can be explained by collisionally excited emission . taking into account the plasma parameters determined , it was found that below this height , the resonant component constitutes less than 10% of the total flux , whereas in the background corona at @xmath158 it may in fact become comparable with contribution due to collisional excitation . however , the contribution of resonant scattering may be lower if the plasma moves outward with a velocity @xmath15940 km s@xmath14 , due to the doppler dimming effect . in conclusion , our results show that the euv emission of a streamer at distances from the limb up to @xmath160 can be correctly modeled by assuming collisional excitation in a plasma in thermal equilibrium . we hope that studies of the euv coronal emission at larger distances will be continued by forthcoming solar missions such as solar orbiter @xcite and aspiics @xcite . we would like to acknowledge dr . d. berghmans , dr . d. seaton and the rob team for providing us with swap data and useful discussions . we are grateful to prof . harra with her colleagues for organizing the coordinated hinode / eis and swap observations ( hop 165 session ) . the authors are thankful to prof . l. golub for interest to our work and valuable advices . the research leading to these results has received funding from the european commission s seventh framework programme ( fp7/2007 - 2013 ) under the grant agreement eheroes ( project no 284461 , www.eheroes.eu ) , the proba2 guest investigator programme grant and partial financial support from russian foundation for basic research ( grant 11 - 02 - 01079 ) . swap is a project of the centre spatial de liege and the royal observatory of belgium funded by the belgian federal science policy office ( belspo ) . hinode is a japanese mission developed and launched by isas / jaxa , with naoj as domestic partner and nasa and stfc ( uk ) as international partners . it is operated by these agencies in co - operation with esa and nsc ( norway ) . the mk4 data were used by courtesy of the mauna loa solar observatory , operated by the high altitude observatory , as part of the national center for atmospheric research ( ncar ) . ncar is supported by the national science foundation . chianti is a collaborative project involving george mason university , the university of michigan ( usa ) and the university of cambridge ( uk ) . feldman , u. , mandelbaum , p. , seely , j. l. , doschek , g. a. , gursky , h. 1992 , , 81 , 387 feldman , u. , doschek , g.a . , schhle , u. , & wilhelm , k. 1999 , , 518 , 500 frazin , r.a . , & jansen , p. 2002 , , 570 , 408 frazin , r.a . 2005 , , 530 , 1026 gabriel a.h . , et al . 1971 , , 169 , 595 gibson s.e . , et al . 1999 , , 104 , 9691 gibson s.e . , et al . 2010 , , 724 , 1133 gimnez de castro c.g . , 2007 , , 476 , 369 golub , l. , & pasachoff , j. , the solar corona . 2nd edition . cambridge university press , 2010 guhathakurta m. , holzer t.e . , macqueen r.m . 1996 , , 458 , 817 habbal s.r . , 2007 , , 663 , 598 habbal s.r . , 2011 , , 734:120 , 18pp halain , j .- p . , berghmans , d. , seaton , d.b . , et al . 2013 , , 286 , 67 hyder c.l . , & lites b.w . 1970 , , 14 , 147 joselyn , j. , munro , r.h . , holzer , t.e . 1979 , , 64 , 57 kohl j.l . , & withbroe g.l . 1982 , , 256 , 263 kohl j.l . 1995 , , 162 , 313 kohl , j.l . , noci g. , cranmer s.r . , raymond j.c . 2006 , , 13 , 31 kucera t.a . , et al . 2012 , , 757:73 , 13 pp lamy , p. , dam , l. , vivs , s. , zhukov , a. 2010 , proc . of the spie , vol . 7731 , i d . 773118 , 12 pp landi , e. , young , p.r . , dere , k.p . , del zanna , g. , mason , h.e . 2013 , , 763 , 86 lemen , j.r . , et al . 2012 , , 275 , 17 mazzotta , p. , mazzitelli , g. , colafrancesco , s. , vittorio , n. 1998 , , 133 , 403 mierla m. , schwenn r. , teriaca l. , stenborg g. , podlipnik b. 2008 , , 480 , 509 mller d. , marsden , r.g . , st . cyr , o.c . , and gilbert , h.r . 2013 , , 285 , 25 noci g. , kohl j.l . , & withbroe g.l . 1987 , , 315 , 706 nuevo , f.a . , vsquez , a.m. , frazin , r.a . , huang , zh . , & manchester , w.b . 2012 , iaus 286 , 238 parenti , s. , bromage , b.j.i . , poletto , g. , noci , g. , raymond , j.c . , & bromage , g.e . 2000 , , 363 , 800 pasachoff , j.m . , et al . 2011 , , 734:114 , 10 pp . phillips k.j.h , et al . 1997 , , 324 , 381 raftery , c.l . , bloomfield , d.s . , gallagher , p.t . , et al . 2013 , , 286 , 111 rugge h.r . , & mckenzie d.l . 1985 , , 297 , 338 saito k. , makita m. , nishi k. , hata s. 1970 , annals of the tokyo astronomical observatory , second ser . 12 , 53120 saito k. et al . 1977 , , 55 , 121 seaton d.b . , 2013 , , 286 , 43 schmit , d.j . , & gibson , s.e . 2011 , , 733:1 , 9 pp schrijver c.j . , & mcmullen r.a . 2000 , , 531 , 1121 vsquez a.m. , et al . 2003 , , 598 , 1361 vsquez , a.m. , huang , zh . , manchester , w.b . , & frazin , r.a . 2011 , , 274 , 259 vibert d. , et al . , 1997 , in asp conf . 125 , astronomical data analysis software and systems vi , ed . g. hunt and h.e . payne ( san francisco : asp ) , 230 waljeski k. , et al . 1994 , , 429 , 909 wang y .- m . , et al . 2007 , , 660 , 882 lcccccc ion & @xmath9 , & @xmath161 & @xmath34 & solar flux , & phot @xmath52 s@xmath14 sr@xmath14 & swap response @xmath119 , + & & & & swap & eit & dn / ph cm@xmath8 str pix + fe ix & 171.08 & 5.9 & 2.946 & 1.1@xmath8310@xmath163 & 1.2@xmath8310@xmath163 & 1.63@xmath8310@xmath164 + fe x & 174.53 & 6.0 & 1.252 & 4.3@xmath8310@xmath165 & 5.8@xmath8310@xmath165 & 1.97@xmath8310@xmath164 + fe x & 177.24 & 6.0 & 0.708 & 4.5@xmath8310@xmath165 & 3.2@xmath8310@xmath163 & 1.38@xmath8310@xmath164 + fe xi & 180.41 & 6.1 & 0.957 & 3.2@xmath8310@xmath165 & 4.9@xmath8310@xmath165 & 3.01@xmath8310@xmath166 +

we investigated the properties of a streamer observed on october 2021 , 2010 by the _ proba2_/swap euv telescope together with the _ hinode_/eis spectrometer ( hop 165 ) and the mauna loa mk4 white - light coronagraph . in the swap 174 band comprising the fe ix fe xi lines , the streamer was detected to a distance of 2 . we assume that the euv emission is dominated by collisional excitation and resonant scattering of monochromatic radiation coming from the underlying corona .

wide - field euv telescopes imaging in spectral bands sensitive to 1 mk plasma on the sun often observe extended ray - like coronal structures stretching radially from active regions to distances of 1.52 , which represent the euv counterparts of white - light streamers . to explain this phenomenon , we investigated the properties of a streamer observed on october 2021 , 2010 by the _ proba2_/swap euv telescope together with the _ hinode_/eis spectrometer ( hop 165 ) and the mauna loa mk4 white - light coronagraph . in the swap 174 band comprising the fe ix fe xi lines , the streamer was detected to a distance of 2 . we assume that the euv emission is dominated by collisional excitation and resonant scattering of monochromatic radiation coming from the underlying corona . below 1.2 , the plasma density and temperature were derived from the _ hinode_/eis data by a line - ratio method . plasma conditions in the streamer and in the background corona above 1.2 from disk center were determined by forward - modeling the emission that best fit the observational data in both euv and white light . it was found that plasma in the streamer above 1.2 is nearly isothermal , with a temperature mk . the hydrostatic scale - height temperature determined from the evaluated density distribution was significantly higher ( 1.72.08 mk ) , which suggests the existence of outward plasma flow along the streamer . we conclude that , inside the streamer , collisional excitation provided more than 90% of the observed euv emission ; whereas , in the background corona , the contribution of resonance scattering became comparable with that of collisions at .

hep-th0508038

i

anti - de sitter ( ads ) spacetime is remarkable from different points of view . the early interest to this spacetime was motivated by the questions of principal nature related to the quantization of fields propagating on curved backgrounds . the investigation of the dynamics of fields on ads is of interest not only because ads space is a space of high symmetry , and hence exact solutions for the free field theory can be written down , but also because it is a space of constant nonzero curvature , and thus field theory in ads background is not a trivial rewriting of minkowski spacetime field theory . the presence of the both regular and irregular modes and the possibility of interesting causal structure lead to many new phenomena . the importance of this theoretical work increased when it has been discovered that ads spacetime generically arises as ground state in extended supergravity and in string theories . further interest in this subject was generated by the appearance of two models where ads geometry plays a special role . the first model , the so called ads / cft correspondence ( for a review see @xcite ) , represents a realization of the holographic principle and relates string theories or supergravity in the ads bulk with a conformal field theory living on its boundary . it has many interesting consequences and provides a powerful tool to investigate gauge field theories . the second model is a realization of a braneworld scenario with large extra dimensions and provides a solution to the hierarchy problem between the gravitational and electroweak mass scales ( for reviews in braneworld gravity and cosmology see ref . @xcite ) . in this model the main idea to resolve the large hierarchy is that the small coupling of four dimensional gravity is generated by the large physical volume of extra dimensions . braneworlds naturally appear in string / m - theory context and provide a novel setting for discussing phenomenological and cosmological issues related to extra dimensions . the model introduced by randall and sundrum @xcite is particularly attractive . the corresponding background solution consists of two parallel flat branes , one with positive tension and another with negative tension embedded in a five dimensional ads bulk . the fifth coordinate is compactified on @xmath6 , and the branes are on the two fixed points . in the original version of the model it is assumed that all matter fields are confined on the branes and only the gravity propagates freely in the five dimensional bulk . more recently , alternatives to confining particles on the brane have been investigated and scenarios with additional bulk fields have been considered . apart from the hierarchy problem it has been also tried to solve the cosmological constant problem within the braneworld scenario . the braneworld theories may give some alternative discussion of the cosmological constant . the basic new ingredient is that the vacuum energy generated by quantum fluctuations of fields living on the brane may not curve the brane itself but instead the space transverse to it . randall - sundrum scenario is just the simplest possibility within a more general class of higher dimensional warped geometries . such a generalization is of importance from the viewpoint of a underlying fundamental theory in higher dimensions such as ten dimensional superstring theory . from a phenomenological point of view , higher dimensional theories with curved internal manifolds offer a richer geometrical and topological structure . the consideration of more general spacetimes may provide interesting extensions of the randall - sundrum mechanism for the geometric origin of the hierarchy . spacetimes with more than one extra dimension can allow for solutions with more appealing features , particularly in spacetimes where the curvature of the internal space is non - zero . more extra dimensions also relax the fine - tunings of the fundamental parameters . these models can provide a framework in the context of which the stabilization of the radion field naturally takes place . several variants of the randall sundrum scenario involving cosmic strings and other global defects of various codimensions has been investigated in higher dimensions ( see , for instance , @xcite-@xcite and references therein ) . in particular , much work has been devoted to warped geometries in six dimensions ( see references in kofi05 ) . in braneworld models the investigation of quantum effects is of considerable phenomenological interest , both in particle physics and in cosmology . the braneworld corresponds to a manifold with boundaries and all fields which propagate in the bulk will give casimir - type contributions to the vacuum energy ( for reviews of the casimir effect see ref . @xcite ) , and as a result to the vacuum forces acting on the branes . casimir forces provide a natural alternative to the goldberger - wise mechanism for stabilizing the radion field in the randall - sundrum model , as required for a complete solution of the hierarchy problem . in addition , the casimir energy gives a contribution to both the brane and bulk cosmological constants and , hence , has to be taken into account in the self - consistent formulation of the braneworld dynamics . motivated by these , the role of quantum effects in braneworld scenarios has received a great deal of attention @xcite-@xcite . however , in the most part of these papers the authors consider the global quantities such as the total casimir energy , effective action or conformally invariant fields . the investigation of local physical characteristics in the casimir effect , such as expectation value of the energy - momentum tensor and the field square , is of considerable interest . local quantities contain more information on the vacuum fluctuations than the global ones . in addition to describing the physical structure of the quantum field at a given point , the energy - momentum tensor acts as the source in the einstein equations and therefore plays an important role in modelling a self - consistent dynamics involving the gravitational field . quantum fluctuations play also an important role in inflationary cosmology as they are related to the power spectrum . as it has been shown in ref . pujo05 , the quantum fluctuations of a bulk scalar field coupled to a brane located scalar field with a bi - quadratic interaction generate an effective potential for the field on the brane with a true vacuum at the nonzero values of the field . in particular , these calculations are relevant to the bulk inflaton model @xcite , where the inflation on the brane is driven by the bulk scalar field . in the case of two parallel branes on ads background , the vacuum expectation value of the bulk energy - momentum tensor for a scalar field with an arbitrary curvature coupling is investigated in refs . @xcite . in particular , in ref . @xcite the application of the generalized abel - plana formula @xcite to the corresponding mode sums allowed us to extract manifestly the parts due to the ads spacetime without boundaries and to present the boundary induced parts in terms of exponentially convergent integrals for the points away the boundaries . the interaction forces between the branes are investigated as well . depending on the coefficients in the boundary conditions , these forces can be either attractive or repulsive . the local vacuum effects for a bulk scalar field in brane models with ds branes are discussed in refs . pujo04,nayl05 . on background of manifolds with boundaries , the physical quantities , in general , will receive both volume and surface contributions . for scalar fields with general curvature coupling , in ref . @xcite it has been shown that in the discussion of the relation between the mode sum energy , evaluated as the sum of the zero - point energies for each normal mode of frequency , and the volume integral of the renormalized energy density for the robin parallel plates geometry it is necessary to include in the energy a surface term located on the boundary . an expression for the surface energy - momentum tensor for a scalar field with general curvature coupling parameter in the general case of bulk and boundary geometries is derived in ref . the corresponding vacuum expectation values are investigated in ref . @xcite for the model with two flat parallel branes on ads bulk and in @xcite for a ds brane in the flat bulk . in particular , for the first case it has been shown that in the randall - sundrum model the cosmological constant induced on the visible brane by the presence of the hidden brane is of the right order of magnitude with the value suggested by the cosmological observations without an additional fine tuning of the parameters . the purpose of the present paper is to study the wightman function and the vacuum expectation value of the field square for a scalar field with an arbitrary curvature coupling parameter obeying robin boundary conditions on two codimension one parallel branes embedded in the background spacetime @xmath1 with a warped internal space @xmath2 . the quantum effective potential and the problem of moduli stabilization in the orbifolded version of this model with zero mass parameters on the branes are discussed recently in ref . in particular , it has been shown that one loop - effects induced by bulk scalar fields generate a suitable effective potential which can stabilize the hierarchy without fine tuning . the corresponding results are extended to the type of models with unwarped internal space @xmath2 in ref . we organize the present paper as follows . in the next section we evaluate the wightman function in the region between the branes . by using the generalized abel - plana formula , we present this function in the form of a sum of the wightman function for the bulk without boundaries and boundary induced parts . the vacuum expectation value of the field square for a general case of the internal space @xmath2 is discussed in section [ sec : vevphi2 ] for the case of a single brane geometry and in section [ sec : phi2twopl ] in the region between two branes . various limiting cases are discussed when the general formulae are simplified . a simple example with the internal space @xmath7 is then considered in section [ sec : example ] . the last section contains a summary of the work . the vacuum expectation values of the energy - momentum tensor and the interaction forces between the branes will be discussed in the forthcoming paper .

wightman function and vacuum expectation value of the field square are evaluated for a massive scalar field with general curvature coupling parameter subject to robin boundary conditions on two codimension one parallel branes located on-dimensional background spacetime with a warped internal space . the general case of different robin coefficients on separate branes is considered . the application of the generalized abel - plana formula for the series over zeros of combinations of cylinder functions allows us to extract manifestly the part due to the bulk without boundaries . unlike to the purely ads bulk

wightman function and vacuum expectation value of the field square are evaluated for a massive scalar field with general curvature coupling parameter subject to robin boundary conditions on two codimension one parallel branes located on-dimensional background spacetime with a warped internal space . the general case of different robin coefficients on separate branes is considered . the application of the generalized abel - plana formula for the series over zeros of combinations of cylinder functions allows us to extract manifestly the part due to the bulk without boundaries . unlike to the purely ads bulk , the vacuum expectation value of the field square induced by a single brane , in addition to the distance from the brane , depends also on the position of the brane in the bulk . the brane induced part in this expectation value vanishes when the brane position tends to the ads horizon or ads boundary . the asymptotic behavior of the vacuum densities near the branes and at large distances is investigated . the contribution of kaluza - klein modes along is discussed in various limiting cases . in the limit when the curvature radius for the ads spacetime tends to infinity , we derive the results for two parallel robin plates on background spacetime . for strong gravitational fields corresponding to large values of the ads energy scale , the both single brane and interference parts of the expectation values integrated over the internal space are exponentially suppressed . as an example the case is considered , corresponding to the bulk with one compactified dimension . an application to the higher dimensional generalization of the randall - sundrum brane model with arbitrary mass terms on the branes is discussed . pacs numbers : 04.62.+v , 11.10.kk , 04.50.+h

1003.0932

i

advanced nanostructuring techniques permit the creation of specific superconducting structures for controlling vortex motion in type - ii superconductors . experiments and simulations for square and triangular artificial pinning arrays demonstrate that pronounced commensurability effects occur when the number of vortices is an integer multiple of the number of pinning sites , and that these effects can be observed as peaks in the critical current.@xcite above the first matching field , multiple vortices may occupy individual pinning sites,@xcite or only a portion of the vortices may be captured by the pinning sites with the remaining vortices located in interstitial sites where they can still be pinned by the repulsive interactions with vortices at the pinning sites.@xcite vortex matter in these periodic pinning arrays can also exhibit a remarkably rich variety of distinct dynamical phases originally predicted in simulations.@xcite these include one - dimensional flow of interstitial vortices between immobile vortices in the pinning sites , disordered or turbulent phases where the number of moving vortices fluctuates strongly , and laminar states where the vortex flow can organize along the rows of pinning sites . the transitions between these different states appear as specific features in the voltage - current curves , including negative differential conductivity where the number of moving vortices or the average vortex velocity decreases with increasing drive . in very recent experiments , these dynamical phases were observed in both low temperature @xcite and high temperature @xcite superconductors with periodic pinning arrays . it is also possible to create periodic pinning arrays that contain intrinsic asymmetry , such as with asymmetric thickness modulation,@xcite funnel geometries,@xcite composite pinning sites,@xcite or arrays of triangular traps.@xcite this asymmetry can produce a diode effect when the depinning force is higher in one direction , and can give a ratchet effect in which a net dc vortex flow occurs upon application of an ac drive.@xcite reversals of the ratchet flow from the easy asymmetry direction to the hard asymmetry direction can occur as a function of magnetic field and other parameters @xcite due to various collective interactions of the vortices . one of the earliest proposals for a vortex ratchet involved a periodic asymmetric channel or funnel,@xcite and such geometries have now been experimentally fabricated.@xcite the first experiments on this system verified the existence of ratchet effects , but also detected boundary effects caused by the disordered injection of vortices at the edge of the sample.@xcite the edge effect can be overcome by using sample geometries where the vortices flow in annular asymmetric channels so that vortices need not enter or exit the sample.@xcite such a technique may also provide the resolution required to investigate individual vortex motion through the channels.@xcite in this work we study the dynamics of vortices in a periodic asymmetric channel geometry or funnel array and show that a variety of new types of vortex dynamics and behaviors can arise , including a jamming effect and flow patterns that are organized such that only one vortex at a time passes through the funnel tip . such a geometry could be realized by etching the edge of a single superconducting strip into a periodic funnel shape so that the vortices would flow in a true single channel . funnel geometries created with periodic channels in two - dimensional superconducting samples should also exhibit many of the same properties we observe ; however , in these systems vortices located between the asymmetric channels could be important and under high drives could depin . the presence of vortices in the regions between the channels can be deduced from the onset of hysteresis in the critical current curves @xmath1 at fields higher than the fields at which many of the ratchet effects are observed.@xcite although our study focuses on interacting vortices in type - ii superconductors , we expect that the same dynamics will occur for other systems of repulsively interacting particles in funnel geometries . these include charged colloidal assemblies,@xcite magnetic colloids,@xcite charged metallic dots,@xcite and classical electron crystals.@xcite additionally , in recent experiments of ion flow through a single funnel , effects such as negative differential conductivity were observed.@xcite our results suggest that the same type of clogging effect we observe could be occurring in these artificial ion channels .

with advances in fabrication technologies it is now possible to create precisely controlled geometries and pinning landscapes for vortex matter in type - ii superconductors . here we show that this system exhibits a number of different commensurability effects when the vortex configurations match to both the periodicity of the array and the geometry of the funnels . we observe a series of elastic and plastic vortex flow phases which produce pronounced features such as jumps or dips in the transport curves . in all of the flow phases we also show how noise fluctuations can be used to distinguish the different flow phases .

with advances in fabrication technologies it is now possible to create precisely controlled geometries and pinning landscapes for vortex matter in type - ii superconductors . here we use numerical simulations to examine vortex states and dynamics in periodic funnel geometries where a drive is applied in the easy flow direction . we show that this system exhibits a number of different commensurability effects when the vortex configurations match to both the periodicity of the array and the geometry of the funnels . the vortex configurations in this system are generally different from those observed for single isolated triangular superconducting samples due to the coupling of vortices in adjacent funnels . at certain matching fields , peaks in the critical current are absent due to the particular vortex configurations that occur at these fields . we find that the overall depinning force increases with increasing vortex density as a result of the enhanced vortex - vortex interactions caused by a crowding effect at the funnel tips . when a system becomes less mobile as a result of increased particle interactions , it is said to exhibit a jamming behavior . under an applied drive we observe a series of elastic and plastic vortex flow phases which produce pronounced features such as jumps or dips in the transport curves . in all of the flow phases , only one vortex can pass through the funnel tip at a time due to the vortex - vortex repulsion forces . as a consequence of this constraint , we observe the remarkable result that the sum of the vortex velocities at a fixed drive remains nearly constant with increasing magnetic field rather than increasing linearly . this result is similar to the behavior of sand in an hourglass . we also show how noise fluctuations can be used to distinguish the different flow phases . our results should be readily generalizable to other systems of particles flowing in periodic funnel geometries , such as colloids or wigner crystals .

1003.0932

i

in summary , we have used numerical simulations to examine the vortex configurations and dynamics in a periodic funnel array . the vortex configurations we observe are generally different from those found for a single isolated triangular sample due to the coupling between vortices in adjacent funnels . as a function of field we find a series of depinning threshold peaks at the matching fields where the vortex configurations are ordered . in some cases , matching peaks are missing due to the fact that the vortex configuration contains pairs of vortices that are located close together near the funnel apertures . we also observe a general increase in the depinning threshold with increasing vortex density , which is opposite from the normal trend for vortices in two - dimensional pinning arrays where the vortices are directly trapped by pinning sites . in the funnel geometry , the pinning is a result of the repulsive vortex - vortex interaction forces , and as the vortex density increases it becomes more difficult for the vortices to overcome these repulsive forces and flow through the funnel tip . we also find a rich variety of dynamical phases , including ordered elastic and ordered plastic phases where the vortices follow fixed trajectories and disordered phases where vortices mix chaotically . the phases generally organize in such a way that only one vortex passes through the tip of the funnel at a time . due to this constraint , the average velocity of an individual vortex decreases with increasing field such that the sum of the velocities of all of the vortices at fixed drive remains close to constant for increasing field rather than increasing with increasing field . this behavior is similar to the response of grains in an hourglass . transitions between the different dynamical phases appear as jumps or cusps in the velocity - force curves , and there are even regimes where the average vortex motion decreases with increasing drive , producing a negative differential conductivity . at higher fields , moving states can form in which a single vortex remains immobile at the center of a funnel while other vortices flow around it . in general , ordered flow phases occur at the matching fields , while at non - matching fields the flow is disordered for at least some regime of driving forces . the ordered phases are associated with sharp narrow band or washboard velocity noise signals while the disordered phases have @xmath187 velocity noise spectra . our results should also be generalizable to other systems of repulsively interacting particles moving through a funnel geometry , such as colloids or wigner crystals . 99 m. baert , v.v . metlushko , r. jonckheere , v.v . moshchalkov , and y. bruynseraede , phys . 74 * , 3269 ( 1995 ) ; k. harada , o. kamimura , h. kasai , t. matsuda , a. tonomura , and v.v . moshchalkov , science * 274 * , 1167 ( 1996 ) . mart ' in , m. v ' elez , j. nogu ' es , and i.k . schuller , phys . lett . * 79 * , 1929 ( 1997 ) ; d.j . morgan and j.b . ketterson , phys . 80 * , 3614 ( 1998 ) ; j.e . villegas , m.i . montero , c .- p . li , and i.k . schuller , phys . lett . * 97 * , 027002 ( 2006 ) . field , s.s . james , j. barentine , v. metlushko , g. crabtree , h. shtrikman , b. ilic , and s.r.j . brueck , phys . lett . * 88 * , 067003 ( 2002 ) ; a.n . grigorenko , g.d . howells , s.j . bending , j. bekaert , m.j . van bael , l. van look , v.v . moshchalkov , y. bruynseraede , g. borghs , i.i . kaya , and r.a . stradling , phys . b * 63 * , 052504 ( 2001 ) . siwy , m.r . powell , e. kalman , r.d . astumian and r.s . eisenberg , nano lett . * 6 * , 473 ( 2006 ) ; z.s . siwy , m.r . powell , a. petrov , e. kalman , c. trautmann , and r.s . eisenberg , nano lett . * 6 * , 1729 ( 2006 ) .

we use numerical simulations to examine vortex states and dynamics in periodic funnel geometries where a drive is applied in the easy flow direction . the vortex configurations in this system are generally different from those observed for single isolated triangular superconducting samples due to the coupling of vortices in adjacent funnels . at certain matching fields , peaks in the critical current are absent due to the particular vortex configurations that occur at these fields . as a consequence of this constraint , we observe the remarkable result that the sum of the vortex velocities at a fixed drive remains nearly constant with increasing magnetic field rather than increasing linearly . this result is similar to the behavior of sand in an hourglass . our results should be readily generalizable to other systems of particles flowing in periodic funnel geometries , such as colloids or wigner crystals .

with advances in fabrication technologies it is now possible to create precisely controlled geometries and pinning landscapes for vortex matter in type - ii superconductors . here we use numerical simulations to examine vortex states and dynamics in periodic funnel geometries where a drive is applied in the easy flow direction . we show that this system exhibits a number of different commensurability effects when the vortex configurations match to both the periodicity of the array and the geometry of the funnels . the vortex configurations in this system are generally different from those observed for single isolated triangular superconducting samples due to the coupling of vortices in adjacent funnels . at certain matching fields , peaks in the critical current are absent due to the particular vortex configurations that occur at these fields . we find that the overall depinning force increases with increasing vortex density as a result of the enhanced vortex - vortex interactions caused by a crowding effect at the funnel tips . when a system becomes less mobile as a result of increased particle interactions , it is said to exhibit a jamming behavior . under an applied drive we observe a series of elastic and plastic vortex flow phases which produce pronounced features such as jumps or dips in the transport curves . in all of the flow phases , only one vortex can pass through the funnel tip at a time due to the vortex - vortex repulsion forces . as a consequence of this constraint , we observe the remarkable result that the sum of the vortex velocities at a fixed drive remains nearly constant with increasing magnetic field rather than increasing linearly . this result is similar to the behavior of sand in an hourglass . we also show how noise fluctuations can be used to distinguish the different flow phases . our results should be readily generalizable to other systems of particles flowing in periodic funnel geometries , such as colloids or wigner crystals .

1406.4121

c

since we analyzed the bulge of m31 , which is comprised of an old stellar population and thus globular clusters , it is not surprising that our x - ray point sources are predominantly gc - lmxbs ( table [ tab : scxrmatches ] ) . when comparing the averages of star cluster colour , magnitude , and effective radius our results showed that redder , brighter , and compact star clusters were more likely to host x - ray sources however , a logistic regression analysis showed that the f475w magnitude is the most significant predictor followed by the effective radius . the f475w@xmath0f814w color ( an indicator of metallicity in old stellar populations ) was not a significant predictor of whether a cluster hosted an x - ray source . a statistical analysis using logistic regression is a more robust method than comparing averages and as such accurately represents trends in the data . @xcite found different trends when using _ xmm - newton _ observations of m31 to identify 45 gc - lmxbs , namely that the stellar collision rate ( proportional to stellar density and core radius ) , luminosity , and metallicity are all significant . however , @xcite came to similar conclusions to ours when using _ hst _ data to derive structural parameters for 29 gc - lmxbs , and complementing the sample with published values for a total of 41 gc - lmxbs and 65 non - lmxb gcs . they found the probability of a gc hosting an x - ray source increased with increasing collision rate and proximity to the galaxy center . metallicity was not as important a predictor but an increasing cluster mass at fixed collision rate decreased the probability of hosting an x - ray source ( although the authors stress this may be a sample selection effect ) . the latter result does not agree with our positive trend between gc magnitude ( which scales with mass ) and a gc s probability of hosting an lmxb . this discrepancy could be due to our limited sample of bulge gcs that do not have as wide a range in metallicity as gcs at larger galactocentric distances . studies of the gc - lmxb connection in spiral galaxies are limited . @xcite studied xrbs in the antennae galaxies and found that massive young star clusters are more likely to host an x - ray source than less massive young clusters . when studying 32 gc - lmxbs in the spiral galaxy m104 with _ chandra _ , @xcite found that metal - rich gcs were more likely to host an x - ray source . @xcite found similar trends in the milky way . @xcite does mention that the observed trends in m31 are weaker than those found for elliptical galaxies , which further stresses the need to analyze the updated star cluster data from phat with _ chandra _ , along with surveys of other spiral galaxies . our stacking results gave upper limits of @xmath2 erg s@xmath3 across all bands for different stacks . when stacking star clusters that were brightest ( f475w magnitude ) , most compact ( smallest @xmath89 ) , and a combination of the two , we found that the detection significance increased across all bands , although not to a statistically significant level . due to the proximity of m31 the upper limits are approximately two orders of magnitude smaller than for star clusters in m51 @xcite . studies of globular clusters in the milky way have found a plethora of faint x - ray sources that include quiescent xrbs ( typically @xmath126 erg s@xmath3 ) @xcite . in gc 47 tucanae , five classified quiescent lmxbs had a mean @xmath127 kev ) @xmath2 erg s@xmath3 @xcite . therefore , assuming m31 s gcs are similar to those in the milky way , we should be probing this population with our stacking analysis . given that a single gc may only have a handful of faint lmxbs , even our stacked sample of 4 of the brightest and smallest gcs fails to provide a detection . at this point it seems that stacking star clusters to identify faint xrbs is proving difficult , at least in spiral galaxies / crowded fields . with the higher concentration of x - ray sources in galaxy bulges source crowding is a problem . along with diffuse emission in spiral disks , this complicates stacking analyses . specifically , the background level of each image in a stack is larger making it more difficult to detect faint sources in the aperture . ultimately a detailed , deep survey of a large sample of gcs in an early - type galaxy would be most promising for obtaining a stacking detection . h ii regions emit thermal x - rays at @xmath128 and @xmath129 kev due to shocks from ob star winds and supernovae / supernova remnants @xcite . the lifetimes of h ii regions ( a few myr ) are long enough that hmxbs can form , providing another possible source of x - ray emission . therefore we would expect x - ray emission in h ii regions to come from various sources , with bright hmxbs and supernova remnants ( if present ) dominating . @xcite found an hmxb in the giant h ii region ic131 in m33 , while @xcite found 2 hmxb candidates in h ii regions in m83 . @xcite studied ultraluminous x - ray sources in nearby galaxies and concluded that 18 of 27 were located inside ob associations or star forming regions . however , most hmxbs are not found in h ii regions or ob associations . in the milky way , @xcite found clustering between 79 hmxbs and 458 ob associations ( 7@xmath113 for distances @xmath130 kpc ) . the average offset of 0.4 @xmath20 0.2 kpc between hmxbs and ob associations was consistent with compact object natal kicks of 100 @xmath20 50 km s@xmath3 . the average kinematical age ( time from supernova to hmxb phase ) was @xmath44 myr . a follow up to this work by @xcite found the upper limit on kinematical age to be @xmath43 myr . therefore unless natal kicks are small hmxbs could be located @xmath11 6.5 ( 400 pc ) from h ii regions in m31 . based on these results one would expect most x - ray emission from h ii regions to be thermal rather than from xrbs . from table [ tab : htwoxrmatches ] most of the previous classifications for h ii regions hosting x - ray point sources in m31 have been supernova remnants as opposed to hmxbs . however , these are only supernova remnant candidates that have been found using optical line ratios ( h@xmath1/s ii ) . in addition , our x - ray color - color plot ( figure [ fig : xraycc ] ) shows that none of the x - ray point sources appear in the supernova remnant regime . when comparing the average radii of matched and unmatched h ii regions those that were more compact were the most likely hosts of x - ray sources . nevertheless , a logistic regression analysis showed that both the luminosity and radius of an h ii region were not significant predictors of it hosting an x - ray source . the four h ii region matches that are previously unidentified can be classified as hmxb candidates and require further analysis to determine their nature . as with star clusters our stacking results of h ii regions gave upper limits of @xmath2 erg s@xmath3 across all bands for most stacks . we saw the most improvement in detection significance ( soft band ) when filtering by the smallest radii ( @xmath131 pc ) and @xmath132 erg s@xmath3 , although not to a statistically significant level . while most of the _ chandra _ observations have been restricted to the central region of m31 , an extension of the data to the disk is necessary to probe both young star clusters and the numerous h ii regions . the resolution of x - ray data that does cover most of m31 ( i.e. _ xmm - newton _ and _ rosat _ ) is not sufficient to distinguish individual x - ray point sources in crowded regions or reliably associate them with clusters . more specifically , with the exquisite resolution of _ hst _ observations such as the phat survey only _ chandra _ will allow for robust identification of x - ray counterparts . figure [ fig : acis - fov ] is truly striking . chandra _ acis - i data does cover a large portion of the first 8 bricks of the phat survey , the remaining bricks and almost the entire northeast quadrant of m31 are unobserved . in m31 , _ chandra _ has been used mostly for a long - term monitoring program of the supermassive black hole in the nucleus . other observations throughout the galaxy were used to study supersoft x - ray sources . due to the degradation of the psf at large off - axis angles , data outside of the acis - s3 chip has poor resolution and therefore is not useful even for stacking . further motivation lies in the absence of a confirmed hmxb in m31 , which can be addressed by using both the h ii region and star cluster catalogues available to identify candidates . investigating the spiral arm regions that the phat survey has observed with ( future ) complementary _ chandra _ data would be invaluable to furthering our understanding of the xrb population in m31 .

this population is composed predominantly of globular cluster low - mass xrbs , with one previously unidentified star cluster x - ray source . star clusters that were brighter and more compact preferentially hosted an x - ray source . specifically , logistic regression showed that the f475w magnitude was the most important predictor followed by the effective radius , while color ( f475wf814w ) was not statistically significant .

x - ray binaries ( xrbs ) are probes of both star formation and stellar mass , but more importantly remain one of the only direct tracers of the compact object population . to investigate the xrb population in m31 , we utilized all 121 publicly available observations of m31 totalling over 1 ms from _ chandra s _ acis instrument . we studied 83 star clusters in the bulge using the year 1 star cluster catalogue from the panchromatic hubble andromeda treasury survey . we found 15 unique star clusters that matched to 17 x - ray point sources within 1 ( 3.8 pc ) . this population is composed predominantly of globular cluster low - mass xrbs , with one previously unidentified star cluster x - ray source . star clusters that were brighter and more compact preferentially hosted an x - ray source . specifically , logistic regression showed that the f475w magnitude was the most important predictor followed by the effective radius , while color ( f475wf814w ) was not statistically significant . we also completed a matching analysis of 1566 h ii regions and found 10 unique matches to 9 x - ray point sources within 3 ( 11 pc ) . the h ii regions hosting x - ray point sources were on average more compact than unmatched h ii regions , but logistic regression concluded that neither the radius nor h luminosity was a significant predictor . four matches have no previous classification and thus are high - mass xrb candidates . a stacking analysis of both star clusters and h ii regions resulted in non - detections , giving typical upper limits of erg s , which probes the quiescent xrb regime .

1406.4121

i

we used all 121 publicly available _ chandra _ acis observations of m31 to complete a study of star clusters and h ii regions . specifically , we analyzed 83 star clusters in the bulge of m31 from the phat survey and found 15 unique matches ( 18% ) to 17 x - ray point sources within 1 ( 3.8 pc ) . when correcting our percentage of matches to completeness limits of past surveys we found similar results . the most compact , brightest , and reddest clusters preferentially hosted x - ray sources , on average . logistic regression showed that the star cluster f475w magnitude was the most important predictor of finding a star cluster x - ray source . this follows from the fact that the most luminous and therefore most massive star clusters are more likely to host xrbs . a less significant predictor was @xmath89 , which associated smaller star clusters ( probes compactness to some extent ) with x - ray sources . the link between these two properties and xrbs stems from the high densities and larger number of stars that create dynamical conditions most favorable for the formation of xrbs . the f475w@xmath0f814w color , an indicator of metallicity in old stellar populations , was not a significant predictor for star clusters hosting x - ray point sources . the majority of clusters in our sample are metal - rich and thus we do not have an evenly distributed sample of blue and red clusters . a more complete survey with a larger spread in metallicity is required to confirm this result . a stacking analysis resulted in non - detections across all energy bands and average upper limits of @xmath2 erg s@xmath3 . this is consistent with quiescent xrb luminosities in the milky way . from 1566 h ii regions in the field of view of the _ chandra _ data only 10 matched to 9 unique x - ray point sources within 3 ( 11 pc ) . on average , the matches corresponded to the most compact h ii regions . however , a logistic regression analysis showed that neither the radius nor h@xmath1 luminosity was a significant predictor of an h ii region hosting an x - ray source . from previous optical emission - line classifications most of these sources were supernova remnant candidates . four sources that have no previous optical identifications are hmxb candidates . a stacking analysis resulted in upper limits of @xmath2 erg s@xmath3 for all energy bands . to advance our understanding of the xrb population in m31 , specifically the disk , and probe the faintest extragalactic xrbs , a complete _ chandra _ survey of the phat region is necessary . we thank the referee for detailed comments that improved the manuscript . we also thank ben williams for helpful comments and cliff johnson for the phat footprint . support for this work was provided by discovery grants from the natural sciences and engineering research council of canada and by ontario early researcher awards . we have also used the canadian advanced network for astronomical research ( canfar ; @xcite ) . this research has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . we acknowledge the following archives : the hubble legacy archive ( hla.stsci.edu ) , chandra data archive ( cda.harvard.edu/chaser ) , and 2mass ( ipac.caltech.edu/2mass ) . + _ facilities : _ hst ( acs , wfc3 ) , cxo ( acis ) , s. , armstrong , p. , ball , n. , et al . 2011 , in astronomical society of the pacific conference series , vol . 442 , astronomical data analysis software and systems xx , ed . i. n. evans , a. accomazzi , d. j. mink , & a. h. rots , 61 , d. e. , evans , i. n. , glotfelty , k. , et al . 2006 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 6270 , the chandra x - ray observatory calibration database ( caldb ) : building , planning , and improving none & 1386 & 1720 & 1.889 & 2.18 & 0.018 & 2.389 & 1.122 & 0.012 & 1.421 & 0.892 & 0.011 + r @xmath1917 pc & 711 & 865 & 1.116 & 2.257 & 0.023 & 0.117 & 1.123 & 0.015 & 13.02 & 0.854 & 0.013 + l@xmath133 erg s@xmath3 & 476 & 617 & 3.186 & 2.032 & 0.041 & 6.678 & 0.983 & 0.025 & 3.435 & 0.674 & 0.021 + r @xmath634 pc & 83 & 106 & 113.128 & 1.794 & 0.08 & 35.079 & 0.175 & 0.011 & 379.804 & 0.064 & 0.005 + l@xmath134 erg s@xmath3 & 1231 & 1515 & 1.3 & 2.16 & 0.02 & 2.087 & 1.104 & 0.013 & 1.121 & 0.872 & 0.012 + l@xmath133 erg s@xmath3 & r @xmath1917 pc & 132 & 172 & 105.83 & 1.442 & 0.061 & 63.978 & 0.131 & 0.007 & 28.521 & 0.04 & 0.003 + none & 54 & 86 & 24.058 & 4.641 & 0.054 & 0.632 & 1.573 & 0.03 & 0.187 & 3.054 & 0.045 + r@xmath1350.4 pc & 33 & 51 & 2.302 & 4.42 & 0.069 & 0.74 & 1.473 & 0.038 & 0.553 & 2.871 & 0.057 + f475w @xmath620.5 & 21 & 28 & 1.678 & 3.073 & 0.09 & 1.157 & 1.283 & 0.05 & 1.158 & 1.651 & 0.073 + r@xmath1360.4 pc & 21 & 35 & 0.711 & 4.952 & 0.089 & 2.156 & 1.693 & 0.05 & 0.07 & 3.276 & 0.074 + f475w @xmath1919 & 15 & 25 & 1.044 & 6.528 & 0.113 & 3.587 & 1.685 & 0.055 & 0.818 & 4.723 & 0.097 + r@xmath1360.4 pc & f475w @xmath1919 & 4 & 7 & 3.315 & 7.475 & 0.222 & 2.827 & 1.565 & 0.091 & 2.413 & 5.602 & 0.197 +

we studied 83 star clusters in the bulge using the year 1 star cluster catalogue from the panchromatic hubble andromeda treasury survey . we found 15 unique star clusters that matched to 17 x - ray point sources within 1 ( 3.8 pc ) . four matches have no previous classification and thus are high - mass xrb candidates .

x - ray binaries ( xrbs ) are probes of both star formation and stellar mass , but more importantly remain one of the only direct tracers of the compact object population . to investigate the xrb population in m31 , we utilized all 121 publicly available observations of m31 totalling over 1 ms from _ chandra s _ acis instrument . we studied 83 star clusters in the bulge using the year 1 star cluster catalogue from the panchromatic hubble andromeda treasury survey . we found 15 unique star clusters that matched to 17 x - ray point sources within 1 ( 3.8 pc ) . this population is composed predominantly of globular cluster low - mass xrbs , with one previously unidentified star cluster x - ray source . star clusters that were brighter and more compact preferentially hosted an x - ray source . specifically , logistic regression showed that the f475w magnitude was the most important predictor followed by the effective radius , while color ( f475wf814w ) was not statistically significant . we also completed a matching analysis of 1566 h ii regions and found 10 unique matches to 9 x - ray point sources within 3 ( 11 pc ) . the h ii regions hosting x - ray point sources were on average more compact than unmatched h ii regions , but logistic regression concluded that neither the radius nor h luminosity was a significant predictor . four matches have no previous classification and thus are high - mass xrb candidates . a stacking analysis of both star clusters and h ii regions resulted in non - detections , giving typical upper limits of erg s , which probes the quiescent xrb regime .

1509.06814

i

gj1214b is a warm sub - neptune orbiting a nearby m dwarf and discovered by the mearth survey @xcite . it is one of the rare low - mass planets whose atmosphere is characterizable in transit spectroscopy by current telescopes . gj1214b is therefore considered as a privileged archetype of this new category of planets also called mini - neptunes . it has a mass of 6.55@xmath40.98 @xmath5 and a radius of 2.68@xmath40.13 @xmath6 , giving it a density of around 1.88 g @xmath7 @xcite . this low density necessarily implies the presence of a thick atmosphere . interior models suggest that the planet possesses either a dense iron / rock core surrounded by a thick hydrogen / helium - rich atmosphere or a water - rich core surrounded by a thick steam atmosphere @xcite . @xcite found that a water - rich planet depleted in hydrogen would require a water - to - rock ratio larger than 6:1 . they considered such a large ratio as unlikely and favored instead an intermediate case with a hydrogen / helium / water - rich atmosphere . gj1214b has a tight orbit ( i.e. semi - major axis of 0.014 au ) and is very likely tidally locked , with a permanent dayside and nightside . several observations in transit spectroscopy were performed to probe gj1214b s atmosphere and to break the degeneracy of possible compositions . first observations by @xcite revealed a lack of spectral features between 0.78 and 1 @xmath8 m , ruling out the hypothesis of a cloud - free solar composition . other observations @xcite confirmed this flat spectrum between 0.6 and 4.5 @xmath8 m while one group found a significant difference in the transit depth measured in j - band ( @xmath91.25 @xmath8 m ) and in ks - band ( @xmath92.15 @xmath8 m ) @xcite . finally , precise measurements with the wide field camera 3 ( wfc3 ) instrument on the hubble space telescope ( hst ) revealed a very flat spectrum between 1.15 and 1.65 @xmath8 m @xcite . that implied the presence of high cloud / haze diffusing or absorbing the stellar radiation at low pressure . the presence of clouds is required even for a high mean - molecular - mass atmosphere with a composition dominated by water , methane , carbon monoxide , nitrogen or carbon dioxide . the cloud - top pressure in transit spectroscopy should be less than 10@xmath10 mbar for a solar - like composition and 10@xmath11 mbar for a water - dominated atmosphere @xcite . for the conditions on gj1214b , these clouds / haze could be either condensate clouds of potassium chloride ( kcl ) and zinc sulfide ( zns ) or photochemical haze produced by the photolysis of methane in the upper atmosphere @xcite . kcl and zns clouds are supposed to form between 0.1 and 1 bar @xcite . their presence at low pressure would thus require a strong atmospheric circulation lofting cloud particles over several scale heights . the persistence of photochemical haze at low pressure would also require a sufficiently strong vertical mixing , counteracting particle sedimentation and bringing methane to altitudes where photolysis occurs . therefore , the formation of high and thick cloud / haze on gj1214b is strongly linked to the atmospheric circulation . the latter has been investigated in previous studies using general circulation models ( gcms ) for cloud - free atmospheres @xcite . @xcite used gray opacities and showed that the superrotating zonal winds and the thermal phase curves would vary greatly with the atmospheric metallicity . @xcite analyzed the atmospheric dynamics and thermal phase curves with a more accurate gcm using non - gray opacities for different atmospheric compositions , but they did not analyze the vertical winds and the vertical mixing . in this paper , we analyze the circulation and the vertical mixing of gj1214b for a cloud - free atmosphere with different compositions using the generic lmdz gcm , a very versatile 3d model developed to simulate any kind of planetary atmosphere . in the next section , we describe the model and the parameters used for gj1214b . in section 3 , we analyze the thermal structure and atmospheric circulation ( zonal , meridional and vertical winds ) . in section 4 , we analyze the vertical mixing of tracers and discuss its implications for cloud / haze formation in section 5 . the 3d modeling of realistic clouds with our gcm will be described in a dedicated paper , analyzing their formation , dynamics and impacts on spectra .

gj1214b is a warm sub - neptune transiting in front of a nearby m dwarf star . recent observations indicate the presence of high and thick clouds or haze whose presence requires strong atmospheric mixing . in order to understand the transport and distribution of such clouds / haze , we study the atmospheric circulation and the vertical mixing of gj1214b with a 3d general circulation model for cloud - free hydrogen - dominated atmospheres ( metallicity of 1 , 10 and 100 times the solar value ) and for a water - dominated atmosphere . we analyze the effect of the atmospheric metallicity on the thermal structure and zonal winds . these values should favor an efficient formation of photochemical haze in the upper atmosphere of gj1214b .

gj1214b is a warm sub - neptune transiting in front of a nearby m dwarf star . recent observations indicate the presence of high and thick clouds or haze whose presence requires strong atmospheric mixing . in order to understand the transport and distribution of such clouds / haze , we study the atmospheric circulation and the vertical mixing of gj1214b with a 3d general circulation model for cloud - free hydrogen - dominated atmospheres ( metallicity of 1 , 10 and 100 times the solar value ) and for a water - dominated atmosphere . we analyze the effect of the atmospheric metallicity on the thermal structure and zonal winds . we also analyze the zonal mean meridional circulation and show that it corresponds to an anti - hadley circulation in most of the atmosphere with upwelling at mid - latitude and downwelling at the equator in average . this circulation must be present on a large range of synchronously rotating exoplanets with strong impact on cloud formation and distribution . using simple tracers , we show that vertical winds on gj1214b can be strong enough to loft micrometric particles and that the anti - hadley circulation leads to a minimum of tracers at the equator . we find that the strength of the vertical mixing increases with metallicity . we derive 1d equivalent eddy diffusion coefficients and find simple parametrizations from m/s for solar metallicity to m/s for the 100solar metallicity . these values should favor an efficient formation of photochemical haze in the upper atmosphere of gj1214b .

1509.06814

c

in this study , we analyzed the atmospheric dynamics of gj1214b for a cloud - free atmosphere with different metallicities as a first application of the generic lmdz gcm to a non - rocky exoplanet . we obtained results for radiative transfer , temperatures and winds very similar to those from the other state - of - the - art gcm @xcite , validating our model for this kind of planet . in addition to this intercomparison , we showed that the zonal mean circulation of gj1214 is characterized by the presence of an anti - hadley circulation on the nightside , which leads to zonally - averaged subsidence at the equator . this particular regime likely occurs on a wide range of synchronously rotating exoplanets , from warm mini - neptunes to hot jupiters . using simple tracers , we analyzed the vertical mixing in the atmosphere of gj1214b . the tracers showed that atmospheric transport is primarily driven by the zonal mean circulation , leading to an upwelling at mid - latitudes and a downwelling at the equator . in particular , a minimum of tracer abundance appears at the equator , strengthened in the upper atmosphere by a poleward meridional transport . this should be a fundamental feature of the cloud / haze distribution on many synchronously rotating warm exoplanets . we also found that the vertical mixing increases with metallicity for h - rich atmospheres . for a solar metallicity , the circulation can not loft micrometer particles into the upper atmosphere . therefore , if the upper atmosphere of gj1214b is opaque because of condensate clouds , the atmospheric metallicity must be higher than solar and likely more than 10@xmath3solar . from these simulations , we derived equivalent 1d eddy coefficients . we found that : @xmath0 m@xmath1/s is a good fit for 1@xmath3solar metallicity and @xmath2 m@xmath1/s for 100@xmath3solar metallicity . we compared these values to classical formulae for @xmath72 used for instance in @xcite , showing how these simple formulae can overestimate the mixing by one order of magnitude . our parametrizations of @xmath72 can be used in 1d cloud or photochemical models @xcite for which they are expected to lead to an efficient formation of photochemical haze . finally , we showed that the atmospheric circulation of gj1214b could be strong enough to loft micrometric particles of kcl or zns from 1 bar to 0.1 - 0.01 mbar . however , the radiative effects of clouds , by absorbing or diffusing stellar radiation , could modify the strength of the circulation . the next step will be to simulate the atmosphere of gj1214b with realistic kcl and zns clouds , taking into account the latent heat release and the radiative effects . for this next study , the generic lmdz gcm benefits from all the developments done for previous studies of cloudy rocky planets . such 3d simulations would give strong indications of the possibility of high condensate clouds producing the observed flat transit spectrum . such simulations could also help identify the best observations for probing cloudy atmospheres , with , for example , emission / reflection spectra and phase curves . b.c . acknowledges support from an appointment to the nasa postdoctoral program at nai virtual planetary laboratory , administered by oak ridge affiliated universities . vsm is supported by the nasa astrobiology institute s virtual planetary laboratory lead team , under the national aeronautics and space administration solicitation nnh12zda002c and cooperative agreement number nna13aa93a . this work was facilitated though the use of advanced computational , storage , and networking infrastructure provided by the hyak supercomputer system at the university of washington . solar ( black ) metallicity . right panel : maximum dayside - nightside temperature difference as a function of pressure . the differences are computed at each latitude and pressure level . the figure shows their maximum value at a given pressure.,title="fig:",width=264 ] solar ( black ) metallicity . right panel : maximum dayside - nightside temperature difference as a function of pressure . the differences are computed at each latitude and pressure level . the figure shows their maximum value at a given pressure.,title="fig:",width=264 ] ( right ) as a function of pressure . solid lines correspond to the heating rate and the stellar net flux . dashed lines correspond to the cooling rate and the thermal net flux . , title="fig:",width=264 ] ( right ) as a function of pressure . solid lines correspond to the heating rate and the stellar net flux . dashed lines correspond to the cooling rate and the thermal net flux . , title="fig:",width=264 ] solar metallicity . the top panels show the temperature ( left ) and vertical velocity ( right ) at the equator versus longitude and pressure . the bottom panels show the map of temperature ( left ) and vertical velocity ( right ) at 1.1 mbar . black vectors correspond to the directions of horizontal winds.,title="fig:",width=264 ] solar metallicity . the top panels show the temperature ( left ) and vertical velocity ( right ) at the equator versus longitude and pressure . the bottom panels show the map of temperature ( left ) and vertical velocity ( right ) at 1.1 mbar . black vectors correspond to the directions of horizontal winds.,title="fig:",width=264 ] solar metallicity . the top panels show the temperature ( left ) and vertical velocity ( right ) at the equator versus longitude and pressure . the bottom panels show the map of temperature ( left ) and vertical velocity ( right ) at 1.1 mbar . black vectors correspond to the directions of horizontal winds.,title="fig:",width=264 ] solar metallicity . the top panels show the temperature ( left ) and vertical velocity ( right ) at the equator versus longitude and pressure . the bottom panels show the map of temperature ( left ) and vertical velocity ( right ) at 1.1 mbar . black vectors correspond to the directions of horizontal winds.,title="fig:",width=264 ] solar metallicity case for the dayside ( top ) , the nightside ( middle ) and globally ( bottom ) . positive ( negative ) values correspond to anti - clockwise ( clockwise ) circulation . dashed ( solid ) lines are contours for the value of @xmath410@xmath111 kg / m / s . the dayside streamfunction was calculated by integrating longitudes between -39@xmath12 and + 90@xmath12e . the nightside streamfunction was calculated by integrating the other longitudes ( -180 @xmath12 to -39@xmath12e and + 90@xmath12 to + 180@xmath12 e ) . the global mass streamfunction was calculated by integrating all longitudes and is equal to the sum of the dayside and nightside streamfunctions.,title="fig:",width=264 ] + solar metallicity case for the dayside ( top ) , the nightside ( middle ) and globally ( bottom ) . positive ( negative ) values correspond to anti - clockwise ( clockwise ) circulation . dashed ( solid ) lines are contours for the value of @xmath410@xmath111 kg / m / s . the dayside streamfunction was calculated by integrating longitudes between -39@xmath12 and + 90@xmath12e . the nightside streamfunction was calculated by integrating the other longitudes ( -180 @xmath12 to -39@xmath12e and + 90@xmath12 to + 180@xmath12 e ) . the global mass streamfunction was calculated by integrating all longitudes and is equal to the sum of the dayside and nightside streamfunctions.,title="fig:",width=264 ] + solar metallicity case for the dayside ( top ) , the nightside ( middle ) and globally ( bottom ) . positive ( negative ) values correspond to anti - clockwise ( clockwise ) circulation . dashed ( solid ) lines are contours for the value of @xmath410@xmath111 kg / m / s . the dayside streamfunction was calculated by integrating longitudes between -39@xmath12 and + 90@xmath12e . the nightside streamfunction was calculated by integrating the other longitudes ( -180 @xmath12 to -39@xmath12e and + 90@xmath12 to + 180@xmath12 e ) . the global mass streamfunction was calculated by integrating all longitudes and is equal to the sum of the dayside and nightside streamfunctions.,title="fig:",width=264 ] solar metallicity case into heat transport by the mean meridional circulation ( black dashed line ) , by stationary waves ( black dashed - dotted line ) and by transient perturbations ( black dotted line ) . positive ( negative ) values correspond to northward ( southward ) heat fluxes.,title="fig:",width=377 ] solar metallicity case into heat transport by the mean meridional circulation ( black dashed line ) , by stationary waves ( black dashed - dotted line ) and by transient perturbations ( black dotted line ) . positive ( negative ) values correspond to northward ( southward ) heat fluxes.,title="fig:",width=377 ] solar metallicity with particle radii from 0.1 to 10 microns . for both figures , the relative abundance is fixed to 1 below 1 bar . the dashed lines correspond to the analytical profiles using a parametrized @xmath72 ( see section 4.4 ) . , title="fig:",width=264 ] solar metallicity with particle radii from 0.1 to 10 microns . for both figures , the relative abundance is fixed to 1 below 1 bar . the dashed lines correspond to the analytical profiles using a parametrized @xmath72 ( see section 4.4 ) . , title="fig:",width=264 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] , 10@xmath3 , 100@xmath3solar and pure h@xmath17o from top to down ) and for pressure of 12 mbar ( left ) 1.1 mbar ( middle ) and 0.1 mbar ( right).,title="fig:",width=188 ] for the 100@xmath3solar metallicity case . red lines are from the gcm for particle radii of 0.1 , 0.3 , 1 , 3 microns . the blue line is the simple fit ( @xmath112 @xmath3p@xmath113@xmath114 m@xmath1/s ) . solid and dashed black lines are estimations from simple formula @xcite . the right panel shows k@xmath115 derived from the gcm for the different atmospheric compositions with particle radius of 1 micron . the dashed lines are the simple fits ( @xmath72=@xmath116 with @xmath102=@xmath103 , @xmath104 , @xmath105 , @xmath106 m@xmath1/s for the 1 , 10 , 100@xmath3solar metallicity and pure water case respectively ) . , title="fig:",width=302 ] for the 100@xmath3solar metallicity case . red lines are from the gcm for particle radii of 0.1 , 0.3 , 1 , 3 microns . the blue line is the simple fit ( @xmath112 @xmath3p@xmath113@xmath114 m@xmath1/s ) . solid and dashed black lines are estimations from simple formula @xcite . the right panel shows k@xmath115 derived from the gcm for the different atmospheric compositions with particle radius of 1 micron . the dashed lines are the simple fits ( @xmath72=@xmath116 with @xmath102=@xmath103 , @xmath104 , @xmath105 , @xmath106 m@xmath1/s for the 1 , 10 , 100@xmath3solar metallicity and pure water case respectively ) . ,

we also analyze the zonal mean meridional circulation and show that it corresponds to an anti - hadley circulation in most of the atmosphere with upwelling at mid - latitude and downwelling at the equator in average . , we show that vertical winds on gj1214b can be strong enough to loft micrometric particles and that the anti - hadley circulation leads to a minimum of tracers at the equator .

gj1214b is a warm sub - neptune transiting in front of a nearby m dwarf star . recent observations indicate the presence of high and thick clouds or haze whose presence requires strong atmospheric mixing . in order to understand the transport and distribution of such clouds / haze , we study the atmospheric circulation and the vertical mixing of gj1214b with a 3d general circulation model for cloud - free hydrogen - dominated atmospheres ( metallicity of 1 , 10 and 100 times the solar value ) and for a water - dominated atmosphere . we analyze the effect of the atmospheric metallicity on the thermal structure and zonal winds . we also analyze the zonal mean meridional circulation and show that it corresponds to an anti - hadley circulation in most of the atmosphere with upwelling at mid - latitude and downwelling at the equator in average . this circulation must be present on a large range of synchronously rotating exoplanets with strong impact on cloud formation and distribution . using simple tracers , we show that vertical winds on gj1214b can be strong enough to loft micrometric particles and that the anti - hadley circulation leads to a minimum of tracers at the equator . we find that the strength of the vertical mixing increases with metallicity . we derive 1d equivalent eddy diffusion coefficients and find simple parametrizations from m/s for solar metallicity to m/s for the 100solar metallicity . these values should favor an efficient formation of photochemical haze in the upper atmosphere of gj1214b .

astro-ph0510106

i

it is generally accepted that the dipole signature in the cosmic microwave background ( cmb ) is due to a doppler effect arising from the motion of the local group ( lg ) through the cosmological reference frame . although the direction and amplitude of this motion is known to high accuracy , its source has yet to be conclusively determined . while linear perturbation theory predicts that the lg s peculiar velocity is induced by anisotropies in the surrounding matter distribution , there has been disagreement regarding the distance out to which inhomogeneities in the density field continue to affect the lg s dynamics . the debate has centered on whether the lg is principally accelerated by a massive , nearby attractor which has remained hidden behind the galactic plane , or whether a significant portion of its motion is in the form of a large - scale bulk flow induced by more distant structures , as has been suggested by an increasing number of studies . resolving the source of the lg s motion and the bulk flow in which it participates carries many interesting cosmographical and cosmological implications . for example , in order for a distant supercluster like the shapley concentration ( shapley 1930 ) to induce an infall at the lg as large as the one produced by the more nearby hydra - centaurus complex , its mass would need to be sixteen times greater than that of the largest overdensity observed in the local volume . furthermore , if distant structures contribute to the lg s peculiar velocity , then anisotropies in the large - scale matter distribution must exist to at least those structures , implying that the universe becomes isotropic only at larger distances . early attempts to determine the source of the lg s peculiar velocity largely suggested a local origin . the nearest large - scale overdensity , the virgo cluster , which generates a 240 km s@xmath8 infall velocity at the lg ( jerjen & tammann 1993 ) , accounts for 27% of the lg s 627 km s@xmath8 velocity toward the cmb dipole ( kogut 1993 ) . virgo s inability to explain all of the lg s motion led shaya ( 1984 ) to suggest an additional flow toward the hydra - centaurus supercluster . this flow was subsequently detected by lynden - bell et al . ( 1988 , hereafter lb88 ) as a systematic distortion in the peculiar velocities of 400 early - type galaxies within @xmath9 mpc and its amplitude at the lg was estimated to be 570 km s@xmath8 . assuming this motion was due to infall into a single `` great attractor '' ( ga ) , lb88 estimated that the source of the flow was located roughly @xmath10 mpc away , or about @xmath11 mpc behind centaurus . this distance , coupled with the large infall velocity , implied the rather high mass of @xmath12 m@xmath13 for the ga complex . the lb88 findings suggested that the ga was responsible for the remaining @xmath14 of the lg s peculiar velocity not induced by the virgo cluster . despite the lb88 findings , subsequent redshift surveys that have encompassed the ga region have failed to detect a mass overdensity as large as the one implied by the lb88 peculiar velocity data ( dressler 1988 ; strauss et al . 1992 ; hudson 1993 , 1994 ) , nor have they conclusively measured the backside infall into the ga one would expect if the region were best described as a single , stationary attractor ( mathewson et al . 1992 , courteau et al . 1993 ) . even with the more recent discoveries of rich clusters such as norma ( abell 3627 , kraan - korteweg et al . 1996 ) and ciza j1324.7 - 5736 ( ebeling , mullis & tully 2002 ) near the hydra - centaurus region , there remains a significant discrepancy between the mass concentration observed in the ga and the mass originally proposed by lb88 ( staveley - smith et al . 2000 , kocevski et al . 2006 ) . there is now a growing volume of work suggesting the dynamical significance of the ga was originally overestimated and that some component of the lg s peculiar velocity is in the form of a large - scale bulk flow which continues past the ga region and is induced by more distant structures . one of the first suggestions of a non - local component was put forth by plionis ( 1988 ) , who proposed that the anisotropy observed in the galaxy number - counts of the lick catalog ( shane & wirtanen 1967 ) implied a portion of the lg s motion originating from beyond @xmath15 mpc . more recently , hudson et al . ( 2003 ) show that results from the peculiar velocity studies of hudson et al . ( 1999 ) , dale et al . ( 1999 ) , willick ( 1999 ) , and colless et al . ( 2001 ) are all consistent with a 350 km s@xmath8 bulk flow continuing beyond @xmath16 mpc , ruling out nearby overdensities such as the ga as the source of the motion . likewise , zaroubi et al . ( 1999 ) show that if the local velocity field is decomposed into its divergent ( locally produced ) and tidal ( externally produced ) components , only @xmath17 of the flow toward the ga is due to infall into the hydra - centaurus region , while the remaining velocity is due to a continuing bulk flow generated by attractors beyond @xmath18 mpc . in addition , tonry et al . ( 2000 ) , using surface brightness fluctuation ( sbf ) distances , find a mass for the ga that is @xmath19 times less than the original lb88 estimate . their best - fit models suggest the ga is well centered on the centaurus cluster ( as opposed to @xmath11 mpc behind it ) and that part of the flow toward the ga is due to a @xmath20 km s@xmath8 residual bulk motion . tonry et al . essentially propose that the lg s motion , which was mistakenly identified as infall into a single , massive attractor slightly behind centaurus , is in fact the result of two flows , one into the hydra - centaurus region and a second flow toward a more distant source . many of the studies finding evidence for a continuing flow beyond the ga have suggested that some fraction of the motion may be due to infall into the shapley supercluster ( ssc ) , located @xmath21 mpc behind the hydra - centaurus complex . the ssc region is unique in the local universe , containing the richest concentration of clusters out of all the 220 identified superclusters out to @xmath22 ( einasto et al . in fact , the ssc contains more than 4 times the number of rich clusters present in the ga region . the ssc s possible dynamical significance was pointed out by scaramella et al . ( 1989 , 1991 ) and plionis & valdarnini ( 1991 ) because of the high concentration of abell clusters in the region and its directional alignment with the ga . since the two regions are only separated by @xmath23 on the sky , kocevski et al . ( 2004 ) suggest this alignment causes a bootstrap effect that sets in place the large - scale density anisotropy that is responsible for the lg s peculiar velocity . despite the significant overdensity present in the ssc , its dynamical impact on the lg has been a matter of debate . rowan - robinson et al . ( 2000 ) use the dipole anisotropy present in the iras point source catalog redshift sample ( pscz , saunders et al . 1995 ) to conclude that the ssc has a marginal influence on the lg , inducing only @xmath24 km s@xmath8 of its motion . likewise , erdogdu et al . ( 2005 ) , using the dipole anisotropy of the 2 micron all - sky redshift survey ( 2mrs , huchra et al . 2005 ) , find that structures beyond @xmath25 mpc induce only a negligible acceleration on the lg . on the other hand , lucey et al . ( 2005 ) combine the cluster peculiar velocity data from the smac ( hudson et al . 1999 ) , sci / scii ( giovanelli et al . 1999 ) , enearc ( bernardi et al . 2002 ) and sbf ( tonry et al . 2000 ) surveys and find that both the ga and the ssc generate an equal amount of the lg s peculiar velocity . this higher estimate concurs with the results from dipole analyses of various cluster samples ; branchini & plionis ( 1996 ) and plionis & kolokotronis ( 1998 ) use the dipole anisotropy in the distribution of optically selected abell / aco ( abell 1958 , abell et al . 1989 ) and x - ray brightest abell - type cluster ( xbac , ebeling et al . 1996 ) samples , respectively , to determine that @xmath26 of the lg s motion is due to the ssc . kocevski et al . ( 2004 ) recently added x - ray selected clusters from the ciza survey ( named for clusters in the zone of avoidance , ebeling , mullis , & tully 2002 ) to the xbac distribution to fill in the zone of avoidance ( zoa ) and found an even larger ssc contribution ( @xmath27 ) . in this study we aim to settle the debate regarding the fraction of the lg s peculiar velocity that is induced by structures beyond the ga by calculating the dipole anisotropy of the largest , all - sky , truly x - ray selected cluster sample compiled to date . the sample is the combination of the rosat - eso flux limited x - ray catalog ( reflex , bhringer et al . 2004 ) in the southern hemisphere , the extended brightest cluster sample ( ebcs , ebeling et al . 1998 , 2000 ) in the north , and the ciza survey in the galactic plane . the composite reflex+ebcs+ciza sample ( hereafter rbc ) overcomes many of the problems inherent to previous galaxy and cluster catalogs which limited their effectiveness in determining the origin of the lg s motion . first of all , due to its x - ray selected nature , the rbc sample maps the distribution of massive x - ray luminous clusters which tend to be the accelerators of large - scale flows . in this sense , the rbc sample traces the peaks of the density fluctuation field better than galaxy samples such as the pscz , which has been shown to undersample dense regions such as the ssc ( kaiser et al . x - ray bright clusters are also luminous enough for statistically complete samples to be constructed out to larger distances than galaxy samples , which face an increasing incompleteness beyond 60 @xmath4 mpc . we suspect that the estimate for a marginal ssc acceleration from the pscz data may be a result of these two factors . second , the x - ray selected rbc sample overcomes several limitations of early cluster catalogs such as abell / aco , which are optically selected . since optical selection methods rely on identifying individual clusters through overdensities in the projected galaxy distribution and assigning cluster masses based on the size , or richness , of those overdensities , fluctuations in the surface density of field galaxies as well as superpositions of poor clusters or filamentary structure along the line of sight can lead to false detections or overestimates of a system s richness ( e.g. van haarlem 1997 , see sutherland 1988 ) . these projection effects work to systematically amplify the measured dipole amplitude . in addition , optical cluster searches suffer from severe extinction and stellar obscuration in the direction of the milky way , leading to catalogs with poor coverage in a @xmath28 wide strip centered on the plane of the galaxy . this is particularly troubling since large - scale structures associated with the ga and the ssc are known to exist in , or extend into , the zoa ( tully et al . 1992 ) . a variety of techniques have been used to reconstruct the zoa , ranging from uniform filling ( strauss & davis 1988 ; lahav 1987 ) to a spherical - harmonics approach which extends structures above and below the plane into the zoa ( plionis & valdarnini 1991 , cf . brunozzi et al . 1995 ) , but the value of these reconstruction techniques is limited if the milky way does indeed obscure dynamically significant regions , as has been suggested . the x - ray selected nature of the rbc sample makes it preferable over its optically selected counterparts since ( 1 ) cluster x - ray emission originates from the @xmath29 k intracluster medium , which is more peaked at the gravitational center of the cluster than the projected galaxy distribution . this minimizes projection effects since clusters would need to be in almost perfect alignment to be mistaken for a single , more luminous object , ( 2 ) x - ray luminosity is closely correlated with cluster mass ( reiprich & bhringer 1999 ) , thus providing a better estimate to a system s dynamical impact than a clusters projected galaxy richness , and ( 3 ) x - ray emission does not suffer as severe an extinction in the plane of the galaxy ( ebeling , mullis & tully 2002 ) . finally , the rbc s relatively low flux limit makes it a better tracer of large - scale structures than previous x - ray confirmed cluster samples , such as the xbac catalog which has recently been used by plionis & kolokotronis ( 1998 ) and kocevski et al . ( 2004 ) to investigate the origin of the lg s motion . due to the xbac s fairly high x - ray flux limit , the sample is limited to only the most massive clusters , which , although tracing the deepest potential wells , only sparsely sample the underlying density field and can lead to an increased level of shot - noise . in addition , although x - ray confirmation effectively eliminates projection effects in xbac , the catalog remains optically selected , therefore clusters missed by the abell / aco sample will not be included in the xbac sample . this essentially means very nearby , very extended clusters are systematically missed as they often do not contrast strongly with the background galaxy population . the undersampling of clusters at low redshifts would lead to an overestimate of the contribution to the dipole from distances greater than 60 @xmath4 mpc , where the xbac incompleteness is minimal . the rbc s x - ray flux limit is nearly half of the one used in the xbac survey , which means the sample is no longer limited to extremely massive clusters . this increased depth more than triples the number of clusters present in the rbc sample , which in turn affords us a greater resolution in tracing the overdensities which give rise to the lg s motion . the rbc sample is currently the largest , most complete x - ray selected cluster sample for which to trace the large - scale structure of the local universe and determine the origin of the lg s peculiar velocity . in what follows we use the rbc sample to ( 1 ) determine the role of the cluster distribution in producing the lg s peculiar velocity , ( 2 ) determine the fraction of the lg s motion that is induced from distances greater than 60 @xmath4 mpc , and ( 3 ) estimate the relative contribution of various superclusters such as the ga and ssc regions , to the final dipole amplitude . we proceed in the following manner : in 2 we give an overview of the reflex , ebcs , and ciza samples , 3 describes the details of the dipole analysis , and our results are put forward in 4 . finally we summarize our primary conclusions in section 5 . throughout this paper we assume an einstein - de sitter universe with @xmath30 and @xmath31 @xmath32 km s@xmath8mpc@xmath8 unless otherwise stated , so that our results are directly comparable to those of previous studies .

we aim to settle the debate regarding the fraction of the local group s peculiar velocity that is induced by structures beyond the great attractor by calculating the dipole anisotropy of the largest , all - sky , truly x - ray selected cluster sample compiled to date . , we find that additional superclusters play an important role in shaping the local group s peculiar velocity . locally , the perseus - pisces region counteracts much of the great attractor s effect on the acceleration field beyond mpc . at larger distances finally we discuss reasons for the discordant results obtained using cluster and galaxy samples in determining the origin of the local group s motion .

we aim to settle the debate regarding the fraction of the local group s peculiar velocity that is induced by structures beyond the great attractor by calculating the dipole anisotropy of the largest , all - sky , truly x - ray selected cluster sample compiled to date . the sample is the combination of the reflex catalog in the southern hemisphere , the ebcs sample in the north , and the ciza survey in the galactic plane . the composite reflex+ebcs+ciza sample overcomes many of the problems inherent to previous galaxy and cluster catalogs which limited their effectiveness in determining the origin of the local group s motion . from the dipole anisotropy present in the cluster distribution we determine that of the local group s peculiar velocity is due to infall into the great attractor region , while is in the form of a large - scale flow induced by more distant overdensities between and mpc away . in agreement with previous analyses , we find that the shapley supercluster is the single overdensity most responsible for the increase in the dipole amplitude beyond mpc , generating of the large - scale contribution . despite the dynamical significance of both the great attractor and shapley regions , we find that additional superclusters play an important role in shaping the local group s peculiar velocity . locally , the perseus - pisces region counteracts much of the great attractor s effect on the acceleration field beyond mpc . at larger distances we find that numerous groupings and loose associations of clusters at roughly the same distance as the shapley region induce a significant acceleration on the local group . these include the well known horologium - reticulum concentration , as well as newly noted associations centered on abell 3667 and abell 3391 and a string of ciza clusters near c1410 which may trace an extension of the shapley complex into the zone of avoidance . we also note the presence of a significant underdensity of clusters in the northern hemisphere roughly mpc away and suggest that the large - scale anisotropy observed in the cluster distribution near this distance may have as much to do with the presence of large overdensities in the south as it does with the lack of superclusters in the north . finally we discuss reasons for the discordant results obtained using cluster and galaxy samples in determining the origin of the local group s motion .

astro-ph0510106

c

we have combined the reflex catalog in the southern hemisphere , the ebcs sample in the north , and the ciza survey in the galactic plane to produce the largest , all - sky , truly x - ray selected cluster sample compiled to date and used it to investigate the origin of the lg s peculiar velocity . the x - ray selected nature of the rbc catalog largely does away with projection effects , the poor sampling of nearby clusters , and the incompleteness in the plane of the galaxy introduced as a result of the optical selection methods used to construct previous cluster catalogs . in addition , the rbc s relatively low x - ray flux limit allows us to better sample the underlying density field , which in turn affords us a greater resolution in tracing the structures which give rise to the lg s motion . from the dipole anisotropy present in the cluster distribution we determine that @xmath0 of the lg s peculiar velocity is due to infall into the ga region , while @xmath1 is induced by more distant overdensities between @xmath2 and @xmath3 @xmath4 mpc away . of the large - scale contribution , we find that the ssc has the largest dynamical impact , being responsible for @xmath5 of the increase in the dipole amplitude beyond @xmath2 @xmath4 mpc . despite the significance of the ga and ssc regions , our findings are not consistent with a simple two - attractor model for generating the lg s motion . there exists numerous groupings and loose associations of clusters at roughly the same distance as the ssc that have a significant effect on the dipole amplitude . these include the well - known hr region , as well as the newly noted a3667 and a3391 associations and the c1410 filament which may trace an extension of the ssc complex into the zoa . in addition , we find that the region of sky within @xmath123 of the dipole pointing between @xmath2 and @xmath3 @xmath4 mpc is 2.7 times as dense as the opposite part of the sky . we suggest that the anisotropy in the cluster distribution near @xmath7 @xmath4 mpc has as much to do with the presence of large overdensities such as the ssc and the hr concentrations in the south as it does with the lack of superclusters in the north . we thank brent tully and chris mullis for many valuable discussions and contributions , as well as manolis plionis for his useful suggestions . dk is supported by the nasa graduate student research program . allen , s.w . , schmidt , r.w . & fabian , a.c . 2003 , mnras , 342 , 287 basilakos , s. , & plionis , m. 1998 , mnras , 299 , 637 bhringer , h. , voges , w. , huchra , j.p . , mclean , b. , giacconi , r. , rosati , p. , burg , r. , mader , j. , schuecker , p. , simic , d. , komossa , s. , reiprich , t.h . , retzlaff , j. , & trmper , j. 2000 , apjs , 129 , 435 bhringer , h. , schuecker , p. , guzzo , l. , collins , c.a . , voges , w. , schindler , s. , nuemann , d.m . , cruddace , r.g , de grandi , s. , chincarini , g. , edge , a. , macgillivray , h.t . , & shaver , p. 2001 , a&a , 369 , 826 bhringer , h. , schuecker , p. , guzzo , l. , collins , c.a . , voges , w. , cruddace , r.g , ortiz - gil , a. , chincarini , g. , de grandi , s. , edge , a. , macgillivray , h.t . , nuemann , d.m . , schindler , s. , & shaver , p. 2004 , a&a , 425 , 367 branchini , e. , et al . 1999 , mnras , 308 , 1 branchini , e. , & plionis , m. 1996 , apj , 460 , 569 brunozzi , p. tini , borgani , s. , plionis , m. , & moscardini , l. 1995 , 277 , 1210 courteau , s. , faber , s.m . , dressler , a. , & willick , j.a . 1993 , apj , 412 , l51 colless m. , saglia r.p . , burstein , d. , davies , r.l . , mcmahan , r.k . , & wegner , g. 2001 , mnras , 321 , 277 dale , d.a . , giovanelli , r. , haynes , m.p . , campusano , l.e . , hardy , e. & borgani , s. 1999 , apj , 510 , l11 dickey , j.m . , & lockman , f.j . 1990 , ara&a , 28 , 215 dressler , a. 1988 , apj , 329 , 519 ebeling , h. 1993 , ph.d . thesis , ludwig - maximilians - univ . mnchen ebeling , h. , & wiedenmann , g. 1993 , phys . e , 47 , 704 ebeling , h. , edge , a.c . , bhringer , h. , allen , s.w . , crawford , c.s . , fabian , a.c . , voges , w. , huchra , j.p . 1998 , mnras , 301 , 881 ebeling , h. , edge , a.c . , allen , s.w . , crawford , c.s . , fabian , a.c . , huchra , j.p . 2000 , mnras , 318 , 333 ebeling , h. , mullis , c.r . , & tully r.b . 2002 , apj , 580 , 774 einasto , m. , tago e. , jaaniste , j. , einasto , j. , & andernach , h. 1997 , a&as , 123 , 119 erdogdu , p. , et al . 2005 , mnras , _ in press _ huchra , j.p . , et al . 2005 , _ in prep _ hudson , m.j . 1993 , mnras , 265 , 72 hudson , m.j . 1994 , mnras , 266 , 475 hudson , m.j . , smith , r.j . , lucey , j.r . , schlegel , d.j . , & davies , r.l . 1999 , apj , 512 , l79 jerjen , h. , & tammann , g.a . 1993 , a&a , 276 , 1 kaiser , n. , efstathiou , g. , saunders , w. , ellis , r. , frenk , c. , lawrence , a. , rowan - robinson , m. 1991 , mnras , 252 , 1 kocevski , d.d . , mullis , c.r . , & ebeling , h. 2004 , apj , 608 , 721 kocevski , d.d . , ebeling , h. , mullis , c.r . , tully , r.b . 2006 , _ in press _ ( astro - ph/0512321 ) kogut , a. , et al . 1993 , apj , 419 , 1 knopp , g.p , henry , j.p . , briel , u.g . 1996 , apj , 472,125 kraan - korteweg , r.c . , woudt , p.a . , cayatte , v. , fairall , a.p . , balkowski , c. , & henning , p.a . 1996 , nature , 379 , 519 lahav , o. 1987 , mnras , 225 , 213 lynden - bell , d. , et al . 1988 , apj , 326 , 19 macgillivray , h.t . & stobie , r.s . 1984 , vistas astron . , 27 , 433 markevitch , m. , sarazin , c.l . , vikhlinin , a. , apj , 521 , 526 mathewson , d.s . , ford , v.l . , & buchhorn , m. 1992 , apj , 389 , l5 mattig , w. 1958 , astron . nachr . , 284 , 109 peebles , p.j.e . 1976 , apj , 205 , 318 plionis , m. 1988 , mnras , 234 , 401 plionis , m. , & kolokotronis , v. 1998 , apj , 500 , 7 plionis , m. , & valdarnini , r. 1991 , mnras , 249 , 46 reiprich , t.h . , & bhringer , h. 1999 , astron . nachr . , 320 , 296 rowan - robinson , m. , et al . 2000 , mnras , 314,375 rowan - robinson , m. , et al . 1990 , mnras , 247,1 saunders , w. , et al . 1999 , in _ density and velocity fields from the pscz survey _ , ed courteau , s. & willick , j. ( asp conf . ser . , 201 ; san francisco : astron . soc . pac . ) , 228 saunders , w. , et al . 1995 , in _ wide field spectroscopy and the distant universe _ , ed maddox , s.j . ( singapore : world scientific ) , 88 scaramella , r. , baiesi - pillastrini , g. , chincarini , g. , vettolani , g. , & zamorani , g. 1989 , nature , 338 , 562 scaramella , r. , vettolani , g. , & zamorani , g. 1991 , apj , 376 , l1 shapley , h. 1930 , harvard obs . , 874 , 9 shane , c.d . , & wirtanen , c.a . 1967 , publs lick obs . , xxii , part 1 shaya , e.j . 1984 , apj , 280 , 470 schmoldt , i.m . , 1999 , aj , 118 , 1146 staveley - smith , l. , juraszek , s. , henning , p.a . , koribalski , b.s . , & kraan - korteweg , r.c . 2000 , in _ mapping the hidden universe : the universe behind the milky way - the universe in hi _ , ed kraan - korteweg , r.c . , henning p.a . , & andernach h. ( asp conf . ser . , 218 ; san francisco : astron . soc . pac . ) , 207 strauss , m.a . , davis , m. , yahil , a. , & huchra , j.p . 1992 , apj , 385 , 421 strauss , m. , & davis , m. 1988 , in large - scale motions in the universe , ed . rubin & g.v . coyne ( princeton : princeton univ . press ) , 256 sutherland , w. 1988 , mnras,234 , 159 tonry , j.l . , blakeslee , j.p . , & ajhar , e.a . , apj , 530 , 625 tully , r.b . , scaramella , r. , vettolani , g. , zamorani , g. 1992 , apj , 388 , 9 van haarlem , m.p . , frenck , c.s . , & white , s.d.m . 1997 , mnras , 287 , 637 voges , w. 1992 , proc . satellite symp . 3 , esa isy-3 , 9 voges , w. , et al . 1999 , a&as , 349 , 389 willick , j.a . , courteau , s. , faber , s.m . , burstein , d. , & dekel , a. 1995 , apj , 446 , 12 willick , j.a . , courteau , s. , faber , s.m . , burstein , d. , dekel , a. , & strauss , m. 1997 , apjs , 109 , 333 willick , j.a . 1999 , apj , 522 , 647 zaroubi , s. , hoffman , y. , & dekel , a. 1999 , apj , 520 , 413 zwicky , f. , herzog , e. , wild , p. , karpowicz , m. , & kowal , c.t . 1961 - 68 , catalogue of galaxies and cluster galaxies , vols 1 - 6

the sample is the combination of the reflex catalog in the southern hemisphere , the ebcs sample in the north , and the ciza survey in the galactic plane . the composite reflex+ebcs+ciza sample overcomes many of the problems inherent to previous galaxy and cluster catalogs which limited their effectiveness in determining the origin of the local group s motion . from the dipole anisotropy present in the cluster distribution we determine that of the local group s peculiar velocity is due to infall into the great attractor region , while is in the form of a large - scale flow induced by more distant overdensities between and mpc away . in agreement with previous analyses , we find that the shapley supercluster is the single overdensity most responsible for the increase in the dipole amplitude beyond mpc , generating of the large - scale contribution . despite the dynamical significance of both the great attractor and shapley regions we find that numerous groupings and loose associations of clusters at roughly the same distance as the shapley region induce a significant acceleration on the local group . these include the well known horologium - reticulum concentration , as well as newly noted associations centered on abell 3667 and abell 3391 and a string of ciza clusters near c1410 which may trace an extension of the shapley complex into the zone of avoidance . we also note the presence of a significant underdensity of clusters in the northern hemisphere roughly mpc away and suggest that the large - scale anisotropy observed in the cluster distribution near this distance may have as much to do with the presence of large overdensities in the south as it does with the lack of superclusters in the north .

we aim to settle the debate regarding the fraction of the local group s peculiar velocity that is induced by structures beyond the great attractor by calculating the dipole anisotropy of the largest , all - sky , truly x - ray selected cluster sample compiled to date . the sample is the combination of the reflex catalog in the southern hemisphere , the ebcs sample in the north , and the ciza survey in the galactic plane . the composite reflex+ebcs+ciza sample overcomes many of the problems inherent to previous galaxy and cluster catalogs which limited their effectiveness in determining the origin of the local group s motion . from the dipole anisotropy present in the cluster distribution we determine that of the local group s peculiar velocity is due to infall into the great attractor region , while is in the form of a large - scale flow induced by more distant overdensities between and mpc away . in agreement with previous analyses , we find that the shapley supercluster is the single overdensity most responsible for the increase in the dipole amplitude beyond mpc , generating of the large - scale contribution . despite the dynamical significance of both the great attractor and shapley regions , we find that additional superclusters play an important role in shaping the local group s peculiar velocity . locally , the perseus - pisces region counteracts much of the great attractor s effect on the acceleration field beyond mpc . at larger distances we find that numerous groupings and loose associations of clusters at roughly the same distance as the shapley region induce a significant acceleration on the local group . these include the well known horologium - reticulum concentration , as well as newly noted associations centered on abell 3667 and abell 3391 and a string of ciza clusters near c1410 which may trace an extension of the shapley complex into the zone of avoidance . we also note the presence of a significant underdensity of clusters in the northern hemisphere roughly mpc away and suggest that the large - scale anisotropy observed in the cluster distribution near this distance may have as much to do with the presence of large overdensities in the south as it does with the lack of superclusters in the north . finally we discuss reasons for the discordant results obtained using cluster and galaxy samples in determining the origin of the local group s motion .

quant-ph0611228

i

light - matter quantum interface is a basic element of any quantum information network aiming at long distance quantum communication , cryptography protocols or quantum computing , see @xcite . light is a natural carrier of quantum information and a macroscopic atomic system can be efficiently used for its storage . critical ingredients of the quantum interface are the quantum memory and entanglement protocols , which allow high - fidelity interchange ( transfer , storage and readout ) of quantum states between the light and relatively long - lived atomic subsystems . a number of promising theoretical proposals for the high - fidelity memory and entanglement protocols has been put forward , which can be classified as based on off - resonant interaction , such as raman interaction @xcite , quantum non - demolition ( qnd ) interaction with quantum feedback - qndf @xcite , multiple qnd interactions ref.@xcite , and on resonant interaction using electromagnetically induced transparency - eit @xcite . in spite of a large number of proposals , experimental realization of the complete storage plus retrieval quantum memory with the fidelity higher than classical is yet to be achieved . high fidelity storage ( but not complete retrieval ) has been demonstrated via the qndf approach @xcite and as light - to - atoms teleportation @xcite . low fidelity storage and retrieval of the coherent and single photon pulses based on eit @xcite and raman @xcite processes have been recently demonstrated . all experiments on light - atoms quantum interface to date are conducted with alkali atoms . previously the off - resonant quantum interface protocols @xcite utilized light with the detuning higher than the hyperfine splitting of the excited state . under this condition magnetic sublevels of a hyperfine state of an alkali atom can be effectively reduced to a spin - half system . as shown in the present paper eliminating this restriction and thus using the complete magnetic multipole system of the alkali atom ground state opens up new possibilities for quantum memory and entanglement generation with ensembles of such atoms . the quantum description of correlations in coherent raman scattering in the heisenberg formalism has a long history @xcite . however in quantum information applications the raman process is often discussed in terms of formal @xmath3-scheme configuration . in contrast in our treatment we describe this process in terms of polarization multipoles for multilevel ground state alkali atoms : gyrotropy ( orientation ) , linear birefringence ( alignment ) and higher multipole components . the field subsystem is described by a set of polarization stokes components . this approach allows for complete description of the mean values and fluctuations of the light and optically thick atomic medium . although examples treated in this paper concern atoms initially pumped to one level corresponding to a single @xmath3-scheme ( as shown in figures [ fig.1]and [ fig.2 ] ) , our formalism also allows to treat more complex initial states consisting of several coupled @xmath3-schemes . the formalism is also applicable beyond the heisenberg equations in a linearized form . finally , the multipole expansion facilitates systematic and compact calculation of the coupling constants in the effective hamiltonian taking into account the full hyperfine structure of the relevant atomic levels @xcite . we shall discuss the raman quantum memory scheme first considered in @xcite . we shall add the retrieval step to the protocol and analyze the complete procedure for a realistic model , taking full account of the multilevel hyperfine and magnetic sublevel structure of an alkali atom . we derive the polarization - sensitive coupled wave - type dynamics of an optically thick atomic ensemble and optical field . using spectral mode decomposition for light and spatial mode picture for the atomic ensemble we show that the quantum states of light and the quasi - spin of atoms can be effectively swapped or entangled . the general mathematical formalism for such atomic system with angular momentum higher or equal than one , has been developed in refs.@xcite . an important advantage of the memory and entanglement schemes in such a scenario is in that they can be realized in a single pass of light through atoms and without any feedback channel , which makes experimental realizations more feasible . as an elementary carrier of the quantum information we consider a squeezed state of light . the relevance of quantum memory for these states for quantum information processing has been illustrated in proposals @xcite . we introduce stokes operators for a light pulse consisting of a circularly polarized strong classical mode and the quantum squeezed light in the orthogonal circularly polarized mode . we show that for the quantum stokes variables there is a convenient symmetric interaction with the alignment tensor components of atoms , whose spin angular momenta are equal or greater than one . in the quantum memory scenario the quantum information of the light subsystem can be effectively mapped into the alignment subsystem of atoms . in the entanglement scenario the excitation of atomic spins with coherent pulse generates a parametric - type interaction process , which results in creation of the strong correlations between the quantum fluctuations of the stokes components of the transmitted light and the alignment components in the spin subsystem of atoms . we consider the interaction via the @xmath1 line of @xmath2rb , as an important example , where a convenient spin - one system exists in the lower hyperfine sublevel of its ground state . for verification of the memory protocol we discuss its figure of merit for the mapping of the input squeezed state and for its retrieval after reading the quantum copy out from the spin subsystem with a second coherent light pulse . we discuss how the fidelity for the proposed quantum memory channel could be defined and compared with the respective classical benchmark based on direct measurement of the squeezed state parameters . we show that in an optimal configuration the quantum fidelity is always higher than the limit for the optimal competing classical channel . throughout our analysis we neglect coupling of the ground state atomic degrees of freedom to other variables than the forward propagating light field . this approximation is justified on time scales which ar short compared to dephasing time of the ground state coherence . neglecting coupling to light modes propagating in other than the forward direction can only be a good approximation in the limit of high optical depth as detailed in section [ iiia ] . finally , the influence of the atomic motion capable of washing out spatial spin patterns is not taken into account , which restricts our analysis to cold atomic samples .

we discuss theoretically quantum interface between light and a spin polarized ensemble of atoms with the spin based on an off - resonant raman scattering . we present the spectral theory of the light - atoms interaction and show how particular spectral modes of quantum light couple to spatial modes of the extended atomic ensemble . we show how this interaction can be used for quantum memory storage and retrieval and for deterministic entanglement protocols . the proposed protocols are attractive due to their simplicity since they involve just a single pass of light through atoms without the need for elaborate pulse shaping or quantum feedback . as a practically relevant example we consider the interaction of a light pulse with hyperfine components of line ofrb . the quality of the proposed protocols is verified via analytical and numerical analysis .

we discuss theoretically quantum interface between light and a spin polarized ensemble of atoms with the spin based on an off - resonant raman scattering . we present the spectral theory of the light - atoms interaction and show how particular spectral modes of quantum light couple to spatial modes of the extended atomic ensemble . we show how this interaction can be used for quantum memory storage and retrieval and for deterministic entanglement protocols . the proposed protocols are attractive due to their simplicity since they involve just a single pass of light through atoms without the need for elaborate pulse shaping or quantum feedback . as a practically relevant example we consider the interaction of a light pulse with hyperfine components of line ofrb . the quality of the proposed protocols is verified via analytical and numerical analysis .

cond-mat0102521

i

phase ordering dynamics describes the way in which domains of an ordered state develop when an initially disordered system is placed in an environment which promotes ordering . for instance , when a simple ferromagnet or alloy is quenched rapidly from very high to very low temperatures @xmath14 , domains of equilibrium low-@xmath14 ordered phases form and grow to macroscopic sizes . a quantitative description of the ordering process is provided by the time development of the two - point correlation function ; asymptotically , it is a function only of the separation scaled by a length which increases with time , typically as a power law @xcite . new phenomena and effects can arise when we deal with phase ordering in systems which are approaching _ nonequilibrium _ steady states . in this paper , we study a coupled - field nonequilibrium system in which one field evolves autonomously and influences the dynamics of the other . the system shows phase ordering of a new sort , whose principal characteristic is that fluctuations are very strong and do not damp down in the thermodynamic limit hence the term fluctuation - dominated phase ordering ( fdpo ) . in usual phase ordering systems such as ferromagnetic ising model , if one considers a finite system and waits for infinite time , then the system reaches a state with magnetization per site very close to the two possible values of the spontaneous magnetization , @xmath15 or @xmath16 , with very infrequent transitions between the two . this is reflected in a probability distribution for the order parameter which is sharply peaked at these two values , with the width of the peaks approaching zero in the thermodynamic limit ( fig . [ fdpo](a ) ) . by contrast , in the fdpo steady state , the system continually shows strong fluctuations in time without , however , losing macroscopic order . accordingly , the order parameter shows strong variations in time , reflected eventually in a probability distribution which remains broad even in the thermodynamic limit ( fig . [ fdpo](b ) ) . the physical system we study consists of an independently stochastically fluctuating surface of zero average slope , on which reside particles which tend to slide downwards guided by the local slopes of the surface . somewhat surprisingly , a state with uniform particle density is unstable towards large scale clustering under the action of surface fluctuations . eventually it is driven to a phase - ordered state with macroscopic inhomogeneities of the density , of the fdpo sort . besides exhibiting a broad order parameter distribution , this state shows unusual scaling of two - point correlation functions and cluster distributions . it turns out that much of the physics of this type of ordering is also captured by a simpler model involving a coarse - grained characterization of the surface alone , and we study this as well . a brief account of some of our results has appeared in @xcite . in the remainder of the introduction , we first discuss the characteristics of fdpo _ vis a vis _ normal phase - ordered states . we then discuss , in a qualitative way , the occurrence of fdpo in the surface - driven models under study . the layout of the rest of the paper is as follows . in section [ fdpo_cd ] , we define and study the coarsening and steady states of three different coarse - grained depth models of the fluctuating surfaces . in section [ understandfdpo ] , we demonstrate the existence of a power - law in the cluster size distribution , and show how it can give rise to fdpo . in section [ fdpo_sp ] , we discuss ordering of sliding particles on fluctuating surfaces . in section [ robust ] , we explore the robustness of fdpo with respect to changes in various rates defining the nonequilibrium process . finally , in section [ conclusion ] we summarize our principal results , and discuss the possible occurrence of fdpo in models of other physical systems . with the aim of bringing out the features of fluctuation dominated phase ordering ( fdpo ) in nonequilibrium systems , let us recall some familiar facts about phase ordered states in equilibrium statistical systems . we first discuss different characterizations of spontaneous ordering , following the paper of griffiths @xcite on the magnetization of idealized ferromagnets . we follow this with a discussion of fluctuations about the ordered state . * ( a ) * in the absence of a conservation law , the magnetization @xmath17 is an indicator of the ordering : m= 1 l^d _ n s_n [ defm11 ] where @xmath18 is the linear size , @xmath19 is the dimension and @xmath20 is spin at site @xmath21 . in the thermodynamic limit , the thermal average of the absolute value m_1= lim_l |m| ( nonconserved ) [ defm1 ] with boltzmann - gibbs weights for configurations provides an unequivocal measure of the order . this is because in the low - temperature ordered phase , the probability @xmath22 of occurrence of magnetization @xmath17 is peaked at @xmath23 and @xmath16 ; the peak widths approach zero in the thermodynamic limit @xmath24 , so that the average value @xmath25 coincides with the peak value @xmath15 ( fig . [ fdpo]@xmath26 ) . for the conserved order parameter case , the value of the magnetization is a constant and is same in both the disordered and ordered phase . one therefore needs a quantity that is sensitive to the difference between order and disorder . the simplest such quantity is the lowest nonzero fourier mode of the density @xcite |q| = 1 l|_n e^2i n / l(1+s_n)2| [ defq*1 ] where @xmath27 denotes the average magnetization in the @xmath28-dimensional plane @xmath21 oriented perpendicular to the @xmath29 direction . the modulus in eq . [ defq*1 ] above leads to the same value for all states which can be reached from each other by a translational shift . in the low-@xmath14 ordered phase , @xmath30 is expected to be a sharply peaked function , with peak widths vanishing in the thermodynamic limit . then the mean value @xmath31 defined by q_1= lim_l |q| ( conserved ) [ defq * ] serves as an order parameter . a disordered state corresponds to @xmath32 , while a perfectly ordered state with @xmath33 in half of the system and @xmath34 in the other half corresponds to @xmath35 * ( b ) * another characterization of the order is obtained from the asymptotic value of the 2-point spatial correlation function @xmath36 . at large separations @xmath37 , @xmath38 is expected to decouple : s_o s_o+r= s_o s_o+r = m_c^2 . [ defmc ] a finite value of @xmath39 indicates that the system has long - range order . a value @xmath40 would indicate a perfectly ordered pure phase without any droplets of the other species ( like the @xmath41 state of an ising ferromagnet ) , while @xmath42 would indicate that the phase has an admixture of droplets of the other species ( like the state of an ising ferromagnet for @xmath43 ) . in a finite system , @xmath44 is a function only of the scaled variable @xmath45 in the asymptotic scaling limit @xmath46 ( see also * ( d ) * below ) . an operational way to find the value of @xmath39 is then to read off the intercept ( @xmath47 ) in a plot of @xmath44 versus @xmath45 ; it gives @xmath48 in the @xmath24 limit . in equilibrium systems of the type discussed above , @xmath25 ( defined in eq . [ defm1 ] ) and @xmath39 coincide . * ( c ) * with a conserved scalar order parameter , the low-@xmath14 state is phase - separated , with each phase occupying a macroscopically large region , and separated from the other phase by an interface of width @xmath49 . the interfacial region is quite distinct from either phase , and on the scale of system size , it is structureless and sharp . * ( d ) * customarily in phase - ordered steady states , the spatial correlation function @xmath38 has a scaling form in @xmath50 , for @xmath51 where @xmath18 is the size of the system . in the limit @xmath52 , @xmath38 follows the form @xcite c(r ) m_c^2(1 - 2|r / l| ) ( |r / l| 0 ) [ porodr ] the origin of the linear fall in eq . [ porodr ] is easy to understand in systems where phases are separated by sharp boundaries on the scale of the system size , as in * ( c ) * above : a spatial averaging of @xmath53 produces @xmath54 with probability @xmath55 ( within a phase ) and @xmath56 with probability @xmath50 ( across phases ) . the linear drop with @xmath50 implies that the structure factor @xmath57 , which is the fourier transform of @xmath38 , is given , for large wave - vectors @xmath58 ) , by : ~1 ^d+1 . [ porod ] this form of the decay of the structure factor for scalar order parameters is known as the porod law . it is worth remarking that the forms eqs . [ porodr ] and [ porod ] also describe the behaviour of the two - point correlation function in an infinite system undergoing phase ordering starting from an initially disordered state . in such a case , @xmath18 denotes the coarsening time - dependent length scale which is the characteristic size of an ordered domain . * ( e ) * for usual phase - ordered systems , spatial fluctuations are negligible in the limit of the system size going to infinity . hence the averages of 1-point and 2-point functions over an ensemble of configurations are well represented by a spatial average for a single configuration in a large system . the phase ordering of interest in this paper occurs in certain types of nonequilibrium systems , and the resulting steady state differs qualitatively from the ordered state of equilibrium systems and other types of nonequilibrium systems considered earlier @xcite . the primary difference lies in the effects of fluctuations . customarily , fluctuations lead to large variations of the order parameter which scale sublinearly with the volume , and so are negligible in the thermodynamic limit . fluctuation effects are much stronger here , and lead to variations of the order parameter in time , without , however , losing the fact of ordering . below we discuss how the properties * ( a)-(e ) * discussed above are modified . * ( a ) * nonzero values of the averages @xmath59 and @xmath31 ( eqs . [ defm1 ] and [ defq * ] ) continue to indicate the existence of order , but no longer provide an unequivocal measure of the order parameter . this is because the probability distributions @xmath22 and @xmath30 remain broad even in the limit @xmath60 ( as shown schematically in fig [ fdpo]@xmath61 ) . * ( b ) * the measure @xmath62 of long - range order is nonzero , and its value can be found from the intercept @xmath63 . however , the value of @xmath39 is , in general , quite different from @xmath25 . * ( c ) * as with usual ordered states , the regions of pure phases are of the order of system size @xmath18 . but in contrast to the usual situation , there need not be a well - defined interfacial region , distinct from either phase . rather , the region between the two largest phase stretches is typically a finite fraction of the system size , and has a lot of structure ; this region itself contains stretches of pure phases separated by further such regions , and the pattern repeats . representative spin configurations @xmath64 for the two cases are depicted schematically in fig . [ cusp1 ] . this nested structure is consistent with a power - law distribution of cluster sizes , and thus of a critical state . the crucial extra feature of the fdpo state is that the largest clusters occupy a finite fraction of the total volume , and it is this which leads to a finite value of @xmath39 as in ( b ) above . representative spin configurations @xmath64 for the two cases are depicted schematically in fig . [ cusp1 ] . * ( d ) * the ensemble - averaged spatial correlation function @xmath38 continues to show a scaling form in @xmath50 . however , in contrast to eq . [ porod ] it exhibits a cusp ( fig . [ cusp1 ] ) at small values of @xmath50 : c(r ) m_c^2(1 - b|r l|^ ) . [ scale ] this implies that the scaled structure factor varies as ~1 ^d+ [ cusp ] with @xmath65 . this represents a marked deviation from the porod law ( eq . [ porod ] ) . we will demonstrate in some cases that this deviation is related to the power - law distribution of clusters in the interfacial region separating the domains of pure phases , as discussed in * ( c ) * above . * ( e ) * the spatial average of 1-point functions ( @xmath17 or @xmath66 ) and the 2-point function @xmath44 as a function of @xmath50 in a single configuration of a large system typically do not represent the answers obtained by averaging over an ensemble of configurations . this reflects the occurrence of macroscopic fluctuations . having described the general nature of fluctuation - dominated phase ordering , we now discuss the model systems that we have studied and which show fdpo . we consider physical processes defined on a fluctuating surface with zero average slope . the surface is assumed to have no overhangs , and so is characterized by a single - valued local height variable @xmath67 at position @xmath29 at time @xmath68 as shown in fig . the evolution of the height profile is taken to be governed by a stochastic equation . the height - height correlation function has a scaling form @xcite for large separations of space and time : ^2~|x - x|^2f(|t - t| |x - x|^z ) . [ hhcorr ] here @xmath69 is a scaling function , and @xmath70 and @xmath2 are the roughness and dynamical exponents , respectively . a common value of these exponents and scaling function for several different models of surface fluctuations indicate a common universality class for such models . in this paper we will study one - dimensional surfaces belonging to three such universality classes of surface growth . similar studies of two - dimensional surfaces @xcite show that similar fluctuation - dominated phase - ordered states arise in these cases as well . before turning to the physical model of particles sliding on such fluctuating surfaces , we address the notion of phase ordering in coarse - grained depth models associated with these surface fluctuations . in fig . [ sur1 ] we show the function @xmath71 which take values @xmath72 , @xmath73 and @xmath74 depending on whether the height is below , above or at the same level as some reference height @xmath75 . explicitly , we have @xmath76 . different definitions of @xmath77 define variants of the model ; these are studied in section ii . starting from initially flat surfaces , we study the coarsening of of up - spin or down spin phases , which arise from the evolution of surface profiles . with the passage of time , the surface gets rougher up to some length scale @xmath78 . the profile has hills and valleys , the base lengths of which are of the order of @xmath78 , implying domains of like - valued @xmath79 whose size is of the same order . once the steady state is reached , there are landscape arrangements of the order of the system size @xmath18 which occur on a time scale @xmath80 . however , these landscape fluctuations do not destroy long - range order , but cause large fluctuations in its value . now let us turn to the problem of hard - core particles sliding locally downwards under gravity on these fluctuating surfaces . figure [ par1 ] depicts the evolution of particles falling to the valley bottoms under gravity . when a local valley forms in a region ( fig . 3(a ) @xmath81 fig . 3(b ) ) , particles in that region tend to fall in and cluster together . the point is that particles stay together even when there is a small reverse fluctuation ( valley @xmath82 hill as in fig . [ par1](b ) @xmath82 ( c ) ) ; declustering occurs only if there is a rearrangement on length scales larger than the size of the valley . the combination of random surface fluctuations and the external force due to gravity drive the system towards large - scale clustering . results of our numerical studies show that in the coarsening regime , the typical scale of ordering in the particle - hole system is comparable to the length scale over which surface rearrangements take place . further , the steady state of the particle system exhibits uncommonly large fluctuations , reflecting the existence of similar fluctuations in the underlying coarse - grained depth models of the hill - valley profile . similar effects are seen in 1-point and 2-point correlation functions .

we study a new kind of phase ordering phenomenon in coarse - grained depth models of the hill - valley profile of fluctuating surfaces with zero overall tilt , and for hard - core particles sliding on such surfaces under gravity . the particles on the gbdt surface show conventional coarsening ( porod ) behavior with . 0.5 cm pacs numbers : 05.70.ln , 05.40.-a , 02.50.-r , 64.75.+g # 1#2#3 = 0.75 2

we study a new kind of phase ordering phenomenon in coarse - grained depth models of the hill - valley profile of fluctuating surfaces with zero overall tilt , and for hard - core particles sliding on such surfaces under gravity . we find that several such systems approach an ordered state with large scale fluctuations which make them qualitatively different from conventional phase ordered states . we consider surfaces in the edwards - wilkinson ( ew ) , kardar - parisi - zhang ( kpz ) and golubovic - bruinsma - das sarma - tamborenea ( gbdt ) universality classes . for ew and kpz surfaces , coarse - grained depth models of the surface profile exhibit coarsening to an ordered steady state in which the order parameter has a broad distribution even in the thermodynamic limit , the distribution of particle cluster sizes decays as a power - law ( with an exponent ) , and the 2-point spatial correlation function has a cusp ( with an exponent ) at small values of the argument . the latter feature indicates a deviation from the porod law which holds customarily , in coarsening with scalar order parameters . we present several numerical and exact analytical results for the coarsening process and the steady state . for linear surface models with dynamical exponent , we show that for , for , and there are logarithmic corrections for , implying for the ew surface and for the gbdt surface . within the independent interval approximation we show that . we also study the dynamics of hard - core particles sliding locally downwards on these fluctuating one - dimensional surfaces and find that the surface fluctuations lead to large - scale clustering of the particles . we find a surface - fluctuation driven coarsening of initially randomly arranged particles ; the coarsening length scale grows as . the scaled density - density correlation function of the sliding particles shows a cusp with exponent , and for the ew and kpz surfaces . the particles on the gbdt surface show conventional coarsening ( porod ) behavior with . 0.5 cm pacs numbers : 05.70.ln , 05.40.-a , 02.50.-r , 64.75.+g # 1#2#3 = 0.75 2